Polarized Light and Optical Systems [1 ed.] 149870056X, 9781498700566

Table of contents :
Cover
Half Title
Title Page
Copyright Page
Table of Contents
Authors
Acknowledgments
Preface
How This Book Came to Be
Suggested Curricula
Guided Tour of the Chapters
Learning Features
Color Figures
Poincaré Sphere
Viewgraphs
Worked Examples
Problem Sets and Solution Manual
Three-Dimensional Polarization Ray Tracing Calculus
Reference Tables
List of Abbreviations
Chapter 1: Introduction and Overview
1.1 Polarized Light
1.2 Polarization States and the Poincaré Sphere
1.3 Polarization Elements and Polarization Properties
1.4 Polarimetry and Ellipsometry
1.5 Anisotropic Materials
1.6 Typical Polarization Problems in Optical Systems
1.6.1 Angle Dependence of Polarizers
1.6.2 Wavelength and Angle Dependence of Retarders
1.6.3 Stress Birefringence in Lenses
1.6.4 Liquid Crystal Displays and Projectors
1.7 Optical Design
1.7.1 Polarization Ray Tracing
1.7.2 Polarization Aberrations of Lenses
1.7.3 High Numerical Aperture Wavefronts
1.8 Comment on Historical Treatments
1.9 Reference Books on Polarized Light
1.10 Problem Sets
References
Chapter 2: Polarized Light
2.1 The Description of Polarized Light
2.2 The Polarization Vector
2.3 Properties of the Polarization Vector
2.4 Propagation in Isotropic Media
2.5 Magnetic Field, Flux, and Polarized Flux
2.6 Jones Vectors
2.7 Evolution of Overall Phase
2.8 Rotation of Jones Vectors
2.9 Linearly Polarized Light
2.10 Circularly Polarized Light
2.11 Elliptically Polarized Light
2.12 Orthogonal Jones Vectors
2.13 Change of Basis
2.14 Addition of Jones Vectors
2.15 Polarized Flux Components
2.16 Converting Polarization Vectors into Jones Vectors
2.17 Decreasing Phase Sign Convention
2.18 Increasing Phase Sign Convention
2.19 Polarization State of Sources
2.20 Problem Sets
References
Chapter 3: Stokes Parameters and the Poincaré Sphere
3.1 The Description of Polychromatic Light
3.2 Phenomenological Definition of the Stokes Parameters
3.3 Unpolarized Light
3.4 Partially Polarized Light and the Degree of Polarization
3.5 Spectral Bandwidth
3.6 Rotation of the Polarization Ellipse
3.7 Linearly Polarized Stokes Parameters
3.8 Elliptical Polarization Parameters
3.9 Orthogonal Polarization States
3.10 Stokes Parameter and Jones Vector Sign Conventions
3.11 Polarized Fluxes and Conversions between Stokes Parameters and Jones Vectors
3.12 The Stokes Parameters’ Non-Orthogonal Coordinate System
3.13 The Poincaré Sphere
3.14 Flat Mappings of the Poincaré Sphere
3.15 Summary and Conclusion
3.16 Problem Sets
References
Chapter 4: Interference of Polarized Light
4.1 Introduction
4.2 Combining Light Waves
4.3 Interferometers
4.4 Interference of Nearly Parallel Monochromatic Plane Waves
4.5 Interference of Plane Waves at Large Angles
4.6 Polarization Considerations in Holography
4.7 The Addition of Polarized Beams
4.7.1 Addition of Polarized Light of Two Different Frequencies
4.7.2 Addition of Polychromatic Beams
4.7.3 A Gaussian Wave Packet Example
4.8 Conclusion
4.9 Problem Sets
References
Chapter 5: Jones Matrices and Polarization Properties
5.1 Introduction
5.2 Dichroic and Birefringent Materials
5.3 Diattenuation and Retardance
5.3.1 Diattenuation
5.3.2 Retardance
5.4 Jones Matrices
5.4.1 Eigenpolarizations
5.4.2 Jones Matrix Notation
5.4.3 Rotation of Jones Matrices
5.5 Polarizer and Diattenuator Jones Matrices
5.5.1 Polarizer Jones Matrices
5.5.2 Linear Diattenuator Jones Matrices
5.6 Retarder Jones Matrices
5.6.1 Linear Retarder Jones Matrices
5.6.2 Circular Retarder Jones Matrices
5.6.3 Vortex Retarders
5.7 General Diattenuators and Retarders
5.7.1 Linear Diattenuators
5.7.2 Elliptical Diattenuators
5.7.3 Elliptical Retarders
5.8 Non-Polarizing Jones Matrices for Amplitude and Phase Change
5.9 Matrix Properties of Jones Matrices
5.9.1 Hermitian Matrices: Diattenuation
5.9.2 Unitary Matrices and Unitary Transformations: Retarder
5.9.3 Polar Decomposition: Separating Retardance from Diattenuation
5.10 Increasing Phase Sign Convention
5.11 Conclusion
5.12 Problem Sets
References
Chapter 6: Mueller Matrices
6.1 Introduction
6.2 The Mueller Matrix
6.3 Sequences of Polarization Elements
6.4 Non-Polarizing Mueller Matrices
6.5 Rotating Polarization Elements about the Light Direction
6.6 Retarder Mueller Matrices
6.7 Polarizer and Diattenuator Mueller Matrices
6.7.1 Basic Polarizers
6.7.2 Transmittance and Diattenuation
6.7.3 Polarizance
6.7.4 Diattenuators
6.8 Poincaré Sphere Operations
6.8.1 The Operation of Retarders on the Poincaré Sphere
6.8.2 The Operation of a Rotating Linear Retarder
6.8.3 The Operation of Polarizers and Diattenuators
6.8.4 Indicating Polarization Properties
6.9 Weak Polarization Elements
6.10 Non-Depolarizing Mueller Matrices
6.11 Depolarization
6.11.1 The Depolarization Index and the Average Degree of Polarization
6.11.2 Degree of Polarization Surfaces and Maps
6.11.3 Testing for Physically Realizable Mueller Matrices
6.11.4 Weak Depolarizing Elements
6.11.5 The Addition of Mueller Matrices
6.12 Relating Jones and Mueller Matrices
6.12.1 Transforming Jones Matrices into Mueller Matrices Using Tensor Product
6.12.2 Conversion of Jones Matrices to Mueller Matrices Using Pauli Matrices
6.12.3 Transforming Mueller Matrices into Jones Matrices
6.13 Ray Tracing with Mueller Matrices
6.13.1 Mueller Matrices for Refraction
6.13.2 Mueller Matrices for Reflection
6.14 The Origins of the Mueller Matrix
6.15 Problem Sets
References
Chapter 7: Polarimetry
7.1 Introduction
7.2 What Does the Polarimeter See?
7.3 Polarimeters
7.3.1 Light-Measuring Polarimeters
7.3.2 Sample-Measuring Polarimeters
7.3.3 Complete and Incomplete Polarimeters
7.3.4 Polarization Generators and Analyzers
7.4 Mathematics of Polarimetric Measurement and Data Reduction
7.4.1 Stokes Polarimetry
7.4.2 Measuring Mueller Matrix Elements
7.4.3 Mueller Data Reduction Matrix
7.4.4 Null Space and the Pseudoinverse
7.5 Classes of Polarimeters
7.5.1 Time-Sequential Polarimeters
7.5.2 Modulated Polarimeters
7.5.3 Division of Amplitude
7.5.4 Division of Aperture
7.5.5 Imaging Polarimeters
7.6 Stokes Polarimeter Configurations
7.6.1 Simultaneous Polarimetric Measurement
7.6.1.1 Division-of-Aperture Polarimetry
7.6.1.2 Division-of-Focal-Plane Polarimetry
7.6.1.3 Division-of-Amplitude Polarimetry
7.6.2 Rotating Element Polarimetry
7.6.2.1 Rotating Analyzer Polarimeters
7.6.2.2 Rotating Analyzer Plus Fixed Analyzer Polarimeter
7.6.2.3 Rotating Retarder and Fixed Analyzer Polarimeters
7.6.3 Variable Retarder and Fixed Polarizer Polarimeter
7.6.4 Photoelastic Modulator Polarimeters
7.6.5 The MSPI and MAIA Imaging Polarimeters
7.6.6 Example Atmospheric Polarization Images
7.7 Sample-Measuring Polarimeters
7.7.1 Polariscopes
7.7.1.1 Linear Polariscope
7.7.1.2 Circular Polariscope
7.7.1.3 Interference Colors
7.7.1.4 Polariscope with Tint Plate
7.7.1.5 Conoscope
7.7.2 Mueller Polarimetry Configurations
7.7.2.1 Dual Rotating Retarder Polarimeter
7.7.2.2 Polarimetry Near Retroreflection
7.8 Interpreting Mueller Matrix Images
7.9 Calibrating Polarimeters
7.10 Artifacts in Polarimetric Images
7.10.1 Pixel Misalignment
7.11 Optimizing Polarimeters
7.12 Problem Sets
Acknowledgments
References
Chapter 8: Fresnel Equations
8.1 Introduction
8.2 Propagation of Light
8.2.1 Plane Waves and Rays
8.2.2 Plane of Incidence
8.2.3 Homogeneous and Isotropic Interfaces
8.2.4 Light Propagation in Media
8.3 Fresnel Equations
8.3.1 s- and p-Polarization Components
8.3.2 Amplitude Coefficients
8.3.3 The Fresnel Equations
8.3.4 Intensity Coefficients
8.3.5 Normal Incidence
8.3.6 Brewster’s Angle
8.3.7 Critical Angle
8.3.8 Intensity and Phase Change with Incident Angle
8.3.9 Jones Matrices with Fresnel Coefficients
8.4 Fresnel Refraction and Reflection
8.4.1 Dielectric Refraction
8.4.2 External Reflection
8.4.3 Internal Reflection
8.4.4 Metal Reflection
8.4.4.1 Normal Incidence Reflectance
8.4.4.2 Retardance and Diattenuation of Metal at Non-Normal Incidence
8.5 Approximate Representations of Fresnel Coefficients
8.5.1 Taylor Series for the Fresnel Coefficients
8.6 Conclusion
8.7 Problem Sets
References
Chapter 9: Polarization Ray Tracing Calculus
9.1 Definition of Polarization Ray Tracing Matrix, P
9.2 Formalism of Polarization Ray Tracing Matrix Using Orthogonal Transformation
9.3 Retarder Polarization Ray Tracing Matrix Examples
9.4 Diattenuation Calculation Using Singular Value Decomposition
9.5 Example—Interferometer with a Polarizing Beam Splitter
9.5.1 Ray Tracing the Reference Path
9.5.2 Ray Tracing through the Test Path
9.5.3 Ray Tracing through the Analyzer
9.5.4 Cumulative P Matrix for Both Paths
9.6 The Addition Form of Polarization Ray Tracing Matrices
9.6.1 Combining P Matrices for the Interferometer Example
9.7 Example—A Hollow Corner Cube
9.8 Conclusion
9.9 Problem Sets
References
Chapter 10: Optical Ray Tracing
10.1 Introduction
10.2 Goals for Ray Tracing
10.3 Specification of Optical Systems
10.3.1 Surface Equations
10.3.2 Apertures
10.3.3 Optical Interfaces
10.3.4 Dummy Surfaces
10.4 Specifications of Light Beams
10.5 System Descriptions
10.5.1 Object Plane
10.5.2 Aperture Stop
10.5.3 Entrance and Exit Pupils
10.5.4 Importance of the Exit Pupil
10.5.5 Marginal and Chief Rays
10.5.6 Numerical Aperture and Lagrange Invariant
10.5.7 Etendué Ξ
10.5.8 Polarized Light
10.6 Ray Tracing
10.6.1 Ray Intercept
10.6.2 Multiplicity of Ray Intercepts with a Surface
10.6.3 Optical Path Length
10.6.4 Reflection and Refraction
10.6.5 Polarization Ray Tracing
10.6.6 s- and p-Components
10.6.7 Amplitude Coefficients and Interface Jones Matrix
10.6.8 Polarization Ray Tracing Matrix
10.7 Wavefront Analysis
10.7.1 Normalized Coordinates
10.7.2 Wavefront Aberration Function
10.7.3 Polarization Aberration Function
10.7.4 Evaluation of the Aberration Function
10.7.5 Seidel Wavefront Aberration Expansion
10.7.6 Zernike Polynomials
10.7.7 Wavefront Quality
10.7.8 Polarization Quality
10.8 Non-Sequential Ray Trace
10.9 Coherent and Incoherent Ray Tracing
10.9.1 Polarization Ray Tracing with Mueller Matrices
10.10 The Use of Polarization Ray Tracing
10.11 Brief History of Polarization Ray Tracing
10.12 Summary and Conclusion
10.13 Problem Sets
10.14 Appendix: Cell Phone Lens Prescription
References
Chapter 11: The Jones Pupil and Local Coordinate Systems
11.1 Introduction: Local Coordinates for Entrance and Exit Pupils
11.2 Local Coordinates
11.3 Dipole Coordinates
11.4 Double Pole Coordinates
11.5 High Numerical Aperture Wavefronts
11.6 Converting P Pupils to Jones Pupils
11.7 Example: Cell Phone Lens Aberrations
11.8 Wavefront Aberration Function Difference between Dipole and Double Pole Coordinates
11.9 Conclusion
11.10 Problem Sets
References
Chapter 12: Fresnel Aberrations
12.1 Introduction
12.2 Uncoated Single-Element Lens
12.3 Fold Mirror
12.4 Combination of Fold Mirror Systems
12.5 Cassegrain Telescope
12.6 Fresnel Rhomb
12.7 Conclusion
12.8 Problem Sets
References
Chapter 13: Thin Films
13.1 Introduction
13.2 Single-Layer Thin Films
13.2.1 Antireflection Coatings
13.2.2 Ideal Single-Layer Antireflection Coating
13.2.3 Metal Beam Splitters
13.3 Multilayer Thin Films
13.3.1 Algorithms
13.3.2 Quarter and Half Wave Films
13.3.3 Reflection-Enhancing Coatings
13.3.4 Polarizing Beam Splitters
13.4 Contributions to Wavefront Aberrations
13.5 Phase Discontinuities
13.6 Conclusion
13.7 Appendix: Derivation of Single-Layer Equations
13.8 Problem Sets
References
Chapter 14: Jones Matrix Data Reduction with Pauli Matrices
14.1 Introduction
14.2 Pauli Matrices and Jones Matrices
14.2.1 Pauli Matrix Identities
14.2.2 Expansion in a Sum of Pauli Matrices
14.2.3 Pauli Sign Convention
14.2.4 Pauli Coefficients of a Polarization Element Rotated about the Optical Axis
14.2.5 Eigenvalues and Eigenvectors and Matrix Functions for the Pauli Sum Form
14.2.6 Canonical Summation Form
14.3 Sequences of Polarization Elements
14.4 Exponentiation and Logarithms of Matrices
14.4.1 Exponentiation of Matrices
14.4.2 Logarithms of Matrices
14.4.3 Retarder Matrices
14.4.4 Diattenuator Matrices
14.4.5 Polarization Properties of Homogeneous Jones Matrices
14.5 Elliptical Retarders and the Retarder Space
14.6 Polarization Properties of Inhomogeneous Jones Matrices
14.7 Diattenuation Space and Inhomogeneous Polarization Elements
14.7.1 Superposing the Diattenuation and Retardance Spaces
14.8 Weak Polarization Elements
14.9 Summary and Conclusion
14.10 Problem Sets
References
Chapter 15: Paraxial Polarization Aberrations
15.1 Introduction
15.2 Polarization Aberrations
15.2.1 Interaction of Weakly Polarizing Jones Matrices
15.2.2 Polarization of a Sequence of Weakly Polarizing Ray Intercepts
15.3 Paraxial Polarization Aberrations
15.3.1 Paraxial Angle and Plane of Incidence
15.3.2 Paraxial Diattenuation and Retardance
15.3.3 Diattenuation Defocus
15.3.4 Diattenuation Defocus and Retardance Defocus
15.3.5 Diattenuation and Retardance across the Field of View
15.3.6 Polarization Tilt and Piston
15.3.7 Binodal Polarization
15.3.8 Summation of Paraxial Polarization Aberrations over Surfaces
15.4 Paraxial Polarization Analysis of a Seven-Element Lens System
15.5 Higher-Order Polarization Aberrations
15.5.1 Electric Field Aberrations
15.5.2 Orientors
15.5.3 Diattenuation and Retardance
15.6 Polarization Aberration Measurements
15.7 Summary and Conclusion
15.8 Appendix
15.8.1 Paraxial Optics
15.8.2 Setting Up the Optical System
15.8.3 The Paraxial Ray Trace
15.8.4 Reduced Thicknesses and Angles
15.8.5 Paraxial Skew Rays
15.9 Problem Sets
References
Chapter 16: Image Formation with Polarization Aberration
16.1 Introduction
16.2 Discrete Fourier Transformation
16.3 Jones Exit Pupil and Jones Pupil Function
16.4 Amplitude Response Matrix (ARM)
16.5 Mueller Point Spread Matrix (MPSM)
16.6 The Scale of the ARM and MPSM
16.7 Polarization Structure of Images
16.8 Optical Transfer Matrix (OTM)
16.9 Example—Polarized Pupil with Unpolarized Object
16.10 Example—Solid Corner Cube Retroreflector
16.11 Example—Critical Angle Corner Cube Retroreflector
16.12 Discussion and Conclusion
16.13 Problem Sets
References
Chapter 17: Parallel Transport and the Calculation of Retardance
17.1 Introduction
17.1.1 Purpose of the Proper Retardance Calculation
17.2 Geometrical Transformations
17.2.1 Rotation of Local Coordinates: Polarimeter Viewpoint
17.2.2 Non-Polarizing Optical Systems
17.2.3 Parallel Transport of Vectors
17.2.4 Parallel Transport of Vectors with Reflection
17.2.5 Parallel Transport Matrix, Q
17.3 Canonical Local Coordinates
17.4 Proper Retardance Calculations
17.4.1 Definition of the Proper Retardance
17.5 Separating Geometric Transformations from P
17.5.1 The Proper Retardance Algorithm for P, Method 1
17.5.2 The Proper Retardance Algorithm for P, Method 2
17.5.3 Retardance Range
17.6 Examples
17.6.1 Ideal Reflection at Normal Incidence
17.6.2 An Aluminum-Coated Three-Fold Mirror System Example
17.7 Conclusion
17.8 Problem Sets
References
Chapter 18: A Skew Aberration
18.1 Introduction
18.2 Definition of Skew Aberration
18.3 Skew Aberration Algorithm
18.4 Lens Example—U.S. Patent 2,896,506
18.5 Skew Aberration in Paraxial Ray Trace
18.6 Example of Paraxial Skew Aberration
18.7 Skew Aberration’s Effect on PSF
18.8 PSM for U.S. Patent 2,896,506
18.9 Statistics—CODE V Patent Library
18.10 Conclusion
18.11 Problem Sets
References
Chapter 19: Birefringent Ray Trace
19.1 Ray Tracing in Birefringent Materials
19.2 Description of Electromagnetic Waves in Anisotropic Media
19.3 Defining Birefringent Materials
19.4 Eigenmodes of Birefringent Materials
19.5 Reflections and Refractions at Birefringent Interface
19.6 Data Structure for Ray Doubling
19.7 Polarization Ray Tracing Matrices for Birefringent Interfaces
19.7.1 Case I: Isotropic-to-Isotropic Intercept
19.7.2 Case II: Isotropic-to-Birefringent Interface
19.7.3 Case III: Birefringent-to-Isotropic Interface
19.7.4 Case IV: Birefringent-to-Birefringent Interface
19.8 Example: Ray Splitting through Three Biaxial Crystal Blocks
19.9 Example: Reflections Inside a Biaxial Cube
19.10 Conclusion
19.11 Problem Sets
References
Chapter 20: Beam Combination with Polarization Ray Tracing Matrices
20.1 Introduction
20.2 Wavefronts and Ray Grids
20.3 Co-Propagating Wavefront Combination
20.4 Non-Co-Propagating Wavefront Combination
20.5 Combining Irregular Ray Grids
20.5.1 General Steps to Combine Misaligned Ray Data
20.5.2 Inverse-Distance Weighted Interpolation
20.6 Conclusion
20.7 Problem Sets
References
Chapter 21: Uniaxial Materials and Components
21.1 Optical Design Issues in Uniaxial Materials
21.2 Descriptions of Uniaxial Materials
21.3 Eigenmodes of Uniaxial Materials
21.4 Reflections and Refractions at a Uniaxial Interface
21.5 Index Ellipsoid, Optical Indicatrix, and K- and S-Surfaces
21.6 Aberrations of Crystal Waveplates
21.6.1 A-Plate Aberrations
21.6.2 C-Plate Aberrations
21.7 Image Formation through an A-Plate
21.8 Walk-Off Plate
21.9 Crystal Prisms
21.10 Problem Sets
References
Chapter 22: Crystal Polarizers
22.1 Introduction to Crystal Polarizers
22.2 Materials for Crystal Polarizers
22.3 Glan–Taylor Polarizer
22.3.1 Limited FOV
22.3.2 Multiple Potential Ray Paths
22.3.3 Multiple Polarized Wavefronts
22.3.4 Polarized Wavefronts Exiting from the Polarizer
22.4 Aberrations of the Glan–Taylor Polarizer
22.5 Pairs of Glan–Taylor Polarizers
22.6 Conclusion
22.7 Problem Sets
References
Chapter 23: Diffractive Optical Elements
23.1 Introduction
23.2 The Grating Equation
23.3 Ray Tracing DOEs
23.3.1 Reflection Diffractive Gratings
23.3.2 Wire Grid Polarizers
23.3.3 Diffractive Retarders
23.3.4 Diffractive Subwavelength Antireflection Coatings
23.4 Summary of the RCWA Algorithm
23.5 Problem Sets
Acknowledgments
References
Chapter 24: Liquid Crystal Cells
24.1 Introduction
24.2 Liquid Crystals
24.2.1 Dielectric Anisotropy
24.3 Liquid Crystal Cells
24.3.1 Construction of Liquid Crystal Cells
24.3.2 Restoring Forces
24.3.3 Liquid Crystal Display: High Contrast Ratio Intensity Modulation
24.4 Configurations of Liquid Crystal Cells
24.4.1 The Fréedericksz Cell
24.4.2 90° Twisted Nematic Cell
24.4.3 Super Twisted Nematic Cell
24.4.4 Vertically Aligned Nematic Cell
24.4.5 In-Plane Switching Cell
24.4.6 Liquid Crystal on Silicon Cells
24.4.7 Blue Phase LC Cells
24.5 Polarization Models
24.5.1 Extended Jones Matrix Model
24.5.2 Single Pass with Polarization Ray Tracing Matrices
24.5.3 Multilayer Interference Models
24.5.4 Calculation for Liquid Crystal Cell ZLI-1646
24.6 Issues in the Construction of LC Cells
24.6.1 Spacers
24.6.2 Disclinations
24.6.3 Pretilt
24.6.4 Oscillating Square Wave Voltage
24.7 Limitations on LC Cell Performance
24.7.1 LC Cell Speed
24.7.2 Spectral Variation of Exiting Polarization State
24.7.3 Variation of Retardance with Angle of Incidence
24.7.4 Compensating LC Cells’ Polarization Aberrations with Biaxial Films
24.7.5 Polarizer Leakage
24.7.6 Depolarization
24.8 Testing Liquid Crystal Cells
24.8.1 Twisted Nematic Cell Example
24.8.2 IPS Tests
24.8.3 VAN Cell
24.8.4 MVA Cell Test
24.8.5 Sheet Retarder Defect
24.8.6 Misalignment between Analyzer and Exiting Polarization State
24.9 Problem Sets
Acknowledgment
References
Chapter 25: Stress-Induced Birefringence
25.1 Introduction to Stress Birefringence
25.2 Stress Birefringence in Optical Systems
25.3 Theory of Stress-Induced Birefringence
25.4 Ray Tracing in Stress Birefringent Components
25.5 Ray Tracing through Stress Birefringence Components with Spatially Varying Stress
25.5.1 Storage of System Shape
25.5.2 Refraction and Reflections
25.5.3 Stress Data Format
25.5.4 Polarization Ray Tracing Matrix for Spatially Varying Biaxial Stress
25.5.5 Examples of Spatially Varying Stress Function
25.6 Effects of Stress Birefringence on Optical System Performance
25.6.1 Observing Stress Birefringence Using Polariscope
25.6.2 Simulations of Injection-Molded Lens
25.6.3 Simulation of a Plastic DVD Lens
25.7 Conclusion
25.8 Problem Sets
Acknowledgments
References
Chapter 26: Multi-Order Retarders and the Mystery of Discontinuities
26.1 Introduction
26.2 Mystery of Retardance Discontinuity
26.3 Retardance Unwrapping for Homogeneous Retarder Systems Using a Simple Dispersion Model
26.3.1 Dispersion Model
26.3.2 Retardance of the Homogeneous Retarder System
26.3.3 Homogeneous Retarder’s Trajectory and Retardance Unwrapping in Retarder Space
26.4 Discontinuities in Unwrapped Retardance Values for Compound Retarder Systems with Arbitrary Alignment
26.4.1 Compound Retarder Jones Matrix Decomposition
26.4.2 Compound Retarder’s Trajectory in Retarder Space
26.4.3 Multiple Modes Exit the Compound Retarder System
26.4.4 Compound Retarder Example at 45°
26.5 Conclusion
26.6 Appendix
26.7 Problem Sets
References
Chapter 27: Summary and Conclusions
27.1 Difficult Issues
27.2 Polarization Ray Tracing Complications
27.2.1 Optical System Description Complications
27.2.2 Elliptical Polarization Properties of Ray Paths
27.2.3 Optical Path Length and Phase
27.2.4 Definition of Retardance
27.2.5 Retardance and Skew Aberration
27.2.6 Multi-Order Retardance
27.2.7 Birefringent Ray Tracing Complications
27.2.8 Coherence Simulation
27.2.9 Scattering
27.2.10 Depolarization
27.3 Polarization Ray Tracing Concepts and Methods
27.3.1 Jones Matrices and Jones Pupil
27.3.2 P Matrix and Local Coordinates
27.3.3 Generalization of PSF and OTF
27.3.4 Ray Doubling, Ray Trees, and Data Structures
27.3.5 Mode Combination
27.3.6 Alternative Simulation Methods
27.4 Polarization Aberration Mitigation
27.4.1 Analyzing Polarization Ray Tracing Output
27.5 Comparison of Polarization Ray Tracing and Polarization Aberrations
27.5.1 Aluminum Coating and Polarization Aberration Expression
27.5.2 Polarization Ray Trace and the Jones Pupil
27.5.3 Aberration Expression for the Jones Pupil
27.5.4 Diattenuation and Retardance Contributions
27.5.5 Design Rules Based on Polarization Aberrations
27.5.5.1 Diattenuation at the Center of the Pupil
27.5.5.2 Retardance at the Center of the Pupil
27.5.5.3 Linear Variation of Diattenuation
27.5.5.4 Linear Variation of Retardance, the PSF Shear between the XX- and YY-Components
27.5.5.5 The Polarization-Dependent Astigmatism
27.5.5.6 The Fraction of Light in the Ghost PSF in XY- and YX-Components
27.5.6 Amplitude Response Matrix
27.5.7 Mueller Matrix Point Spread Matrices
27.5.8 Location of the PSF Image Components
References
Index