Optical Polarimetric Modalities for Biomedical Research (Biological and Medical Physics, Biomedical Engineering) [1st ed. 2023] 303131851X, 9783031318511

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Biological and Medical Physics, Biomedical Engineering

Nirmal Mazumder Yury V. Kistenev Ekaterina Borisova Shama Prasada K.   Editors

Optical Polarimetric Modalities for Biomedical Research

Biological and Medical Physics, Biomedical Engineering

Editor-in-Chief Bernard S. Gerstman, Department of Physics, Florida International University, Miami, FL, USA Series Editors Masuo Aizawa, Tokyo Institute Technology, Tokyo, Japan Robert H. Austin, Princeton, NJ, USA James Barber, Wolfson Laboratories, Imperial College of Science Technology, London, UK Howard C. Berg, Cambridge, MA, USA Robert Callender, Department of Biochemistry, Albert Einstein College of Medicine, Bronx, NY, USA George Feher, Department of Physics, University of California, San Diego, La Jolla, CA, USA Hans Frauenfelder, Los Alamos, NM, USA Ivar Giaever, Rensselaer Polytechnic Institute, Troy, NY, USA Pierre Joliot, Institute de Biologie Physico-Chimique, Fondation Edmond de Rothschild, Paris, France Lajos Keszthelyi, Biological Research Center, Hungarian Academy of Sciences, Szeged, Hungary Paul W. King, Biosciences Center and Photobiology, National Renewable Energy Laboratory, Lakewood, CO, USA Gianluca Lazzi, University of Utah, Salt Lake City, UT, USA Aaron Lewis, Department of Applied Physics, Hebrew University, Jerusalem, Israel Stuart M. Lindsay, Department of Physics and Astronomy, Arizona State University, Tempe, AZ, USA Xiang Yang Liu, Department of Physics, Faculty of Sciences, National University of Singapore, Singapore, Singapore David Mauzerall, Rockefeller University, New York, NY, USA Eugenie V. Mielczarek, Department of Physics and Astronomy, George Mason University, Fairfax, USA Markolf Niemz, Medical Faculty Mannheim, University of Heidelberg, Mannheim, Germany

V. Adrian Parsegian, Physical Science Laboratory, National Institutes of Health, Bethesda, MD, USA Linda S. Powers, University of Arizona, Tucson, AZ, USA Earl W. Prohofsky, Department of Physics, Purdue University, West Lafayette, IN, USA Tatiana K. Rostovtseva, NICHD, National Institutes of Health, Bethesda, MD, USA Andrew Rubin, Department of Biophysics, Moscow State University, Moscow, Russia Michael Seibert, National Renewable Energy Laboratory, Golden, CO, USA Nongjian Tao, Biodesign Center for Bioelectronics, Arizona State University, Tempe, AZ, USA David Thomas, Department of Biochemistry, University of Minnesota Medical School, Minneapolis, MN, USA

This series is intended to be comprehensive, covering a broad range of topics important to the study of the physical, chemical and biological sciences. Its goal is to provide scientists and engineers with monographs- both, authored and contributed volumes to address the growing need for information. The fields of biological and medical physics and biomedical engineering are broad, multidisciplinary and dynamic. They lie at the crossroads of frontier research in physics, biology, chemistry, and medicine. Books in the series emphasize established and emergent areas of science including molecular, membrane, and mathematical biophysics; photosynthetic energy harvesting and conversion; information processing; physical principles of genetics; sensory communications; automata networks, neural networks, and cellular automata. Equally important is coverage of applied aspects of biological and medical physics and biomedical engineering such as molecular electronic components and devices, biosensors, medicine, imaging, physical principles of renewable energy production, advanced prostheses, and environmental control and engineering.

Nirmal Mazumder • Yury V. Kistenev • Ekaterina Borisova • Shama Prasada K. Editors

Optical Polarimetric Modalities for Biomedical Research

Editors Nirmal Mazumder Department of Biophysics Manipal Academy of Higher Education Manipal, Karnataka, India

Yury V. Kistenev Laboratory of Biophotonics National Research Tomsk State University Tomsk, Russia

Ekaterina Borisova Bulgarian Academy of Sciences Institute of Electronics Sofia, Bulgaria

Shama Prasada K. Department of Cell and Molecular Biology Manipal Academy of Higher Education Manipal, Karnataka, India

ISSN 1618-7210 ISSN 2197-5647 (electronic) Biological and Medical Physics, Biomedical Engineering ISBN 978-3-031-31851-1 ISBN 978-3-031-31852-8 (eBook) https://doi.org/10.1007/978-3-031-31852-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

An understanding of tissue microstructure and its composition plays a crucial role in the diagnosis and surgical guidance of tissue abnormality. With conventional microscopes, pathologists require an hour to prepare frozen and stained tissue slices from suspected patients, hence making diagnosis time-consuming. On the other hand, polarization microscopy, a powerful optical tool to study anisotropic properties of biomolecules, can distinguish normal and abnormal tissue features in a shorter period, even in the absence of staining, and provides better microstructural information of a sample as compared to conventional microscopy. Interaction of polarized light with healthy and abnormal regions of tissue reveals structural information associated with its pathological condition. Even a slight variation in structural alignment can induce a change in polarization property, which can play a major role in the early detection of abnormal tissue morphology. In this book, Optical Polarimetric Modalities for Biomedical Research, we discuss the recent developments in optical polarimetry and their advancements in biomedical research. We discuss the various advanced optical techniques including optical coherence tomography (OCT), reflectance and transmission spectroscopy, fluorescence, multiphoton excitation, harmonic generation, Raman microscopy, etc. Also, the potential and challenges for future research in exploring possible applications are discussed. The further development of polarization technologies will offer an enormous chance to improve diagnostic tools for biomedical applications. In this book, we have gathered articles exploring the various exciting aspects of polarization microscopy techniques and their technological development as well as applications. The first chapter by Alexander et al. discusses the scalability of the field of view and resolution of polarization imaging techniques based on the application making it an ideal choice for non-destructive imaging of optical/structural anisotropy in soft tissues at a macroscopic scale. The chapter outlines the fundamentals of such techniques and reviews some of their applications in measuring optical anisotropy in soft tissues. Chapter 11 by Sriharikrishnaa et al. gives an elaborate discussion regarding cancer, its causes, and its hallmarks. In this chapter, the authors outline various cancer detection techniques and available treatment methods. Thi-Thu-Hien et al. in the third chapter discuss the effective optical v

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parameters of anisotropic materials using the Stokes-Mueller matrix decomposition method. The feasibility of the proposed technique is confirmed by performing measuring the effective parameters of optical fiber and free-space media. The validity of the proposed approach is also confirmed by experimental measuring of the effective parameters of various types of anisotropic media including human blood plasma, collagen, and skin tissue samples. Finally, the combination of artificial intelligent classifier technique and effective parameters is proposed for skin cancer detection. In the fourth chapter by Oriol and Subiao, the authors review the main aspects of Mueller matrix imaging of biomedical tissues, including the most suitable imaging configurations and their optimization, the deciphering of Mueller matrix measurements, and the most suitable presentation for polarimetric images. In Chap. 5, Aymeric et al. provide a focused review of Mueller-matrix scanning microscopy-based imaging of biological samples. The chapter introduces the Mueller matrix formalism and discusses the techniques involved in modeling as well as the calibration of optical scanning microscopes. The chapter presents the experimentalist paradigm for finding the proper trade-off between the highspeed control and the most optimal optical components for controlling polarization. Despite optical scanning imaging being commonly dedicated to the collection of non-linear light/matter interaction, the authors show the combined modalities with the Mueller matrix that can acquire a complete overview of the 3D structure of the sample. At last, an argument was given on the capability of Mueller matrix scanning microscopy of yielding to tissue diagnosis easily without any need for sophisticated sample preparation protocol from the histopathologist. Chapter 2 gives a detailed idea of the optical properties of biological samples involved in polarization microscopy. The authors outlined the application of polarized light in major microscopic techniques for various disease diagnoses. In Chap. 6, by Mahima et al., the fundamentals of polarization are discussed, emphasizing the various exploits of Mueller polarimetry in biomedical applications reported through the literature. Several theoretical and experimental approaches to extract and analyze the fundamental polarization properties contained in the Mueller matrix have been introduced. The studies on tissue-mimicking phantoms, polarimetric intervention at different stages of the tissue preparation process, in vivo tissue analysis, and biofluid profiling for diagnosing diseases demonstrate the potential clinical applications of Mueller polarimetry. Furthermore, the challenges in experimental and analytical implementation are presented, with the scope to be addressed and resolved for the advancement and clinical translation of Mueller polarimetry with possible extensions to biotechnology applications. In Chap. 7, by Farhana et al., the scattering phase function and the polarimetric responses by using the light scattering technique for the selected bioparticles are discussed. The chapter is important for selecting the proper choice of refractive index in light scattering investigations, particularly for theoretical investigations. It is a very significant aspect of morphological quantification, observation of phase function, and polarimetric responses of bioparticles. In Chap. 12, Divya et al. brief the principles and applications of several polarization-enabled cancer detection approaches. The techniques outlined include fluorescence spectroscopy, near-infrared (NIR) spectroscopy, hyperspectral

Preface

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spectroscopy, Raman spectroscopy, fluorescence microscopy, confocal microscopy, two-photon (2p) fluorescence microscopy, second-harmonic generation (SHG), third-harmonic generation (THG), coherent anti-stokes Raman scattering (CARS), stimulated Raman scattering (SRS) microscopy, surface-enhanced Raman scattering (SERS), and optical coherence tomography (OCT). The potential application of the polarization technology combined with the aforementioned microscopic techniques showed positive results in differentiating the cancerous from the non-cancerous cells and the polarization property of light just added more detail to the analysis at a molecular level. Chapter 13, by Spandana et al., explains the application of various imaging modalities employed with polarization light imaging in different disease diagnoses, starting from conventional polarization microscopic technique to optical coherence tomography, fluorescence microscopy, second-harmonic generation microscopy, and so on. Chapter 8, by Mehdi and Virginijus, reviews the polarimetric nonlinear microscopy techniques for biomedical imaging. It is beneficial to utilize the technique described in this chapter for the retrieval of ultrastructural information about the specimens. The polarimetric techniques can detect ultrastructural changes in biological tissues caused by diseases such as cancer, which makes polarimetric microscopy attractive for biomedical and clinical applications. Richard et al., in Chap. 9, address the future of polarization-resolved second-harmonic generation microscopy and briefly describe advances being performed to use this technique for in vivo functional tissue studies. The imaging techniques discussed in the chapter have been used to investigate collagenous tissues, muscle tissues, and much more. Chapter 10, Ming-Chi et al., discusses the principle and applications of polarizationresolved second-harmonic generation for tissue imaging. The chapter emphasizes PSHG microscopy is discussed starting with the theory that uses an analytical model to connect SHG and second-order nonlinear susceptibility tensor, followed by the structural constraint for SHG, relevant techniques including conventional P-SHG microscopy, polarization-in, polarization-out (PIPO) SHG microscopy and Stokes vector-based SHG microscopy and the corresponding applications, and finally conclusions with future perspectives. In the content, the authors summarize various representative works and guide the readers on how to use P-SHG microscopy in biomedical research, which would aid in understanding the ultrastructure of the molecular assembly resulting in unique biological processes and functions and chirality, as well as the developmental processes about disease progression and tissue regeneration. Chapter 14, by Kausalya et al., provides an overview of current computational techniques used in polarimetric data analysis. The application of advanced tools such as machine learning for the analysis expedites the process without compromising accuracy. This chapter discusses the machine learning techniques used for analyzing polarization images and their applications, along with a brief introduction to polarimetry. We appreciate the authors’ contributions to this book, as well as their prompt answers to the reviewers’ remarks. We are grateful to the reviewers for devoting their time to providing insightful recommendations and comments on the chapters. We also acknowledge our colleagues who helped us with this volume’s suggestions. Herbert Moses and Nemul Khan (Springer Nature Publishing) deserve special

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thanks for their contributions to the book. More importantly, we wish our readers a pleasant and productive browsing experience. Manipal, Karnataka, India Tomsk, Russia Sofia, Bulgaria Manipal, Karnataka, India

Nirmal Mazumder Yury V. Kistenev Ekaterina Borisova Shama Prasada K.

Tribute to Assoc. Prof. Ekaterina Borisova

Her contribution to Biophotonics governs various optical techniques for developments of laser and optical systems for cancer diagnosis and treatment, including fluorescence and diffuse reflectance optical spectroscopy, Raman spectroscopy, photodynamic therapy, photoinactivation of pathogens, optical blood-brain barrier research and tissue polarimetry for cancer diagnosis. Her work was highly recognized with a number of scientific awards in the field of optics and photonics. Assoc. Prof. Ekaterina Borisova was a bright and unique person, brilliant scientist and a true friend. She had immense knowledge, allowing her to have ingenious vision on scientific problems and the courage to follow her dreams with such passion and dedication, which swirled like a hurricane, pulling in and inspiring everyone around her. As her colleagues and students we will be forever grateful for her guidance, mentorship and inspiration throughout the years! Tsanislava Genova Deyan Ivanov

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Contents

Part I Stokes Mueller Based Polarimetry 1

Polarization Imaging of Optical Anisotropy in Soft Tissues . . . . . . . . . . . Alexander W. Dixon, Andrew J. Taberner, Martyn P. Nash, and Poul M. F. Nielsen

3

2

Polarization Techniques in Biological Microscopy . . . . . . . . . . . . . . . . . . . . . . Francisco J. Ávila and Juan M. Bueno

27

3

Stokes –Mueller Matrix Polarimetry: Effective Parameters of Anisotropic Turbid Media: Theory and Application . . . . . . . . . . . . . . . . Thi-Thu-Hien Pham, Quoc-Hung Phan, Thanh-Hai Le, and Ngoc-Bich Le

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4

Mueller Matrix Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oriol Arteaga and Subiao Bian

5

Biological Imaging Through Optical Mueller Matrix Scanning Microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Aymeric Le Gratiet, Colin J. R. Sheppard, and Alberto Diaspro

6

Mueller Polarimetry for Biomedical Applications . . . . . . . . . . . . . . . . . . . . . . 125 Mahima Sharma, Chitra Shaji, and Sujatha Narayanan Unni

7

Scattering Phase Functions and Polarimetric Responses of Selected Bioparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Farhana Hussain, Jamil Hussain, Semima Sultana Khanam, Showhil Noorani, Aranya Bhuti Bhattacherjee, and Sanchita Roy

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Part II Nonlinear Polarization Microscopy 8

Polarization-Resolved Nonlinear Optical Microscopy. . . . . . . . . . . . . . . . . . 179 Mehdi Alizadeh and Virginijus Barzda

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9

Polarization-Resolved SHG Microscopy for Biomedical Applications 215 Richard Cisek, MacAulay Harvey, Elisha Bennett, Hwanhee Jeon, and Danielle Tokarz

10

Polarization-Resolved Second-Harmonic Generation for Tissue Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Ming-Chi Chen, Wei-Hsun Wang, Gagan Raju, Nirmal Mazumder, and Guan-Yu Zhuo

Part III Applications of Polarization Techniques 11

An Introduction to Fundamentals of Cancer Biology . . . . . . . . . . . . . . . . . . 307 S. Sriharikrishnaa, Padmanaban S. Suresh, and Shama Prasada K.

12

Polarization-Enabled Optical Spectroscopy and Microscopic Techniques for Cancer Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Mallya Divya, Madhavi Hegde, Madhu Hegde, Shatakshi Roy, Gagan Raju, Viktor V. Nikolaev, Yury V. Kistenev, and Nirmal Mazumder

13

Polarization Microscopy in Biomedical Applications. . . . . . . . . . . . . . . . . . . 389 K. U. Spandana, Sindhoora Kaniyala Melanthota, Gagan Raju, Aymeric Le Gratiet, and Nirmal Mazumder

14

Machine Learning in Tissue Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 Kausalya Neelavara Makkithaya, Sindhoora Kaniyala Melanthota, Yury V. Kistenev, Alexander Bykov, Tatiana Novikova, Igor Meglinski, and Nirmal Mazumder

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

Part I

Stokes Mueller Based Polarimetry

Chapter 1

Polarization Imaging of Optical Anisotropy in Soft Tissues Alexander W. Dixon, Andrew J. Taberner, Martyn P. Nash, and Poul M. F. Nielsen

Abstract Polarization imaging is a group of quantitative and label-free techniques that can be used to measure the optical anisotropy of fibrous structures, such as collagen and actin–myosin in soft tissues. In general, polarization imaging can have a field of view that is readily scaled for the required application. This functionality combined with the nondestructive nature of the contrast mechanism makes polarization imaging an ideal choice for studying soft tissue fiber architecture at a macroscopic (tissue-level) scale. Moreover, such techniques can be integrated with mechanical testing instrumentation, enabling the investigation of structure– function relationships of soft tissues. Polarization imaging is an exciting field for tissue biomechanics, particularly as technologies develop that enable relatively inexpensive and straightforward implementations of optomechanical instruments. Keywords Polarization imaging · Soft tissue · Tissue anisotropy · Mechanical testing

1 Introduction Polarization imaging techniques, in general, are optical techniques that provide images with quantitative label-free contrast given by the polarization properties of the imaged media. This contrast mechanism is generally quantified by measuring the polarization of light exiting a medium with prior knowledge, or control, of the polarization of the light incident on the medium. The fundamental polarization

A. W. Dixon () Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand e-mail: [email protected] A. J. Taberner · M. P. Nash · P. M. F. Nielsen Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand Department of Engineering Science, University of Auckland, Auckland, New Zealand © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Mazumder et al. (eds.), Optical Polarimetric Modalities for Biomedical Research, Biological and Medical Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-031-31852-8_1

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properties of media are retardance, diattenuation, and depolarization (Goldstein, 2010). Polarization imaging techniques provide measurements of the polarization properties of biological media to reveal morphological, microstructural, and compositional information (Qi & Elson, 2017). Polarization imaging of biological media has been used for a wide range of applications in biomedical studies and clinical diagnosis. Examples include: noninvasive glucose sensing (McNichols & Coté, 2000); cancer identification in various tissues, such as colon, liver, cervix, breast, and skin; and characterization of the structural anisotropy in tissues containing fibrous components, such as collagen and actin–myosin (Qi & Elson, 2017; Ghosh & Vitkin, 2011; Alali & Vitkin, 2015; He et al., 2019). The anisotropy in tissues that arises due to the architecture of fibrous structures can manifest as optical anisotropy, which can be measured using polarization imaging techniques (Ghosh & Vitkin, 2011; Vitkin et al., 2015). Thus, the measurement of optical anisotropy may enable nondestructive characterization of collagen fiber architecture in soft tissues. Such measurements have been previously made on various soft tissues, including: collagen in tendon (Ellingsen et al., 2014; York et al., 2014; Spiesz et al., 2018), native heart valves (Tower et al., 2002; Robinson et al., 2008; Chue-Sang et al., 2016; Yang et al., 2015; Goth et al., 2019), and bovine pericardium (Cuando-Espitia et al., 2015; Dixon et al., 2018, 2021a); and actinmyosin in skeletal muscle (Liao et al., 2010; Sun et al., 2014) and cardiac muscle (Liao et al., 2010; Sun et al., 2014; Wood et al., 2010). These measurements were performed with a variety of polarization imaging techniques. This chapter introduces the concepts of polarization imaging techniques and a review of some recent applications of these techniques for measuring soft tissue fiber architecture at a macroscopic (tissue-level) scale. Recent applications combining polarization imaging with mechanical testing instruments, for studying biomechanical behavior of soft tissues, are also highlighted.

2 Polarization Fundamentals This section introduces the fundamental polarization properties, the associated phenomena, and a formalism for describing these properties for use with Mueller matrix imaging polarimetry. The material presented here is not a complete description of these concepts. For further details, readers are referred to Goldstein (2010) and Chipman (2010), which are the key references for this section. In this chapter, the following conventions have been adopted: the coordinate system is right-handed Cartesian with light propagation along the z-axis; angles in the xyplane are considered counterclockwise positive from the positive x-axis; from the receiver’s point of view, right and left circularly polarized light have resultant optical field vectors rotating in the clockwise and counterclockwise directions, respectively.

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2.1 Optical Anisotropy This section introduces some of the fundamental concepts related to optically anisotropic media and relates them to collagenous soft tissues. A medium is considered to be optically anisotropic if it exhibits a directionally dependent refractive index. This anisotropy gives rise to differing behavior of propagating light depending on its propagation direction, wavelength, and polarization state. The refractive indices of a medium can be defined with respect to the principal axes to give three principal indices of refraction. Media with three equal principal indices do not exhibit directional dependency and are optically isotropic. Anisotropic media with two equal principal indices are classified as uniaxial, and media with three different principal indices are classified as biaxial. Media with two or more distinct principal indices are referred to as birefringent. When considering uniaxially birefringent media, the refractive index for the two equal axes is referred to as the ordinary index no and the refractive index for the distinct axis is the extraordinary index ne . Uniaxial media are said to be positive if ne > no and negative if ne < no . The axis along which the extraordinary index occurs is referred to as the optic axis and defines the axis of anisotropy in materials that are uniaxially birefringent (Goldstein, 2010; Kumar & Ghatak, 2011). Different types of birefringence can arise due to optical anisotropy at different length scales (Matcher, 2009), and types relevant to collagenous soft tissues are outlined below. Intrinsic linear birefringence occurs in media with optical anisotropy at the molecular scale. Noncubic crystalline materials are an example of intrinsically birefringent media. Type I collagen has a refractive index that is higher along the length of the fibers than across their cross-section, giving this collagen a positive uniaxial intrinsic linear birefringence with an optic axis that aligns with the collagen fiber direction (see Fig. 1.1a) (Matcher, 2009; Wolman & Kasten, 1986; Tuchin, 2016). The source of this intrinsic linear birefringence is likely due to a quasicrystalline arrangement of amino acids that are aligned parallel to the fiber axis, in the polypeptide chains of collagen molecules (Wolman & Kasten, 1986). Form linear birefringence can occur in composite media comprising constituents of differing refractive indices, which are ordered in an anisotropic arrangement. The spatial scale of the ordered structure is large compared with the dimensions of the molecules, but small compared with the wavelength of light (Goldstein, 2010; Born & Wolf, 1980). One such ordered structure is a system of parallel cylinders that gives rise to a medium exhibiting uniaxial linear birefringence with an optic axis parallel to the cylinder axis (see Fig. 1.1b) (Tuchin, 2016). Tissues containing Type I collagen can exhibit a positive uniaxial form linear birefringence, due to the parallel arrangement of fibrils embedded in the ground substance of the extracellular matrix, which exhibits a lower refractive index than collagen (Wolman & Kasten, 1986; Tuchin, 2016). Therefore, the optic axes of the form linear birefringence and intrinsic linear birefringence in such tissues are both aligned with the collagen fiber direction (Wolman & Kasten, 1986). The linear birefringence of a medium can

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lead to linear retardance in propagating light, and the fundamental concepts for this property are outlined below.

2.2 Polarization In order to describe the polarization properties of media, an understanding of polarized light is required. For an optical field E propagating in the z direction (Fig. 1.2), the transverse components of the field are represented by Ex (z, t) = E0x cos (ωt − kz + δx )

(1.1)

  Ey (z, t) = E0y cos ωt − kz + δy ,

(1.2)

.

.

where ω = 2πf is the angular frequency, k = 2π/λ is the wave number, E0x and E0y are the maximum amplitudes, and δ x and δ y are arbitrary phases. Elimination of the time-space propagator (ωt − kz) between Eqs. (1.1) and (1.2) gives the equation of an ellipse: .

Ey (z, t)2 2Ex (z, t) Ey (z, t) Ex (z, t)2 + − cos δ = sin2 δ, 2 2 E0x E0y E0x E0y

(1.3)

where the phase shift δ = δ y − δ x . For further details, readers are referred to Collett (2005, pp. 5–7) and Goldstein (2010, Sec. 4.2).

Fig. 1.1 Optical anisotropy in cylindrical media with uniaxial (a) intrinsic linear birefringence and (b) form linear birefringence

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Fig. 1.2 Propagation of an optical field E (shown in red) and its transverse components (shown in black) Table 1.1 Degenerate polarization states Degenerate polarization state Linear horizontal

Symbol H

Conditions E0y = 0

Linear vertical

V

E0x = 0

Linear +45◦ Linear −45◦

P M

E0x = E0y , δ = 0 E0x = E0y , δ = π

Right circular

R

E0x = E0y , δ = π/2

Left circular

L

E0x = E0y , δ = − π/2

Polarization ellipse

The propagating optical field vector in the xy-plane traces an ellipse, as a function of time, which is described by Eq. (1.3). This behavior is called optical polarization, and the ellipse is referred to as the polarization ellipse. In general, an optical field is elliptically polarized; however, there are simpler forms, here referred to as the degenerate polarization states. These states are important as they are relatively easy to create with standard polarization optics, and polarization measurements can be greatly simplified with their use (Goldstein, 2010; Collett, 2005). The degenerate polarization states are summarized in Table 1.1, and their optical fields are demonstrated in Fig. 1.3.

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Fig. 1.3 Propagation of optical fields for the degenerate polarization states: (a) linear horizontal, (b) linear vertical, (c) linear +45◦ , (d) linear −45◦ , (e) right circularly polarized, and (f) left circularly polarized

2.3 Polarization Properties 2.3.1

Linear Retardance

For a light ray incident on a uniaxially birefringent medium, components of the transmitted optical field that are polarized perpendicular and parallel to the optic axis, or its projection in the plane normal to propagation, encounter the ordinary refractive index and effective refractive index nE , respectively. The effective refractive index is direction-dependent with value between no and ne described by .

1 cos2 θE sin2 θE = + , n2o n2e n2E

(1.4)

where θ E is the angle between the light propagation direction and the optic axis. In general, the incident ray undergoes a process known as double refraction, due to differing refractive indices, and splits into two rays. The ordinary ray propagates with phase velocity c/no , is polarized perpendicular to the optic axis, and follows

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Fig. 1.4 Double refraction of light in a uniaxially birefringent medium for incident ray direction that is normal to the surface and oblique (a) or normal (b) to the optic axis

Snell’s law of refraction. The extraordinary ray propagates with phase velocity c/nE , is polarized parallel to the optic axis, and in general does not follow Snell’s law (see Fig. 1.4a). For a positive or negative uniaxial medium, the extraordinary ray is slower or faster than the ordinary ray, and the optic axis is thus referred to as a slow axis or fast axis, respectively (Kumar & Ghatak, 2011). If the propagation direction of the incident ray is parallel to the optic axis (θ E = 0) in the medium, the optical field encounters the ordinary refractive index for any polarization, so the phase velocity is independent of polarization, and no double refraction occurs. When the incident ray direction is normal to the surface and the optic axis (θ E = 90◦ ) of the uniaxially birefringent medium, the ordinary and extraordinary rays will propagate in the same direction but with different phase velocities (see Fig. 1.4b) (Kumar & Ghatak, 2011). The emerging rays will be coaxial and have a relative phase difference, or linear retardance, δ L given by δL =

.

2π (|ne − no |) l, λ

(1.5)

where l is the thickness of the medium in z-direction and |ne − no | is referred to as the total linear birefringence (Hecht, 2017). The refractive indices are, in general, wavelength dependent. The linear retardance, for the case described with Eq. (1.5), may change the polarization state of light incident on a uniaxially linear birefringent medium. This effect is illustrated in Fig. 1.5 for a linear retarder with light propagating in a transmission arrangement. This behavior can be used to measure the linear retardance of collagenous media.

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Fig. 1.5 Linear retarder with quarter-wave (π/2) phase shift transforming incident +45◦ linear polarized light to right circularly polarized light. The optical field is shown in red and its transverse components in black

2.3.2

Circular Retardance

Circular birefringence (or optical activity) occurs in an isotropic medium (or along the optic axis in an anisotropic medium) that lacks a molecular plane of symmetry. The effect of circular birefringence on the behavior of propagating optical fields can be thought of as the medium possessing two differing refractive indices for right circularly polarized (nR ) and left circularly polarized (nL ) light (Goldstein, 2010; Hecht, 2017). The resulting difference in phase velocities for propagating fields, of opposite handedness, introduces a relative phase difference, or circular retardance, δ C given by δC =

.

2π (nR − nL ) l. λ

(1.6)

For an elliptically or linearly polarized field propagating in such a medium, the circular retardance leads to a rotation of the polarization ellipse. Hence, a circular retarder acts as an optical rotator where the optical rotation is given by ψ = δ C /2. This can be demonstrated by considering that an elliptically or linearly polarized field can be represented as the superposition of two circularly polarized fields of opposite handedness (Hecht, 2017). This can be illustrated for an incident linearly polarized field, with circular components of equal amplitude, that rotates and remains linearly polarized as it propagates through a circularly birefringent medium (see Fig. 1.6).

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Fig. 1.6 Circular retarder with quarter-wave (π/2) phase shift rotating incident horizontal linearly polarized light to +45◦ linearly polarized light. The optical field is shown in red, and its R and L components are shown in green and blue, respectively (field vectors omitted for clarity)

2.3.3

Linear Diattenuation

A diattenuating medium attenuates the amplitudes of an optical field’s orthogonal components unequally; that is, a diattenuator (or polarizer) is an anisotropic attenuator. A medium exhibiting linear diattenutation has different attenuation of orthogonal linear polarizations. The two principal axes of maximum and minimum transmission have amplitude transmission coefficients p1 and p2 , respectively. Considering an optical field E propagating in the direction normal to the principal axes of a linear diattenuator (see Fig. 1.7), the exiting components are given by   Ex = p1 cos2 θ + p2 sin2 θ Ex + (p1 + p2 ) sin θ cos θ Ey   . Ey = (p1 + p2 ) sin θ cos θ Ex + p1 sin2 θ + p2 cos2 θ Ey

0 ≤ p1,2 ≤ 1, (1.7)

where θ is the orientation of the axis of linear diattenuation (or transmission axis) that is associated with p1 (Goldstein, 2010). The magnitude of linear diattenuation DL for a medium with maximum intensity transmittance .Tmax = p12 and minimum intensity transmittance .Tmin = p22 , where Tmax ≥ Tmin , is given by DL =

.

Tmax − Tmin Tmax + Tmin

0 ≤ DL ≤ 1.

(1.8)

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Fig. 1.7 Propagation of optical field for an ideal linear diattenuator with p1 = 1, p2 = 0 and transmission axis at 90◦ . The optical field is shown in red and its transverse components in black

Fig. 1.8 Propagation of optical field for a circular diattenuator with amplitude transmissions of TR = 1 and TL = 0.25 for its R (green) and L (blue) components, respectively. The optical field is shown in red (field vectors omitted for clarity)

2.3.4

Circular Diattenuation

Circular diattenuation is the differential attenuation of left and right circularly polarized light. Figure 1.8 demonstrates this property for an incident linearly polarized field, decomposed to circular components of initially equal amplitude, that as the optical field propagates through the medium, one of the orthogonal components is attenuated giving elliptically polarized exiting light. The magnitude of circular diattenuation DC for a medium with intensity transmittances for right circularly polarized light TR and left circularly polarized light TL is given by DC =

.

T R − TL TR + TL

− 1 ≤ DC ≤ 1.

(1.9)

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2.4 Mueller–Stokes Formalism An algebraic system called the Mueller–Stokes formalism is useful for the description of polarization problems. In this formalism, the Stokes vector describes the polarization state of a light beam, using observable parameters, and the Mueller matrix describes the polarization properties of a medium. This formalism is preferable over the other commonly used Jones formalism due to two distinct advantages for experimental work. First, in Mueller–Stokes notation, intensity is represented explicitly, making it suitable for describing irradiance measuring instruments, such as polarimeters. Second, as depolarization can be included in calculations, it is suitable for describing complex turbid media, such as biological tissues, which exhibit this polarization property. The Mueller matrix M is a 4 × 4 matrix of real elements that represents the polarization state altering properties of a medium. The Mueller matrix of a polarizing medium can be used to describe the transformation of incident light  with Stokes vector s to exiting light with Stokes vector s , as a system of linear equations by s = Ms S0 m11 m12 m13 ⎢ S  ⎥ ⎢ m21 m22 m23 ⎢ 1⎥ = ⎢ ⎣ S  ⎦ ⎣ m31 m32 m33 2 S3 m41 m42 m43 ⎡ .

⎤

⎡

⎤⎡ ⎤ m14 S0 ⎥ ⎢ m24 ⎥ ⎢ S1 ⎥ ⎥ m34 ⎦ ⎣ S2 ⎦ m44 S3

(1.10)

The Mueller matrix for a medium is a function of wavelength and light propagation direction. The exiting light may be reflected, transmitted, or scattered (Goldstein, 2010; Chipman, 2010). The three fundamental polarization properties of retardance, diattenuation, and depolarization with all their forms of linear, circular, and elliptical are encoded within the Mueller matrix. Although the Mueller matrix can have 16 independent elements, this can be reduced to seven elements if there is no depolarization in the medium. The Mueller matrices for single polarization properties are given below. The Mueller matrix for a linearly retarding medium with fast axis orientation θ and linear retardance δ L is given by ⎤ 1 0 0 0 ⎢ 0 cos2 2θ + sin2 2θ cos δ sin 2θ cos 2θ (1 − cos δ ) − sin 2θ sin δ ⎥ ⎥ ⎢ L L L .MLR (θ, δL ) = ⎢ δ ⎥. L ⎦ ⎣ 0 sin 2θ cos 2θ (1 − cos δL ) sin2 2θ + cos2 2θ cos δL cos 2θ sin δL 0 sin 2θ sin δL − cos 2θ sin δL cos δL ⎡

(1.11)

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An important case for a linear retarder is the Mueller matrix for an ideal quarter waveplate, given by MLR (θ , π/2). The Mueller matrix for a circularly retarding medium with circular retardance δ C is given by ⎤ 1 0 0 0 ⎢ 0 cos δC sin δC 0 ⎥ ⎥ .MCR (δC ) = ⎢ ⎣ 0 − sin δC cos δC 0 ⎦ . 0 0 0 1 ⎡

(1.12)

Note this is also the Mueller matrix for an optical rotator with counterclockwise rotation of δ C /2. The Mueller matrix for a linear diattenuator with maximum intensity transmittance Tmax , minimum intensity transmittance Tmin , and transmission axis orientation θ is given by ⎡

A B cos 2θ B sin 2θ 1⎢ ⎢ B cos 2θ Acos2 2θ + Csin2 2θ (A − C) sin 2θ cos 2θ .MLD (Tmax , Tmin , θ ) = ⎢ 2 ⎣ B sin 2θ (A − C) sin 2θ cos 2θ Asin2 2θ + Ccos2 2θ 0 0 0

⎤ 0 0⎥ ⎥ ⎥ 0⎦ C

(1.13) where A = Tmax + Tmin

.

B = Tmax − Tmin

C = 2 Tmax Tmin

(1.14)

An important case for a linear diattenuator is the Mueller matrix for an ideal linear polarizer, given by MLD (1, 0, θ ). The Mueller matrix for a circular diattenuator with intensity transmittances for right circularly polarized light TR and left circularly polarized light TL is given by ⎤ 0 0 T R − TL T R + TL √ ⎥ 1⎢ 0 0 0 2 TR TL ⎥ ⎢ √ .MCD (TR , TL ) = ⎦ ⎣ 0 0 0 2 TR TL 2 0 0 T R + TL TR − TL ⎡

(1.15)

The Mueller matrix for a depolarizer is given by ⎤ 1 0 0 0 ⎢ 0 1 − α1 0 0 ⎥ ⎥ .M (α1 , α2 , α3 ) = ⎢ ⎣ 0 0 1 − α2 0 ⎦ 0 0 0 1 − α3 ⎡

(1.16)

where α 1 , α 2 , and α 3 are the linear xy, linear ±45◦ , and circular depolarizations, respectively.

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2.5 Decomposition The direct quantification of polarization properties from Mueller matrices is not possible for complex random media that exhibit multiple properties, such as those measured from soft tissue. One approach to interpret Mueller matrices is to decompose them into their corresponding fundamental polarization properties. A number of methods have been developed to decompose Mueller matrices. Gil (2014) categorizes these as serial, parallel, and differential decompositions based on how polarization is represented using Mueller matrices. A widely used decomposition method in the literature is Lu-Chipman polar decomposition, a serial decomposition method, which expresses an arbitrary depolarizing Mueller matrix as an ordered sequence of pure diattenuator, pure retarder, and depolarizer Mueller matrices (Chipman, 2010). The order of component Mueller matrices, for which the polar decomposition assumes one permutation, is important as, in general, Mueller matrices do not commute (Chipman, 2010). A more recent method, the Mueller matrix logarithm decomposition, is a differential decomposition that has been extended to depolarizing media (Ossikovski, 2011; Ortega-Quijano & Arce-Diego, 2011) from the differential matrix formalism originally proposed by Azzam (1978). Ambiguities associated with noncommutation of Mueller matrices are eliminated with this differential decomposition method (Vitkin et al., 2015). Kumar et al. (2012) performed a comparative study of the two methods above and demonstrated, both experimentally and in simulations, that for media exhibiting simultaneous linear retardance and circular retardance, the polar decomposition systematically underestimated linear retardance and overestimated circular retardance. Alali and Vitkin (2015) reported that the polar decomposition performs well for biological tissues, while inaccuracies mainly arise when media have distinct layers of a sequential order that is different from that assumed by the decomposition. For complex random media, such as soft tissue, where multiple polarization properties are most likely exhibited simultaneously, the logarithm decomposition seems the most appropriate method for decomposing measured Mueller matrices. For a detailed description of the logarithm decomposition, readers are referred to (Ossikovski, 2011; Kumar et al., 2012; Devlaminck & Ossikovski, 2014; Dixon, 2021). An example of Mueller matrix decomposition is demonstrated below for an elliptical retarder MR , that is, with linear and circular retardance occurring simultaneously, given by ⎤ 1 0 0 0 ⎥   ⎢ ⎢ 0 ρδ 2xy + cos δT ρδ xy δ45 + σ δ C ρδ xy δC − σ δ 45 ⎥ .MR δxy , δ45 , δC = ⎢ ⎥ ⎣ 0 ρδ xy δ45 − σ δ C ρδ 245 + cos δT ρδ 45 δC + σ δ xy ⎦ 0 ρδ xy δC + σ δ 45 ρδ 45 δC − σ δ xy ρδ 2C + cos δT (1.17) ⎡

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Fig. 1.9 Logarithm decomposition of simulated Mueller matrix images (a) for an elliptically retarding medium to maps of linear retardance (b), fast axis orientation (c), and circular retardance (d). The linear retardance and circular retardance vary in the x and y directions, respectively. The simulated properties are indicated on the axes labels of (b), (c), and (d), axes labels are omitted on (a) for clarity. Where total retardance exceeded δ T = π (indicated by the dashed lines), phase wrapping occurred, see text for details

where δ xy , δ 45 , δ C , δ T are thelinear xy, linear ±45◦ , circular, and total retardances,

2 + δ 2 , .δ = δ 2 + δ 2 , .ρ = (1 − cos δ ) /δ 2 , respectively. Note that .δL = δ45 L C T xy T T and σ = sin δ T /δ T (Chipman, 2010; Azzam, 1978). Simulated Mueller matrix images for an elliptical retarder with MR (δ L cos 2θ FA , δ L sin 2θ FA , δ C ) for linear retardance δ L = [0, π], with fast axis orientation θ FA = 0, and circular retardance δ C = [−π, π] in the x and y directions, respectively, are shown in Fig. 1.9a. The logarithm decomposition of the simulated Mueller matrix images recovers separate maps of the correct polarization properties, shown in Fig. 1.9b–d. It is noted here that when both linear and circular retardance are present in a medium, phase wrapping of both properties occurs when the total retardance δ T ≥ π (limit indicated by the curve overlaid Fig. 1.9c, d). The phase wrapping of linear retardance gives an offset in the fast axis orientation of π/2.

3 Instrumentation To measure the full Mueller matrix of a medium, incident light with polarization states of at least four linearly independent Stokes vectors are required, and the

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Fig. 1.10 Conceptual diagram of an optical Mueller matrix polarimeter in a transmission arrangement

Stokes vector of the exiting light for each of the incident states should be measured. To satisfy these requirements, a Mueller matrix polarimeter should consist of a light source, a polarization state generator (PSG) that generates the states incident on the medium, a polarization state analyzer (PSA) that analyzes the states exiting the medium, and an optical detector (Fig. 1.10). Implementations of Mueller matrix polarimeters can be broadly classified as using methods that give fully determined Mueller matrices, with 16 independent measurements, or methods that oversample, with >16 measurements, to give overdetermined Mueller matrix elements. The latter may reduce measurement noise (Qi & Elson, 2017). For an overview of the established methods, readers are referred to Goldstein (2010, Ch. 17).

3.1 Polarimeter Architectures The architectures of the PSG and the PSA, which determine the manner in which the required polarization states are generated and analyzed, can be broadly classified as: division-of-time (DoT), division-of-aperture (DoA), division-of amplitude (DoAm), and division-of-focal-plane (DoFP) (Chipman, 1995; Tyo et al., 2006). DoT architectures are commonly implemented in Mueller matrix polarimeters. DoT architectures, in which the PSG and/or PSA enable time-sequential measurements at various polarization states, can be realized with various optical polarization devices, including: rotating elements (e.g., polarizers and waveplates) (Guo et al., 2013; He et al., 2015); variable linear retarders, such as liquid crystals (Chue-Sang et al., 2016; De Martino et al., 2003; Laude-Boulesteix et al., 2004) and photoelastic modulators (Arteaga et al., 2012; Alali et al., 2016); and linear retarders with switching fast axes, such as ferroelectric liquid crystals (Ellingsen et al., 2014; Aas et al., 2011). Rotating element architectures are robust and easy to implement but are limited to static scenes (Tyo et al., 2006). DoFP architectures use polarization cameras that contain the PSA, where the neighboring pixels of an image sensor are assigned varying polarization filters, to measure linear polarization states or the full Stokes vector (Myhre et al., 2012). These architectures can enable real-time measurement of Stokes vectors. However, such measurements require spatial interpolation and are limited by pixel registration errors (Tyo et al., 2006). Polarimeters with a DoFP PSA have been used to measure incomplete Mueller matrices (York et al., 2014; Chang et al., 2016). DoFP

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architectures are promising for developing Mueller matrix imaging polarimeters, with simplified instrumentation, that can measure samples with dynamically varying polarization properties, such as mechanically stretched soft tissues.

4 Applications This section presents some applications of polarization imaging techniques for measuring structural anisotropy in soft tissues. Particular focus is given to methods that provide measurements at a macroscopic scale (>5 mm in the lateral field of view).

4.1 Quantitative Polarized Light Microscopy A polarization imaging technique, commonly referred to as quantitative polarized light microscopy (QPLM), evolved from early work using polarized light microscopy (Ross et al., 1997; Massoumian et al., 2003). QPLM techniques have been extended to macroscopic scales to assess structural anisotropy during mechanical testing of heart valve leaflets (Tower et al., 2002; Robinson et al., 2008) and Type I collagen gels (Tower et al., 2002; Chandran & Barocas, 2004; Sander et al., 2009; Raghupathy et al., 2011). In these studies, spatially resolved estimates of the average collagen fiber orientation and the fiber anisotropy (degree of fiber alignment) were derived from the local optic axis orientation and the local magnitude of linear retardance, respectively. However, this approach has some potential limitations. If collagen fibers are out-of-plane (i.e., oriented in a nonperpendicular manner with respect to the light path), the propagating light encounters an apparent, as opposed to a true, birefringence, according to Eq. (1.4) (Matcher, 2009) and thus gives rise to a different sensitivity in measurements of fiber orientation. This issue has been mitigated in some QPLM studies by performing histological sectioning of tissues with prior knowledge of predominant fiber orientation (Spiesz et al., 2018; Rieppo et al., 2008). The linear retardance measurement is dependent on both the sample thickness and the total linear birefringence in the sample (see Eq. 1.5). This ambiguity has been addressed in some QPLM studies with histological sectioning of known sample thickness (Spiesz et al., 2018). However, the total linear birefringence is also dependent on the (unknown) collagen density in the imaged regions, and the relative contributions of the intrinsic linear birefringence and form linear birefringence, which combine to give total linear birefringence, are not resolved with these measurements (Rieppo et al., 2008). Linear retardance measurements are thus only capable of providing relative measures of fiber anisotropy (Sander et al., 2009).

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QPLM techniques typically assume that samples exhibit only linear retardance (Tower et al., 2002; Chandran & Barocas, 2004). However, biological tissues are, in general, complex turbid media with heterogeneous microstructural constituents (such as extracellular proteins, cell structures, vascular elements, and water) that give rise to highly scattering and absorbing behavior (Qi & Elson, 2017; Ghosh & Vitkin, 2011). The propagation of polarized light in scattering media may lead to multiple scattering events that randomize the direction of light propagation and lead to depolarization (Qi & Elson, 2017; Tuchin, 2016). For optically thin samples and collagen gels with low scattering, the QPLM techniques may be appropriate. However, transmission measurements of optically thick turbid media may be limited by significant depolarization that confound the estimates of optical anisotropy, which are contained in the polarized signal (Ghosh & Vitkin, 2011; Alali & Vitkin, 2015). Complex turbid biological media may also exhibit other polarization properties that, if unaccounted for, may confound the interpretation of optical anisotropy.

4.2 Mueller Matrix Imaging Polarization imaging techniques that measure the full Mueller matrix are referred to as Mueller matrix imaging (MMI), yielding a transfer function that represents all of the polarization properties of a sample (Ghosh & Vitkin, 2011). Mueller matrix decomposition can then be performed to separate the effects of multiple polarization properties, if present. This imaging technique has seen widespread application in the general field of tissue polarimetry due to developments in instrumentation and data analysis (Qi & Elson, 2017; Ghosh & Vitkin, 2011; Alali & Vitkin, 2015; He et al., 2019). MMI has been recently applied at a macroscopic scale to thin soft tissue membranes of pericardium in a transmission arrangement (see Fig. 1.11) (Dixon et al., 2021a). This application largely avoided the issue of out-of-plane fiber orientation, as such membranes have a predominantly in-plane fiber orientation. These measurements revealed the presence of circular retardance in these tissues, and it was demonstrated that when using incomplete Mueller polarimeters, such as Stokes sample polarimeters, this polarization property leads to misinterpretation in fiber orientation (Dixon et al., 2018, 2021a). It is noted that there may be redundancy in measuring the full Mueller matrix for soft tissues when, for example, they exhibit low diattenuation (Vitkin et al., 2015; Dixon et al., 2021a). MMI techniques are in general more complex in terms of instrumentation compared to other polarization imaging techniques. The measurement of polarization properties, other than optical anisotropy, may provide novel insight into the structure–function relations of soft tissues when such measurements become more widespread in combined mechanical testing and polarization imaging studies.

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Fig. 1.11 Mueller matrix imaging of 16 regions of calf bovine pericardium (a) giving maps of linear retardance (b), circular retardance (c), and net depolarization (d). This technique measured spatially varying polarization properties across a 70 mm × 70 mm region of the membrane, which exhibited strong linear and circular retardance. Significant depolarization occurs over the membrane thickness but does not cause complete depolarization of light (Adapted from Dixon et al., 2021a)

4.3 Polarized Spatial Frequency Domain Imaging A polarization imaging technique, referred to as polarized spatial frequency domain imaging (pSFDI), was developed to overcome some limitations associated with performing bulk tissue polarimetry of thick turbid multilayered samples (Yang et al., 2015; Goth et al., 2019). pSFDI is particularly useful for applications where soft tissues have a distinct multilayered structure, such as in native heart valves, in which predominant fiber orientations vary through the thickness of the tissues. This technique can provide macroscopic measurements of fiber orientation and anisotropy (degree of alignment), by assuming collagen fibers are in-plane cylinders exhibiting linear retardance and linear diattenuation in a reflectance arrangement. The use of structured illumination allows control of the effective imaging depth, that is, optical sectioning, and has given estimates of collagen fiber architecture in

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Fig. 1.12 (a) Polarized spatial frequency domain imaging (pSFDI) system for macroscopic measurements of optical anisotropy in heart valve leaflets. Digital micromirror device (DMD), fold mirrors (FM1 and FM2), linear polarizer (LP), projection and imaging lenses (L1 and L2), bandpass filter (BP), and camera (CMOS). (b) Estimates of fiber orientation and fiber alignment (normalized orientation index (NOI)) for both sides of ovine aortic valve leaflet derived from measurements from the system in (a). Results demonstrate the ability of the pSFDI technique to separate fiber alignments from different layers of the leaflet tissue (Adapted with permission from Goth et al., 2019)

superficial layers (approximately 250 μm) on each side of a valve leaflet (see Fig. 1.12) (Goth et al., 2019), as well as at various imaging depths (Jett et al., 2020). This technique has also enabled the estimation of absolute, as opposed to relative, measures of fiber anisotropy (Goth et al., 2019). Spatial frequency domain imaging has been recently combined with Mueller matrix imaging, giving optically sectioned macroscopic measurements of all the polarization properties of skin (Angelo et al., 2019). It should be noted that polarization-sensitive optical coherence tomography is a depth-resolved technique that overcomes many of the limitations noted in this section. However, this technique is currently complex and expensive to scale up to the large lateral fields of view for measurements at the macroscopic scale. It is thus not covered here.

4.4 Optomechanical Testing Early optomechanical studies have been carried out by combining QPLM with uniaxial mechanical testing (Tower et al., 2002). Due to recent developments and improvements in polarization imaging and analysis, there has been a renewed focus in research combining such techniques with mechanical testing instrumentation

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Fig. 1.13 (a) An optomechanical instrument combining a Mueller matrix imaging polarimeter and a mechanical tester. PSG polarization state generator, PSA polarization state analyzer, MT mechanical testing instrument. (b) Retardance polarization properties for a sample of pericardium mounted in a uniaxial tester at stretch ratios of 1 and 1.15 demonstrates the strain-induced changes in optical anisotropy (Adapted from Dixon et al., 2021a)

to study structure–function relationships in soft tissues. As polarization imaging methods can have a field of view and resolution that can be scaled by choice of imaging lens and imaging sensor, combined optomechanical devices offer a unique opportunity to study macroscopic tissue response in a nondestructive manner, using instrumentation that is relatively inexpensive and straightforward to implement. Figure 1.13a shows an example of an optomechanical instrument where a Mueller matrix imaging polarimeter has been integrated with a multiaxial mechanical testing instrument capable of stretching planar tissues along four axes. This instrument is limited to quasi-static mechanical tests due to the limited rate at which Mueller matrix images can be measured (Dixon et al., 2021b). Dynamic mechanical testing enables the measurement of viscoelastic mechanical properties of fibrous soft tissues by observing the time-dependent behavior of such tissues using, for example, frequency-rich stress/strain perturbation or stressrelaxation experiments (Emig et al., 2021). Dynamic optomechanical tests can be carried out by using polarimeter architectures and devices that enable real-time measurements, such as those implementing polarization cameras, and/or through reduced measurement of Mueller matrix elements, for example, with incomplete Stokes sample measuring polarimeters (York et al., 2014). Figure 1.13b demonstrates the change in the retardance polarization properties of a uniaxially stretched soft tissue membrane of pericardium using the instrument

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in Fig. 1.13a. Reorganization of the collagen fiber architecture during stretch led to strain-induced changes in the retardance across the sample. Changes in the fast axis orientation of the linear retardance indicated realignment of fibers along the direction of stretch in some regions (Dixon et al., 2021a). While this optomechanical technique shows promise for understanding structure–function behavior of such tissues, some technical challenges remain. First, phase wrapping effects that occur when these tissues undergo large changes in retardance lead to ambiguous measures of optic axis orientation and thus predominant fiber orientation. Secondly, the relative contributions of form and intrinsic birefringence to retardance measurements are still not well understood. Further development in the optical technique and the analysis of the load-dependent behavior of the tissue are needed to overcome such challenges. pSFDI has recently been integrated with biaxial mechanical testing instruments and applied to soft tissue membranes of native heart valves and pericardium (Jett et al., 2020; Dover et al., 2022). This optomechanical technique enables analysis of collagen fiber architecture in multilayered tissues under various biaxial loading conditions. To characterize the mechanical behavior of soft tissues, it is necessary to obtain load and deformation data. The deformation data for spatially heterogenous planar soft tissues is typically measured through digital image correlation (DIC), which require sufficient intrinsic texture. This presents a challenge for optomechanical techniques where any addition of markers to tissue may interfere with the polarization imaging. It was recently demonstrated the fiber property maps measured with pSFDI itself can act as a texture source for performing DIC (Dover et al., 2022).

5 Conclusion Polarization imaging techniques can have a field of view and resolution that can be readily scaled for the required applications, making these techniques an ideal choice for nondestructive imaging of optical/structural anisotropy in soft tissues at a macroscopic scale. In this chapter, we have outlined the fundamentals of such techniques and reviewed some of their applications in measuring optical anisotropy in soft tissues. Of particular interest are recent developments in the application of polarization imaging in optomechanical testing to investigate the biomechanical behavior of biological tissues.

References Aas, L. M. S., Ellingsen, P. G., & Kildemo, M. (2011). Near infra-red Mueller matrix imaging system and application to retardance imaging of strain. Thin Solid Films, 519(9), 2737–2741. https://doi.org/10.1016/j.tsf.2010.12.093

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Alali, S., & Vitkin, A. (2015). Polarized light imaging in biomedicine: Emerging Mueller matrix methodologies for bulk tissue assessment. Journal of Biomedical Optics, 20(6), 61104. https:// doi.org/10.1117/1.JBO.20.6.061104 Alali, S., Gribble, A., & Vitkin, I. A. (2016). Rapid wide-field Mueller matrix polarimetry imaging based on four photoelastic modulators with no moving parts. Optics Letters, 41(5), 1038. https:/ /doi.org/10.1364/ol.41.001038 Angelo, J. P., Germer, T. A., & Litorja, M. (2019). Structured illumination Mueller matrix imaging. Biomedical Optics Express, 10(6), 2861. https://doi.org/10.1364/BOE.10.002861 Arteaga, O., Freudenthal, J., Wang, B., & Kahr, B. (2012). Mueller matrix polarimetry with four photoelastic modulators: Theory and calibration. Applied Optics, 51(28), 6805. https://doi.org/ 10.1364/AO.51.006805 Azzam, R. M. A. (1978). Propagation of partially polarized light through anisotropic media with or without depolarization: A differential 4 x 4 matrix calculus. Journal of the Optical Society of America, 68(12), 1756–1767. https://doi.org/10.1364/JOSA.68.001756 Born, M., & Wolf, E. (1980). Principle of optics (6th ed.). Cambridge University Press. Chandran, P. L., & Barocas, V. H. (2004). Microstructural mechanics of collagen gels in confined compression: Poroelasticity, viscoelasticity, and collapse. Journal of Biomechanical Engineering, 126(2), 152–166. https://doi.org/10.1115/1.1688774 Chang, J., et al. (2016). Division of focal plane polarimeter-based 3 × 4 Mueller matrix microscope: A potential tool for quick diagnosis of human carcinoma tissues. Journal of Biomedical Optics, 21(5), 056002. https://doi.org/10.1117/1.JBO.21.5.056002 Chipman, R. A. (1995). Polarimetry. In M. Bass (Ed.), Handbook of optics: Volume II – Devices, measurements, and properties (2nd ed.). McGraw-Hill. Chipman, R. A. (2010). Mueller matrices. In M. Bass (Ed.), Handbook of optics: Volume I – Geometrical and physical optics, polarized light, components and instruments (3rd ed.). McGraw Hill. Chue-Sang, J., Bai, Y., Stoff, S., Straton, D., Ramaswamy, S., & Ramella-Roman, J. C. (2016). Use of combined polarization-sensitive optical coherence tomography and Mueller matrix imaging for the polarimetric characterization of excised biological tissue. Journal of Biomedical Optics, 21(7), 071109. https://doi.org/10.1117/1.JBO.21.7.071109 Collett, E. (2005). Field guide to polarization. SPIE. https://doi.org/10.1117/3.626141 Cuando-Espitia, N., Sánchez-Arévalo, F., & Hernández-Cordero, J. (2015). Mechanical assessment of bovine pericardium using Müeller matrix imaging, enhanced backscattering and digital image correlation analysis. Biomedical Optics Express, 6(8), 2953. https://doi.org/10.1364/ BOE.6.002953 De Martino, A., Kim, Y.-K., Garcia-Caurel, E., Laude, B., & Drévillon, B. (2003). Optimized Mueller polarimeter with liquid crystals. Optics Letters, 28(8), 616–618. https://doi.org/ 10.1364/OL.28.000616 Devlaminck, V., & Ossikovski, R. (2014). Uniqueness of the differential Mueller matrix of uniform homogeneous media. Optics Letters, 39(11), 3149–3152. https://doi.org/10.1364/ OL.39.003149 Dixon, A. W. (2021). Polarisation imaging of soft tissue membranes. PhD Thesis, University of Auckland. Accessed: 24 Mar 2022 [Online]. Available https://hdl.handle.net/2292/58120 Dixon, A., Taberner, A., Nash, M., & Nielsen, P. (2018). Extended depth measurement for a stokes sample imaging polarimeter. In Imaging, manipulation, and analysis of biomolecules, cells, and tissues XVI (p. 43). https://doi.org/10.1117/12.2289311 Dixon, A. W., Taberner, A. J., Nash, M. P., & Nielsen, P. M. F. (2021a). Quantifying optical anisotropy in soft tissue membranes using Mueller matrix imaging. Journal of Biomedical Optics, 26(10). https://doi.org/10.1117/1.JBO.26.10.106001 Dixon, A. W., Taberner, A. J., Nash, M. P., & Nielsen, P. M. F. (2021b). Assessing fibre reorientation in soft tissues with simultaneous Mueller matrix imaging and mechanical testing. In Computational biomechanics for medicine. https://doi.org/10.1007/978-3-031-09327-2_10

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Dover, C. M., Goth, W., Goodbrake, C., Tunnell, J. W., & Sacks, M. S. (2022). Simultaneous widefield planar strain–fiber orientation distribution measurement using polarized spatial domain imaging. Annals of Biomedical Engineering, 50(3), 253–277. https://doi.org/10.1007/s10439021-02889-7 Ellingsen, P. G., Aas, L. M. S., Hagen, V. S., Kumar, R., Lilledahl, M. B., & Kildemo, M. (2014). Mueller matrix three-dimensional directional imaging of collagen fibers. Journal of Biomedical Optics, 19(2), 026002–026002. https://doi.org/10.1117/1.JBO.19.2.026002 Emig, R., et al. (2021). Passive myocardial mechanical properties: Meaning, measurement, models. Biophysical Reviews, 13(5), 587–610. https://doi.org/10.1007/s12551-021-00838-1 Ghosh, N., & Vitkin, A. (2011). Tissue polarimetry: Concepts, challenges, applications, and outlook. Journal of Biomedical Optics, 16(11), 110801. https://doi.org/10.1117/1.3652896 Gil, J. J. (2014). Review on Mueller matrix algebra for the analysis of polarimetric measurements. Journal of Applied Remote Sensing, 8(1), 081599. https://doi.org/10.1117/1.jrs.8.081599 Goldstein, D. H. (2010). Polarized light (3rd ed.). CRC Press. [Online]. Available: http:// www.crcnetbase.com/isbn/978-1-4398-3040-6 Goth, W., Potter, S., Allen, A. C. B., Zoldan, J., Sacks, M. S., & Tunnell, J. W. (2019). Nondestructive reflectance mapping of collagen fiber alignment in heart valve leaflets. Annals of Biomedical Engineering, 47(5), 1250–1264. https://doi.org/10.1007/s10439-019-02233-0 Guo, Y., et al. (2013). A study on forward scattering Mueller matrix decomposition in anisotropic medium. Optics Express, 21(15), 18361. https://doi.org/10.1364/oe.21.018361 He, C., et al. (2015). Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images. Journal of Biomedical Optics, 20(10), 105009. https:// doi.org/10.1117/1.JBO.20.10.105009 He, H., et al. (2019). Mueller matrix polarimetry – An emerging new tool for characterizing the microstructural feature of complex biological specimen. Journal of Lightwave Technology, 37(11), 2534–2548. https://doi.org/10.1109/JLT.2018.2868845 Hecht, E. (2017). Optics (5th ed.). Pearson Education Limited. Jett, S. V., et al. (2020). Integration of polarized spatial frequency domain imaging (pSFDI) with a biaxial mechanical testing system for quantification of load-dependent collagen architecture in soft collagenous tissues. Acta Biomaterialia, 102, 149–168. https://doi.org/10.1016/ j.actbio.2019.11.028 Kumar, A., & Ghatak, A. (2011). Polarization of light with applications in optical fibers. SPIE. https://doi.org/10.1117/3.861761 Kumar, S., Purwar, H., Ossikovski, R., Vitkin, I. A., & Ghosh, N. (2012). Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media. Journal of Biomedical Optics, 17(10), 105006. https:/ /doi.org/10.1117/1.JBO.17.10.105006 Laude-Boulesteix, B., De Martino, A., Drévillon, B., & Schwartz, L. (2004). Mueller polarimetric imaging system with liquid crystals. Applied Optics, 43(14), 2824–2832. https://doi.org/ 10.1364/AO.43.002824 Liao, R., et al. (2010). Rotating linear polarization imaging technique for anisotropic tissues. Journal of Biomedical Optics, 15(3), 036014. https://doi.org/10.1117/1.3442730 Massoumian, F., Juskaitis, R., Neil, M. A. A., & Wilson, T. (2003). Quantitative polarized light microscopy. Journal of Microscopy, 209(Pt 1), 13–22. https://doi.org/10.1046/j.13652818.2003.01095.x Matcher, S. J. (2009). A review of some recent developments in polarization-sensitive optical imaging techniques for the study of articular cartilage. Journal of Applied Physics, 105(10). https://doi.org/10.1063/1.3116620 McNichols, R. J., & Coté, G. L. (2000). Optical glucose sensing in biological fluids: An overview. Journal of Biomedical Optics, 5(1), 5. https://doi.org/10.1117/1.429962 Myhre, G., et al. (2012). Liquid crystal polymer full-stokes division of focal plane polarimeter. Optics Express, 20(25), 27393–27409. https://doi.org/10.1364/OE.20.027393 Ortega-Quijano, N., & Arce-Diego, J. L. (2011). Mueller matrix differential decomposition. Optics Letters, 36(10), 1942. https://doi.org/10.1364/OL.36.001942

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Ossikovski, R. (2011). Differential matrix formalism for depolarizing anisotropic media. Optics Letters, 36(12), 2330–2332. https://doi.org/10.1364/OL.36.002330 Qi, J., & Elson, D. S. (2017). Mueller polarimetric imaging for surgical and diagnostic applications: A review. Journal of Biophotonics, 10(8), 950–982. https://doi.org/10.1002/jbio.201600152 Raghupathy, R., Witzenburg, C., Lake, S. P., Sander, E. A., & Barocas, V. H. (2011). Identification of regional mechanical anisotropy in soft tissue analogs. Journal of Biomechanical Engineering, 133(September), 091011. https://doi.org/10.1115/1.4005170 Rieppo, J., Hallikainen, J., Jurvelin, J. S., Kiviranta, I., Helminen, H. J., & Hyttinen, M. M. (2008). Practical considerations in the use of polarized light microscopy in the analysis of the collagen network in articular cartilage. Microscopy Research and Technique, 71(4), 279–287. https:// doi.org/10.1002/jemt.20551 Robinson, P. S., Johnson, S. L., Evans, M. C., Barocas, V. H., & Tranquillo, R. T. (2008). Functional tissue-engineered valves from cell-remodeled fibrin with commissural alignment of cell-produced collagen. Tissue Engineering – Part A, 14(1), 83–95. https://doi.org/10.1089/ ten.a.2007.0148 Ross, S., Newton, R., & Zhou, Y. (1997). Quantitative image analysis of birefringent biological material. Journal of Microscopy, 187(February), 62–67. https://doi.org/10.1046/j.13652818.1997.2160776.x Sander, E., Stylianopoulos, T., Tranquillo, R., & Barocas, V. (2009). Image-based biomechanics of collagen-based tissue equivalents. IEEE Engineering in Medicine and Biology Magazine, 28(3), 10–18. https://doi.org/10.1109/MEMB.2009.932486 Spiesz, E. M., Thorpe, C. T., Thurner, P. J., & Screen, H. R. C. (2018). Structure and collagen crimp patterns of functionally distinct equine tendons, revealed by quantitative polarised light microscopy (qPLM). Acta Biomaterialia, 70, 281–292. https://doi.org/10.1016/ j.actbio.2018.01.034 Sun, M., et al. (2014). Characterizing the microstructures of biological tissues using Mueller matrix and transformed polarization parameters. Biomedical Optics Express, 5(12), 4223. https:// doi.org/10.1364/boe.5.004223 Tower, T. T., Neidert, M. R., & Tranquillo, R. T. (2002). Fiber alignment imaging during mechanical testing of soft tissues. Annals of Biomedical Engineering, 30(10), 1221–1233. https://doi.org/10.1114/1.1527047 Tuchin, V. V. (2016). Polarized light interaction with tissues. Journal of Biomedical Optics, 21(7), 071114. https://doi.org/10.1117/1.JBO.21.7.071114 Tyo, J. S., Goldstein, D. L., Chenault, D. B., & Shaw, J. A. (2006). Review of passive imaging polarimetry for remote sensing applications. Applied Optics, 45(22), 5453–5469. https:// doi.org/10.1364/AO.45.005453 Vitkin, A., Ghosh, N., & de Martino, A. (2015). Tissue polarimetry. Photonics: Scientific Foundations, Technology and Applications, 4, 239–321. https://doi.org/10.1002/9781119011804.ch7 Wolman, M., & Kasten, F. H. (1986). Polarized light microscopy in the study of the molecular structure of collagen and reticulin. Histochemistry and Cell Biology, 85(1), 41–49. https:// doi.org/10.1007/BF00508652 Wood, M. F. G., et al. (2010). Polarization birefringence measurements for characterizing the myocardium, including healthy, infarcted, and stem-cell-regenerated tissues. Journal of Biomedical Optics, 15(4), 047009. https://doi.org/10.1117/1.3469844 Yang, B., Lesicko, J., Sharma, M., Hill, M., Sacks, M. S., & Tunnell, J. W. (2015). Polarized light spatial frequency domain imaging for non-destructive quantification of soft tissue fibrous structures. Biomedical Optics Express, 6(4), 1520. https://doi.org/10.1364/BOE.6.001520 York, T., Kahan, L., Lake, S. P., & Gruev, V. (2014). Real-time high-resolution measurement of collagen alignment in dynamically loaded soft tissue. Journal of Biomedical Optics, 19(06), 1. https://doi.org/10.1117/1.jbo.19.6.066011

Chapter 2

Polarization Techniques in Biological Microscopy Francisco J. Ávila and Juan M. Bueno

Abstract Optical microscopy approaches have been extensively employed for three-dimensional imaging of biological tissues at subcellular scales. Image quality and resolution of traditional imaging microscopes are limited by diffraction, aberrations, and scattering contributions from both the microscope objectives and the sample itself. Optimized optical designs including aberration correction can provide high-resolution imaging with magnification. However, the transparency of living (or ex vivo) organisms require labeling techniques due to the lack of image contrast to make visible the biological structure. The application of polarization techniques and new polarization elements provides a label-free contrast mechanism for imaging biological tissues characterized by optical anisotropy. This approach may improve the image quality and axial resolution in stained tissues and/or makes visible those unstained birefringent specimens. In addition, the application of polarimetric techniques allows to compute the optical properties of the biological sample, not accessible through nonpolarized optical microscopes. This chapter presents a review of polarization techniques applied to some of the main optical microscopy approaches. Keywords Polarization · Microscopy · Stokes–Mueller formalism

1 Optical Properties of Biological Samples Light can be described as a propagating transverse electromagnetic wave of electric and magnetic fields. When a vectorial formalism is adopted, the instantaneous

F. J. Ávila () Departamento de Física Aplicada, Universidad de Zaragoza, Zaragoza, Spain e-mail: [email protected] J. M. Bueno Laboratorio de Óptica, Universidad de Murcia, Murcia, Spain © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Mazumder et al. (eds.), Optical Polarimetric Modalities for Biomedical Research, Biological and Medical Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-031-31852-8_2

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electric field oscillation is expressed as a 2-D vector centered on the propagation axis with Cartesian components (Ex , Ey ). When the rotational position of the electric field vector changes in a continuous and nonrandom way during wave propagation, different polarization states are defined in function of the geometric trajectory of the electric field vector tip projection onto the transversal plane. Linear polarization states arise when electric oscillation direction occurs always in the same angular direction during propagation, so a polarization plane is determined together with the direction of the propagation axis. Elliptical polarization states occur when the electric field vector rotates during propagation determining over the transverse plane an ellipse curve with main axes angle orientation (χ) and ellipticity degree (). Moreover, any polarization states can be understood as a linear combination of two mutually orthogonal linear polarization states oscillating with some characteristic maximum amplitude component ratio (E0y /E0x ) and temporal phase shift (ϕ) between them. When the phase shift between main linear modes changes in a random way during a short timescale, it is not possible to define a deterministic polarization direction giving place to an unpolarized light state. Polarization states can be modified with optical elements, so unpolarized light can be easily transformed to linear polarized light by means of linear polarizers since linear polarized light can be transformed to elliptical polarized light by means of optical retarder plates; moreover, light interaction with random media can convert an elliptical polarized light in unpolarized light. Stokes vector (Chandrasekhar, 1960) is the most suitable formalism to represent general electromagnetic polarization states when we are dealing with time-averaged experimental measurements of the electric field intensity (I0 ). It was originally described as a column vector S = [S0 S1 S2 S3 ]T whose components are directly related with the maximum amplitude of electric field Cartesian components (E0x , E0yx ), the azimuth (χ), and ellipticity () values of the polarization ellipse: S0 = E0x 2 + E0y 2 = I0 S1 = E0x 2 − E0y 2 = I0 cos 2χ cos 2ψ . S2 = 2E0x E0y cosϕ = I0 sin 2χ cos 2ψ S3 = 2E0x E0y sinϕ = I0 sin 2ψ

(2.1)

where the components of the Stokes vector fulfill the following relation: S0 ≥



.

S12 + S22 + S32

(2.2)

This relationship transforms to equality for fully polarized light. From the Stokes vector, the azimuth and ellipticity values can be obtained in a simple way: 2χ = tan−1

.



S2 S1

 ;

2ψ = sin−1



S3 S0

 (2.3)

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29

Fig. 2.1 Polarization state P with coordinates 2χ y 2ψ over the Poincaré sphere. LH, LV , L+45◦ , L-45◦ , C+ y C− correspond to linear horizontal, linear vertical, linear at 45◦ , linear at −45◦ , circular right and circular left polarization states, respectively

Then, the degree of polarization (G) of a light beam is defined as (Azzam & Bashara, 1977):  G=

S12 + S22 + S32

.

S0

(2.4)

G ranges between 0 (unpolarized light) and 1 (fully polarized light). Intermediate values correspond to partially polarized light. Every polarization state associated with a fully polarized light beam can be represented on the Poincaré sphere by the coordinates 2χ and 2ψ (Theocaris & Gdoutos, 1979). A representation of the Poincaré sphere is shown in Fig. 2.1, the linear states are in the equatorial plane, where the right-handed are in the upper hemisphere and the left-handed states are in the lower. The points over the Poincaré sphere surface correspond to fully polarized light; the inner points correspond to partially polarized light, so the distance from the point P to the center of the sphere is the polarization degree G. When light interacts with a material medium, a change in polarization state may occur. In a very general way, such a change is equivalent to a certain combination of linear polarizers and retarders (Jones, 1941). Linear polarizers produce selective transmission of light in function of the incident polarization state, while retarders produce a phase shift between the orthogonal components of the electric field. If a light beam with an associated Stokes vector S is incident on a sample, the Stokes vector corresponding to the output light, S , is given by: ⎡ 0 ⎤ m00 m01 SIN ⎢ S 1 ⎥ ⎢ m10 m11 IN ⎥ ⎢ =⎢ ⎣ S 2 ⎦ = ⎣ m20 m21 IN 3 SIN m30 m31 ⎡

(i)

SIN

.

m02 m12 m22 m32

⎤ ⎡ 0 ⎤ m03 SOUT ⎢ S1 ⎥ m13 ⎥ ⎥ · ⎢ OUT ⎥ = MM · S (i) OUT m23 ⎦ ⎣ S 2 ⎦ m33

OUT 3 SOUT

(2.5)

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Table 2.1 Summary of the main polarization properties Diattenuation Dichroism Birefringence Optical rotation Depolarization Polarization

Dependence of the intensity of light emerging from the sample (transmitted or reflected) as a function of the incoming polarization state. When the diattenuation observed on the transmission (or reflection) function of the sample is due to absorption. Selective propagation retardation of the transversal components of electric field due to refractive index anisotropy. Rotation of the polarization ellipse. It is also known in chemistry field as optical activity. It is related to birefringent media. Decrease in the degree of depolarization. Related to scattering effects. Transformation from unpolarized to polarized light.

where MM is called the Mueller matrix, and is a 4 × 4 square matrix of real mij elements, containing all polarization properties of the system (Shurcliff, 1962). The interaction of polarized light with biological tissues (Bennett, 1961) reveals intrinsic optical properties of the biological specimen that are directly related to its molecular arrangement, that is, the optical properties of the tissue modify the polarization state of the light interacting with it (Chipman, 1995). The main polarization properties characterizing an optically anisotropic biological material are summarized in Table 2.1.

2 Polarized Microscopy Polarization-sensitive microscopy (PSM) concept includes any optical microscopy technique involving polarized light. PSM is extensively used to observe specimens characterized by optical anisotropy. The sensitivity of polarized microscopy to birefringent samples enables to understand the molecular organization of biological tissues even if the spatial resolution of the microscope is far from the submicron scale. PSM has demonstrated capabilities to measure optical properties from optically anisotropic biological samples such as birefringence or dichroism and, therefore, to extract microstructure and chemical homogeneity (Weaver, 2003). Polarized light microscopes are designed to incorporate two polarization units: a polarizer unit placed in the illumination pathway before the sample and a second polarizer element positioned between the microscope objective and the intensity sensor detector. Then, after the interaction of the polarized light with a hypothetically anisotropic biological sample (Fig. 2.2), the light emerging from the sample (in both reflection and transmission microscope configurations) has changed its own polarization state. Finally, the second polarizer unit acting as analyzer transmits a final polarized state, which is the function of the polarization state of the light emerging from the sample. The simplest configuration of a polarized light microscope uses linear polarizers in cross-configuration in both the polarizer and the analyzer polarization units.

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Fig. 2.2 Schematic of a polarized light microscopy in transmission configuration

However, to compute a representative number of polarization properties for full optical characterization of the biological sample, Mueller matrix (MM) polarimetric setups (Pezzentini & Chipman, 1995) have been traditionally employed, which incorporate rotating retarders at both the polarizer and analyzer units. An MM polarimeter is composed of two polarization subsystems: a polarization state generator (PSG) to control the polarization state of the light beam, which is going to reach the sample, and a polarization state analyzer (PSA) whose output light reaches the detector. The combination of different polarization states generated at both PSG and PSA allows computation of the elements of the MM of the sample containing all its polarization properties (Morgan et al., 1997). Fig. 2.3 shows a typical configuration of a MM polarimeter operating in transmission (Fig. 2.3a) and reflection (Fig. 2.3b) modes. A detailed description of an MM polarimeter configuration can be found elsewhere (Bueno & Campbell, 2002; Abubaker & Tomanek, 2011). Let us consider an MM polarimeter, wherein the PSG and PSA are composed of fixed linear polarizers and rotating retarders (quarter-wave plates, λ/4). Then the PSG and PSA units generate polarization states represented by the Stokes vectors SPSG and SPSA (Bueno & Jaronski, 2001): ⎛ ⎞ ⎞T ⎛ 1 ⎞T ⎛ 1 ⎞ 1 SIN SOUT 1 ⎜ S 2 ⎟ ⎜ c2 ⎟ ⎜ 2 ⎟ ⎜ 2 ⎟ IN ⎟ = ⎜ ⎟ ; SP SA = SOU T = ⎜ SOUT ⎟ = ⎜ c ⎟ =⎜ 3 3 ⎠ ⎝S ⎠ ⎝s · c⎠ ⎝S ⎝s · c⎠ ⎛

SPSG = SIN

.

IN

4 SIN

OUT

s

4 SOUT

s (2.6)

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Fig. 2.3 Schematics of transmission (a) and reflection (b) Mueller matrix polarimeter configurations. LS laser source, CL collimating lens, P linear polarizer, R retarder plate, FL focusing lens, PSG polarization state generator, PSA polarization state analyzer

where c = cos2α, s = sin2α, and α is the angle between the fast axis of the quarterwave plate retarder (λ/4) and the linear polarizer axis. Then, the optical properties (i) of the sample modifies any incident Stokes vector .SIN , into an output Stokes vector (i) .S OUT (i) (i) SOUT = MM · SIN

.

(2.7)

To obtain the full MM elements, four independent polarization states in both PSG and PSA must be generated (Hauge, 1978). Let MPSA and MPSG be the 4 × 4 matrices whose elements are the Stokes vector generated at the PSG and PSA, respectively:   (1) (2) (3) (4) MPSG = SPSG SPSG SPSG SPSG

.

(2.8)

  (1) (2) (3) (4) MPSA = SPSA SPSA SPSA SPSA

.

(i)

Then the .SOUT vector can be computed by recording a set of 16 intensity images intensity corresponding to different combinations of independent PSG–PSA (i j ) polarization states .ID , (i, j = 1,2,3,4) (Bueno & Jaronski, 2001): ⎞ (i _1) ID ⎜ (i _2) ⎟ ⎟ ⎜I −1 ⎜ D = MPSA · ⎜ i _3 ⎟ ⎟ ⎝ ID  ⎠ i _4 ID ⎛

(i)

SOUT

.

(2.9)

2 Polarization Techniques in Biological Microscopy

33

(i)

where .ID (I = 1,2,3,4) corresponds to images recorded by four PSA polarization states and a fixed PSG independent state. Finally, the Mueller matrix can be computed as: −1 MM = MOUT · MPSG

.

(2.10)

(i) where MOUT is the auxiliary matrix, which columns are the four .SOUT vectors. As stated, the MM of a system contains information of all its polarization properties (Chipman, 1995). Furthermore, using polar decomposition methods (Chipman, 1995; Gil & Bernabeu, 1987), three matrices can be obtained from the MM:

MM = M · MR · MD

.

(2.11)

where M , MR , and MD are the depolarization, retardation, and diattenuation matrices, respectively.

3 Polarized Light Microscopy Approaches Throughout the following subsections, the most representative polarization microscopy techniques will be described based on their applications and limitations, from traditional wide-field microscopy to nonlinear multiphoton imaging.

3.1 Wide-Field Polarized Microscopy Regular wide-field imaging microscopy provides high-resolution visualization of biological tissues; however, the illumination extends to the whole field of view incorporating to the emission light scattering background from out-of-focus planes. Then, wide-field microscopy is limited by blurring effects and limited 3D imaging capabilities as the scattering increases as a function of depth and usually requires deconvolution post processing to restore the image quality (Lee et al., 2014). In that sense, the incorporation of polarized light provides a contrast-enhanced approach to investigate optically anisotropic biological samples (Oldenbourg, 2013). The gold standard in cancer diagnosis is still the pathological analysis of stained histopathological samples of patient biopsies (Saikia et al., 2008). However, the irruption of MM polarimetry provided improved image contrast, label-free imaging, and invaluable quantitative characterization of the malignant tissue through the determination of its optical properties (Alali & Vitkin, 2015; Qi & Elson, 2017). The capabilities of MM microscopy to detect anisotropy changes at the external layers of the cancerous tissues allows early stage diagnosis improving the survival probability (Jacques et al., 2002).

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Fig. 2.4 Mueller matrix image composition of a porcine liver tissue for transmission (a) and backscattering (b) microscope configurations. The mij elements are normalized to m00 (Reproduced from Liu et al. (2018)

Figure 2.4 shows a comparison of a MM obtained with backscattered (Fig. 2.4a) and transmission (Fig. 2.4b) configurations of a wide-field imaging polarimeter of a liver sample. From the MMs, the polarization properties of the malignant tissues can be computed by polar decomposition methods (see Polarized Microscopy subsection).

3.2 Polarized Fluorescence Microscopy Fluorescence microscopy is mainly used to detect target molecules in biological labeled tissues with fluorescent probes. The molecular arrangement of intrinsically birefringent biological tissues can be determined by measuring its retardance (Inoué & Bajer, 1961); however, the main limitation lies in the inability to discriminate specific molecules. In that sense, the combination of fluorescence microscopy with polarized light allows to determinate the orientation of the fluorescent proteins dipoles merged to those proteins of interest (McQuilken et al., 2015). Polarized fluorescence microscopy (PFM) can determine the position and orientation of fluorescent molecules and, therefore, analyze the dynamics of living proteins such as actin (Nakai et al., 2019). The optimization of PFM techniques has made possible to perform pharmacokinetic and pharmacodynamics measurements of intracellular drug distribution (Vinegoni et al., 2019), to understand the bacteria invasion (Yu et al., 2021) or virus infection (Cong et al., 2015) into epithelial cells through the cells polarity, among other clinical applications in immunofluorescence imaging.

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Fig. 2.5 Fluorescence intensity images (a–c), lifetime images (d–f) and fluorescence histograms (g–i) of a network of blood vessels (Reproduced from Sun et al. (2010)

One of the potential applications of PFM lies on live-cell and lifetime imaging (see an example of lifetime imaging in Fig. 2.5) due to its capabilities to measure the time that a fluorophore takes to emit a photon from its excited state (Chang et al., 2017). The sensitivity of fluorescence lifetime imaging microscopy allows in vivo detection of molecular dynamics of biological processes and cellular metabolism. Lifetime imaging has allowed to obtain new biomarkers for metabolic abnormalities (Heikal, 2010) and gene expression (Chalfie et al., 1994) or advanced real-time image-guided augmented reality for cancer surgery (Sun et al., 2010; Gorpas et al., 2019).

3.3 Polarized Total Internal Reflection Fluorescence Microscopy Total internal reflection microscopy (TIRFM) is based on total internal reflection (TIR) phenomenon that takes place when a light beam arrives at the interface of two media with different refraction index n1 and n2 (with n1 > n2 ) and incident angle higher than the critical angle θ TIR given by: −1

θTIR = sin

.



n2 n1

 (2.12)

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F. J. Ávila and J. M. Bueno

Fig. 2.6 Representation of total internal reflection fluorescence in living cells (Reproduced from Yang et al. (2017))

The first demonstration of TIR as microscopy technique was reported in 1956 by Ambrose [34](Ambrose, 1956). The operating principle of TIR microscopy lies in the generation of an evanescent field in the medium of lower refractive index when the incident angle is higher than θ TIR ; this formation is due to total internal reflection at the interface. If cellular structures are placed in close contact with the denser medium, they will scatter the light and appear bright within the evanescent field (Ambrose, 1956). When the light beam undergoes TIR, electromagnetic evanescent wave fields are generated (Axelrod et al., 1984). Although evanescent fields do not propagate as a function of position, they still oscillate as a function of time and then excite those molecules near to the interface. TIR microscopy concept is illustrated in Fig. 2.6. TIR microscopy has been employed for single fluorophore imaging (Yildiz et al., 2003) detection, real-time analysis of endocytosis (Rappoport & Simon, 2003), or the measurement of colloidal forces (Prieve, 1999). Despite the capabilities of TIR microscopy to study the dynamics of single molecules, the acquired signals depend on uncontrolled factors such as polarization state of the excitation light or the orientation of the fluorophore’s dipoles (Nikolaus et al., 2021). Then, the application of polarization-controlled excitation light gave rise to polarized total internal reflection fluorescence microscopy (PTIRFM) concept (Beausang et al., 2012). PTIRFM allowed to measure the spatial angular orientation of fluorophores (Beausang et al., 2012) or to optimize the detection of the dynamics of fusing membranes (Nikolaus et al., 2021). Fig. 2.7 shows an example of the measurement of optical anisotropy and protein polymerization in human embryonic kidney cells compared with episcopic illumination (EPI) (Fig. 2.7a) and PTIRFM (Fig. 2.7b) (Ströhl et al., 2017).

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Fig. 2.7 Polymerization and optical anisotropy measurements in HEK293T cells with episcopic illumination (EPI) and polarized total internal reflection fluorescence (PTIRF) (Adapted from Ströhl et al. (2017))

3.4 Confocal Scanning Laser Polarimetric Microscopy In wide-field microscopy, the emitted signal from the sample recorded by the detector arises from both in-focus and out-of-focus planes within the specimen. That out-of-focus light adds an unwanted background that blurs the acquired images and reduces the image quality. The image degradation depends on the thickness and scattering properties of the biological sample as main factors (Dang et al., 2019). The basic principle of confocal microscopes is similar to wide-field microscopy. The main difference consists of the incorporation of pinholes that block the out-offocus light emission ensuring that only a diffraction-limited spot from the desired axial plane focuses on the detector as schematized in Fig. 2.8. This configuration allows plane-by-plane imaging or optical sectioning. Then, to reconstruct an entire field-of-view of the specimen at a given depth, the laser spot needs to be scanned over the sample (scanning microscopy). Confocal laser scanning microscopes (CLSM) require longer exposure times and more sensitive detectors than widefield approaches since the pinholes act as spatial filters dimming the emission from the sample to be detected. Lateral resolution of CLSMs is given by the diffraction-limited spot, providing sharpened, contrast-enhanced, and completely in-focus images without residual background blurring the image quality. On the other hand, the capability of optical sectioning (axial resolution) allows 3D rendering of the specimen (Schneckenburge & Richter, 2021). Despite the advantages of standard CLSM, the use of depolarized light does not allow extracting any other information from the sample in its spatially resolved structure (texture and structural information). Then, polarizing techniques are required not only to enhance the contrast but also to measure the polarization properties associated to anisotropic molecular structure such as dichroism, birefringence, or depolarization due to scattering effects in non-anisotropic tissue structures (Van Eeckhout et al., 2021).

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Fig. 2.8 Comparison between widefield (a) and confocal (b) microscopy modalities (Adapted from Kim et al. (2016))

The application of Stokes–Mueller polarimetry to CLSM has allowed to perform visualization of cytomembranes (Wang et al., 2021) to diagnose amyloidosis (Wang et al., 2021) or imaging melanoma in malignant tissues (Gareau et al., 2005). The incorporation of new radial polarization elements to polarized CLSM brought new advantages such as the formation of subwavelength focal spots, improved axial resolution, and enhanced image quality of tomographic scans (Wang et al., 2020; Kitamura et al., 2010). Fig. 2.9 shows scans of fluorescence beads suspension acquired at different depths with regular scanning microscopy (Fig. 2.9a–c) and a single scan applying image scanning microscopy annular radially polarized (ISMaPR) approach. The application of radial polarization allows obtaining extended

2 Polarization Techniques in Biological Microscopy

39

Fig. 2.9 Axial scans of beads suspension acquired with regular scanning microscopy (a–c) and single scan using annular radially polarized light (d) (Reproduced from Wang et al.(2020))

transverse resolution, which is a single scan that contains projected volume viewing equivalent to multiple axial scans acquired with regular scanning microscopy.

3.5 Polarization-Sensitive Second Harmonic Microscopy Second harmonic generation (SHG) is a nonlinear optical process in which two photons (typically of infrared light), propagating through (or interacting with) a noncentrosymmetric material at the fundamental frequency, become a single visible photon with twice the frequency. No energy losses occur in this process (Campagnola & Loew, 2003). The induced electric dipole moment by the fundamental − →2 electric field ( . E ω ) can be expressed as (Willets et al., 1992): 1 1 − → − → 2 − → 3 − → μ = μ0 + α · E ω + β · E ω + γ · E ω 2! 3!

.

(2.13)

where μ0 is the permanent dipolar moment and α, β, and γ are the linear polarizability and first and second order hyperpolarizabilities, respectively. SHG process is governed by the nonlinear susceptibility tensor χ (2) that depends on the second-order hyperpolarizability β, a property related at the molecular level to the electronic transition in the material (Erikson et al., 2009; Tuer et al., 2011). The second-order term becomes null for centrosymmetric structures (Moreaux et al., 2000); therefore only noncentrosymmetric structures, such as type-I fibrillary collagen, are able to generate second harmonic signals. SHG radiation arises from absorption-induced polarization endogenous process (Campagnola et al., 2002), which significantly reduces the photobleaching and phototoxic effects of fluorescence microscopy approaches. The previously reviewed microscopy approaches, provide a noninvasive approach to assess the structure of biological tissues at subcellular scale. However, the main volume of the biological tissues is not composed of cells but of extracellular matrix (ECM). In that sense, collagen is the most abundant structural protein forming the ECM; there are more than 20 classified collagen types, of which 80% corresponds to fibrillar type-I collagen (Seeley et al., 2003). During

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the past two decades, nonpolarized SHG microcopy has been extensively used for visualization of the connective tissue mainly composed of collagen, such as skin (Lin et al., 2006), bones (Lee et al., 2006), or corneal stroma (Yeh et al., 2002). The application of polarization to SHG microscopy makes it possible to analyze and detect changes in the collagen structure at molecular scale (Stoller et al., 2002; Odin et al., 2008; Psilodimitrakopoulos et al., 2009; Chen et al., 2012). Elliptically polarized incident light is often used. With it, the SHG signal is obtained regardless of their orientation of the fibers in relation with the polarized light. This is of interest in cases where it is required to obtain images of fibers in tissues undergoing remodeling, as is the case of fibrosis (Strupler et al., 2008). Fibrillar collagen exhibits structural anisotropy that can be characterized by the ratio of hyperpolarizabilities, ρ (Stoller et al., 2003; Gusachenko et al., 2010). This parameter depends on the orientation of the triple helix of molecular collagen and on the orientation of the dipoles along the peptide bonds in the triple helix, thus providing information on the organization of collagen internally and/or of the fibrils forming collagen fibers. The structural organization of collagen can be affected by aging traumatic or pathological processes. The combination of polarization SHG microscopy has been used for the clinical diagnosis of cancer (Campagnola, 2011), the analysis of denaturation due to aging (Aït-Belkacem et al., 2012), and the study of the organization of the corneal extracellular matrix (Latour et al., 2012), among others. This subsection focuses on the particular application of circular dichroism analysis to quantify the molecular arrangement of type-I fibrillar collagen based on SHG Stokes vector imaging polarimetry. Figure 2.10 shows a schematic of a custom-built polarimetric SHG microscope (details on the experimental system can be found elsewhere (Avila et al., 2015)). The polarization unit is based on a polarization state generator (PSG) placed at the  illumination pathway allowing to reach the sample an incident Stokes vector ( (i) (i) .S IN that turns into another emerging ( .SSHG ), which represents the polarization state of the radiated SHG signal (ISHG ). If four independent polarization states are (i) generated at the PSG, the changes in .SIN after the sample interaction through the (i) emerging vector .SSHG are due to polarization properties of the specimen represented by the first row of the Mueller matrix (MCSHG ), which contains information on the diattenuation properties: ⎞ ⎛ (i) ⎞ S0(i) S0_IN _SHG (i) ⎟ ⎟  ⎜ S (i) ⎜  ⎜ _SHG ⎟ (i) SHG mSHG mSHG · ⎜ S1_IN ⎟ = MC = ⎜ 1(i) m ⎟ = mSHG ⎟ ⎜ SHG · SIN 0 1 2 3 ⎠ ⎝ S2_SHG ⎠ ⎝ S2(i) _IN (i) S3(i) S _SHG 3_IN (2.14) ⎛

(i) SSHG

.

(i)

The first element of a Stokes vector ( .S0SHG ) represents the SHG intensity (Chipman, 1995); then the MM elements of the sample (MCSHG ) can be computed

2 Polarization Techniques in Biological Microscopy

41

Fig. 2.10 Schematic diagram of the polarization-sensitive second harmonic microscope reported in (Avila et al., 2015)

by matrix inversion: MC SHG = ISHG · (MIN )−1

(2.15)

.

(i)

where MIN is a 4 × 4 matrix whose columns correspond to the .SIN Stokes vectors. Once the elements of MCSHG are known, the SHG circular dichroism (CDSHG ) can be computed as (Avila et al., 2017): CD SHG = 2 •

.

mSHG 3 mSHG 0

(2.16)

Figure 2.11 shows SHG images corresponding to an ex vivo collagen-based ocular tissue (scleral tissue) acquired for four independent polarization states generated at the PSG (upper row) and its representation in the Poincaré sphere. From the polarimetric SHG imaging, the first row of the Mueller matrix (bottom row) is computed using the Eq. (15). Once the elements of the first row are computed, CDSHG can be computed pixel-by-pixel using the Eq. (2.16). The information provided by the CDSHG lies on a double clinical relevance: its modulus quantifies the internal organization of collagen, and the sign gives information about the polarity of the fibrils composing the fibers that are visible at micrometric scale in SHG imaging microscopy.

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Fig. 2.11 SHG images corresponding to an ex vivo human scleral tissue, acquired for four independent polarization states represented in the Poincaré sphere (upper row). The corresponding first row of the Mueller matrix is shown at the bottom

References Abubaker, H., & Tomanek, P. (2011). Polarization of scattered light in biological tissue. Proceedings of SPIE – The International Society for Optical Engineering, 830600. Aït-Belkacem, D., Guilbert, M., Roche, M., et al. (2012). Microscopic structural study of collagen aging in isolated fibrils using polarized second harmonic generation. Journal of Biomedical Optics, 17(8), 080506. Alali, S., & Vitkin, A. (2015, 061104). Polarized light imaging in biomedicine: Emerging Mueller matrix methodologies for bulk tissue assessment. Journal of Biomedical Optics, 20(6). Ambrose, E. J. (1956). A surface contact microscope for the study of cell movements. Nature, 178, 1194. Avila, F., del Barco, O., & Bueno, M. (2015). Polarization dependence of aligned collagen tissues imaged with second harmonic generation microscopy. Journal of Biomedical Optics, 20(8), 086001. Avila, F., del Barco, O., & Bueno, M. (2017). Quantifying external and internal collagen organization from stokes-vector-based second harmonic generation imaging polarimetry. Journal of Optics, 19(2017), 1–11. Axelrod, D., Burghardt, T. P., & Thompson, N. L. (1984). Total internal reflection fluorescence. Annual Reviews in Biophysics and Bioengineering, 13, 247–268. Azzam, R. M., & Bashara, N. M. (1977). Ellipsometric measurement of the polarization transfer function of an optical system. Journal of the Optical Society of America, 62(3), 336–340. Beausang, J. F., Sun, Y., Quinlan, M. E., et al. (2012). The polarized total internal reflection fluorescence microscopy (polTIRFM) twirling filament assay. Cold Spring Harbor Protocols, 2012(6), 719–721. Bennett, H. S. (1961). The microscopical investigation of biological materials with polarized light. In C. E. McClung (Ed.), Handbook of microscopical technique. Hafner Pub Co. Bueno, J. M., & Campbell, M. C. W. (2002). Confocal scanning laser ophthalmoscopy improvement by use of Mueller-matrix polarimetry. Optics Letters, 17, 830–832. Bueno, J. M., & Jaronski, J. (2001). Spatially resolved polarization properties for in vitro corneas. Ophthalmic and Physiological Optics, 21, 384–392.

2 Polarization Techniques in Biological Microscopy

43

Campagnola, P. J. (2011). Second harmonic generation imaging microscopy: Applications to diseases diagnostics. Analytical Chemistry, 83(9), 3224–3231. Campagnola, P. J., & Loew, L. M. (2003). Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms. Nature Biotechnology, 21(11), 1356–1360. Campagnola, P. J., Millard, A. C., Terasaki, M., et al. (2002). Three-dimensional high-resolution second-harmonic generation imaging of endogenous structural proteins in biological tissues. Biophysical Journal, 82(1), 493–508. Chalfie, M., et al. (1994). Green fluorescent protein as a marker for gene expression. Science, 263(5148), 802–805. Chandrasekhar, S. (1960). Radiative transfer. Dover Publications. Chang, C. W., Sud, D., & Mycek, M. A. (2017). Fluorescence lifetime imaging microscopy. Methods in Cell Biology, 8, 495–524. Chen, X., Nadiarynkh, O., Plotnikov, S., et al. (2012). Second harmonic generation microscopy for quantitative analysis of collagen fibrillar structure. Nature Protocols, 7(4), 654–669. Chipman, R. A. (1995). Polarimetry. In M. Bass, E. W. van Stryland, D. R. Williams, & W. L. Wolfe (Eds.), Handbook of optics (pp. 22.21–22.37). McGraw-Hill Inc. Cong, Y., Li, X., Bai, Y., et al. (2015). Porcine aminopeptidase N mediated polarized infection by porcine epidemic diarrhea virus in target cells. Virology, 478, 1–8. Dang, X., Bardhan, N., Qi, J., et al. (2019). Deep-tissue optical imaging of near cellular-sized features. Scientific Reports, 9, 3873. Erikson, A., Ortegren, J., Hompland, T., et al. (2009). Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope. Journal of Biomedical Optics, 12(4), 044002. Gareau, D. S., Lagowski, J., Rossi, V. M., et al. (2005). Imaging melanoma in a murine model using reflectance-mode confocal scanning laser microscopy and polarized light imaging. The Journal of Investigative Dermatology. Symposium Proceedings, 10(2), 164–169. Gil, J. J., & Bernabeu, E. (1987). Obtainment of the polarizing and retardation parameters of a non depolarizing optical system from the polar decomposition of its Mueller matrix. Optik, 76(2), 67–71. Gorpas, D., et al. (2019). Autofluorescence lifetime augmented reality as a means for real-time robotic surgery guidance in human patients. Scientific Reports, 9(1), 1187. Gusachenko, I., Latour, G., & Schanne-Klein, M. C. (2010). Polarization-resolved second harmonic microscopy in anisotropic thick tissues. Optics Express, 18(18), 19339–19352. Hauge, P. S. (1978). Mueller matrix ellipsometry with imperfect compensators. Journal of the Optical Society of America, 68, 1519–1528. Heikal, A. A. (2010). Intracellular coenzymes as natural biomarkers for metabolic activities and mitochondrial anomalies. Biomarkers in Medicine, 4(2), 241–263. Inoué, S., & Bajer, A. (1961). Birefringence in endosperm mitosis. Chromosoma, 12, 48–63. Jacques, S. L., Ramella-Roman, J. C., & Lee, K. (2002). Imaging skin pathology with polarized light. Journal of Biomedical Optics, 7(3), 329–340. Jones, R. C. (1941). A new calculus for the treatment of optical systems I. Description and discussion of the calculus. Journal of the Optical Society of America A, 31(7), 448–503. Kim, A., Suleiman, H., & Shaw, A. (2016). New approaches in renal microscopy. Current Opinion in Nephrology and Hypertension, 25, 1–10. Kitamura, K., Sakai, K., & Noda, S. (2010). Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam. Optics Express, 18(5), 4518– 4525. Latour, G., Gusachenko, I., Kowalczuk, L., et al. (2012). In vivo structural imaging of the cornea by polarization-resolved second harmonic microscopy. Biomedical Optics Express, 3(1), 1–15. Lee, H. S., Teng, S. W., & Dong, C. Y. (2006). Imaging human bone marrow stem cell morphogenesis in polyglycolic acid scaffold by multiphoton microscopy. Tissue Engineering, 12(10), 2835–2841. Lee, J. S., Wee, T. L., & Brown, C. M. (2014). Calibration of wide-field deconvolution microscopy for quantitative fluorescence imaging. Journal of Biomolecular Techniques, 25(1), 31–40.

44

F. J. Ávila and J. M. Bueno

Lin, S. J., Jee, S. H., & Dong, C. Y. (2006). Discrimination of basal cell carcinoma from normal dermal stroma by quantitative multiphoton imaging. Optics Letters, 31(18), 2756–2758. Liu, T., Sun, T., He, H., et al. (2018). Comparative study of the imaging contrasts of Mueller matrix derived parameters between transmission and backscattering polarimetry. Biomedical Optics Express, 9(9), 4413–4428. McQuilken, M., Mehta, S. B., Verma, A., et al. (2015). Polarized fluorescence microscopy to study cytoskeleton assembly and organization in live cells. Current Protocols in Cell Biology, 67, 4.29.1–4.29.13. Moreaux, L., Sandrea, O., & Mertz, J. (2000). Membrane imaging by second harmonic generation microscopy. Journal of the Optical Society of America B: Optical Physics, 17(10), 1685–1689. Morgan, S. P., Khong, M. P., & Somekh, M. G. (1997). Effects of polarization state and scatterer concentration on optical imaging through scattering media. Applied Optics, 36(7), 1560–1565. Nakai, N., Sato, K., Tani, T., et al. (2019). Genetically encoded orientation probes for F-actin for fluorescence polarization microscopy. Microscopy (Oxford), 68(5), 359–368. Nikolaus, J., Hancock, K., Tsemperouli, M., et al. (2021). Optimal detection of fusion pore dynamics using polarized total internal reflection fluorescence microscopy. Frontiers in Molecular Biosciences, 8, 740408. Odin, C., Le Grand, Y., Renault, A., et al. (2008). Orientation fields of nonlinear biological fibrils by second harmonic generation microscopy. Journal of Microscopy, 229(1), 32–38. Oldenbourg, R. (2013). Polarized light microscopy: principles and practice. Cold Spring Harbor Protocols, 2013(11), pdb.top078600. Pezzentini, J., & Chipman, R. A. (1995). Mueller matrix imaging polarimetry. Optics Communications, 34, 1558–1562. Prieve, D. C. (1999). Measurement of colloidal forces with TIRM. Advances in Colloid and Interface Science, 82, 93–125. Psilodimitrakopoulos, S., Santos, S., Amat-Roldan, I., et al. (2009). In vivo, pixel resolution mapping of thick filaments’ orientation in non-fibrilar muscle using polarization sensitive second harmonic generation microscopy. Journal of Biomedical Optics, 14(1), 014001. Qi, J., & Elson, D. S. (2017). Mueller polarimetric imaging for surgical and diagnostic applications: A review. Journal of Biophotonics, 10(8), 950–982. Rappoport, J. Z., & Simon, S. M. (2003). Real-time analysis of clathrin-mediated endocytosis during cell migration. Journal of Cell Science, 116, 847–855. Saikia, B., Gupta, K., & Saikia, U. N. (2008). The modern histopathologist: In the changing face of time. Diagnostic Pathology, 3(1), 25–29. Schneckenburge, H., & Richter, V. (2021). Laser scanning versus wide-field – Choosing the appropriate microscope in life sciences. Applied Sciences, 11(733), 1–16. Seeley, R., Stephens, T., & Tate, P. (2003). Anatomy and physiology. McGraw-Hill. Shurcliff, W. A. (1962). Polarized light: Production and use. Harvard University Press. Stoller, P., Reiser, K., Celliers, P., et al. (2002). Polarization-modulated second harmonic generation in collagen. Biophysical Journal, 82(6), 3330–3342. Stoller, P., Celliers, P., Reiser, K., et al. (2003). Quantitative second-harmonic generation microscopy in collagen. Applied Optics, 42(25), 5209–5219. Ströhl, F., Wong, H. H. W., Holt, C. E., et al. (2017). Total internal reflection fluorescence anisotropy imaging microscopy: Setup, calibration, and data processing for protein polymerization measurements in living cells. Methods and Applications in Fluorescence, 6(1), 014004. Strupler, M., Hernest, M., Fligny, C., et al. (2008). Second harmonic microscopy to quantify renal interstitial fibrosis and arterial remodeling. Journal of Biomedical Optics, 13(5), 054041. Sun, Y. H., et al. (2010). Fluorescence lifetime imaging microscopy for brain tumor image-guided surgery. Journal of Biomedical Optics, 15(5), 056022. Theocaris, P. S., & Gdoutos, E. E. (1979). Matrix theory of photoelasticity (Springer Series in Optical Sciences) (Vol. 11). Springer. Tuer, A. E., Krouglov, S., Prent, N., et al. (2011). Nonlinear optical properties of type I collagen fibers studied by polarization dependent second harmonic generation microscopy. The Journal of Physical Chemistry. B, 115(44), 12759–12769.

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Van Eeckhout, A., Garcia-Caurel, E., Garnatje, T., et al. (2021). Polarimetric imaging microscopy for advanced inspection of vegetal tissues. Scientific Reports, 11, 3913. Vinegoni, C., Feruglio, P. F., Gryczynski, I., et al. (2019). Fluorescence anisotropy imaging in drug discovery. Advanced Drug Delivery Reviews, 151(152), 262–288. Wang, W., Zhang, B., Wu, B., et al. (2020). Image scanning microscopy with a long depth of focus generated by an annular radially polarized beam. Optics Express, 28(26), 39288–39298. Wang, J., He, Y., Wu, Y., et al. (2021). Cytomembrane visualization using Stokes parameter confocal microscopy. Applied Optics, 60(17), 5081–5086. Weaver, R. L. (2003). Rediscovering polarized light microscopy. American Laboratory, 35, 55–61. Willets, A., Rice, J. E., & Burland, M. (1992). Problems in the comparision of theoretical and experimental hyperpolarizabilities. The Journal of Chemical Physics, 97(10), 7590–7599. Yang, Y., Xia, T., Zhang, W., et al. (2017). Single-molecule fluorescence imaging of membranebound proteins for studies of cell signal transduction. Chinese Science Bulletin, 5, 1063–1067. Yeh, A. T., Nassif, N., & Tromberg, B. J. (2002). Selective corneal imaging using combined second-harmonic generation and two-photon excited fluorescence. Optics Letters, 27(23), 2082–2084. Yildiz, A., Forkey, J. N., McKinney, S. A., et al. (2003). Myosin V walks hand-over-hand: Single fluorophore imaging with 1.5 nm localization. Science, 300, 2061–2065. Yu, Q., Wang, L. C., Di Benigno, S., et al. (2021, e1009592). Gonococcal invasion into epithelial cells depends on both cell polarity and ezrin. PLoS Pathogens, 17(12).

Chapter 3

Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic Turbid Media: Theory and Application Thi-Thu-Hien Pham, Quoc-Hung Phan, Thanh-Hai Le, and Ngoc-Bich Le

Abstract A novel approach for determining the effective optical parameters of anisotropic materials based on Stokes–Mueller matrix decomposition method is proposed. The feasibility of the proposed technique is confirmed by measuring the effective parameters of optical fiber and free-space media. The validity of the proposed approach is also confirmed by experimental measuring of the effective parameters of various types of anisotropic media including human blood plasma, collagen, and skin tissue samples. Finally, the combination of artificial intelligent classifier technique and effective parameters is proposed for skin cancer detection. Keywords Polarization · Stokes–Mueller matrix · Polarimetry

1 Introduction The techniques for extracting the optical properties of turbid media or biological material are important in developing devices for biomedical inspection and diagnostic applications (Tuchin, 1994, 2002). Much research has been performed on polarized light propagating behavior in highly scattering turbid media. It has been confirmed that the optical properties of turbid media are obtained by analyzing the response of the medium to a polarized light source (Jacques et al., 1996; Hielscher et al., 1997a; Rakovic et al., 1999; Wang et al., 2002). For example,

T.-T.-H. Pham () · N.-B. Le School of Biomedical Engineering, International University, Ho Chi Minh City, Vietnam Vietnam National University HCMC, Ho Chi Minh City, Vietnam e-mail: [email protected] Q.-H. Phan Mechanical Engineering Department, National United University, Miaoli, Taiwan T.-H. Le Department of Information Technology, FPT University, Ho Chi Minh City, Vietnam © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Mazumder et al. (eds.), Optical Polarimetric Modalities for Biomedical Research, Biological and Medical Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-031-31852-8_3

47

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linear birefringence (LB) is the difference in the refraction of linear polarized light with the orthogonal plan of polarization. LB is used for characterizing the properties of liquid crystal display (LCD) films or biological tissues. Meanwhile, circular birefringence (CB) (i.e., optical rotation angle) is the rotation of orientation of the polarization plane about the optical axis of linear polarized light. CB is commonly used for glucose concentration detection and its application in diabetes diagnosis (Huang & Knighton, 2002, 2003a, 2005; Huang et al., 2004; Wood et al., 2007, 2010; Pappada et al., 2008; Liu et al., 2002; Baba et al., 2002). Linear dichroism (LD) (i.e., linear diattenuation) is the difference between the absorption of two orthogonal, linear polarized lights. LD is used for characterizing the properties of human tissue or tumor for facilitating tumor diagnosis. Circular dichroism (CD) is defined as the difference between the absorption of right and left circularly polarized lights. CD is used for classifying or characterizing protein structures (Todorovi et al., 2004; Huang & Knighton, 2003b; Berova et al., 2000; Kelly et al., 2005; Swords & Wallace, 1993; Zsila et al., 2005). For depolarization properties, linear depolarization (LDep) and circular depolarization (CDep) are used for characterizing tumors or the surface roughness of the thin film (Ghosh et al., 2008, 2009a, b, 2010; Wood et al., 2008, 2009a, b, 2011; Wallenburg et al., 2010; Ahmad et al., 2011). Stokes vectors and Mueller matrix are presented for the state of polarization (SOP) of total or partial polarization light and the change of SOP when light incident on the media, respectively. Hielscher et al. (1997b) employed the Stokes– Mueller matrix polarimetry technique for highly scattering media to record the spatial intensity patterns of polarized light using diffuse backscattering. Cameron et al. (1998) and Rakovic et al. (1999) extracted the diffusely backscattered Mueller matrix elements of turbid media with a polarized laser beam. Kapil Dev and Anand Asundi (2012) determined the optical properties of transmissive liquid crystal (TLC) by Stokes–Mueller matrix polarimetry. The study has proved that circularly polarized light was highly degraded by depolarization within TLC. Yao and Wang (2000) applied the Monte Carlo method to simulate the propagating of polarization light in turbid media. The mentioned study above (Hielscher et al., 1997b; Cameron et al., 1998; Dev & Asundi, 2012; Yao & Wang, 2000) successfully characterizes the optical properties of highly scattering turbid media with polarized light. However, the effect of birefringence on polarization was neglected. In other to fill the gap, the Mueller matrix decomposition was developed by considering all birefringence, diattenuation, and depolarization of turbid media in both reflection and transmission configuration (Ghosh et al., 2008; Phan & Lo, 2017). Furthermore, the Mueller matrix decomposition method was able to use for extracting optical properties of samples with both multiple scattering and polarization effects (Ghosh & Vitkin, 2011). Recently, the Mueller matrix decomposition method has been widely used for inspection, detection, and characterizing properties of the biological sample and turbid media. For example, Edu et al. (2014) employed the backscattering Mueller matrix to characterize the microstructure of biological tissue. The study confirmed that various Mueller matrix elements indicated different effects con-

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

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sisting of scattering particles, birefringence, and optical activity effects. Martin et al. (2013) applied methods developed by Lu and Chipman (1996) and Ossikovski (2011) for characterizing the optical properties of pig skin. The study confirmed that the Mueller matrix elements of the sample indicated various properties such as retardance (i.e., birefringence), diattenuation (i.e., dichroism), and depolarization. Furthermore, the Mueller matrix imaging technique is comparable with conventional polarization microscopy (Ellingsen et al., 2011) or second-harmonic generation imaging (Ellingsen et al., 2014; Bancelin et al., 2014) for biomedical diagnoses such as liver fibrosis diagnosis (Dubreuil et al., 2012) or cancer detection (He et al., 2015). Although the Mueller matrix decomposition method confirmed the feasibility of analyzing the optical properties of anisotropic materials, the method required a restricted order of properties when modeling. To overcome this limitation, the differential Mueller matrix polarimetry for anisotropic media without scattering effect was proposed by Azzam (1978). Ossikovski (2011, 2012) further developed the differential Mueller matrix of Azzam with a depolarization effect. Later, Ortega-Quijano and Arce-Diego (2011a, b) extended the differential Mueller matrix for anisotropic media with backward scattering. Furthermore, a combination of differential Mueller matrix and decomposition method was proposed for extracting effective parameters of anisotropic media (Liao & Lo, 2013). A decoupled technique based on Mueller matrix decomposition method was proposed for extracting nine effective optical parameters of anisotropic material including LB, CB, LD, CD, LDep, and CDep (Lo et al., 2010; Pham & Lo, 2012a, b; Pham et al., 2011). The validity of the method was confirmed by measuring the optical properties of skin/liver cancer tissues, neuroblastoma, human blood plasma, collagen-rich tendons, and cartilage (Pham et al., 2018; Le et al., 2018, 2021). These studies demonstrated that the extracted effective parameters can be used for classifying normal skin and various skin cancer tissues, including basal cell carcinoma (BCC), squamous cell carcinoma (SCC), and malignant melanoma. Notably, the effective parameters are used as an input variable for artificial intelligence mode for human skin detection in Luu et al. (2021, 2022).

2 Stokes Vector and Mueller Matrix Formalism The Stokes vector S, which is used to describe the state of polarization (SOP) of the polarized light beam, has the form as ⎤ ⎡ ⎤ Ix + Iy S0 ⎢ S1 ⎥ ⎢ Ix − Iy ⎥ ⎥ ⎢ ⎥ .S = ⎢ ⎣ S2 ⎦ = ⎣ I45◦ − I−45◦ ⎦ ⎡

S3

IR − IL

(3.1)

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where Si , i = 0, 1, 2, and 3 are the Stokes vectors. Ix , Iy , I45◦ , and I−45◦ are the intensity of polarizer oriented at the vertical, horizon, angle of 45◦ and −45◦ . Meanwhile, IR and IL are the intensity of a quarter-wave plate and a polarizer oriented at ±45◦ concerning the fast axis of the wave plate transmits circularly polarized light. Mueller matrix is presented for the changes of SOP. The relation between Mueller matrix and Stokes vectors of any optical samples has the form as ⎤ S0 ⎢ S1 ⎥ ⎥ =⎢ ⎣ S2 ⎦ ⎡

Sout

.

S3

⎡

out

m11 ⎢ m21 = [Ms ] S = ⎢ ⎣ m31 m41

m12 m22 m32 m42

m13 m23 m33 m43

⎤⎡ ⎤ m14 S0 ⎢ S1 ⎥ m24 ⎥ ⎥⎢ ⎥ m34 ⎦ ⎣ S2 ⎦ m44

(3.2)

S3

where S and Sout are the Stokes vectors of the polarization state of the incident light and the light exiting the optical sample; [Ms ] is the Mueller matrix (with size 4 × 4) of a turbid media. Given the Stokes parameters of S0◦ , S45◦ , S90◦ , S135◦ , SR , and SL provided efficient conditions for extracting the MS in Eq. (3.2). The output Stokes vectors are determined as Eqs. (3.3 ~ 3.8): ⎡

Sout_0◦ .

m11 ⎢ m21 =⎢ ⎣ m31 m41

m12 m22 m32 m42

m13 m23 m33 m43

⎤⎡ ⎤ m14 1 ⎢1⎥ m24 ⎥ ⎥ ⎢ ⎥ ⇒ Sout_0◦ m34 ⎦ ⎣ 0 ⎦ m44

(3.3)

0

= [m11 + m12, m21 + m22, m31 + m32, m41 + m42]T ⎤⎡ ⎤ 1 m11 m12 m13 m14 ⎢ m21 m22 m23 m24 ⎥ ⎢ 0 ⎥ ⎥⎢ ⎥ =⎢ ⎣ m31 m32 m33 m34 ⎦ ⎣ 1 ⎦ ⇒ Sout_45◦ m41 m42 m43 m44 0 T  = m11 + m13 , m21 + m23 , m31 + m33 , m41 + m43

(3.4)

⎤⎡ ⎤ 1 m11 m12 m13 m14 ⎢ m21 m22 m23 m24 ⎥ ⎢ − 1 ⎥ ⎥⎢ ⎥ =⎢ ⎣ m31 m32 m33 m34 ⎦ ⎣ 0 ⎦ ⇒ Sout_90◦ m41 m42 m43 m44 0 T  = m11 − m12 , m21 − m22 , m31 − m32 , m41 − m42

(3.5)

⎡

Sout_45◦ .

⎡

Sout_90◦ .

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

⎤ ⎤⎡ 1 m11 m12 m13 m14 ⎢ m21 m22 m23 m24 ⎥ ⎢ 0 ⎥ ⎥ ⎥⎢ =⎢ ⎣ m31 m32 m33 m34 ⎦ ⎣ − 1 ⎦ ⇒ Sout_135◦ 0 m41 m42 m43 m44 T  = m11 − m13 , m21 − m23 , m31 − m33 , m41 − m43

51

⎡

Sout_135◦ .

(3.6)

⎤⎡ ⎤ 1 m11 m12 m13 m14 ⎢ m21 m22 m23 m24 ⎥ ⎢ 0 ⎥ ⎥⎢ ⎥ Sout_R = ⎢ ⎣ m31 m32 m33 m34 ⎦ ⎣ 0 ⎦ ⇒ Sout_R . m41 m42 m43 m44 1 T  = m11 + m14 , m21 + m24 , m31 + m34 , m41 + m44

(3.7)

⎤⎡ ⎤ 1 m11 m12 m13 m14 ⎢ m21 m22 m23 m24 ⎥ ⎢ 0 ⎥ ⎥⎢ ⎥ Sout_L = ⎢ ⎣ m31 m32 m33 m34 ⎦ ⎣ 0 ⎦ ⇒ Sout_L . m41 m42 m43 m44 −1 T  = m11 − m14 , m21 − m24 , m31 − m34 , m41 − m44

(3.8)

⎡

⎡

It is noted that while just three input polarization states S0◦ , S45◦ , and S90◦ and one circular state SR are sufficient to obtain Ms in Eq. (3.2), the two polarization states S135◦ and SL are used for double checking and improving the accuracy of the extracted results.

3 Decomposition Mueller Matrix for Extracting Effective Optical Parameters As shown in Fig. 3.1, the properties of an anisotropic sample are arranged in order consequence of dichroism, retardance, and depolarization such as CD/LD/CB/LB/CDep/LDep (Lu & Chipman, 1996; Morio & Goudail, 2004; Boulvert et al., 2009; Ossikovski et al., 2008; Ossikovski, 2008). According to (Khoo & Simoni, 1991), the Mueller matrix of an LB material has the form ⎡ MLB =

.

⎤

1 0 0 0 ⎢ 0 cos (4α) sin2 (β/2) + cos2 (β/2) sin (4α) sin2 (β/2) sin (2α) sin (β) ⎥ ⎦ ⎣0 sin (4α) sin2 (β/2) − cos (4α) sin2 (β/2) + cos2 (β/2) − cos (2α) sin (β) 0 − sin (2α) sin (β) cos (2α) sin (β) cos (β)

(3.9)

52

T.-T.-H. Pham et al.

CD LD CB CD CDep LDep

Sout

S He-Ne laser source

QW1

P0

P1

Sample

Stokes Polarimeter

Fig. 3.1 Experimental setup of the proposed model for characterizing an anisotropic material

where α and β are orientation angle (i.e., a slow axis principal angle) and a value of linear birefringence (i.e., a retardance), respectively. Meanwhile, the Mueller matrix of an LD material has the form

 

⎡ 1−D 1 1 cos (2θd ) 1 − 1−D 2 1 + 1+D 2 1+D ⎢



2 2 



⎢1 1−D 1 1−D 1−D ⎢ 2 cos (2θd ) 1 − 1+D 4 1 + 1+D + cos (4θd ) 1 − 1+D MLD = ⎢ ⎢

 2



⎢1 1 1−D ⎣ 2 sin (2θd ) 1 − 1−D sin 1 − (4θ ) d 1+D 4 1+D 0

0 

1 1−D 2 sin (2θd ) 1 − 1+D

2

1 1−D sin 1 − (4θ ) d 4 1+D

2 2 

1 1−D 1−D 1 + − cos 1 − (4θ ) d 4 1+D 1+D

.

0

⎤ 0 0

0 1−D 1+D

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(3.10) where θ d and D are the orientation angle and linear dichroism properties, respectively. The Mueller matrix of CB material has the form ⎡

MCB

.

1 0 0 ⎢ 0 cos (2γ ) sin (2γ ) =⎢ ⎣ 0 − sin (2γ ) cos (2γ ) 0 0 0

⎤ 0 0⎥ ⎥ 0⎦ 1

(3.11)

where γ is the optical rotation angle. The Mueller matrix of CD material has the form

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

⎤ 1 + R2 0 0 2R ⎢ 0 1 − R2 0 0 ⎥ ⎥ =⎢ 2 ⎣ 0 0 ⎦ 0 1−R 2R 0 0 1 + R2

53

⎡

MCD

.

(3.12)

where R is the circular amplitude anisotropy and is defined as (rR −rL )/(rR + rL ), in which rR and rL are the absorptions of right and left circularly polarization, respectively (Savenkov, 2007). The degree of polarization (DOP) of a Stokes vector is defined as (DeBoo et al., 2005).

DOP =

.

S12 + S22 + S32 S0

(3.13)

It is noted that DOP = 1 when the incident light is completely polarized. Depolarization is defined as the conversion of polarized light to unpolarized light. Depolarization is inextricably associated with scattering, dichroism, and retardance which vary in space, time, and/or wavelength. Depolarization was exhibited in depolarizing optical systems, which the polarized light is transformed into a partially polarized (or depolarized) one caused by the loss of spatial or temporal coherence (Lu & Chipman, 1996; Ossikovski et al., 2008; Savenkov, 2002; Ossikovski, 2009). According to Lu and Chipman (1996), one Mueller matrix can be decomposed into three components including a diattenuator, a retarder, and a purely depolarizing factor. Except for singular Mueller matrices, these factors are uniquely defined. Therefore, Mueller matrix [M] has the form of decomposition as follows: M = M MB MD

.

(3.14)

where MD is the dichroism Mueller matrix; MB is the birefringence Mueller matrix, and M is the depolarization Mueller matrix and consisted of LDep and CDep properties. The Mueller matrix of nonuniform depolarizer (DeBoo et al., 2005; Chipman, 2005) has the form ⎡

1 ⎢ p1 .M = ⎢ ⎣ p2 p3

0 e1 0 0

0 0 e2 0

⎤ 0 0⎥ ⎥ and |e1 | , |e2 | , |e3 | ≤ 1 0⎦ e3

(3.15)

T  − → where the polarizing vector . P  = p1 p2 p3 ; e1 , e2 , and e3 are the degrees of LDep, LDep, and CDep, respectively. It is noted that the depolarization factor, , which quantifies the depolarization, equals 0 for a nondepolarizer and equals 1 for an ideal depolarizer (Gil & Bernabeu, 1986). The depolarization factor, according to (DeBoo et al., 2005; Chipman, 2005), can be expressed as

54

T.-T.-H. Pham et al.

Table 3.1 The definitions of effective optical parameters of an anisotropic turbid medium with hybrid properties (Kobayashi & Asahi, 2000; Schellman & Jensen, 1987; Arteaga & Canillas, 2010) Name Orientation angle of LB Retardance (or linear birefringence) Optical rotation angle Orientation angle of LD Linear dichroism Circular dichroism Linear depolarization Circular depolarization Depolarization factor

Symbol α β γ θd DL RC e1 and e2 e3 Δ

Range 0◦ ~ 180◦ 0◦ ~ 360◦ 0◦ ~ 180◦ 0◦ ~ 180◦ 0~1 −1 ~ 1 −1 ~ 1 −1 ~ 1 0~1

Definition (*) 2π (ns – nf )l/λ0 2π (n− – n+ )l/λ0 2π (μs – μf )l/λ0 2π (μ− – μ+ )l/λ0

(*) n, μ, l, and λ0 are the refractive index, the absorption coefficient, the optical path length, and the vacuum wavelength

=1−

.

   e2   i=1−3 i 3

,0 ≤  ≤ 1

(3.16)

The detailed information on these parameters is described in Table 3.1 (Kobayashi & Asahi, 2000; Schellman & Jensen, 1987; Arteaga & Canillas, 2010). Equation (3.2) can be rewritten as ⎤ ⎡ S0 m11 ⎢ S1 ⎥ ⎢ m21 ⎥ ⎢ =⎢ ⎣ S2 ⎦ = M MLB MCB MLD MCD S = ⎣ m31 S3 out m41 ⎡

Sout

.

m12 m22 m32 m42

m13 m23 m33 m43

⎤⎡ ⎤ S0 m14 ⎥ ⎢ m24 ⎥ ⎢ S1 ⎥ ⎥ m34 ⎦ ⎣ S2 ⎦ m44 S3 (3.17)

where MΔ , MLB , MCB , MLD , and MCD are the effective Mueller matrices describing the depolarization, LB, CB, LD, and CD properties of the anisotropic turbid media, respectively. Then θ d is calculated as 2θd = tan

.

−1



Sout_45◦ (S0 ) − Sout_135◦ (S0 ) Sout_0◦ (S0 ) − Sout_90◦ (S0 )

 (3.18)

The DL is obtained as     Sout_0◦ (S0 ) −Sout_90◦ (S0 ) 2 + Sout_45◦ (S0 ) −Sout_135◦ (S0 ) 2  .DL =  2  2 Sout_0◦ (S0 ) + Sout_90◦ (S0 ) − Sout_R (S0 ) −Sout_L (S0 ) (3.19)

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

55

or DL =

.

Sout_0◦ (S0 ) − Sout_90◦ (S0 )

 2  2 cos (2θd ) Sout_0◦ (S0 ) + Sout_90◦ (S0 ) − Sout_R (S0 ) − Sout_L (S0 ) (3.20)

or DL =

.

Sout_45◦ (S0 ) − Sout_135◦ (S0 )

 2  2 sin (2θd ) Sout_0◦ (S0 ) + Sout_90◦ (S0 ) − Sout_R (S0 ) − Sout_L (S0 ) (3.21)

The RC is obtained as RC = .



2  2  Sout_0◦ (S0 ) − Sout_90◦ (S0 ) − Sout_0◦ (S0 ) + Sout_90◦ (S0 ) − Sout_R (S0 ) − Sout_L (S0 )  Sout_R (S0 ) − Sout_L (S0 )

(3.22) Consequently, the Mueller matrix of LD/CD sample is obtained as ⎤ ⎡ K11 K12 K13 K14 ⎢ K21 K22 K23 K24 ⎥ ⎥ .MD = MLD MCD = ⎢ ⎣ K31 K32 K33 K34 ⎦ K41 K42 K43 K44

(3.23)

where K11 ~ K44 elements is calculated from Eqs. (3.10), (3.12), (3.18), (3.19), and (3.22). It is noted that the elements of MD are function of θ d , DL , and RC . There is only K42 and K43 that are nonzero, the other elements of MD are zero. The Mueller matrix of LB/CB sample has the form ⎡

MB = MLB MCB

.

1 ⎢0 =⎢ ⎣0 0

0 L22 L32 L42

0 L23 L33 L43

⎤ 0 L24 ⎥ ⎥ L34 ⎦

(3.24)

L44

where L22 ~ L44 elements are functions of α, β, and γ . Then, the Mueller matrix of LB/CB properties is obtained as ⎤ ⎡ 1 1 0 0 0 ⎢ p1 e1 L22 e1 L23 e1 L24 ⎥ ⎢ w21 ⎥ ⎢ =⎢ ⎣ p2 e2 L32 e2 L33 e2 L34 ⎦ = ⎣ w31 p3 e3 L42 e3 L43 e3 L44 w41 ⎡

MB = M MLB MCB

.

0 w22 w32 w42

0 w23 w33 w43

⎤ 0 w24 ⎥ ⎥ w34 ⎦ w44 (3.25)

56

T.-T.-H. Pham et al.

where w21 ~ w44 elements are functions of α, β, γ , p1 , p2 , p3 , e1 , e2 , and e3 . From Eqs. (3.14), (3.15), (3.23), (3.24), and (3.25), the Eq. (3.2) is rewritten as MS = MBD ⎡

.

K11 K12 ⎢ w21 K11 + w22 K12 + w23 K13 + w24 K41 w21 K12 + w22 K22 + w23 K23 =⎢ ⎣ w31 K11 + w32 K12 + w33 K13 + w34 K41 w31 K12 + w32 K22 + w33 K23 w41 K11 + w42 K12 + w43 K13 + w44 K41 w41 K12 + w42 K22 + w43 K23 ⎤ K13 K14 w21 K13 + w22 K23 + w23 K33 w21 K14 + w22 K24 + w23 K34 + w24 K44 ⎥ ⎥ w31 K13 + w32 K23 + w33 K33 w31 K14 + w32 K24 + w33 K34 + w34 K44 ⎦ w41 K13 + w42 K23 + w43 K33 w41 K14 + w42 B24 + w43 K34 + w44 K44 (3.26)

Note that the elements in Mueller matrix [MS ] (i.e., the Mueller matrix product [MΔBD ]) are calculated from Eqs. (3.3) to (3.8). Once the Mueller matrix MD and MΔBD have been determined, the Mueller matrix MΔB can be derived from the inverse matrix. Based on Pham and Lo (2012a, b), there are two methods to calculate α, β, and γ of a turbid sample. The first method utilizes the known elements wij in matrix product [MΔB ] (in Eq. 3.25) to extract the LB/CB/depolarization properties. Particularly, the polarizance vector is obtained as ⎡ ⎤ ⎡ ⎤ p w − → ⎣ 1 ⎦ ⎣ 21 ⎦ .P = p2 = w31 p3 w41

(3.27)

Meanwhile, β can be calculated as  β = cos

.

−1

− (w22 w42 + w23 w43 ) (w32 w42 + w33 w43 ) (w22 w43 − w23 w42 ) (w32 w43 − w33 w42 )

 (3.28)

or β = tan−1



.

w43 cos (2α + 2γ ) w44

 (3.29)

where 2α + 2γ = tan

.

The value of α is then obtained as

−1

 w42 − w43

(3.30)

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

1 −1 tan .α = 2



− (w22 w42 + w23 w43 ) cos (β) (w22 w43 − w23 w42 )

57

 (3.31)

or 1 −1 tan 2

α=

.



cos (β) (w32 w43 − w33 w42 ) w32 w42 + w33 w43

 (3.32)

Meanwhile, the γ is obtained as 1 −1 tan .γ = 2



−A2 w22 + A1 w23 A1 w22 + A2 w23

 (3.33)

or 1 −1 tan .γ = 2



−A3 w22 + A2 w23 A2 w22 + A3 w23

 (3.34)

where A1 = cos2 (2α) + cos (β) sin2 (2α)

(3.35)

A2 = cos (2α) (1 − cos (β)) sin (2α)

(3.36)

A3 = cos2 (2α) cos (β) + sin2 (2α)

(3.37)

.

.

.

It is noted that, during the derivation, the term cos(2α + 2γ ) and cos(β) are decoupled and canceled out. Once again, in Eqs. (3.33) and (3.34), the calculated γ value is decoupled from α and β values since the equations have involved α and β terms that were canceled out in the calculating process. Besides, γ can be also derived in the other way as γ =

.

 w42 1 −1 −α − tan w43 2

(3.38)

Notably, the calculated γ value is affected (i.e., coupled with) by the values of α. For depolarization properties, the parameters e1 , e2 , and e3 are obtained as e1 =

.

where

w22 w33 w44 , e2 = , e3 = L22 L33 L44

(3.39)

58

T.-T.-H. Pham et al.

.

.

L22 = − cos (2α) [1 − cos (β)] sin (2α) sin (2γ )   + cos2 (2α) + cos (β) sin2 (2α) cos (2γ )

(3.40)

L33 = cos (2α) [1 − cos (β)] sin (2α) sin (2γ )   + cos2 (2α) cos (β) + sin2 (2α) cos (2γ )

(3.41)

L44 = cos (β)

.

(3.42)

Note that the values of e1 , e2 , and e3 are all separated from the calculated values of α, β, and γ since the terms of α, β, and γ are present in both the numerator and the denominator in Eq. (3.39), and are, therefore, canceled out. For the particular case of a turbid sample with the value of linear dichroism approximately one (i.e., D ≈ 1), K41 and K44 elements of LD/CD Mueller matrix are approximately zero. Thus, the Mueller matrix MB cannot be obtained if MD is a singular matrix. In this case, the calculated values of α, β, γ, e1 , e2 , and e3 that were obtained from Eqs. (3.28), (3.31), (3.33), (3.34), and (3.39), respectively, are unreliable. Accordingly, an alternative method (i.e., the second method) for determining the LB/CB/LDep/CDep properties of a turbid sample with a high value of linear dichroism (i.e., D ≈ 1) is proposed. Therefore, all of the elements of the product of [MB ] other than w24 , w34 , and w44 are obtained as: ⎡

K11 ⎢ K12 ⎢ ⎢K ⎢ 13 ⎢ 0 ⎢ ⎢ .⎢ 0 ⎢ ⎢ 0 ⎢ ⎢ 0 ⎢ ⎣ 0 0

K12 K22 K23 0 0 0 0 0 0

K13 K23 K33 0 0 0 0 0 0

0 0 0 K11 K12 B13 0 0 0

0 0 0 K12 K22 K23 0 0 0

0 0 0 K13 K23 K33 0 0 0

0 0 0 0 0 0 K11 K12 K13

0 0 0 0 0 0 K12 K22 K23

⎤⎡ ⎤ ⎡ ⎤ w21 m21 0 ⎢ ⎥ ⎢ ⎥ 0 ⎥ ⎥ ⎢ w22 ⎥ ⎢ m22 ⎥ ⎢ ⎢ ⎥ ⎥ 0 ⎥ ⎢ w23 ⎥ ⎢ m23 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ 0 ⎥ ⎥ ⎢ w31 ⎥ ⎢ m31 ⎥ ⎥⎢ ⎥ ⎢ ⎥ 0 ⎥ ⎢ w32 ⎥ = ⎢ m32 ⎥ ⎥⎢ ⎥ ⎢ ⎥ 0 ⎥ ⎢ w33 ⎥ ⎢ m33 ⎥ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ K13 ⎥ ⎥ ⎢ w41 ⎥ ⎢ m41 ⎥ ⎣ ⎣ ⎦ ⎦ K23 w42 m42 ⎦ K33 w43 m43

(3.43)

Once the elements in the product of [MΔB ] are known, the LB/CB/LDep/CDep properties of a turbid sample are simple to derive. For example, β is determined from Eq. (3.28), while α can be calculated using Eqs. (3.31) or (3.32) with known elements w22 , w23 , w32 , w33 , w42 , and w43 . When α and β were extracted, then γ can be calculated using Eq. (3.38). Similarly, e1 and e2 can then be obtained from Eq. (3.39). Straightaway, the e3 can be calculated as e3 =

.

w43 L43

(3.44)

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

59

where L43 = cos (2α + 2γ ) sin (β). Notably, e3 is not affected (i.e., decoupled with) by the calculated values of α, β, and γ .

4 Experimental Results and Discussion 4.1 Optical Fibers and Free-Space Media In this section, the effective parameters of optical fiber are obtained using the proposed technique. The birefringence and dichroism of fiber optics sometimes affect the accuracy of the polarization controller; thus, a compensation process is required, and trial-and-error method is used, thus increasing the time consumed for the experimental process. Accordingly, the proposed Stokes–Mueller matrix technique is employed for extracting five effective parameters of optical fiber samples in four differential configurations and free-space media construction using variable retarder (VR) and half-wave plate (HP) (Lo et al., 2010; Pham et al., 2011). Figure 3.2 shows the schematic illustration of the experimental setup for characterizing the optical fiber. For the cases of sample in optical fibers (shown in Fig. 3.2, setup 1), the experiments were conducted out employing a singlemode optical fiber with a length of 47 cm. The measurement system consists of a polarizer for generating the six input polarization lights, a neutral density filter with a power detector to guarantee the uniform intensity of input light, a fiber coupler (630 HP), and a commercial Stokes parameter. The extracted values of five effective parameters of 100 data points per configuration were shown in Table 3.1. For free-space media (shown in Fig. 3.2, setup 2), the sample was constructed with a variable retarder that compensates for the LB property and a half-wave plate that compensates for the CB property. The Mueller matrix of the free-space sample has the form Mf = [MLD ] [MLB ] [MCB ] [MHP ] [MVR ] = [MFiber ] [MHP ] [MVR ]

.

(3.45)

where [MFiber ]=[MLD ][MLB ][MCB ]. Since [MLD ] ≈ [1], and thus, [MHP ] ≈ [MCB ]−1 and [MVR ] ≈ [MLB ]−1 . [MHP ] and [MVR ] are the Mueller matrix of the HP and VR, respectively. In this study, the genetic algorithm (GA) method was applied for calculating the optimal values of HP and VR (i.e., α V , β V , and γ H ). The GA is a natural selection-based approach for resolving both constrained and unconstrained optimization problems (Lo et al., 2010; Pham et al., 2011). When performing the GA technique, the candidate solution strings are the orientation angle of the VR (α V ), the retardance of the VR (β V ), and the optical rotation of the HP (γ H ). The fitness function of the GA has the form 16

2  φi,[MFiber ]−1 − φi,[MHP ][MVR ] .Eφ = i=1

(3.46)

60

T.-T.-H. Pham et al.

Fig. 3.2 Schematic illustration of Stokes–Mueller matrix measurement of fiber optics

where .φi,[MFiber ]−1 is the element of the inverse of Mueller matrix of the optical fiber and .φi,[MHP ][MVR ] is the corresponding element of [MHP ][MVR ]. For the polarization controller, the validity of the GA optimization procedure was confirmed experimentally. When performing experiments, a series of linearly polarized lights orientated to the horizontal plane from 0◦ to 180◦ (increasing to 15◦ for each measurement), right- and left-hand circular polarization lights, and elliptical polarization lights were generated. The results are shown in Table 3.2 that the average error between the GA and experimental results of α V , β V , and γ H are 6%, 0.1%, and 7%, respectively. Furthermore, the proposed method is employed for extracting the effective parameters a quarter-wave plate (LB sample) and a polarizer (LD sample) (Pham et al., 2011). The optimal values are obtained by the GA technique. When performing the experiments, the samples were set as the slow axes oriented from 0◦ to 180◦

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

61

Table 3.2 Comparison between GA and experimental results for α V , β V , and γ H values that warranted to obtain free-space condition in Fig. 3.2 Free-space sample Configuration no./fiber effective parameters #1 α = 126.27◦ β = 19.69◦ γ = −22.71◦

#2

α = 112.82◦ β = 24.02◦ γ = −22.28◦

#3

α = 114.81◦ β = 25.67◦ γ = −23.55◦

#4

α = 122.24◦ β = 132.07◦ γ = −62.04◦

(a)

630 HP optical α = 126.27◦ β = 19.69◦ θ d = 8.25◦ D = 0.06 γ = −22.71◦ α = 112.82◦ β = 24.02◦ θ d = 55.41◦ D = 0.07 γ = −22.28◦ α = 114.81◦ β = 25.67◦ θ d = 109.5◦ D = 0.07 γ = −23.55◦ α = 122.24◦ β = 132.07◦ θ d = 46.03◦ D = 0.1 γ = −62.04◦

GA α V = 13.56◦ β V = 19.69◦ γ H /2 = 11.6◦

Experiment α V = 12.5◦ β V = 19.7◦ γ H /2 = 13◦

Error α V : −1.06◦ β V : 0.01◦ γ H /2: 1.4◦

α V = 0.54◦ β V = 24.03◦ γ H /2 = 11.13◦

α V = 0.5◦ β V = 24◦ γ H /2 = 12◦

α V : −0.04◦ β V: −0.03◦ γ H /2: 0.87◦

α V = 1.26◦ β V = 25.67◦ γ H /2 = 11.75◦

α V = 1◦ β V = 25.7◦ γ H /2 = 11◦

α V: −0.26◦ β V: 0.03◦ γ H /2: −0.75

α V = 150.2◦ β V = 132.07◦ γ H /2 = 31.02◦

α V = 151◦ β V = 132◦ γ H /2 = 32◦

α V: 0.8◦ β V : −0.07◦ γ H /2: −0.02◦

(b)

Fig. 3.3 Experimental results for (a) linear birefringence (LB) of quarter-wave plate and (b) linear dichroism (LD) of polarizer obtained utilizing variable retarder and half-wave plate (α s1 , β s1 , θ s1 , and Ds1 ) and two quarter-wave plate and a half-wave plate (α s2 , β s2 , θ s2 , and Ds2 ) as a polarization controller. (Pham et al., 2011)

(increasing to 35◦ for each measurement). The measured values of LB and LD properties were shown in Fig. 3.3.

62

T.-T.-H. Pham et al.

Fig. 3.4 Measured effective parameters of a baked polarizer. (Pham & Lo, 2012b)

Fig. 3.5 Measured effective parameters of depolarizer. (Lo et al., 2010)

4.2 Baked Polarizer (LB and LD Properties) The proposed technique was used for extracting the effective parameter of a polymer polarizer baked at 150 ◦ C for 100 min in an oven (Pham & Lo, 2012b). Figure 3.4 presents the measured values of the effective parameters of the baked polarizer. As shown, the measured values of γ , R, and Δ of the baked polarizer are approximately zero (see Fig. 3.4c, d, e). Meanwhile, the mean value of D is found to be 0.974 (see Fig. 3.4b). The mean value of β is determined to be 16.92◦ (see Fig. 3.4a). The results showed a strong agreement between two set of results obtained for LD/LB parameters.

4.3 Depolarizer (LDep and CDep Properties) Figure 3.5 shows the experimental results of effective parameters of the depolarizer. As shown in Fig. 3.5e, the measured depolarization values are in the range from 0 to 1 over the considered range. The measured  values are in range of 0.2–0.6 (see Fig. 3.5f). The higher value of the depolarization factor was obtained when the azimuth angle was close to 75◦ and 30◦ . Otherwise, the values of the depolarization index were approximate 0.2. The measured phase retardance (see Fig. 3.5a) and LD (see Fig. 3.5b) vary randomly over the considered range. The linear dichroism (see Fig. 3.5b), the optical rotation angle (see Fig. 3.5c), and the circular dichroism (see Fig. 3.5d) are close to zero. Especially, the measured values of LB (see Fig. 3.5a) vary linearly with the azimuth angle over the considered range of 0–90◦ .

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

63

Table 3.3 Measured effective parameters of composite samples 30°

Degree QuarterParameters

wave plate

Depolarizer

45° Quarter-wave plate

Quarter-

+ Depolarizer

wave plate

Quarter-wave Depolarizer

plate + Depolarizer

α

29.77°

29.8°

30.34°

44.97°

45.31°

44.98°

β

90.39°

126.17°

36.4° (≈216.4°)

89.98°

46.06°

136.05°

θd

2.9°

40.65°

108.14°

32.09°

127.37°

15.95°

D

0.03

0.05

0.06

0.01

0.02

0.02

γ

0.11°

0.7°

0.72°

0.03°

0.64°

0.23°

R

0.01

0.001

0.02

0.002

0.01

0.01

e1

1

0.602

0.605

0.998

0.815

0.816

e2

1

0.167

0.169

1

0.998

1.000

e3

1

0.128

0.127

1

0.819

0.817

∆

0

0.632

0.630

0

0.119

0.118

4.4 Quarter-Wave Plate and Depolarizer (LB, LDep, and CDep Properties) The results of effective parameters of the composite sample with two principal axes of 30◦ and 45◦ are shown in Table 3.3 (Pham & Lo, 2012b). As shown, the measured α are close to 30◦ and 45◦ for all samples corresponding to the two principal axes, and the average error is about 0.1%. The LB values of the quarter-wave plate, depolarizer, and composite sample exist a good agreement. The values of e1 , e2 , and e3 are equal to 1 for quarter-wave plate and less than 0 for the other two samples in all cases. The value of  is equal to 0 for the quarter-wave plate in both cases. However,  is equal to 0.6 and 0.1 for depolarizer and for quarter-wave plate + depolarizer with the principal axis of 30◦ and 45◦ , respectively.

4.5 Dissolved Glucose Aqueous Solution (CB, LDep, and CDep Properties) In this section, the effective parameters of the glucose aqueous solution with different particles were extracted. The sample were prepared by dissolving Dglucose power into deionized (DI) water, with an additional 5 μm diameter polystyrene beads, and 9 μm diameter of polystyrene beads (Pham & Lo, 2012b). The concentration and density of polystyrene bead suspensions were 0.32% and 1.05 g/cm3 , respectively, for every case. As shown in Figs. 3.6 and 3.7, the measured value of the optical rotation angle and depolarization increase linearly with concentration of D-glucose ranging from 0 to 1 M. Whereas the measured

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Fig. 3.6 Measured effective parameters of glucose aqueous solution with 5 μm polystyrene microsphere suspension. (Pham & Lo, 2012b)

Fig. 3.7 Measured effective parameters of glucose aqueous solution with 9 μm polystyrene microsphere suspension. (Pham & Lo, 2012b)

values of the depolarization factor decrease linearly with concentration of D-glucose ranging from 0 to 1 M. The values of linear dichroism were about 0–15◦ since Dglucose is a chiral molecule, while circular dichroism of the D-glucose sample was small and close to zero. The other extracted values varied randomly as the D-glucose concentration increased.

4.6 Healthy and Nonmelanoma-Induced Mouse Skin Tissue Sample Skin cancer is the abnormal growth of skin cells developed commonly on skin exposed to the sun. Generally, melanoma, basal cell carcinoma, and squamous cell carcinoma are three primary types of skin cancer. Melanoma is detected easily by observation; however, nonmelanoma type is not able to detect in the early stages by observation because without signs and symptoms. In this section, the proposed Mueller matrix decomposition technique is performed for detecting skin cancer in its early stages using the extracted effective parameters (Le et al., 2018). The nonmelanoma-induced mice skin tissue samples were prepared with a thickness of 5 μm and embedded on quartz slides. The histopathological images of the sample are shown in Fig. 3.8. The measured values of effective properties of samples are presented in Fig. 3.9. As shown, the parameters of LB and CD are uniform and similar. The value of α and β are all close to 82◦ and 135◦ , respectively (see Fig. 3.9a). The measured value of D is nearly 0.06 (see Fig. 3.9b), whereas the measured value of RS is small and close to 0 (see Fig. 3.9d). All the measured value of e1 , e2, and e3 are approximately 0.99, 0.96, and 1, respectively (see Fig. 3.9e). However, depolarization indices vary slightly from 0.20 to 0.28. Furthermore, most of the

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Fig. 3.8 Histopathological results of nonmelanoma-induced mice (a) sample 1, (b) sample 2, (c) sample 3, and (d) sample 4. (Le et al., 2018)

Fig. 3.9 Measured effective parameters of (a) LB (α & β), (b) LD (θ and D), (c) CB (γ ), (d) CD (R), (e) (e1 , e2 , and e3 ), and (f)  of mice skin tissue. (Le et al., 2018)

Fig. 3.10 Measured effective parameters: (a) LB-α, (b) LB-β, (c) CB-γ , (d) LD-R, and (e)  of normal and squamous cell skin cancer in mice. (Le et al., 2018)

subjects showed properties of θ at almost 20◦ (see Fig. 3.9b), and the measured value of γ varied from 0.025◦ to 0.08◦ (see Fig. 3.9). The measured effective parameters of the control samples and melanoma skin cancer are shown in Fig. 3.10. As shown, the measured values of LB, CB, and LD of squamous cell skin cancer are remarkably lower than in normal skin samples (see Fig. 3.10a, b, c, d). While the measured value of the depolarization factor of squamous cell skin cancer is higher than in normal skin samples (see Fig. 3.10e). However, its values are small and close to 0. It explained that both samples have a low concentration of fiber and low scattering effects. The detailed values of effective parameters were shown in Table 3.4. As shown, the measured value of γ of normal samples fluctuates around 0.88◦ with a standard deviation of 0.53. While the measured value of γ of cancerous samples is close to 0.05◦ with a standard deviation of 0.02. The D value of control samples is approximate 0.13◦ with a standard deviation of 0.006, whereas those of cancer mice oscillate around 0.06◦ with a deviation of 0.003. The measured value of depolarization factor in 12 samples of cancer mice fluctuates around 0.015 with a deviation of 0.02, while normal skin tissues have mean values of  around 0.011 with a deviation of 0.03.

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Table 3.4 Measured effective parameters of normal and squamous cell skin cancer in mice Squamous cell mouse skin cancer Control mouse

a SD:

Mean

β γ θd D α 82.56 0.90 0.05 18.69 0.06

R −0.006

e1 0.99

e2 0.96

e3  1 0.015

0.43 0.03 0.02 0.63 0.003 0.0004 0.003 0.005 0 0.02 SDa Mean 145.7 1.26 0.88 60.24 0.13 −0.014 0.99 −0.98 1 0.011 29.0 0.04 0.53 5.87 0.006 0.13 0.009 0.01 0 0.03 SDa

Standard deviation

Fig. 3.11 Measured effective parameters of blood plasma samples containing dissolved Dglucose. (Pham et al., 2018)

4.7 Human Blood Plasma The effective parameters of blood plasma samples with different D-glucose concentrations over the range of 0–1 M increasing of 0.1 mol/L are shown in Fig. 3.11. It is noted that the results were obtained from five repeated tests at 4 ~ 5 measurement points for each sample. As shown in Fig. 3.11a, b, the values of α and β have a large deviation caused by the small extraction values of LB/LD (β ≤ 3◦ and D ≤ 0.05). It is noted that when the small value of β = D = 0◦ , the LB/LD Mueller matrices are unit matrices with any value of the orientation angle in its range (0◦ ~ 180◦ ). As shown in Fig. 3.11a, the measured values of β increase slightly from 0◦ to 2◦ as the D-glucose concentration increase from 0 to 1 M. Furthermore, the measured values of α and θ d vary randomly to the glucose concentration. As shown in Fig. 3.11c, the measured γ values increase linearly with the increment of D-glucose concentration. The remaining are essentially insensitive to the D-glucose concentration. More experiments were performed to evaluate the sensitivity of optical rotation angle (γ ) with glucose concentration. The measurement of γ values of glucose sample in blood plasma and the phantom solution is demonstrated over the concentration range of 0–1 mol/L. The result is shown in Fig. 3.12. As shown, the γ values vary linearly to the glucose concentration with coefficient R2 equal to 0.9782 and 0.9939 for the phantom solution and blood plasma, respectively. The rate of increase of γ for the blood plasma samples and phantom samples are 1.07◦ and 0.75◦ per 1 M D-glucose, respectively. It means the sensitivity of the detection of glucose in blood plasma samples is higher. The sensitivity of detection of the phantom solution is lower caused by the scattering of particles without the solution.

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Fig. 3.12 Measured γ values of D-glucose samples. (Pham et al., 2018)

Fig. 3.13 Measured effective parameters of collagen solutions. (Pham et al., 2018)

4.8 Collagen Solution The measured effective parameters of collagen solution are shown in Fig. 3.13. The 0.1 M acetic acid collagen solution samples were prepared with concentrations ranging from 0 ~ 2 mg/mL. As shown, only measured values of α varied linearly to the increment of collagen concentration. In other words, only β is sensitive to the collagen concentration and can be used to detect the changing concentration of collagen. The β values fall in the range of 20–50◦ over the considered range of collagen concentration of 0 ~ 2 mg/mL. The other parameters are insensitive to the collagen concentration. Furthermore, as shown in Fig. 3.13d, the CD parameters are small and close to 0 in the considered range of collagen concentration. Thus, it is confirmed that collagen does not have CD properties. As shown in Fig. 3.13f, the  value represents the average depolarization behavior of the medium and remains roughly constant as collagen concentration increases. In order to evaluate the sensitivity of the LB value to the concentration of collagen, more experiments are performed, and the results are shown in Fig. 3.14. As shown, the β values increase linearly with the increase of collagen concentration with coefficient R2 = 0.9936. The sensitivity is calculated as S = δβ/δC = 0.33 ◦ /(mg/dL), where δβ and δC are the changes of β and collagen concentration. The practicability of the proposed technique for collagen detection is further verified by measuring the β values of calfskin samples treated with and without collagenase. The calfskin samples were prepared in 0.7 × 0.7 cm2 , 10-μm thickness, in collagen solution with concentrations of 2 mg/mL, 1 mg/mL, 0.5 mg/mL, 0.25 mg/mL, and 0.125 mg/mL. As shown in Fig. 3.15, the measured values of β of noncollagenase treatment samples are approximately 0.44◦ to 0.46◦ . After

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Fig. 3.14 Measured values of linear birefringence (LB) property of collagen solution. (Pham et al., 2018)

Fig. 3.15 Measured values of phase retardance (β) of calfskin samples before and after collagenase treatment. (Pham et al., 2018)

treatment, the measured values of β dropped to approximately 0.21◦ (square symbols). It is also observed that the values of β are reduced with the collagenase treatment (circular symbols). Furthermore, the treatment time also affected the values of β. From the beginning, the values of β were slightly reduced with the time treatment less than 1 h, but quickly decreased in the time treatment of 2 h, and then continued to decrease to 0.14◦ after 4 h of treatment. The measured values of β and time treatment correlated exponentially with a coefficient of r2 = 0.9689. The standard deviation of β for four repeated tests is 0.06◦ .

4.9 Healthy and Cancerous Human Skin Tissue The nonmelanoma skin cancer samples include 12 squamous cell carcinoma (SCC), 12 basal cell carcinoma (BCC), and 3 melanoma skin cancer (MSC) samples. The sample was prepared with 5 μm thickness and placed on quartz slides. The histopathological analysis of three cancerous human skin tissue samples are shown in Fig. 3.16. The measured effective parameters of SCC, BCC, and MSC samples are shown in Figs. 3.17, 3.18, and 3.19, respectively. For SCC samples, as shown in Fig. 3.17a, the measured value of α and β are approximate of 3◦ and 0.35◦ , respectively, for every sample. As shown in Fig. 3.17b, the measured values of θ d and D are 124.49◦ and 0.08, respectively, for every sample, while the measured

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Fig. 3.16 The histopathological image of (a) squamous cell carcinoma, (b) basal cell carcinoma, and (c) melanoma skin cancer samples. (Le et al., 2021)

Fig. 3.17 Effective parameters of SCC samples: (a) α, (b) θ d and D, (c) γ , (d) R, (e) e1 , e2 , e3 , and (f) . (Le et al., 2021)

Fig. 3.18 Effective parameters of basal cell carcinoma (BCC) samples: (a) α, (b) θ d and D, (c) γ , (d) R, (e) e1 , e2 , e3 , and (f) . (Le et al., 2021)

values of γ and R are 0.054◦ and −0.022, respectively (see Fig. 3.17c, d). The measured values of e1 and e2 are close to 9.6 × 10−6 , while the measured values of e3 vary in the range of 2.9 × 10−6 to 4.8 × 10−6 (see Fig. 3.17e). Finally, the measured values of  are approximate to 1. I confirmed that the SCC induces a small scattering effect. For BCC samples, as shown in Fig. 3.18a, the measured value of α and β are approximate 7◦ and 0.55◦ , respectively, for every sample. As shown in Fig. 3.18b, the measured values of θ d and D are 125.31◦ and 0.05, respectively, for every sample. While the measured values of γ and R are 0.054◦ and −0.023, respectively (see Fig. 3.18c, d), the measured values of e1 , e2 , and e3 are approximately 2.1 × 10−6 , 3.4 × 10–6, and 1.6 × 10−5 , respectively, (see Fig. 3.17e). Finally, the measured values of  are approximate 0.999. For MSC samples, as shown in Fig. 3.19a, the measured value of α and β are approximate 6◦ and 0.45◦ , respectively, for every sample. As shown in Fig. 3.19b, the measured values of θ d and D are 115.31◦ and 0.17, respectively, for every sample. While the measured values of γ varies in the range of 0.1 to 0.5 (see Fig. 3.19c), the measured values of R are small and close to 0 (see Fig. 3.18d). The measured values of e1 and e1 are small and close to 0, while the values of e3 are approximate of 2 × 10−5 (see Fig. 3.17e). Finally, the measured values of  are approximate to 0.999. Figure 3.20 shows the comparison of measured values of β and D of the normal and squamous cell carcinoma samples. As shown in Fig. 3.20a, the measured β values of SCC samples are approximately 0.35◦ , which is much smaller than that obtained for normal samples of 1.4◦ . In other words, the β values of SCC are 75%

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Fig. 3.19 Effective parameters of melanoma skin cancer (MSC) samples: (a) α, (b) θ d and D, (c) γ , (d) R, (e) e1 , e2 , e3 , and (f) . (Le et al., 2021)

Fig. 3.20 Comparison of effective parameters of (a) β of squamous cell carcinoma (SCC) samples, (b) D of SCC samples, (c) β of basal cell carcinoma (BCC) samples, (d) D of BCC samples, (e) β of MSC samples, and (f) D of MSC samples. (Le et al., 2021)

lower than normal samples. As shown in Fig. 3.20b, the measured values of D of SCC samples are approximate 0.08, which is 27% smaller than that obtained for normal samples of 0.1. Similarly, in Fig. 3.20c, the measured values β of BCC samples (0.55◦ ) is around 62% lower than that obtained for normal samples (1.43◦ ). Meanwhile, the measured values of D (0.05) are around 58% lower than D value of the control samples (0.11) (Fig. 3.20d). As shown in Fig. 3.20e, the measured values β of BCC samples (0.44◦ ) are around 70% lower than that of obtained for normal samples (1.43◦ ). Meanwhile, the measured values of D (0.07) are around 42% lower than that of the control samples (0.12) (see Fig. 3.20f). It is confirmed that LB properties can be used for the detection of skin cancer in its early stages.

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Fig. 3.21 AI classifiers training results. (Luu et al., 2022)

4.10 Combination of Effective Parameters and Artificial Intelligent Classification Models for Human Skin Detection AI-based classification has become common nowadays for biomedical detection applications. In this section, the combination of proposed extracted effective parameters and artificial intelligence (AI) classification for human skin detection is discussed. The effective parameters are used as the input variables for the AI classification models (Luu et al., 2022). A total of 198 values of optical parameters of SCC, BCC, and MSC were inserted into a total of nine machine learning classifiers (decision tree (DT), extremely randomized trees (ExtraTree), k-nearest neighbors (k-NN), multilayer perceptron (MLP), random forest (RF), radius neighbors (RN), ridge, support vector machine (SVM), and extreme gradient boosting (XGBoost)). Primary results show that all the classification models other than RN and Ridge obtain an accuracy of 100% in training. Moreover, the ExtraTree, k-NN, and MLP classifiers also achieve a testing performance of 100% in Precision, Recall, and F1 Score (Luu et al., 2022) (Fig. 3.21).

5 Conclusion This chapter reviews the method for determining effective optical parameters of anisotropic turbid media using decomposition Mueller matrix polarimetry. The validity of the method was performed by measuring the effective parameters of optical fibers and free-space material with a different configuration. The validity of the proposed approach is performed by measuring effective parameters of glucose

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solution, blood plasma, and different skin tissue samples. It is confirmed that the optical rotation angle of CB properties varies linearly with the concentration of glucose; thus, it provides a potential tool for glucose detection application. While the phase retardance of LB is useful for collagen concentration detection. Furthermore, the phase retardance and LD properties are useful for distinguishing the skin cancer samples. Notably, the effective parameters are used as input data for AI classification mode for human skin detection. In general, the nine effective parameters of anisotropic turbid media provide much useful information for characterizing and detecting biological materials and their application in biomedical applications. Acknowledgments This chapter is completed as a special thanks to my respected advisor, Prof. Lo Yu Lung, who inspired me an interest in polarization measurement, and to the financial support from International University, Vietnam National University Ho Chi Minh City. Disclosures The authors declare no conflicts of interest.

References Ahmad, M., et al. (2011). Do different turbid media with matched bulk optical properties also exhibit similar polarization properties? Biomedical Optics Express, 2(12), 3248–3258. Arteaga, O., & Canillas, A. (2010). Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media. Optics Letters, 35(4), 559–561. Azzam, R. M. A. (1978). Propagation of partially polarized light through anisotropic media with or without depolarization: A differential 4 × 4 matrix calculus. Journal of the Optical Society of America, 68(12), 1756–1767. Baba, J. S., et al. (2002). Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye. Journal of Biomedical Optics, 7(3), 321–328. Bancelin, S., et al. (2014). Determination of collagen fiber orientation in histological slides using Mueller microscopy and validation by second harmonic generation imaging. Optics Express, 22(19), 22561–22574. Berova, N., Nakanishi, K., & Woody, R. W. (2000). Circular dichroism: Principles and applications. Wiley-VCH. Boulvert, F., et al. (2009). Decomposition algorithm of an experimental Mueller matrix. Optics Communication, 282(5), 692–704. Cameron, B. D., et al. (1998). Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium. Optics Letters, 23(7), 485–487. Chipman, R. A. (2005). Depolarization index and the average degree of polarization. Applied Optics, 44(13), 2490–2495. DeBoo, B. J., Sasian, J. M., & Chipman, R. A. (2005). Depolarization of diffusely reflecting manmade objects. Applied Optics, 44(26), 5434–5445. Dev, K., & Asundi, A. (2012). Mueller Stokes polarimetric characterization of transmissive liquid crustal spatial light modulator. Optics and Lasers in Engineering, 50(4), 599–607. Du, E., et al. (2014). Characteristic features of mueller matrix patterns for polarization scattering model of biological tissues. Journal of Innovative Optical Health Sciences, 07(01), 1350028. Dubreuil, M., et al. (2012). Mueller matrix polarimetry for improved liver fibrosis diagnosis. Optics Letters, 37(6), 1061–1063. Ellingsen, P., et al. (2011). Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy. Journal of Biomedical Optics, 16(11), 116002.

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

73

Ellingsen, P., et al. (2014). Mueller matrix three-dimensional directional imaging of collagen fibers. Journal of Biomedical Optics, 19(2), 026002. Ghosh, N., & Vitkin, I. A. (2011). Tissue polarimetry: Concepts, challenges, applications, and outlook. Journal of Biomedical Optics, 16(11), 110801. Ghosh, N., Wood, M. F. G., & Vitkin, I. A. (2008). Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence. Journal of Biomedical Optics, 13(4), 044036–044014. Ghosh, N., et al. (2009a). Mueller matrix decomposition for polarized light assessment of biological tissues. Journal of Biophotonics, 2(3), 145–156. Ghosh, N., Wood, M. F. G., & Vitkin, I. A. (2009b). Polarimetry in turbid, birefringent, optically active media: A Monte Carlo study of Mueller matrix decomposition in the backscattering geometry. Journal of Applied Physics, 105(10), 102023–102028. Ghosh, N., et al. (2010). Mueller matrix polarimetry for the characterization of complex random medium like biological tissues. Pramana, 75(6), 1071–1086. Gil, J. J., & Bernabeu, E. (1986). Depolarization and polarization indices of an optical system. Optica Acta: International Journal of Optics, 33(2), 185–189. He, C., et al. (2015). Characterizing microstructures of cancerous tissues using multispectral transformed Mueller matrix polarization parameters. Biomedical Optics Express, 6(8), 2934– 2945. Hielscher, A. H., Mourant, J. R., & Bigio, I. J. (1997a). Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions. Applied Optics, 36(1), 125–135. Hielscher, A., et al. (1997b). Diffuse backscattering Mueller matrices of highly scattering media. Optics Express, 1(13), 441–453. Huang, X.-R., & Knighton, R. W. (2002). Linear birefringence of the retinal nerve fiber layer measured in vitro with a multispectral imaging micropolarimeter. Journal of Biomedical Optics, 7(2), 199–204. Huang, X.-R., & Knighton, R. W. (2003a). Theoretical model of the polarization properties of the retinal nerve fiber layer in reflection. Applied Optics, 42(28), 5726–5736. Huang, X.-R., & Knighton, R. W. (2003b). Diattenuation and polarization preservation of retinal nerve fiber layer reflectance. Applied Optics, 42(28), 5737–5743. Huang, X.-R., & Knighton, R. W. (2005). Microtubules contribute to the birefringence of the retinal nerve fiber layer. Investigative Ophthalmology & Visual Science, 46(12), 4588–4593. Huang, X.-R., et al. (2004). Variation of peripapillary retinal nerve fiber layer birefringence in normal human subjects. Investigative Ophthalmology & Visual Science, 45(9), 3073–3080. Jacques, S. L., et al. (1996). Polarized light transmission through skin using video reflectometry: Toward optical tomography of superficial tissue layers. In Lasers in surgery: Advanced characterization, therapeutics, and systems VI. SPIE. Kelly, S. M., Jess, T. J., & Price, N. C. (2005). How to study proteins by circular dichroism. Biochimica et Biophysica Acta (BBA) – Proteins & Proteomics, 1751(2), 119–139. Khoo, I. C., & Simoni, F. (1991). Physics of liquid crystalline materials (Vol. Chapter 13). Gorden and Breach Science Publishers. Kobayashi, J., & Asahi, T. (2000). Development of HAUP and its applications to various kinds of solids. In Proceedings of the SPIE. SPIE. Le, D. L., et al. (2018). Characterization of healthy and nonmelanoma-induced mouse utilizing the Stokes–Mueller decomposition. Journal of Biomedical Optics, 23(12), 125003. Le, D. L., et al. (2021). Characterization of healthy and cancerous human skin tissue utilizing Stokes–Mueller polarimetry technique. Optics Communication, 480, 126460. Liao, C. C., & Lo, Y. L. (2013). Extraction of anisotropic parameters of turbid media using hybrid model comprising differential- and decomposition-based Mueller matrices. Optics Express, 21(14), 16831–16853. Liu, G. L., Li, Y., & Cameron, B. D. (2002). Polarization-based optical imaging and processing techniques with application to the cancer diagnostics. In Proceedings of the SPIE. SPIE.

74

T.-T.-H. Pham et al.

Lo, Y. L., Pham, T. T. H., & Chen, P. C. (2010). Characterization on five effective parameters of anisotropic optical material using Stokes parameters-demonstration by a fiber-type polarimeter. Optics Express, 18(9), 9133–9150. Lu, S.-Y., & Chipman, R. A. (1996). Interpretation of Mueller matrices based on polar decomposition. Journal of the Optical Society of America. A, 13(5), 1106–1113. Luu, N. T., et al. (2021). Characterization of Mueller matrix elements for classifying human skin cancer utilizing random forest algorithm. Journal of Biomedical Optics, 26(7), 075001. Luu, T. N., et al. (2022). Classification of human skin cancer using Stokes-Mueller decomposition method and artificial intelligence models. Optik, 249, 168239. Martin, L., Le Brun, G., & Le Jeune, B. (2013). Mueller matrix decomposition for biological tissue analysis. Optics Communication, 293, 4–9. Morio, J., & Goudail, F. (2004). Influence of the order of diattenuator, retarder, and polarizer inpolar decomposition of Mueller matrices. Optics Letters, 29(19), 2234–2236. Ortega-Quijano, N., & Arce-Diego, J. L. (2011a). Mueller matrix differential decomposition. Optics Letters, 36(10), 1942–1944. Ortega-Quijano, N., & Arce-Diego, J. L. (2011b). Mueller matrix differential decomposition for direction reversal: Application to samples measured in reflection and backscattering. Optics Express, 19(15), 14348–14353. Ossikovski, R. (2008). Interpretation of nondepolarizing Mueller matrices based on singular-value decomposition. Journal of the Optical Society of America. A, 25(2), 473–482. Ossikovski, R. (2009). Analysis of depolarizing Mueller matrices through a symmetric decomposition. Journal of the Optical Society of America. A, 26(5), 1109–1118. Ossikovski, R. (2011). Differential matrix formalism for depolarizing anisotropic media. Optics Letters, 36(12), 2330–2332. Ossikovski, R. (2012). Differential and product Mueller matrix decompositions: A formal comparison. Optics Letters, 37(2), 220–222. Ossikovski, R., et al. (2008). Depolarizing Mueller matrices: How to decompose them? Physica Status Solidi A: Applications and Materials Science, 205(4), 720–727. Pappada, S. M., Cameron, B. D., & Rosman, P. M. (2008). Development of a neural network for prediction of glucose concentration in type 1 diabetes patients. Journal of Diabetes Science and Technology, 2, 792–801. Pham, T. T. H., & Lo, Y. L. (2012a). Extraction of effective parameters of anisotropic optical materials using a decoupled analytical method. Journal of Biomedical Optics, 17(2), 025006. Pham, T. T. H., & Lo, Y. L. (2012b). Extraction of effective parameters of turbid media utilizing the Mueller matrix approach: Study of glucose sensing. Journal of Biomedical Optics, 17(9), 097002. Pham, T. T. H., Lo, Y. L., & Chen, P. C. (2011). Design of polarization-insensitive optical fiber probe based on effective optical parameters. Journal of Lightwave Technology, 29(8), 1127– 1135. Pham, H. T. T., et al. (2018). Optical parameters of human blood plasma, collagen, and calfskin based on the Stokes-Mueller technique. Applied Optics, 57(16), 4353–4359. Phan, Q.-H., & Lo, Y.-L. (2017). Stokes–Mueller matrix polarimetry technique for circular dichroism/birefringence sensing with scattering effects. Journal of Biomedical Optics, 22(4), 047002. Rakovic, M. J., et al. (1999). Light backscattering polarization patterns from turbid media: Theory and experiment. Applied Optics, 38(15), 3399–3408. Savenkov, S. N. (2002). Mueller-matrix description of depolarization in elastic light scattering. In Polarization analysis and measurement IV. SPIE. Savenkov, S. (2007). Invariance of anisotropy properties presentation in scope of polarization equivalence theorems. Proceedings of SPIE, 6536(1), 65360G. Schellman, J., & Jensen, H. P. (1987). Optical spectroscopy of oriented molecules. Chemical Reviews, 87(6), 1359–1399.

3 Stokes–Mueller Matrix Polarimetry: Effective Parameters of Anisotropic. . .

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Swords, N. A., & Wallace, B. A. (1993). Circular-dichroism analyses of membrane proteins: Examination of environmental effects on bacteriorhodopsin spectra. The Biochemical Journal, 289(1), 215–219. Todorovi, M., et al. (2004). Determination of local polarization properties of biologicalsamples in the presence of diattenuation by use of Muelleroptical coherence tomography. Optics Letters, 29(20), 2402–2404. Tuchin, V. V. (1994). Selected papers on tissue optics: Applications in medical diagnostics and therapy (Vol. MS102, p. 700). SPIE Optical Engineering Press. Tuchin, V. V. (2002). Handbook of optical biomedical diagnostics (Vol. PM107). SPIE Optical Engineering Press. Wallenburg, M. A., et al. (2010). Polarimetry-based method to extract geometry-independent metrics of tissue anisotropy. Optics Letters, 35(15), 2570–2572. Wang, X., Yao, G., & Wang, L. V. (2002). Monte Carlo model and single-scattering approximation of the propagation of polarized light in turbid media containing glucose. Applied Optics, 41(4), 792–801. Wood, M. F. G., Guo, X., & Vitkin, I. A. (2007). Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology. Journal of Biomedical Optics, 12(1), 014029–014010. Wood, M. F. G., et al. (2008). Phantoms for polarized light exhibiting controllable scattering, birefringence, and optical activity. In Design and performance validation of phantoms used in conjunction with optical measurements of tissue. SPIE. Wood, M. F. G., et al. (2009a). Turbid polarimetry for tissue characterization. In Novel optical instrumentation for biomedical applications IV. SPIE. Wood, M. F. G., et al. (2009b). Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo. Journal of Biomedical Optics, 14(1), 014029–014025. Wood, M. F. G., et al. (2010). Polarization birefringence measurements for characterizing the myocardium, including healthy, infarcted, and stem-cell-regenerated tissues. Journal of Biomedical Optics, 15(4), 047009–047009. Wood, M. F. G., et al. (2011). Effects of formalin fixation on tissue optical polarization properties. Physics in Medicine & Biology, 56(8), N115. Yao, G., & Wang, L. (2000). Propagation of polarized light in turbid media: Simulated animation sequences. Optics Express, 7(5), 198–203. Zsila, F., et al. (2005). Circular dichroism and absorption spectroscopic data reveal binding of the natural cis-carotenoid bixin to human [alpha]1-acid glycoprotein. Bioorganic Chemistry, 33(4), 298–309.

Thi-Thu-Hien Pham received BS degree in mechatronics from Ho Chi Minh City University of Technology-Vietnam National University, Ho Chi Minh City, Vietnam, in 2003 and MS and PhD degrees in mechanical engineering from Southern Taiwan University of Technology and National Cheng Kung University, Tainan, Taiwan, in 2007 and 2012, respectively. She is currently Head of Biomedical Photonics Lab and Associate Professor in School of Biomedical Engineering, International University-Vietnam National University HCMC, Ho Chi Minh City, Vietnam. Her research interests are in the areas of polarized light-tissue studies, polarimetry, optical techniques in precision measurement to determine the optical properties of biomedical samples (glucose, collagen, and tumor) or cancer detection (skin, liver, and breast), noninvasive glucose measurement, cell/tissue characterization, laser/LED applications, and artificial intelligence (AI) applications.

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Quoc-Hung Phan received his BS degree in mechanical engineering from HCM University of Technology, Vietnam in 2004, MS degree from the Department of Mechanical Engineering at Southern Taiwan University, Taiwan in 2007 and Ph D degree from the Department of Mechanical Engineering at National Cheng Kung University in 2016. He is currently Head of Optical Sensing Laboratory and Professor of Department of Mechanical Engineering, National United University, Taiwan. His research interests include surface plasmon resonance, Stokes–Mueller matrix polarimetry, optical biosensing, and noninvasive glucose monitoring devices. Thanh-Hai Le received BS degree in mechatronic engineering from Ho Chi Minh City University of Technology, Vietnam and MS and PhD degrees in bio-mechatronic engineering from Sungkyunkwan University, South Korea in 2007 and 2011, respectively. From 2011 to 2022, he was lecturer at HCMC University of Technology - VNU HCMC. In December 2022, he joined the FPT University HCMC, where he is currently lecturer at Department of Information Technology. His current research interests are AI-based approaches for computer vision systems, diagnostic imaging systems using MRIs, CT scans and X-rays.

Chapter 4

Mueller Matrix Imaging Oriol Arteaga and Subiao Bian

Abstract Polarimetric imaging is a technique of great interest to study fiber-like macromolecules present in biological tissues. As they exhibit a certain degree of anisotropy, it can be used as an indicator to assess their microstructure that is an important analysis for medical diagnostics. Because of the highly scattering nature of bulk biological tissues, this imaging technique is best implemented with the full Mueller matrix approach, which allows quantifying the entirety of the polarimetric properties, including depolarization. This chapter reviews the main aspects of Mueller matrix imaging of biomedical tissues, including the most suitable imaging configurations and their optimization, the deciphering of Mueller matrix measurements, and the recommended presentation of polarimetric images.

1 Introduction Mueller matrix (MM) imaging is a versatile technique capable of providing space-resolved measurements of polarization-dependent properties in materials and biological systems. The measurement of the complete MM is the most comprehensive experimental polarimetry study of linear interactions between light and matter. The real 4.×4 Mueller matrix is an operator that contains complete information about polarization and depolarization properties of the scattering medium and that allows for quantitative evaluation of the measurement. In the biomedical field, MM imaging has already shown its potential for a number of applications due to its sensitivity to microstructural tissue changes that alter light polarization. Despite MM imaging was pioneered decades ago (Pezzaniti & Chipman, 1995; Chipman et al., 1996), it has more recently grown in popularity as a technique well-suited for biological and biomedical applications due to advantages like being harmless, non-invasive, with a good resolution, and well-suited to study highly scattering media, such as biological

O. Arteaga () · S. Bian Universitat de Barcelona, Barcelona, Spain e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Mazumder et al. (eds.), Optical Polarimetric Modalities for Biomedical Research, Biological and Medical Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-031-31852-8_4

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tissues (Baldwin et al., 2003; Antonelli et al., 2010; Ellingsen et al., 2011; He et al., 2014; Du et al., 2014; Wang et al., 2015; Novikova et al., 2016; He et al., 2017; Chue-Sang et al., 2017; Dong et al., 2020; Lee et al., 2021; Le Gratiet et al., 2021; Le et al., 2022; Rehbinder et al., 2022). The basic principles of MM imaging are surveyed in this chapter. We give an overview of the multiple aspects involved in polarimetric imaging, with special focus on applications related to biomedical research. We present the definitions of the main polarimetric effects and how they are recovered from the measured Mueller matrices, a description of the most useful instrumental configurations for imaging as well as notions for their optimization and data reductions. We also discuss other aspects such as how the imaging results can be best presented to streamline their physical or biomedical interpretation. This chapter is by no means an exhaustive review of all the many contributions to polarimetric imaging over the past few decades.

2 Polarimetric Optical Properties In polarimetry, a medium is described by six basic polarization properties (magnitudes of linear retardation and linear diattenuation, orientations of linear retardation and linear diattenuation, and circular retardation and circular diattenuation) that are produced by the samples (Jones, 1948). To these polarization properties, one must add the depolarization effects that depend not only on the studied medium (e.g., the amount of multiple scattering) but on the instrument used for the measurement (e.g., the spatial resolution and the numerical aperture of the imaging optics).

2.1 Physical Origin of Polarimetric Effects Linear retardance and depolarization are the two main effects observed in the polarimetric analysis of tissue samples. The anisotropic organized nature of many tissues that stems from their fibrous structure (for example in collagen and elastin) generally leads to linear retardance. Linear diattenuation (that is related to anisotropic extinction) is usually a less prominent effect, and, if present, it typically reduces the average propagation pathlengths, or the average number of scattering events, leading to a weaker depolarization effect. A schematic representation of the origin of linear retardance, linear diattenuation, and depolarization is shown in Fig. 4.1. The optical activity of the glucose present in biological tissues can give rise to circular retardance (Phan & Lo, 2017), but these signals will be on most occasions below the experimental sensitivity limits of imaging instruments. Likewise, circular diattenuation effects typically get negligible values. In optically thick turbid media such as tissues, multiple scattering causes extensive depolarization, something that does not happen when imaging thin histological cuts.

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Fig. 4.1 Schematic representation of the polarization changes induced by three basic polarimetric effects. The linear retardation and linear diattenuation between perpendicular components of polarization can be produced, respectively, by the birefringent and dichroic effects of anisotropic structures present in bio-tissues. The depolarization effect is usually dominated by multiple scattering in the bulk

From an experimental point of view, extensive depolarization may hinder the measurement and analysis of the other polarimetric effects, because it makes the other polarization signals residual, and sometimes even become undetectable if the polarimeter does not have a very high sensitivity. In this sense, the research to develop new polarimetric imaging instrumentation with enhanced sensitivity and accuracy is essential to deal with the complexities due to multiple scattering. Experimental observations have shown that the retardance and depolarization induced by tissues can be used as indicators to assess their microstructure, and thus, they can be helpful for diagnostics (e.g., for cancer, cirrhosis, and different types of tissue lesions). An increasing number of publications have reported how MM polarimetric imaging is very sensitive to small pathological alterations in fibrous tissue (Antonelli et al., 2010; Du et al., 2014; He et al., 2014; Wang et al., 2015; Kupinski et al., 2018).

2.2 Quantitative Interpretation of Mueller Matrix Polarimetry Data Quantitative analysis of measured MM images is a key process to obtain images that show a good level of contrast that can be linked to physiological features

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of the tissues. In this section, we will focus our attention on the interpretation given by the differential MM formalism, as it is well adapted for biomedical polarimetric measurements since it is based on a continuously scattering medium model that is a good match for most biological tissues. This method can decouple the individual contributions of several polarimetric effects occurring simultaneously. Other analysis methods based on product decompositions, such as the popular Lu– Chipman decomposition (Lu & Chipman, 1996), may be less suitable since their results may depend on the order of matrix terms representing each one of the optical properties. If a measurement is obtained in the backscattering configuration (scattering angle of .∼ 180◦ ), the most general Mueller matrix has certain symmetries and has only 10 independent parameters: ⎛

m00 ⎜ m01 .M = ⎜ ⎝−m02 m03

m01 m11 −m12 m13

m02 m12 m22 −m23

⎞ m03 m13 ⎟ ⎟. m23 ⎠

(4.1)

m33

A matrix with these symmetries remains the same if the input and output beams are interchanged, as is to be expected in the backscattering configuration. Any measurement obtained in backscattering is expected to follow (at least approximately, due to the presence of noise or other systematic errors) this pattern of symmetries. Given a general depolarizing experimental Mueller matrix .M, the differential Mueller matrix .L expresses the local evolution of the Mueller matrix for light propagating through a homogeneous optical medium. Over the last decade, the methods based on a differential analysis of the Mueller matrix (Ossikovski, 2011, 2012; Arteaga, 2017; Ossikovski & Arteaga, 2014) have gained increasing popularity, and they are well-suited for the interpretation polarimetry measurements in the biomedical field. .L can be obtained by taking the matrix logarithm of .M, L = lnM.

.

(4.2)

Algorithms for the numerical calculation of a matrix logarithm are available in all modern programming software packages, but not all Mueller matrices have a logarithm. For most depolarizing measurements in the backscattering configuration, there exists no real matrix logarithm unless the sign of the last two rows is flipped by left-multiplying the experimental Mueller matrices measured in the backscattering configuration by the diagonal matrix .diag(1, 1, −1, −1) (Arteaga & Ossikovski, 2023). With this transformation of the measured matrix, the form of the matrix is made to resemble those measured in transmission, and the matrix logarithm in Eq. (4.2) can usually be applied. The polarization properties can be found from the elements of differential Mueller matrix .L as: • Horizontal linear retardance: .LR = (l32 − l23 )/2

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45.◦ linear retardance: .LR = (l13 − l31 )/2 Horizontal linear diattenuation: .LD = (−l01 − l10 )/2 45.◦ linear diattenuation: .LD = (−l02 − l20 )/2 Circular retardance: .CR = (l12 − l21 )/2 Circular diattenuation: .CD = (l03 + l30 )/2

where .lij indicate the elements of .L. For imaging applications involving high-resolution images (or those that require fast, real-time monitoring of the above polarimetric effects), the differential analysis based on the computation of the Mueller matrix logarithm (Eq. 4.2) might be computation-wise too time-consuming.1 A faster solution to the differential method is possible using the analytic inversion process (Arteaga & Canillas, 2010b,a), which can be easily applied to a Jones matrix. In order to apply this method to a depolarizing Mueller matrix, one needs to find first the nondepolarizing estimate, which is commonly done with the Cloude sum decomposition (Cloude, 1986). This est to an approach finds the closest nondepolarizing MM, .Mest J , or Jones matrix .J experimentally determined depolarizing one. This matrix minimizes the sum-ofsquares estimator: δ2 =

.

 2 (Mij − Mest J ij ) → min.

(4.3)

i,j

The calculation of this nondepolarizing estimate starts by reorganizing the information available in the MM (after left-multiplying it by .diag(1, 1, −1, −1) if the measurement was obtained in backreflection) to construct the following 4.×4 Hermitian positive semi-definite coherency matrix: ⎛

m00 + m11 ⎜ m22 + m33 ⎜ ⎜ m +m 01 10 ⎜ 1⎜ ⎜ +i(m23 − m32 ) .C = ⎜ 4 ⎜ m02 + m20 ⎜ ⎜ −i(m13 − m31 ) ⎜ ⎝ m03 + m30 +i(m12 − m21 )

m01 + m10 −i(m23 − m32 ) m00 + m11 −m22 − m33 m12 + m21 −i(m03 − m30 ) m13 + m31 +i(m02 − m20 )

m02 + m20 +i(m13 − m31 ) m12 + m21 +i(m03 − m30 ) m00 − m11 +m22 − m33 m23 + m32 −i(m01 − m10 )

⎞ m03 + m30 −i(m12 − m21 ) ⎟ ⎟ m13 + m31 ⎟ ⎟ ⎟ −i(m02 − m20 ) ⎟ ⎟ m23 + m32 ⎟ ⎟ +i(m01 − m10 ) ⎟ ⎟ m00 − m11 ⎠ −m22 + m33 . (4.4)

The nondepolarizing estimate is found from the eigenvector corresponding to the largest eigenvalue of .C. If this eigenvector is .c = (c0 c1 c2 c3 )T , then the Jones matrix that represents the closest nondepolarizing estimate is given by

1 We have noticed large differences in the time necessary to process MM imaging data using the matrix logarithm depending on the software used for the analysis. At the time of writing this chapter, Matlab or Labview were around 10 times faster than Python when performing such calculations.

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est

J

.

j j = 00 01 j10 j11





c0 + c1 c2 − ic3 = . c2 + ic3 c0 − c1

(4.5)

Finally, the following analytic equations are used to find the polarization properties: LR − iLD = i(j00 − j11 ),

(4.6a)

LR − iLD = i(j01 + j10 ),

(4.6b)

CR − iCD = i(j01 + j10 ),

(4.6c)

 K = 1/ det(Jest ),

(4.7a)

.

.

.

where .

=

.

K(T + 2π n) , 2 sin(T /2)

T = 2acos(K(j00 + j11 )/2).

.

(4.7b) (4.7c)

The extra factor .2π n, where n is an integer, accounts for the multi-valued nature of the trigonometric functions that makes it possible that samples with increasing amounts of polarization properties have the same Jones/Mueller matrices. In biomedical applications, the retardance usually is not too high so in most cases, one can safely set .n = 0. Overall, this analytic method gives, for most situations, results almost identical or very similar to the solution based on Eq. (4.2). Instead of reporting the values of .LR, .LR , .LD, and .LD , it is usually advisable to calculate the following four related quantities that allow for a more straightforward physical interpretation of these optical effects (Arteaga, 2010): LR2 + LR 2 , . 

LR 1 ,. Rθ = atan2 2 LR Dm = LD2 + LD 2 , . 

LD 1 , Dθ = atan2 LD 2 Rm =

.

(4.8a) (4.8b) (4.8c) (4.8d)

where .atan2 stands for the four-quadrant inverse tangent. .Rm and .Dm , respectively, denote the magnitudes of linear retardation and linear diattenuation, while .Rθ and .Dθ respectively indicate their orientation angles with respect to the horizontal. As an additional metric to quantify the depolarization, we use the depolarization index (DI) (Gil & Bernabeu, 1986)

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⎛ ⎞  3    1 ⎝ m2 − m200 ⎠. .DI =  3m200 i,j =0 ij

(4.9)

Many other methods for the quantitative interpretation of MM polarimetric data have been proposed. For a more comprehensive review of the methods, check Arteaga and Ossikovski (2023) and Gil and Ossikovski (2016).

3 Imaging MM Instrumentation A Mueller matrix polarimeter is composed of a polarization-state generator (PSG) that generates at least four independent states of polarization that interact with a sample. A polarization-state analyzer (PSA) analyzes these resulting states by measuring its projections over at least four other linear independent states. The Stokes vector reaching the detector in a MM polarimetry experiment is given by Sout = MP SA Msample MP SG Sin ,

.

(4.10)

as the detector used in most imaging systems is only sensitive to the first component of the Stokes vector total intensity I and only the first column of .MP SG and the first row of .MP SA will affect this intensity. Therefore, we may write ⎡

 Ik = ak,0 ak,1 ak,2

.

m00  ⎢m10 ak,3 ⎢ ⎣m20 m30

m01 m11 m21 m31

m02 m12 m22 m32

⎤⎡ ⎤ m03 gk,0 ⎢ ⎥ m13 ⎥ ⎥ ⎢gk,1 ⎥ , ⎦ ⎣ m23 gk,2 ⎦ m33 gk,3

(4.11)

where k refers to the .k th intensity measurement made at the detector (usually obtained sequentially). In compact notation, Ik = ATk MGk .

.

(4.12)

Using linear algebra properties, one finds that it is possible to rewrite it as the scalar product between two vectors − → Ik = WTk · M,

.

(4.13)

where .Wk may be regarded as the basis vector of the instrument T  Wk = ATk ⊗ Gk = a0 g0 a0 g1 a0 g2 a0 g3 · · · a3 g0 a3 g1 a3 g2 a3 g3 k ,

.

(4.14)

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− → where .⊗ denotes the Kronecker product, and . M is the 16-component Mueller vector defined as T − →  M = m00 m01 m02 m03 · · · m30 m31 m32 m33 .

.

(4.15)

Polarimetric data analysis consists of solving Eq. (4.13) for the Mueller vector. If the measurements contain N intensity measurements (.k = 1, · · · , N), we may rewrite this equation as matrix–vector multiplication: − → I = W M,

.

(4.16)

where .I = (I1 , I2 , · · · , IN )T is the intensity vector over all measurements and .W is a matrix of dimension .N × 16 that relates the measured intensities with the Mueller matrix elements. The Mueller matrix of the sample can be solved as (Chipman, 2009) − → M = (WT W)−1 WT I = W+ I,

.

(4.17)

and .W+ = (WT W)−1 WT is the pseudo-inverse of .W, which gives the least squares estimate of the inverse (if .N = 16 the pseudo-inverse will coincide with the matrix inverse). Since the problem of solving for the MM of the sample reduces to solving a matrix inversion, a minimum of .N = 16 measurements must be taken, and the matrix must be well-conditioned to reduce noise in the setup. The conditioning can be usually improved by taking .N > 16 measurements, thus over-specifying the calculations, although the highest speed in most systems is achieved when .N = 16. A considerable number of different imaging MM instruments have been proposed during the last few years; they essentially differ on the type of compensating element used in PSG and PSA. Here we will review systems based on rotating compensators, systems based on liquid crystals compensators, and systems using polarization cameras. These three techniques seem to be the most successful and popular technologies for clinical applications of polarimetry that use cameras as detectors. However, there are several other polarimetry methods that be applied, such as compensators based on photoelastic modulators (Alali & Vitkin, 2013), or systems using a division of amplitude method (Zaidi et al., 2022).

3.1 System Based on Two Rotating Compensators This device has a PSG and PSA composed of a rotating compensator and a polarizer as shown in Fig. 4.4a. The Mueller matrices of the PSG and PSA are MP SG = R(−θ0 )MLR0 R(θ0 )P0 ,

.

(4.18a)

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MP SA = P1 R(θ1 )MLR1 R(−θ1 ),

.

(4.18b)

where .P and .R are the Mueller matrices of a linear polarizer and the usual rotation matrix, respectively. .MLR is the Mueller matrix of compensator with linear retardance .δ:

MLR

.

⎡ 1 ⎢0 =⎢ ⎣0 0

0 0 1 0 0 Cδ 0 Sδ

⎤ 0 0 ⎥ ⎥, −Sδ ⎦ Cδ

(4.19)

where the shorthand notation .Cx = cos(x), and .Sx = sin(x) is used. The value of this retardance is stable with time and only its orientation changes. Therefore, the PSG and PSA: ⎡ ⎡ ⎤ ⎤ 1 1 ⎢ −(C 2 + C S 2 ) ⎥ ⎢ C2 + C S2 ⎥ ⎢ ⎢ 2θ0 δ0 2θ0 ⎥ δ1 2θ1 ⎥ 2θ1 .G = ⎢ (4.20) ⎥, A = ⎢ ⎥. ⎣−C2θ1 S2θ1 (1 − Cδ1 )⎦ ⎣C2θ0 S2θ0 (1 − Cδ0 )⎦ Sδ1 S2θ1 Sδ0 S2θ0 The Kronecker product of these two vectors gives (Arteaga et al., 2014) ⎤ 1 ⎥ ⎢ 2 + C S2 C2θ ⎥ ⎢ δ0 2θ0 0 ⎥ ⎢ ⎥ ⎢ C2θ0 S2θ0 (1 − Cδ0 ) ⎥ ⎢ ⎥ ⎢ Sδ0 S2θ0 ⎥ ⎢ 2 2 ⎥ ⎢ −(C2θ1 + Cδ1 S2θ1 ) ⎥ ⎢ ⎢ −(C 2 + C S 2 )(C 2 + C S 2 ) ⎥ ⎥ ⎢ δ0 2θ0 δ1 2θ1 2θ0 2θ1 ⎢ 2 + C S2 ) ⎥ ⎥ ⎢ −C2θ0 S2θ0 (1 − Cδ0 )(C2θ δ 1 2θ1 1 ⎥ ⎢ 2 2 ⎥ ⎢ −(Sδ0 S2θ2 )(C2θ1 + Cδ1 S2θ1 ) ⎥ . ⎢ .Wk = ⎥ ⎢ −C2θ1 S2θ1 (1 − Cδ1 ) ⎥ ⎢ ⎥ ⎢ 2 2 ⎢ −(C2θ0 + Cδ0 S2θ0 )[C2θ1 S2θ1 (1 − Cδ1 )] ⎥ ⎥ ⎢ ⎢−[C2θ0 S2θ0 (1 − Cδ0 )][C2θ1 S2θ1 (1 − Cδ1 )]⎥ ⎥ ⎢ ⎥ ⎢ −Sδ0 S2θ0 [C2θ1 S2θ1 (1 − Cδ1 )] ⎥ ⎢ ⎥ ⎢ Sδ1 S2θ1 ⎥ ⎢ ⎥ ⎢ 2 + C S2 ] Sδ1 S2θ1 [C2θ ⎥ ⎢ δ 0 2θ 0 0 ⎥ ⎢ ⎦ ⎣ Sδ1 S2θ1 [C2θ0 S2θ0 (1 − Cδ0 )] Sδ0 S2θ0 Sδ1 S2θ1 k ⎡

(4.21)

For imaging applications in the visible and NIR ranges, the most suitable compensators are polymer film retarders. They have several advantages over retarders based on crystals such as being available in large sizes (thus not limiting the field of view

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Fig. 4.2 Values of the determinant of .W+ (normalized to its maximum value) as a function of the retardance of the compensator. All the retardance values where the determinant drops to zero should be avoided because those cases .W+ become a singular matrix. The two regions close to the maximum values, where the retardances are .∼ 132◦ and .∼ 234◦ , are recommended

of the instrument), being very thin, which avoid beam displacements upon rotation, and having a cheap price. The optimal retardance for the rotating compensator present in the PSG and PSA is .δ ∼ 132◦ or .∼ 234◦ (Sabatke et al., 2000; Gottlieb & Arteaga, 2021b), which can be deduced from studying the determinant of .W+ as a function of the retardance and checking which retardance leads to a maximum value of the determinant. This analysis is shown in Fig. 4.2. However, the commercial film compensators available in the market are designed for the non-optimal retardance of quarter wave .δ ∼ 90◦ or half-wave .180◦ , which reduces the noise tolerance of the setup. However, as these commercial retarders are not fully achromatic, at certain wavelengths outside of their design wavelength, they offer the optimal value for a Mueller matrix ellipsometer. As shown in Fig. 4.3, the commercial half-wave polymer film compensator from Edmund Optics (WP280) provides two optimal regions: one is between .∼680 nm–750 nm when the retardance is around .132◦ and another is .∼ 448 nm–465 nm where retardance is close to .234◦ . This type of compensator is ideally suited for polarimetry imaging applications at this range of wavelengths. To make an optimal film compensator in other wavelength ranges, one can combine two misaligned quarter wave film retarders effectively constructing an elliptical retarder (Gottlieb & Arteaga, 2021b). There are two possible work modes for rotating compensator imaging systems: continuous and discrete rotations. In continuous rotation, the signal acquisitions are at evenly spaced consecutive angles determined by a certain rotation speed, which results in a periodic signal. The number of acquisitions N , which depends on the rotation speed of the compensators and integration time of the detector, can typically reach several hundreds or thousands of images. In continuous mode, the data processing for imaging becomes a consuming work as Eq. (4.17) that scales with N needs to be repeated for all the pixels of the detector. Instead, in the discrete mode, compensators are oriented to a collection of pre-determined angles that are not evenly spaced. This mode is a better choice (Bian et al., 2021) when N is

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Fig. 4.3 The retardance provided by a commercial polymer half-wave film compensator reaches the optimal values of .132◦ and ◦ .234 at the wavelengths of 728 nm and 456 nm, respectively

low, particularly when using the lowest number of acquisitions (.N = 16). The optimal angles for discrete mode can be obtained using an optimization algorithm that uses the condition number as a merit function; for example, when .N = 16, an optimal measurement is achieved when the compensators in PSG and PSA use angles +/.−51.7 degrees and +/.−15.1 degrees (Sabatke et al., 2000). An additional advantage of the discrete mode is that it is fully independent of the integration time at the detector and rotation speed of compensators, so in the case of a lowsignal level one can increase the exposure of the camera without affecting the data processing. Accordingly, we consider that discrete rotation is especially well-suited for imaging applications.

3.2 Systems Based on Tunable Liquid Crystals Compensators Liquid crystal (LC) devices are optically anisotropic media that exhibit optical retardation depending on an externally applied voltage and therefore can be used as tunable compensating elements in MM polarimeters. The most employed liquid crystals in polarimetry are nematic liquid crystals,2 in which the driving voltage affects the magnitude of their retardance but not their azimuth. When no voltage is applied, the molecules in the liquid crystal are aligned in one direction parallel to the surface the retardance is at a maximum. When the angle of the molecules with respect to the surface is increased, the retardance decreases.

2 Ferroelectric LC cells can also be used in polarimetry. This type of LCs has fixed retardation, and the orientation of the optical axis can be controlled by an applied drive voltage, so they “mimic” the working principle of the rotating compensators that we have described previously. In this section, we do not discuss systems based on ferroelectric LC.

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Fig. 4.4 Schematic of the Mueller matrix imaging system based on rotating compensators (a) and liquid crystal variable retarders (b). S, source; P, linear polarizer; LR, linear retarder; LC, liquid crystal retarder. The linear retarder has a fixed retardance but a variable orientation angle. The liquid crystal retarders are oriented at fixed azimuth angles but with variable retardance. The xy axes in the transverse plane define the laboratory coordinate system

For complete MM polarimetry, two independent LCs at different azimuth angles must be used in both the PSG and the PSA. Thus, in total, the instrument requires four different LCs, as shown in Fig. 4.4b. Therefore, for these systems, we must replace Eq. (4.18) by .

MP SG = R(−θ1 )MLR1 R(θ1 )R(θ0 )MLR0 R(−θ0 )P0

(4.22a)

MP SA = P1 R(θ3 )MLR3 R(−θ3 )R(θ2 )MLR2 R(−θ2 ),

(4.22b)

.

where .MLR0 , .MLR1 , .MLR2 , and .MLR3 are the Mueller matrices of the four LCs, all of them given by Eq. (4.19). The modulation of polarization is executed by the variation of controlled electrical voltage between at least two levels (high or low level) for each LC, so that there are two different retardances associated with the high and low voltages. Thus, the two LC compensators present in the PSG or PSA can realize four different states of polarization in PSG and PSA, which combined together in the full system can realize the minimum sixteen independent polarization measurements necessary for a complete Mueller matrix calculation. Of course, it is also possible to use more than two levels of voltage so that the inversion process of Eq. (4.17) is overdetermined. However, the retardance is a nonlinear function of the applied voltage, and it may also change from device to device and with temperature, so each new applied voltage requires precise calibration.

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The choice of the retardance value and azimuth angle of each liquid crystal in the system can be obtained from an optimization procedure, similar to the method commented for the rotating compensators in discrete mode. For example, an optimal configuration (but not the only one possible) for PSG is achieved when the retardance in each LCs is switched between 135.◦ and 315.◦ (i.e., using a sequence of retardations .(δ0 , δ1 ) = (135◦ , 135◦ ), (135◦ , 315◦ ), (315◦ , 135◦ ), (315◦ , 315◦ ), and the first LC is oriented at .θ0 = 27.4◦ and the second at .θ1 = 72.4◦ with respect to the transmission axis of the first polarizer (De Martino et al., 2003; Garcia-Caurel et al., 2004). The same results apply to the optimization of the PSA. The advantage of tunable liquid crystal compensators is that they can operate without any mechanical movement, and there is a rapid response of the LC retardance with the applied voltage, allowing for fast acquisition times, and they are usually well-suited for in-live applications. The switching times are typically on the order of 5 to 100 ms, and it is usually not the same when increasing the voltage as when decreasing it. However, LC compensators also have some drawbacks that are not present in rotating compensator systems, as, for example, they tend to exhibit not fully uniform retarding properties across their clear aperture, which may require pixel-by-pixel calibration procedures. Other issues come from their temperature dependence, the small acceptance angle (meaning that the value of the retardance changes significantly with the angle of incidence), and the non-negligible scattering caused by LC molecules, which can introduce some depolarization (Chipman, 2009).

3.3 Use of Polarization Cameras for MM Imaging To speed up the measurement time of the MM, a polarization-sensitive camera can be used to measure multiple linear polarization states of the light simultaneously. Polarization cameras with sensor-integrated polarizing filters are an easy and costeffective method to acquire polarization information simultaneously. The micropolarizer array is made of blocks of four linear polarizers at different angles (90.◦ , 45.◦ , 135.◦ , and 0.◦ ) repeating across the camera sensor, as shown in Fig. 4.5. Every block of four pixels makes up a superpixel that has information about the direction and degree of linear polarization. Combining the intensities measured by each one of the 4 pixels contained in every superpixel, the camera can directly measure the first [.S0 = (I0◦ +I90◦ )/2 = (I45◦ +I135◦ )/2 = (I0◦ +I90◦ +I45◦ +I135◦ )/4], second [.S1 = (I0◦ − I90◦ )/2], and third [.S2 = (I45◦ − I135◦ )/2] components of the Stokes vector. The fourth component (.S3 ) cannot be obtained by the camera because it does not include any compensating optical element that allows quantifying the ellipticity of the incoming radiation. The integration of a micro-polarizer layer above the photodiodes of camera sensors was proposed and implemented several years ago (Guo & Brady, 2000; Nordin et al., 1999), but polarization cameras have only recently become widely commercially available (Sony Polarization Image Sensor, 2021). A polarization

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Fig. 4.5 Layout of the camera sensor, showing the 2.×2 grid of polarizers forming a superpixel

camera can be combined with a time-varying PSG to measure the top three rows of the MM, without the need for any other polarization-changing element in a PSA. The detection of the top three rows (12 MM elements) is sufficient for the complete characterization of nondepolarizing samples. Complete MM polarimetry setups using two polarization-sensitive cameras have also been proposed (Huang et al., 2021), relying on a division of focal plane technique to acquire complete MM data. Here we discuss systems using a single polarization camera. When a polarization camera is used as a detector in combination with a PSG, Eq (4.11) can be simplified to ⎡ m00 ⎢m10 .Sk = ⎢ ⎣m20 m30

m01 m11 m21 m31

m02 m12 m22 m32

⎤⎡ ⎤ gk,0 m03 ⎢ ⎥ m13 ⎥ ⎥ ⎢gk,1 ⎥ , ⎦ ⎣ m23 gk,2 ⎦ m33 gk,3

(4.23)

where the first 3 components of .Sk are measured by the camera (the fourth one is not measured because the polarization camera cannot determine the ellipticity of polarization). In the case of a PSG based on a rotating compensator, the components reaching the polarization camera will be ⎤T ⎡ ⎤ mi0 1 ⎢ (C 2 + Cδ S 2 ) ⎥ ⎢mi1 ⎥ 2θ 2θ ⎥ ⎢ ⎥ =⎢ ⎣−C2θ S2θ (Cδ − 1)⎦ ⎣mi2 ⎦ S2θ Sδ mi3 ⎡

Sout,i

.

with i = 0, 1, 2.

(4.24)

As the measurement process consists of taking a collection of intensity measurements for N different positions of the compensator, Eq. (4.24) can be rewritten as Sout,i = WT Ai ,

.

(4.25)

where .Sout,i is a vector of N elements, .Ai is the 4-component vector containing the i-th row of the MM, and .W is a matrix with dimension .N × 4. If 4 intensity

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measurements are made each at different angles of the compensator (.N = 4), .W is a square matrix, and by inverting it, it is possible to solve for .A. If .N > 4, the calculation is overspecified and noise can be reduced. In this case, the Moore– Penrose pseudo-inverse of .W can be used, as it was discussed in Eq. (4.17). A Mueller matrix microscope based on a polarization camera was recently reported (Gottlieb & Arteaga, 2021a) showing advantages in terms of instrumental simplicity and speed. For nondepolarizing situations, the measurement of the top three MM rows is sufficient for complete characterization of the sample, and in fact, the last row can be rigorously recovered using an algebraic method (Ossikovski & Arteaga, 2019). In case a significant amount of depolarization is present, a single polarization camera cannot offer a complete characterization, and it is advisable to use instruments that measure all 16 MM elements. However, for a backreflection measurement, one can still rely on the matrix symmetries shown in Eq. (4.1), and from them, it is possible to deduce the values of .m30 (.m30  m03 ), .m31 (.m31  m13 ), and .m32 (.m32  −m23 ). In such case, only the MM element .m33 would remain as unknown. In biological scattering tissue, .|m33 | (mostly depicting the depolarization of circularly polarized light) can differ from .|m11 | and .|m22 | (depicting the depolarization of linearly polarized light), but the values are, in most cases, not too far apart. Therefore, as an approximation, one can use .m33 = −(m11 −m22 )/2 to estimate this remaining unknown element, thus enabling the application of the methods described in Sect. 2.2.

4 Practical Considerations and Examples Most instrumental implementations for Mueller matrix imaging are based on one of these three basic configurations: • Transmission. Illumination by the transmission of light through the sample. It is analog to the transillumination configuration in microscopy. • Retroreflection using a beam splitter. Light is retroreflected from the sample and the PSG and PSA and placed forming a 90.◦ angle. • Reflection at a very small angle of incidence. Light is reflected from the sample at a very small angle of incidence (usually the smallest angle allowed by the physical dimensions of the PSG and PSA). These three configurations have been illustrated in Fig. 4.6. The two first configurations mimic the typical layouts of optical microscopes, so they are suitable to be used with microscope objectives. Compared to transmission, the retroreflection configuration with a beam splitter tends to bring some additional practical difficulties. Beam splitters, even those marketed as “non-polarizing,” do alter the polarization state of light in a significant way, as light reaching the camera has double-interacted with the beam splitter. Therefore, in polarimetry implementations, it is necessary to calibrate the effect of the beam splitter, as has been discussed in

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several works (Chen et al., 2018, 2020). Recalibration may be necessary every time there is a change in the alignment or a different microscope objective is used. The third configuration also works in reflection, and it has the advantage that it does not require any beam splitter, so it is much easier to calibrate. This configuration is usually employed in wide-field imaging systems, where the imaging optic elements are placed at a long distance from the sample. This also brings the advantage that the imaging objective can be placed outside the region comprised between the PSG and PSA, so it cannot produce polarization perturbation (e.g., due to strains) in the measurement. The angle of incidence for systems working in this mode is limited by the physical dimensions of the PSG and PSA and usually cannot be smaller than .∼ 10◦ . There are MM imaging instruments that may involve additional optical elements from those shown in Fig. 4.6, for example, in instruments imaging the back-focal plane of the objective (Arteaga et al., 2017), in fluorescence systems (Mazumder et al., 2017), or in confocal setups (Lara & Dainty, 2005). As an illustrative MM imaging measurement for biomedical research, we show in Fig. 4.7 the measurement of the palm of one of our hands. The analysis of this measurement can be challenging because it involves an optically thick tissue with a very prominent three dimensionality. From a polarimetric perspective, the analysis of thin histological samples is usually simpler than this example because it involves planar samples with negligible depolarization. This measurement was performed with the instrument described in Gottlieb et al. (2022) that uses the configuration for reflection at a very small angle incidence (Fig. 4.6c). This instrument uses the rotating compensators as PSG and PSA, using a discrete angle implementation requiring 16 image acquisitions. The complete measurement took around 2s, and a 660 nm LED was used as a light source.

Fig. 4.6 Usual configurations in MM imaging. (a) Transmission; (b) retroreflection using a beam splitter; (c) reflection at a very small angle of incidence

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Fig. 4.7 Imaging of palm of the hand. The Mueller matrices have been normalized to element In place of element .m00 , we show the measured intensity for unpolarized light

.m00 .

Figure 4.7 shows a normalized MM. The most obvious feature of this matrix is that off-diagonal elements are very small (the maximum absolute values are around .0.05) and the diagonal elements do not take absolute values larger than .0.2. All these low values in a normalized MM are indicating that the measurement is strongly depolarizing, which is a very common situation in biomedical measurements. Note also that .|m11 |  |m22 | > |m33 |, which is a very usual situation for biological tissues. This is indicating that circularly polarized light is more depolarized than linearly polarized, which is an expected outcome of the Rayleigh scattering regime (in the case of Mie scattering, circular polarization would be less depolarized). The small values of the off-diagonal elements of Fig. 4.7 illustrate the importance of instrumental sensitivity and accuracy in order to be able to detect the small amount of polarimetric information that has survived the randomization caused by multiple scattering and that produces this extensive depolarization. Note also that the matrix in this figure shows a good qualitative agreement with the expected backreflection symmetries presented in Eq. (4.1). This is a further indication that

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the measured data are physically meaningful and above the noise level of the experiment. In Fig. 4.7, we have applied a mask to avoid showing the pixel where the intensity of light was too low (dark regions surrounding the hand in the intensity image). This is a preferable choice, especially when plotting normalized Mueller matrices because otherwise those “dark pixels” will show a large amount of meaningless noise. Elements .m12 and .m21 (satisfying .m12  −m21 ) show rather interesting color changes that are indicative of small changes in orientation of the optical anisotropy of skin tissue. This happens because these elements have a stronger rotational dependence (scaling as .4θ ) than the other elements of the MM (that, at most, scale as .2θ ), where .θ is the direction of anisotropy. This can be demonstrated by considering the effect of a rotation on backreflection measurement, which can be described as 3 .R(θ )MR(θ ), where .M is given by Eq. (4.1). Now the rotated .m12Rot and .m21Rot elements are .m12Rot = −m21Rot = m12 cos(4θ ) + (m11 − m22 ) sin(4θ )/2. Further analysis of the Mueller matrix measurement is possible after calculating the polarimetric properties described in Sect. 2.2. Therefore, the measured Mueller matrix is best saved as “raw” data point instead of just images. Usually, the most informative properties to be shown are the four properties described in Eq. (4.8), the magnitudes and orientations of linear retardation and linear diattenuation, together with the DI (Eq. 4.9) and measured intensity for unpolarized light (.m00 element before normalization). All these 6 images are shown in Fig. 4.8 for our example of the palm of the hand. Despite depolarization levels being high at all points of the image, regions with higher brightness are those that show slightly less depolarization (higher values of DI) as these areas may have a higher contribution from photons that have undergone few scattering events (sometimes called sneak photons). Overall, there is a moderate amount of linear retardance and linear diattenuation, respectively, given by the magnitudes of .Rm and .Dm . The values of .Rm are distributed rather homogeneously at all parts of the palm, while the values of .Dm take maximum values at the edges of the palm. A rich amount of polarimetric information is seen in the .Rθ and .Dθ plots of Fig. 4.8. The orientation of linear retardance (.Rθ ) is generally correlated to the orientation of the fibers of collagen in the dermis, which in the case of the palm is correlated with the direction of the fingers. This is the reason why there is a predominating color (in this example yellow) in the .Rθ plot, but there are many subtle local changes of orientation that indicate changes in direction of the fibrous tissue. On the contrary, the values of .Dθ are clearly more sensitive to the topography of the hand and the skin. Note, for example, that there are rather abrupt changes of orientation of the diattenuation at the edges of the fingers. This indicates that most of this diattenuation is not a consequence of anisotropic absorption processes (i.e., dichroic effect) in fibrous tissues but comes from the change of polarization by reflection on inclined surfaces (i.e., the anisotropic extinction produced by Fresnel

3 In

the transmission configuration, the same effect is observed, but the rotation would be given by and .M would be the most general MM with 16 independent elements.

.R(−θ)MR(θ),

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Fig. 4.8 Different images (intensity, DI, .Rm , .Dm , .Rθ , and .Dθ ) obtained from the analysis of the measured MM

reflection effect). It is therefore obvious that the .Dθ image is sensitive to the three dimensionality of the hand. Figure 4.9 shows amplified detail of a region of the palm. The DI and .Dm images show very clear detail of the small lines, furrows, and wrinkles that are present in the epidermis of the palms. Such details are not visible in the .Rm , and they are only moderately visible in the intensity image. As linear retardance has its origin in deeper parts of the tissue, where collagen is present, it has very little sensitivity to the surface features. On the contrary, linear diattenuation shows high sensitivity to the topography of the skin, as it mostly originates from subtle changes of polarization after surface reflections.

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Fig. 4.9 Amplified detail of the intensity, DI, .Rm and .Dm images shown in Fig. 4.8

5 Summary and Outlook Technologies based on MM imaging are being developed for non-destructive analysis in biology and biomedicine. This method is relatively inexpensive to implement and can be easily automated but requires certain expertise and attention to detail to apply and use. In this chapter, we have seen that for accurate polarimetry it is fundamental a mastering of all the instrumental aspects associated with polarimetric imaging. High-quality and fast polarimetric measurements can be made only if the polarization-state generator and polarization-state analyzer are well optimized, and their polarization response is fully calibrated. Rotating systems based on polymer film compensators are possibly the best solution for accurate polarimetric imaging because they are relatively easy to optimize and they have a very good polarization uniformity, good acceptance angle, and low price. Compensators based on liquid crystals allow instruments without any mechanical movement and can offer slightly faster measurements, but their polarization uniformity and purity are lower than those for polymer film compensators. Polarization cameras are very useful devices for polarimetric imaging, since they parallelize the detection of the first 3 components of the Stokes vector, speeding up the measurement process of the Mueller matrix by a factor .∼ 4. However, their main application is for imaging nondepolarizing systems or backreflection configurations with limited degrees of freedom, since instruments with a single polarization camera as a detector cannot measure the last row of the Mueller matrix.

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MM imaging increases the quality of visualization of biological tissues. We have shown how the MM contains rich, microstructural information about tissues. Some qualitative understanding of this information can be obtained from direct observation of the different MM elements, although a better quantitative interpretation is obtained after computing the magnitudes and orientations of linear retardance and linear diattenuation. We have discussed the physical interpretation of these parameters in a backreflection measurement of biological tissue. Ideally, these polarimetric parameters should be accurately analyzed by medical doctors to translate these quantifiable optical properties into clinically meaningful information that, for example, could be used in surgical and diagnostic applications. The application of Mueller matrix imaging in biomedical research is still relatively novel, but it is highly promising because it has a fully quantitative character. Furthermore, it has complete safety, and the instrumentation required is relatively simple and affordable. Instruments compatible with the study of optically thick tissues in backscattering mode are possibly among the ones having the greatest interest in future developments, as they offer compatibility with in vivo measurements used in diagnostics or in optical biopsy.

References Alali, S., & Vitkin, I. A. (2013). Optimization of rapid Mueller matrix imaging of turbid media using four photoelastic modulators without mechanically moving parts. Optical Engineering, 52(10), 103114. Antonelli, M.-R., Pierangelo, A., Novikova, T., Validire, P., Benali, A., Gayet, B., & De Martino, A. (2010). Mueller matrix imaging of human colon tissue for cancer diagnostics: how monte carlo modeling can help in the interpretation of experimental data. Optics Express, 18(10), 10,200–10,208. Arteaga, O. (2010). Mueller matrix polarimetry of anisotropic chiral media. Ph.D. thesis, University of Barcelona. Arteaga, O. (2017). Historical revision of the differential stokes–Mueller formalism: discussion. Journal of the Optical Society of America A, 34(3), 410–414. Arteaga, O., Baldrís, M., Antó, J., Canillas, A., Pascual, E., & Bertran, E. (2014). Mueller matrix microscope with a dual continuous rotating compensator setup and digital demodulation. Applied Optics, 53(10), 2236–2245. Arteaga, O., & Canillas, A. (2010a). Analytic inversion of the Mueller–Jones polarization matrices for homogeneous media: erratum. Optics Letters, 35(20), 3525–3525. Arteaga, O., & Canillas, A. (2010b). Analytic inversion of the Mueller–Jones polarization matrices for homogeneous media. Optics Letters, 35(4), 559–561. Arteaga, O., Nichols, S. M., & Antó, J. (2017). Back-focal plane Mueller matrix microscopy: Mueller conoscopy and Mueller diffractrometry. Applied Surface Science, 421, 702–706. Arteaga, O., & Ossikovski, R. (2023). Mueller matrix analysis, decompositions and novel quantitative approaches to data analysis. In Polarized light in biomedical imaging and sensing (chapter 5). Springer. Baldwin, A., Chung, J., Baba, J., Spiegelman, C., Amoss, M., & Cote, G. (2003). Mueller matrix imaging for cancer detection. In Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No. 03CH37439) (vol. 2, pp. 1027–1030). IEEE.

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Bian, S., Cui, C., & Arteaga, O. (2021). Mueller matrix ellipsometer based on discrete-angle rotating fresnel rhomb compensators. Applied Optics, 60(16), 4964–4971. Chen, C., Chen, X., Gu, H., Jiang, H., Zhang, C., & Liu, S. (2018). Calibration of polarization effect of a high-numerical-aperture objective lens with Mueller matrix polarimetry. Measurement Science and Technology, 30(2), 025201. Chen, Z., Meng, R., Zhu, Y., & Ma, H. (2020). A collinear reflection Mueller matrix microscope for backscattering Mueller matrix imaging. Optics and Lasers in Engineering, 129, 106055. Chipman, R. A. (2009). Polarimetry. In Handbook of optics (chapter 15, 3rd edn.). OSA. Chipman, R. A., Sornsin, E. A., & Pezzaniti, J. L. (1996). Mueller matrix imaging polarimetry: an overview. In International Symposium on Polarization Analysis and Applications to Device Technology (vol. 2873, pp. 5–12). SPIE. Chue-Sang, J., Bai, Y., Stoff, S., Gonzalez, M., Holness, N. A., Gomes, J., Jung, R., Gandjbakhche, A. H., Chernomordik, V. V., & Ramella-Roman, J. C. (2017). Use of Mueller matrix polarimetry and optical coherence tomography in the characterization of cervical collagen anisotropy. Journal of Biomedical Optics, 22(8), 086010. Cloude, S. R. (1986). Group theory and polarisation algebra. Optik (Stuttgart), 75(1), 26–36. De Martino, A., Kim, Y.-K., Garcia-Caurel, E., Laude, B., & Drévillon, B. (2003). Optimized Mueller polarimeter with liquid crystals. Optics Letters, 28(8), 616–618. Dong, Y., Liu, S., Shen, Y., He, H., & Ma, H. (2020). Probing variations of fibrous structures during the development of breast ductal carcinoma tissues via Mueller matrix imaging. Biomedical Optics Express, 11(9), 4960–4975. Du, E., He, H., Zeng, N., Sun, M., Guo, Y., Wu, J., Liu, S., & Ma, H. (2014). Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues. Journal of Biomedical Optics, 19(7), 076013. Ellingsen, P. G., Lilledahl, M. B., Aas, L. M. S., de Lange Davies, C., & Kildemo, M. (2011). Quantitative characterization of articular cartilage using Mueller matrix imaging and multiphoton microscopy. Journal of Biomedical Optics, 16(11), 116002. Garcia-Caurel, E., De Martino, A., & Drevillon, B. (2004). Spectroscopic Mueller polarimeter based on liquid crystal devices. Thin Solid Films, 455, 120–123. Gil, J. J., & Bernabeu, E. (1986). Depolarization and polarization indices of an optical system. Optica Acta, 33(2), 185–189. Gil, J. J., & Ossikovski, R. (2016). Polarized light and the Mueller matrix approach. Series in optics and optoelectronics; Boca Raton: CRC Press, Taylor and Francis Group. “A Taylor and Francis book.” Gottlieb, D., Aguado, S., Gomis-Brescó, J., Canillas, A., Pascual, E., & Arteaga, O. (2022). Widefield nir imaging Mueller polarimetric system for tissue analysis. In Polarized light and optical angular momentum for biomedical diagnostics 2022 (vol. 11963, pp. 54–61). SPIE. Gottlieb, D., & Arteaga, O. (2021a). Mueller matrix imaging with a polarization camera: application to microscopy. Optics Express, 29(21), 34723–34734. Gottlieb, D., & Arteaga, O. (2021b). Optimal elliptical retarder in rotating compensator imaging polarimetry. Optics Letters, 46(13), 3139–3142. Guo, J., & Brady, D. (2000). Fabrication of thin-film micropolarizer arrays for visible imaging polarimetry. Applied Optics, 39(10), 1486–1492. He, H., He, C., Chang, J., Lv, D., Wu, J., Duan, C., Zhou, Q., Zeng, N., He, Y., & Ma, H. (2017). Monitoring microstructural variations of fresh skeletal muscle tissues by Mueller matrix imaging. Journal of Biophotonics, 10(5), 664–673. He, H., Sun, M., Zeng, N., Du, E., Liu, S., Guo, Y., Wu, J., He, Y., & Ma, H. (2014). Mapping local orientation of aligned fibrous scatterers for cancerous tissues using backscattering Mueller matrix imaging. Journal of Biomedical Optics, 19(10), 106007. Huang, T., Meng, R., Qi, J., Liu, Y., Wang, X., Chen, Y., Liao, R., & Ma, H. (2021). Fast Mueller matrix microscope based on dual DoFP polarimeters. Optics Letters, 46(7), 1676–1679. Jones, R. C. (1948). A new calculus for the treatment of optical systems. vii. properties of the n-matrices. Journal of the Optical Society of America, 38(8), 671–685.

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Kupinski, M., Boffety, M., Goudail, F., Ossikovski, R., Pierangelo, A., Rehbinder, J., Vizet, J., & Novikova, T. (2018). Polarimetric measurement utility for pre-cancer detection from uterine cervix specimens. Biomedical Optics Express, 9(11), 5691–5702. Lara, D., & Dainty, C. (2005). Double-pass axially resolved confocal Mueller matrix imaging polarimetry. Optics Letters, 30(21), 2879–2881. Le, H.-M., Le, T. H., Phan, Q. H., et al. (2022). Mueller matrix imaging polarimetry technique for dengue fever detection. Optics Communications, 502, 127420. Le Gratiet, A., Mohebi, A., Callegari, F., Bianchini, P., & Diaspro, A. (2021). Review on complete Mueller matrix optical scanning microscopy imaging. Applied Sciences, 11(4), 1632. Lee, H. R., Saytashev, I., Du Le, V. N., Mahendroo, M., Ramella-Roman, J., & Novikova, T. (2021). Mueller matrix imaging for collagen scoring in mice model of pregnancy. Scientific Reports, 11(1), 1–12. Lu, S.-Y., & Chipman, R. A. (1996). Interpretation of Mueller matrices based on polar decomposition. Journal of the Optical Society of America A, 13(5), 1106–1113. Mazumder, N., Qiu, J., Kao, F.-J., & Diaspro, A. (2017). Mueller matrix signature in advanced fluorescence microscopy imaging. Journal of Optics, 19(2), 025301. Nordin, G. P., Meier, J. T., Deguzman, P. C., & Jones, M. W. (1999). Micropolarizer array for infrared imaging polarimetry. Journal of the Optical Society of America A, 16(5), 1168–1174. Novikova, T., Rehbinder, J., Deby, S., Haddad, H., Vizet, J., Pierangelo, A., Validire, P., Benali, A., Gayet, B., Teig, B., et al. (2016). Multi-spectral Mueller matrix imaging polarimetry for studies of human tissues. In Clinical and translational biophotonics (pp. TTh3B–2). Optical Society of America. Ossikovski, R. (2011). Differential matrix formalism for depolarizing anisotropic media. Optics Letters, 36(12), 2330–2332. Ossikovski, R. (2012). Differential and product Mueller matrix decompositions: a formal comparison. Optics Letters, 37(2), 220–222. Ossikovski, R., & Arteaga, O. (2014). Statistical meaning of the differential Mueller matrix of depolarizing homogeneous media. Optics Letters, 39(15), 4470–4473. Ossikovski, R., & Arteaga, O. (2019). Completing an experimental nondepolarizing Mueller matrix whose column or row is missing. Journal of Vacuum Science & Technology B: Nanotechnology. Microelectronics: Materials Processing, Measurement, Phenom, 37(5), 052905. Pezzaniti, J. L., & Chipman, R. A. (1995). Mueller matrix imaging polarimetry. Optical Engineering, 34(6), 1558–1568. Phan, Q.-H., & Lo, Y.-L. (2017). Differential Mueller matrix polarimetry technique for noninvasive measurement of glucose concentration on human fingertip. Optics Express, 25(13), 15179–15187. Rehbinder, J., Vizet, J., Park, J., Ossikovski, R., Vanel, J.-C., Nazac, A., & Pierangelo, A. (2022). Depolarization imaging for fast and non-invasive monitoring of cervical microstructure remodeling in vivo during pregnancy. Scientific Reports, 12(1), 1–13. Sabatke, D., Descour, M., Dereniak, E., Sweatt, W., Kemme, S., & Phipps, G. (2000). Optimization of retardance for a complete stokes polarimeter. Optics Letters, 25(11), 802–804. Sony Polarization Image Sensor. (2021). https://www.sony-semicon.co.jp/e/products/IS/industry/ product/polarization.html. Wang, Y., He, H., Chang, J., Zeng, N., Liu, S., Li, M., & Ma, H. (2015). Differentiating characteristic microstructural features of cancerous tissues using Mueller matrix microscope. Micron, 79, 8–15. Zaidi, A., McEldowney, S., Lee, Y.-H., Chao, Q., & Lu, L. (2022). Towards compact and snapshot channeled Mueller matrix imaging. Optics Letters, 47(3), 722–725.

Chapter 5

Biological Imaging Through Optical Mueller Matrix Scanning Microscopy Aymeric Le Gratiet, Colin J. R. Sheppard, and Alberto Diaspro

Abstract The 4x4 Mueller matrix (MM) has been proven to be a powerful approach for understanding the whole optical properties of any sample. It is based on the analysis of the transformed polarization states from the excitation light through interaction with the optical medium. The main challenge for this technique is: (1) encoding and decoding the polarized light at the pixel-dwell time rate for the scanning light microscopy (SLM) architecture and (2) taking into account the polarimetric artifacts from the optical devices composing the instrument in a simple calibration step. In this chapter, we briefly describe the MM formalism and how SLM setups can be modeled and thus calibrated. Next, we present the experimentalist paradigm for finding the proper trade-off between the high-speed control and the most optimal optical components for controlling the polarization. Despite SLM imaging is commonly based on the collection of the non-linear signal from the sample, we show the combined modalities with MM that can acquire a complete overview of the 3D structure of the sample. At last, we discuss the capability of MM-SLM of providing tissues diagnosis in an easy way without any needs of sophisticated sample preparation protocol from the histopathologist. Keywords Mueller matrix · Polarimetry · Optical scanning microscopy · Imaging · Biomedical diagnosis

A. Le Gratiet () Université de Rennes, CNRS, Institut FOTON - UMR 6082, Lannion, France Nanoscopy and NIC@IIT, Istituto Italiano di Tecnologia, Via Enrico Melen, Genoa, Italy e-mail: [email protected] C. J. R. Sheppard Nanoscopy and NIC@IIT, Istituto Italiano di Tecnologia, Via Enrico Melen, Genoa, Italy Molecular Horizons, School of Chemistry and Molecular Biosciences, University of Wollongong, Wollongong, NSW, Australia A. Diaspro Nanoscopy and NIC@IIT, Istituto Italiano di Tecnologia, Via Enrico Melen, Genoa, Italy Dipartimento di Fisica, University of Genoa, Genoa, Italy © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Mazumder et al. (eds.), Optical Polarimetric Modalities for Biomedical Research, Biological and Medical Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-031-31852-8_5

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1 Introduction Over the last few decades, polarization-based imaging techniques have shown their efficiency in multiple areas showcasing the particular sensitivity to the medium structure and orientation (Huard, 1997; Snik et al., 2014). Especially, Mueller matrix (MM) microscopy are the most comprehensive imaging method as it provides the optical anisotropic properties, in amplitude and phase, of biological samples at the sub-micrometer scale summarized in a single .4 × 4 matrix. For this purpose, at least 16 intensity measurements must be performed for retrieving all the 16 real independent elements of the MM, named .mij , by adding the polarization states generator (PSG) and analyzer (PSA) to their existing optical paths appropriately (Mueller, 1948). As measuring the 16 elements is not as trivial as most of the conventional imaging techniques, the challenge is acquiring the full MM in a frame rate compatible with the PSG/PSA speed control. Added to this issue, such technique should respect the requirement imposed by the biomedical research, by means of visualizing and quantifying the optical properties of the specimen in real time, in vivo/in situ (Alali & Vitkin, 2015; Qi et al., 2017). To overcome these limitations, numerous various methods have been emerged based on either temporal or spectral polarization encoding and decoding. It results an expansion of MM microscopy methods during the past few years, explained by an improvement of the optical quality and speed achieved by the polarization devices (He et al., 2019). Thus, the experimentalist should always design the most suitable PSG/PSA solution depending on numerous factors such as the financial cost, the space allocated for the implementation of the method, and the speed requested (i.e., pixel- or frame-dwell time). First of all, the simplest and most common approach has been proposed by wide-field microscopy for developing MM microscopy imaging. The methodology consists of a sequential acquisition of at least 16 polarization-resolved intensity images using a charge coupled device (CCD) or a complementary metal–oxide–semiconductor (CMOS) camera of the sample for reconstructing the complete MM in just few seconds up to few minutes. Recent works have been developed snapshot MM microscopes based on the simultaneous encoding/decoding of the polarization states physically split in the plane of the sensor that/ is of great interest for biomedical diagnosis. This technique proposes to place a micro-polarizer array on the camera sensor. Each pixel of the camera is encoded by a linear polarization states encoded and the calculation through a cluster of pixels allowing the reconstruction of the MM coefficients by “super-pixel” in real time (Tyo et al., 2006). Nowadays, since this passive technique does not require any sophisticated numerical model or expansive optical features, it exists numerous commercial polarization-resolved camera, dedicated to remote sensing or wide-field imaging (Rankin et al., 2019; Kudenov et al., 2012; Hasegawa et al., 2017). Nevertheless, such microscopes still have limited performance for retrieving the whole 16 elements of the MM with a suitable signal-to-noise ratio. Indeed, the difficulty of displaying these polarimetric parameters in real time is still suffering on a long post-processing stage latency to compute the MM. Second, in an attempt

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to preserve the axial optical resolution through the illumination volume, the second approach consists of point-by-point SLM of the sample with a typical pixel-dwell time around .10μs. Particularly, in this chapter, we demonstrate the capability of this method for imaging localized contrasts based on the single optical and structural properties of the sample at the microscale. Thus, this technique is known to be a label-free method, and the contrast is based on the single interpretation of the light–matter interaction arisen from the sample optical fingerprint. We show that developing full MM in a scanning microscopy configuration offers the advantage to be easily implementing into commercial setups giving the capability toward multimodal imaging. First, we come back on the parameters of interest MM is dedicated for, and the problem of using polarization optics in such technique in transmission and reflection mode. Then, we discuss on how to develop such technique for scanning configuration. Furthermore, we present different applications of this technique and demonstrated its performances from the earliest works to the most recent advances in SLM imaging for the biomedical researched.

2 Complete Mueller Matrix Measurements 2.1 Back to the Mueller Matrix Formalism In general, two optical modules compose MM polarimeters aiming to encode/decode the polarization states through the light–matter interaction. In one side, the PSG encodes the polarization states of the incoming light source (emitted by a lamp or a laser source), as described by the Stokes vector .Sin = [S0, S1, S2, S3]in , where S0 is the total collected light, S1, S2 are related to the linear horizontal/vertical, and +45.◦ /.−45.◦ polarization components and S3 describe the circular right/left one (Stokes, 1992). Their combinations provide numerous valuable information about the light, such as the Degree of Linear Polarization (DOLP) and Circular (DOCP). In other side, the transformation of the polarized light after the sample is collected by a photodetector and decoded by the PSA describing the output Stokes vector .Sout = [S0, S1, S2, S3]out . In the literature, the PSA and the detector part are also referred as the polarization states detector (PSD). From .Sin to .Sout , the bridge is made by the MM of the sample, noted .[M], that describes how the polarization state of the input light changes upon interaction with the sample by Sout = [M].Sin .

.

(5.1)

Contrary to Jones formalism, a crucial advantage of dealing with Stokes parameters is that they are explicitly determined by measurable intensities rather than from the complex electric field that is difficult to describe turbid media (Ghosh & Vitkin, 2011; Li et al., 2022). To graphically display any possible polarization

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states of the light, a Euclidean space constructed by three standard orthogonal bases corresponding to the last three elements of a Stokes vector S1-S2-S3, referred to as Poincare sphere, is widely used (Brosseau, 1998). The fully polarized light constitutes a sphere with a radius 1, while vectors for partially polarized light are distributed within the sphere. By convention, the northern and southern poles correspond to RCP and LCP polarization states, respectively. The linear polarization states are located at the equator of the sphere, and any polarization evolving elsewhere is elliptical. In general, three fundamental polarization properties of matter can be attributed and extracted from the MM, namely, depolarization, diattenuation, and retardance (Lu & Chipman, 1996). First, the dichroism refers to a differential transmittance (or reflectance) of matter depending on the polarization states of the incident light. The physical parameter for measuring it is the diattenuation (D) corresponding to a scalar defined by a maximum and a minimum transmittance (or reflectance), .Tmax and .Tmin , respectively. It can be readily obtained from the first row of the Mueller matrix, and D is defined as D=

.

Tmax − Tmin , Tmax + Tmin

(5.2)

where Tmax = m00 +



.

Tmin = m00 −



.

m201 + m202 + m203

(5.3)

m201 + m202 + m203

(5.4)

with .m01 , .m02 refer to 0.◦ , 45.◦ linear D parameters, and .m03 represents circular D. Thus, the magnitude of diattenuation D is the length of the diattenuation vector D and ranges from 0 (no diattenuation) to 1 (perfect diattenuator). Second, in comparison to D that affects the amplitude component of the light, the birefringence, quantified by its retardance (R), may affect the phase component. Basically, it refers to the phase difference between two orthogonally polarized components of the light when propagating through some medium. Therefore, R is the effective rotation angle (in radians) determined from the 3D rotation matrix .MR by R = cos

.

−1



 T r(MR ) −1 . 2

(5.5)

As for D, R can be broken down into linear retardance and circular retardance. Third, depolarization refers to a process of loss in coherency of phase or amplitude of the components of light. Physically, depolarization could originate from the average effects of fast temporally, spatially, and/or spectrally fluctuations, which are normally related to disordered media such as turbid media and rough surfaces. A common way for describing its effects is the depolarization index .Pd , expressed as

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  3  i,j =0 m2 − m2 ij 00  .Pd = . 2 m00

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(5.6)

This index ranges between 0 and 1, from a perfect depolarizer to a pure deterministic medium.

2.2 Interpreting the Mueller Matrix The main challenge after measuring the whole MM is the interpretation of the physical quantities induced by the light–matter interaction. Beside the .mij linear combinations that provide a drastic increasing of information from the complete MM, numerous methods have been proposed during the past decade for separating polarimetric parameters from each other. The analysis of the c-vectors (coherence vectors) through the coherency matrix (Cloude’s coherency matrix) has shown its specific sensitivity for depolarizing samples (Cloude & Chipman, 1986). This also has the advantages of preserving the raw MM, without applying any mathematical filters contrary to many other methods. This parallel decomposition is based on a sum of four deterministic matrices, weighted by the strengths of components proportional to the eigenvalues (Gil, 2007). Analyzing the real and non-negative eigenvalues of the coherency matrix is an important step allowing for an evaluation of the physical realizability of the Mueller matrix and the determination of the distance from a pure depolarizing medium (Sheppard et al., 2018b,a). From the eigenvalues, it is possible to introduce the indices of polarimetric purity (IPPs), providing an easy and an extremely sensitive quantification of these effects (Van Eeckhout et al., 2018; Kupinski et al., 2018). The most common approach is the polar decomposition, based on modeling the propagation of the light through a successive arrangement of elementary optical features composed of a dichroic, a birefringent element, and a depolarizer. Numerous approaches have been emerged during the past decades, proposing of distinguishing the different decomposition families depending on the elementary optical features order, assisted nowadays by iterative or machine learning algorithms (Boulvert et al., 2009; Roa et al., 2021), such as the “reverse” decompositions (Ossikovski et al., 2007), the symmetric decomposition (Ossikovski, 2009), or the logarithmic decomposition (or differential) (Ossikovski, 2011). Among all these decomposition methods, the gold standard Lu–Chipman (LC) polar decomposition has proven to face the issue of modeling adequately biological system in a robust way (Lu & Chipman, 1996). In ellipsometry, another method proposes to group six real elementary properties into three complex pairs, labeled L, .L and C, separated into D and R (Jones, 1948; Azzam, 1978). Thus, the elementary polarization properties fully describe the polarimetric response of a continuous medium, depolarizing or not.

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Fig. 5.1 Mindmap resuming the tools available for dealing with MM. The interpretation of the MM is divided into three methods: (red) the decomposition and modeling of the MM, (green) the interpretation in terms of polarization states through the Stokes vector, and (blue) the conversion of the MM into the coherency matrix

However, the physical model to quantify all the polarimetric effects characterizing the structural organization of the non-labeled sample is an important issue and is strongly based on an priori knowledge of the sample. Additionally, multiplication of two matrices results in a Mueller matrix where, in general, each element depends on all of the elements of the original matrices. This means that interpretation of the Mueller matrix is not at all straightforward. Recently, another representation of the polarimetric changes has been proposed based on the extraction of the linear components of the MM for simulating the excitation light has a modulation, and converted into the phasor space (Le Gratiet et al., 2021). In order to resume all these methods when dealing with MM is required, a mindmap is proposed in Fig. 5.1.

2.3 Optical Scanning Microscopy Architecture In MM polarimetry, the imaging contrasts erase from the only linear optical response of the medium with the polarized light. It means that no high power

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laser source or extremely sensitive photodetectors are requested, which decreased drastically the cost and the complexity of polarization-resolved techniques. Adapted to a SLM architecture, the polarized light beam scanned the specimen by a diffraction-limited spot after reflections on galvanometric mirrors (GM). Then, the light is transmitted or reflected by the in-focus illuminated volume element of the specimen and is imaged (after a long journey across a lot of optical features) onto a single point detector, such as a photodiode or a photomultiplier. For MM SLM, the lateral resolution is simply approaching the diffraction limitation given by the objective numerical aperture expressed as Rlateral =

.

λ . 2.N A

(5.7)

An important point to keep in mind when the experimentalist deals with the polarized intensities is finding an adequate trade-off between light dose and a sufficient signal-to-noise ratio (SNR). Indeed, if temporal or spatial fluctuations of the specimen are short enough compared to the detector integration time, a high degree of polarization randomness can be introduced, leading to an artificial depolarization. Later in this chapter, the importance of this physical parameter in biomedical research is justified. We present the different configurations available from such a technique (Fig. 5.2), meaning in transmission and reflection modes. The transmission configuration is the easiest architecture, and the amplitude of D and R is related to the thickness of the sample due to the absorption. Consequently,

Fig. 5.2 Block diagram for implementing a general Mueller matrix (MM) polarimeter into a scanning laser microscopy (SLM) architecture: (a) in transmission and (b) in confocal reflection configuration. PSG: polarization states generator. Obj: microscope objective. GM: galvanometric mirrors. TL: tube lens. S: sample. BS: beamsplitter. P: pinhole. PSD: polarization states detector

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if the sample exhibits a complex three-dimensional (3D) organization, a high depolarization can be obtained. The reflection mode is based on measuring the exact backscattering sample of diffusive and thick samples, as it is performed in classical reflectometry, non-linear microscopy, or in OCT (Sheppard et al., 2022). However, MM is the only method able to provide a full understanding of scattering media since it offers the capability of decomposing it into a cascade of elementary optical layers. The simpler case is when the sample is approximated by an isotropic and homogeneous medium; the .Pd can be estimated in the whole volume, and the model is performed through Mie theory (Tuchin et al., 2006). If the degree of randomness increases, it becomes arduous of distinguishing the origin of the polarimetric signal, as it is commonly done in confocal microscopy, since it originates from an averaging and accumulation of single-layer polarimetric fingerprints. In parallel, for dealing with the spatial sectioning for 3D polarization imaging, the confocal mode uses an aperture slightly smaller in diameter than the Airy disc image and it is positioned in the image plane before the detector (Sheppard & Shotton, 1997). The ability of this method is to permit accurate non-invasive optical sectioning that makes confocal scanning microscopy so well-suited for the imaging and three-dimensional tomography of biological specimens. Another difficult aspect of reflectance MM imaging is the low signal collected back to the detector, and a solution can be placing a mirror right after the sample (Le Gratiet et al., 2015, 2019). In this situation, one has to take care the .π -dephasing for D and R after reflection if any quantification is requested. If the plane-polarized light is focused by a high numerical aperture (NA) lens, then the cross-components of polarization are produced upon focusing (Sheppard et al., 2009; Oldenbourg & Torok, 2019). The most general approach provides a full description of the beam-spot distribution in the whole 3D point-spread-function (PSF) volume, modeled by means of a 3x3 Hermitian polarization matrix that can be expanded in terms of Gell–Mann matrices, the nine independent coefficients being the generalized Stokes parameters (Sheppard et al., 2016). This complex numerical description results in a 9x9 MM, experimentally grinding to measure since the .mij have to be measured in the 3D independently (Sheppard et al., 2009). A direct experimental approach to remove any in-plane longitudinal polarization artifacts is to introduce a phase compensator, a vortex phase plate, or a polarization converter (Tang et al., 2010) before the objective lens (Rivet et al., 2015), or to reduce drastically the field of view (FOV) (Le Gratiet et al., 2018).

2.4 Calibration of the SLM Mueller Matrix The critical point in a SLM is to retrieve the full MM free from any polarization artifacts for each XY position of the GS in the FOV. Generally, the calibration steps consist in precisely determining the polarimetric contributions of: (1) the PSG and PSA blocks (alignments) and (2) the optical microscope features fingerprints before considering the sample (lenses and mirrors).

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First, the PSG and PSA are calibrated using dedicated methods according to its framework. Studying the conditioning of the measurement matrix is commonly used to optimize the polarimeter performance. Particularly, if a simple set of rotated polarizer and waveplate are used for encoding the polarization states, a simple model such as eigenvalue calibration method (ECM) (Compain et al., 1999). It is based on determining the trace of the matrices from simple reference optics giving a condition number (CN) that resumes the robustness against noise propagation through the whole system. The improvement in SLM has forced the development of ECM variants taking into account the double pass using a flat silver mirror (Lara & Dainty, 2006) in reflection, the influence of high numerical aperture objective or even the pinhole size in a confocal mode (Torok et al., 1998). However, calibrating the system for each pinhole size is required in a confocal mode increasing the number of measurements and the complexity of the experiments. With the improvement of the PSG/PSA speed, the PSG and PSA are more complex to model, for instance, when using electro-optics devices (Pockels cells or photoelastic modulators) (Kemp, 1969; Hunt & Huffman, 1973); thus the system is considered as a “black box” evaluated by a figure of merit named equally weighted variance (EWV) criterion where only the global experimental noise propagation is considered (Sabatke et al., 2000). Second, the microscope body is composed of a cascade of multiple optics (lenses, filters, and mirrors) that transform completely the generated polarization states. Thus, the measurement pixel-by-pixel of its optical properties could be easily performed by removing any sample in transmission or by placing a simple reflective mirror in reflection. The double-pass ECM method could also be used and provides simultaneously the MM of the encoding/decoding blocks and of the microscope body (Macias-Romero & Torok, 2012). Without any calibration numerical simulation, the sample MM is simply isolated by using matrices inversion based on Mueller/Stokes formalism, as follows: [Msample (x, y)] = [Mmes (x, y)].[Mmicro (x, y)]−1 ,

.

(5.8)

where .[Msample ], .[Mmicro ], and .[Mmes ] are the Mueller matrices of the sample, the microscope, and the whole system (microscope + sample).

3 Optical Scanning Imaging Architecture 3.1 Temporal Domain Before the 1980s, the very first development in polarization-resolved microscopy was of interest for its advantage of extracting the label-free contrasts. Due to the low technological requirement, the temporal control of the polarized light was the

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first approach for such instrumentation based on the use of rotating optical features or electro-optics modulators. After the 2000s, the only few first complete MM imaging polarimeters associated to a SLM configuration have been proposed, mostly for ophthalmology based on OCT imaging [44]. It allows the imaging of the full MM in reflection configuration using liquid crystal variable retarders (LCVRs) (Laude-Boulesteix et al., 2004). The transition time for LCVR, thus for the PSG/PSA, is typically tens of ms, so one order of magnitude slower than the pixel-dwell time required for SLM (few .μs). Fortunately, this limitation has been cut off by simply acquiring successive images with different polarization states by scanned frame. Practically, the faster PSG/PSA consisted in measuring 16 successive double-pass images with an exposure time of few seconds, resulting in a full MM acquisition in one minute. Another work proposed to completely automatize and despite it required 72 successive images polarization resolved, the full acquisition time decreased down to few s with 20 .μm lateral resolution (Twietmeyer et al., 2008). In 2005, the first confocal Mueller reflection microscope was developed for the retinal diagnosis (Lara & Dainty, 2006). The scheme is suggested to increase the polarization encoding/decoding speed rate allowing the highest number of measurements for improving optically the SNR. For this reason, the PSG used two Pockels Cells (PC) allowing the encoding of the polarization in few MHz per pixel. Another method consists of a transmission SLM using simple motorized optical devices as linear polarizer (LP) or waveplate (WP) (Mazumder et al., 2017). It allows the acquisition of only four images coded by four distinct polarization states (horizontal, vertical, 45.◦ , and right circular) sequentially. In an effort to speed up the decoding time, it has been coupled with a combination of multiple polarizationresolved detectors based on the division of amplitude (DoA) method (Azzam, 2008). Similarly, a similar approach has been extended in the reflection configuration (Le Gratiet et al., 2019). Thus, the overall time for getting the complete MM is around few seconds. However, the implementation of such a technique into multimodal system is spacy, and using multiple polarization optics leads to errors in aligning the axis possibly taken into account using ECM (Powell & Gruev, 2013). Nowadays, the multiple reflection optics used for this method, such as polarized beamsplitters or Fresnel rhombs, could be reduced in very miniature modules of few centimeters designing from metasurfaces (Intaravanne & Chen, 2020). A block diagram resuming this technique in transmission configuration is proposed in Fig. 5.3.

3.2 Spectral Domain The previous described approach is based on acquiring a set of sequential polarization-resolved frames and recombined it into a post-data process. Consequently, this approach is limited for any dynamic characterization for in vivo microscopy imaging.

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Fig. 5.3 (a) Block diagram of a typical MM SLM configuration based on the sequential encoding/decoding of the polarization states from Reference (Le Gratiet et al., 2019). (b) Schematic presenting the extraction of the MM images from the measured intensities images in the sequential approach. PSG: polarization states generator. PSA: polarization states analyzer. Obj: microscope objective. Cond: Condenser. GS: galvanometric scanner. TL: tube lens. S: sample. PMT: Photomultiplier tube. t: temporal polarization states generation. .I H , .I V , .I 45 , .I RCP : intensities collected at the generated horizontal, vertical, 45.◦ , and right circular polarization (RCP) polarized states

In wide-field microscopy imaging, the PSG/PSA speed has been drastically improved by analyzing the time variation of the intensity induced by cascade multiple electro-optics devices such as photoelastic modulators (PEMs) or PC triggered with the camera frame rate via a data acquisition (DAQ) board (Alali et al., 2016). Therefore, the collected signal is a channeled spectrum described by a Fourier series composed by numerous modulation frequencies. A FPGA could count the edges of each PEM modulation signal and lock when a unique phase between all the electro-optics modulators is occurring within a short time in a nanosecond timescale. Then, the FPGA sends a trigger to the CCD to gate the signal (in around few .μs) giving an overall image acquisition in approximately tens of ms. A less complex approach consists of dealing directly with the Fourier transform of such modulated signal where the complex amplitudes are linear combinations of the MM elements (Alenin & Tyo, 2014). In this method, the multiple frequencies are created from choosing electro-optics with separated working frequencies. Thus, the multiple of the first harmonics and the combined frequencies provide numerous equations for solving the whole MM. The detection is usually coupled with a lockin amplifier at the reference frequency of the PEM and improves the SNR at tens of kHz. To speed up the acquisition rate and the number of .mij accessible, common solutions are proposed to add another PEM in the PSA synchronized with the first one (Jellison et al., 1999). In recent works, this technique has been upgraded by dealing with 3 and 4 PEMs (Arteaga et al., 2012). The main advantage brought by

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adding multiple PEMs is that all the elements of the MM can be retrieved without any mechanical moving part. Thus, this experimental approach has been proven to be of interest for studying ultrafast conformational changes in biopolymers (Narushima & Okamoto, 2016; Arteaga et al., 2019). For such a technique, the acquisition speed has reached 100 .μs (10 kHz repetition rate), closer to the pixeldwell time from any GM. Recent works have proposed to adapt this technique with a pixel-by-pixel lock-in detection at the pixel-dwell time rate (100 kHz) in a SLM to study the circular dichroism (CD) emerged from the interaction with chiral biopolymers (Le Gratiet et al., 2018; Marongiu et al., 2020). Despite the last methods have been proven to be powerful for fast spectroscopy or even wide-field imaging, an emerging method for fast polarization encoding has recently emerged and is based on spectral coding of polarization (channeled spectropolarimeters) by using highly birefringent materials WPs (Oka et al., 2003). The principle is the parallelization of polarization states using the wavelength so that the polarimetric response of a sample can be calculated when using a singlechannel spectrum I(.ν), where .ν is the optical frequency. Each channeled spectrum I(.ν) is periodic and is composed of discrete frequencies from 0 to n.f0 (n an integer), multiples of the fundamental one f0. This last one depends on both the thickness e and the birefringence .n of the retarders by the relation f0 .ne/c, where c is the celerity of light in vacuum. Such polarimeters have the potential of conducting MM SLM thanks to their speed provided that the thickness ratio of the retarders is well-chosen (Oka et al., 2011). The first experimental snapshot Mueller polarimeter was based on spectral coding of polarization using a broad spectrum source (superluminescent diode), thick retarder plates, and a CCD-based spectrometer (Dubreuil et al., 2007). At this early stage, the device was developed in a non-imaging transmission configuration but upgraded for SLM polarizationresolved second harmonic generation (SHG) (Dubreuil et al., 2018). The acquisition rate of this approach is limited by only the spectrometer performances that can be high (hundreds of MHz). Then, inspired by OCT technology, the technique has been upgraded by using a wavelength-swept laser source, high-order retarders, and a single-channel detector (Le Gratiet et al., 2015), measuring the complete MM at few hundreds of kHz. The device uses a wavelength-swept source (SS) laser instead of the broad spectrum source and a photodiode instead of the spectrometer, which results in a much simpler optical setup as shown in Fig. 5.4a, and the PSG/PSA has been miniaturized in passive mechanical blocks with centimeter dimensions (Le Gratiet et al., 2016; Rivet et al., 2015).

3.3 Pros/Cons of the Different Mueller Matrix Approaches The typical performances and acquisition speed for the 16 MM images reached by the methods presented in this chapter have been reported in Fig. 5.5.

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Fig. 5.4 (a) Block diagram of a MM SLM based on the spectral encoding/decoding of the polarization states from Reference (Le Gratiet et al., 2016). (b) Schematic presenting the extraction of the MM images of the measured intensities images in the spectral approach. PSG: polarization states generator. PSA: polarization states analyzer. Reti: retarder. Obj: microscope objective. GS: galvanometric scanner. TL: tube lens. S: sample. PMT: photomultiplier tube. In the configuration, the sum stops at .n = 12 leading to 12 Fourier amplitudes in real and imaginary parts, giving finally 25 values used to retrieve the 16 Mueller elements simultaneously

4 Multimodal Mueller Matrix Imaging The ability of such MM paves the way of acquiring the full optical fingerprint of the sample simultaneously with other microscopy modalities. In the last section, we demonstrated that the main reason is due to its cost-less optical features needed to build a complete MM polarimeter, its compactness and versatility. Numerous recent works have been proposed to combine other SLM techniques, such as fluorescence, multiphotonic microscopy, or OCT. This could be of interest for: (1) multiplying the information available from the light–matter interaction providing by different imaging contrasts, (2) benefiting the advantage from other modality, such as confocal imaging, for improving MM microscopy, and (3) tracking the source of the label-free contrasts for thick objects where the polarimetric imaging modality gives only an average information of the scattering sample fingerprint through the PSF volume.

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Fig. 5.5 Tree diagram of evolutionary development of the complete MM SLM and methods. The diagram is divided for the sequential and spectral approaches according to the literature. LP: Linear Polarizer; WP: Waveplate; DoA: Division of Amplitude; LCVR: Liquid Crystal Variable Retarder; ECM: Eigenvalue Calibration Method

4.1 MM and Non-Linear SLM Modality It has been shown that the orientation of anisotropies can be imaged through a non-linear modality with the cost of multiplying the number of measurements, only available by numerous frames polarized-resolved acquisition. This information can be interesting for biomedical imaging since the presence of a pathology results in disorganizing the tissues. For reducing the number of frames and retrieving the whole MM directly at the single pixel level, a spectral encoding/decoding approach has been implemented in parallel with two-photon excitation fluorescence (TPEF) and second harmonic generation (SHG) SLM (Le Gratiet et al., 2016). The

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advantages of such approach have demonstrated its capability of comparing the linear and non-linear optical fingerprint localizing the structure of interest at the pixel level and having its local orientation of a sample simultaneously, at the pixeldwell time rate without any mechanical switch. This approach paves the way of measuring the dynamics of microscopic objects, even if it requires computational resources for extracting and filtering at the pixel level the whole MM from the unique channel spectra. Non-linear microscopy SLM presents the inconvenience for the users on the instrument cost, from the ultra-short laser source (usually Ti:Sa) to the whole microscope body, and provides some limitations in the optical low field of view ( N =1 sN for impure states. The 3D Stokes vector can also be expressed as the terms of the intensities of linear polarized lights at 0.◦ , 90.◦ , 45.◦ , .−45.◦ , and right- and left-handed circular polarized (RCP and LCP) lights for the signal propagating in x, y, and z directions of the Cartesian laboratory reference frame (Krouglov & Barzda, 2019): ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢  .s = ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

⎤

1 ◦ ◦ ◦ ◦ ◦ ◦ 6 (Iyz (0 ) + Iyz (90 ) + Ixz (0 ) + Ixz (90 ) + Ixy (0 ) + Ixy (90 ))⎥ ⎥ 1 ◦ ◦ ◦ ◦ ⎥ 3 (Iyz (0 ) − Iyz (90 ) + Ixz (0 ) − Ixz (90 )) ⎥ ◦ ◦ ⎥ Ixy (0 ) − Ixy (90 ) ⎥ ⎥ ◦ ◦ Ixy (45 ) − Ixy (−45 ) ⎥ ⎥. ◦ ◦ Iyz (45 ) − Iyz (−45 ) ⎥ ⎥ ◦ ◦ ⎥ Ixz (45 ) − Ixz (−45 )

Ixy (RCP ) − Ixy (LCP ) Iyz (RCP ) − Iyz (LCP ) Ixz (RCP ) − Ixz (LCP )

⎥ ⎥ ⎥ ⎦

(8.7) The subscripts in Eq. (8.7) indicate the indexes of the normal planes with respect to the beam propagation directions. Here we continue the derivation with the general case of SFG in mind. The interaction between pure polarization state of fundamental electric field components ˜ i = E˜ 0i exp[−i(k·r−ωi t +φi )] (with index .i = 1, 2) and the susceptibility tensor .E elements is described by the polarization vector as follows: Pi = χij k j (ω1 )k (ω2 ) = χiA  A (ω1 , ω2 ),

.

(8.8)

where .r is the propagation direction, .A = 1, 2,. . . , 9, and we use the contracted notation. The state vector is defined as follows:  A (ω1 , ω2 ) = j (ω1 ) ⊗ k (ω2 ) = (E˜ x (ω1 )E˜ x (ω2 ), E˜ x (ω1 )E˜ y (ω2 ), E˜ x (ω1 )E˜ z (ω2 ), .

E˜ y (ω1 )E˜ x (ω2 ), E˜ y (ω1 )E˜ y (ω2 ), E˜ y (ω1 )E˜ z (ω2 ), E˜ z (ω1 )E˜ x (ω2 ), E˜ z (ω1 )E˜ y (ω2 ), E˜ z (ω1 )E˜ z (ω2 ))T ,

(8.9)

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where T denotes conjugate transposed and .⊗ denotes the Kronecker product. The 9 × 9 coherency matrix is given by .(ω1 , ω2 ) ·  † (ω1 , ω2 ). To introduce the double Stokes vector, we need 81 base matrices .ηN (.N =0,1,. . . ,80) with the properties .T r(ηM ηN ) = 2δMN . The matrices can be found in Krouglov and Barzda (2019). The SFG intensity is .

∗ I ∝ |Pi |2 = χiA χiB  A  ∗B ,

.

(8.10)

and the coherency matrix of incoming light for pure state is ρ =  ·  †.

.

(8.11)

The double Stokes vector can be represented in the form: SN = T r(ρηN ) =  † ηN .

.

(8.12)

The number of components can be contracted to 36 for a degenerate double Stokes vector of SHG, but for a rotational covariant coherency matrix .C a full basis with 81 components has to be kept (Krouglov & Barzda, 2019). Equation (8.1) can be rewritten by the use of Eqs. (8.11) and (8.12) as follows: † λα  = MαN  † ηN .

.

(8.13)

By considering the .E˜ i = APi as the electric field of outgoing radiation that is proportional to the polarization vector, Eq. (8.2) becomes ⎡

⎤ χxB  B  . = A ⎣χyB  B ⎦ , χzB  B

(8.14)

and substituting Eq. (8.14) in Eq. (8.13) results in ∗ A2 χiB  ∗B (λα )ij χj A  A = MαN  ∗B (ηN )BA  A .

.

(8.15)

This equation holds for any functions . ∗B and . A , and therefore, ∗ A2 χiB (λα )ij χj A = MαN (ηN )BA .

.

(8.16)

Since .T r(ηM ηN ) = 2δMN , multiplying Eq. (8.16) by .(ηM )AB gives MαN =

.

and in the matrix form

1 2 ∗ A χiB (λα )ij χj A (ηN )AB 2

(8.17)

8 Polarization-Resolved Nonlinear Optical Microscopy

MαN =

.

1 2 A T r(λα χ ηN χ † ). 2

187

(8.18)

The nonlinear properties of the material under study are characterized by Mueller ∗ matrix. The .MαN can be obtained from measurements, and the product .χaA χbB is calculated from Eq. (8.18). These products help to study the ultrastructure of the material. By transforming the .9×81 Mueller matrix into a .27×27 square coherencylike matrix X and by considering different decompositions of the X matrix, it is possible to obtain nonlinear susceptibility tensors of the biological sample. The 3D polarimetry can be applied for nonlinear microscopy with high numerical aperture objectives and can be utilized in all polarization-sensitive nonlinear optical modalities. More details about 3D Stokes–Mueller polarimetry can be found in Krouglov and Barzda (2019).

4 Nonlinear 2D Polarimetric Microscopy Techniques The 2D polarimetry is often used in microscopy with moderate NA objectives. Since SHG is highly sensitive to the polarization, it is the most popular polarimetric nonlinear microscopy technique for studying biological structures. The theory of two-dimensional (2D) polarimetric SHG and THG microscopy techniques is reviewed in more detail in the following subsections.

4.1 Polarization-Sensitive SHG Microscopy Techniques The main goal in polarimetric nonlinear microscopy is to extract structural information about molecular organization in each focal volume of the imaged samples (Golaraei et al., 2019b; Chen et al., 2012; Plotnikov et al., 2006; Chu et al., 2004; Psilodimitrakopoulos et al., 2009; Stoller et al., 2002). In the case of SHG, the (2) ultrastructure is described by second-order susceptibility tensor elements (.χij k ). Various SHG polarimetry techniques have been used to reveal ultrastructure of biological samples (Golaraei et al., 2019b; Alizadeh et al., 2019a; Amat-Roldan et al., 2010; Golaraei et al., 2019a; Samim et al., 2015; Psilodimitrakopoulos et al., 2014). A complete Stokes–Mueller polarimetry in 2D can extract complexvalued measurable nonlinear susceptibility tensor components (Golaraei et al., 2019a; Samim et al., 2015, 2016a). The reduced polarimetry techniques may employ linear incident polarization states (Alizadeh et al., 2019b; Chu et al., 2004; Psilodimitrakopoulos et al., 2009; Amat-Roldan et al., 2010) or incident and outgoing linear polarizations (Golaraei et al., 2019b; Tuer et al., 2012; Golaraei et al., 2014; Tokarz et al., 2015b, 2020; Tuer et al., 2011). Circular polarization states are also used for the in-image-plane orientation independent measurements, revealing the susceptibility ratios (Alizadeh et al., 2019a; Psilodimitrakopoulos

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et al., 2014; Golaraei et al., 2020a). In this section, different 2D polarimetric SHG techniques are briefly described.

4.1.1

2D Double Stokes–Mueller Polarimetric SHG Microscopy

2D double Stokes–Mueller polarimetry (DSMP) is a polarimetric technique for obtaining all possible polarization information with the smallest number of measurements and without using prior symmetry assumptions on the investigated structure (Samim et al., 2015, 2016a). For the focusing objectives with .NA ≤ 0.8, the polarization orientations of the focused incoming laser beam remain in the image plane to a good extent; therefore, a plane-wave approximation can be considered (Sandkuijl et al., 2013). In this situation, 2D polarimetry, such as DSMP, can be performed, and six complex-valued laboratory frame .χij(2)k tensor components can be extracted. Similar to 3D polarimetry (see Eq. (8.1)), the polarization of fundamental and SHG beams is described by the double Stokes vector, S, and the Stokes vector, .s  , respectively. These two vectors are related by the double Mueller matrix .M as it is shown by Eq. (8.1). The .M matrix for SHG can be characterized by measuring 36 (2) different polarization states. The complex susceptibility tensor elements of .χxxx , (2) (2) (2) (2) (2) .χxzz ,.χxxz ,.χzxx ,.χzzz , and .χzxz can be obtained by DSMP technique. In order to measure these tensor elements, the polarization state generator (PSG) can be used to produce five linear polarization states at 0.◦ , .±45.◦ , 90.◦ , 157.5.◦ along with two elliptical and two circularly polarization states. Also, for each PSG state, four polarization states of SHG signal have to be obtained. Those states are usually obtained with polarization state analyzer (PSA). The PSA measurements include 0.◦ , .±45.◦ , 90.◦ linear polarizations and two circular polarizations. The polarization states can be controlled, for example, by implementing a half-wave plate (HWP) and a quarter-wave plate (QWP) in PSG and PSA (Golaraei et al., 2016). In DSMP measurements, four Stokes parameters of the SHG signal are measured for each incoming polarization state. In these measurements, .S(ω) and .s  (2ω) are known for incoming polarization states and measured outgoing SHG Stokes components, respectively, and the Mueller matrix elements can be calculated from Eq. (8.1) (Samim et al., 2015, 2016a; Golaraei et al., 2019a). By assuming that the propagation direction is along Y axis of laboratory coordinate system, the Stokes elements can be expressed in terms of electric field components. The electric field of the SHG radiation can be formulated by a Jones vector, . , as follows: =

.

  E˜ X , E˜ 

(8.19)

Z

 e−i(kY −ωt) ei(φj ) is the electric field of the radiation and j = X or where .E˜ j = E0j Z. The coherency matrix, .C , is

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189

   ∗  E ˜ ∗  E˜ X E˜ X  E˜ X Z , .C  =  ·  = E˜  E˜ ∗  E˜  E˜ ∗  †

Z

X

Z

(8.20)

Z

where prime denotes for the SHG radiation. The Stokes parameters for a signal can be obtained using the following equation: sγ = T r(C τγ ) =  † τγ ,

.

(8.21)

where .γ = 0, 1, 2, and 3 and .τγ represent the four .2 × 2 Pauli matrices (Samim et al., 2015). The SHG Stokes vector is as follows: ⎡  ⎤ ⎡ E˜  E˜ ∗  + E˜  E˜ ∗  ⎤ s0 Z Z X X ˜  E˜ ∗  − E˜  E˜ ∗  ⎥  E ⎢s  ⎥ ⎢ ⎢ ⎥ Z Z X X . . ⎢ 1⎥ = ⎢ ∗  + E ˜  E˜ ∗  ⎥ ⎣s  ⎦ ⎣ E˜ Z E˜ X X Z ⎦ 2 E˜  E˜ ∗  − E˜  E˜ ∗  i s Z

3

X

X

(8.22)

Z

The components of .S(ω) are a function of the four linear Stokes components of the incoming laser beam. By using the coherency matrix for the fundamental radiation at frequency .ω, the elements of .S(ω) can be found. The polarization of the SHG radiation is defined as follows: (2)

(2)

Pi2ω = χij k Ej Ek = χiA A ,

.

(8.23)

where index .i = X or Z and index A is the contracted index representing XX, ZZ, XZ, or ZX, and . is written as follows: (ω, ω) =



.

j,k

2 ⎤ E˜ X E˜ j E˜ k = ⎣ E˜ Z2 ⎦ , 2E˜ X E˜ Z

⎡

(8.24)

and the coherency matrix for two interacting electric fields can be written as ⎡

⎤ 2E ˜ 2 E˜ ∗2  ˜ 2 E˜ ∗ E˜ ∗  ˜ ∗2   E 2 E E˜ X X Z X X Z X 2 ⎢ † ∗2  ∗E ˜∗ ⎥ .ρ = (ω, ω) ·  (ω, ω) = ⎣ , E˜ Z2 E˜ Z∗  2E˜ Z2 E˜ X E˜ Z2 E˜ X Z ⎦ 2 2 ∗ ∗ ∗ ∗ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ 2EX EZ EX  2EX EZ EZ  4EX EZ EX EZ  (8.25) and the double Stokes vector is SN = T r(ρλN ) = ρAB (λN )BA = A B∗ (λN )BA =  † λN ,

.

(8.26)

where .N = 1. . . 9 and .λN are the Gell–Mann matrices (Samim et al., 2015; Krouglov & Barzda, 2019). Now the double Stokes vector expression in terms of the linear Stokes parameters of the fundamental radiation is

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⎡ ⎤ ⎤ ⎡ ⎡ ⎤ 1 2 2 − s2) 2 E ∗2  + E 2 E ∗2  + 4E E E ∗ E ∗ ) (3s (E X Z X Z S1 X X Z Z 1 ⎥ ⎢ 3 ⎥ ⎢ 6 0 ⎢S2 ⎥ ⎢ 1 ⎥ ⎥ ⎢ 1 2 ∗2 2 ∗2 ∗ ∗ 2 ⎢ ⎥ ⎢ 3 (EX EX  + EZ EZ  − 8EX EZ EX EZ )⎥ ⎢ 12 (5s1 − 3s02 )⎥ ⎢S ⎥ ⎢ ⎥ ⎥ ⎢ 2 E ∗2  − E 2 E ∗2  ⎢ 3⎥ ⎢ ⎥ ⎢ ⎥ −s0 s1 EX ⎢S ⎥ ⎢ ⎥ ⎢ ⎥ X Z Z ⎢ ⎢ 4⎥ ⎢ ⎥ ⎥ 1 2 2 ∗2 2 ∗2 2 EX EZ  + EZ EX  ⎢ ⎥ ⎢ ⎥ ⎢ 2 (s2 − s3 ) ⎥ . ⎢S5 ⎥ = ⎢ ⎥. ⎥=⎢ 2 ∗ ∗ ∗2 2(EZ EX EZ  + EX EZ EZ ) ⎢ ⎥ ⎢ ⎥ ⎢ s2 (s1 + s0 ) ⎥ ⎢S6 ⎥ ⎢ ⎥ ⎥ ⎢ 2 ∗ ∗ ∗2 ⎢ ⎥ ⎢ ⎥ ⎢ −s2 (s1 − s0 ) ⎥ 2(EX EX EZ  + EX EZ EX ) ⎢ ⎢S7 ⎥ ⎢ ⎥ ⎥ 2 E ∗2  − E 2 E ∗2 )i ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ −s2 s3 (EX Z Z X ⎢ ⎥ ⎥ ⎣S8 ⎦ ⎢ 2 ∗ ∗ ∗2 ⎣ ⎣ ⎦ s3 (s1 + s0 ) ⎦ 2(EZ EX EZ  − EX EZ EZ )i S9 2 E ∗ E ∗  − E E E ∗2 )i s3 (s1 − s0 ) 2(EX X Z X X Z (8.27) After substituting the linear and nonlinear Stokes vector expressions in Eq. (8.1), the Double Mueller matrix .M can be extracted:   τγ   = Mγ N  † λN . †

.

(8.28)

Using Eqs. (8.20) and (8.23), the .  matrix can be rewritten as follows:   (2) χXA A . = , (2) χZA A 

(8.29)

and substituting Eq. (8.29) in Eq. (8.28) results in (2)∗

χaA A∗ (τγ )ab χbB B  = Mγ N A∗ (λN )AB B ,

.

(2)

(8.30)

where a and b indicate X or Z as the outgoing polarization orientations. The double Mueller matrix components can be written as Mγ N =

.

1 T r(τγ χ (2) λN χ †(2) ). 2

(8.31)

The double Mueller matrix elements depend on the sample structure and the 3D orientation of the sample. The dependency of Mueller matrix on the sample structure can be expressed as M = T Xrec H−1 ,

.

(8.32)

where .T is a .4 × 4 matrix containing vectorized Pauli matrices as rows, and .H is a .9 × 9 matrix containing vectorized second-order Gell–Mann matrices as rows, which do not depend on the sample or the experimental setup, and hence, they only need to be calculated once for SHG (Samim et al., 2015). The .Xrec matrix is the second-order susceptibility product matrix that contains products of susceptibility tensor components and their complex conjugates and defined as (Samim et al., 2015; Golaraei et al., 2019a)

8 Polarization-Resolved Nonlinear Optical Microscopy

191 ∗

⎡

.

∗ χ χ∗ χ11 χ11 11 12 ⎢χ11 χ ∗ χ11 χ ∗ 21 22 =⎢ ⎣χ21 χ ∗ χ21 χ ∗ 11 12 ∗ χ χ∗ χ21 χ21 21 22

∗ χ11 χ13 ∗ χ11 χ23 ∗ χ21 χ13 ∗ χ21 χ23

∗ χ12 χ11 ∗ χ12 χ21 ∗ χ22 χ11 ∗ χ22 χ21

∗ χ12 χ12 ∗ χ12 χ22 ∗ χ22 χ12 ∗ χ22 χ22

∗ χ12 χ13 ∗ χ12 χ23 ∗ χ22 χ13 ∗ χ22 χ23

Xrec = χ 2 ⊗ χ 2  ∗ χ χ∗ χ χ∗ ⎤ χ13 χ11 13 12 13 13 ∗ χ χ∗ χ χ∗ ⎥ χ13 χ21 13 22 13 23 ⎥ ∗ χ χ∗ χ χ∗ ⎦ , χ23 χ11 23 12 23 13 ∗ χ χ∗ χ χ∗ χ23 χ21 23 22 23 23 (8.33)

where the indices 1, 2, 3 are contracted notation for the second-order susceptibility (2) .χ iA as follows: .

jk : XX ZZ XZ, ZX . A: 1 2 3

(8.34)

An ensemble average is assumed for each element of .Xrec matrix, and it can be obtained as follows: Xrec = T −1 M H.

(8.35)

.

By reshaping .Xrec to a 6.×6 coherency matrix, X, we get ∗ χ χ∗ · · · χ χ∗ ⎤ χ11 χ11 11 12 11 23 ⎢χ12 χ ∗ χ12 χ ∗ · · · χ12 χ ∗ ⎥ 11 12 23 ⎥ , .X = ⎢ ⎦ ⎣ ··· ∗ ∗ ∗ χ23 χ11 χ23 χ12 · · · χ23 χ23

⎡

(8.36)

and by assuming that one of the .χ elements is real and positive: ∗ 2 X11 = χ11 χ11 = χ11 ⇒ χ11 =



.

X11

(8.37)

and χ12 =

.

4.1.2

X12 X13 , χ13 = ,··· χ11 χ11

(8.38)

PIPO SHG Microscopy

Polarization-in polarization-out (PIPO) microscopy is a reduced 2D polarimetric SHG microscopy technique. In PIPO microscopy, the incoming fundamental radiation is a linear polarization oriented at different orientations, and the linearly polarized SHG response is detected after passing the signal through a linear analyzer oriented at different angles. The PIPO microscope employs eight incident linear polarizations at orientations from 0 to 157.5.◦ with respect to the Z laboratory

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axis by steps of 22.5.◦ . The SHG signal is detected after passing through the analyzer oriented at eight different orientations from the Z laboratory coordinate axis similarly to the incoming polarization orientations. The SHG intensity obtained with PIPO measurements for each pixel containing C.6 symmetry nonlinear material is as follows (Golaraei et al., 2019b): I ∝A2 |K sin(φ − δ) sin 2(θ − δ) + cos(φ − δ) sin2 (θ − δ) .

+ R cos(φ − δ) cos2 (θ − δ)

(8.39)

+ C exp (i) cos(θ − δ) sin(θ − φ))|2 , where .K = (2)

χzzz

(2) χzxx

(2)

χxxz

(2)

χzxx

and .K = 1 is assumed for off-resonance excitation conditions, .R =

is the achiral susceptibility ratio, .C =

(2)

χxyz

(2)

χzxx

is the chiral susceptibility ratio, .δ is

the in-image-plane effective orientation angle of the fibers, .θ is the incoming linear polarization orientation angle, and .φ is the outgoing linear polarization orientation angle. The chiral susceptibility is assumed to be complex-valued with a phase retardancy . between achiral and chiral susceptibility components (Golaraei et al., (2) 2019a; Schmeltz et al., 2020; Abramavicius et al., 2021). A contains .χzxx . The sample plane is located in the XZ plane of the laboratory coordinate system, and Y is the beam propagation direction. The molecular coordinate system of the fiber has z axis along the fiber axis, and x, y perpendicular to the fiber. The prime of the susceptibility elements indicates the implicit dependence on the out-of-plane tilt angle .α and can be expressed in terms of the susceptibility tensor elements in the molecular frame as follows (Golaraei et al., 2019b):    (2)  χzzz   cos2 (α) + 3 sin2 (α) .R =  (8.40)  (2)  χzxx     (2)  χxyz   sin (α) .C =   (2)  χzxx 

A= 

.

   (2)  ab χzxx  cos (α) (a cos (α))2 + (b sin (α))2

(8.41)

(8.42)

where a and b denote semi-major and semi-minor axial width of the focal volume spheroid. By fitting the intensity equation (see Eq. (8.39)) in each pixel R and C ratios along with fiber orientation, .δ can be obtained. PIPO microscopy is a powerful and robust polarimetric nonlinear microscopy technique that has been used to study various biological and organic structures

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(Golaraei et al., 2014; Tokarz et al., 2015b, 2020, 2019; Burke et al., 2017; Pleckaitis et al., 2022). The only drawback of PIPO microscopy is its acquisition time that takes .∼20 min per imaged area to do the measurement that is a long time for in vivo measurements (Cisek et al., 2021). Also, analyzing the PIPO measurement data with conventional fitting methods requires a lengthy data processing. Furthermore, the PIPO microscopy is applied for forward direction, and applying it for backward imaging needs additional calibration of optical elements, such as dichroic mirror, for PSG and PSA. This technique is powerful for analyzing histopathology slides for cancer diagnostics (Golaraei et al., 2014; Tokarz et al., 2015b, 2020, 2019; Burke et al., 2017; Golaraei et al., 2020b, 2016).

4.1.3

pSHG Microscopy

Polarization-sensitive SHG (pSHG) microscopy is another reduced 2D polarimetric nonlinear microscopy approach that uses only incident linear polarization states and is able to extract .δ and R ratio in each pixel of the image. Various biological samples have been studied by pSHG microscopy (Rao et al., 2009b,a; Freund et al., 1986; Plotnikov et al., 2006; Odin et al., 2009; Psilodimitrakopoulos et al., 2010; Tiaho et al., 2007; Alizadeh et al., 2019b; Odin et al., 2008; Chen et al., 2009). It is assumed that the sample includes SHG active supramolecular assembly with cylindrical symmetry of group C.6 and the Kleinman symmetry condition is valid. By exciting the sample with a linearly polarized beam at .θ with respect to the laboratory frame axis, the intensity of the SHG signal follows the equation (Psilodimitrakopoulos et al., 2009; Alizadeh et al., 2019a,b): ISH G = a0 + a2 cos 2(δ − θ ) + a4 cos 4(δ − θ ),

.

(8.43)

where .δ is the fiber orientation in the image plane and coefficients a.0 , a.2 , and a.4 are related to R ratio and .δ. The pSHG measurement can use excitation light along 9 different polarization directions in steps of 20.◦ (from 0.◦ to 160.◦ ). The analyzer in front of the PMT is removed for pSHG measurements and the whole intensity is detected. After fitting with Eq. (8.43), the R ratio and .δ can be extracted for each pixel of the image. Similar to PIPO microscopy, fitting the intensity equation is a time-consuming process (for example .∼6 hours for a 512.×512 pixel frame (Amat-Roldan et al., 2010)) in pSHG microscopy. Instead of fitting, there is an alternative data analyzing method based on Fourier transform (FT) that reduces the data analyzing time to several seconds in pSHG microscopy (Amat-Roldan et al., 2010). Taking FT of Eq. (8.43) over the polarization orientation angle .θ results in i() = a0 D(0) + a2 exp(i2δ)D(1 − ) + a4 exp(i4δ)D(2 − ) + c.c.,

.

(8.44)

where .D is the Kronecker delta, . is the spatial frequency in the Fourier domain, and c.c. indicates the complex conjugate. The biophysically relevant parameters R

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and .δ can be calculated directly from Eq. (8.44) as follows (Alizadeh et al., 2019a; Amat-Roldan et al., 2010; Lombardo et al., 2015): δ = arg[a2 exp(i2δ)]

.

(8.45)

and  R=

.

a0 + a2 + a4 . a0 − a2 + a4

(8.46)

The pSHG microscopy is faster than PIPO microscopy, but PIPO measurements provide more ultrastructural information about the sample including the C ratio. We will compare the results of PIPO and pSHG measurements using a numerical simulation at the end of this chapter.

4.1.4

SS-pSHG Microscopy

One of the main goals of nonlinear microscopy is a fast polarimetric imaging related to the clinical applications and in vivo monitoring of biological samples. Therefore, fast imaging of molecular changes with high temporal resolution and label-free conditions are essential for achieving in vivo investigations. Although the FT analysis in pSHG increased the speed of polarimetric SHG measurements, but scanning with several linear polarizations requires for the sample to remain stationary during the measurements (usually with the help of anesthesia for in vivo imaging (Psilodimitrakopoulos et al., 2009)) for .∼10 seconds in the fastest case (Psilodimitrakopoulos et al., 2014; Alizadeh et al., 2019a). One method to speed up the polarimetry measurement is using liquid crystal modulators that results in acquisition speed of 3 s (Lien et al., 2013). This speed is adequate for some in vivo applications, but there are still many biological processes that take place on a shorter time scale. Another technique to speed up the acquisition time in polarimetric SHG microscopy is to excite the sample with a single-shot circular polarization and to detect the SHG signal simultaneously into three channels containing differently oriented linear analyzers (Alizadeh et al., 2019a; Psilodimitrakopoulos et al., 2014). The circular polarization excites all polarization orientations at once, and an elliptical SHG signal is generated. The orientation of main axis of the ellipse can be used for extracting .δ, and the ellipticity can be retrieved, which is related to the susceptibility ratio R. The SS-pSHG technique is an order of magnitude faster than pSHG technique. The intensity of the elliptically polarized SHG signal after passing through the analyzer is expressed as follows (Alizadeh et al., 2019a; Psilodimitrakopoulos et al., 2014):   (2) 2  1 χzzz 2 ISH G ∝ E02 sin2 (φ − δ) + − 1 cos (δ − φ) , (2) 4 χzxx

.

(8.47)

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where .E02 is the incoming electric field amplitude. The ellipticity of the polarization is determined by the term . 12 (

(2)

χzzz

(2)

χzxx

− 1) (Psilodimitrakopoulos et al., 2014). This term

includes the susceptibility components ratio R. For the biological structures with R < 3 such as collagen (Golaraei et al., 2019b; Tuer et al., 2012; Stoller et al., 2002, 2003; Tiaho et al., 2007), the long axis of the ellipse is perpendicular to the axis of the cylindrical structure, while for the structure with .R > 3 such as Starch (Cisek et al., 2015, 2018) or meso-tetra (4-sulfonatophenyl) porphine (.TPPS4 ) aggregates (Pleckaitis et al., 2022; Alizadeh et al., 2022a), the long axis of the ellipse is parallel to the axis of the cylindrical structure. For .R = 3, a circular polarized SHG signal is generated. The ratio .R = 3 is a critical value, and it is referred to as magic angle in SHG microscopy literature, and it shows the maximum disorder in the structure (Simpson & Rowlen, 1999; Psilodimitrakopoulos et al., 2014; Alizadeh et al., 2022a). By setting the analyzers at .φ = 0◦ , .φ = 45◦ , and .φ = 90◦ and 90 0 45 acquiring corresponding intensities .ISH G , .ISH G , and .ISH G , the filament orientation in the image plane can be obtained from Eq. (8.47) as follows:

.

δ=

.

2I 45 − I 0 − I 90 1 arctan SH G0 SH G90 SH G , 2 ISH G − ISH G

and the R ratio can be calculated as  90 2 0 2 ISH G cos (δ) − ISH G sin (δ) .R = 1 ± 2 , 90 2 0 2 ISH G cos (δ) − ISH G sin (δ)

(8.48)

(8.49)

where the positive sign is used for .R > 1 (collagen and starch) and negative sign is used for .R < 1 (myosin in muscle) (Psilodimitrakopoulos et al., 2014). Note that a prior knowledge about the sample is needed for using this technique. Moreover, SSpSHG and pSHG techniques do not take into account birefringence and scattering effects and the out-of-image-plane fiber orientation in the sample.

4.1.5

SHGCD Microscopy

SHG circular dichroism (.SHGCD ) is another polarimetric nonlinear microscopy technique for revealing the chirality and ultrastructural properties of biological specimens. .SHGCD is defined as the normalized difference of the SHG signals when the sample is excited with LCP versus RCP polarized fundamental beam (Golaraei et al., 2019a; Schmeltz et al., 2020; Alizadeh et al., 2022b). In terms of Stokes vector component, .SHGCD is expressed as follows (Golaraei et al., 2020a; Mirsanaye et al., 2022): SHGCD = 2

.

s0LCP − s0RCP s0LCP + s0RCP

.

(8.50)

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SHGCD is a useful technique for revealing the out-of-image-plane orientation of structures and the chirality of sample under study (Alizadeh et al., 2022b; Schmeltz et al., 2020; Zhuo et al., 2017; Campbell & Campagnola, 2017). This effect comes (2) from the interaction between electric field with .χxyz of the sample and only shows up when the sample is tilted out of the image plane. It also shows that there are different chiral structures in the sample, and, therefore, they respond differently to the LCP and RCP incoming laser beam. It should be mentioned here that although .SHGCD is introduced as an individual polarimetric SHG microscopy technique, it can be calculated from DSMP measurements. Also, PIPO microscopy gives a good estimation of the out-of-image-plane orientation of the sample by calculating  C ratio. If complex-valued .χ (2) is assumed, the C ratio obtained with the linear polarization states (PIPO measurement) is actually .C cos(), while .SHGCD depends on .C sin(), where . is the retardancy between achiral and chiral susceptibility elements. .

4.1.6

Circular Anisotropy of Circular Dichroism Microscopy

Fast imaging of R ratio can be obtained with circular anisotropy of circular dichroism (.CACD ) measurements. It requires two circular incident polarizations like in .SHGCD measurement and in addition employs two outgoing circular polarization measurements. Therefore, fast dual-shot measurements can be implemented (Golaraei et al., 2020a). The expression for .CACD can be derived from SHG Stokes vector components (see Eq. (8.22)) as follows (Golaraei et al., 2020a): CACD = 2

.

s3LCP − s3RCP s0LCP + s0RCP

(8.51)

,

where the .s0LCP , .s0RCP , and .s3LCP , .s3RCP are the Stokes components corresponding to the LCP and RCP fundamental beam polarizations, respectively. The .CACD can be expressed in terms of R and C ratio (Golaraei et al., 2020a): CACD = 2

.

4R + 8C2 − 4 R − 2R + 8C2 + 5 2

.

(8.52)

Neglecting .C2 in Eq. (8.52) for the biological structures having a relatively small chiral susceptibility tensor components, or when the structures are in the image plane, results in an equation for R ratio in terms of .CACD :  1 2 ±2 − 1. .R = 1 + CACD (CACD )2

(8.53)

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If .C2 considered to be small, R ratio can be extracted from the measurements. When .SHGCD is small, in case of fibers oriented within the image plane, .CACD can be measured with just one circular incident polarization state and two orthogonal outgoing circular polarization states. In this case, R values can be obtained very quickly, rendering live measurements of R values (Golaraei et al., 2020a).

4.2 Polarimetric THG Microscopy 4.2.1

2D Triple Stokes–Mueller Polarimetric THG Microscopy

THG microscopy signal occurs at interfaces and is used for extracting unique structural information about the samples (Barad et al., 1997). Due to Gouy phase shift, the THG signal cannot be generated in the homogeneous media when focused beams are used (Barad et al., 1997; Boyd, 1980). Therefore, when symmetry of the focal volume is broken due to the presence of interfaces or sub-resolution structures that change locally the susceptibility or refractive index, the third harmonic signal is generated. Similarly to the case of SHG, applying polarimetry to THG allows to extract ultrastructural information about the samples. It is possible to use different polarimetry techniques in THG microscopy (Kontenis et al., 2017; Samim et al., 2016a,b). The theory of 3D NSMP, described briefly in Sect. 3, can be applied for polarimetric THG microscopy, which allows to extract .χ (3) tensor component values. For 2D triple Stokes–Mueller polarimetry (TSMP), the polarimetric measurements obtain the Stokes vector of outgoing THG radiation for each incoming laser polarization state from a complete set of polarization states described by the triple Stokes vector. Sixteen incoming polarization states are required to form an orthogonal basis. For example, seven linearly polarized (LP), two circularly polarized (LCP and RCP), and seven elliptically polarized √ (five rightand two left-handed, REP and LEP, respectively) all with ellipticity of . 2/2. The order of the states is as follows: 0.◦ , 90.◦ , 45.◦ , -45.◦ , RCP, LCP, .−22.5.◦ , REP (major axis at 90.◦ ), LEP (45.◦ ), 22.5.◦ , 67.5.◦ , REP2 (22.5.◦ ), LEP2 (90.◦ ), REP3 (45.◦ ), REP4 (0.◦ ), and REP5 (.−22.5.◦ ) (Kontenis et al., 2017). The relation between the outgoing THG Stokes vector .s  , the sample Mueller matrix .M , and the incoming triple Stokes vector S is given by Eq. (8.1). The linear Stokes vector .s  includes four components:     .s is the total intensity, while .s , .s , and .s give the differences in intensities between 0 1 2 3 ◦ the horizontal and vertical, 45. and .−45.◦ , and RCP and LCP polarization states, respectively (Kontenis et al., 2017). By extracting the sample Mueller matrix .M from Eq. (8.1), the .χij(3)kl components can be calculated. The 2D TSMP measurements performed on .C6 symmetry materials provide with (3) (3) (3) (3) (3) 6 unique molecular susceptibility components .χzzzz , .χxxxx , .χzzxx , .χxxzz , .χxyzz , and (3)

(3)

(3)

(3)

χxyyy , and when achiral cylindrical symmetry .C6v is assumed, .χzzzz , .χxxxx , .χzzxx

.

(3)

(3)

(3)

χxxzz components are obtained (Kontenis et al., 2017). If .χzzxx =.χxxzz is assumed,

.

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χzzxx

the two molecular ratios .RTHG1 =

(3) χxxxx

and .RTHG2 =

(3)

χzzzz

(3) χxxxx

characterize the

fibrillar structure. The THG signal can be generated at interfaces of isotropic materials. The (2) (3) (3) isotropic tensor susceptibility components are related as .χzzzz = χxxxx = 3χzzxx = (3) 3χxxzz (Boyd, 2020). Assuming fully polarized light, the outgoing Stokes vector of THG for isotropic case can be expressed as (Kontenis et al., 2017) 2 s  ∝ I03 pL2 χzzzz (1, s1 , s2 , s3 )T ,

.

(8.54)

where .si are Stokes components of laser beam, and .pL is the degree of linear polarization .pL2 =

s12 +s22 . s02

The outgoing Stokes vector components scale with

laser intensity cubed and depend on degree of linear polarization as well as the susceptibility .χzzzz . The THG signal in isotropic materials is not generated by circularly polarized laser beam. This phenomenon can be used to check the laser circular polarization state in the focus of microscope objective by loss of THG signal at the interface of isotropic materials.

4.2.2

PIPO THG Microscopy

PIPO THG microscopy can be employed to extract the third-order nonlinear optical susceptibility tensor ratios and the in-image-plane fiber orientation .δ in the microscopic samples (Tokarz et al., 2014b,a). The same set of incident and outgoing linear polarization states as PIPO SHG microscopy is needed to employ PIPO THG. The THG intensity equation for PIPO measurements is as follows (Tokarz et al., 2014b,a): I3ω ∝ | sin(φ − δ) sin(θ − δ)(cos2 (θ − δ)(3RTHG1 − 1) + 1) .

+ cos(φ − δ) cos(θ − δ)(3RTHG1 − cos2 (θ − δ)(2RTHG1 − RTHG2 ))|2 ,

where .RTHG1 =

(3)

χzzxx (3)

χxxxx

, .RTHG2 =

(8.55)

(3)

χzzzz (3)

χxxxx

, and the prime indicates that polarizer and

analyzer angles as well as the third-order nonlinear optical susceptibility ratios are defined with respect to the molecular z axis (see Fig. 8.2). PIPO THG has been used to obtain the molecular organization of .β-carotene in orange carrots (Tokarz et al., 2014b) and astaxanthin within oil bodies (Tokarz et al., 2014a). Since THG often gives contrast to structures different from SHG, applying THG polarimetry is beneficial for obtaining complementary information about the structural organization of the samples.

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5 Polarimetric Nonlinear Microscopy Parameters Several parameters related to the ultrastructure of biological tissues can be extracted using polarimetric nonlinear microscopy techniques. The 3D NSMP can extract all complex-valued susceptibility tensor components in the laboratory frame of reference. However, this requires multi-directional measurements with .9 × 9n polarization states, where .n = 2 is for three-wave mixing and .n = 3 is for four-wave mixing processes. For moderate NA objectives, it is sufficient to employ 2D NSMP polarimetry (Sandkuijl et al., 2013), which gives 6 complex-valued susceptibility components in laboratory coordinate system for SHG (Kontenis et al., 2016; Golaraei et al., 2019a) and 8 components for THG (Kontenis et al., 2017). When pure polarization states are assumed, the measured laboratory frame susceptibilities can be reduced to molecular susceptibilities via tensor rotation. The tensor rotation for cylindrical structures can be performed using two angles: the .δ angle describes in-image-plane rotation from Z laboratory axis to the projection of cylindrical axis onto the image plane, and the .α angle describes the tilt of cylindrical axis out of the image plane. The effective orientation angle .δ can be extracted directly from the polarimetric measurements. The .δ angle shows dominant in-image-plane orientation of fibrillar structure in each pixel of the image. The map of .δ orientation angles of the imaged area shows spatial distribution of the fibrillar structures, which is informative for studying spatial organization of fibers in a specimen. The tilt angle .α is not directly accessible with 2D polarimetric measurements. It is contained within the projected susceptibility tensor components onto the image plane and indicated by prime in the equations. The angle .α can be extracted by assuming molecular susceptibilities of the fibers. Alternatively, the molecular susceptibilities of the fibers can be obtained with polarimetric measurements at several sample orientations with different tilts from the image plane. Due to fibrillar material of biological specimens, a cylindrical .C6 symmetry can (2) (2) (2) be assumed with real susceptibilities .χzzz , .χzxx , .χxxz , and complex-valued chiral  (2) component .χxyz for SHG (Golaraei et al., 2019b). This renders real achiral R and K (2)

and complex chiral C ratios. The achiral susceptibility ratio, R=.

χzzz

(2)

χzxx

(which is also

called anisotropy parameter .ρ in the literature (Roth & Freund, 1979; Amat-Roldan et al., 2010; Lombardo et al., 2015; Alizadeh et al., 2019b)), is an ultrastructural parameter that many SHG polarimetric techniques can extract. R is the susceptibility ratio of the fiber projection onto the image plane. It is dependent on the molecular (2)

susceptibility ratio .

χzzz (2) χzxx

and the out-of-image-plane tilt angle .α, according to Eq.

(8.40). The physical meaning of R can be appreciated from the susceptibility indices showing the ratio corresponding to the second harmonic generation along the active cylindrical structure axis (or the projected fiber axis onto the image plane) in response to the incident linearly polarized laser beam parallel vs. perpendicular polarization orientations. This parameter is able to provide information about the ultrastructural organization on the fibrillar structure. The fibrillar biological

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structures have hierarchical organization comprising of elementary helical structures organized into fibrils and then into fibers that can assume different configurations, e.g., parallel, antiparallel, crossing in 2D and 3D in the focal volume. For a single fiber in the image plane, the R ratio corresponds to the molecular ratio. The high molecular ratio with .R >3 means that the nonlinear dipoles are aligned close to the fiber axis. This organization is observed in hydrated starch granules (Cisek et al., 2015, 2018) and .TPPS4 aggregates (Pleckaitis et al., 2022; Alizadeh et al., 2022a). The lower ratios (.R < 3) can be observed for collagen and myosin fibers, which shows that the nonlinear dipoles are tilted at some angle with respect to the fiber axis and have a cone structure around the axis. For example, modeling and measurements confirm that achiral contribution of type I collagen originates from a small tilt of methylene groups in the pyrrolidine rings of proline and hydroxyproline amino acid residues that are stabilized normal to the main axis of collagen molecule (Tuer et al., 2011; Rocha-Mendoza et al., 2007). Note that R ratio depends on the out-of-imageplane tilt angle of the fibrillar structures, which modifies the observed R values (see Eq. (8.40)). The R ratio increases with .α for structures with .R < 3 and decreases for structures with .R > 3 (Alizadeh et al., 2022a). .R = 3 is for isotropically oriented fibers for which susceptibility ratio . K = Chiral ratio C is the ratio of

(2) χxyz . (2) χzxx

(2)

χxxz (2) χzxx

= 1 is assumed.

, and it has a sinusoidal dependency on the

out-of-image-plane tilt angle .α (see Eq. (8.41)). The sign of C depends on the polarity and the orientation of fibrillar structures in the sample. C ratio is beneficial for reconstructing the 3D orientation of biological fibers in the focal volume of the nonlinear microscope. It should be mentioned here that not all polarimetric nonlinear microscopy techniques are able to extract C ratio and out-of-imageplane orientation. Only DSMP, PIPO, and .SHGCD can provide information about chirality and out-of-image-plane orientation. Note also that if complex-valued C ratio is considered with phase retardance . between the susceptibility components, polarimetry with linear polarizations, i.e., PIPO extracts C.cos() values, while circular polarizations such as .SHGCD provide with C.sin() values. The DSMP extracts complex values for all measurable susceptibility components; therefore, both the C ratio modulus and the . phase retardance between the components is obtained (Golaraei et al., 2019a). In the case of type I collagen, the NH and COgroups are approximately normal to the main axis of the triple helix and that the C-H bonds are mostly perpendicular to the main axis (Freund et al., 1986). SFG spectroscopy analysis of amide I band shows that the chiral effects in collagen, most likely, can be related to orientational chirality of amide harmonophores within individual collagen molecules (Reiser et al., 2012). The chiral contribution to the second-order optical nonlinearity in collagen fibrils may also originate from the helical arrangement of CO- groups around the main axis of collagen molecule (Rocha-Mendoza et al., 2007). For THG, .C6 symmetry provides with 6 unique molecular susceptibility compo(3) (3) (3) (3) (3) (3) nents .χzzzz , .χxxxx , .χzzxx , .χxxzz , .χxyzz , and .χxyyy . Achiral cylindrical symmetry

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201 (3)

C6v reduces the number of susceptibility components to 4 and includes .χzzzz , (3) (3) (3) (3) (3) .χxxxx , .χzzxx .χxxzz (Kontenis et al., 2017). With assumption of .χzzxx =.χxxzz , two .

molecular ratios can be measured .RTHG1 =

(3)

χzzxx

(3) χxxxx

and .RTHG2 =

(3)

χzzzz (3)

χxxxx

. Those ratios

describe the structure of material and can be obtained by TSMP and also by PIPO (3) measurements for THG (Tokarz et al., 2013, 2014a). If chiral susceptibilities .χxyzz (3)

(3)

(3)

(3)

(3)

(3)

and .χxyyy are small compared to .χxxxx , and .χzzzz = χxxxx = 3χzzxx = 3χxxzz , the cylindrical symmetry tensor reduces to isotropic case (Samim et al., 2016a). It means that for the isotropic materials .RTHG2 is approximately equal to .3RTHG1 (Tokarz et al., 2014a; Kontenis et al., 2017). In contrast, a well-oriented fibrillar (3) structure has dominant .χzzzz component with a secondary contribution from a (3) complex-valued chiral component .χxyzz (Tokarz et al., 2013, 2014a; Kontenis et al., 2017). Several parameters can also be extracted from Stokes measurements. Equation (8.22) shows that .s0 is the total intensity, .s1 is the intensity difference between linear polarization states at 0.◦ and 90.◦ , .s2 is the intensity difference between linear polarization states at 45.◦ and .−45.◦ , and .s3 is the intensity difference between LCP and RCP polarization states (Samim et al., 2015; Mazumder et al., 2012). From these measurements, the degree of polarization (DOP), the degree of linear polarization (DOLP), the degree of circular polarization (DOCP), and the anisotropy parameter r of the SHG signal (Mazumder et al., 2012), or the THG signal (Samim et al., 2016a), for each pixel of the image, can be defined as follows: DOP =

s12 + s22 + s32

.

s0

DOLP =

s12 + s22

.

DOCP =

.

r=

.

s0 |s3 | s0

2s  Ipar − Iperp =  1 , 3s0 − s1 Ipar + 2Iperp

(8.56)

(8.57)

(8.58)

(8.59)

Where .0 ≤ DOP ≤ 1 and indicates the polarization property of the nonlinear signal. .DOP = 1 refers to a perfectly polarized light, and .DOP = 0 shows a nonpolarized light. Similarly, .0 ≤ DOLP ≤ 1 and indicates the crystalline alignment of molecules parallel to the linear polarization states, and .0 ≤ DOCP ≤ 1 shows how effectively the molecules scatter the circularly polarized light within the focal volume. The anisotropy ratio .−0.5 ≤ r ≤ 1 represents the anisotropy of the linear polarization signals (Mazumder et al., 2012).

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6 Experimental Setups for Polarimetric Nonlinear Microscopy All nonlinear polarimetric measurement techniques mentioned in the Sects. 3 and 4 can be implemented in the same principle microscope setup by exchanging a few optical elements. Figure 8.2 shows a general setup for 2D NSMP microscopy. The femtosecond (fs) pulsed lasers often are used for nonlinear microscopy (Carriles et al., 2009). The laser beam is coupled into the microscope. The raster scanning of a sample is provided by a beam scanner usually comprised of a set of galvo mirrors. Polarization state generator (PSG) is inserted before the excitation objective. PSG is comprised of a linear polarizer (LP), a half-wave plate (HWP), and a quarterwave plate (QWP) and can set any required incident polarization of the laser beam. An excitation objective with NA.90%) material in otoconia (Brittain et al., 2022).

4 Conclusions and Outlook Polarization-resolved SHG microscopy has proven itself valuable in biomedical applications. Many research groups are currently looking toward improving polarization-resolved SHG microscopy techniques. For instance, several research groups have developed methods for rapid imaging and quick data analysis while preserving high measurement accuracy. For example, to reduce imaging time, liquid crystal or electro-optic modulators have been used (Dewalt et al., 2014; Dow et al., 2016; Lien et al., 2013; Reiser et al., 2017). Faster imaging could also be achieved by interleaving laser beams with different polarizations. Fourier techniques have also been applied for faster data analysis (Alizadeh et al., 2019; Mercatelli et al.,

9 Polarization-Resolved SHG Microscopy for Biomedical Applications

247

2020; Tsafas et al., 2020). Higher repetition rate pulsed lasers, quicker scanning mirrors such as spinning mirrors, or a wide-field imaging approach to expand the field of view can be used to improve imaging speeds (Zhao et al., 2019). Other improvements include the use of fewer input laser polarizations, such as in SMP-SHG which uses four polarizations in a PI-SHG setup. This technique was used to investigate the orientation of collagen fibers in ocular tissues (Ávila et al., 2017). Alternatively, polarization-resolved SHG analysis can be performed using a circularly polarized input laser polarization requiring a single scan (Alizadeh et al., 2019; Psilodimitrakopoulos et al., 2014). Many research groups are also using backward polarization-resolved SHG techniques paving the way to performing ultrastructural determination in vivo. When performing backward polarization-resolved SHG imaging, care must be taken to account for alterations of the linear polarization state of the laser due to the presence of a dichroic mirror (Chou et al., 2008). Care must also be taken to ensure that the polarimetric SHG response is conserved with sample depth. A conservation of polarimetric response for backward PI-SHG studies of bone was seen up to 70 μm deep (Pendleton et al., 2020); however, changes in the signature of the SHG signal with linear laser polarization angle were observed at a similar depth in tendon (Mansfield et al., 2008). The signature of the SHG signal with linear laser polarization angle can be preserved in thick tendon if optical clearing strategies are used such as treatment with 50% glycerol-phosphate buffered saline solution (Nadiarnykh & Campagnola, 2009) or by calibrating the polarization setup using a QWP and a HWP (Romijn et al., 2018). In order to use polarization-resolved SHG to differentiate between different biomedical tissues, caution should be given to sample preparation techniques, the quality of the polarization-resolved SHG images, and the specific image analysis methods used. For example, PI-SHG studies on skin tissue stained with hematoxylin and eosin (H&E) and unstained were also performed to assess the influence of H&E staining on the determination of ρ values. The ρ values were found to change indicate an average over molecular orientations. Similar to χ(2) , β is proportional to the square of imposed electric field and has a maximal value when the SHG-active molecules are parallel to the transition dipoles of the constituted molecules in the material. Thus, SHG can be enhanced when the incident polarization is parallel to molecular transition dipoles due to the highest coupling efficiency (Prasad, 2003). Additionally, SHG is generated by a coherent illumination source, like a pulse laser, and as a result, the intensity of SHG is proportional to N2 as opposed to N in the case of incoherent fluorescence. Due to the small scattering cross-section, the signal from a single SHG-active molecule is weak. However, the dense molecules in crystalline samples and the high photon density of ultrashort laser pulses can make up for the weak signal. Following Eq. (10.5), there are 3 × 3 × 3 = 27 χ(2) tensor elements for describing nonlinear couplings in the case of ω3 = ω1 + ω2 . Numerous elements are tedious to extract by experiments. Whereas due to multiple symmetry constraints of molecules and experimental configuration, lots of elements can be eliminated and the aggregation of independent elements to 10 according to the constraints of the characteristic of a measurable physical quantity, intrinsic permutation symmetry, full permutation symmetry (or energy conservation symmetry), and Kleinman symmetry that are all detailed in (Boyd, 2019). Notably, Kleinman symmetry is used where incident and SHG frequencies are distant from any resonant frequencies. The 10 independent elements are listed as (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) (2) based .χxxx , χyyy , χzzz , χxyy , χxzz , χyxx , χyzz , χzxx , χzyy , χxyz . To express χ on Kleinman symmetry, the effective second-order nonlinear coefficient, d, is specifically used for convenience (i.e., there is no relationship with the interacting frequencies). Thus, the contracted notation with numbers can be used to express the 10 χ(2) elements, as shown in Eq. (10.7). ⎡

⎤ ⎡ ⎤ xx xy xz 165 . [j, k] = ⎣ yx yy yz ⎦ = ⎣ 6 2 4 ⎦ = [l] ⇒ dij k = dil zx zy zz 543

(10.7)

In image analysis, χ(2) or d is conventionally used to explain optical nonlinearities when the Kleinman symmetry condition is valid, i.e., dijk = dikj , for the case of ω3 = ω1 + ω2 . The two parameters follow the equations of ⎧ (2) (2) ⎪ ⎨ Pi (ω3 ) = 2ε0 χij k (ω3 = ω1 + ω2 ) Ej (ω1 ) Ek (ω2 ) (2) . Pi (ω3 ) = 4ε0 dij k (ω3 = ω1 + ω2 ) Ej (ω1 ) Ek (ω2 ) . ⎪ ⎩ (2) dij k = 12 χij k

(10.8)

Therefore, the tensorial expression for second-order nonlinear polarization is

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⎡

⎤

Ex (ω1 ) Ex (ω2 ) ⎥ ⎡ ⎤ ⎡ ⎤⎢ Ey (ω1 ) Ey (ω2 ) ⎥ Px (2ω) d11 d12 d13 d14 d15 d16 ⎢ ⎢ ⎥ E E (ω ) (ω ) z 1 z 2 ⎢ ⎥, ⎣ ⎦ ⎣ ⎦ = 4 d21 d22 d23 d24 d25 d26 ⎢ . Py (2ω) ⎥ E + E E E (ω ) (ω ) (ω ) (ω ) z 1 y y z 2 ⎥ 2 1 ⎢ d31 d32 d33 d34 d35 d36 ⎣ Pz (2ω) Ex (ω1 ) Ez (ω2 ) + Ez (ω1 ) Ex (ω2 ) ⎦ Ex (ω1 ) Ey (ω2 ) + Ey (ω1 ) Ex (ω2 )

(10.9) while SHG polarization is ⎡

⎡

⎤ ⎡ Px (2ω) d11 d12 d13 d14 d15 . ⎣ Py (2ω) ⎦ = 2 ⎣ d21 d22 d23 d24 d25 d31 d32 d33 d34 d35 Pz (2ω)

⎤ Ex 2 (ω) ⎥ ⎤⎢ Ey 2 (ω) ⎥ d16 ⎢ ⎢ ⎥ 2 E (ω) ⎢ ⎥ z d26 ⎦ ⎢ ⎥ ⎢ 2Ey (ω) Ez (ω) ⎥ ⎥ d36 ⎢ ⎣ 2Ex (ω) Ez (ω) ⎦ 2Ex (ω) Ey (ω)

⎡

⎡

.

χ11 χ12 χ13 χ14 χ15 = ⎣ χ21 χ22 χ23 χ24 χ25 χ31 χ32 χ33 χ34 χ35

⎤ Ex 2 (ω) ⎥ ⎤⎢ Ey 2 (ω) ⎥ χ16 ⎢ ⎢ ⎥ 2 E (ω) ⎢ ⎥ z χ26 ⎦ ⎢ ⎥. ⎢ 2Ey (ω) Ez (ω) ⎥ ⎥ χ36 ⎢ ⎣ 2Ex (ω) Ez (ω) ⎦ 2Ex (ω) Ey (ω)

(10.10)

3 Quantitative Measurement of P-SHG 3.1 Theory for Conventional χ (2) Tensor Analysis According to Eq. (10.10), the induced SHG polarization changes in response to changes in the electric field. The χ(2) tensor, which is the central component of PSHG microscopy, connects them by encoding the molecular structure in χ(2) tensor elements. In tissue imaging, fibril collagen, articular cartilage, muscle myosin, and starch granules are the frequently discussed bio-tissues as they have wellaligned SHG-active molecules been proven to exhibit intense SHG in the past (Cox et al., 2003; Zhuo et al., 2010; Yeh et al., 2005; Plotnikov et al., 2006). Before image analysis, a generalized biophysical modal (Fig. 10.2a) defining the spatial coordinates is required, which assists to correlate the molecular frame (x’z’) with the laboratory frame (x-z) through a tensor transformation corresponding to a rotation angle θ 0 , i.e., the angle between the z-axis and the fibril. In this geometry, the laser propagation direction is along the y axis, the principle axis of the fibrillike molecule is on the z’ axis, and the interacted laser polarization, which lies in

10 Polarization-Resolved Second-Harmonic Generation for Tissue Imaging

267

Fig. 10.2 (a) A schematic diagram of the model for χ(2) tensor analysis displaying the fibril orientation relative to the laser polarization direction. (b) The model with a fibril tilt angle (the angle between the fibril and the x-z plane) and an analyzer at an angle ϕ with respect to the z-axis

the x-z plane (image plane), is rotated counterclockwise with an angle θ relative to the z-axis, α = (θ 0 – θ ) is the angle between the fibril axis and the direction of laser polarization. Thus, the magnitudes of electric field with projection onto the directions parallel and perpendicular to the fibril axis are Ez = cosα and Ex = sinα, respectively. A light blue pattern overlaid on the fibril-like molecule indicates that it is constituted by a helical structure with a pitch angle θ e (Leray et al., 2004). Because the focal volume of the excitation laser contains a great number of fibril-like molecules and the diffraction-limited resolution is unable to observe the ultrastructure on the molecular level, the measured χ(2) is an ensemble effect over these randomly oriented molecules in the cross-section of molecular packing that is at the scale much larger than the microfibrillar level. Therefore, the symmetry assumption for the SHG-active molecules is mostly modeled by cylindrical symmetry C6v to approximate the underlying hexagonal 6 mm symmetry or other similar geometrical configurations (Both et al., 2004; Chu et al., 2004; Tuer et al., 2012; Plotnikov et al., 2006). For more simplicity, some works further utilize the hypothesis of Kleinman symmetry (i.e., the χ(2) tensor is wavelength independent), and thus, the remaining tensor elements are χ31 (= χ15 ) and χ33 only. If the molecular structure is assumed to be hexagonal symmetry, the independent elements are χ14 , χ15 , χ31 , and χ33 . Once Kleinman symmetry holds for this case, χ15 = χ31 and χ14 = 0 returns to the result obtained under the assumption of cylindrical symmetry (Chu et al., 2004). In the following, the χ(2) tensor analysis is discussed by hypothesizing the molecular structure with cylindrical symmetry. In this case, the tensorial expression for SHG polarization is simplified into Eq. (10.11) in which only χ15 , χ31 , and χ33 are left in the χ(2) tensor. According to Eq. (10.11), the obtained polarization is shown as Eq. (10.12). The resulting SHG intensity ISHG proportional to the square of P(2) varying with α is given by Eq. (10.13), which is used to fit the polarization dependency on SHG images pixel by pixel and then to obtain information on both the fibril (planar) orientation and the susceptibility tensor ratios.

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⎡

⎡

⎤ ⎡ Px (2ω) 0 0 0 . ⎣ Py (2ω) ⎦ = ⎣ 0 0 0 Pz (2ω) χ31 χ31 χ33

⎤ Ex 2 (ω) ⎥ ⎤⎢ Ey 2 (ω) ⎥ 0 χ15 0 ⎢ ⎢ ⎥ 2 E (ω) ⎢ ⎥ z χ15 0 0 ⎦ ⎢ ⎥ ⎢ 2Ey (ω) Ez (ω) ⎥ ⎥ 0 0 0 ⎢ ⎣ 2Ex (ω) Ez (ω) ⎦ 2Ex (ω) Ey (ω)

(10.11)

⎧ ⎨ Px = 2χ15 Ex Ez = 2χ15 sin α cos α = χ15 sin 2α . Py = 0 ⎩ Pz = χ31 Ex 2 + χ33 Ez 2 = χ31 sin2 α + χ33 cos2 α

(10.12)

 2 2  χ33 χ15 sin 2α cos2 α + ISH G ∝ |Pz |2 + |Px |2 ∝ sin2 α + χ31 χ31

(10.13)

.

After χ(2) tensor analysis, the obtained ratios of χ33 /χ31 and χ15 /χ31 describe how SHG polarization correlates with the orientation and order of molecules. As distinct molecular structures potentially have dissimilar χ(2) ratios, P-SHG image contrast makes it possible to identify the localized structural inhomogeneities, which is difficult to do with just SHG intensity images (Chen et al., 2009). Compared with χ33 /χ31 , χ15 /χ31 is presented with the form of (sin2α)2 , and thus it is more sensitive to fluctuations (noise) in SHG intensity, which makes it less accurate to be determined and used for material characterization (Chen et al., 2009). By contrast, χ33 /χ31 (or χ33 /χ15 ) that defines the fiber’s axial polarizing effects (Williams et al., 2005) has been proven to be a sensitive signature used to discriminate between different molecular structures or fibrillar collagen types in the same specimen (Pinsard et al., 2019; Rouède et al., 2017; Chen et al., 2009; Tiaho et al., 2007; Psilodimitrakopoulos et al., 2009a; Su et al., 2011; Romijn et al., 2019), showing diagnostic value for the assessment on various pathological conditions related to the SHG-active architecture. As stated in Eq. (10.6), χ(2) is the consequence of a fibril-like molecule organized with the hyperpolarizability tensor β of the constituted molecules following a specific arrangement. Similarly, the relationship between χ(2) and β can be established through a transformation from the molecular to the laboratory coordinate systems. In addition, the azimuthal angle of the constituted molecules is randomly oriented in the x’-y’ plane with an angle γ with respect to the z’ axis. Through coherent summation of the individual constituted molecules, the relationship between χ(2) and β is represented as (Tiaho et al., 2007; Leray et al., 2004).  .

χ15

  χ33 = Nβ cos3 γ    .   = 12 Nβ cos γ sin2 γ = 12 Nβ cos γ  − cos3 γ

(10.14)

The definitions of N and the brackets are the same with Eq. (10.6). With χ33 /χ15 derived from Eq. (10.13), the orientation parameter D is written as below according to Eq. (10.14).

10 Polarization-Resolved Second-Harmonic Generation for Tissue Imaging

 3  cos γ χ33 /χ15 .D = = cos2 θe , = cos γ  2 + χ33 /χ15

269

(10.15)

where θ e is the effective orientation of the constituted molecules as well as the helical pitch angle of the fibril-like molecule. Notably, θ e originally defined in (Leray et al., 2004) is an effective angle corresponding to the orientation of dye molecules with maximum probability when the width of the orientation distribution function is very narrow. Similar to χ33 /χ31 or χ33 /χ15 , a distinct organization of SHG-active molecules showing the difference in D or θ e can also be used as a factor to distinguish between different molecular structures in the same specimen (Psilodimitrakopoulos et al., 2009a; Su et al., 2011). In addition, as D or θ e is an intrinsic property of fibrillar protein determined by the orientation of the constituted molecules, its deviation implying the degree of organization (orientation order) could be used for disease diagnosis concerning the structural disorders in the helices (Tiaho et al., 2007). A detailed discussion of the effective orientation angle and disorder can be found in (Leray et al., 2004). Notably, the derived θ e can be close to the data measured by x-ray diffraction, showing that P-SHG microscopy possesses the ability to obtain structural information at the nanoscale, which outperforms other diffraction-limited optical imaging techniques. Regarding the absence of fibril tilt angle in the biophysical model that would reduce the precision of the measured χ(2) ratios and the request to determine 3D molecular orientation, the following works have demonstrated the correlation between the tilt angle δ and χ(2) ratios. First, Erikson et al. (2007) simulated this phenomenon for the tensor elements of χ16 and χ21 in Type-I collagen corresponding to different δ in which the shape of polar plots is significantly different, as shown in Fig. 10.3. Notably, χ16 = χ15 , χ21 = χ31 and χ22 = χ33 for different coordinate definitions. It also claims that for most bio-tissues, it can assume δ is smaller than 10◦ because it only contributes a minor effect to χ(2) tensor elements, which can be neglected without producing much uncertainty in the result. However, introducing the effect of δ in frozen sectioned biopsies and malignant tissues is needed for χ(2) tensor analysis in which the fibril axis may be largely tilted out by the image plane during sample preparation. Later, a similar argument is presented by Chen et al. (2009) and described using Eq. (10.16). It manifests that χ33 /χ31 can still be used to separate different molecular structures in most biotissues but fails in the sample with larger angle deviation due to a non-negligible sectioning effect. 

χ33 χ31

 .



χ33 χ15

 = cos2 δ

.



 = sin2 δ

χ33 χ31 χ33 χ15



  χ15 + sin2 δ 2 + or χ31



  χ31 + cos2 δ 2 + . χ15

(10.16)

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Fig. 10.3 Pictorial representation of (a) d16 and (b) d22 contributions to SHG intensity when the fiber is tilted above the x-y plane using parallel polarizers. The angle is defined as the angle formed by the x-y plane and the fiber axis. (Figure and caption used with permission from Erikson et al., 2007)

With the biophysical model including δ proposed by (Erikson et al., 2007), Zhuo et al. (2010) performed the coordinate transformation as stated previously to establish a new χ(2) tensor and validated it to resolve the 3D molecular orientation of amylopectin molecules in starch granules. The SHG polarization varying with α and δ and the resulting SHG intensity is written by Eqs. (10.17) and (10.18), respectively. ⎧ ⎨ Px = χ15 cos δ sin 2α . P =0 ⎩ y Pz = χ31 cos δsin2 α + (χ31 + 2χ15 ) cos δsin2 δcos2 α + χ33 cos3 δcos2 α (10.17) ISH G ∝ |Pz |2 + |Px |2    χ31 χ31 2 . cos δsin α + + 2 cos δsin2 δcos2 α + ∝ χ χ 15 15

χ33 3 2 χ15 cos δcos α

2

+ (cos δ sin 2α)2 (10.18) δ is denoted as the angle of the fibril-like molecule as for x-z plane and the definition of α is the same as previously stated. Similarly, by analyzing the SHG polarization anisotropy with Eq. (10.18), the relevant χ(2) ratios as well as the orientation angle θ 0 on x-z plane can be determined. In addition, the tilt angle δ can be derived by analyzing the SHG variation along the y direction of an image stack, as shown in Fig. 10.4. As a result, the 3D molecular orientation of SHG-active molecules within a volume less than 1 fL is obtained. Similarly, the helical pitch angle of the fibril-

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Fig. 10.4 Graphical representation of depth dependence of SHG intensity (hollow rectangles) with 1 μm depth resolution, which enable to calculate the tilt angles δ of local amylopectin molecule (solid circles). Amylopectin’s full 3D orientation can be determined in a sub-fL volume. (Figure and caption used with permission from Zhuo et al., 2010)

like molecules can also be derived by Eq. (10.15). Assuming a constant density of amylopectin molecules within starch granules with amylopectin oriented in a radial layout from its hilum, this strategy makes the tilt angle the only significant factor determining SHG intensity along the y direction. However, it is not applicable to collagen fibrils for determining δ because its orientation in y direction is not the same way oriented with starch granules. Even so, it is a breakthrough to establish the dependency of SHG intensity on the relevant χ(2) ratios, 3D molecular orientation angle, as well as helical pitch angle. Moreover, using the simulation results, Romijn et al. (2019) showed that under the assumptions of cylindrical symmetry for collagen fibrils oriented in the same direction is incorrect to extract the χ33 /χ31 value of Type-II collagen caused birefringence of δ. Therefore, the actual value of χ33 /χ31 should correspond to the minimum value in the histogram of B/A when the fibrils are in-plane, which is in accordance with Eq. (10.16). A similar concept of conventional P-SHG microscopy but a dissimilar formula for extracting the structural parameters was proposed by the group of Prof. Sophie Brasselet at the Institut Fresnel, CNRS. The resulting SHG intensity based on a fourth-order dependence on α is represented as (Mansfield et al., 2019; Duboisset et al., 2012; Brasselet, 2011) ISH G (α) ∝ a0 + a2 cos 2α + b2 sin 2α + a4 cos 4α + b4 sin 4α.

.

(10.19)

The above coefficients can be grouped into amplitude and phase coefficients of the second (I2 , ϕ2 ) and fourth (I4 , ϕ4 ) order of symmetry, which is rewritten as ISH G (α) ∝ a0 + I2 cos 2 (α − ϕ2 ) + I4 cos 4 (α − ϕ4 ) ,

.

where

(10.20)

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 I2 =

.

a22 + b22 a0

, I4 =

 a42 + b42 a0

, ϕ2 = 0.5 tan

−1



b2 a2

 , ϕ4 = 0.25 tan

−1



 b4 . a4 (10.21)

(I2 , ϕ2 ) represent the anisotropic contribution to the SHG intensity in magnitude and orientation used to determine the modulation depth and its relative phase, respectively. On the other hand, (I4 , ϕ4 ) are the signatures of its more complex fourth-order dependence in magnitude and orientation. As these parameters are calculated from the angular distribution of individual transition dipoles in the image plane equivalent to molecules organized into a cone surface with an aperture angle (i.e., the same meaning with the effective orientation of the constituted molecules θ e as stated previously), they are associated with the structural organization of fibrous tissues and can be used to deduce the relevant χ(2) ratios (Deniset-Besseau et al., 2009; Odin et al., 2008a). For example, ϕ2 indicates the preferred orientation of fibrils, while I2 indicates the degree of orientation order of individual fibrils within the focal volume (Wang et al., 2021; Dora et al., 2012). Thus, a higher I2 shows a tighter arrangement of transition dipoles along the principal axis of the fibrillike molecule, thus providing a higher value of χ33 /χ31 . On the other hand, I4 is for discriminating between different shapes or surfaces and ϕ4 is related to tissue birefringence; however, they are outside the scope of this section and disregarded here. Following the model of Fig. 10.2a where the fibril lies in the x-z plane with cylindrical and Kleinman symmetry considerations, the relationship between χ33 /χ31 and I2 is given by Eq. (10.22), which is developed by the circular functions (Duboisset et al., 2012). Notably, the phase of the P-SHG modulation leading to ρ = ϕ2 = ϕ4 is assumed in this analysis. Consequently, (I2 , ϕ2 ) can be calculated pixel by pixel from the polarization-dependent SHG images. .

χ33 2 = χ31 tan2 I2 (θe )

(10.22)

In the generic model (Duboisset et al., 2012), a 2D molecular distribution derived from Fourier coefficients can be used to determine the molecular order and asymmetry of the distribution without the need to know the distribution in advance. Currently, various theories for conventional P-SHG microscopy have been proposed and validated in a wide array of applications such as the biophysical model proposed by Stoller et al. (2002; Patrick Christian et al., 2002) and orientation field SHG microscopy (Odin et al., 2008a, b). Although they are presented in different forms of formulas under specific hypotheses, the measured parameters based on the fundamental physics of P-SHG are the same.

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3.2 Theory for Polarization-In, Polarization-Out (PIPO) SHG Microscopy The theory of polarization-in, polarization-out (PIPO) SHG microscopy that accounts for δ is developed by the group of Prof. Virginijus Barzda at the Department of Physics, the University of Toronto, which is detailed in (Golaraei et al., 2019a, 2020; Tuer et al., 2011, 2012). Compared to conventional P-SHG microscopy, it further analyzes the polarization properties of SHG sorted by an analyzer placed before the detector. As it deals with 11 × 12 = 132 polarimetric combinations of incident polarization direction, θ , and the polarization direction of SHG, ϕ, it thus provides more structural information. The biophysical model used for image analysis is presented in Fig. 10.2b which contains a rotating analyzer at an angle ϕ with respect to the z-axis. Thus, under the cylindrical symmetry assumption, the SHG polarization is the same as Eq. (10.12), but the resulting SHG intensity is represented as ISH G ∝ |sin ϕPx + cos ϕPz |2     2 . χ15  χ33  2 2 cos ϕcos θ + sin ϕ sin 2θ + cos ϕsin θ . ∝ χ31 χ31

(10.23)

where  R=

.

χ33 χ31



 = 

χ33 χ31 χ33 χ31

 − 3 cos2 δcos2 θ0 + 3 χ33  = cos2 δ + 3sin2 δ χ31 − 3 cos2 δsin2 θ0 + 1

(10.24)

and (χ15 /χ31 ) = χ15 /χ31 = 1 by assuming Kleinman symmetry. Notably, the ratios with prime indicate that they are projected onto the x-z plane, while those without prime signify the values measured in the molecular frame that is freely oriented in 3D. Eq. (10.23) neglects the effect of tissue birefringence when the sample is a thin section. To further consider the birefringence effect in thick tissues, a phase delay term can be introduced in the electric field in z-direction and the corresponding SHG intensity can be found in (Gusachenko et al., 2010; Samim et al., 2014). In this framework, the R-ratio is orientation-dependent and is equivalent to Eq. (10.16) if the Kleinman symmetry condition is met. A higher R-ratio is anticipated if the fibril axis is oriented at an angle with respect to the image plane. Trabecular bone, cornea, and dermis examinations reveal the phenomenon. The reality is that it is the lowest for a perfect distribution where parallel-oriented collagen fibrils lying in the image plane, supporting the argument from the previous section. Furthermore, it is discovered that fibrils outside of the image plane are not lengthened during fixation, causing a significant shift in the R-favor ratios toward a higher value. Therefore, the R-ratio can be minimized when the sample is dissected along the fibril axis; whereas, it is higher when the sample is longitudinally cut (Tuer et al., 2012).

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Fig. 10.5 Characterization of the intervertebral disk in rat vertebrae section. (a) 3D visualization of intervertebral disk in which average fibril is shown as cylinders at each pixel. Calculated R-ratio is shown in blue (~1.45) and red (~1.95). (b) Images of H&E stained region. (c) Second-harmonic generation microscopy image. (d) Scanning electron microscope image of same region of intervertebral disk. Figure and caption used with permission from (Tuer et al., 2012)

In this theory, to quantify the orientation and order of SHG-active molecules in tissues, measures of the fibril distribution asymmetry, |A|, the weighted-average fibril orientation, , and degree of linear polarization (DOLP) showing how the linear polarization of SHG varies out from the sample (Golaraei et al., 2020; Tokarz et al., 2015, 2019) are usually employed. In the experiment, the R-ratio incorporated with the above factors can be derived from P-SHG images with pixel resolution. Importantly, with the information of θ 0 and δ for a single fibril (cylindrical rod) obtained from Eqs. (10.23) and (10.24), the 3D organization of collagen fibrils in a lamella of intervertebral disk can be reconstructed and visualized, as shown in Fig. 10.5, in which the blue (−20◦ for the x-z plane in average) and red (40◦ for the x-z plane in average) colors are registered according to the measured R-ratios from ~1.35 to ~1.65 for each voxel. It presents alternating stacked lamellae similar to the result observed with SEM images (Fig. 10.5d). In P-SHG imaging, the effect of molecular chirality could be ignored and the results can be interpreted using a model based on C6v symmetry. For fibrils lying in the image plane, the models based on C6 and C6v symmetry are indistinguishable. However, the chiroptical effect has a non-vanishing contribution to the SHG signal when δ = 0. Thus, the model for C6 symmetry could be a better fit to analyze the helical structure organized by active molecules. According to the above argument, the same research group extended the original model to a universal one based on C6 symmetry to extract the structural parameters as stated in the original model and the chiral susceptibility tensor ratio, χ14 /χ31 , as a new parameter related to the chiral structure of fibrils (Golaraei et al., 2019a; Tokarz et al., 2019). In this framework, the resulting SHG intensity is written by

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ISH G

.

275

   2  χ15   χ31 sin (ϕ − θ0 ) sin 2 (θ − θ0 ) + cos (ϕ − θ0 ) sin2 (θ − θ0 ) +      ∝     χ33 χ 2 14  χ cos (ϕ − θ0 ) cos (θ − θ0 ) + 2 χ31 cos (θ − θ0 ) sin (θ − ϕ)  31 (10.25)

where  C=

.

χ14 χ31



=

χ14 sin δ. χ31

(10.26)

Except (χ14 /χ31 ) , the definitions of the involved parameters in Eq. (10.25) are the same with Eqs. (10.23) and (10.24). Equation (10.26) shows that the chiroptical effect becomes more pronounced for fibrils tilted out of the image plane. The Cratio expresses the relative polarity of collagen fibrils inside the tissue and, like the R-ratio, is orientation dependent and can have a positive or negative value. When the fibrils lie in the image plane, C = 0, and the R-ratio returns to the molecular ratio χ33 /χ31 . Consequently, the 3D collagen fibril organization in tissues can be reconstructed by molecular chirality according to Eq. (10.25) and the orientationindependent χ(2) ratios in the molecular frame are determined. They analyzed the collagen in pig tendon at various sectioning angles to test the orientation-dependent characteristics extracted by PIPO SHG, and the assessed result presented in Fig. 10.6 is consistent with the model of Fig. 10.2b. Notably, the C-distributions in the scanned areas shown in Fig. 10.6d have both positive and negative values, which can be explained by the three possible reasons: (a) collagen may have the fibers containing both right- and left-handed enantiomer simultaneously existing in tissues, (b) since Eq. (10.26) is a function of sinδ, the orientation of collagen fibers that possess a positive or negative δ would change the sign of C, (c) opposite orientation (polarity) within the tendon tissues assembled by collagen fibers of the same chirality, which is more favored than the other two. Thus, by flipping the collagen fibers from 90◦ to −90◦ , Eqs. (10.24) and (10.26) demonstrate that the R-ratio remains unchanged, while the C-ratio changes the sign. Following the measurements of Fig. 10.6, the R- and C-ratio depending on δ are deduced and compared with the simulation result, as shown in Fig. 10.7. The absolute values of both ratios increase with the rise in δ. In general, the deviation in the experimental data is within the prediction by simulation. However, the deviation is large at δ = 90◦ , which ascribes to the fiber deviation at a large cut angle and the relatively weak SHG signal that provides a lower signal-to-noise ratio (SNR) lowering the precision. The fiber oriented orthogonal to the x-z plane should produce nearly zero SHG; however, in Fig. 10.6b, since 90◦ tilt angle still presents some noticeable SHG intensity, it implies that some of the fibers are tilted at an angle smaller than 90◦ , resulting in the measured χ(2) ratios being smaller than the predicted values. Consequently, the C-map offers the ultrastructural information of collagen fibers through the extraction of χ14 /χ31 and the relative polarity in tissues. By incorporating the R-ratio, an insight into the 3D orientation of collagen fibers

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Fig. 10.6 3D orientation of collagen fibers within pig tendons analyzed using PIPO SHG. Column (a) shows H&E stained ROI imaged using bright field microscope. (b) SHG intensity images of same ROI (Represents sum of SHG images for various degree of polarization states). (c) displays R-maps and (d) shows C-maps, which are fitted from the corresponding P-SHG images shown in (b) and color coded with the values ranging from 1 to 3. Column (e) representative images displays the map of planar orientation for each pixel of the image in which red and blue bars indicate positive and negative polarity, respectively, while black bars represent fibers lying in the image plane where the polarity is unable to be determined. Scale bar = 25 μm. Figure and caption used with permission from (Golaraei et al., 2019a)

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Fig. 10.7 Representation shows the comparative analysis of α-dependence between experimental and calculated R- and C-ratios. Figure and caption used with permission from (Golaraei et al., 2019a)

is thus obtained with exceptional clarity. The χ(2) ratios obtained in this work is under the assumption that the measurable physical quantity is real. However, the C-ratio depends on the phase difference between the chiral and achiral elements in χ(2) tensor, χ14 /χ31 should contain the real and imaginary parts, which is unable to separate them using linear polarization. For this, the same research group used double Stokes–Mueller polarimetry (DSMP) to extract the χ(2) ratios in the form of complex values, providing a new approach to characterize the ultrastructure of chiral molecules, especially collagen (Golaraei et al., 2019b).

3.3 Theory for Stokes Vector-Based SHG Microscopy As incident light travels through the sample to micrometer depths, it is subject to sample-induced polarization distortion. The overall symmetry characteristics of molecules can be learned through spatially resolved polarization measurements, which also enable through examination of variations in the magnitude and sign of polarization parameters. Jones calculus (Collett, 2005) can be used in polarization analysis; however, it can only be applied to polarized light. The Stokes algebra (Schmieder, 1969; KU et al., 2019), on the other hand, is more relevant to all states of light, including incoherent, partially polarized, and unpolarized states. Thus, a light beam can be fully represented by a 4 × 4 Mueller matrix in quantities called “Stokes parameters,” as shown in Fig. 10.8. The output polarization state of SHG cannot be measured by conventional P-SHG microscopy, but it can be used to examine the linear birefringence and polarization anisotropy of tissues. An imaging system that can measure the entire range of Stokes parameters of SHG using transmission microscope configuration has been developed for quantitative polarization measurements (Mazumder et al., 2012, 2013,

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Fig. 10.8 Schematic diagram showing difference in the working principle of Stokes polarimetry and Mueller polarimetry. In Stokes polarimeter, a Polarization State Analyzer (PSA) is used to measure the polarization state of an output optical signal, while a Mueller polarimeter considers how the polarization state that is produced by a Polarization State Generator (PSG) is influenced by the sample (M), which helps to characterize both sample properties and the polarization state of an output optical signal. Figure and caption used with permission from (Mazumder et al., 2014)

2014, 2017b, 2018). By using a Stokes polarimeter and SHG microscopy that is based on Stokes vectors and four-channel photon counting, it is possible to characterize the macromolecular and molecular structures of tissues by determining the full polarization state of SHG in terms of the degree of polarization, degree of linear and circular polarization, and the circular birefringence property. The Stokes vector, S describes the complete polarization state, labeled as S0 , S1 , S2 , and S3 where S0 is the total intensity, S1 and S2 are the intensity difference between linear polarization states at 0◦ , 90◦ at 45◦ , −45◦ , respectively and S3 is the intensity difference between the left and right-handed circular polarizations, namely, LCP and RCP. Therefore, any changes in the polarization state of SHG signal can be represented by the Stokes vector as ⎤ ⎡ I0 + I90 S0 ⎢ S1 ⎥ ⎢ I0 − I90 ⎥ ⎢ .S = ⎢ ⎣ S2 ⎦ = ⎣ I45 − I−45 S3 IRCP + ILCP ⎡

⎤ ⎥ ⎥, ⎦

(10.27)

where the subscripts on I are the intensities of 0◦ , 90◦ , 45◦ , −45◦ , RCP and LCP, respectively. The output Stokes vector is represented by the Sout = [S0 , S1 , S2 , S3 ]t where t represents the transpose. In case of four channel-based SHG microscopy, the four SHG intensities I = [Ia , Ib , Ic , Id ]t that are detected by time-correlated single photon counting (TCSPC) electronics connected by the 4 × 4 instrument matrix A4×4 and the 4 × 1 Stokes parameter as I = A4×4 · Sout .

.

(10.28)

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The several key polarization parameters can be inferred from the measured Stokes vector, including the degree of polarization (DOP), the degree of linear polarization (DOLP), and the degree of circular polarization (DOCP) that are defined as  S1 2 + S2 2 + S3 2 (10.29) .DOP = S0  DOLP =

.

S1 2 + S2 2 S0

DOCP =

.

|S3 | . S0

(10.30)

(10.31)

DOP represents the polarization property of scattered light, which ranges from 0 (unpolarized light) to 1 (fully polarized light). For partially polarized light, DOP is between 0 and 1. Similarly, DOLP describes the proportion of a perfect linear polarization. DOLP is 0 for an unpolarized light, while 1 for a perfect linear polarization. DOCP range between 0 and 1 is a measure of how effectively the molecules flip the circularly scattered light within the focal volume.

4 Structural Constraint and Tissue Sources for SHG Not all materials can produce SHG as it is forbidden in a centrosymmetric material when light before and after the focus experiences destructive interference. For instance, a glass or a homogeneous solution with randomized molecular orientation is not allowed for SHG. Conversely, a material with the noncentrosymmetric organization is able to produce SHG, which can be explained by the following mathematical deductions. If the incident field is the same as Eq. (10.2) and the sample obeys centrosymmetry, the induced polarization, as well as incident field, becomes –P and –E after coordinate transformation according to r → –r (Both et al., 2004). Thus, the polarization is altered by .

− P (r, t) = χ(2) [−E (r, t)]2 .

(10.32)

By comparing Eq. (10.32) to P(r, t) = χ(2) [E(r, t)]2 , it only holds for χ(2) = 0. Thus, a sample with centrosymmetry is prohibited for SHG. Here, we summarize three types of SHG sources: (a) noncentrosymmetric materials (bulk SHG), (b) interfaces between two dielectrics as well as cell membranes (surface SHG) (Campagnola et al., 1999; Flörsheimer et al., 1997), and (c) artificially made molecular orientation with electric polling, e.g., periodically poled lithium niobate (PPLN) (Tzeng et al., 2011; Harris et al., 2008). Notably, the tight focus at the

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sub-μm scale used in P-SHG imaging can automatically fulfill the phase matching condition due to the micron-scaled structures in tissues (Chu et al., 2004). Regarding the SHG sources, they are organized with ordered periodical nanostructures similar to photonic crystals (Yablonovitch, 1987; John, 1987), which can alter the fundamental process of light–matter interactions. Various photonic structures have been found in bio-tissues such as collagen fibrils, cartilage, myofibrils, cellulose, starch granules, etc. and exhibit intense SHG (Chu et al., 2002). These structures have the same characteristics as stacked membranes or arranged proteins of which the organized scale is much smaller than one optical wavelength similar to man-made nanophotonic crystals. This structure-induced SHG on native crystalline bacteriorhodopsin in the purple membrane, which disappears after the protein is hydrolyzed, was examined by Clays et al. (2001). This work illustrates that the densely packed nanostructures as well as well-ordered molecular arrangements in biophotonic crystals are crucial for SHG. Thus, an in-depth understanding of the SHG sources in various tissues can be applied to imaging applications in many aspects. Collagen is ranked as the top one studied sample because it is the most abundant structural protein in mammals and the most important connective tissue in the human body. The human body contains approximately 16% protein, 30% of which is collagen and forms the extracellular matrix (ECM). Collagen’s structure has been extensively investigated because of its importance in biological and therapeutic studies. The structure of collagen consists of three parallel polypeptide chains entangled in a left-handed polyproline type II (PPII) helical conformation with one residue interleaved to create a right-handed triple helix. Collagen plays a central role in the structure and biological function of nearly every organ system, and thus there has long been a desire to exploit its SHG properties to better understand the mechanisms by which they affect cellular behaviors and, in turn, affects them. With great interest, a better understanding of the basic structure of collagen has been shifted to study the dynamics of collagen-based tissues and the subsequent impact on structural integrity and biological function of tissues that are related to diseases, especially cancers (Orgel et al., 2011; Pena et al., 2007; Brown & McKee, 2003). Furthermore, cartilage mostly exists between the hard bones as one of the connective tissues. Cartilage contains less cells (chondrocytes) and mostly the ECM that is made up of about 20% Type-II collagen, 8% proteoglycan, and about 70% water. Thus, the mechanical function of cartilage has a great relationship with the structural organization of collagen fibers. It is known from the SHG signal that the orientation and composition of collagen are related to the depth of cartilage tissues (i.e., a structure stacked with various zones) (Yeh et al., 2005; Chaudhary et al., 2015). The signal analysis of SHG allows monitoring the variation in the internal structure responding to a mechanical load and osteoarthritis (OA) helpful in understanding the mechanism of cartilage repair and regeneration (Mansfield et al., 2019; Werkmeister et al., 2010). On the other hand, skeletal muscle fibers are formed by the spatial arrangement of myofibrils incorporating myosin and actin filaments, which are repeatedly arranged in Z lines and form a cross-striped structure called a sarcomere. The arrangement of

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myofibrils, which are connected in series and range in length from 2 to 3 microns, can identify the type of muscle. A section of the A band (dark areas) and I band surround the Z line (light areas). The helical and hexagonal symmetry of myosin and actin filaments are well known. When muscle contracts or stretches, these monomer structures (i.e., filaments of myosin, actin, titin, or an arrangement of the above) will change or interact resulting in the SHG signal variation that can be analyzed and quantified (Samim et al., 2014; Psilodimitrakopoulos et al., 2009b; Mazumder & Kao, 2021). It has been pointed out that the birefringence of myofibrils is due to the spatial anisotropy of the A-band in sarcomeres, which results in the sarcomere SHG being influenced by the overlapping between thick and thin filaments. To know exactly the molecular origin of SHG in sarcomeres, scientists conducted detailed studies using pure sarcomeres extracted from muscles (Plotnikov et al., 2006). The dissociated sarcomeres were fluorescently labeled and imaged with SHG and TPEF simultaneously. The results show that when the muscle is not contracted, the fluorescence signal (green) is from actin, which is not overlapped with the SHG signal (purple), indicating that actin is not the SHG source, as shown in Fig. 10.9a. However, when the muscle contracts, the actin fluorescence partially overlaps

Fig. 10.9 SHG is found localized in mature sarcomeres which is the overlap zone of both thick filament and thin filament. (a, b) In isolated mouse myofibrils, SHG was visualized simultaneously with either actin in immunofluorescent staining (a) or in phalloidin staining (b). The top, middle, and bottom panels depict SHG, fluorescence and the overlapping of the two channels (purple: SHG, green: fluorescence). It can be found that SHG is dependent on myosin filaments. (c) AlexaFluor 488-phalloidin stained SHG (purple) and fluorescence (green) from isolated mouse myofibrils. (d) The fluorescence signals of myofibril when myosin is under contraction. In panel (b), SHG channel was collected with a fourfold increase in detector gain compared to panel (a), but there is no signal from sarcomeres. Scale bar = 2.5 μm in panels (a) and (b); 5 μm in panels (c) and (d). Figure and caption used with permission from (Plotnikov et al., 2006)

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with the SHG signal, as shown in Fig. 10.9b. Thus, it is concluded that the SHG signal of muscle closely resembles the structure of the sarcomere but is not from actin. Then myosin was further fluorescently labeled and performed the two-channel imaging as stated above. The fluorescence signal from myosin almost overlaps with its SHG signal whenever the muscle is contracted or not, as shown in Fig. 10.9c, d, which suggests the main SHG signal is from myosin instead of actin. Besides, when the muscle is contracted, some of the fluorescence signals from actin overlap with the SHG signal, manifesting that the SHG signal could also be generated by the interaction of thick filaments (myosin polymer) and thin filaments (actin polymer). Plant structures also produce intense SHG providing information about the mechanism of energy transfer in plant physiology. Starch granules are macromolecular polymers of glucose that are widely present in plants as a form of energy storage. They are composed of two different polymers, amylose and amylopectin. The former is a straight linear chain of glucose molecules linked by α-l,4 glycosidic linkages, while the latter is organized into a huge branched structure (Buleon et al., 1998). Starch granules are elliptical and granular and the macroscopic structure shown by a white light microscope is concentric circles of crystalline or semicrystalline shells with a size of about 120–400 nm. These crystalline shells are double-stranded helix branches with different orientations intertwined, which are mainly composed of amylopectin branches surrounding the single-stranded helix of amylose. Both amylose and amylopectin are considered to be the SHG source in starch granules, but strong evidence is scarce to support which one is the main source. For confirmation, two different varieties of starch granules, namely RF (amylopectin: 86%, amylose: 14%) and WR (amylopectin: 99.5%, amylose: 0.5%) were used (Zhuo et al., 2010). In principle, SHG would be related to the source molecule and is proportional to the square of the content ratio. The results show that the SHG intensity ratio between the two species is 1.15 ± 0.37, manifesting that the main source of SHG in starch granules is amylopectin rather than amylose. Another piece of evidence is provided by Psilodimitrakopoulos et al. and Zhuo et al. that the measured helical pitch angle of the SHG-active molecules corresponds to the x-ray diffraction data of amylopectin (Zhuo et al., 2010; Psilodimitrakopoulos et al., 2010). On the other hand, cellulose is a polysaccharide that consists of a linear chain of β-1,4 linked D-glucose units in which the well-ordered molecular chains gradually progress and eventually crystallize into microfibrils. The supramolecular structure of cellulose microfibrils is highly crystalline, birefringent, and chiral similar to collagen fibers. In addition, the anisotropic cellulose matrices are regularly organized, which facilitate P-SHG studies (Nadiarnykh et al., 2007; Brown Jr et al., 2003).

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5 Polarization-Resolved SHG (P-SHG) Microscopy: Techniques In general, P-SHG microscopy is easily implemented in a conventional confocal or two-photon laser scanning microscope, which is integrated with a NIR femtosecond laser, 2D galvo mirrors, a combination of polarization optics, and a synchronized detection system, as shown in Fig. 10.10a. Due to the longer excitation wavelength, the laser beam can penetrate deeper into bio-tissues. However, the depolarization effects such as scattering and birefringence from tissues would scramble the quality of incident polarization, which limits the working range (or sample thickness) of P-SHG imaging to about 200 μm due to the scattering length of NIR wavelengths to bio-tissues (Balu et al., 2009). The average laser power used on the sample ranges from several to several tens of mW, ensuring no photodamage occurs on sample after continuous observation. The laser beam guided to the 2D galvo mirrors is deflected in x and y directions and then focused into a small spot with an objective lens to scan on sample point by point within the region of interest. The SHG photons separated and sorted from the intense excitation laser by an appropriate combination of optical filters and dichroic beam splitters are finally collected with photomultiplier tubes in either forward, backward, or both directions. The operation interface for scanners, motorized stage, and detection electronics can be synchronized and displayed by the program based on LabVIEW, MATLAB, or Python. For the polarimetric measurements, a polarization state generator (PSG) composed of a polarizer, a half-wave plate, and a quarter-wave plate inserted in the optical path is used to rotate the direction of linear polarization, exchange between linear, elliptical and circular polarization, and compensate for the polarization ellipticity altering effect from the used optics in the system (Chen et al., 2021; Chen-Kuan et al., 2008). Before imaging, it is needed to define the polarization direction respect to the laboratory coordinate system depending on the relative

Fig. 10.10 (a) Schematic diagram of instrumental set-up for second-harmonic anisotropy microscopy. Figure and caption used with permission from (Mazumder et al., 2017a). (b) Experimental set-up of module-based P-SHG four-channel Stokes polarimeter. Figure and caption are used with permission from (Mazumder et al., 2014)

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angle between the principal axis of the half-wave plate and quarter-wave plate. To guarantee an informative and accurate SHG polarization anisotropy, great attention should be paid to the quality of imposed linear polarization to suppress the deviation in the measured parameters. In general, the extinction ratio of linear polarization for excitation is measured to be larger than 50:1 after a high numerical aperture (NA) objective lens. By manipulating the polarization state with PSG, the polarizationdependent SHG images are acquired without sample rotation and an analyzer is placed before the detector which greatly simplifies the technique. The experimental configuration of PIPO SHG microscopy is similar to conventional P-SHG microscopy. However, a polarization state analyzer (PSA) is a combination of various optical components and detector to measure the polarization state of the SHG signal in forward direction. Similar to PIPO SHG microscopy, Stokes vector-based SHG microscopy detects the signal in the forward direction that is analyzed by PSA to reveal the polarization properties of SHG passing through samples under study. Notably, the SHG signal is split into four intensity components. The details can be found in reference (Mazumder et al., 2014). Finally, the Stokes image “Sout ” is determined by the four SHG intensity images with pixel resolution as Sout = (A4 × 4 )−1 ·I.

6 Polarization-Resolved SHG (P-SHG) Microscopy: Applications P-SHG microscopy is regarded as a touchstone approach to determining the architecture and function of fibrous tissues according to the derivation of χ(2) ratios, molecular packing scheme, 3D molecular orientation, orientation order at the molecular scale, and ultrastructure of fibrils. The above parameters can be obtained with the theory as described in Sect. 3.1, which assists to map and address any structure-related issues in normal, diseased, and engineered tissues. Importantly, the molecular orientation and order determining the degree of the organization both at the molecular and macromolecular scales can alter the fundamental process of light–matter interactions, providing a major impact to biophysical and biomedical research. The relevant results have shown that the χ(2) ratio such as χ33 /χ31 (χ33 /χ15 ) can be used to monitor the process of decrimping and thermal denaturation of Type-I collagen (Liao et al., 2011), estimate the age of living organisms that is associated with the radius of collagen fibers and fibrosisrelated diseases (Williams et al., 2005; Chen et al., 2018), and distinguish between different molecular structures in the same specimen (Chen et al., 2009; Tiaho et al., 2007; Psilodimitrakopoulos et al., 2009a; Su et al., 2011). In pathologies, cancer invasion and metastasis would cause the changes in content, distribution, and fibril structure of type-I collagen which is a dominant phenomenon leading to the variation in χ33 /χ31 that can be potentially used for discriminating between normal, pre-cancerous, and cancerous tissues (Erikson et al., 2007; Campbell et

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al., 2018). In the following, we select some representative works on the current applications, which are roughly divided into two parts: (1) non-clinical applications of studying collagen biophysics, the correlation between structural organization and mechanical properties of tissues, fundamentals of tissue engineering, etc. and (2) clinical applications of diagnosing diseases, especially cancers. Because collagen is abundant in the human body, its damage or variation is highly correlated with various diseases. Thus, the use of P-SHG microscopy in analyzing the collagen fibril organization and fiber orientation can be extended to explore the process of disease development. In addition to cell lesions that affect the organization of collagen fibrils, the morphological structure of collagen may also be damaged under mechanical stimulation by an external force. Figure 10.11 shows the needle punctures of different sizes onto the surface of bovine annulus fibrosus used to simulate the injury to collagen fibril organization in the intervertebral disc during a spinal diagnostic procedure, and the degree of injury is quantified by the image analysis for the parameter I2 as stated in Sect. 3.1 (Mansfield et al., 2019; Wang et al., 2021). The higher the value, the more collagen fibrils in each pixel on the map are arranged in the same direction. When the I2 values of the needle group are compared to those of the control group, it changes with cyclic loading. Furthermore, as needle size increases, the I2 value decreases. The aforementioned phenomena confirm that the I2 value is dependent on collagen fibril organization and can be influenced by external stimuli. It is noticed in Fig. 10.11 that the mechanical damage of collagen bundles mostly occurs in the areas surrounding the puncture, but little change is shown in the control experiment. Furthermore, the dynamic processes in thick tissues during mechanical stretching are monitored and analyzed by P-SHG microscopy (Ducourthial et al., 2019). In this study, the collagen orientation is mapped and color-coded in images, showing the reorganization of the collagen network under different stretch ratios in the murine skin dermis. The collagen orientation distribution and the measured entropy, which are discovered to be inversely proportional to the stretch ratio, are then used to quantify the microstructure reorganization. Additionally, it can be used to study how collagen-rich tissues, particularly cartilage, respond microstructurally to mechanical loading or strain. SHG in cartilage depends on the collagen content in tissues and the relative orientation between polarized excitation and collagen fibers. Following the theory of P-SHG as stated in Sect. 3.1, the zonal collagen architecture, the structural difference of collagen fibrils around chondrocytes, fibril reorganization in cartilage strips exposed to tensile loading, and a weak correlation between tensile modulus and a rise in local fibril organization in the superficial zone are all revealed. Furthermore, investigating the issues about OA provides useful information of micron-scale fiber arrangement, sub-micron scale fibril organization, and the mechanisms of collagen degradation (Mansfield et al., 2019). These phenomena are found between the superficial and deep zones in the lateral and medial femoral cartilage samples from patients who have experienced a knee replacement surgery for OA. Notably, once the fibril orientation is noticeable (i.e., of high contrast) on the SHG intensity image such as Type-I collagen, the 3D molecular orientation can be extracted directly by

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Fig. 10.11 I2 maps of collagen organization calculated from the respective P-SHG images. Each group received one representative sample. The top, middle, and bottom row images were taken right after the puncture before cyclic loadings, after 30 cyclic loadings and after 70 cyclic loadings, respectively. All scale bars = 200 μm. Figure and caption used with permission from (Wang et al., 2021)

the analysis of gradient, fast Fourier transform (FFT), or variance (Bueno et al., 2016). However, it is challenging to apply the above-mentioned methods to Type-II collagen in cartilage. Besides, a qualitative method of the macroscopic organization by analyzing the SHG intensity ratio of the forward to backward scattering only provides information on fibril size and density of collagen (Houle et al., 2015; Légaré et al., 2007), which makes it difficult to reveal 3D fibril orientation of TypeII collagen in cartilage. Alternatively, P-SHG microscopy is the best fit for the structure analysis of Type-II collagen. In Fig. 10.12, even in the same specimen, a variety of different collagen structures can still be seen according to the derived (I2 , ϕ2 ). The results demonstrate that region (a) shows relatively lower I2 values and a broad range of fibril angles; region (b) shows largely disordered fibrils with moderate I2 values; region (c) shows many parallel aligned fibrils with higher I2 values. Changes in ϕ2 indicate the collagen fibril reorientation on a relatively large scale, while changes in I2 indicate the alteration in collagen fibrillar structure on a sub-micron scale. The cornea is the exterior part of the eye, which holds two-third of the refractive power of the eyeball and protects the eye from external damage. Currently available technologies such as reflection confocal microscopy or ophthalmic OCT enable 3D imaging of cornea on the cellular level (Guthoff et al., 2009; Gora et al., 2009). When looking at the fibril organization in the corneal stroma, which makes up about 90% of the total thickness of the cornea and is made up of a stack of more than 250

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Fig. 10.12 Total knee replacement surgery resulted in osteoarthritic cartilage. (a–c) are the SHG images taken from different regions. (d) and (e) are the distributions of I2 and ϕ2 respectively. Figure and caption used with permission from (Mansfield et al., 2019)

collagen lamellae with a thickness of 1–3 m, they offer less specificity or contrast. Each collagen lamella is about 10–100 μm wide and consists of stacked collagen fibrils with a diameter of 30 nm to form a hexagonal lattice. The extremely ordered arrangement is responsible for its mechanical strength as well as transparency. However, cornea destruction may occur in the event of injuries, trauma, lesions (e.g., keratoconus), or after laser surgery (Plamann et al., 2010; Krachmer, 2011). To this end, the fibril orientation and heterogeneity of the collagen fibril distribution in the corneal stroma have been mapped and quantified using P-SHG microscopy to provide structural information. SHG has a diffraction-limited image resolution unable to see the objects below the resolution limit such as the fibrils in collagen lamella. However, it can be resolved by exploiting the high sensitivity of SHG polarization anisotropy to optically anisotropic structures. Consequently, the 3D fibril distribution in collagen lamella at each depth in the human cornea is obtained, which is in good agreement with numerical simulations, as shown in Fig. 10.13 (Latour et al., 2012). Regarding the application of PIPO SHG microscopy, it has been used to investigate the myosin nanomotor organization in the light meromyosin (LMM) domains (Su et al., 2011; Samim et al., 2014), which is the main constituent of myofilaments. As a result of the change in the deflection angle of the myosin S2

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Fig. 10.13 The orientation maps of human corneal stroma derived from P-SHG images taken in (a) forward and (b) backward direction of the same ROI, respectively, in which only the arrow lengths larger than 0.7 are displayed. SHG anisotropy ratio. The maps of SHG anisotropy ratio obtained by the same P-SHG images are shown in (c) and (d), respectively. Scale bar = 50 μm. Figure and caption used with permission from (Latour et al., 2012)

domain and other contributions from myosin heads during myocyte contraction, the results demonstrate that a lower χ33 /χ31 value along anisotropic bands of sarcomeres is found at the head-less regions of myofibrils as compared to that of head-containing regions. This method was also used to compare the χ33 /χ31 values of various myosin protein domains in the IFMs of fruit flies with and without myosin mutations with values in the range from 0.45 to 0.49, suggesting that it is a sensitive and accurate technique to study conformational changes of biotissues and the derived χ(2) ratios could be served as a database for the related studies of myosin molecular structures. On the other hand, it has been shown that changes in UNC-45 or gene expression patterns would have negative impact on muscle function, resulting in deficits in muscle structure, physiology, and motor behavior. Thus, the same research group studied the structural changes induced by different myosin contents using the achiral and chiral susceptibility tensor ratios, R and C as stated previously (Karunendiran et al., 2022). It was found that SHG intensity is significantly reduced in UNC-45 knockdown muscle. However, UNC45 knockdown muscle still has a streaky appearance presenting with a higher R-ratio

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Fig. 10.14 (a) Representative 2D stokes vector images of type-I collagen from experimental PSHG response. (b) 2D reconstructed DOP, DOLP, DOCP, and polarization anisotropy images of polarization-resolved SHG response from type I collagen for the input polarization of horizontally polarized light. The color scale shows the values of each parameter. The figure is used with permission from (Mazumder et al., 2012)

than the control, which indicates that the molecular organization in the striated muscle is incomplete. Furthermore, the C-ratio is lower as compared to the control, which means that the molecular chirality in muscle becomes lower due to the destruction of myosin organization. On the other hand, Stokes vector-based SHG microscopy was used to investigate the SHG signal from type-I collagen fiber (Mazumder et al., 2012, 2014, 2017a; Mazumder & Kao, 2021). The 2D Stokes vector images were reconstructed at horizontally input polarized light as shown in Fig. 10.14a, indicating that the relative phase shift of incident light propagating through the entire fiber, to an oscillation function between linear (S1 , S2 ) and circular (S3 ) polarization states. Again Fig. 10.14b shows the spatial distribution of DOP, DOLP, DOCP, and anisotropy images. It is clear in DOP image that the SHG signals are partially polarized due to inhomogeneity within the sample and orientation of the fibril axis. In addition, the DOLP image represents the crystalline arrangement of fibers parallel to the linear polarization state, whereas the optical activity of collagen was observed in DOCP image DOCP represents how SHG signal is a mixture of LCP and RCP generated due to the helicity of scattered light within the focal volume. With the Stokes parameter-S3 and DOCP, circular dichroism (CD) can be used to determine the helicity of SHG and the chirality of collagen molecules, respectively. Furthermore, the birefringent effect on SHG polarization can be revealed by the anisotropy measurement. Observations of polarization parameters suggest that collagen fibrils are highly anisotropic, consistent with the known pitch of various collagen helices in tissues. The orientation distribution of myofibrils can be determined by measuring different Stokes vector along with the intensity SHG image (Mazumder & Kao,~2021),

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Fig. 10.15 (a) 2D Stokes vector images of P-SHG response from skeletal muscle fiber. (b) 2D reconstructed DOP, DOLP, DOCP, and polarization anisotropy images of P-SHG response from skeletal muscle fiber for the horizontal and vertical polarized light. The color scale shows the values of each parameter. Scale bar = 10 μm. The figure is used with permission from (Mazumder & Kao, 2021)

and hence, isotropic (I) and anisotropic (A) bands in the sarcomere are identified to appear as alternating dark and bright bands, helping to measure the sarcomere length of around 3 μm, as shown in Fig. 10.15. Myofibrils are tightly packed and continuously connected through the intermediate filaments of the sarcomere, providing a unique SHG polarization anisotropy to be analyzed. A higher DOP value indicates that myofibrils are aligned parallel to a fixed orientation and that these sarcomeres are aligned in the same direction with each other. DOLP value shows that the myofibrils are parallel to the vertical/horizontal polarization state of incident light and are higher for horizontally polarized than vertically polarized excitation due to the strong dependency of SHG on the direction of input polarizations. DOCP image determines how the coil-like structure of myofibrils changes the polarization state between the incident light waves and SH waves. Furthermore, the orientation of microfibrils in skeletal muscle is measured by anisotropy r, which ranges from −0.5 to 1. The molecules are better aligned vertically for vertically polarized excitation is approximately −0.5. However, in the case of horizontally polarized excitation, the r value is approximately 0. The above phenomena show that the polarization properties of SHG vary significantly with different excitation polarization directions. The changes in DOLP are attributed to the depolarization of SHG, whereas the changes in DOCP are due to a combination of depolarization and muscle birefringence. On the other hand, the same method is validated in starch granules (Zhuo et al., 2021; Mazumder et al., 2013, 2017b, 2018). The starch granule produces the distinctive SHG polarization sensitivity due to the anisotropic and concentric-shelllike structure. By altering the incident laser polarization states and detecting various polarization components of SHG signal by PSA, distinct SH intensity patterns are obtained to understand the molecular orientation in starch granules. As shown in Fig. 10.16, left, the SHG intensity images (S0 ) exhibit a double-lobed pattern that is oriented parallel to the direction of linear polarization, which confirms the radial arrangement of amylopectin molecules in starch granules. SHG intensity is a

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Fig. 10.16 Left: 2D Stokes images of the SHG response from starch granules for (a) horizontal, (b) vertical, (c) right, and (d) left circularly polarized illumination, respectively. Polarization is indicated by white arrows in the leftmost images. The color scale depicts the value of each Stokes parameter as it progresses from blue to red. Right: 2D reconstructed DOP, DOLP, DOCP, and polarization anisotropy images of P-SHG response from starch granule for the following polarizations: (a) horizontal, (b) vertical, (c) right, and (d) left circularly polarized illumination. A white arrow indicates the polarization direction and color scale depicts the values of each parameter as they progress from blue to red. The figure is used with permission from (Mazumder et al., 2013)

function of the angle between the linear polarization and the SHG radiation dipole orientation within the focal volume. Thus, the distribution of the lobe direction in S0 reflects the polarization state of the input beam. Furthermore, it is noted from the reconstructed Stokes images that the various locations within a single starch granule produces different polarization states, which is the result of chiral and anisotropic properties of starch granules. The images of DOP, DOLP, DOCP, and anisotropy r can be calculated from the Stokes images irradiated with different polarization states, as shown in Fig. 10.16 (right). As these polarization parameters are related to the arrangement of SHG transition dipoles within the granule, the different morphologies of crystallites present in starch granules are highlighted. In the image, the value of DOP is approximately unity, indicating that the SHG from starch granules is fully polarized regardless of the illumination polarization state due to the well-ordered crystalline layer of amylopectin branches. The DOLP distributions shown in Figs. 10.16, right (a) and (b) depict the degree of parallel crystalline alignment of molecules in the horizontal and vertical directions, respectively. It can be seen that the DOLP excited by the horizontal and vertical polarization peaks at approximate coincidence and varies sinusoidally with the angle. However, linearly polarized light interacting with amylopectin molecules would be optically rotated due to the circular birefringence. The results of Fig. 10.16, right (c) and (d) with circular polarizations are similar to the above, while DOLP ranges from 1 to 0, the accompanying DOP images

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exhibit greater homogeneity than linearly polarized illumination. Notably, due to the unequal proportions of amylopectin molecules presenting different chiralities, a strong SHG signal is thus produced for the non-centrosymmetric structure. Consequently, Stokes vector-based SHG microscopy can be used to visualize the molecular structure distribution in highly ordered bio-tissues by examining the resulting polarization properties, which could be a very powerful tool for studying the structural dynamics of fibrils in tissues under different biological and physiological conditions. For clinical applications, especially cancer diagnosis, quantitative analysis of PSHG microscopy can improve the sensitivity and specificity of the examination of diseased tissues. The fact that progression of cancer is not only the proliferation of cancer cells but also changes in the tumor microenvironment that is mainly composed of ECM. As ECM contains many components that affect tissue specificity, among which collagen accounts for the largest proportion, it is crucial to study tissue variability by analyzing P-SHG of collagen fibrils during tumor progression (Cisek et al., 2021). Previous studies have shown that the structure and organization of ECM play an important role in tumor growth (Bonnans et al., 2014; Lu et al., 2012). The subsequent structural changes include the collagen degradation in the basement membrane and the main component of fibrillar collagen in connective tissue transformed into Type-I collagen that has been a favorable biomarker (Kalluri, 2003). The incomplete winding of triple helix and the reorganization of collagen molecules would cause lesions in tissues, accelerate the differentiation and migration of tumor cells, and infiltrate other tissues and organs, resulting in distant metastasis (Torzilli et al., 2012). As an important biomarker, collagen can provide much important information in identifying normal or diseased tissues and quantifying the process of cancer development. In recent years, there have been many uses of PIPO SHG microscopy that incorporate multiple structural parameters to differentiate between normal from tumor tissues or stage cancers, which are illustrated below. Lung cancer is ranked as the second most common cancer worldwide, with 85% being detected as non-small cell carcinomas (Paech et al., 2011). One of the most important indicators to determine treatment procedures and the prognosis is cancer staging which commonly uses TNM index. It includes T (Tumor) tumor size, N (Lymph node) lymph node spread, and M (metastases) distant metastasis and divides the progression of lung cancer into stages I–IV, and the stage of cancer will be used to determine different treatments. As the 5-year survival rate of stage I can reach 70%, early detection and accurate staging are important in administering drug treatment and improving quality of life. For this, a study uses PIPO SHG microscopy to extract the structural parameters of the stage-I, -II, and -III non-small cell lung carcinoma (NSCLC) tissue sections, which are characterized by the R and C ratios, DOLP, and in-plane collagen fiber orientation (Golaraei et al., 2020) as stated previously. With the above information, a texture analysis based on a graylevel co-occurrence matrix (GLCM) (Haralick et al., 1973) is especially used to calculate the entropy, correlation, and contrast of the textural features on the SHG intensity image.

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The ultrastructure of collagen is varying with different stages, which is detailed in Fig. 10.17. Compared with normal tissues, the R-ratio in diseased tissues increases significantly, which is possibly due to the overexpression of ECM proteinases leading to the rearrangement of collagen fibrils in tissues and an increase in collagen fiber stiffness. These phenomena show that the structural organization of ECM plays a major regulatory role in tumor progression. Previous studies have pointed out that the hardening of collagen is related to the expression of integrin α11 in ECM, and it is thought to reorganize Type-I collagen by shortening the molecular interval and linearizing collagen fibers linking to tumor cells at which the interface between the tumor cell and stroma is formed with disorganized collagen fibers that are consistent with the R-ratio results. Similarly, the C-ratio increases with the cancer stages due to the increased variation in collagen fibers oriented out of the image plane. In addition, it is found that compared with normal tissues, collagen molecules in the diseased tissue have better alignment (a lower value of the contrast parameter), which is contradicting the hypothesis that collagen fibrils are well aligned in normal tissues. This phenomenon can also be found in studies of other malignancies such as breast cancer and pancreatic cancer. The increased alignment of collagen fibrils could be one of the mechanisms of distant metastases from solid tumors. Moreover, because the orientation order of collagen fibers is increased during tumor progression, and thus, the DOLP value of tumor tissues is smaller than normal lung tissues. The entropy of tumor tissues in the texture analysis is increased with stages due to the gradual fragmentation and loss of structural organization of collagen fibers, and the values are larger than that of normal tissues. Conversely, the correlation parameter decreases with the tumor stage for the same reason as the entropy parameter. A similar approach is validated in pancreatic cancer tissue (Tokarz et al., 2019). The PIPO SHG microscopy based on C6v structural symmetry is used as a diagnostic tool for early pancreatic cancer and to study the progression of tumors. The Rratio is correlated with the supercoiling and tilt angle of collagen fibrils. Besides, it has been used to extensively study collagen fibril types in different animals, including normal and tumor tissues, and to detect and quantify the degree of collagen damage. The results show that the R-ratio of normal tissues is much lower than that of tumor tissues (p < 0.05), indicating a lower directionality of collagen fibrils in tumor tissues. In more detail, periductal and lobular tissue is quite distinct from a tumor according to the FWHM of R occurrence, whereas tumor tissue and parenchymal tissue are very distinct according to the FWHM of C occurrence. Furthermore, compared to the tumor tissue, parenchymal and periductal tissues exhibit considerably differing DOLP values. On the other hand, thyroid cancer is the most common malignant tumor in the endocrine system, among which the highest incidence is primary thyroid papillary carcinoma accounting for about 85–90% of the total thyroid cancer cases, and the other is follicular thyroid cancer in about 10% of the cases (La Vecchia et al., 2015). Both types of malignant tumors differentiated from thyroid follicular epithelial cells easily metastasize to the lungs or bones through cervical lymph nodes, and the metastasis rate of follicular carcinoma is higher than that of mastoid carcinoma. As they are well differentiated, a better therapeutic effect can be achieved through

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Fig. 10.17 Analysis of PIPO SHG in normal and NSCLC tissue sections. Bright-field images with H&E stained are shown in column (a) in which a square area (110 μm × 110 μm) was chosen for the subsequent P-SHG data analyses shown in columns (b) to (e). Column (b) depicts the SHG intensity images for the areas indicated in (a). The R-map is shown in column (c). The C-ratio map is shown in column (d). Column (e) displays the orientation map of collagen cylinders analyzed for each image pixel and a polar plot elucidates the angle distribution. The DLP map is shown in column (f). Figure and caption used with permission from (Golaraei et al., 2020)

early diagnosis. Thus, the 10-year survival rate after surgery or other treatments for the above two thyroid cancers is approximately 92% and 80% (Lloyd et al., 2004; Elsheikh, 2008). However, patients with incompletely differentiated (unclassified) or poorly differentiated thyroid cancers usually have a poor prognosis, and such type of thyroid cancer accounts for about 1–10% of all the cases. Undifferentiated thyroid cancer is highly malignant and is more likely to metastasize to other organs. The 10-year survival rate after treatment is only about 3%. To effectively treat thyroid cancer, early detection and quick type identification are crucial. Based on the PIPO SHG microscopy findings, as shown in Fig. 10.18, large changes in χ(2) ZZZ’ /χ(2) ZXX’ are observed in thyroid tumors and non-tumor tissues. This indicates that the helical pitch angle of collagen molecules as well as the folding of collagen triple helices or the arrangement of collagen fibers are altered. It also indicates an increase in the content of collagen fibers in diseased tissues. The decrease in DOLP value manifests that the collagen in thyroid tumor tissue would

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Fig. 10.18 Images showing ultrastructural changes in collagen for non-tumorous and cancerous thyroid tissue sections using PIPO SHG microscopy, bright field (with H&E stained) microscopy and DOLP counted from P-SHG images. The regions of interest marked by black boxes in brightfield images (a, g, m) were imaged by PIPO SHG microscopy (b, h, n). The χ(2) ZZZ’ /χ(2) ZXX’ were subsequently analyzed and displayed as color-coded images (c, i, o) with values from 1 to 4 and frequency histograms (d, j, p). The calculated DOLP were also presented as color-coded images (e, k, q) with values from 0 to 1 and frequency histograms (f, l, r). Figure and caption used with permission from (Tokarz et al., 2015)

become increasingly disordered as the tumor progresses, which coincides with the increase in χ(2) ZZZ’ /χ(2) ZXX’ in which the fibrillar collagen structure is destroyed rather than well ordered. Breast cancer is regarded as the most prevalent form of malignant tumor in women worldwide and is recognized as one of the classic examples of lesions caused by the reorganization of collagen fibrils (Tsafas et al., 2020). Efficient diagnosis and treatment can greatly improve the recovery rate of breast cancer. Unfortunately, so far an ideal biomarker for rapid diagnosis has not been found in breast cancer, and thus the development of a noninvasive, label-free optical diagnostic method could provide a major finding in the study of breast cancer and assist to develop new treatment strategies. A recent study on investigating breast cancer (Tsafas et al., 2020) is conducted by P-SHG microscopy with (FFT) analysis to extract the structural parameters, which are used to discriminate benign from breast cancer tissues. It is found that the tissue anisotropy parameter B (i.e., χ33 /χ15 ) becomes larger when the tumor develops at a later stage. This phenomenon ascribes to the mechanical tensions imposed on collagen in the process of tumor development. On the other hand, when cancer progresses, the decomposition of protease causes the collagen triple helix to distort and the fibrils to break up, as shown in Fig. 10.19d. According to the results of the ratio parameter, a decreased value is found at grade III, which can be explained by the fact that the arrangement of collagen fibrils

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Fig. 10.19 Depicts the application of P-SHG for distinguishing different grades of breast tumor from benign tissue. Images on the top panel (a–d) represents PSHG of collagen in various grades of breast tumor and results of Fast Fourier Transform (FFT) analysis is shown in bottom panel (e–h). Figure and caption used with permission from (Tsafas et al., 2020)

becomes compact due to mechanical tension, which reduces the effective helical angle and changes the collagen’s cylindrical symmetric structure. In recent years, the biggest challenge of diagnosing ovarian cancer among most cases is encountered in limited information about the microenvironment of ovarian and fallopian tube tumors. The current diagnostic tools such as computed tomography and magnetic resonance imaging do not provide sufficient image resolution and sensitivity to analyze changes in the tumor microenvironment of ovarian cancer during cancer growth (Levanon et al., 2008; Miller, 2005). In addition, the commonly used serological diagnostic methods also lack sufficient specificity and sensitivity to effectively determine tumor growth (McIntosh et al., 2004). In past cases, only about 15% of ovarian cancers can be diagnosed at the stage of carcinoma in situ. Thus, it is required to develop a high-resolution and high-specificity imaging tool to diagnose ovarian cancer before it develops distant metastasis, especially for High-Grade Serous (HGS) tumors (i.e., the metastases can be observed under a light microscope) (Kurman et al., 2008). For confirmation, a study used P-SHG microscopy to determine the changes in the morphological structure of ovarian tissue and whether there is hyperplasia of connective tissue (Campbell et al., 2018). It is observed in Fig. 10.20a that the SHG image of normal tissue is characterized by more linear and intersecting collagen fibers, while benign tumor tissue consists of clustered fibrous structures with a combination of linear and curved features compared to normal tissues. However, stage III and IV ovarian tumor tissue presents long, wavy, and unidirectional fibers that appear to be more abundant in their morphology and concentration. In Fig. 10.20b, with χ(2) tensor analysis, the calculated peptide pitch angle of normal tissue is 48.66◦ . The angle is larger for benign tumor tissue at 49.08◦ , which is explained by the increased TypeIII collagen content. The angle of stage III (47.4◦ ) and stage IV (48.38 ◦ ) tumor tissues are both lower than that of normal stroma, manifesting that no increase in

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Fig. 10.20 Illustrates the potential of P-SHG microscopy in probing the molecular changes in ovarian cancer. (a) SHG images of normal, benign tumor, stage III and stage IV (from left to right) of ovarian tumor tissues, respectively. (b) Map showing collagen peptide pitch angle for stage III tumor. (c) Graphical representation of reconstructed polarization response data for different grades of tumor tissue. (d) Bar graph showing calculated pitch angles with error bars indicating the standard deviation. These data are with statistical differences p < 0.05. Figure and caption used with permission from (Campbell et al., 2018)

Type-III collagen is found in HGS cancers. In addition, the results of SHG signal anisotropy at 0◦ excitation show that the collagen molecules are misaligned with the axis of collagen fibrils in the benign and HGS tumor tissues.

7 Conclusion and Future Perspectives Conventional optical microscopes provide limited image resolution due to light diffraction that is unable to observe the ultrastructure of underlying molecules, resulting in poor specificity to the molecular structure. However, P-SHG microscopy is a sensitive tool that has shown great potential to elucidate the hierarchical multiscale (i.e., from nanometer to micrometer scale) structure in bio-tissues using the fingerprint data determined by the χ(2) tensor-based image analysis. Thus, it is of diagnostic value in providing the molecular organization of fibril-like molecules and the macroscopic orientation of fibers, which are associated with the structural disorder mostly in collagen and muscle. Although the manifestations of most diseases can be observed through biochemical detection and analysis of lesions in sliced tissues, early diagnosis is usually difficult to achieve due to the variability between each disease pathology and the ignorance of subtle variations in tissues. With multiple structural parameters quantitatively measured by P-SHG microscopy,

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it has contributed to the early diagnosis and improved survival rate of certain diseases such as cancers. Based on the well-established theory of P-SHG and successful results, studying the relevant χ(2) ratios to reveal in-depth microstructures and surface morphologies will be of great research importance in structural biology and material science. In addition, the interesting structures organized with specific point symmetry in biotissues would inspire further studies of biophysics regarding tissue regeneration and remodeling. Due to the helicity of SHG signal related to tissue chirality, considering the chiral tensor element and tilt angle of fibril-like molecules in P-SHG microscopy will help decipher molecular organization and interpreting the SHG-CD imaging with RCP and LCP. In clinical research, complex tissue preparation procedures including physical sectioning, fixation processes, and fluorescent labeling are not required in P-SHG imaging, thus enabling the measurement close to the original pathological state. Furthermore, with the great development of artificial intelligence (AI) technologies, a rapid, high-precision optical diagnosis will be developed for P-SHG microscopy to detect early lesions of disease, assess formal versus diseased tissues, and stage cancers, and eventually, realize AI-assisted pathology. Acknowledgments We thank the National Science and Technology Council, Taiwan [Project Number: 110-2112-M-039-001, 110-2923-M-039-001-MY3], and Global Innovation and Technology Alliance (GITA), Department of Science and Technology (DST) [Project Number: GITA/DST/TWN/P-95/2021], Government of India, for financial support.

References Alali, S., & Vitkin, I. A. (2015). Polarized light imaging in biomedicine: Emerging Mueller matrix methodologies for bulk tissue assessment. Journal of Biomedical Optics, 20(6), 061104. Balu, M., Baldacchini, T., Carter, J. L., Krasieva, T. B., Zadoyan, R., & Tromberg, B. J. (2009). Effect of excitation wavelength on penetration depth in nonlinear optical microscopy of turbid media. Journal of Biomedical Optics, 14(1), 010508. Bautista, G., & Kauranen, M. (2016). Vector-field nonlinear microscopy of nanostructures. ACS Photonics, 3(8), 1351–1370. Bonnans, C., Chou, J., & Werb, Z. (2014). Remodelling the extracellular matrix in development and disease. Nature Reviews Molecular Cell Biology, 15(12), 786–801. Both, M., Vogel, M. Q., Friedrich, O., Wegner, F. V., Künsting, T., Fink, R. H., & Uttenweiler, D. (2004). Second harmonic imaging of intrinsic signals in muscle fibers in situ. Journal of Biomedical Optics, 9(5), 882–892. Boyd, R. W. (2019). Nonlinear optics. Elsevier Science. Brasselet, S. (2011). Polarization-resolved nonlinear microscopy: Application to structural molecular and biological imaging. Advances in Optics and Photonics, 3(3), 205. Brown, R. M., Jr., Millard, A. C., & Campagnola, P. J. (2003). Macromolecular structure of cellulose studied by second-harmonic generation imaging microscopy. Optics Letters, 28(22), 2207–2209. Brown, E., & McKee, T. (2003). E. di Tomaso, A. Pluen, B. Seed, Y. Boucher, and RK Jain, “Dynamic imaging of collagen and its modulation in tumors in vivo using second-harmonic generation”. Nat. Med, 9(6), 796–801.

10 Polarization-Resolved Second-Harmonic Generation for Tissue Imaging

299

Bueno, J. M., Ávila, F. J., & Artal, P. (2016). Second harmonic generation microscopy: A tool for quantitative analysis of tissues. Microscopy and Analysis, 99–119. Buleon, A., Colonna, P., Planchot, V., & Ball, S. (1998). Starch granules: Structure and biosynthesis. International Journal of Biological Macromolecules, 23(2), 85–112. Campagnola, P. J., Wei, M. D., Lewis, A., & Loew, L. M. (1999). High-resolution nonlinear optical imaging of live cells by second harmonic generation. Biophysical Journal, 77(6), 3341–3349. Campbell, K. R., Chaudhary, R., Handel, J. M., Patankar, M. S., & Campagnola, P. J. (2018). Polarization-resolved second harmonic generation imaging of human ovarian cancer. Journal of Biomedical Optics, 23(6), 066501. Chaudhary, R., Campbell, K. R., Tilbury, K. B., Vanderby, R., Jr., Block, W. F., Kijowski, R., & Campagnola, P. J. (2015). Articular cartilage zonal differentiation via 3D second-harmonic generation imaging microscopy. Connective Tissue Research, 56(2), 76–86. Chen, W. L., Li, T. H., Su, P. J., Chou, C. K., Fwu, P. T., Lin, S. J., et al. (2009). Second harmonic generation χ tensor microscopy for tissue imaging. Applied Physics Letters, 94(18), 183902. Chen, X., Nadiarynkh, O., Plotnikov, S., & Campagnola, P. J. (2012). Second harmonic generation microscopy for quantitative analysis of collagen fibrillar structure. Nature Protocols, 7(4), 654– 669. Chen, Y., Jiang, G., Zhou, Y., & Xia, X. (2018). Second harmonic generation in two different arrangement of type I collagen on nonlinear microscopy. Results in Physics, 10, 391–394. Chen, S. Y., Su, Z. T., Lin, D. J., Lee, M. X., Chan, M. C., Das, S., et al. (2021). Optimizing imaging depth of anisotropic scattering tissues with polarization engineered second harmonic generation microscopy. Results in Physics, 28, 104653. Chen-Kuan, C., Wei-Liang, C., Peter Tramyeon, F., Sung-Jan, L., Hsuan-Shu, L., & Chen Yuan, D. (2008). Journal of Biomedical Optics, 13, 1–7. Chu, S. W., Chen, I. H., Liu, T. M., Sun, C. K., Lee, S. P., Lin, B. L., et al. (2002). Nonlinear bio-photonic crystal effects revealed with multimodal nonlinear microscopy. Journal of Microscopy, 208(3), 190–200. Chu, S. W., Chen, S. Y., Chern, G. W., Tsai, T. H., Chen, Y. C., Lin, B. L., & Sun, C. K. (2004). Studies of χ (2)/χ (3) tensors in submicron-scaled bio-tissues by polarization harmonics optical microscopy. Biophysical Journal, 86(6), 3914–3922. Cisek, R., Joseph, A., Harvey, M., & Tokarz, D. (2021). Polarization-sensitive second harmonic generation microscopy for investigations of diseased collagenous tissues. Frontiers in Physics, 480. Clays, K., Van Elshocht, S., Chi, M., Lepoudre, E., & Persoons, A. (2001). Bacteriorhodopsin: A natural, efficient (nonlinear) photonic crystal. JOSA B, 18(10), 1474–1482. Collett, E. (2005). Society of Photo-optical Instrumentation Engineers. Field Guide to. Polarization. Cox, G., Kable, E., Jones, A., Fraser, I., Manconi, F., & Gorrell, M. D. (2003). 3-dimensional imaging of collagen using second harmonic generation. Journal of Structural Biology, 141(1), 53–62. de Campos Vidal, B. (2003). Image analysis of tendon helical superstructure using interference and polarized light microscopy. Micron, 34(8), 423–432. Deniset-Besseau, A., Duboisset, J., Benichou, E., Hache, F., Brevet, P. F., & Schanne-Klein, M. C. (2009). Measurement of the second-order hyperpolarizability of the collagen triple helix and determination of its physical origin. The Journal of Physical Chemistry B, 113(40), 13437– 13445. Dora, A.-B., Muriel, R., Julien, D., Patrick, F., Sophie, B., Marie, G., Ganesh, D. S., & Pierre, J. (2012). Journal of Biomedical Optics, 17, 1–4. Duboisset, J., Aït-Belkacem, D., Roche, M., Rigneault, H., & Brasselet, S. (2012). Generic model of the molecular orientational distribution probed by polarization-resolved second-harmonic generation. Physical Review A, 85(4), 043829. Ducourthial, G., Affagard, J. S., Schmeltz, M., Solinas, X., Lopez-Poncelas, M., Bonod-Bidaud, C., et al. (2019). Monitoring dynamic collagen reorganization during skin stretching with fast

300

M.-C. Chen et al.

polarization-resolved second harmonic generation imaging. Journal of Biophotonics, 12(5), e201800336. Elsheikh, T. M. (2008). Asa SL. Chan JK. DeLellis RA. Heffess CS. LiVolsi VA. Wenig BM. Interobserver and intraobserver variation among experts in the diagnosis of thyroid follicular lesions with borderline nuclear features of papillary carcinoma. American Journal of Clinical Pathology, 130, 736–744. Erikson, A., Ortegren, J., Hompland, T., de Lange Davies, C., & Lindgren, M. (2007). Quantification of the second-order nonlinear susceptibility of collagen I using a laser scanning microscope. Journal of Biomedical Optics, 12(4), 044002. Fine, S., & Hansen, W. P. (1971). Optical second harmonic generation in biological systems. Applied Optics, 10(10), 2350–2353. Flörsheimer, M., Bösch, M., Brillert, C., Wierschem, M., & Fuchs, H. (1997). Interface imaging by second-harmonic microscopy. Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena, 15(4), 1564–1568. Franken, P. A., Hill, A. E., Peters, C. E., & Weinreich, G. (1961). Generation of optical harmonics. Physical Review Letters, 7(4), 118. Freund, I., & Deutsch, M. (1986). Second-harmonic microscopy of biological tissue. Optics Letters, 11(2), 94–96. Golaraei, A., Mirsanaye, K., Ro, Y., Krouglov, S., Akens, M. K., Wilson, B. C., & Barzda, V. (2019a). Collagen chirality and three-dimensional orientation studied with polarimetric secondharmonic generation microscopy. Journal of Biophotonics, 12(1), e201800241. Golaraei, A., Kontenis, L., Mirsanaye, K., Krouglov, S., Akens, M. K., Wilson, B. C., & Barzda, V. (2019b). Complex susceptibilities and chiroptical effects of collagen measured with polarimetric second-harmonic generation microscopy. Scientific Reports, 9(1), 1–12. Golaraei, A., Mostaço-Guidolin, L. B., Raja, V., Navab, R., Wang, T., Sakashita, S., et al. (2020). Polarimetric second-harmonic generation microscopy of the hierarchical structure of collagen in stage I-III non-small cell lung carcinoma. Biomedical Optics Express, 11(4), 1851–1863. Gora, M., Karnowski, K., Szkulmowski, M., Kaluzny, B. J., Huber, R., Kowalczyk, A., & Wojtkowski, M. (2009). Ultra high-speed swept source OCT imaging of the anterior segment of human eye at 200 kHz with adjustable imaging range. Optics Express, 17(17), 14880–14894. Graham, L., & Orenstein, J. M. (2007). Processing tissue and cells for transmission electron microscopy in diagnostic pathology and research. Nature Protocols, 2(10), 2439–2450. Gusachenko, I., Latour, G., & Schanne-Klein, M. C. (2010). Polarization-resolved second harmonic microscopy in anisotropic thick tissues. Optics Express, 18(18), 19339–19352. Guthoff, R. F., Zhivov, A., & Stachs, O. (2009). In vivo confocal microscopy, an inner vision of the cornea – A major review. Clinical & Experimental Ophthalmology, 37(1), 100–117. Guy, C. C., Nuno, M., & Jose, F. (2005). Journal of Biomedical Optics, 10, 1–6. Haralick, R. M., Shanmugam, K., & Dinstein, I. H. (1973). Textural features for image classification. IEEE Transactions on Systems, Man, and Cybernetics, 6, 610–621. Harris, J., Norris, G., & McConnell, G. (2008). Characterisation of periodically poled materials using nonlinear microscopy. Optics Express, 16(8), 5667–5672. Houle, M. A., Couture, C. A., Bancelin, S., Van der Kolk, J., Auger, E., Brown, C., et al. (2015). Analysis of forward and backward second harmonic generation images to probe the nanoscale structure of collagen within bone and cartilage. Journal of Biophotonics, 8(11–12), 993–1001. Hung, C. W., Mazumder, N., Lin, D. J., Chen, W. L., Lin, S. T., Chan, M. C., & Zhuo, G. Y. (2021). Label-free characterization of collagen crosslinking in bone-engineered materials using nonlinear optical microscopy. Microscopy and Microanalysis, 27(3), 587–597. Jiang, B. Y., & Chu, S. W. (2008). Trigonal symmetry of type I collagen probed by SHG polarization anisotropy. In Conference on lasers and electro-optics (p. JWA30). Optica Publishing Group. John, S. (1987). Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, 58(23), 2486. Kalluri, R. (2003). Basement membranes: Structure, assembly and role in tumour angiogenesis. Nature Reviews Cancer, 3(6), 422–433.

10 Polarization-Resolved Second-Harmonic Generation for Tissue Imaging

301

Karunendiran, A., Mirsanaye, K., Stewart, B. A., & Barzda, V. (2022). Second harmonic generation properties in chiral sarcomeres of drosophila larval muscles. Frontiers in Physics, 4. Krachmer, J. H. M. M. J. H. E. J. (2011). Cornea volume 1. Mosby/Elsevier. KU, S., Mahato, K. K., & Mazumder, N. (2019). Polarization-resolved Stokes-Mueller imaging: A review of technology and applications. Lasers in Medical Science, 34(7), 1283–1293. Kurman, R. J., Visvanathan, K., Roden, R., Wu, T. C., & Shih, I. M. (2008). Early detection and treatment of ovarian cancer: Shifting from early stage to minimal volume of disease based on a new model of carcinogenesis. American Journal of Obstetrics and Gynecology, 198(4), 351–356. La Vecchia, C., Malvezzi, M., Bosetti, C., Garavello, W., Bertuccio, P., Levi, F., & Negri, E. (2015). Thyroid cancer mortality and incidence: A global overview. International Journal of Cancer, 136(9), 2187–2195. Latour, G., Gusachenko, I., Kowalczuk, L., Lamarre, I., & Schanne-Klein, M. C. (2012). In vivo structural imaging of the cornea by polarization-resolved second harmonic microscopy. Biomedical Optics Express, 3(1), 1–15. Légaré, F., Pfeffer, C., & Olsen, B. R. (2007). The role of backscattering in SHG tissue imaging. Biophysical Journal, 93(4), 1312–1320. Leray, A., Leroy, L., Le Grand, Y., Odin, C., Renault, A., Vié, V., et al. (2004). Organization and orientation of amphiphilic push−pull chromophores deposited in Langmuir−Blodgett monolayers studied by second harmonic generation and atomic force microscopy. Langmuir, 20(19), 8165–8171. Levanon, K., Crum, C., & Drapkin, R. (2008). New insights into the pathogenesis of serous ovarian cancer and its clinical impact. Journal of Clinical Oncology, 26(32), 5284. Liao, C.-S., Zhuo, Z.-Y., Yu, J.-Y., Tzeng, Y.-Y., Chu, S.-W., Yu, S.-F., & Chao, P.-H. G. (2011). Applied Physics Letters, 98, 153703. Lixin, C., Xiaojie, Y., Robert, A. M., Peter, B. N., & David, D. S. (2013). Journal of Biomedical Optics, 18, 1–6. Lloyd, R. V., Erickson, L. A., Casey, M. B., Lam, K. Y., Lohse, C. M., Asa, S. L., et al. (2004). Observer variation in the diagnosis of follicular variant of papillary thyroid carcinoma. The American Journal of Surgical Pathology, 28(10), 1336–1340. Lu, P., Weaver, V. M., & Werb, Z. (2012). The extracellular matrix: A dynamic niche in cancer progression. Journal of Cell Biology, 196(4), 395–406. Mansfield, J. C., Mandalia, V., Toms, A., Winlove, C. P., & Brasselet, S. (2019). Collagen reorganization in cartilage under strain probed by polarization sensitive second harmonic generation microscopy. Journal of the Royal Society Interface, 16(150), 20180611. Mascorro, J. A., & Bozzola, J. J. (2007). Processing biological tissues for ultrastructural study. In Electron microscopy (pp. 19–34). Humana Press. Mazumder, N., & Kao, F. J. (2021). Stokes polarimetry-based second harmonic generation microscopy for collagen and skeletal muscle fiber characterization. Lasers in Medical Science, 36(6), 1161–1167. Mazumder, N., Qiu, J., Foreman, M. R., Romero, C. M., Hu, C. W., Tsai, H. R., et al. (2012). Polarization-resolved second harmonic generation microscopy with a four-channel Stokespolarimeter. Optics Express, 20(13), 14090–14099. Mazumder, N., Qiu, J., Foreman, M. R., Romero, C. M., Török, P., & Kao, F. J. (2013). Stokes vector based polarization resolved second harmonic microscopy of starch granules. Biomedical Optics Express, 4(4), 538–547. Mazumder, N., Hu, C. W., Qiu, J., Foreman, M. R., Romero, C. M., Török, P., & Kao, F. J. (2014). Revealing molecular structure and orientation with Stokes vector resolved second harmonic generation microscopy. Methods, 66(2), 237–245. Mazumder, N., Deka, G., Wu, W. W., Gogoi, A., Zhuo, G. Y., & Kao, F. J. (2017a). Polarization resolved second harmonic microscopy. Methods, 128, 105–118. Mazumder, N., Xiang, L. Y., Qiu, J., & Kao, F. J. (2017b). Investigating starch gelatinization through Stokes vector resolved second harmonic generation microscopy. Scientific Reports, 7(1), 1–9.

302

M.-C. Chen et al.

Mazumder, N., Yun-Xiang, L., Qiu, J., & Kao, F. J. (2018). Revealing molecular structure of starch with Stokes-vector based second harmonic generation microscopy. Journal of Optics, 47(1), 40–46. Mazumder, N., Balla, N. K., Zhuo, G. Y., Kistenev, Y. V., Kumar, R., Kao, F. J., et al. (2019). Label-free non-linear multimodal optical microscopy—Basics, development, and applications. Frontiers in Physics, 7, 170. Mazza, D., Bianchini, P., Caorsi, V., Cella, F., Mondal, P. P., Ronzitti, E., Testa, I., Vicidomini, G., & Diaspro, A. (2008). In L. P. Biophotonics & P. M. Fauchet (Eds.), Non-linear microscopy (pp. 47–69). Springer. McIntosh, M. W., Drescher, C., Karlan, B., Scholler, N., Urban, N., Hellstrom, K. E., & Hellstrom, I. (2004). Combining CA 125 and SMR serum markers for diagnosis and early detection of ovarian carcinoma. Gynecologic Oncology, 95(1), 9–15. Miller, B. E. (2005). Role of CT and MR imaging in predicting optimal cytoreduction of newly diagnosed primary epithelial ovarian cancer: Aliya Qayyum, Fergus V. Coakley, Antonia C. Westphalen, Hedvig Hricak, William T. Okuno, Bethan Powell. Gynecol Oncol 2005; 96 (2): 301–6. The Women’s Oncology Review, 5(3), 159–160. Murti, Y. V. G. S., & Vijayan, C. (2021). Physics of nonlinear optics. Springer Nature. Nadiarnykh, O., LaComb, R., Campagnola, P. J., & Mohler, W. A. (2007). Coherent and incoherent SHG in fibrillar cellulose matrices. Optics Express, 15(6), 3348–3360. Odin, C., Le Grand, Y., Renault, A., Gailhouste, L., & Baffet, G. (2008a). Orientation fields of nonlinear biological fibrils by second harmonic generation microscopy. Journal of Microscopy, 229(1), 32–38. Odin, C., Guilbert, T., Alkilani, A., Boryskina, O. P., Fleury, V., & Grand, Y. L. (2008b). Optics Express, 41(16), 16151–16165. Orgel, J. P. R. O., San Antonio, J. D., & Antipova, O. (2011). Molecular and structural mapping of collagen fibril interactions. Connective Tissue Research, 52(1), 2–17. Paech, D. C., Weston, A. R., Pavlakis, N., Gill, A., Rajan, N., Barraclough, H., et al. (2011). A systematic review of the interobserver variability for histology in the differentiation between squamous and nonsquamous non-small cell lung cancer. Journal of Thoracic Oncology, 6(1), 55–63. Paris, O. (2008). Biointerphases, 3, FB16–FB26. Parodi, V., Jacchetti, E., Osellame, R., Cerullo, G., Polli, D., & Raimondi, M. T. (2020). Nonlinear optical microscopy: From fundamentals to applications in live bioimaging. Frontiers in Bioengineering and Biotechnology, 8, 585363. Patrick Christian, S., Beop-Min, K., Alexander, M. R., Karen, M. R., & Luiz Barroca Da, S. (2002). Journal of Biomedical Optics, 7, 205–214. Pena, A. M., Fabre, A., Débarre, D., Marchal-Somme, J., Crestani, B., Martin, J. L., et al. (2007). Three-dimensional investigation and scoring of extracellular matrix remodeling during lung fibrosis using multiphoton microscopy. Microscopy Research and Technique, 70(2), 162–170. Pendleton, E. G., Tehrani, K. F., Barrow, R. P., & Mortensen, L. J. (2020). Second harmonic generation characterization of collagen in whole bone. Biomedical Optics Express, 11(8), 4379–4396. Pinsard, M., Laverty, S., Richard, H., Dubuc, J., Schanne-Klein, M. C., & Légaré, F. (2019). Maturation of the meniscal collagen structure revealed by polarization-resolved and directional second harmonic generation microscopy. Scientific Reports, 9(1), 1–11. Plamann, K., Aptel, F., Arnold, C. L., Courjaud, A., Crotti, C., Deloison, F., et al. (2010). Ultrashort pulse laser surgery of the cornea and the sclera. Journal of Optics, 12(8), 084002. Plotnikov, S. V., Millard, A. C., Campagnola, P. J., & Mohler, W. A. (2006). Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres. Biophysical Journal, 90(2), 693–703. Prasad, P. N. (2003). Introduction to biophotonics. Wiley. Psilodimitrakopoulos, S., Artigas, D., Soria, G., Amat-Roldan, I., Planas, A. M., & Loza-Alvarez, P. (2009a). Quantitative discrimination between endogenous SHG sources in mammalian tissue, based on their polarization response. Optics Express, 17(12), 10168–10176.

10 Polarization-Resolved Second-Harmonic Generation for Tissue Imaging

303

Psilodimitrakopoulos, S., Santos, S. I., Amat-Roldan, I., Nair, A. T. K., Artigas-García, D., & Loza-Alvarez, P. (2009b). In vivo, pixel-resolution mapping of thick filaments’ orientation in nonfibrilar muscle using polarization-sensitive second harmonic generation microscopy. Journal of Biomedical Optics, 14(1), 014001. Psilodimitrakopoulos, S., Amat-Roldan, I., Loza-Alvarez, P., & Artigas, D. (2010). Estimating the helical pitch angle of amylopectin in starch using polarization second harmonic generation microscopy. Journal of Optics, 12(8), 084007. Romijn, E. I., Finnøy, A., & Lilledahl, M. B. (2019). Analyzing the feasibility of discriminating between collagen types I and II using polarization-resolved second harmonic generation. Journal of Biophotonics, 12(1), e201800090. Roth, S., & Freund, I. (1979). Second harmonic generation in collagen. The Journal of Chemical Physics, 70(4), 1637–1643. Rouède, D., Schaub, E., Bellanger, J. J., Ezan, F., Scimeca, J. C., Baffet, G., & Tiaho, F. (2017). Determination of extracellular matrix collagen fibril architectures and pathological remodeling by polarization dependent second harmonic microscopy. Scientific Reports, 7(1), 1–12. Samim, M., Prent, N., Dicenzo, D., Stewart, B., & Barzda, V. (2014). Second harmonic generation polarization properties of myofilaments. Journal of Biomedical Optics, 19(5), 056005. Schmieder, R. W. (1969). Stokes-algebra formalism. JOSA, 59(3), 297–302. Stoller, P., Reiser, K. M., Celliers, P. M., & Rubenchik, A. M. (2002). Polarization-modulated second harmonic generation in collagen. Biophysical Journal, 82(6), 3330–3342. Su, P. J., Chen, W. L., Chen, Y. F., & Dong, C. Y. (2011). Determination of collagen nanostructure from second-order susceptibility tensor analysis. Biophysical Journal, 100(8), 2053–2062. Tiaho, F., Recher, G., & Rouède, D. (2007). Estimation of helical angles of myosin and collagen by second harmonic generation imaging microscopy. Optics Express, 15(19), 12286–12295. Tokarz, D., Cisek, R., Golaraei, A., Asa, S. L., Barzda, V., & Wilson, B. C. (2015). Ultrastructural features of collagen in thyroid carcinoma tissue observed by polarization second harmonic generation microscopy. Biomedical Optics Express, 6(9), 3475–3481. Tokarz, D., Cisek, R., Joseph, A., Golaraei, A., Mirsanaye, K., Krouglov, S., et al. (2019). Characterization of pancreatic cancer tissue using multiphoton excitation fluorescence and polarization-sensitive harmonic generation microscopy. Frontiers in Oncology, 9, 272. Torzilli, P. A., Bourne, J. W., Cigler, T., & Vincent, C. T. (2012). A new paradigm for mechanobiological mechanisms in tumor metastasis. In Seminars in cancer biology 22, 5–6, pp. 385–395). Academic Press. Tsafas, V., Gavgiotaki, E., Tzardi, M., Tsafa, E., Fotakis, C., Athanassakis, I., & Filippidis, G. (2020). Polarization-dependent second-harmonic generation for collagen-based differentiation of breast cancer samples. Journal of Biophotonics, 13(10), e202000180. Tuer, A. E., Krouglov, S., Prent, N., Cisek, R., Sandkuijl, D., Yasufuku, K., et al. (2011). Nonlinear optical properties of type I collagen fibers studied by polarization dependent second harmonic generation microscopy. The Journal of Physical Chemistry B, 115(44), 12759–12769. Tuer, A. E., Akens, M. K., Krouglov, S., Sandkuijl, D., Wilson, B. C., Whyne, C. M., & Barzda, V. (2012). Hierarchical model of fibrillar collagen organization for interpreting the second-order susceptibility tensors in biological tissue. Biophysical Journal, 103(10), 2093–2105. Tzeng, Y. Y., Zhuo, Z. Y., Lee, M. Y., Liao, C. S., Wu, P. C., Huang, C. J., et al. (2011). Observation of spontaneous polarization misalignments in periodically poled crystals using second-harmonic generation microscopy. Optics Express, 19(12), 11106–11113. Wang, X. H., Chang, S. J., Lin, L., Wang, L. R., Huo, B. Z., & Hao, S. J. (2010). Vector model for polarized second-harmonic generation microscopy under high numerical aperture. Journal of Optics, 12(4), 045201. Wang, J. Y., Mansfield, J. C., Brasselet, S., Vergari, C., Meakin, J. R., & Winlove, C. P. (2021). Micro-mechanical damage of needle puncture on bovine annulus fibrosus fibrils studied using polarization-resolved second harmonic generation (P-SHG) microscopy. Journal of the Mechanical Behavior of Biomedical Materials, 118, 104458.

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Werkmeister, E., De Isla, N., Netter, P., Stoltz, J. F., & Dumas, D. (2010). Collagenous extracellular matrix of cartilage submitted to mechanical forces studied by second harmonic generation microscopy. Photochemistry and Photobiology, 86(2), 302–310. Williams, R. M., Zipfel, W. R., & Webb, W. W. (2005). Interpreting second-harmonic generation images of collagen I fibrils. Biophysical Journal, 88(2), 1377–1386. Yablonovitch, E. (1987). Inhibited spontaneous emission in solid-state physics and electronics. Physical Review Letters, 58(20), 2059. Yeh, A. T., Hammer-Wilson, M. J., Van Sickle, D. C., Benton, H. P., Zoumi, A., Tromberg, B. J., & Peavy, G. M. (2005). Nonlinear optical microscopy of articular cartilage. Osteoarthritis and Cartilage, 13(4), 345–352. Zhuo, Z. Y., Liao, C. S., Huang, C. H., Yu, J. Y., Tzeng, Y. Y., Lo, W., et al. (2010). Second harmonic generation imaging–a new method for unraveling molecular information of starch. Journal of Structural Biology, 171(1), 88–94. Zhuo, G. Y., KU, S., KM, S., Kistenev, Y. V., Kao, F. J., Nikolaev, V. V., et al. (2021). Labelfree multimodal nonlinear optical microscopy for biomedical applications. Journal of Applied Physics, 129(21), 214901.

Part III

Applications of Polarization Techniques

Chapter 11

An Introduction to Fundamentals of Cancer Biology S. Sriharikrishnaa, Padmanaban S. Suresh, and Shama Prasada K.

1 Introduction Cancer is an illness wherein cells multiply and grow abnormally, invading other tissues and organs via the bloodstream and lymphatic systems (Thiagalingam, 2015). The human body contains trillions of cells, and cancer can manifest itself practically anywhere in the body of human beings. Cell division is how human cells grow and divide to form new cells (Weinberg & Weinberg, 2006). Old and damaged cells die and are replaced by new cells. Once this tightly controlled process fails, affected cells divide and grow when they are supposed to undergo cell death. Tumors are tissue lumps that are originated from these abnormal cells. Tumor cells can be cancerous or not (benign). By metastasis, the malignant cell can invade the neighboring tissue, enter the circulation, travel to distant organs, colonize them, and develop into new tumors (Chaffer & Weinberg, 2011). Malignant tumors invade surrounding tissues and enter into circulation and distant areas of the body to form new tumors. Many forms of cancer grow into solid tumors. However, a few cancer, namely, leukemia, do not generate solid tumors (Coghlin & Murray, 2010). Benign tumors, however, do not infiltrate or expand into the underlying tissue. Benign tumors rarely recur after their removal, whereas malignant tumors occasionally show recurrence. However, benign tumors, when grown in large, can be fatal. Some, like brain tumors of benign type, can cause serious illnesses or even death.

S. Sriharikrishnaa · Shama Prasada K. () Department of Cell and Molecular Biology, Manipal School of Life Sciences, Manipal Academy of Higher Education, Manipal, Karnataka, India e-mail: [email protected] P. S. Suresh School of Biotechnology, National Institute of Technology, Calicut, Kerala, India © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Mazumder et al. (eds.), Optical Polarimetric Modalities for Biomedical Research, Biological and Medical Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-031-31852-8_11

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2 Difference Between Cancer Cells and Normal Cells Cancer cells are distinct from normal cells in numerous ways. Cancer cells show differences in morphology, lifespan, growth rate, cell-to-cell communication, and immune response. Cancer cells grow and proliferate even in the absence of mitogenic signaling pathways (Pani et al., 2010). However, normal cells grow and proliferate only in the presence of growth signals. Cancer cells harbor deregulated apoptosis signaling and show resistance to apoptosis. Cancer cells can sometimes enter surrounding tissue areas and show metastasis. Normal cells cannot generally move around the body. Normal cells stop growing when they come in contact with other types of cells. However, cancer cells can move around the body and continue to grow even if they come in contact with other types of cells (Friedl & Wolf, 2003). Cancer cells promote angiogenesis and escape from the innate and adaptive immune system. Cancer cells show numerous genetic and epigenetic aberrations than normal cells. Cancer cells undergo metabolic reprogramming for their growth and survival (Gupta et al., 2017). The distinguishing characteristic features of normal and cancer cells are shown in Table 11.1.

3 Types of Cancer Cancer can develop from abnormal cell proliferation and growth in any organ. As a result, cancers behave and respond to treatment differently depending on the tissue and cell type. Cancer is classified as benign or malignant based on its ability to invade and spread to nearby structures. Benign tumors are capsulated cells that grow slowly, are noninvasive, and do not spread. They have distinct, smooth, and regular borders. Malignant tumors are noncapsulated, fast-growing, invasive cancerous cells that spread to distant organs via the lymphatic system or bloodstream (Raymond & Ruddon, 2007). Based on cells’ origin, benign and malignant tumors are categorized into carcinomas, adenoma, sarcoma, and leukemia or lymphoma. The most common cancer in humans arising from epithelial cells is carcinoma. Likewise, a benign tumor with glandular formation is an adenoma; its malignant form is adenocarcinoma. Cancer that arises from muscle cells and connective tissues is called sarcoma. Other types of cancer are leukemia and lymphoma, derived from hemopoietic cell precursors and white blood cells. Melanoma is pigment cells of the skin that form pigment granules. Further subsets of each tumor type are presently based on the cell type, location, and microscopic aspects (Jemal et al., 2019). Table 11.2 (a) and (b) show the top ten cancers incidence and morbidity rates in males and females, respectively.

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Table 11.1 Distinguising characteristic features between normal and tumor cell S. no. 1

Feature Shape, size, appearance, organization, lifespan of cell

Normal cell Regular, proportionate, even, well organized, finite

2 3

Nucleus Nucleus to cytoplasm ratio Chromosomes Cells nature Maturation

Small and light Small

Cancer cell Irregular, disproportionate, variable, disorganized, infinite Large and dark Large

Normal karyotype Specialized Undergoes maturation and follows senescence Contact inhibition Systematic and controlled Clearly demarcated Angiogenesis during repair Visible Normal Present Apoptosis, autophagy Alkaline Glucose Aerobic and 36

Abnormal Nonspecialized Undifferentiated and immature Overlapping growth Out of control Poorly defined Neo angiogenesis Evades Increased Absent No Acidic Fat, Ketone, glucose Anaerobic and 2

Required No Normal, quiescent, self-renewable, differentiable with organogenic capacity Less Less Very high Tight

Not required Metastasis and Invasion Abnormal, mitotic, dysregulated differentiation with tumorigenic capacity High High Very low Loose

4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21

Cell–cell communication Growth Cell boundaries Blood supply Immune cells DNA and RNA synthesis DNA repair mechanism Cell death Cell environment Energy source Glycolysis and ATP production Oxygen Ability to spread Stem cells

22 23 24 25

Proliferation Migration Energy efficiency Adherence

4 Cancer Development Cancer generally develops when normal cells lose their ability to control the abnormal behavior of cells due to genetic and epigenetic changes (Baylin, 2001). The faulty cell thus produce acts as a progenitor cell, from which an abnormal mass of cells is produced. Chemicals, infections, ultraviolet rays, and radioactive materials can cause considerable DNA damage (genetic and epigenetic aberration), resulting in the development of defective cells. The selection and multiplication of defective cells with abnormal properties can be due to epigenetic changes resulting

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Table 11.2 Global cancer incidence and mortality rate in male and female S. no. Cancer type Incidence (%) (a) Top 10 cancer incidence and mortality rate in female globally 1 Breast 24.5 2 Lung 8.4 3 Colorectal 9.4 4 Cervix uteri 6.5 5 Thyroid 4.9 6 Liver 3.0 7 Stomach 4.0 8 Pancreas 4.9 9 Ovary 4.7 10 Leukemia 2.8 (b) Top 10 cancer incidence and mortality rates in males globally 1 Lung 14.3 2 Prostate 14.1 3 Liver 10.5 4 Colorectal 10.6 5 Stomach 7.1 6 Bladder 4.4 7 Esophagus 6.8 8 Pancreas 4.5 9 Non-Hodgkin Lymphoma 3.0 10 Leukemia 2.7

Mortality (%) 15.5 13.7 9.5 7.7 3.1 5.7 3.0 3.0 3.4 3.0 21.5 6.8 6.3 9.3 9.1 2.9 4.2 2.7 2.7 3.2

in uncontrolled proliferation, growth, and tumor formation, as shown in Fig. 11.3 (Ren et al., 2017). Tumor clonality is a crucial fundamental characteristic of cancer cells. Tumor clonality refers to the formation of a tumor from a single cell that multiplies abnormally. The origin of cancer from single cells or tumor clonality does not indicate that the original progenitor cells from cancer developed and possessed all of the attributes of cancer cells. Surprisingly, cancer development is a multistep process in which cells progressively become malignant due to the continued accumulation of epigenetic changes (Marusyk & Polyak, 2010). Cancer is viewed as a multistep process at the cellular level, consisting of continuous epigenetic changes and the selection of cells with a greater capacity to proliferate, grow, survive, invade, and metastasize (Joyce & Pollard, 2009). A schematic representation of cancer progression is shown in Fig. 11.1. The first step in tumor development is tumor initiation. Tumors are thought to begin because of abnormal genetic changes (mutation) in single cells, which lead to abnormal growth and proliferation. The abnormal growth and proliferation may produce a population of cells derived from a single clone. During tumor progression, additional epigenetic changes occur, resulting in the evolution of more rapidly growing and aggressive cells. The descendant of such cells will consequently become more dominant within a tumor mass, contributing

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Fig. 11.1 Progression and causes of cancer

to clonal selection. Interestingly, the clonal selection is a continuous process during tumor progression resulting in cells with more malignant behavior (Couch, 1996).

5 Causes of Cancer Experimental and epidemiological studies suggest that many substances can cause cancer. Any cancer-causing agents are called carcinogens. Cancer development is a multistep process involving a complex interaction between epigenetic and environmental factors. Further, carcinogens can be categorized into three groups such as (a) physical carcinogens (ultraviolet, X-ray, ionization radiation, and radioactive elements from industry), (b) chemical carcinogens (asbestos, benzidene, benze ne, cadmium, radon, nickel, and vinyl chloride), and (c) biological carcinogens (Hepatitis-B virus, Hepatitis-C virus, Human papillomaviruses, Epstein-Barr virus, human herpes virus-8, Helicobacter pylori, and Toxoplasma gondii) (Das et al., 2020). Carcinogens can be categorized into four groups such as groups 1, 2A, 2B, and 3. These are classified by the International Agency for Research on Cancer (IARC). Group 1 (for example, smoking, asbestos, and processed meat) have been shown to cause human cancer as shown in Fig. 11.1. The most likely carcinogenic agents are classified as group 2A carcinogens (for example, anabolic steroids, Nnitrosodiethylamine, and pioglitazone). Carcinogens in group 2B category have limited proof of carcinogenicity in human beings and less than adequate scientific evidence in animals (for example, gasoline, engine exhaust, and progestin). The

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group 3 agents are not classified as carcinogens as evidence of carcinogenicity in humans and animals are insufficient (for example, dental materials, ceramic implants). Tumor promoters are agents that do not have tumorigenic features (IARC, 2020). However, when exposed to a carcinogen, they increase tumorigenicity. Tumor promotes by enhancing cell proliferation, acting as tumor promoters, and helping establish tumors during the early stages of tumor development. Hormones such as estrogen act as tumor promoters in certain types of cancer (for example, endometrial cancer) (Rodriguez et al., 2019) (Table 11.3).

6 Properties of Cancer Cells Cancer cells have several cellular and molecular property that distinguish them from normal cells. Cancer cells proliferate uncontrollably and grow in an unorganized manner, in contrast to normal cells. Cancer cells exhibit decreased cell-to-cell and cell-to-matrix adhesion and are less adherent than normal cells. Cancer cells differ significantly from normal cells in terms of intracellular and extracellular changes. Cancer cells show a loss of differentiation and control by growth factor signaling (Janiszewska et al., 2020). Normal cells have a rate-limiting mechanism called density-dependent inhibition, controlled by well-organized signaling networks. Growth factor signaling generally drives normal cells to proliferate. On the contrary, tumor cell grows and proliferates even when deprived of growth factor signaling via auto stimulation. Cancer cells have a distinct genome and epigenome than normal cells. Normal and cancer cells have very different intracellular and extracellular microenvironments (Wei et al., 2020). Cancer cells undergo metabolic reprogramming and adaptation to support their growth and survival. Cancer cells are resistant to radiation and chemotherapy. Cancer cells exhibit a loss of anchorage dependence, contact inhibition, a lower requirement for growth factors, sustained cell division, angiogenesis, resistance to apoptosis, immune system escape, and metabolic reprogramming (Pickup et al., 2014). These abnormalities convert normal cells to get transformed into benign or malignant tumors.

7 Hallmarks of Cancer The development and progression of cancer are highly complex processes. Many researchers are experimenting to understand the complexities associated with carcinogenesis. The concept of “the hallmarks of cancer” was proposed by Hanahan and Weinberg in the year 2000. The complexities of cancer biology were categorized into six major classes: resistance to apoptosis, sustaining proliferative signaling, evading growth suppressors, activating invasion and metastasis, enabling replication immortality, and induction of angiogenesis (Hanahan & Weinberg, 2011). The

(a) Virus-associated cancer S. no Causative agent 1 Hepatitis – B 2 Papilomavirus 3 Epstein- Barr Virus 4 Herpesvirus 8 5 Human T-Cell Leukemia virus 6 Human Immunodeficiency virus 7 Hepatitis-C (b) Environmental factors – Cancer S. no Carcinogens 1 Arsenic 2 Asbestos 3 Benzene 4 Beryllium 5 Cadmium 6 Chromium 7 Ethylene oxide

Table 11.3 Causes of cancer

References Martinez et al. (2011) Heintz et al. (2010) Snyder (2012) Boffetta et al. (2012) Chen et al. (2016) Urbano et al. (2012) Vincent et al. (2019)

Cancer sites Lungs, skin Mesothelioma, lungs Blood and lymph nodes Lungs Prostate Lung Blood

(continued)

References Zhang et al. (2021a) Burd (2003) Brady et al. (2008) and Young and Dawson (2014) Mesri et al. (2010) Ratner (2005) Grigoriou et al. (2017) Andrade et al. (2009)

Cancer type Lung Cervix Burkitt’s Lymphoma, Nasopharyngeal Kaposi’s Sarcoma Leukemia/Lymphoma Kaposi carcinoma Liver

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(d) Epigenetic causes of cancer S. no Modification 1 H3K4me1 2 H3K4me 2 3 H3K27me3 4 p53 5 RB1 6 PTEN 7 BRCA1, BRCA2 8 EGFR2 9 MYC 10 miR-17/92 family 11 miR-21 12 miR-372/373 13 miR-155 14 miR-15a/16 family 15 let-7 family 16 miR-29 family 17 miR-34 family

(c) Genetic causes of cancer S. no Gene 1 Ras family 2 N-Myc 3 c-Myc 4 Bcl-2 5 EGFR 6 p53 7 RB1 8 WT1 9 DCC 10 NF1 11 FAP 12 APC

Table 11.3 (continued)

Alteration Decreased Decreased Decreased Hypermethylation Hypermethylation Hypermethylation Hypermethylation Hypermethylation Hypomethylation Upregulated Upregulated Upregulated Upregulated Downregulated Downregulated Downregulated Downregulated

Chromosome abnormality Point mutation Gene amplification Translocation Translocation Deletion loss of function Deletion of Chromosome Imprinting defect in chromosome Deletion of gene segment Point mutation Nonsense mutation Gene deletion Cancer Bladder, prostate Lung, kiver, prostate, kidney, breast, pancreas Lung, ovarian, breast Brain, breast, osteosarcoma Retinoblastoma Glioma, uterus Breast,ovary Head and neck, glioblastoma Head and neck, lung, breast Breast, lung, liver, colon AML, CLL, breast, lung, liver, colon, stomach Testicular AML, CLL, colon, lung, breast CLL Breast, lung AML, CLL, lung, breast Pancreas, colon, breast

Cancer type Melanoma, colon, pancreas Neuroblastoma, lung CML, Burkitt Lymphoma B-Cell lymphoma Squamous cell carcinoma Breast, lung , liver, ovarian Retinoblastoma, breast, lung, bladder Wilm’s Tumor Colon Neurofibromatosis Colon Colorectal References Martinez et al. (2019) Li et al. (2018) Wei et al. (2008) Li et al. (2006) Anwar and Lehmann (2018) Zhang et al. (2021b) Otani et al. (2014) and Chan et al. (2002) Montero et al. (2006) Poole and van Riggelen (2017) Concepcion et al. (2012) Feng and Tsao (2016) Shah et al. (2021) Tili et al. (2009) Calin et al. (2008) Chirshev et al. (2019) Jiang et al. (2014) Zhang et al. (2019)

References Prior et al. (2012) Liu et al. (2021) Li et al. (2003) Schuetz et al. (2012) Lee et al. (2005) Olivier et al. (2010) Di Fiore et al. (2013) Ruteshouser et al. (2008) Mehlen & Fearon (2004) Abramowicz and Gos (2014) Talseth-Palmer (2017) Fodde (2002)

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Fig. 11.2 Pictorial representation of 8 hallmarks of cancer and its associated genes

revision of Hanahan and Weinberg’s cancer hallmarks suggested categorizing the complexities of cancer biology into ten major categories: sustaining proliferative signal, evading growth suppressors, avoiding immune destruction, enabling replicative immortality, tumor-promoting inflammation, activating invasion and metastasis, inducing angiogenesis, genome instability and mutations, resisting cell death, and deregulating cellular energetics (Fouad & Aanei, 2017). The biological features acquired by cancer cells during cancer development and progression are explained below and pictorially represented in Fig. 11.2.

7.1 Uncontrolled and Sustained Proliferation Cell proliferation is the rate at which a cancer cell duplicates its DNA and divides into two different cells. Uncontrolled cell proliferation is one of the critical hallmarks of cancer cells. Cancer cells develop the ability to proliferate uncontrollably due to disrupting cellular genes and pathways that usually control cell proliferation. Uncontrolled and sustained cell proliferation is primarily associated with mutations in cell proliferation pathway genes and activating proto-oncogenes to oncogenes (Golias et al., 2004). Uncontrolled and sustained cell proliferation, in turn, contributes to the acquisition of properties of cancer cells, such as uncontrolled growth, invasion and spread to other tissues, insensitivity to anti-growth signals, sustained nutrient supply, and resistance to apoptosis (Nenclares & Harrington, 2020). If the cancer cells divide more quickly, the disease grows faster or more aggressively. One of the critical steps toward uncontrolled cell proliferation is the

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activation of proto-oncogenes into oncogenes. Oncogenes typically encode proteins that differ structurally and functionally from their proto-oncogene counterparts. Aberrant activation of oncogenes and downregulation of tumor suppressor genes were reported to contribute to sustained cell proliferation. For example, in unmutated conditions, Ras is activated by the binding of growth factors to its receptor leading to the activation of cell division and proliferation. However, oncogenic Ras can induce cell division and proliferation even without growth factors. This suggests that the mutation and subsequent activation of Ras can promote cell proliferation even in the absence of stimulus resulting in cell-controlled proliferation (Riesco et al., 2017). Many signal transduction pathways are aberrantly activated in cancer cells. Cell proliferation and dysregulated cell cycle are interconnected. Aberrations in Wnt, Hedgehog, Steroid, Integrin, Receptor tyrosine kinase, Cytokine, and Notch signaling are a few pathways connected with sustained and uncontrolled proliferation of cells in multiple cancer types (Pelullo et al., 2019).

7.2 Evading Growth Suppressor The absence of growth regulatory systems enables neoplastic cells to replicate indefinitely and avoid elimination, growth arrest, and senescence by tumor suppressor proteins. Evading growth suppressor signaling is another crucial hallmark of cancer cells. Cancer cells resist a signaling pathway that would typically halt their growth. Cancer cells must disentangle themself from the various signals that slow down cellular proliferation. Cancer cells escape from growth suppressors to promote continuous cell proliferation (Sever & Brugge, 2015). p53 and pRB are the two crucial tumor suppressor proteins. Many potential oncogenes target p53 and pRB to promote cell proliferation and apoptosis resistance. Usually, p53 and pRB activation promotes senescence, apoptosis, or cell cycle arrest. Many cancers lose the regulation of pathways linked to growth suppression by p53 and pRB. Interestingly, p53 loss of function mutations has been discovered in 65% of colon and 50% of lung cancers (Hickman, 2002). pRB combines extracellular and intracellular signals to determine whether cells should grow and divide. Functional loss of pRB activity via genetic or epigenetic means promotes cell cycle progression, resulting in continuous cell proliferation (Sachdeva & O’Brien, 2012). p53 protein is critical to sensing intracellular stress and DNA damage. Cells undergo cell cycle arrest via activating p53 in response to cellular stress and DNA damage until the conditions are normalized. p53 promotes apoptosis if the intracellular damage is not reversible (Ozaki & Nakagawara, 2011). Many growth factors signaling pathways (Example: VEGF, FGF, EGF, PDGF) are aberrantly activated in cancer cells, promoting uncontrolled and sustained growth via activation of cell cycle progression. Thus, identifying and targeting the direct signaling pathways activated by tumor suppressor loss and suppressor is an effective method for overcoming tumor suppressor evasion (Witsch et al., 2010). Furthermore, numerous in vitro and in vivo functional studies demonstrated the

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importance of Tumor suppressor genes in cancer formation inhibition. Therefore, Evasion and suppression is a distinct feature of cancer, and it is required to maintain continuous cancer cell proliferation and, later, tumor growth.

7.3 Resistance Against Cell Death Cancer cells show resistance to apoptosis, also known as “programmed cell death,” for sustained growth and proliferation. Induction of apoptosis is a natural process of controlling cancer development. Both intrinsic and extrinsic factors control apoptosis. The apoptotic machinery consists of both upstream regulator proteins and downstream effector proteins (Elmore, 2007). The upstream regulators include extracellular or extrinsic pathways such as Fas ligand and receptor and tumor necrosis factor receptors. The intracellular or intrinsic pathway consists of a series of intracellular signals. The downstream effectors include inactive proteases such as caspase 8 and 9 that are activated in response to apoptotic stimulus leading to proteolytic cleavage of inactive proteases resulting in the disassembly of intracellular structures and apoptosis (Parrish et al., 2013). Cancer cells resist apoptosis by suppressing pro-apoptotic gene expression and activating anti-apoptotic genes. Loss of p53 function disrupts the balance between the pro- and anti-apoptotic family of genes (e.g., Bax and Bcl-2). Compromise in death receptors and their ligand expression has been shown to evade apoptosis in cancer cells. Cancer cells avoid cell death by enhancing the expression of anti-apoptotic proteins (e.g., Bcl2, Akt, Mcl-1) and reducing pro-apoptotic proteins (e.g., Bax, Bak, Bad) (Fernald & Kurokawa, 2013). Besides apoptosis, cells also use necrosis and autophagy to maintain cellular homeostasis. Necrosis is the passive breakdown of a dying cell, but it can also be an active, controlled process governed by different cellular regulators and effectors than apoptosis. A wide range of conditions can cause necroptosis, including a deficit of oxygen and energy, a viral infection, and inflammation. Autophagy, a program that can cause cell death, functions as a cellular organelle recycling system, allowing cells to respond to nutrient shortages by digesting nonessential cellular organelles or recycling their component elements (Fink & Cookson, 2005). Cancer cells modify the autophagy pathway to promote cell survival.

7.4 Induction of Angiogenesis Induction of angiogenesis is a crucial feature cancer cells use for their growth and survival. Angiogenesis is the generation and development of blood vessels from existing blood vessels. It normally occurs as part of healing of wounds and also during the female reproductive cycle (Bielenberg & Zetter, 2015). Tumor-associated vasculature ensures a constant supply of oxygen, glucose, and nutrients needed for

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cancer cell proliferation and survival. Benign tumors can survive in an inactive form that the insufficient blood supply could cause. The “angiogenic switch” takes place when angiogenesis is stimulated in a silent tumor, and growth factors are secreted to stimulate endothelial cell sprouting and chemotaxis toward the tumor mass. The angiogenic switch is regulated by factors that control angiogenesis inducers and inhibitors (Menzel et al., 2020). The hypoxia-inducible transcription factor (HIF) system activation drives the expression of hundreds of genes that either directly or indirectly regulate angiogenesis. HIF-1 stabilization under the hypoxic conditions of the tumor mass activates several angiogenic process-associated genes (Ziello et al., 2007). The genes activated in response to HIF-1 stabilization are vascular endothelial growth factor (VEGF), fibroblast growth factor (bFGF), or platelet-derived growth factor (PDGF). VEGF via the VIGFR receptor promotes angiogenesis. Angiogenic factors secreted from tumors (VEGF, bFGF, EGF, and HGF) stimulate endothelial cells from new blood vessels (Zimna & Kurpisz, 2015). Thrombospondin 1, angiostatin, and endostatin are angiogenesis inhibitors that negatively regulate angiogenesis signaling. These proteins regulate normal transient angiogenesis during wound healing and angiogenesis induced by cancer cells. Mechanisms leading to angiogenesis are diverse. For example, increased expression of VEGF due to hypoxia or Ras or Myc (oncogene signaling) can promote angiogenesis to support the growth and survival of cancer cells. Furthermore, overexpression of FGF and other pro-angiogenic factors can promote angiogenesis, thereby boosting cancer cell growth and survival. Leukocytes invading malignant lesions can activate the angiogenic switch, allowing angiogenesis to continue (DeNardo et al., 2008).

7.5 Metabolic Reprogramming Metabolic reprogramming is another critical hallmark of cancer. Cancer cells undergo metabolic reprogramming to support the high energy demand of the growing tumor. The metabolic reprogramming is achieved via the activation of an oncogene, silencing of tumor suppressor genes, and mutant metabolic enzymes. Metabolic reprogramming supports cancer cells’ growth, proliferation, migration, invasion, and metastasis (Mullen & DeBerardinis, 2012). Cancer cells, for example, switch from oxidative phosphorylation to aerobic glycolysis to produce adenosine triphosphate, a process known as the Warburg effect (Vander Heiden et al., 2009). Numerous mechanisms have been discovered to facilitate cancer cell metabolic reprogramming. Genome instability, activation of specific oncogenes (K-ras, MYC, mTOR, and p53), and epigenetic changes have contributed to the Warburg effect (Schiliro & Firestein, 2021). Changes in mitochondrial structure and function have been linked to increased glycolytic rates in cancer cells. Extrinsic factors, including the tumor microenvironment, also contribute to the metabolic reprogramming of cancer cells. In solid cancers, the tumor microenvironment is commonly hypoxic, which activates HIF-1 (Abou Khouzam et al., 2021).

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The activation of HIF-1 negatively regulates mitochondrial respiratory chain function to induce glycolysis. Stromal cells, such as tumor-associated macrophages, have been linked to the formation of a hypoxic tumor microenvironment to promote anaerobic glycolysis and metabolic reprogramming (Sormendi & Wielockx, 2018). Cancer cells exhibit increased glutamine uptake and glutaminolysis. Using glutamine as an oxidative phosphorylation substrate produces more than 50% of the ATP tumor cells require (Yang et al., 2014). Furthermore, glutamine is a starting material for several molecules (fatty acids, pyrimidines, purines, and amino acids) that are required for rapidly proliferating cells. Lipid metabolism appears to be reprogrammed in rapidly dividing cells. Upregulation of fatty acid synthase (FASN), followed by de novo fatty acid synthesis, occurs commonly in cancer cells (Zhu & Thompson, 2019). The higher fatty acid levels would then act as signaling molecules, energy storage molecules, and cell membrane components, allowing tumor cells to fulfill the rising demands for energy and cellular components. Mutations in oncogenes and tumor suppressor genes have been linked to glutamine and lipid metabolism changes (Ohshima & Morii, 2021).

7.6 Metastasis and Invasion Activation Cancer cells use invasion and metastasis to infiltrate surrounding tissue and spread to distant organs within the body. Invasion is the first step in cancer metastasis, wherein cancer cells invade or infiltrate into the surrounding tissues (Jiang et al., 2015). Metastasis is a process whereby tumor cells separate from the primary tumor and relocate to a distant organ or tissue to form secondary tumors. These two complex processes rely on already existing cellular mechanisms to allow tumor cells to invade and migrate. The invasion and metastasis cascade consist of localized invasion, intravasation, transport, extravasation, formation of micrometastasis, and colonization. To invade surrounding tissues, primary tumor cells should detach from the normal molecular constraints that connect adjacent cells (Fares et al., 2020). One of the most notable changes during invasion and metastasis is the loss of E-cadherin (CDH1). CDH1 is reported as an anti-invasive and anti-metastatic gene in several cancers (Onder et al., 2008). Cancer cell invasion into adjacent tissue requires the activation of proteases such as matrix metalloproteinases (MMPs), which aid in the degradation of extracellular matrix proteins. Induction of Epithelial to Mesenchymal Transition (EMT) aids cancer cell invasion, resistance to apoptosis, and spread. During EMT, closely connected cells lose their epithelial property and acquire more motile and aggressive mesenchymal properties (Barillari, 2020). Growth factors and cytokines activate the EMT transcription factors (Slug, Snail, Zeb1/2, Twist) to suppress epithelial genes (E-cadherin, Claudins, Occludins) and induction of mesenchymal genes (N-cadherin, Vimentin, Fibronectin). Mesenchymal cells are capable of invasion, metastasis, anti-apoptosis, and drug resistance. Intravsation refers to tumor cells entering a blood or lymph vessel (Du & Shim, 2016). Cancer cells enter the circulation via anoikis after intravasation. Tumor cells

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escape from blood or lymphatic vessel by penetrating the surrounding tissue during extravasation. They also go through a mesenchymal to epithelial transition (MET) to help with micrometastasis. When cancer cells spread to the tissue parenchyma, they form small clumps of disseminated cancer cells known as micrometastasis. The micrometastasis tumor cells then grow into macroscopic tumors (Lambert et al., 2017).

7.7 Replication Immortality Activation One of the crucial hallmarks of cancer is the ability to replicate limitlessly. Tumor cells have an infinite capacity for replication. They do so by maintaining their telomeres intact by upregulation of telomerase production or activation of alternative lengthening of telomeres pathway (Jafri et al., 2016). As a result, cells replicate continuously, producing large tumor masses. The loss of tumor-suppressor genes like TP53 also helps this process. Telomerase is an enzyme that maintains the telomere length. Studies have shown a positive correlation between telomerase activity and resistance to senescence or apoptosis (Shammas et al., 2005; Panneer Selvam et al., 2018).

7.8 Evading Immune Destruction An increasing number of studies suggest that the immune system within the human body functions prevent the development and progression of tumors. Cancer immune surveillance is how immune cells detect, identify, and eliminate newly emerging tumor cells (Swann & Smyth, 2007). Elimination, equilibrium, and escape are the three essential phases of cancer immune surveillance. A few cancers devise strategies to avoid the detection and destruction of cancer cells by the host’s immune system. Cancer cells achieve immune evasion by hijacking immune checkpoint control and modulation of innate immune responses. Both innate and adaptive immune responses have been shown to control tumor growth during tumor development. Tumor cells are identified in response to acute inflammatory responses, which result in the secretion of pro-inflammatory cytokines (IL12, IFN-) and tumor cell killing through the action of innate immune cells (natural killer cells, dendritic cells, and macrophages). Dendritic cells migrate to neighboring lymph nodes after maturation, introducing tumor antigens and activating tumor-specific CD4+ and CD8+ T cells. Tumor-specific CD4+ and CD8+ T cells, upon activation, then migrate to the tumor site and aid in its destruction (Messerschmidt et al., 2016). Tumor cells are either entirely eliminated or resulted in the development of resistant clones or clonal variants. Clonal variants sometimes develop resistance and escape from immune surveillance by reducing immunogenicity or recruiting immunosuppressive factors. When another cycle of immune responses fails to remove the newly emerging cancer

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cells, this may lead to a phase of immune escape, ultimately resulting in clinical manifestation of the disease (Waldman et al., 2020). Consequently, cells in the growing tumor and immune system engage in a silent war wherein cancer cells regain the upper hand after a period of equilibrium and progression and manifest macroscopically and clinically.

8 Methods of Cancer Detection The recent advancement and development in the field of the molecular biology of cancer cells resulted in a focus on the disease at three main levels: prevention, diagnosis, and therapy. Extremely sensitive molecular assays hold great promise for an earlier and more accurate diagnosis to determine primary cancers while they are still small but have not metastasized. Clinically cancer is treated by surgery and radiation of their combination (Mehta et al., 2010). Biopsy and histopathological examinations are the gold-standard cancer detection and classification method. Radiography, computed tomography (CT) scans, and magnetic resonance imaging (MRI) can detect internal organ tumors, as shown in Fig. 11.3. Cancer biomarkers, especially ones associated with epigenetic changes, could provide a measurable way of determining if people are predisposed to any cancers (Fass, 2008). Colon cancer, esophageal cancer, liver cancer, and pancreatic cancer, for example, show mutations in KRAS, p53, EGFR, and erbB2; cancers of the breast and the ovary show mutations in BRCA1 and BRCA2; brain cancer shows abnormal methylation of p16, CDKN2B, and p14ARF; cervical cancer shows hypermethylation of MYOD1 and CDH1; and oral cancer shows frequent hypermethylation of p16, p14, and RB1 (Verma et al., 2006). Cancers are diagnosed and staged using advanced methods such as computed tomography (CT), ultrasound, magnetic resonance imaging (MRI), single-photon emission computed tomography (SPECT), positron emission tomography (PET), and optical imaging (Frangioni, 2008). Finally, a technique called tissue biopsy is performed for confirmation and staging of cancer. Based on the location of tissue malignancy, various approaches are used, namely needle, endoscopic, skin, surgical, and bone marrow biopsy, and graded as low to high grade (Stage 1–4) according to the appearance of cells features under the microscope (Raskin & Messick, 2012).

9 Treatment Cancer can be managed by surgery or treatment with chemotherapeutic agents or radiation. Recently hormonal therapy, targeted therapy, and synthetic lethality-based approaches are also being considered for cancer treatment. The treatment chosen is determined by the location, grade, and tumor stage, as well as the patient’s overall health (Masoud & Pagès, 2017). Cancer genome analysis by sequencing and

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Fig. 11.3 Flow chart showing different strategies for cancer diagnosis

other molecular approaches can now be used to determine the best cancer therapy. Surgery is the process of removal of tumor tissue from the body. Surgery has been proven successful in treating solid tumors. Full surgical resection of the tumor is difficult if the tumor is already metastasized before surgery. Tumors develop and grow locally, spreading to lymph nodes and then to the rest of the body, according to the Halstedian cancer progression model (Naxerova, 2020). As a result, small cancers are treated by local treatments like surgery. Even a small tumor localized in each tissue has the potential to grow, metastasize and spread. Prostatectomy and mastectomy are surgical procedures used to treat prostate and breast cancer. The cancer is staged by histopathological examination of the primary tumor biopsy removed by surgery. Surgery can be carried out either before or after other treatment forms. Radiation therapy refers to the application of ionizing radiation to destroy cancer cells by inducing damage to DNA. This makes the cells unable to grow and divide. Radiotherapy kills cancer cells by inducing direct or indirect (via free radicals) DNA damage (Baskar et al., 2014). Based on the mode of administration, radiation therapy can be either external beam radiotherapy (EBRT) or brachytherapy. Almost any type of solid tumor, leukemia, and lymphoma can be treated with radiotherapy (Wang et al., 2019). Chemotherapy refers to the use of drugs to destroy cancer cells in treating cancer, as shown in Table 11.4. Most chemotherapeutic agents target rapidly dividing cells and disrupt cell division to kill cancer cells. Chemotherapy can kill both normal and cancer cells as they are not specific to target cancer cells. Cancer cells are sometimes treated by combining two or more drugs, a process known as “combination chemotherapy” (Mokhtari et al., 2017). Targeted therapy employs agents that are specific to abnormally expressed proteins of cancer cells, for

Drug Tamofexin, Methotrexate,Avastin 5-Flurouracil

Cisplatin, Paclitaxel, Carboplatin Mitomycin C, Cisplatin Vinblastine

Doxorubicin, Methotrexate Crizotinib

Pazopanib, Axintinib

Ixabepilone Dasatinib

Bevacizumab

S. no. 1 2

3 4 5

6 7

8

9 10

11

Mode of action Inhibit DNA replication Inhibit thymidine formation and DNA synthesis Inhibit DNA replication Inhibits DNA synthesis Prevents cell division at metaphase by binding to mitotic spindle Blocks DNA topoisomerase Blocks certain chemical messengers responsible for cancer cell growth Multiple kinase inhibitor by inhibiting angiogenesis Supressor of microtubules Blocking the action of an abnormal protein that signals for growth Inhibiting the binding of vascular endothelial growth factor (VEGF) to its cell surface receptors

Table 11.4 Drugs used for the treatment of cancer

Brain

Breast Blood

Renal

Breast, lung, liver, Cervix, Lung

Ovarian, cervix Colon Bladder

Cancer type Breast, glioblastoma Breast, lung, ovarian, prostate, liver

Rinne et al. (2013)

Rivera and Gomez (2010) Hochhaus et al. (2007)

Rini and Al-Marrawi (2011)

Costantini et al. (2010) Forde and Rudin (2012)

Lorusso et al. (2014) Dimou et al. (2010) Takata et al. (2005)

References Ko´zmi´nski et al. (2020) Longley et al. (2003)

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example, tyrosine kinase inhibitors imatinib (Gleevec/Glivec) and gefitinib (Iressa) (Metibemu et al., 2019). Treatment with monoclonal antibodies uses antibodies to target the proteins expressed on the surface of cancer cells. An example includes using anti-HER2/neu antibody (Herceptin) against breast cancer. Targeted therapy can also use radionuclides attached to small peptides to target the cancer cells. Photodynamic therapy is another type of targeted therapy that uses photosensitizers to treat cancer, such as basal cell carcinoma (BCC) or lung cancer (Collier & Rhodes, 2020). Immunotherapy, hormonal therapy, angiogenesis inhibitors, and synthetic lethality are emerging options for cancer treatment (Liu & Tewari, 2018).

References Abou Khouzam, R., Brodaczewska, K., Filipiak, A., Zeinelabdin, N. A., Buart, S., Szczylik, C., et al. (2021). Tumor hypoxia regulates immune escape/invasion: Influence on angiogenesis and potential impact of hypoxic biomarkers on cancer therapies. Frontiers in Immunology, 11. https://doi.org/10.3389/fimmu.2020.613114 Abramowicz, A., & Gos, M. (2014). Neurofibromin in neurofibromatosis type 1 – Mutations in NF1gene as a cause of disease. Developmental Period Medicine, 18, 297–306. Andrade, L. D. O., D’Oliveira, A., Melo, R., De Souza, E., Silva, C. C., & Parana, R. (2009). Association between hepatitis C and hepatocellular carcinoma. Journal of Global Infectious Diseases, 1, 33. https://doi.org/10.4103/0974-777X.52979 Anwar, S. L., & Lehmann, U. (2018). Detection of aberrant DNA methylation patterns in the RB1 gene. Methods in Molecular Biology, 35–47. https://doi.org/10.1007/978-1-4939-7565-5_5 Barillari, G. (2020). The impact of matrix metalloproteinase-9 on the sequential steps of the metastatic process. International Journal of Molecular Sciences, 21, 4526. https://doi.org/ 10.3390/ijms21124526 Baskar, R., Dai, J., Wenlong, N., Yeo, R., & Yeoh, K.-W. (2014). Biological response of cancer cells to radiation treatment. Frontiers in Molecular Biosciences, 1. https://doi.org/10.3389/ fmolb.2014.00024 Baylin, S. B. (2001). Aberrant patterns of DNA methylation, chromatin formation and gene expression in cancer. Human Molecular Genetics, 10, 687–692. https://doi.org/10.1093/hmg/ 10.7.687 Bielenberg, D. R., & Zetter, B. R. (2015). The contribution of angiogenesis to the process of metastasis. Cancer Journal, 21, 267–273. https://doi.org/10.1097/PPO.0000000000000138 Boffetta, P., Fryzek, J. P., & Mandel, J. S. (2012). Occupational exposure to beryllium and cancer risk: A review of the epidemiologic evidence. Critical Reviews in Toxicology, 42, 107–118. https://doi.org/10.3109/10408444.2011.631898 Brady, G., MacArthur, G. J., & Farrell, P. J. (2008). Epstein-Barr virus and Burkitt lymphoma. Postgraduate Medical Journal, 84, 372–377. https://doi.org/10.1136/jcp.2007.047977 Burd, E. M. (2003). Human papillomavirus and cervical cancer. Clinical Microbiology Reviews, 16, 1–17. https://doi.org/10.1128/CMR.16.1.1-17.2003 Calin, G. A., Cimmino, A., Fabbri, M., Ferracin, M., Wojcik, S. E., Shimizu, M., et al. (2008). MiR15a and miR-16-1 cluster functions in human leukemia. Proceedings of the National Academy of Sciences, 105, 5166–5171. https://doi.org/10.1073/pnas.0800121105 Chaffer, C. L., & Weinberg, R. A. (2011). A perspective on cancer cell metastasis. Science (80), 331, 1559–1564. https://doi.org/10.1126/science.1203543 Chan, K. Y. K., Ozçelik, H., Cheung, A. N. Y., Ngan, H. Y. S., & Khoo, U. S. (2002). Epigenetic factors controlling the BRCA1 and BRCA2 genes in sporadic ovarian cancer. Cancer Research, 62, 4151–4156.

11 An Introduction to Fundamentals of Cancer Biology

325

Chen, C., Xun, P., Nishijo, M., Carter, S., & He, K. (2016). Cadmium exposure and risk of prostate cancer: A meta-analysis of cohort and case-control studies among the general and occupational populations. Scientific Reports, 6, 25814. https://doi.org/10.1038/srep25814 Chirshev, E., Oberg, K. C., Ioffe, Y. J., & Unternaehrer, J. J. (2019). Let – 7 as biomarker, prognostic indicator, and therapy for precision medicine in cancer. Clinical and Translational Medicine, 8. https://doi.org/10.1186/s40169-019-0240-y Coghlin, C., & Murray, G. I. (2010). Current and emerging concepts in tumour metastasis. The Journal of Pathology, 222, 1–15. https://doi.org/10.1002/path.2727 Collier, N. J., & Rhodes, L. E. (2020). Photodynamic therapy for basal cell carcinoma: The clinical context for future research priorities. Molecules, 25, 5398. https://doi.org/10.3390/ molecules25225398 Concepcion, C. P., Bonetti, C., & Ventura, A. (2012). The microRNA-17-92 family of microRNA clusters in development and disease. Cancer Journal, 18, 262–267. https://doi.org/10.1097/ PPO.0b013e318258b60a Costantini, D. L., Villani, D. F., Vallis, K. A., & Reilly, R. M. (2010). Methotrexate, paclitaxel, and doxorubicin radiosensitize HER2 -amplified human breast cancer cells to the Auger electron– emitting radiotherapeutic agent 111 In-NLS-Trastuzumab. Journal of Nuclear Medicine, 51, 477–483. https://doi.org/10.2967/jnumed.109.069716 Couch, D. B. (1996). Carcinogenesis: Basic principles. Drug and Chemical Toxicology, 19, 133– 148. https://doi.org/10.3109/01480549608998231 Das, S., Kundu, M., Jena, B. C., & Mandal, M. (2020). Causes of cancer: Physical, chemical, biological carcinogens, and viruses. Biomaterials 3D Tumor Model, Elsevier, 607–641. https:/ /doi.org/10.1016/B978-0-12-818128-7.00025-3 DeNardo, D. G., Johansson, M., & Coussens, L. M. (2008). Immune cells as mediators of solid tumor metastasis. Cancer Metastasis Reviews, 27, 11–18. https://doi.org/10.1007/s10555-0079100-0 Di Fiore, R., D’Anneo, A., Tesoriere, G., & Vento, R. (2013). RB1 in cancer: Different mechanisms of RB1 inactivation and alterations of pRb pathway in tumorigenesis. Journal of Cellular Physiology, 228, 1676–1687. https://doi.org/10.1002/jcp.24329 Dimou, A., Syrigos, K. N., & Saif, M. W. (2010). Is there a role for mitomycin C in metastatic colorectal cancer? Expert Opinion on Investigational Drugs, 19, 723–735. https://doi.org/ 10.1517/13543784.2010.485191 Du, B., & Shim, J. (2016). Targeting epithelial–mesenchymal transition (EMT) to overcome drug resistance in cancer. Molecules, 21, 965. https://doi.org/10.3390/molecules21070965 Elmore, S. (2007). Apoptosis: A review of programmed cell death. Toxicologic Pathology, 35, 495–516. https://doi.org/10.1080/01926230701320337 Fares, J., Fares, M. Y., Khachfe, H. H., Salhab, H. A., & Fares, Y. (2020). Molecular principles of metastasis: A hallmark of cancer revisited. Signal Transduction and Targeted Therapy, 5, 28. https://doi.org/10.1038/s41392-020-0134-x Fass, L. (2008). Imaging and cancer: A review. Molecular Oncology, 2, 115–152. https://doi.org/ 10.1016/j.molonc.2008.04.001 Feng, Y.-H., & Tsao, C.-J. (2016). Emerging role of microRNA-21 in cancer. Biomedical Reports, 5, 395–402. https://doi.org/10.3892/br.2016.747 Fernald, K., & Kurokawa, M. (2013). Evading apoptosis in cancer. Trends in Cell Biology, 23, 620–633. https://doi.org/10.1016/j.tcb.2013.07.006 Fink, S. L., & Cookson, B. T. (2005). Apoptosis, pyroptosis, and necrosis: Mechanistic description of dead and dying eukaryotic cells. Infection and Immunity, 73, 1907–1916. https://doi.org/ 10.1128/IAI.73.4.1907-1916.2005 Fodde, R. (2002). The APC gene in colorectal cancer. European Journal of Cancer, 38, 867–871. https://doi.org/10.1016/S0959-8049(02)00040-0 Forde, P. M., & Rudin, C. M. (2012). Crizotinib in the treatment of non-small-cell lung cancer. Expert Opinion on Pharmacotherapy, 13, 1195–1201. https://doi.org/10.1517/ 14656566.2012.688029

326

S. Sriharikrishnaa et al.

Fouad, Y. A., & Aanei, C. (2017). Revisiting the hallmarks of cancer. American Journal of Cancer Research, 7, 1016–1036. Frangioni, J. V. (2008). New technologies for human cancer imaging. Journal of Clinical Oncology, 26, 4012–4021. https://doi.org/10.1200/JCO.2007.14.3065 Friedl, P., & Wolf, K. (2003). Tumour-cell invasion and migration: Diversity and escape mechanisms. Nature Reviews. Cancer, 3, 362–374. https://doi.org/10.1038/nrc1075 Golias, C. H., Charalabopoulos, A., & Charalabopoulos, K. (2004). Cell proliferation and cell cycle control: A mini review. International Journal of Clinical Practice, 58, 1134–1141. https:/ /doi.org/10.1111/j.1742-1241.2004.00284.x Grigoriou, M., Kofina, K. E., Ioannidis, A., Gerasimidou, D. K., Efthymiadis, C., & Zaramboukas, T. (2017). Kaposi sarcoma in an human immunodeficiency virus (HIV)-seronegative mediterranean female: Report of a rare case. American Journal of Case Reports, 18, 830–833. https:// doi.org/10.12659/AJCR.903537 Gupta, S., Roy, A., & Dwarakanath, B. S. (2017). Metabolic cooperation and competition in the tumor microenvironment: Implications for therapy. Frontiers in Oncology, 7. https://doi.org/ 10.3389/fonc.2017.00068 Hanahan, D., & Weinberg, R. A. (2011). Hallmarks of cancer: The next generation. Cell, 144, 646–674. https://doi.org/10.1016/j.cell.2011.02.013 Heintz, N. H., Janssen-Heininger, Y. M. W., & Mossman, B. T. (2010). Asbestos, lung cancers, and mesotheliomas. American Journal of Respiratory Cell and Molecular Biology, 42, 133– 139. https://doi.org/10.1165/rcmb.2009-0206TR Hickman, E. (2002). The role of p53 and pRB in apoptosis and cancer. Current Opinion in Genetics & Development, 12, 60–66. https://doi.org/10.1016/S0959-437X(01)00265-9 Hochhaus, A., Kantarjian, H. M., Baccarani, M., Lipton, J. H., Apperley, J. F., Druker, B. J., et al. (2007). Dasatinib induces notable hematologic and cytogenetic responses in chronic-phase chronic myeloid leukemia after failure of imatinib therapy. Blood, 109, 2303–2309. https:// doi.org/10.1182/blood-2006-09-047266 IARC. (2020). List of classifications by cancer sites with sufficient or limited evidence in humans , Volumes 1 to 113 * Cancer site Carcinogenic agents with sufficient evidence in humans Agents with limited evidence in humans Lip, oral cavity, and pharynx List of Cl 2020, pp. 1–12. Jafri, M. A., Ansari, S. A., Alqahtani, M. H., & Shay, J. W. (2016). Roles of telomeres and telomerase in cancer, and advances in telomerase-targeted therapies. Genome Medicine, 8, 69. https://doi.org/10.1186/s13073-016-0324-x Janiszewska, M., Primi, M. C., & Izard, T. (2020). Cell adhesion in cancer: Beyond the migration of single cells. The Journal of Biological Chemistry, 295, 2495–2505. https://doi.org/10.1074/ jbc.REV119.007759 Jemal, A., Torre, L., Street, W., & Bray, F. (2019). The cancer atlas – ACS, The burden of cancer (3rd ed.). American Cancer Society. Jiang, H., Zhang, G., Wu, J.-H., & Jiang, C.-P. (2014). Diverse roles of miR-29 in cancer (Review). Oncology Reports, 31, 1509–1516. https://doi.org/10.3892/or.2014.3036 Jiang, W. G., Sanders, A. J., Katoh, M., Ungefroren, H., Gieseler, F., Prince, M., et al. (2015). Tissue invasion and metastasis: Molecular, biological and clinical perspectives. Seminars in Cancer Biology, 35, S244–S275. https://doi.org/10.1016/j.semcancer.2015.03.008 Joyce, J. A., & Pollard, J. W. (2009). Microenvironmental regulation of metastasis. Nature Reviews. Cancer, 9, 239–252. https://doi.org/10.1038/nrc2618 Ko´zmi´nski, P., Halik, P. K., Chesori, R., & Gniazdowska, E. (2020). Overview of dual-acting drug methotrexate in different neurological diseases, autoimmune pathologies and cancers. International Journal of Molecular Sciences, 21, 3483. https://doi.org/10.3390/ijms21103483 Lambert, A. W., Pattabiraman, D. R., & Weinberg, R. A. (2017). Emerging biological principles of metastasis. Cell, 168, 670–691. https://doi.org/10.1016/j.cell.2016.11.037 Lee, J. W., Soung, Y. H., Kim, S. Y., Nam, H. K., Park, W. S., Nam, S. W., et al. (2005). Somatic mutations of EGFR gene in squamous cell carcinoma of the head and neck. Clinical Cancer Research, 11, 2879–2882. https://doi.org/10.1158/1078-0432.CCR-04-2029

11 An Introduction to Fundamentals of Cancer Biology

327

Li, Z., Van Calcar, S., Qu, C., Cavenee, W. K., Zhang, M. Q., & Ren, B. (2003). A global transcriptional regulatory role for c-Myc in Burkitt’s lymphoma cells. Proceedings of the National Academy of Sciences, 100, 8164–8169. https://doi.org/10.1073/pnas.1332764100 Li, S., Rong, M., & Iacopetta, B. (2006). DNA hypermethylation in breast cancer and its association with clinicopathological features. Cancer Letters, 237, 272–280. https://doi.org/ 10.1016/j.canlet.2005.06.011 Li, S., Shen, L., & Chen, K.-N. (2018). Association between H3K4 methylation and cancer prognosis: A meta-analysis. Thoracic Cancer, 9, 794–799. https://doi.org/10.1111/1759-7714.12647 Liu, M. C., & Tewari, K. S. (2018). Anti-angiogenesis therapy, synthetic lethality, and checkpoint inhibition in ovarian cancer: State of the science and novel combinations. Drugs Context, 1–9. https://doi.org/10.7573/dic.212558 Liu, R., Shi, P., Wang, Z., Yuan, C., & Cui, H. (2021). Molecular mechanisms of MYCN dysregulation in cancers. Frontiers in Oncology, 10. https://doi.org/10.3389/fonc.2020.625332 Longley, D. B., Harkin, D. P., & Johnston, P. G. (2003). 5-Fluorouracil: Mechanisms of action and clinical strategies. Nature Reviews. Cancer, 3, 330–338. https://doi.org/10.1038/nrc1074 Lorusso, D., Petrelli, F., Coinu, A., Raspagliesi, F., & Barni, S. (2014). A systematic review comparing cisplatin and carboplatin plus paclitaxel-based chemotherapy for recurrent or metastatic cervical cancer. Gynecologic Oncology, 133, 117–123. https://doi.org/10.1016/ j.ygyno.2014.01.042 Martinez, V. D., Vucic, E. A., Becker-Santos, D. D., Gil, L., & Lam, W. L. (2011). Arsenic exposure and the induction of human cancers. Journal of Toxicology, 2011, 1–13. https://doi.org/10.1155/ 2011/431287 Martinez, V. G., Munera-Maravilla, E., Bernardini, A., Rubio, C., Suarez-Cabrera, C., Segovia, C., et al. (2019). Epigenetics of bladder cancer: Where biomarkers and therapeutic targets meet. Frontiers in Genetics, 10. https://doi.org/10.3389/fgene.2019.01125 Marusyk, A., & Polyak, K. (2010). Tumor heterogeneity: Causes and consequences. Biochimica et Biophysica Acta, Reviews on Cancer, 1805, 105–117. https://doi.org/10.1016/ j.bbcan.2009.11.002 Masoud, V., & Pagès, G. (2017). Targeted therapies in breast cancer: New challenges to fight against resistance. World Journal of Clinical Oncology, 8, 120. https://doi.org/10.5306/ wjco.v8.i2.120 Mehlen, P., & Fearon, E. R. (2004). Role of the dependence receptor DCC in colorectal cancer pathogenesis. Journal of Clinical Oncology, 22, 3420–3428. https://doi.org/10.1200/ JCO.2004.02.019 Mehta, S., Shelling, A., Muthukaruppan, A., Lasham, A., Blenkiron, C., Laking, G., et al. (2010). Predictive and prognostic molecular markers for cancer medicine. Therapeutic Advances in Medical Oncology, 2, 125–148. https://doi.org/10.1177/1758834009360519 Menzel, L., Höpken, U. E., & Rehm, A. (2020). Angiogenesis in lymph nodes is a critical regulator of immune response and lymphoma growth. Frontiers in Immunology, 11. https://doi.org/ 10.3389/fimmu.2020.591741 Mesri, E. A., Cesarman, E., & Boshoff, C. (2010). Kaposi’s sarcoma and its associated herpesvirus. Nature Reviews. Cancer, 10, 707–719. https://doi.org/10.1038/nrc2888 Messerschmidt, J. L., Prendergast, G. C., & Messerschmidt, G. L. (2016). How cancers escape immune destruction and mechanisms of action for the new significantly active immune therapies: Helping nonimmunologists decipher recent advances. The Oncologist, 21, 233–243. https://doi.org/10.1634/theoncologist.2015-0282 Metibemu, D. S., Akinloye, O. A., Akamo, A. J., Ojo, D. A., Okeowo, O. T., & Omotuyi, I. O. (2019). Exploring receptor tyrosine kinases-inhibitors in Cancer treatments. Egyptian Journal of Medical Human Genetics, 20, 35. https://doi.org/10.1186/s43042-019-0035-0 Mokhtari, R. B., Homayouni, T. S., Baluch, N., Morgatskaya, E., Kumar, S., Das, B., et al. (2017). Combination therapy in combating cancer. Oncotarget, 8, 38022–38043. https:// doi.org/10.18632/oncotarget.16723

328

S. Sriharikrishnaa et al.

Montero, A. J., Díaz-Montero, C. M., Mao, L., Youssef, E., Estecio, M. R., Shen, L., et al. (2006). Epigenetic inactivation of EGFR by CpG island hypermethylation in cancer. Cancer Biology & Therapy, 5, 1494–1501. https://doi.org/10.4161/cbt.5.11.3299 Mullen, A. R., & DeBerardinis, R. J. (2012). Genetically-defined metabolic reprogramming in cancer. Trends in Endocrinology and Metabolism, 23, 552–559. https://doi.org/10.1016/ j.tem.2012.06.009 Naxerova, K. (2020). Defining the role of lymph node metastasis in systemic breast cancer evolution. eBioMedicine, 57, 102852. https://doi.org/10.1016/j.ebiom.2020.102852 Nenclares, P., & Harrington, K. J. (2020). The biology of cancer. Medicine (Baltimore), 48, 67–72. https://doi.org/10.1016/j.mpmed.2019.11.001 Ohshima, K., & Morii, E. (2021). Metabolic reprogramming of cancer cells during tumor progression and metastasis. Metabolites, 11, 28. https://doi.org/10.3390/metabo11010028 Olivier, M., Hollstein, M., & Hainaut, P. (2010). TP53 mutations in human cancers: Origins, consequences, and clinical use. Cold Spring Harbor Perspectives in Biology, 2, a001008. https:/ /doi.org/10.1101/cshperspect.a001008 Onder, T. T., Gupta, P. B., Mani, S. A., Yang, J., Lander, E. S., & Weinberg, R. A. (2008). Loss of E-cadherin promotes metastasis via multiple downstream transcriptional pathways. Cancer Research, 68, 3645–3654. https://doi.org/10.1158/0008-5472.CAN-07-2938 Otani, Y., Miyake, T., Kagara, N., Shimoda, M., Naoi, Y., Maruyama, N., et al. (2014). BRCA 1 promoter methylation of normal breast epithelial cells as a possible precursor for BRCA 1 -methylated breast cancer. Cancer Science, 105, 1369–1376. https://doi.org/10.1111/cas.12506 Ozaki, T., & Nakagawara, A. (2011). Role of p53 in cell death and human cancers. Cancers (Basel), 3, 994–1013. https://doi.org/10.3390/cancers3010994 Pani, G., Galeotti, T., & Chiarugi, P. (2010). Metastasis: Cancer cell’s escape from oxidative stress. Cancer Metastasis Reviews, 29, 351–378. https://doi.org/10.1007/s10555-010-9225-4 Panneer Selvam, S., Roth, B. M., Nganga, R., Kim, J., Cooley, M. A., Helke, K., et al. (2018). Balance between senescence and apoptosis is regulated by telomere damage – Induced association between p16 and caspase-3. The Journal of Biological Chemistry, 293, 9784–9800. https://doi.org/10.1074/jbc.RA118.003506 Parrish, A. B., Freel, C. D., & Kornbluth, S. (2013). Cellular mechanisms controlling caspase activation and function. Cold Spring Harbor Perspectives in Biology, 5, a008672. https:// doi.org/10.1101/cshperspect.a008672 Pelullo, M., Zema, S., Nardozza, F., Checquolo, S., Screpanti, I., & Bellavia, D. (2019). Wnt, notch, and TGF-β pathways impinge on Hedgehog signaling complexity: An open window on cancer. Frontiers in Genetics, 10. https://doi.org/10.3389/fgene.2019.00711 Pickup, M. W., Mouw, J. K., & Weaver, V. M. (2014). The extracellular matrix modulates the hallmarks of cancer. EMBO Reports, 15, 1243–1253. https://doi.org/10.15252/embr.201439246 Poole, C. J., & van Riggelen, J. (2017). MYC – Master regulator of the cancer epigenome and transcriptome. Genes (Basel), 8, 142. https://doi.org/10.3390/genes8050142 Prior, I. A., Lewis, P. D., & Mattos, C. (2012). A comprehensive survey of Ras mutations in cancer. Cancer Research, 72, 2457–2467. https://doi.org/10.1158/0008-5472.CAN-11-2612 Raskin, R. E., & Messick, J. B. (2012). Bone marrow cytologic and histologic biopsies: Indications, technique, and evaluation. The Veterinary Clinics of North America. Small Animal Practice, 42, 23–42. https://doi.org/10.1016/j.cvsm.2011.10.001 Ratner, L. (2005). Human T cell lymphotropic virus-associated leukemia/lymphoma. Current Opinion in Oncology, 17, 469–473. https://doi.org/10.1097/01.cco.0000174037.84903.fb Raymond, W., & Ruddon, M. D. (2007). Characteristics of human cancers (Cancer biology) (4th ed., pp. 3–15). Oxford University Press. Ren, N., Atyah, M., Chen, W.-Y., & Zhou, C.-H. (2017). The various aspects of genetic and epigenetic toxicology: Testing methods and clinical applications. Journal of Translational Medicine, 15, 110. https://doi.org/10.1186/s12967-017-1218-4 Riesco, A., Santos-Buitrago, B., De Las Rivas, J., Knapp, M., Santos-García, G., & Talcott, C. (2017). Epidermal growth factor signaling towards proliferation: Modeling and logic inference using forward and backward search. BioMed Research International, 2017, 1–11. https:// doi.org/10.1155/2017/1809513

11 An Introduction to Fundamentals of Cancer Biology

329

Rini, B., & Al-Marrawi, M. Y. (2011). Pazopanib for the treatment of renal cancer. Expert Opinion on Pharmacotherapy, 12, 1171–1189. https://doi.org/10.1517/14656566.2011.571206 Rinne, M. L., Lee, E. Q., Nayak, L., Norden, A. D., Beroukhim, R., Wen, P. Y., et al. (2013). Update on bevacizumab and other angiogenesis inhibitors for brain cancer. Expert Opinion on Emerging Drugs, 18, 137–153. https://doi.org/10.1517/14728214.2013.794784 Rivera, E., & Gomez, H. (2010). Chemotherapy resistance in metastatic breast cancer: The evolving role of ixabepilone. Breast Cancer Research, 12, S2. https://doi.org/10.1186/bcr2573 Rodriguez, A. C., Blanchard, Z., Maurer, K. A., & Gertz, J. (2019). Estrogen signaling in endometrial cancer: A key oncogenic pathway with several open questions. Hormones and Cancer, 10, 51–63. https://doi.org/10.1007/s12672-019-0358-9 Ruteshouser, E. C., Robinson, S. M., & Huff, V. (2008). Wilms tumor genetics: Mutations inWT1,WTX, and CTNNB1 account for only about one-third of tumors. Genes, Chromosomes & Cancer, 47, 461–470. https://doi.org/10.1002/gcc.20553 Sachdeva, U. M., & O’Brien, J. M. (2012). Understanding pRb: Toward the necessary development of targeted treatments for retinoblastoma. The Journal of Clinical Investigation, 122, 425–434. https://doi.org/10.1172/JCI57114 Schiliro, C., & Firestein, B. L. (2021). Mechanisms of metabolic reprogramming in cancer cells supporting enhanced growth and proliferation. Cell, 10, 1056. https://doi.org/10.3390/ cells10051056 Schuetz, J. M., Johnson, N. A., Morin, R. D., Scott, D. W., Tan, K., Ben-Nierah, S., et al. (2012). BCL2 mutations in diffuse large B-cell lymphoma. Leukemia, 26, 1383–1390. https://doi.org/ 10.1038/leu.2011.378 Sever, R., & Brugge, J. S. (2015). Signal transduction in cancer. Cold Spring Harbor Perspectives in Medicine, 5, a006098–a006098. https://doi.org/10.1101/cshperspect.a006098 Shah, J. A., Khattak, S., Rauf, M. A., Cai, Y., & Jin, J. (2021). Potential biomarkers of miR-371– 373 gene cluster in tumorigenesis. Life, 11, 984. https://doi.org/10.3390/life11090984 Shammas, M. A., Koley, H., Batchu, R. B., Bertheau, R. C., Protopopov, A., Munshi, N. C., et al. (2005). Telomerase inhibition by siRNA causes senescence and apoptosis in Barrett’s adenocarcinoma cells: Mechanism and therapeutic potential. Molecular Cancer, 4, 24. https:// doi.org/10.1186/1476-4598-4-24 Snyder, R. (2012). Leukemia and benzene. International Journal of Environmental Research and Public Health, 9, 2875–2893. https://doi.org/10.3390/ijerph9082875 Sormendi, S., & Wielockx, B. (2018). Hypoxia pathway proteins as central mediators of metabolism in the tumor cells and their microenvironment. Frontiers in Immunology, 9. https:/ /doi.org/10.3389/fimmu.2018.00040 Swann, J. B., & Smyth, M. J. (2007). Immune surveillance of tumors. The Journal of Clinical Investigation, 117, 1137–1146. https://doi.org/10.1172/JCI31405 Takata, R., Katagiri, T., Kanehira, M., Tsunoda, T., Shuin, T., Miki, T., et al. (2005). Predicting response to methotrexate, vinblastine, doxorubicin, and cisplatin neoadjuvant chemotherapy for bladder cancers through genome-wide gene expression profiling. Clinical Cancer Research, 11, 2625–2636. https://doi.org/10.1158/1078-0432.CCR-04-1988 Talseth-Palmer, B. A. (2017). The genetic basis of colonic adenomatous polyposis syndromes. Hereditary Cancer in Clinical Practices, 15, 5. https://doi.org/10.1186/s13053-017-0065-x Thiagalingam, S. (2015). Systems biology of cancer. Cambridge University Press. Tili, E., Croce, C. M., & Michaille, J.-J. (2009). miR-155: On the crosstalk between inflammation and cancer. International Reviews of Immunology, 28, 264–284. https://doi.org/10.1080/ 08830180903093796 Urbano, M., Ferreira, M. R., & Alpoim, C. (2012). Molecular and cellular mechanisms of hexavalent chromium-induced lung cancer: An updated perspective. Current Drug Metabolism, 13, 284–305. https://doi.org/10.2174/138920012799320464 Vander Heiden, M. G., Cantley, L. C., & Thompson, C. B. (2009). Understanding the Warburg effect: The metabolic requirements of cell proliferation. Science (80), 324, 1029–1033. https:// doi.org/10.1126/science.1160809

330

S. Sriharikrishnaa et al.

Verma, M., Seminara, D., Arena, F. J., John, C., Iwamoto, K., & Hartmuller, V. (2006). Genetic and epigenetic biomarkers in cancer: Improving diagnosis, risk assessment, and disease stratification. Molecular Diagnosis & Therapy, 10, 1–15. https://doi.org/10.1007/BF03256438 Vincent, M. J., Kozal, J. S., Thompson, W. J., Maier, A., Dotson, G. S., Best, E. A., et al. (2019). Ethylene oxide: Cancer evidence integration and dose–response implications. Dose-Response, 17, 155932581988831. https://doi.org/10.1177/1559325819888317 Waldman, A. D., Fritz, J. M., & Lenardo, M. J. (2020). A guide to cancer immunotherapy: From T cell basic science to clinical practice. Nature Reviews. Immunology, 20, 651–668. https:// doi.org/10.1038/s41577-020-0306-5 Wang, S., Liu, Y., Feng, Y., Zhang, J., Swinnen, J., Li, Y., et al. (2019). A review on curability of cancers: More efforts for novel therapeutic options are needed. Cancers (Basel), 11, 1782. https://doi.org/10.3390/cancers11111782 Wei, Y., Xia, W., Zhang, Z., Liu, J., Wang, H., Adsay, N. V., et al. (2008). Loss of trimethylation at lysine 27 of histone H3 is a predictor of poor outcome in breast, ovarian, and pancreatic cancers. Molecular Carcinogenesis, 47, 701–706. https://doi.org/10.1002/mc.20413 Wei, R., Liu, S., Zhang, S., Min, L., & Zhu, S. (2020). Cellular and extracellular components in tumor microenvironment and their application in early diagnosis of cancers. Analytical Cellular Pathology, 2020, 1–13. https://doi.org/10.1155/2020/6283796 Weinberg, R. A., & Weinberg, R. A. (2006). The biology of cancer. W.W. Norton & Company. https://doi.org/10.1201/9780203852569 Witsch, E., Sela, M., & Yarden, Y. (2010). Roles for growth factors in cancer progression. Physiology, 25, 85–101. https://doi.org/10.1152/physiol.00045.2009 Yang, L., Moss, T., Mangala, L. S., Marini, J., Zhao, H., Wahlig, S., et al. (2014). Metabolic shifts toward glutamine regulate tumor growth, invasion and bioenergetics in ovarian cancer. Molecular Systems Biology, 10, 728. https://doi.org/10.1002/msb.20134892 Young, L. S., & Dawson, C. W. (2014). Epstein-Barr virus and nasopharyngeal carcinoma. Chinese Journal of Cancer. https://doi.org/10.5732/cjc.014.10197 Zhang, L., Liao, Y., & Tang, L. (2019). MicroRNA-34 family: A potential tumor suppressor and therapeutic candidate in cancer. Journal of Experimental & Clinical Cancer Research, 38, 53. https://doi.org/10.1186/s13046-019-1059-5 Zhang, X., Tian, D., Chen, Y., Chen, C., He, L.-N., Zhou, Y., et al. (2021a). Association of hepatitis B virus infection status with outcomes of non-small cell lung cancer patients undergoing antiPD-1/PD-L1 therapy. Translational Lung Cancer Research, 10, 3191–3202. https://doi.org/ 10.21037/tlcr-21-455 Zhang, P., Meng, X., Liu, L., Li, S., Li, Y., Ali, S., et al. (2021b). Identification of the prognostic signatures of glioma with different PTEN status. Frontiers in Oncology, 11. https://doi.org/ 10.3389/fonc.2021.633357 Zhu, J., & Thompson, C. B. (2019). Metabolic regulation of cell growth and proliferation. Nature Reviews. Molecular Cell Biology, 20, 436–450. https://doi.org/10.1038/s41580-019-0123-5 Ziello, J. E., Jovin, I. S., & Huang, Y. (2007). Hypoxia-Inducible Factor (HIF)-1 regulatory pathway and its potential for therapeutic intervention in malignancy and ischemia. The Yale Journal of Biology and Medicine, 80, 51–60. Zimna, A., & Kurpisz, M. (2015). Hypoxia-inducible factor-1 in physiological and pathophysiological angiogenesis: Applications and therapies. BioMed Research International, 2015, 1–13. https://doi.org/10.1155/2015/549412

Chapter 12

Polarization-Enabled Optical Spectroscopy and Microscopic Techniques for Cancer Diagnosis Mallya Divya, Madhavi Hegde, Madhu Hegde, Shatakshi Roy, Gagan Raju, Viktor V. Nikolaev, Yury V. Kistenev, and Nirmal Mazumder

Abstract Millions of people die each year from cancer, which is caused by a combination of lifestyle and hereditary factors. It is characterized by unregulated cell division and proliferation. Mohs micrographic surgery, which involves tissue excision followed by H&E staining, is the most common procedure for cancer diagnosis. However, this procedure is time-consuming, necessitates the use of qualified professionals, and there is a considerable risk of misdiagnosis, resulting in ineffective treatment. Cancer cells have different optical characteristics than healthy tissues due to their abnormal nature. Polarization-resolved techniques can take advantage of this feature for faster, more accurate, and non-invasive disease diagnosis. The principles and applications of several polarization-enabled cancer detection approaches are described in this chapter. The techniques outlined include fluorescence spectroscopy, near-infrared (NIR) spectroscopy, hyperspectral spectroscopy, Raman spectroscopy, fluorescence microscopy, confocal microscopy, two-photon (2p) fluorescence microscopy, second-harmonic generation (SHG), third-harmonic generation (THG), coherent anti-stokes Raman scattering (CARS), stimulated Raman scattering (SRS) microscopy, surface-enhanced Raman scattering (SERS), and optical coherence tomography (OCT).

Authors “Mallya Divya”, “Madhavi Hegde”, “Madhu Hegde” , and “Shatakshi Roy” have equally contributed to this chapter. M. Divya · M. Hegde · M. Hegde · S. Roy · G. Raju · N. Mazumder () Department of Biophysics, Manipal School of Life Sciences, Manipal Academy of Higher Education (MAHE), Manipal, Karnataka, India e-mail: [email protected] V. V. Nikolaev Laboratory of Biophotonics, Tomsk State University, Tomsk, Russia Y. V. Kistenev Laboratory of Biophotonics, Tomsk State University, Tomsk, Russia Central Research Laboratory, Siberian State Medical University, Tomsk, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Mazumder et al. (eds.), Optical Polarimetric Modalities for Biomedical Research, Biological and Medical Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-031-31852-8_12

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Keywords Polarization · Microscopy · Spectroscopy · Cancer diagnosis · Tumor

1 Introduction Estimated to affect up to 22 million people worldwide by 2030, cancer is one of the leading causes of death (Muellner et al., 2018). This increase is attributed to the growth of the population and the change in lifestyle and behavior (Torre et al., 2016). Normal cells can reproduce only when required, thus maintaining the size and architecture of the body. When this property is lost, it results in cancer (Weinberg, 1996). Therefore, very early cancer detection is based on the difference between cancer cells and normal cells and also the difference in their metabolism. It can be established by the methods of nano- and microspectroscopy. Cancer development is strongly dependent on the cancer cells’ microenvironment. The specificity of the latter is reflected not only in metabolism but also in microstructure, which can be detected by a polarization-sensitive technique. Cancer cells possess a unique property of migrating from the site of formation and invading surrounding tissues, resulting in the formation of tumors in those sites. If not detected early, they can get aggressive over time and become lethal when they interrupt the vital organs of the body (Weinberg, 1996). There is a need for advanced technologies to accurately detect, diagnose, and provide more information on its biology (Muellner et al., 2018). The gold standard for histological visualization of excised tissue sections is Mohs micrographic surgery, which was developed by Dr. Frederic Mohs in the 1930s. The technique is widely used in tumor removal because it helps in the conservation of the surrounding healthy tissue (Hui et al., 2012). The process consists of various steps and is time-consuming, and there are many chances of errors with each step (Bouzari & Olbricht, 2011). For example, improper preoperative curettage can lead to irregular removal of tissues which can compromise the thickness of the subsequent sections, and H&E staining can reduce the quality of the sections. The staining process alone can take up to 10 min if it is automated or between 10 and 30 min if done manually (Robinson, 2001). Pathologists require extensive training for proper interpretation of the sections. Even with sufficient training and experience, however, there are chances of misdiagnosis. For example, some inflammatory regions or benign structures may look like tumors, and the reduced contrast of cytoplasmic and extracellular structures can lead to improper interpretation. Optical imaging techniques seem very promising in this case.

1.1 Skin Structure and Optical Properties First of all, noninvasive cancer detection by optical imaging is associated with superficial tissues. The optical properties of the latter are defined by cell types

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Fig. 12.1 (i) Triple helix consisting of α–chains forming collagen (Optics et al., 1994). (ii) Spatial structure of collagen fibers (Optics et al., 1994). (iii) Schematic representation of an elastin fiber. (iv) The epidermis structure. (v) The structure of the dermis. (vi) Schematic representation of hypoderma

and their spatial organization. The skin consists of the epidermis, dermis, and hypodermis (skin-fat) (Optics et al., 1994). The epidermis is located on the surface of the skin. Keratinocytes are the main cells of the skin epidermis, contain the protein keratin, which creates the outer layer of the skin and, together with collagen and elastin, gives the skin elasticity and strength. Collagen belongs to the family of fibrillar proteins. Collagen is synthesized by many cells, but the fibroblast cells of the connective tissue are the main sources of collagen synthesis (Andriotis et al., 2015). Depending on the amino acid sequence, proteins can form α–chains or β–folded structures. The collagen–tropocollagen molecule consists of three α–chains forming a triple helix (see Fig. 12.1i). Collagen forms fibrils consisting of repeating tropocollagen molecules packed in parallel bundles arranged “head to tail” and oriented in one direction along the long axis of the fibrils (see Fig. 12.1ii). In fibrils, neighboring collagen molecules are displaced from each other by 67 nm, which explains the characteristic cross-links that repeat within the same period. Thicker collagen bundles may include glycoproteins and proteoglycans (Gelse, 2003). The amino acid sequence of the triple helix α-chain consists of a repeating Gly-X-Y structure, where Gly is glycine, X is usually proline (Pro), and Y can be any amino acid, usually hydroxyproline (Hyp) or hydroxylysine (see Fig. 12.1i). Currently, 28 types of collagen have been described, differing in amino acid sequences (Kapuler et al., 2015). Elastin consists of two components: fibrillar and amorphous. Glycoproteins and fibrillin are the basis of the fibrillar component, the amorphous component consists of the elastin protein. The mesh layer of the dermis contains structures mainly consisting of an amorphous component, there is less elastin in the papillary layer. Elastin contains about 27% glycine, 19% alanine, 10% valine, 4.7% leucine. Tropoelastin is a precursor of elastiná. It is a soluble monomer consisting of hydrophilic and hydrophobic sites. Hydrophilic sites are enriched with leasing residues. Lysine residues are oxidized by copper-dependent lysyl oxidase to ally-

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sine, and then cross-links (desmosins) are formed (Yamauchi et al., 2018). Due to them, elastin fibers are combined into a network of strong covalent bonds. A schematic representation of the elastin structure is shown in Fig. 12.1iii. The thickness of the epidermis is about 0.1 mm, but on the palm and the feet can reach a thickness of up to 3–5 mm. The epidermis is divided into five layers: horny, shiny, granular, spiny, and basal (see Fig. 12.1iv). The stratum corneum consists of corneocytes (Roop, 1995; Nemes & Steinert, 1999). Corneocytes consist of keratin fibrils with a diameter of 7–8 nm separated by an amorphous material (consisting of 70% water, minerals (4–7%), glycoproteins (4–5%), proteoglycan aggregates (4– 5%) in a ratio of 1:1 and surrounded by a shell with a thickness of 12–15 nm. The size of the corneocytes: diameter about 30 microns, thickness 50–1000 nm (Ratner, 2012). The formation of corneocytes is one of the main functions of the epidermis. The thickness of the stratum corneum varies from 5–15 mm, up to 1 mm on the palms and feet (Czekalla et al., 2019). The shiny layer of the epidermis is a thin layer consisting of one or two rows of flat keratinocytes filled with eleidin (an intermediate form of keratin), in which the nuclei and organelles are destroyed (Optics et al., 1994). The size of keratinocytes in this layer is about 10 microns, the thickness is 0.1–20 microns. This layer is found only on thick areas of the skin, such as the sole or palms. The main function of this layer is protective. The granular layer consists of 1–4 rows of keratinocytes (Yousef et al., 2022). The number of organelles in the cells of this layer is small compared to younger cells located in the thorny layer. The cytoplasm of keratinocytes in this layer contains keratogialin granules and keratonosomes. The release of these granules occurs in the upper rows of the granular layer, where the lamellar structures of the shiny layer are formed. In the same layer, keratolinin and filaggrin are synthesized, which leads to subsequent keratinization of epidermal cells. The thickness of the layer is approximately 3 microns (Optics et al., 1994). The isolation of intercellular lipids that bind the cells of the stratum corneum is the main function of this layer. The spiny layer consists of 10 or more rows of spiny keratinocytes, in the lower rows, there are Langerhans cells that transform from bone marrow cells (less than 5% of the cells of the entire epidermis). Keratinocytes are covered with a thick shell (7–8 nm thick), which has characteristic processes (spikes) that connect cells. Langerhans cells transport antigens to the lymph nodes, thereby activating the immune defense (Yousef et al., 2022). The thickness of the spiked layer is 50–150 mm (Optics et al., 1994). The spiny layer secretes lipids that fill the intercellular space in the spiny, granular, shiny, and horny layers. As a result, the keratinized layers have a protective function. The basal layer contains basal keratinocytes, Langerhans cells, and melanocytes. The cells in this layer are interconnected by intercellular bridges and are attached to the basement membrane. In this layer of the skin, keratinocytes divide, which subsequently evolve and move into the upper layers. Fibrillar proteins, polysaccharides, and lipids are synthesized in the basal layer. Melanocytes located in the basal layer form melanosomes and synthesize melanin, which protects the body from ultraviolet radiation (Optics et al., 1994). Each melanocyte contacts approximately 30 keratinocytes and distributes

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melanin to them. This layer is the supporting layer of the epidermis, connects the epidermis with the dermis, but does not allow keratocytes to enter the dermis. The dermis is the next layer of skin after the epidermis. This layer is separated from the epidermis by the basement membrane and is a complex network containing cellular and non-cellular components: blood vessels, nerves, hair roots, and sweat glands. The main structural proteins in the dermis are collagen and elastin. Fibroblasts are the main cells of the dermis and are responsible for the synthesis and degradation of dermal proteins (collagen and elastin), participate in the restoration of the skin (Darby et al., 2014; Bainbridge, 2013; Hesketh et al., 2017; McDougall et al., 2006), stimulate the growth of keratinocytes and blood vessels to form a response to autocrine and paracrine signals (Ploeger et al., 2013; Desjardins-Park et al., 2018; Hinz, 2007). There are several types of fibroblastic cells: fibroblasts, myofibroblasts, fibrocytes, fibroblasts, progenitor cells, and differentiated fibroblasts (Shurygina et al., 2012). These cell types are differentiated by their functional properties, although they are initially formed from stem cells. The process of converting “dormant” cells into cells that allow the production of extracellular matrix (ECM) is called fibroblast activation (Zeisberg et al., 2000). Fibroblasts produce collagen and elastin proteins, such as procollagen, proelastin, fibronectin, laminin, tenascin, depending on their location in the tissue and functional activity (Abe et al., 2001; Aumailley et al., 2005; Clark, 1990; Kistenev et al., 2019). Fibrocytes produce intercellular substances and have an anti-inflammatory effect (Reilkoff et al., 2011; Shekhter & Milovanova, 1975). Myofibroblasts belong to a differentiated cell type (Hinz, 2016). The leukocytes located in the dermis are part of the immune system (Mahla et al., 2021; Janeway et al., 2001). Leukocytes are divided into five main types: neutrophils, eosinophils, basophils, lymphocytes, and monocytes. Neutrophils are among the first to migrate to the site of inflammation, capture and cleave pathogenic microorganisms with lysosomal enzymes (Yoo et al., 2011). The main function of eosinophils is to fight multicellular parasites (Uhm et al., 2012). Basophils are involved in the development of allergic reactions (Mukai & Galli, 2013). Lymphocytes provide the production of antibodies and cellular immunity, and also regulate the activity of other types of cells (Janeway et al., 2001). Monocytes are the largest type of leukocytes that can differentiate into macrophages and dendritic cells. This type of cell performs three main functions of the immune system: phagocytosis, antigen transfer to lymphocytes, and cytokine production (Gahan et al., 2002). The dermis, as a rule, has a thickness of 1.0–1.5 mm; on the heels and palms the thickness can reach up to 3 mm. The dermis consists of two sublayers: papillary (papillary) and reticular (reticular) (see Fig. 12.1v). Vascular and capillary loops of the papillary layer of the dermis provide the epidermis with nutrients and oxygen. The dermis makes up the bulk of the skin, ensures its plasticity and elasticity, retains water and partially participates in thermoregulation. Hypodermic is called subcutaneous fat: the deepest integumentary layer of the skin located under the dermis (see Fig. 12.1vi). The thickness of the hypodermic layer can range from 2 mm to 10 cm and more. It consists mainly of a loose network of fibers (collagen, elastin) and adipose tissue. Among the cells, adipocytes (fat cells), fibroblasts, and

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macrophages can be distinguished. Hypodermic functions: natural shock absorption and thermal insulation of the body, depot for energy. Hypoderma plays a protective role on internal organs, accumulates useful substances, and produces hormones. When a light wave has all its electric field vectors in the same plane, it is said to be plane-polarized. The phenomenon of polarization of light is the conversion of unpolarized light into polarized light. This can be achieved by illuminating the light onto materials like tissue samples causing interactions like absorption, transmission, reflection, refraction, and scattering. The changes in these optical parameters and thus polarization vary from region to region in the tissues depending on their morphology and hence develop a contrast between each region, especially between proliferative tumors, compromised nearby tissue, and healthy tissues. The main optical coefficients which are polarization-sensitive are attenuation of light (birefringence), depolarization of light, and diattenuation of light. A quantitative analysis of tissue is possible by imaging alone, and qualitative analysis is possible by correlating the values obtained with the type of cells present. Cancerous tissue has high proliferation and heterogeneity, disturbing the anisotropy and the normal optical properties of the tissues. Collagen (micro fibrils and fibers) is one of the main components of the extracellular matrix (ECM) and contributes to anisotropy with its ordered arrangement. As a part of the stroma and underlying epithelium, the collagen arrangement is often influenced by neoplastic tissues under tumorous conditions. Being able to scatter light collagen contributes a lot to polarizationdependent birefringence (Arifler et al., 2007). Birefringence is the property of anisotropic tissues and can be detected by the change in the polarization state of the light passed through these materials. Another common polarization-sensitive property is the diattenuation of light, which occurs due to the absorption of light by the tissue components, again providing a way to analyze the microstructure of tissues, commonly used in fluorescence optical techniques. The other optical coefficient is the depolarization ratio, as a result of the depolarization of light by the tissue regions. Depolarization is caused by intrinsic factors like rotational diffusion of the molecules, radiation less energy transfer between fluorophores, etc., and also due to scattering. As a result, the depolarization ratio refers to both parallel and perpendicular polarization states and compares the intensity of signals between them, providing information about the dependence of the property on the orientation of the tissue components (Ly et al., 2010). Therefore, such optical properties that are rendered dependent on polarization due to the optical anisotropy of the sample can be used to create a distinction between healthy and cancerous tissues, often without the use of an exogenous label or dye. More often the images produced by the optical techniques can be studied along with statistical forms of data like spectra and histograms to better understand the structure and functioning of the tissue sample of interest. In this review, we discuss the various optical techniques like microscopy and spectroscopy which use the polarization property of tissues to diagnose cancer.

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2 Experimental Setup Polarization-resolved fluorescence spectroscopy uses the fluorescence and autofluorescence signals emitted by a tissue sample upon excitation with polarized light of appropriate wavelength, to obtain emission spectra and corresponding images. In between the source of illumination and the tissue sample, two polarizers P1 and P2 are kept along the light pathway. P1 is kept at the input laser pulses to produce a linearly polarized light. A narrow band interference filter or a wide band pass filter (WBF) is used in front of P1 to ensure that the illumination light becomes monochromatic and of the desired wavelength and P2 is used as an analyzer in the path of light emitting from the tissue sample. Additionally, the emission light again passes through a wide band pass filter before reaching P2 so that only desired wavelengths can be detected. The P2 is rotated to P1 to create both parallel and perpendicular polarization orientations to record the respective intensity profiles of any fluorescent emissions. The spectra and images are acquired using a CCD similar to fluorescence spectroscopy (Demos et al., 2004). Polarized near-infrared (NIR) spectroscopy uses NIR wavelength to excite and detect tissue components to obtain the NIR emission spectra. It is an advantageous choice as it has high penetrating power and is not carcinogenic, unlike UV or VIS light. The white light illumination is passed through a wide band filter centered at NIR wavelengths (700–2500 nm) to obtain the desired spectral range of illumination and detection. Light beams are illuminated on the sample from two directions, one to measure the backscattering of the light and the other to measure the transmission of light through the sample. A polarizer, P1, is used to polarize the incident light beam into linear polarization to illuminate the sample. After scattering and transmission, the light passes through another band pass filter which selects a longer wavelength than that of the excitation light. To create the required orientation of polarization of the light, another polarizer P2 is placed before the detector. The CCDs are strategically employed to detect both transmission and backscattering emissions (Ali et al., 2004). Figure 12.2i shows the hyperspectral imaging (HSI) system, an optical imaging technique that generates a spatial map where each x-y coordinate gives the spectral information of the sample (Rodrigues et al., 2020). This technique first obtains the spectrum for the 2D images, then assembles these 2D images to reconstruct a 3D datacube (Zhou et al., 2020). Here, the source is not limited to UV, Visible, or NIR light, but extends beyond them to X-rays and other such radiation sources (Rodrigues et al., 2020). Simultaneously, the sample’s image, spectral as well as polarization data can be obtained by polarized hyperspectral imaging as it combines the ideas of polarization measurement, hyperspectral spectroscopy, and space imaging. The HSI component of the device is a hyperspectral camera whereas the components of polarized light imaging are the Liquid Crystal Variable Retarders (LCVR) and polarizer (two of each). The wavelength range in which HSI is performed is 467–700 nm. The device uses a snapscan acquisition method wherein the sample stays fixed while the CCD detectors move. Hence, the device can perform comprehensive Stokes polarimetric imaging thereby producing the entire

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Fig. 12.2 (i) Polarized hyperspectral spectroscopy (hyper spectral imaging HSI) setup consisting of hyperspectral cameras, polarizers, LCVR’s, lenses, and CCD detectors which yield all four components of Stokes vector (S0, S1, S2, S3) (Zhou et al., 2020). (ii) Polarization-resolved confocal microscopy. A dichroic mirror recombines the excitation laser and a halfwave plate (HWP) rotates the incident angle of linear polarization. The objective lens focuses the light on the sample (Valades et al., 2016). (iii) Polarization-resolved fluorescence microscopy. The polarizer filters the incident light, and the objective lens collects the light. The fluorescence emitted by the sample is filtered by an emission filter, which is then split into P and S polarizations (Ross et al., 2019). (iv) Polarization- resolved SERS microscopy. Raman micro-spectrometer equipped with 785 nm laser detects SERS spectra of the sample in the 400–1750 cm−1 region of wavelength within a 10 s integration time using a 20× objective and Peltier CCD detector (Lin et al., 2016). (v) Polarization-resolved second-harmonic generation (SHG) microscopy. The laser beam is linearly polarized, spatially filtered, collimated, and scanned using galvo-scanners. The resulting beam is then passed through relay lenses and reflected through gold mirrors to preserve its polarization state. The SHG signal is filtered by laser-blocking filters and collected using an EMCCD camera (Ambedkar et al., 2012). (vi) In 2-photon fluorescence microscopy, the power and polarization

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Stokes vector’s four elements. The reflectance that concerns the intensity along with the polarization properties can also be defined by the system (Zhou et al., 2020). Raman spectroscopy works on the principle of Raman scattering to obtain a spectrum that provides information about the vibrational bonds of the sample under study. The polarization-resolved Raman spectroscopy enhances the spectral contrast arising from the vibration of the Raman active molecules, which holds for better identification and demarcation of the diseased tissue. A polarized light of a particular wavelength is focused onto the sample using an objective lens. The light is then made to pass through a polarization analyzer which is oriented to the polarizer to obtain either parallel polarized or perpendicular polarized measurements. The Raman Stoke signals obtained are dispersed using a holographic grating device after which the data is collected using a CCD camera. Additionally, a screen image recorder camera, present within the microscopy set up, is used to capture white light images for the selection of the region of interest (ROI) (Guc et al., 2016). Polarization-resolved confocal microscopy scans a small volume element of the sample and provides high-resolution 3D images (Fig. 12.2ii) (Lavrentovich, 2003). It is constructed by modifying a commercially available confocal microscope, adding a rotating linear polarizer that converts the light into linearly polarized light. The pinhole present in the system act as a spatial filter and reduces the signals emitted by the regions which are not in focus, thus achieving optical sectioning. The image is acquired as a stack of submicron horizontal optical slices which can be reconstructed into a 3D representation. Polarization-resolved fluorescence confocal microscopy is carried out by either doping the sample with fluorescent dyes or by considering the endogenous fluorophores present in cells/tissues. In polarization-resolved fluorescence microscopy (Fig. 12.2iii), the absorption of a photon by the fluorophore is dependent on the angle between the absorption dipole moment and the electric vector of the incident light field (Sosa et al., 2010). The  Fig. 12.2 (continued) state of the incident laser are controlled by motorized waveplates and a half-wave plate before the light reaches the microscope. A polarizing beam splitter cube was used to allow only horizontally polarized light to pass. Custom software is used to adjust the polarization and laser power at the sample plane before image acquisition (Micu et al., 2017). (vii) Polarization-resolved coherent anti-stokes Raman scattering (CARS) microscopy. Ti:Sapphire and OPO are used to generate pump and Stokes beams of 808 nm and 1049 nm, respectively. CARS signal generated is collected by the objective lens and two photomultiplier tubes in the backward direction. DL1 and DL2 delay lines, DM1, DM2, DM3 dichroic mirror, F1 3 nm narrow bandpass filter, F2, F3 detection bandpass filter, L1, L2, L3 lens, OPO optical parametric oscillator, PMT photomultiplier tube, SBS beam splitter (Le et al., 2017). (viii) Polarization-sensitive OCT (PSOCT) superluminescent diodes (SLD) produce light which passes through linear polarizer via single-mode fiber (SMF) and then to a collimator via a polarization maintaining fiber (PMF). The collected light is split via a beam splitter to a reference and sample mirror. The light collected back travels back to the collimator where they interfere and interference fringes obtained travel via PMF and are analyzed via spectrometers (Wang et al., 2018). (ix) Polarized stimulated Raman scattering (SRS) microscopy setup consisting of a lab-built multiplex-modulation SRS microscope. D dichroic mirror, G grating, M mirror, OBJ objective, P polarizing beam splitter, PD photodiode, PS polygon scanner, Q quarter waveplate, SL slit, SU scanning unit (Liao et al., 2015)

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two parameters are related as a dot product, which means that absorption does not occur when the two vectors are perpendicular, and there is maximum absorption when they are parallel (Duboisset et al., 2013). The setup consists of a modified confocal fluorescence microscope, and a stack of fluorescence images is recorded for different excitation angles. The setup is upgraded by the addition of a rotating half-wave plate, which controls the state of polarization of the exciting beam. Two photons are simultaneously absorbed in two-photon fluorescence microscopy (Fig. 12.2vi). The combined energy of the two photons induces the molecular transition of the fluorophore to the excited state (So et al., 2000). For the experimental setup, an inverted confocal microscope is modified by the addition of polarizing beam splitters (Ridsdale et al., 2004). Unlike visible laser light sources used in confocal or fluorescence microscopy, this technique utilizes ultrashort pulsed, highintensity NIR lasers (Perry et al., 2012). The laser polarization is generated by rotating a linear polarization in the excitation arm. The fluorescence polarization is measured by an analyzer before the detector (Nag & Goswami, 2010). The photodamage and photobleaching are limited to the small detection volume, and negligible background signals are detected. Second-harmonic generation (Fig. 12.2v) is a second-order non-linear optical microscopy technique. In this technique, interaction between nonlinear material (non-centrosymmetric) and two photons with identical frequency yields a higher energy photon with double the energy of the incident photon (Kumar et al., 2015). This technique possesses higher demand due to its ability to reduce the photodamage and enhance the optical contrast; and when combined with polarization light imaging, it extends its analysis at the molecular level (Mercatelli et al., 2020). The system is built by the combination of Ti:Sapphire laser, galvo-scanners, polarizer and objective lenses, filters, and EMCCD camera for detection. Polarizers and halfwave plates control the polarization incident on the sample (Ambedkar et al., 2012). Third-harmonic generation is a third-order nonlinear optical microscopy technique in which interaction between a nonlinear material and three photons with identical frequency yields a photon of energy that is triple that of the incident photon. When compared to SHG, THG is a more flexible approach since it does not require a specific asymmetry of the structure being imaged. Here, a femtosecond laser is used as the excitation source. The beam from the source is then focused onto the sample mounted on a three-axis piezo scanner by an objective lens. The rest of the THG components of this device include condensers, filters, and photomultiplier tubes which transmit the unpolarized THG signal forward. The presence of half and quarter-wave plates convert the unpolarized signal to a fully polarized THG signal (Bautista et al., 2014). Just a single laser beam can provide crucial morphological information without causing photobleaching and phototoxicity effects on biological tissues (Tsafas et al., 2020). Raman scattering refers to the inelastic light scattering of photons following vibrating molecule and photons interaction. Surface-enhanced and coherent Raman scattering is used to overcome the relatively weak signals obtained by spontaneous Raman spectroscopy. The coherent Raman scattering uses an ultrafast laser that enhances the signal by fivefold in magnitude, allowing real-time in vivo imaging.

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Stimulated Raman scattering (SRS) and coherent anti-Stokes Raman scattering (CARS) are two types of coherent Raman scattering (Xu et al., 2016). CARS (Fig. 12.2vii) is a label-free technique that provides information on the chemical properties of the sample based on intrinsic molecular vibrations (Xu et al., 2013). In polarized CARS, a femtosecond Ti:Sapphire laser is used as a pump beam, and for Stokes beam, a Ti:Sapphire laser pumped optical parametric oscillator (OPO) is used. For pump and Stokes beam, respectively, 808 nm and 1049 nm wavelengths are chosen to keep the frequency difference between the two beams as 2843 cm−1 . This frequency difference is consistent with the CH2 symmetric stretching mode. Delay lines (DL1 and DL2) facilitate the temporary overlap of the laser beams which are later merged via a long-pass dichroic mirror (DM1). The combined beams with a laser power of 17.5 mW reach the objective lens via a galvanometric scanning unit. The signals are gathered and simultaneously separated in the backward direction by the objective lens and dichroic mirror (DM3), respectively. These signals are then detected by two photomultiplier tubes (PMT1 and PMT2) after they are filtered by a band pass detection filter (F3) and short-pass filter (F2) (Le et al., 2017). A third-order nonlinear optical process similar to the CARS technique is SRS (Fig. 12.2ix), which depends on the vibrational properties of macromolecules to generate chemical contrast and allows rapid microscopic imaging (Orringer et al., 2015). The polarized SRS system consists of an 80 MHz pulsed laser with two outputs, a pump beam with a 680–1300 nm tuning range and a fixed 1040 nm Stokes beam. The pump beam is dispersed in the x-direction by a diffraction grating and scanned in the y-direction using a 17 kHz polygon scanner on a photolithography mask. The modulated 800 nm laser beam is reflected by a mirror placed after the photomask, giving a modulation depth of 95%. The pump and Stokes beams are passed to a lab-built microscope, and a 25X objective lens focuses light on the sample. The stimulated Raman gain (SRG) signal collected by the same objective lens is passed through a polarizing beam splitter following which the polarization-scrambled SRG signal is reflected on the photodiode. The induced photocurrent is amplified by the resonant amplifier circuit and is then transferred to a high-speed data acquisition board, synchronized with galvo-mirrors (Liao et al., 2015). Surface-enhanced Raman scattering (SERS) (Fig. 12.2iv) is an optical technique that by using inelastic scattering can provide “fingerprints” of biomolecular compositions and structures. The advantage of using SERS over fluorescence is minimum photobleaching and multiplexing competencies under a single excitation light (Lin et al., 2016). A 785 nm laser-equipped Raman microspectrometer is used to record the SERS spectra. A linear polarizer is employed to change incident light’s polarization state and the polarizer’s direction (parallel or perpendicular) is changed according to the direction of the excitation light source to obtain parallel and perpendicular polarized light, and it is removed to obtain a non-polarized spectrum. The SERS scattering signals in the wavelength range of 400–1750 cm−1 are obtained using a 20× objective lens at a 10 s integration time. The spectral acquisition, as well as data analysis, is done by the Peltier CCD detector and software package WIRE 2.0 (Renishaw) (Lin et al., 2016).

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Polarization-sensitive optical coherence tomography (PS-OCT) uses polarization properties of the tissue samples to develop an enhanced and more specific OCT image. The instrumental setup includes the usage of SLD (superluminescent diode) each centered at its wavelength, as a light source. The light beams are first linearly polarized by an in-line polarizer. This then travels into the Michelson interferometer through polarization-maintaining fibers. The light beams are then split, where one enters into the reference arm and the other enters the sample arm, both containing wave plates with specific orientations. At the reference arm, a mirror reflects the reference light which is passed back through the same pathway. At the sample arm, the beam travels to the sample surface via an objective lens. The incident polarized light suffers a change in polarization due to the birefringent species present in the sample and then travels back on the same path. The two light beams finally interfere and the interference fringes obtained pass through a polarizing beam splitter through the fibers, and the fringes are analyzed by a spectrometer.

3 Applications 3.1 Spectroscopy Techniques 3.1.1

Fluorescence Spectroscopy

Fluorescence spectroscopy is a technique that analyses the fluorescence emitted from a sample to create excitation and emission spectra that gives information on the components or constituents of the sample (Lakowicz, 2006). Polarizationresolved fluorescence spectroscopy uses polarization-resolved light for excitation of the sample while procuring information about its anisotropy by recording properties such as linear diattenuation: the difference between absorption of parallelly polarized light and perpendicularly polarized light (Tuchin, 2016) and polarizing ability to produce polarized light (Jagtap et al., 2014) of fluorescence emissions. Therefore, this technique can be used for quantitative analysis as well as qualitative analyzing by observing characteristic fluorescence peaks (Albani, 2004). In another research (Jagtap et al., 2014), polarization-resolved fluorescence spectroscopy was performed for the detection of cervical cancer using human cervical intraepithelial neoplasia with normal counterpart samples. A fluorescence spectroscopic Mueller matrix measurement system with an excitation wavelength of 405 nm and fluorescence emission detection wavelength in the range of 400–800 nm was used, which recorded 16 sets of spectra using four orientations of polarized lights. Due to the anisotropically arranged collagen in the dysplasia samples (Yang et al., 2018; Aspden, 1988), the fluorescence emission suffered diattenuation and polarizing which further showed different trends with precancerous tissues having significantly lower diattenuation and polarizing than normal tissues (Fig. 12.3iii). The overall fluorescence emission intensity from cancerous tissues was also lower due to the destruction of the organization of collagen (Cox & Erler,

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2011) by the unnecessary proliferation of cells. The experiment thus proved the usage of polarimetric parameters diattenuation and polarizing as diagnostic metrics for cervical cancer through polarized fluorescence spectroscopy. Another study (Gnanatheepam et al., 2020) was performed focusing on polarization-resolved fluorescence spectroscopy to differentiate between the deep and superficial layers of oral cancer using fluorescence redox ratio. The tissue biopsies collected from oral cancer and healthy patients were illuminated with 330 nm excitation wavelength and the emission was collected at 370–600 nm. A polarization gating technique was used for the analysis of turbid conditions (Demos & Alfano, 1996; Chen & Korotkova, 2018; Delfino et al., 2020). The emission spectra obtained from the oral cancerous and healthy tissue had a peak at 440 nm with a shoulder peak at 530 nm, due to NADH and FAD, respectively, as seen in Fig. 12.3iv. The intensity of emission from using parallel polarized light was seen to be three to four times higher than that of using perpendicular polarization of light, in both healthy and cancerous tissues. This was further proved by calculating the redox ratios which is the ratio of the autofluorescent intensity of NADH to that of FAD (Kroemer & Pouyssegur, 2008). The deeper layers of the cancerous tissues showed decreased emission intensity of collagen and NADH and increased emission intensity of FAD when compared to healthy tissues (Fig. 12.3v). On the other hand, superficial layers of cancerous tissues revealed an increase in NADH but no major change in collagen and FAD, when compared to healthy tissues (Fig. 12.3v). These variations in NADH and FAD intensities in cancerous conditions were recorded as a change in the tissue layer’s redox ratio, with superficial tissues having a lower redox ratio and deeper tissue having a higher redox ratio compared to normal. The experiment could prove the usage of fluorophores NADH and FAD in confirming the varying effects of cancer on different layers of oral cancer tissue. Another study (Rajasekaran et al., 2014) to detect and diagnose cervical cancer was performed by analyzing urine samples of patients using polarized fluorescence spectroscopic technique since urine contains many diagnostically important fluorophores, such as neopterin and riboflavin (Croce & Bottiroli, 2014) which show distinct fluorescence emission peaks. Parallelly and perpendicularly polarized light orientations excitation wavelengths were used at 280 nm and 350 nm for riboflavin and neopterin, respectively (Leiner et al., 1987), to determine the steadystate polarization and anisotropy. The emission peaks were visible at 428 nm and 401 nm for cancer and healthy subjects, respectively. This peak obtained at 280 nm excitation, in both was attributed to indoxyl sulphate, a fluorophore compound involved in cell signaling and modification of extracellular matrix (Cheng et al., 2020). At 350 nm excitation, higher fluorescence intensity was in healthy tissues than in cancerous tissues. Also, the cancer samples displayed a shoulder at 515 nm, which was missing in healthy samples. Additionally, the time-resolved fluorescence spectroscopy documented the lifetime of the fluorophores in cancerous samples to be slightly lower than that of healthy samples. The change in the microenvironment of the tissues could thus be detected by the trends in fluorescence spectra and confirm a cancer diagnosis. In a study (Pu & Alfano, 2013) performed to detect prostate cancer from human prostate tissue samples, a fluorescent dye cybesin

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Fig. 12.3 (i) Contrast agent fluorescence polarization images and spectra of cancerous (C) and normal (N) prostate tissue samples. The pump excitation wavelength was 750 nm and the detection wavelength was 850 nm, in orientations of (top) parallel, (middle) perpendicular polarized, (bottom) is the polarization difference image (Pu et al., 2013). (ii) Time-resolved fluorescence emission intensity collected from cybesin-stained cancerous (top) and normal prostate tissues (bottom) (Pu & Alfano, 2013). (iii) Spectral variation of linear diattenuation (top) and linear polarizance (bottom) the triangle symbols represent the corresponding parameter of the graph of the precancerous CT (solid) and normal CT (open). Both show significant values of linear diattenuation and polarizance. The fluorescence emission suffered diattenuation and polarizance which further showed different trends with precancerous tissues having significantly lower diattenuation and polarizance than normal tissues. Their magnitude is lower in the precancerous tissues, especially regarding diattenuation (Jagtap et al., 2014). (iv) Measured using parallel and perpendicular polarization orientations (a) Non-normalized and (b) normalized mean fluorescence polarization emission spectra of normal and cancer tissues. The fluorescence emission spectra of

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that binds especially to bombesin and somatostatin receptors (Bugaj et al., 2001) whose overexpression is a characteristic of cancer (Sun et al., 2000), was used as a contrast agent to obtain fluorescence emissions using 800 nm excitation wavelength and 830 nm fluorescence detection (Fig. 12.3ii) selected using long pass filters. As shown in Fig. 12.3ii, the peak intensity of total fluorescence in cancerous tissues was ~3.43 times greater than that of healthy tissues due to the high affinity of cybesin stain to the receptors present. At the peak position, the fluorescence intensity obtained by parallel orientation was ~1.57 times greater than that obtained by perpendicular orientation, whereas this ratio in normal tissue was ~1.40. This verified that the fluorescence emission from both cancerous and normal tissues showed polarization preservation properties. This experiment provided the intensity information on fluorophores in the microenvironment of the cancerous tissues and experimental results for the preferential uptake of cybesin by prostate cancer tissues. Polarized fluorescence spectroscopy was thus used to find out and compare trends in the fluorescence spectra obtained from healthy and various types of cancerous tissues based on either their optical properties such as diattenuation and polarizance (Jagtap et al., 2014) or the presence of an excess of clinically important fluorophores such as neopterin and riboflavin (Rajasekaran et al., 2014) which resulted in higher intensity peaks. The analysis of these spectra could reveal various hallmarks of cancer such as collagen disorganization characterized by a decrease in diattenuation of fluorescence emissions (Jagtap et al., 2014), presence of mitochondrial mutations, and excess of important molecules which play pathological roles in cancer progression (Rajasekaran et al., 2014) by a significant increase in their fluorescence emission intensities. Among these benefits of polarized fluorescence spectroscopy, the unique property of fluorescence emission is not shown by all clinically important molecules and the usage of dyes such as cybesin is required, making the technique an invasive one. In the case of too many fluorescent molecules present in the sample which can interfere as noise, methods such as diffuse reflectance are applied to focus on required emission spectra, this technique is followed in polarized NIR spectroscopy as well.  Fig. 12.3 (continued) standard collagen, NADH, and FAD are provided. The fluorescence spectra peak at 440 nm with a shoulder peak at 530 nm, due to NADH and FAD, respectively. The peak intensity at parallel polarization is three and four times higher than that of perpendicular polarization for normal and cancer tissues, respectively (Gnanatheepam et al., 2020). (v) Using polarization gating technique normalized mean fluorescence emission from (a) bulk tissue, (b) superficial, and (c) deeper layers from tissue lesion. The deeper layers of the cancerous tissues show decreased emission intensity of collagen and NADH and increased emission intensity of FAD. Superficial layers of cancerous tissues show an increase in the NADH but no significant change in collagen and FAD (Gnanatheepam et al., 2020)

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3.2 NIR Spectroscopy Near Infra-Red Spectroscopy (NIRS) is a variant of IR spectroscopy that uses light in the NIR wavelength range (780–2500 nm) to excite the vibrations and overtones of the molecules present in the sample. Specifically targeting endogenous chromophores containing functional groups and molecule bonds such as N-H (amine, amide) NO2 (nitro group), C=C (aromatics, alkene), and C=O (aldehyde, ketones, acids, ester), the polarized NIRS provides information about the presence or absence of these molecules at various depths of the tissue sample, as the perpendicularly polarized light can analyze deeper areas of the tissue and parallelly polarized light provides information on the surface levels of the tissue (Shao et al., 2010). NIRS emissions can be recorded in transmission mode or reflectance mode or using multi-distance mode for more spatial information. Most of the NIRS instruments follow the Continuous Wave (CW-NIRS) mode as it shows trends in the changing values of emission spectra (Prasad et al., 2019) Usage of NIR wavelength range is an advantageous choice as it has high penetrating power and is not carcinogenic, unlike UV or VIS light. A study (Pu et al., 2005) using polarization-resolved NIRS was performed for distinguishing human prostate cancer tissues from healthy tissues based on the use of cybesin, which as stated earlier (Bugaj et al., 2001) has a high affinity toward prostate cancer tissues. The samples were illuminated at different wavelengths 680– 830 nm and their emission wavelengths were detected at 800–950 nm of NIR optical window using wide band pass filters. The cross-section intensity distributions of NIR emissions showed the highest values near the cancerous tissues and smaller values away from cancerous tissues. Similarly observed in the subsequently obtained NIR emission images, the visibility of the dyed tissue increases along with the increase in excitation-emission wavelength and is strongest at the excitationemission range of cybesin (800–850 nm). This proves that the fluorescence intensity is due to the cybesin attached to the cancerous areas, providing a prostate cancer diagnostic method. A polarization NIRS study (Ali et al., 2004) was conducted to differentiate cancerous from healthy prostate tissues in samples collected from volunteers, using differences in their water content. Water absorbs NIR at around 1450 nm due to the presence of vibrating OH bonds (Curcio & Petty, 1951) and therefore NIR absorption at this wavelength is proportional directly to the water concentration in the tissues. This relationship provides a non-invasive method of differentiating colonic cancerous tissue that has low water content and absorption (Wang et al., 2004) but high scattering (Mourant et al., 1998) during the transmission mode of NIR. Wavelengths of 700 nm, 800 nm, 1200 nm, and 1450 nm were selected for excitation of the sample as well as detection of NIR emissions at parallelly and perpendicularly polarized light orientations (Ali et al., 2004). In the wavelength range of 400–1200 nm in the absorption spectra, normal tissues experience higher forward scattering compared to cancerous tissues, leading to an overall higher forward scattering intensity. The transmission is hence stronger in cancer tissues in the NIR images obtained, especially at 700 nm, 800 nm, 1200 nm,

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Fig. 12.4 (i) Obtained emission spectra from polar decomposition of the 4/4 Mueller matrix focused on three derived spectroscopic polarimetric metrics: Mean diattenuation, Mean depolarization, and Mean retardance for the paired (normal (30) vs cancer (30)) colonic tissue (Wang et al., 2016)

and 1450 nm. The depolarization recorded through the degree of polarization calculation is in direct relationship with the sizes, shapes, and anisotropy of the cells, leading to more multiple scattering events. This technique, therefore, provided a label-free diagnostic technique for prostate cancer. Another study (Wang et al., 2016) involving polarized NIR spectroscopy was performed to study its ability to improve colonic cancer detection. Thirty samples of colonic cancer tissue and healthy tissue collected from 18 men and 12 women were illuminated with 700 nm wavelength and detected at emission wavelengths in the range of 700– 1100 nm using an integrated Mueller matrix (MM) NIR point wise spectroscopy and imaging system. The obtained emission spectra from polar decomposition of the 4/4 Mueller matrix (Fig. 12.4i) showed that the colonic cancer tissues’ NIR emissions suffered significantly lower depolarization and retardance, but showed higher diattenuation when compared with healthy colonic tissues. Considering the combination of these three polarization metrics provided a sensitivity of 93.3% and specificity of 96.7% which is higher than their diagnostic accuracies. The spectra in both tissues were also observed to be dominated by peaks at 970 nm creating a valley that corresponded to water absorption which was more obvious in colonic cancer tissue samples due to increased water content (Abramczyk et al., 2014) (Fig. 12.4i) The experiment thus proved the usage of polarized NIR spectroscopy in the early detection of colonic cancer tissues through quantitative analysis and characterization. Polarized NIRS was used to diagnose cancers such as prostate cancer and colonic cancer by observing trends in their NIR emission spectra when illuminated with polarized light, which provided information on the microenvironment of the region of interest, such as reduced water content in prostate cancer tissues revealed by low intensity of its NIR absorption peak (Ali et al., 2004), and also presence or excess of fluorophores using NIR AF spectroscopy (Shao et al., 2010), which allowed for quantitative analyzing by calculating NIR AF intensity ratios and polarization ratios, thus differentiating cancerous from non-cancerous tissues. Other diagnostic metrics

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obtained from polarized NIRS were depolarization, retardance, and diattenuation values, a combination of which showed high diagnostic accuracies (Wang et al., 2016). Polarized NIRS also involved the usage of fluorescent dyes to obtain crosssection NIR intensity variations in tissues to distinguish tumor regions (Pu et al., 2005). One of the disadvantages is the interference of multiple emissions in the NIR emission spectra leading to noise (Fekete et al., 2011).

3.2.1

Hyperspectral Spectroscopy

Hyperspectral spectroscopy incorporates conventional techniques of imaging and spectroscopy to obtain tissue’s spatial and spectral data. Being a non-invasive, noncontact, label-free, and non-ionizing imaging modality, its application is varied in the medical field to detect tumors and to guide during surgery (Halicek et al., 2019). A study (Zhou et al., 2020) was conducted to develop a dual-modality polarized hyperspectral imaging microscope (PHSIM) combining the approaches of polarized light imaging and hyperspectral imaging (HSI), for SCC (squamous cell carcinoma) detection. The validity of this device for detecting SCC was checked by performing imaging for head and neck cancer. Oral tissues were isolated from selected eight patients with head and neck cancer and from these tissues, eight H&E stained slides were prepared. From each slide, one normal and one cancerous region was selected for imaging. These slides were then imaged under the PHSIM to obtain the spectral curves under different wavelengths. As shown in Fig. 12.5i, it was seen that for a certain wavelength range, there was a difference between the generated spectral curves of the Stokes vector parameters (S0, S1, S2, and S3) for the tissue regions that were normal and cancerous (The Stokes parameters are a set of four elements that define reflectance in terms of intensity and polarization properties). The curves for these parameters showed different peaks due to the absorption of hemoglobin and varying scattering effects due to changes in the nucleus-to-cytoplasmic ratio. The PHSIM was therefore proved to be successful in the sample’s Stokes vector measurement under different wavelengths. Melanoma is a cancer of the melanocytes, the melanin pigment-producing cells. It is the most violent skin cancer type among its other kinds. Hence, early diagnosis is a key requirement to increase the likelihood of its eradication. Acquiring further information sustained by the light’s vector as well as the sample’s polarimetric response such as partial depolarization can be done by bringing together the ideas of conventional optical imaging and polarimetric imaging (Zhou et al., 2020). A study (Ceolato et al., 2015) was conducted aiming to measure the light’s spectral degree of linear polarization (DOLP) from healthy and melanoma cells, as well as to check the reliance of the spectral DOLP on the thickness of the melanoma. B16F10 melanoma murine tumor cell line was injected intradermally into 10–12 week-old C57B1/G female mice and the formation of 5–9 mm diameter tumors took place within 10 days. The tumor and the healthy skin samples were measured for their spectral and polarimetric backscattered radiance to determine the spectral DOLP. The healthy skin sample was revealed to be a strongly depolarizing medium. For

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Fig. 12.5 (i) From the normal and cancerous parts, the average spectral curves of the Stokes Vector parameters (S0, S1, S2, S3) on eight slides from eight patients (Zhou et al., 2020). (ii) Spectral DOLP of healthy skin samples from three different female C57Bl/6 mice (Ceolato et al., 2015). (iii) Spectral DOLP of (a) healthy and cancerous skin from four different female C57Bl/6 mice with B16F10 melanoma areas of (b) 23 mm2 , (c) 26 mm2 , (d) 58 mm2 , and (e) 68 mm2 , respectively (Ceolato et al., 2015). (iv) Total Hb skin lesion analysis before (top) and after (bottom) melanin attenuation correction (v) Scatterplot of normalized total melanin and total Hb in #1 subject (a) before and (b) after correcting melanin-Hb crosstalk. Scatterplot of normalized total melanin and total Hb in #19 subject (c) before (d) after correcting melanin-Hb crosstalk (Vasefi et al., 2016)

all the healthy skin samples, the recorded spectral DOLP were alike (around 0.2) and from visible to near-infrared had no spectral variation (Fig. 12.5ii). Whereas the spectral DOLP recorded for all the melanoma samples (Fig. 12.5iii) was higher than that of the healthy skin samples, and also the melanoma sample tends to maintain polarization states. The melanoma size was found to be directly proportional to the spectral DOLP. This is because, as the disease progresses, the roughness of the melanoma surface reduces, due to which surface scattering is favored. In addition to this, in melanoma samples, spectral dependence of the DOLP was reported and in

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comparison to the healthy skin samples, a decline from 750 to 1000 nm in the NIR region was observed. This decrease in the NIR region was seen to correlate with less absorption by melanin pigments in cancer. Hence, in addition to detecting tumors, this technique is also believed to be efficient in predicting the stage of the disease. For early detection of melanomas, it is vital to use non-invasive imaging techniques which can distinguish melanin from hemoglobin pigments in tissues and further measure only the melanin distribution in these samples (Vasefi et al., 2016). For this purpose, a group of scientists in California developed a multimode dermoscope called SkinSpect using depth-sensitive approaches of polarization and hyperspectral imaging (Vasefi et al., 2016). The main aim was to prevent the melanin fraction, epidermal thickness, and hemoglobin concentration from interacting with each other which could affect the absorption spectra obtained during quantitative skin measurements. The software evaluates melanin and hemoglobin through image datacubes from parallel and cross-polarized measurements. With a field of view of 18 mm, SkinSpect is also capable of imaging the skin’s (predominantly from collagen) fluorescence emission. Additionally, the validity of SkinSpect was checked using spatial frequency domain spectroscopy (SFDS). While the SFDS system is confined to point detection, it is overcome by SkinSpect which can produce morphological data with spatially resolved measurements with a greater processing speed. But at the same time, SkinSpect lacks axial resolution. All the 20 individuals studied for their benign nevi (Fig. 12.5iv) and normal regions showed a low correlation between melanin and total hemoglobin and consequently the validity of SkinSpect to reduce melanin-hemoglobin absorption to those which are biologically plausible was established (Fig. 12.5v). Though the SFDS made use of a slightly different method in comparison to SkinSpect, the result obtained was comparable. Overall, hyperspectral imaging, with its high accuracy and processing speed, shows very promising results in characterizing tumors at a very early stage and facilitating their eradication later on.

3.2.2

Raman Spectroscopy

Raman spectroscopy is a technique that uses the monochromatic light scattered off a sample to determine the vibrational modes in a molecule. Based on the nature of the molecules, the scattered light can be parallelly or perpendicularly polarized with respect to the incident linearly polarized light (Tuschel, 2014). The spectral patterns are unique to the molecules, making this a reliable technique for both identification and studying molecular changes in the samples. Thus, this technique can be used in disease diagnosis by detecting biochemical changes in the tissue microenvironment and by identifying the specific spectral properties of diseaseassociated molecules (Eberhardt et al., 2015). One such disease studied through Raman spectroscopy is cervical cancer, which is the fourth most common cause of cancer and related mortality in women (Arbyn et al., 2020). Currently, diagnosis is done by pap-tests and subsequent image acquisition techniques, which have high specificities but low sensitivities (William et al., 2018; Woo et al., 2020). This can

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be overcome by using polarized Raman spectroscopy (PRS), because in addition to orientation and symmetry of bond vibrations, PRS provides information about the orientation of biomolecules in the 3D environment. A study (Daniel et al., 2016) employed and compared conventional and polarized Raman spectroscopy for cervical cancer diagnosis. As the first step, conventional Raman spectroscopy was carried out on normal and cancerous tissues, and the fingerprint region from 600 to 1800 cm−1 was analyzed. The same samples were subjected to PRS yielding parallel and perpendicular polarization spectra, and the results were compared. It was found that the C-C stretching vibration of the collagen backbone at 937 cm−1 and the amide III vibration at 1265 cm−1 , especially the perpendicular component, was more intense for the normal samples than the cancer samples. The amide I of collagen at 1656 cm−1 was found to be more intense in the parallel component of the normal samples. The 1375 cm−1 peak corresponding to the ring mode of thymine is more intense in the perpendicular direction. The 1578 cm−1 band due to the contributions of both adenine and guanine is more intense in the parallel component. The depolarization values of these bands in normal tissues are the same for all samples, whereas for cancerous tissues, the values always differ. These variations are significant as they provide information about the changes in the orientation of molecules and the normal cells become malignant. This was followed by LDA (linear discriminant analysis) and LOOCV (leave-one-out cross validation), and the inference obtained was that PRS has higher discriminating properties than conventional Raman spectroscopy, making it a better technique for clinical diagnosis applications. Another study (Ly et al., 2010) was performed to detect and monitor the progress of BCC (basal cell carcinoma), specifically the superficial, nodular, and infiltrative variants of it on human skin. Raman micro-spectroscopy involves the usage of both Raman spectroscopy and a microscope with a screen image-recording camera. Four regions: the tumor, peritumoral stroma, healthy epidermis, and healthy dermis of the samples were located and identified using H&E staining followed by spectroscopic analysis using unpolarized, parallel polarized, and perpendicular polarized light orientations at illumination wavelength 785 nm and detection at 600–1750 cm−1 . The depolarization caused by the components such as phenylalanine, tyrosine, polysaccharides, and trans-hydrocarbon chains in the tumor tissue was much lower than in the healthy epidermis. The difference in the excitation spectra obtained from the peritumoral dermis and healthy dermis tissues targeted at lipids, collagen, and collagen-like proteins was not as significant as that from tumor vs. epidermis tissue shown by the P values. This is because the molecular modifications (Crowson, 2006) taking place at the peritumoral stroma are less substantial than in tumor tissues (Lesack & Naugler, 2012). There was a noticeable difference in the tyrosine peaks between the spectra from the peritumoral stroma and normal tissue. The changes in the amide 3 band (1300 cm−1 ) proved that collagen was one of the main components that were degraded at the tumor vicinity. This finally concluded that polarized Raman spectroscopy could be used for qualitative analysis of tumor and differentiation of peritumoral stroma in superficial and nodular BCC from the normal dermis.

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Oral cancer is a result of increased alcohol intake, inactive lifestyle, excessive usage of tobacco and its products, and human papillomavirus infections. Tissue biopsy followed by histopathological screening is considered the gold standard for these abnormal lesions. Early diagnosis will provide better treatment options and improve the survival rate (Prakasarao et al., 2017). A study reported the use of polarized Raman spectroscopy (PRS) to differentiate oral cancer and normal blood plasmas and compare it with conventional Raman spectroscopy (Prakasarao et al., 2017). Raman spectra from 31 normal and 17 histologically confirmed oral cancer patients were obtained in the fingerprint region of 600–800 cm−1 . Vector normalized averaged conventional, parallel, and perpendicular polarized Raman spectra of normal and oral cancer blood plasmas were obtained and their corresponding difference spectra were acquired. In comparison to normal blood plasma, less intense vibrational signals of amide I (1635 cm−1 ), amide III (1246, 1258, and 1268 cm−1 ), carotenoids (1527 cm−1 ), DNA backbone (927 cm−1 ), lactic acid (650 and 730 cm−1 ), and lipids (1300 cm−1 ) were observed for cancerous blood plasma. In the cancerous group, more intense vibrational peaks were observed at the negative region for DNA and its base pairs (1057, 1180, and 1421 cm−1 ) and hydroxyproline (875 and 949 cm−1 ). The difference spectra of the polarized method showed that the bands of lactic acid (650 cm−1 ) and pyrimidine bases (767 cm−1 ) for the parallel laser beam were more intense in comparison to the perpendicular laser beam for cancer samples, whereas 730 cm−1 band of lactic acid was more intense in the normal group. In the case of amide III (1246, 1258, and 1268 cm−1 ), amino acids such as tyrosine, phenylalanine, and tryptophan (1212 and 1328 cm−1 ), deoxyribose vibration of DNA (1462 cm−1 ), DNA backbone (927 cm−1 ), DNA purine bases (1180, 1320, and 1421 cm−1 ), guanine and tryptophan (1365 cm−1 ), and υ(C–C) skeletal trans conformation of lipid (1126 cm−1 ) the peaks were higher in perpendicular orientation for cancers. For the cancer group, the peaks for C-O stretching vibrations (1057 cm−1 ), hydroxyproline (875 and 949 cm−1 ), and lipids (1300 and 1740 cm−1 ) at parallel orientation were higher. The depolarization ratios were higher in cancer cells due to a change in lactic acid orientation in these cells. A 100% testing data accuracy and in receiver operating characteristic curve (ROC) diagnostic performance of area under curve (AUC) with an area of 1.0 was obtained for polarized Raman spectroscopy. PRS could identify the altered biomolecules during the development of disease and variations in biomolecules of biofluids from premalignant patients, thus serving as a tool for cancer screening and diagnosis. Non-melanoma skin cancer (NMSC) is one of the most frequently occurring types of skin cancer and among its 2 types (BCC and SCC), BCC accounts for 80% of the NMSCs. Histopathological diagnosis is still considered the gold standard for diagnosing NMSCs. BCC rarely undergoes metastasis and therefore relevant markers that facilitate its early diagnosis have not yet been found (Piot et al., 2008). A study (Piot et al., 2008) was conducted to check the polarized Raman spectroscopy’s ability to identify the peritumoral stroma disorganization that is induced in BCC. Hematoxylin–Phloxine–Saffron (HPS) stained sections of frozen superficial BCC lesions containing both normal and peritumoral dermis regions were run in the conventional and polarization Raman spectrometer and

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the resulting spectra were compared. That is, for each position in the section, one conventional and two polarized Raman spectra (parallel and perpendicular polarization) were recorded. The signal obtained with perpendicular orientation was weak and noisy and hence they focused on the spectrum obtained through a parallel orientation which was much stronger. The spectrum of the dermis showed different behaviors with polarization. Intense bands were obtained for the peritumoral dermis in comparison with normal dermis at 730 cm−1 and 785 cm−1 (corresponding to DNA vibrations) and 1210 cm−1 (corresponding to collagen). Furthermore, between the normal and peritumoral tissues, variation in the area of each band was observed. Hence, the band area could be used as a marker to distinguish tumor-bordering dermis from normal dermis. The conventional Raman spectra in the case of collagen only identified the collagen triple helix degradation into α-chains. However, the polarized Raman spectra could even predict the presence of a translational state in collage degradation. Polarized Raman spectroscopy also enhanced these spectral differences when compared to the conventional Raman spectrometer. Hence, this study proved that polarization-sensitive Raman spectroscopy was more efficient in differentiating the normal from the peritumoral dermis compared to the conventional methods, along with preventing the need of using time-consuming and destructive sample preparation.

3.3 Microscopy Techniques 3.3.1

Fluorescence Microscopy

The fluorescence of a molecule depends on its orientation in the sample and on the polarization of incident light, and this forms the basis of polarization-resolved fluorescence microscopy (Brasselet, 2019). Fluorescence takes place in two steps: absorption and emission. By using polarized light for excitation and subjecting the emission beams to different polarization states, respectively, images can be obtained based on these two characteristics. This is also a fast technique for obtaining highresolution images since all the pixels of the image are obtained simultaneously (Hayashi et al., 2017). This technique is used in various areas of biomedical sciences mainly for detecting the physiological states of tissues and monitoring cellular metabolism to detect diseased tissues. Breast cancer is responsible for most of cancer-related deaths in women worldwide (Sung et al., 2021). With the aid of medical advancements, instead of direct mastectomy, BCS (breast conservation surgery) is done, followed by radiation treatment or chemotherapy. Thus, it is very important to accurately determine the borders between cancer cells and healthy cells for successful treatment. The fluorescence polarization of tetracycline (TCN) and its derivative demeclocycline (DMN) was used in a study for the imaging of nonmelanoma skin cancers (Yaroslavsky et al., 2007). The freshly excised tissue sections were stained with TCN or DMN, and the images were acquired and compared with the histopathological sections obtained by H&E staining. Figure

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Fig. 12.6 Polarization-resolved fluorescence microscopy. (i) Nodular BCC stained with TCN. (a) Fluorescence emission image (b) Fluorescence polarization image (c) Histopathological section. Tumor margins are outlined with a red line (Yaroslavsky et al., 2007). (ii) Infiltrative BCC stained with DMN. (a) Fluorescence polarization image (b) Histological section with outlined tumor margins (Yaroslavsky et al., 2007). (iii) Invasive SCC stained with DMN. (a) fluorescence polarization image (b) Histopathological section with outlined tumor margins (Yaroslavsky et al., 2007)

12.6i represents the images of nodular BCC tissue sections stained with TCN. Due to the low contrast between the healthy and tumor cells, the fluorescence emission image (a) does not yield desirable results, whereas the fluorescence polarization image, (b) accurately demarcates the tumor from the healthy tissues. Other structures such as sebaceous glands, hair follicles, etc. are also visualized, which are not visualized in the histopathological section (c). Similar results were obtained with infiltrative BCCs (Fig. 12.6ii) and invasive SCCs (Fig. 12.6iii). The success rate of fluorescence emission imaging with DMN is 20%, while the success of fluorescence polarization imaging with DMN is 90%. The success rate of fluorescence emission with TCN is 13%, while the success of fluorescence polarization imaging with TCN is 88%. Similar results were obtained when different concentrations of antibiotics were used. Fluorescence polarization widefield imaging was used in another study (Patel et al., 2014) to determine the lateral extent of breast cancer margins, using methylene blue for contrast enhancement. While the histopathological sections provided satisfactory images, fluorescence polarization imaging enabled the accurate distinguishing of margins due to the difference in contrast. In the case of invasive lobular carcinomas, fluorescence polarization imaging accurately displayed the location and size of the tumor, whereas the histopathological sections yielded unreliable results. A study combined a division-of-plane polarimeter with a polarization-resolved fluorescence microscope to determine the tumor margins of mouse mammary carcinoma 4T1 (Liu et al., 2012). Nanowire polarization filters oriented at different angles were used to construct the filter arrays that analyze the state of polarization of the

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sample. The samples were subjected to various imaging techniques to find out the DoLP and fluorescence characteristics. It was found that the healthy muscle tissues show higher DoLP than the tumors. For fluorescence imaging, LS301 was used as the probe and it was observed that the tumor tissues exhibit higher fluorescence than the healthy tissue. By combining the DoLP and fluorescence contrast images, the invading cancer tissues could be easily and accurately differentiated from the healthy tissue. The samples were also analyzed for the severity of cancer invasion. The DoLP and fluorescence polarization results are consistent with the previous observation. As expected, combining the DoLP and fluorescence contrast images proved useful for assessing tumor density. This has clinical relevance in finding regions with the highest and least tumor density. In conclusion, fluorescence polarization imaging is a reliable method for wide-field, real-time imaging. There is scope for further improvements by calibrating the fluorescence and polarization signals to generate a standard chart for measuring cancer invasion, which can make the diagnosis process faster.

3.3.2

Confocal Microscopy

Confocal microscopy was developed based on the principle of optical sectioning. Pinholes are used to block out-of-focus light; hence, it is a reliable method to obtain high-resolution images of samples (Elliott, 2020). It overcomes the disadvantages of fluorescence microscopy, namely lack of optical sectioning, lower resolution, and lower contrast (Hayashi et al., 2017). A study (Patel et al., 2012) used confocal microscopy for the imaging of two variants of breast cancer, invasive ductal carcinomas and invasive lobular carcinomas. The samples for confocal microscopy were stained with methylene blue, and the samples for histopathology were frozen and stained in the standard way, using H&E. In invasive ductal carcinoma, the tumors initially grow as ducts in the breast and eventually infiltrate the surrounding healthy adipose tissue. While confocal microscopy did not give sharp outlines of the tumor, the images obtained had higher resolution when compared to widefield fluorescence microscopy. The resolution is such that there is cell-to-cell consistency between the confocal images and the sections obtained by H&E staining. Figure 12.7i represents the affected area, three parts of which were subjected to confocal microscopy and histopathological staining. While the histological section of (b) is very consistent with the confocal images, in (c) and (d), the borders are not very clear. Invasive lobular carcinoma is characterized by the diffused spreading of the cancer cells, instead of forming a distinct tumor. The cancer cells are also surrounded by fibrous tissues, making this type of cancer more difficult to visualize and treat. As seen in Fig. 12.7ii, the borders can be distinguished easily with both confocal microscopy and histopathology. Comparing the results in both types of cancers shows that confocal microscopy is more reliable than histopathology alone. Skin cancers can be of two types: melanomas or nonmelanomas. The latter includes basal cell carcinomas (BCC) and squamous cell carcinomas (SCC). In a

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Fig. 12.7 Polarization-resolved confocal microscopy (i) Invasive ductal carcinoma. (b–d) Polarization-resolved confocal images from the squares outlined in (a). (e–g) Respective histopathological sections for the images (b–d) (Patel et al., 2012). (ii) Invasive lobular carcinoma. (b–d) Polarization-resolved confocal images from square areas outlined in (a). (e–g) Respective histopathological sections for images shown in (b–d) (Patel et al., 2012). (iii) Melanoma B16F10 (a) Digital photograph (b) in-vivo polarization-resolved confocal reflectance image, no contrast agent (c) histopathology (Park et al., 2010). (iv) in vivo polarization-resolved confocal images of melanoma B16F10, with contrast agent MB (a) reflectance (b) fluorescence (c) corresponding histopathology (Park et al., 2010). (v) Polarization-resolved images of nodular BCC (a) Confocal image (b) Superficial macro image obtained by MPLI (c) histopathological section, tumor marked with a red line (Yaroslavsky et al., 2005). (vi) Polarization-resolved images of infiltrative BCC. (a) confocal image at 830 nm (b) confocal image at 630 nm (c) superficial macroimage by MPLI. (d) Histopathological sections. Tumor margins are outlined with a red line (Yaroslavsky et al., 2005)

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study (Park et al., 2010), B16F10 melanoma cell lines were introduced in mice and reflectance confocal images of the resulting tumors were obtained. Figure 12.7iii shows that cancer cells exhibit higher contrast and thus appear darker in confocal reflectance images. The high contrast exhibited by the cancer cells is due to the large difference in the refractive indices of healthy cells and cancer cells, owing to the presence of melanin in the cancer cells. The addition of methylene blue increased the contrast and thus provided clearer images. The images obtained by reflectance confocal microscopy and dye-enhanced confocal microscopy were consistent with the histopathological sections. Moreover, the addition of methylene blue also revealed the presence and extent of autophagy in these mouse melanoma cells. Methylene blue binds to positively charged organelles such as mitochondria, which are degraded in autophagic cells; thus, these cells will not be stained by the dye. This is shown in Fig. 12.7iv; the cells in the tumor region marked with the arrow are undergoing autophagy. The absence of organelles in the autophagic cells is noticeable. In another study (Al-Arashi et al., 2007), BCCs were imaged with methylene blue (MB) staining and confocal microscopy. High contrast between the fluorescence level of the tumor and surrounding cells was observed since the surrounding tissues such as collagen do not take up the dye. The borders of the tumors show higher fluorescence than the mass, which is a clinical advantage. The presence of structures such as trabeculae and septa are responsible for the 3D structure of the tumor, and they were represented accurately in the confocal images. Infiltrative BCC is an aggressive carcinoma with small strands and nests of tumor cells that eventually infiltrate the epidermis, subcutaneous fat, and muscles. Polarizationresolved confocal microscopy accurately visualized the tumor strands and other structures present in the healthy tissues. When SCC samples were imaged, the characteristic reticulated pattern was visible. However, SCC cells do not take up MB as easily as BCC cells, leading to a lower difference in contrast between normal cells and cancer cells. As in BCC, the 3D structure of the tumor was visualized by confocal microscopy, whereas it was unnoticed in H&E sections. Confocal images normally have a smaller field of view. To overcome this, a study (Yaroslavsky et al., 2005) combined multispectral polarized light imaging (MSPLI) with confocal microscopy, to increase the field of view. This combined setup was used for visualizing nodal BCC, the results are shown in Fig. 12.7v. Confocal microscopy allowed the visualization of the structure and arrangement of individual tumor lobules, while MSLPI allowed the visualization of a larger area of tissue. Similar desirable results were obtained with infiltrative BCC (Fig. 12.7vi).

3.3.3

Two-Photon Fluorescence Microscopy

In two-photon fluorescence microscopy (2p microscopy), two photons in the NIR range are used to excite the fluorophore, with a small volume of excitation for a short period. By having a smaller focal point, the pinhole effect as in confocal microscopy is achieved and out-of-focus light is blocked. The limitations of

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Fig. 12.8 Steady-state 2p-autofluorescence anisotropy imaging of NADH indicates a heterogeneous environment. (i) parallel, (ii) perpendicular-polarized images of a cancer cell, recorded simultaneously. (iii) estimated average steady-state anisotropy for a particular cancer cell, with the anisotropy color code (Yu & Heikal, 2009)

confocal microscopy such as phototoxicity, scattering, and the like are overcome with this method (Allocca et al., 2016). Polarization-resolved 2p microscopy is suitable for intact or semi-intact tissues (Kobat et al., 2011), making it a useful technique in biomedical sciences. In a study (Yu & Heikal, 2009), the intrinsic levels of NADH in the cells were used as a probe to determine the activities of cancer cells by polarization-resolved two-photon fluorescence anisotropy imaging. NADH is an autofluorescent molecule that gets oxidized in cellular reactions to form NAD, which is not fluorescent. The levels of intrinsic NADH in breast cancer cells (Hs578T) and normal cells (Hs578Bst) from an invasive ductal carcinoma sample were measured in this study. To quantify the population fractions of free and enzyme-bound NADH in the normal and cancerous breast tissues, complementary steady-state 2p-autofluorescence anisotropy imaging was carried out. In this way, the 2P polarization images at parallel and perpendicular components were simultaneously recorded (Fig. 12.8i, ii). A MATLAB-based algorithm was then applied, which revealed the heterogeneous nature of NADH in the cells, the color code showing the anisotropy ranges. The average anisotropy for normal cells is 0.32 ± 0.05 (n = 6) and for cancer cells is 0.30 ± 0.03 (n = 6). Drug–target interactions are an integral part of pharmacology. Conventionally, drug–target interactions are studied by DARTS (drug affinity responsive target stability), PET (positron emission tomography), mass spectroscopy, drug radiolabelling, CETSA (cellular thermal shift assay), etc. Cellular imaging is a better technique because it provides images with high spatial and temporal resolution

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and also quantitatively differentiates between bound and unbound states of the drug. Confocal microscopy has been commonly used, but 2-photon fluorescence microscopy is gaining preference because of its higher penetration depth, higher accuracy (by reducing tissue scattering at near-IR), and lower phototoxicity. A study (Vinegoni et al., 2016) reported the use of 2-photon fluorescence microscopy combined with anisotropy imaging to measure the in vivo interactions between the drug and the target. The PARP-inhibitory drug Olaparib which was fluorescently labeled with BODIPY FL dye (AZD2281-BODIPY FL) and the fibrosarcoma cell line HT1080 were used. Images were collected during drug loading at 173 and 375 s, and higher fluorescence intensity in the cytosol implies that the drugs enter the cell easily through the plasma membrane by drug–organelle lipid interactions. Images were also collected after washing at 691 and 1382 s, respectively. Low fluorescence intensity in the cytosol was noted, which means that the drug cleared from the cytosol and has accumulated in the nucleus, where PARP1 is present. PARP1 is a large molecule, so when the labeled drug binds to it, it undergoes a significant change in anisotropy. Thus, the exact fraction of the introduced drug that binds to the specific target can be quantified, and the efficacy of the drug can be determined. Another study (Fang et al., 2019) employed both polarizationresolved two-photon microscopy and second-harmonic generation microscopy to study angiogenesis associated with tumor growth. Twenty human gliomas and six normal tissues were used, and endogenous fluorophores of the blood vessels such as elastin, NADPH, etc. were considered, making the process label-free. In the healthy samples, blood vessels could be identified by their tube-like appearance. The absence of endogenous fluorophores in the nuclei and the fluorescence signals generated by the cytoplasmic granules and extracellular matrix were useful to identify the individual cells. Tumor blood vessels are malformed, with large diameters and thickened walls. They also proliferate in large numbers and form clusters, which causes irregular blood flow and vascular leakage linked to the failure of systemic chemotherapy. These morphological characters are not observed in the H&E sections. This study is of clinical relevance as it sheds light on an emerging cancer therapy called anti-vascular therapy, where the focus of treatment can be shifted from the cells to the blood vessels.

3.3.4

Second-Harmonic Generation Microscopy

Label-free imaging has recently gained a lot of importance due to its ability to provide crucial structural information without the need of using any expensive and time-consuming labeling procedures. SHG microscopy, being a label-free, non-invasive imaging technique, is therefore under a lot of consideration to assist pathologists to perform fast and reliable tumor diagnosis. A 2D phasor-based approach was applied to polarization-dependent second-harmonic imaging in a study (Sironi et al., 2019) to design μMAPPS (microscopic multiparametric analysis by phasor projection of polarization-dependent SHG signal). It was intended for the detection of microstructural changes in tissues that can lead to early

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Fig. 12.9 (i) μMAPPS analysis of an entire section of the tumor. (a) Maximum intensity projection of the mosaic reconstruction of the entire section of the tumor. Dashed red line-tumorskin boundary. (b, c) The global θ- and γ- maps (Sironi et al., 2019). (ii) Images of H&E stained sections of (a) non-cancerous and (g, m) cancerous thyroid tissue using bright field microscopy. (b, h, n) Images of the region of interest (indicated by the black box in a, g, m panels) imaged by PIPO SHG microscopy. (c, i, o) Calculated ratio values for each pixel displayed as color-coded maps (blue-ratio of 1 and red-ratio of 4. (e, k, q) DOLP values for each pixel displayed as color-coded maps (blue- DOLP of 0 and red- DOLP of 1 (Wilson et al., 2015). (iii) 3D SHG renderings of (a) 0% Col V, (b) 5% Col V, and (c) 20% Col V collagen gels (Campagnola et al., 2011). (iv) (a) F/B ratio for an independent polymerization run of Col V collagen gels (0%, 5%, and 20%) (b) Individual optical sections of the collagen gels (Campagnola et al. 2011)

tumor diagnosis and can also help in verifying the results of tumor treatment. BALB/c female mice were injected with CT26 or 4T1 tumor cell lines and sections were prepared from the resulting tumor. The sections consisted of tumor regions surrounded by skin which were analyzed in two levels. In the first level (Fig. 12.9i(a)), the tumor and the surrounding skin were analyzed separately, while in the second level (Fig. 12.9i(b, c)), different regions of interest (ROIs) within the tumor and skin were analyzed. Both first and the second analysis were capable of identifying the difference in the behavior of the tumor and skin collagen, but the second analysis was found to be more effective. Thyroid cancer is another common cancer of the endocrine organs with a high incidence rate. Two usual forms of this cancer include papillary thyroid carcinoma and follicular thyroid carcinoma, which represent 85–90% and