Microwave and Millimeter-Wave Remote Sensing for Security Applications 9781608071722

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

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Microwave and Millimeter-Wave Remote Sensing for Security Applications Jeffrey A. Nanzer

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Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress. British Library Cataloguing in Publication Data A catalog record for this book is available from the British Library.

ISBN-13: 978-1-60807-172-2 Cover design by Vicki Kane © 2012 Artech House 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark. 10 9 8 7 6 5 4 3 2 1

Contents Preface

xi

CHAPTER 1 Introduction

1

1.1

Security Sensing 1.1.1 Needs for Remote Security Sensing 1.1.2 Advantages of Microwave and Millimeter-Wave Remote Sensors 1.2 Overview of Remote Sensing Techniques 1.2.1 Radiometry 1.2.2 Radar Systems 1.2.3 Imaging Systems 1.2.4 Interferometric Angular Velocity Measurement 1.2.5 Microwave and Millimeter-Wave Remote Sensing in Related Fields 1.3 The Microwave and Millimeter-Wave Spectrum 1.3.1 Frequency Designations 1.3.2 Propagation of Microwave and Millimeter-Wave Radiation 1.4 Examples of Remote Security Sensors 1.4.1 Active Imaging for Contraband Detection 1.4.2 Passive Imaging for Contraband Detection 1.4.3 Detection of Human Presence 1.4.4 Discrimination of Humans and Classification of Human Activity 1.4.5 Through-Wall Detection 1.4.6 Biological Signature Detection References

18 19 20 20

CHAPTER 2 Electromagnetic Plane Wave Fundamentals

27

2.1

Maxwell’s Equations 2.1.1 The Constitutive Parameters 2.2 Time-Harmonic Electromagnetic Fields 2.2.1 The Wave Equation 2.2.2 Plane Waves 2.2.2.1 Phase Velocity 2.2.2.2 Relationship Between E and H 2.2.3 Energy and Power

1 1 2 3 3 4 4 5 5 7 7 8 9 10 10 12

27 30 31 32 33 34 35 37 v

vi

Contents

2.3

Wave Polarization 2.3.1 Linear Polarization 2.3.2 Elliptical Polarization References

CHAPTER 3 Electromagnetic Waves in Media 3.1

38 39 40 42

43

Plane Wave Propagation in Unbounded Media 3.1.1 Good Conducting Media 3.1.2 Good Dielectric Media 3.1.3 Wave Impedance in Media 3.1.4 Complex Permittivity and Dispersion 3.2 Plane Wave Propagation in Bounded Media 3.2.1 Reflection and Transmission of Normally Incident Waves 3.2.2 Reflection and Transmission of Arbitrarily Incident Waves 3.2.2.1 Transverse Electric (Perpendicular) Incidence 3.2.2.2 Transverse Magnetic (Parallel) Incidence 3.2.3 Power Reflection and Transmission 3.2.4 Total Transmission and Total Reflection 3.2.5 Layered Media 3.3 Electromagnetic Propagation in Specific Media 3.3.1 Atmospheric Propagation Effects 3.3.2 Propagation Through Building Materials 3.3.3 Propagation Through Clothing and Garment Materials 3.3.4 Dielectric Properties of Explosives, Plastics, and Metals 3.3.5 Dielectric Properties of Human Tissue References

44 46 47 48 48 51 52 54 54 57 58 60 61 63 63 69 70 71 72 81

CHAPTER 4 Antennas

85

4.1

Electromagnetic Potentials 4.1.1 Electromagnetic Potentials Due to Electric Current Density J 4.1.2 Electromagnetic Potentials Due to Magnetic Current Density Jm 4.1.3 Infinitesimal Dipole Radiation 4.1.4 Far Field Radiation 4.1.5 Infinitesimal Dipole Far-Field Radiation 4.2 Antenna Parameters 4.2.1 Radiated Power Density and Total Radiated Power 4.2.2 Antenna Pattern 4.2.3 Antenna Pattern Beamwidth 4.2.4 Antenna Solid Angles 4.2.5 Directivity 4.2.6 Gain 4.2.7 Aperture Area and Pattern Solid Angle 4.2.8 Antenna Temperature and Noise Power 4.2.9 Polarization

86 86 88 89 90 94 95 95 96 97 99 99 101 102 103 103

Contents

4.3

vii

Properties of Wire Antennas 4.3.1 Infinitesimal Dipole 4.3.2 Long Dipole 4.4 Aperture Antennas 4.4.1 Image theory 4.4.2 The Equivalence Principle 4.4.3 Radiation from a Rectangular Aperture 4.4.4 Radiation from a Circular Aperture 4.5 Antenna Arrays 4.5.1 Linear Array Theory 4.5.2 Planar Arrays 4.5.3 Array Beamwidth 4.5.4 Phased Arrays 4.5.5 Array Architectures 4.5.5.1 Signal Feeds 4.5.5.2 Beam Steering 4.6 Common Microwave and Millimeter-Wave Antennas 4.6.1 Horn Antennas 4.6.2 Slot Antennas 4.6.3 Microstrip Antennas 4.6.4 Reflector Antenna Systems 4.6.5 Lens Antenna Systems References

104 104 105 107 108 109 111 115 117 118 121 122 123 125 125 127 128 128 131 132 134 136 137

CHAPTER 5 Receivers

139

5.1 5.2

General Operation of Receivers Receiver Noise 5.2.1 Sources of Receiver Noise 5.2.1.1 Thermal Noise 5.2.1.2 Shot Noise 5.2.1.3 Flicker Noise 5.2.2 Equivalent Noise Bandwidth 5.2.3 Thermal Noise at Millimeter-Wave Frequencies 5.3 Noise Figure and Noise Temperature 5.3.1 Noise Figure 5.3.2 Noise Temperature 5.3.3 Noise Figure of an Attenuator 5.3.4 Noise in Cascaded Systems 5.3.5 ADC Noise 5.4 Receiver Linearity 5.4.1 Gain Compression 5.4.2 Intermodulation Products 5.4.3 Third Order Intercept Point 5.4.4 Intercept Point of a Cascade 5.4.5 Dynamic Range

140 143 144 144 145 146 146 148 150 150 152 153 154 157 160 162 164 166 168 168

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Contents

5.4.6 Spurious Free Dynamic Range References CHAPTER 6 Radiometry 6.1

6.2

6.3

6.4

6.5

6.6

Radiometry Fundamentals 6.1.1 Brightness 6.1.2 Brightness and Distance 6.1.3 Flux Density and Source Distribution 6.1.4 Effect of the Antenna Blackbody Radiation 6.2.1 Planck’s Blackbody Radiation Law 6.2.2 Approximations of Planck’s Law 6.2.3 Band-Limited Integration of Planck’s Law Applied Radiometry 6.3.1 Source Resolution 6.3.1.1 Resolved Source 6.3.1.2 Unresolved Source 6.3.2 Received Power as a Convolution 6.3.3 Emissivity and Radiometric Temperature 6.3.3.1 Emissivities of Human Skin and Common Materials 6.3.3.2 Radiometric Temperature in an Environment Radiometer Receivers 6.4.1 Sensitivity 6.4.2 Total Power Radiometer 6.4.2.1 Total Power Response 6.4.2.2 Sensitivity 6.4.3 Interferometric Correlation Radiometer 6.4.3.1 Spatial Point Source Response 6.4.3.2 Sensitivity Practical Considerations 6.5.1 Receiver Instabilities 6.5.2 Dicke Radiometer 6.5.3 Radiometer Calibration Scanning Radiometer Systems 6.6.1 Spatial Resolution 6.6.2 Dwell Time 6.6.3 Measurement Uncertainty 6.6.3.1 One-Dimensional Scanning 6.6.3.2 Two-Dimensional Scanning References

CHAPTER 7 Radar 7.1

Radar Fundamentals 7.1.1 Configurations and Measurements

170 171

173 174 174 176 178 179 180 180 184 185 187 188 188 189 190 191 192 194 196 197 200 200 201 206 207 212 215 215 215 217 218 219 222 223 223 225 226

229 230 231

Contents

7.2

7.3

7.4

7.5

7.6

ix

7.1.2 Range Equation Transmitter Systems 7.2.1 Transmitter Functionality 7.2.2 Transmitter Noise 7.2.3 Millimeter-Wave Oscillators Radar Measurement Sensitivity 7.3.1 Measurement Error 7.3.1.1 Range Measurement Error 7.3.1.2 Frequency Measurement Error 7.3.1.3 Angle Measurement Error 7.3.1.4 Example 7.3.2 Impact of the Time-Bandwidth Product on Measurement Error Micro-Doppler 7.4.1 Micro-Doppler in Security Radar 7.4.2 Micro-Doppler Theory 7.4.3 Human Micro-Doppler Signature Continuous-Wave Radar 7.5.1 Continuous-Wave Doppler 7.5.2 Frequency-Modulated CW 7.5.3 Multifrequency CW 7.5.4 Moving Target Indication Radar High-Range Resolution Radar 7.6.1 Pulse Radar 7.6.2 Linear Frequency Modulation 7.6.3 Stepped-Frequency Modulation References

CHAPTER 8 Imaging Systems 8.1

Scanning Imaging Systems 8.1.1 Types of Scanning Imagers 8.1.2 General Characteristics of Scanning Systems 8.1.2.1 Field of View and Spatial Resolution 8.1.2.2 Frame Rate 8.2 Interferometric Imaging Systems 8.2.1 Introduction 8.2.2 Image Formation 8.2.2.1 Visibility Function 8.2.2.2 Fourier Transform Relationship of Visibility and Radiometric Temperature 8.2.2.3 The Correlation Interferometer as a Spatial Filter 8.2.3 Visibility Sampling 8.2.4 Two-Dimensional Visibility 8.2.5 Image Sensitivity 8.2.6 Image Resolution and Field of View 8.2.7 Interferometric Imaging Arrays

233 236 236 239 241 243 243 244 245 245 245 251 253 254 255 260 266 267 271 274 275 279 280 282 285 286

289 291 291 292 292 294 295 295 296 297 299 301 303 308 309 312 318

x

Contents

8.2.7.1 8.2.7.2 8.2.7.3 8.2.7.4 References

Mills Cross Array T-Array Y-Array Circular Arrays

CHAPTER 9 Interferometric Measurement of Angular Velocity

319 321 322 323 325

329

9.1

Interferometer Response to an Angularly Moving Point Source 9.1.1 System Beam Pattern 9.1.2 Frequency Shift Induced by an Angularly Moving Object 9.1.3 Comparison to Doppler Frequency Shift 9.1.4 Frequency Uncertainty at Wide Angles 9.1.5 Small Angle Approximation 9.2 Interferometer Spectral Response 9.2.1 General Spectral Response 9.2.2 Response with a Sinc Function System Beam Pattern 9.2.3 Interferometer Response in the Time-Frequency Domain 9.3 Interferometric Measurement of Moving Humans 9.3.1 Narrow-Beamwidth Response to a Moving Human 9.3.2 Wide-Beamwidth Response to a Moving Human References

330 331 332 333 335 335 336 336 337 341 344 344 346 349

List of Symbols

351

List of Abbreviations and Acronyms

355

About the Author

357

Index

359

Preface Microwave and millimeter-wave remote sensing techniques are quickly becoming important tools as threats to security in various situations become more sophisticated and difficult to counter. Detecting intruders in exterior environments requires all-weather capability; the ability to operate through fog, smoke, and other obscurants; and the ability to detect features that can be used to discriminate humans and nonhumans. Detecting concealed contraband, such as guns, knives, and explosives, requires the ability detect through fabric and wall materials and generate images with resolutions on the order of millimeters. The last decade has seen a dramatic increase in the research and development of microwave and millimeter-wave sensors for these situations, providing a rich body of work covering radiometric and radar imaging systems for contraband detection, radiometry and Doppler radar systems for intruder detection, and micro-Doppler radar analysis for the classification of human activity. The field continues to develop, generating new techniques in response to continually changing security-sensing needs. This book presents the fundamental principles and advanced techniques used in remote security sensing. The motivation for this book came to me during my time at the University of Texas Applied Research Laboratories, where my task was to develop passive and active millimeter-wave sensors for the detection of moving and stationary people, with the goal of automated intruder detection from robotic platforms. I quickly found that applying radiometry to security sensing was a novel idea, in that I could not find sufficient literature to help guide me as I developed various millimeterwave radiometers. I found myself drawing from the fields of radio astronomy and satellite remote sensing for radiometry literature (some of which was long out of print), and I was frustrated by the lack of a textbook directed toward the basic techniques needed for small-scale remote sensing applications. In addition, my colleagues were actively developing radar systems to exploit the micro-Doppler signature of moving humans, with the goal of activity classification. Along with previous work on millimeter-wave radiometric imaging by my colleagues at ARL and the emerging body of literature on security imaging, it was apparent to me that the field of security sensing was emerging as a new area for remote sensing and that a textbook presenting the fundamentals of sensor design would be significantly useful. The goal of this book is to present the principles of microwave and millimeterwave remote sensing for security applications. The two general areas comprising the physical aspects of remote sensing are electromagnetic wave propagation and remote sensing systems. The antenna represents the transition between these two areas. Signal processing may be considered a third area, following the sensor hardware; however, the implementation of signal processing algorithms is highly specific to the security sensing task and thus varies in implementation. As such, signal processing is not specifically covered in this book. Chapter 1 gives an overview of xi

xii

Preface

remote sensing applications in security sensing, with examples of sensors from published literature. Basic electromagnetic wave propagation is covered in Chapter 2, and in Chapter 3 wave propagation through media is covered, focusing on media encountered in security sensing applications, including propagation through air, obscurants such as smoke and dust, precipitants including fog and rain, building walls, clothing material, and interactions with human tissue. In Chapter 4 antenna theory is presented, and Chapter 5 covers receiver theory. Principles of radiometry are presented in Chapter 6, including blackbody and greybody radiation and specific radiometer configurations including the total power and correlation radiometers. Radar principles and systems are covered in Chapter 7, a large portion of which is also devoted to the relatively new field of human micro-Doppler. Imaging systems are covered in Chapter 8, with the majority of the chapter focusing on interferometric imaging, a new and promising application in remote security sensing. The book concludes with Chapter 9 presenting a new technique of measuring the angular velocity of moving objects using a correlation interferometer. This book is intended for practicing engineers and researchers who are developing remote sensors for security-related applications and for graduate and advanced undergraduate students studying remote sensing. Many of the topics covered in the book are relevant to remote sensing in general, and researchers in related remote sensing fields may find the book to be a useful reference. The reader is assumed to have a background in calculus and Fourier analysis, and although the material is derived from basic principles, prior exposure to electromagnetic theory will also be beneficial. I am extremely grateful for the people who have provided support and guidance in the development of this book. In particular, I would like to thank those who have reviewed chapters of the manuscript: Andrew Temme at Michigan State University, and Salvador Talisa and Keir Lauritzen at the Johns Hopkins University Applied Physics Laboratory. I also thank the staff at Artech House for their professionalism and support, and their anonymous reviewer for thorough comments. My thanks to Carl Nielson, for helping with some of the figures in Chapter 3, and to my colleagues at the Johns Hopkins University Applied Physics Laboratory who have provided encouragement and helpful discussions along the way. I am indebted to those who helped shape my educational and professional career: Ed Rothwell at Michigan State University, Bob Rogers at the University of Texas Applied Research Laboratories, and Hao Ling at the University of Texas. Finally, I owe my greatest thanks to my wife and children for supporting this endeavor and tolerating the long hours spent developing this book.

CHAPTER 1

Introduction

1.1 Security Sensing 1.1.1

Needs for Remote Security Sensing

Increased security concerns in the past decade can be traced largely to the threat of terrorism, a result of which has been heightened interest in the detection of humans, the classification of human activity, and the detection of hidden objects that may be carried by a person or concealed in walls. Threats to security are constantly changing, targeting weak areas of security as others are strengthened, and thus there must be a corresponding evolution of security sensing to counter new threats. The applications of security sensing expand beyond counter-terrorism: border security involves detecting illegal immigration and intercepting drugs; military force protection involves detecting humans and determining their intent through activity classification; law-enforcement benefits from the detection and classification of humans through walls; and search-and-rescue operations require the detection of people hidden within buildings or beneath building materials. Addressing these situations requires sensors that can operate in nearly all weather conditions, sense through obscurants and clothing, and measure with resolution fine enough to detect small hidden objects. The increased interest in countering threats has led to the advance of sensor technology to counter a wide range of threats, and the corresponding sensing techniques are continually evolving and developing. Such techniques include x-ray imagers, biological and chemical agent sensors, infrared cameras, spectroscopic sensors, acoustic sensors, and THz imagers. A given sensor or sensing technique often yields good performance in a specific application or setting but cannot counter all perceived threats. For instance, infrared imagers can detect the presence of a human particularly well against a cool background, such as an indoor environment or at night; however, some environments, such as those encountered during the daytime where the background is warm and solar reflections are more ubiquitous, yield poorer human presence detection performance. Infrared sensors are also incapacitated by obscurants such as fog, smoke, or dust. Detection of chemical traces using spectroscopy includes the benefit of remote measurement; however, it generally has lower performance than chemical trace sensors directly analyzing air samples. THz imagers, while providing fine resolution, suffer from high signal attenuation through the atmosphere, obscurants, clothing, and walls, resulting in sensors with short operational ranges. Some sensors are undesirable due to their nature: x-ray imagers, while successful at detecting contraband, can cause concern due to the radiation levels required. Nonionizing radiation, such as microwave and 1

2

Microwave and Millimeter-Wave Remote Sensing for Security Applications

millimeter-wave radiation, is often preferred where detection of people or objects on people is the goal. A single security sensing technique cannot address all security concerns, and microwave and millimeter-wave sensors represent a unique and complementary option to other methods. Microwave and millimeter-wave remote sensors have significant potential to counter threats such as concealed objects (explosives, guns, knives, drugs, and so on) under clothing or hidden in or behind walls, illegal border crossings, intrusion into secured areas, and threatening activities by people. Remote sensing, a mature and robust field, is being applied to these applications of security sensing with increasing ingenuity: millimeter-wave radar systems are being applied to high-range resolution concealed object detection, human presence detection and through-wall sensing; and radiometry, long the domain of radio astronomy and satellite remote sensing, is rapidly developing into the sensing method of choice for detecting hidden contraband through imaging systems. In these implementations, detection and discrimination can be accomplished from a distance, increasing the safety of the operator of the sensor. 1.1.2

Advantages of Microwave and Millimeter-Wave Remote Sensors

Sensors operating in the microwave and millimeter-wave bands have a number of unique characteristics that complement other security sensing methods. As such, research in microwave and millimeter-wave technology has seen a dramatic increase in the past decade. Fueled by reductions in component costs, increased bandwidth capability of digitizers, and advances in signal and image processing techniques, the benefits of microwave and millimeter-wave remote sensors in security applications are now being realized in practice. These benefits will be covered in detail throughout this book and include the following: ·

·

·

· · · ·

·

Propagation through the atmosphere with minimal attenuation at most frequencies; Propagation through obscurants such as fog, haze, smoke, dust, and light to medium rain with negligible attenuation; Propagation through clothing material, baggage material and some building wall material with negligible or minimal attenuation; High thermal radiation power from humans relative to nonhuman objects; Fine range resolution due to wide-bandwidth signal capability; Fine angular resolution due to short wavelength radiation; Fine resolution of the radial velocity of objects due to high carrier frequencies; Physically small systems due to short wavelengths.

These characteristics support detection and imaging of humans and contraband at long ranges and through walls, obscurants, and clothing. The capability to see through obscurants and clothing is a primary benefit that has driven a large portion of research in contraband detection, as well as sensors for imaging through fog and dust for various imaging applications such as aiding in landing of helicopters and other vehicles. The contrast between the thermal radiation emitted by humans

1.2

Overview of Remote Sensing Techniques

3

and that emitted or reflected by other materials supports the detection of human presence in cluttered environments and the detection of objects concealed beneath clothing. The capability to detect humans in nearly all weather conditions, coupled with the fine Doppler frequency resolutions that can be achieved, has pushed the development of radar sensors for remote human presence detection and activity classification. Additionally, because the angular resolution of a sensor is proportional to the physical size of the antenna in terms of the wavelength, systems operating at higher frequencies can generate images with finer resolution without the need for very large apertures.

1.2 Overview of Remote Sensing Techniques Remote sensors determine information about an object or scene by transmitting a signal and analyzing the signal reflected back to the sensor or by measuring a signal intrinsically emitted by the object itself. The signals are in the form of electromagnetic waves, which propagate through space and materials with some loss, which may be negligible. Remote detection and interrogation of an object is beneficial in security sensing, as it allows an operator to investigate a potential threat without the need for physical inspection. This improves safety in the detection of explosives and other weapons, reduces operator burden in border security and site security monitoring, and allows discrete surveillance. Remote sensors can be generally categorized as either active or passive systems. Active systems transmit a signal and measure the signal that reflects off the object and back to the sensor. By analyzing aspects of the return signal, such as the time between the transmit and return signals or the power level or frequency of the return signal, various characteristics of the remote object can be discerned. Passive systems rely on measuring a signal that is intrinsic to the object, such as thermal radiation. Imaging systems use active or passive sensors to generate two-dimensional images of a scene, where image processing is generally required for detection and discrimination. 1.2.1

Radiometry

Radiometers are in essence highly sensitive receivers designed to measure the thermal radiation that is intrinsically emitted by all objects. Radiometers are passive systems: no signal is transmitted and reflected off the object. Because the signals detected are intrinsic to the object, detection can be accomplished regardless of whether the object is moving or stationary. Thermal signatures themselves may be used for detection or discrimination, or a contrast between the thermal radiation of humans and nonhumans may be used to detect people or objects. Thermal radiation is generated by the motion of electrons in a material with a nonzero temperature. The thermal power radiated by an object is determined by Planck’s law, which states that the power is a function of temperature and frequency, and is covered in detail in Chapter 6. An object at the temperature of the human body (310 K) radiates the most power in the infrared region of the electromagnetic spectrum, with lower power levels at lower and higher frequencies. Thermal radiation in the microwave and millimeter-wave regions can be approximated by a linear

4

Microwave and Millimeter-Wave Remote Sensing for Security Applications

relationship between the radiated power and the product of the temperature of the object and the bandwidth of the receiver. In implementing radiometers at millimeterwave frequencies, thermal radiation from the body can be measured through clothing, allowing the detection of hidden people or objects hidden on the body. The radiated power levels are low, on the order of 10–10 W or lower, and thus high-gain systems must be designed in order to measure the differences in power. A radiometer can be implemented in a number of ways. The most common forms are the total power radiometer and the correlation radiometer, discussed further in Chapter 6. The total power radiometer produces a voltage signal that is a measure of the total power present in the bandwidth of the system. This power level includes both power emitted by the object that is directly proportional to the physical temperature of the object and any noise power generated in the system. The correlation radiometer consists of two receivers, the outputs of which are correlated. The resulting signal response is proportional to the power emitted by the object; ideally, uncorrelated noise responses from the receivers are removed by the correlation process. Both the total power and correlation radiometers produce a signal response that is proportional to the temperature of the object. 1.2.2

Radar Systems

Radar systems are active systems that transmit a signal and analyze the signal reflected off the object of interest. They consist of a transmitter and a receiver, which may be collocated on the same platform and may use the same antenna. The transmitted signal may be a continuous-wave signal or it may be pulsed, and it may change in frequency. The received signal, collected after reflecting off the object, is analyzed to determine various characteristics of the object. The difference in time between transmitting a signal and the receipt of the reflected signal is proportional to the distance to the object, and the shift in the frequency of the signal is proportional to the radial velocity of the object. The range extent of objects can be measured, the resolution of which is inversely proportional to the waveform bandwidth, as discussed in Chapter 7. Millimeter-wave radars can support wide bandwidths, yielding fine range resolution. Radar systems can detect objects moving in a radial direction toward or away from the sensor by measuring the frequency shift between the transmitted and received signals, called the Doppler shift, and can thus be applied to the detection of moving humans for intruder detection and border security applications and can be used to measure biological signatures from respiration and heartbeat. Differences in the power levels of the returned signals can also be used to classify different materials by their reflectivity and can thus be applied to concealed object detection. Chapter 7 covers fundamental aspects of radar systems in detail. 1.2.3

Imaging Systems

Millimeter-wave imagers generate two-dimensional representations of a scene through multiple active or passive measurements. Imaging systems are generally implemented at millimeter-wave frequencies rather than microwave frequencies because the shorter wavelengths of millimeter-wave radiation allows for finer

1.2

Overview of Remote Sensing Techniques

5

resolution images with smaller systems than can be achieved at lower microwave frequencies. The images may be of the reflectivity in the case of an active imager or the radiometric temperature profile in the case of a passive radiometric imager. Formation of the images can be achieved using a scanning configuration or a staring configuration. Scanning imagers are implemented using either mechanical steering of a single antenna beam, electronic steering of the beam of an antenna array, or a combination of the two. Mechanically steered imagers generally use a single antenna, often a reflector antenna, and steer the beam across the image pixel locations by placing either the feed antenna, the reflector, or the entire antenna system on a rotator and physically moving the beam. Electrically steered imagers use phased arrays or frequency-steered arrays to move the beam. Mechanically steered imagers are generally slower to form images but benefit from their relative simplicity of implementation and lower cost. Electrically steered imagers are generally faster than mechanically steered imagers; however, they include significant complexity due to the implementation of an array and the associated beam-steering controls. Staring imagers utilize multiple receiving elements corresponding to pixel locations, where the electromagnetic wave is often focused onto the elements using a lens to increase the aperture size and improve the resolution. Interferometric imagers, long used in radio astronomy and satellite remote sensing, have recently been applied to security imaging, and are discussed in detail in Chapter 8. Interferometric imagers do not require steering and can be implemented with a fraction of the elements needed in a full phased array. Generally implemented as passive imagers, the image is formed through the cross–correlation of the received signals between all pairs of antennas. Interferometric imagers thus require a large number of correlation processes, often implemented digitally in modern systems. 1.2.4

Interferometric Angular Velocity Measurement

Whereas radar systems can measure the radial velocity of moving objects by detecting the frequency shift of the return signal, measurement of the angular velocity of moving objects is more difficult and is generally performed by tracking the object through repeated estimates of the angle of the object. Recent demonstrations of a method of measuring the angular velocity of moving objects using a two-element correlation interferometer have shown the potential to measure the angular motion of objects and humans directly, without the need for tracking. With this method, an object moving through the interferometer beam pattern produces a frequency shift on the sensor output signal that is proportional to the angular velocity of the object, in a way that is mathematically similar to how the frequency shift in a radar signal is proportional to the radial velocity. While demonstrating potential, the interferometric measurement of angular velocity is a relatively new technique and must be evaluated through future studies and experiments. The basic theory and initial experimental results of this method are reviewed in Chapter 9. 1.2.5

Microwave and Millimeter-Wave Remote Sensing in Related Fields

The applications of radar and radiometry in remote sensing are broad. Since its development during World War II, radar has become a very general and widespread

6

Microwave and Millimeter-Wave Remote Sensing for Security Applications

remote sensing technique. It is used on ground- and air-based platforms, in large phased arrays, and in small single-element sensors. Initially, radar was used for the detection and tracking of vehicles, primarily airborne, where it is still used today in both military and commercial applications. Measurement of the velocity of moving objects through the induced Doppler shift is used in police radar for determining vehicle speed and weather radar for measuring precipitation. The ranging capability of radars provides one of the more ubiquitous functions of remote sensing in general and is used for vehicle collision avoidance, ionospheric sounding, military guidance applications, intragalactic astronomy, and industrial control, to name a few. Uses of radar systems on airborne and spaceborne platforms include altimetry, topographic mapping, vegetation coverage mapping, oil spill detection and monitoring, and measurements of soil moisture content. Applications of radiometry are less widespread than radar. Traditionally, the two major areas where microwave and millimeter-wave radiometry have found significant use are radio astronomy and satellite remote sensing. Throughout the middle of the twentieth century, radio telescopes and radio interferometers were developed to generate fine angular resolution images of the radio frequency radiation of stellar objects. Radar measurements for this purpose are only practical within our own galaxy due to the distances between our planet and extragalactic objects. A primary development from radio astronomy was the interferometric receiver that utilizes multiple antennas separated by a number of wavelengths to generate images with resolutions equal to that of a single aperture with dimensions equivalent to the distance between the two farthest antennas. The interferometric imaging technique requires at least two antennas; they can be moved to form multiple baselines if the viewing time is long enough. Radio astronomers have the benefit of stationarity when viewing stellar objects: multiple measurements can be taken on successive days because the objects do not move. Significant development of satellite remote sensors occurred in the 1980s. Leveraging the interferometric technique developed in radio astronomy, antenna arrays were developed using a small number of antennas to synthesize a larger aperture. The benefit to satellite remote sensing came in the reduction of necessary antenna hardware (and therefore weight) that needed to be placed into orbit. Measurements that can be conducted using passive satellite remote sensors include soil moisture content, vegetation coverage, surface temperature maps, ocean surface salinity and temperature, ocean wind speed, sea ice coverage, weather conditions, wildfire detection and monitoring, and ionospheric measurements. The application of remote sensing techniques to security is a relatively new endeavor, and one that can leverage developments made in the areas mentioned above. Radar applications are clearly applicable to the detection of moving humans and hidden contraband, as well as respiration and heartbeat detection. Security sensing can be viewed as an emerging significant area of development for microwave and millimeter-wave radiometry, following radio astronomy and satellite remote sensing. Its uses are in the detection of stationary humans through the measurement of intrinsic thermal radiation, and detection of concealed objects by measuring physical temperatures and temperature differences between objects and the human body.

1.3

The Microwave and Millimeter-Wave Spectrum

7

1.3 The Microwave and Millimeter-Wave Spectrum 1.3.1

Frequency Designations

The region of the electromagnetic spectrum designated as the microwave band extends from 3 GHz to 30 GHz, while the millimeter-wave band extends from 30 GHz to 300 GHz. The radio frequency portion of the electromagnetic spectrum as defined by the International Telecommunication Union (ITU) is shown in Table 1.1. The microwave and millimeter-wave regions are covered by the super high frequency (SHF) and extremely high frequency (EHF) bands on the ITU spectrum. Commonly used in the United States are the IEEE letter designations [1], given in Table 1.2. Under this definition, the microwave region may be considered to begin in S-band and extend to Ka-band while the millimeter-wave region extends from Kaband to the millimeter-wave band, which does not have a standard letter designation. Figure 1.1 shows the microwave and millimeter-wave spectrum as defined by the ITU and the IEEE. Frequencies between 300 GHz and 3,000 GHz do not have a designation and are generally called simply terahertz (THz) frequencies, and while the focus of this book is on the microwave and millimeter-wave regions, frequencies extending into the THz region are considered where relevant. Applications exploiting the microwave band are myriad and include communications, RFID, wireless networking, and satellite broadcasting, among others. Remote sensing applications are widely used in the microwave band due to favorable atmospheric propagation characteristics. Modern radar systems are generally implemented in the microwave region, as are radio astronomy arrays and satellite remote sensors. Remote sensing applications in the millimeter-wave region have traditionally consisted primarily of military sensors operating at the W-band; however, there has been significant work toward millimeter-wave remote sensors in other areas in recent years, including radio astronomy arrays that are being developed at frequencies in the hundreds of gigahertz and sensors for imaging applications. Atmospheric attenuation is greater at millimeter-wave frequencies than at microwave frequencies, making satellite remote sensing of the earth more difficult. Driven by the wide bandwidths that can be supported, interest has increased for the development of communication systems and remote sensors at millimeter-wave

Table 1.1

International Telecommunication Union Frequency Bands

Band Number 1 2 3 4 5 6 7 8 9 10 11 12

Designation Extremely low frequency (ELF) Super low frequency (SLF) Ultra low frequency (ULF) Very low frequency (VLF) Low frequency (LF) Medium frequency (MF) High frequency (HF) Very high frequency (VHF) Ultra high frequency (UHF) Super high frequency (SHF) Extremely high frequency (EHF) –

Frequencies 3–30 Hz 30–300 Hz 300–3,000 Hz 3–30 KHz 30–300 KHz 300–3,000 KHz 3–30 MHz 30–300 MHz 300–3,000 MHz 3–30 GHz 30–300 GHz 300–3,000 GHz

8

Microwave and Millimeter-Wave Remote Sensing for Security Applications Table 1.2 IEEE Standard Letter Designations for Radar Frequency Bands Designation HF VHF UHF L S C X Ku K Ka V W mmw

Frequencies 3–30 MHz 30–300 MHz 300–1,000 MHz 1–2 GHz 2–4 GHz 4–8 GHz 8–12 GHz 12–18 GHz 18–26.5 GHz 26.5–40 GHz 40–75 GHz 75–110 GHz 110–300 GHz

carriers. The result has been component and system technology with increased capabilities and reduced cost, making millimeter-wave remote security sensor systems more realizable. 1.3.2

Propagation of Microwave and Millimeter-Wave Radiation

Electromagnetic radiation in remote security sensing encounters various media between the object of interest and the antenna. Radiation travels through the atmosphere in all cases, albeit it over short distances compared to some remote sensing applications such as radio astronomy and satellite remote sensing. Various mechanisms in the atmosphere cause radiation to be absorbed at some frequencies, whereas other frequencies are passed through with negligible attenuation. Figure 1.2 shows the absorption caused by the atmosphere over the microwave and millimeter-wave bands. There are a number of regions, referred to as windows, where radiation can pass through with minimal loss. Other regions, such as that around 60 GHz, have very high losses, making remote sensing over long distances difficult. Obscurants in the air can render sensors such as infrared and optical sensors ineffective; in particular, fog, light rain, smoke, and dust absorb the majority of

ITU microwave and millimeter-wave band designations SHF 3

EHF 300

30

f (GHz)

IEEE microwave and millimeter-wave band designations S 2

C 4

X 8

Ku 12

K Ka

18 26.5 40

V

W 75 110

mmw 300

f (GHz) Figure 1.1 ITU radio frequency band designations and IEEE standard letter band designations for radar frequencies.

1.4

Examples of Remote Security Sensors

9

1

Transmission (%)

0.8 0.6 0.4 0.2 0 0 Figure 1.2

100

200 300 f (GHz)

400

500

Atmospheric absorption in the microwave and millimeter-wave bands.

the radiation at optical and infrared frequencies. Microwave radiation, however, transmits through such obscurants with negligible attenuation, as does the radiation in most of the millimeter-wave band. Attenuation at some specific frequencies can cause additional attenuation due to water absorption. Avoiding these regions, sensors can be developed that can operate in nearly all conditions that would be encountered in an outdoor environment. The detection of human presence and concealed objects is enabled in the microwave and millimeter-wave bands due to favorable propagation characteristics of many building materials. Some materials, such as drywall, are nearly transparent across these bands, whereas some, such as wood, have low transmission loss at low frequencies but higher loss as the frequency increases. Concrete and brick generally exhibit high loss, making detection through such materials difficult with a passive system; however, active systems can be designed with increased transmit power to overcome the loss incurred by the wall materials. The effectiveness of the sensor thus generally depends on the type of building material. The loss incurred by microwave and millimeter-wave radiation as it transmits through clothing materials is also generally negligible, supporting contraband detection and passive radiometric human presence detection where the intrinsic thermal radiation generated by the human body is detected.

1.4 Examples of Remote Security Sensors Remote sensing techniques have been applied to numerous applications in security and related areas, and are continually being investigated for applicability in new areas. In this book, the focus is on the most promising areas that have shown success in practice and those areas of research that have shown potential for securityrelated applications. Many remote security sensors can be grouped roughly into the two categories of concealed object detection and human presence detection and classification.

10

Microwave and Millimeter-Wave Remote Sensing for Security Applications

1.4.1

Active Imaging for Contraband Detection

Detection of objects hidden beneath clothing can be achieved using radar imaging systems [2–11]. There are two approaches: measuring the reflectivity of the object in each pixel of the image, and measuring the range to the object in each pixel. Measurement of the reflectivity gives insight into the material composing the various objects in the image. Metal objects are highly reflective, and the signal scattered off metals will have high amplitude. Other materials are less reflective, such as human tissue, and the scattered signals will be of lower amplitude. By considering the contrast between pixels in the image, hidden objects can be detected; however, objects with reflectivity similar to that of human tissue can be difficult to detect. Another approach is to measure the range extent of objects. Radar imagers with wide frequency bandwidths can resolve range extents short enough to detect objects hidden under clothing by the thickness of the contraband; the resolution is inversely proportional to the bandwidth. Images are thus formed by measuring the range extent in each pixel; and objects hidden on the body can thus be detected if they are thicker than the range resolution of the radar. Range and reflectivity measurements can also be combined in an image. Active imagers are typically implemented at millimeter-wave frequencies in order to achieve fine resolution in angle and to support the bandwidths required for fine resolution in range. Figure 1.3(a) shows a 350-GHz active imaging system with two reflectors, one of which is rotated to steer the beam. The system had a 9.6-GHz bandwidth yielding a longitudinal resolution of 1.5 cm and lateral resolution of 1 cm at ranges up to 10 m. Figure 1.3 shows images from the system of a concealed mock explosive on a person taken at a range of 5 m [8]. A 72–80-GHz active imaging system is shown in Figure 1.4. The antenna was a sparsely populated array, shown in Figure 1.4(a) and consisting of a 4×4 array of antenna clusters, with each of the 16 clusters containing 46 transmit and 46 receive elements. Figure 1.4(b) shows images from the system of a concealed handgun and pocketknife. The lateral resolution achieved was 2 mm, while the 8-GHz bandwidth gives a longitudinal resolution of 1.87 cm [11]. 1.4.2

Passive Imaging for Contraband Detection

Passive imaging techniques provide another useful solution for detecting concealed objects [12–35]. Passive imagers detect intrinsic thermal radiation; different materials radiate with different efficiencies, and thus the detected power level of the thermal radiation from one material will generally be different from that of another material. Using this fact, concealed objects can be detected by the difference in radiated power from the body. Metals and objects with low thermal radiation efficiency reflect the majority of the incident radiation and will appear similar to the surrounding environment. Passive imagers are generally operated at millimeter-wave frequencies to achieve high resolution in angle. Images taken from a 77-GHz video-rate passive imaging system with a frame rate of 4 Hz are shown in Figures 1.5(a) and 1.5(b). This system consisted of a linear array for azimuth scanning and achieved vertical scanning through a dualreflector design and a collimating lens, resulting in a lateral resolution of 20 mm, and had a radiometric temperature resolution of 1.2 K [30]. Figure 1.6(a) shows the

1.4

Examples of Remote Security Sensors

11

Figure 1.3 (a) 350-GHz active imaging system with dual-reflector beam steering. (b) Image of a concealed mock explosive beneath clothing. (© IEEE 2009 [8].)

antenna array of a video-rate interferometric passive radiometric imaging system operating at 22 GHz, with a radiometric temperature sensitivity of 2 K and a frame rate of 25 Hz [33]. The array elements, one of which is shown in Figures 1.6(b) and 1.6(c), are loop-fed waveguides. The radiometric image, shown in Figure 1.6(d), is formed by cross-correlating the outputs of pairs of antennas and shows a metal object concealed under a jacket. Figure 1.7(a) shows a 90-GHz passive imaging system using a vertical mechanical track and a Cassegrain antenna system where the subreflector rotates to scan the beam to form the image [35]. The spatial resolution of this system was 2.5 cm at a range of 2.4 m, and the radiometric resolution was between 0.06 K and 0.3 K. Images of concealed objects are shown in Figure 1.7(b) and (c), where hidden metal objects are clearly visible.

12

Microwave and Millimeter-Wave Remote Sensing for Security Applications

Figure 1.4 (a) 72–80-GHz active imaging system with a sparse array. The transmit elements are placed along the top and bottom edges of each square cluster, with the receive elements placed along the sides. (b) and (c) are images of objects concealed beneath clothing. (© IEEE 2011 [11].)

1.4.3

Detection of Human Presence

Detecting human presence is important in border security, military force protection, site security monitoring, search and rescue, and other related applications. Detection of humans in indoor or outdoor environments can be accomplished using either radar or radiometer systems [36–46]. Radar systems can detect moving

1.4

Examples of Remote Security Sensors

13

Figure 1.5 Images of concealed objects taken from a 77-GHz video-rate passive radiometric imaging system. (© 2010 SPIE [30].)

Figure 1.6 A 22-GHz video-rate interferometric passive radiometric imaging system: (a) Interferometric imaging array. (b) Short waveguide antenna element showing the top of the loop feed and (c) bottom of the loop feed. (d) Video image taken of a person with a foil square concealed under a jacket. The foil presents as a dark spot in the signature, caused by reflecting the colder background temperature. (© 2011 SPIE [33], images courtesy of N. Salmon.)

14

Microwave and Millimeter-Wave Remote Sensing for Security Applications

Figure 1.7 (a) A 90-GHz passive radiometric imager using a Cassegrain antenna system with a rotating subreflector and a vertical mechanical track. (b) and (c) Images showing concealed metal objects. (© 2008 SPIE [35].)

humans from long distances by measuring the Doppler shift in the return signal, whereas radiometers detect the thermal radiation emitted by the human body. Figure 1.8(a) shows a 36-GHz continuous-wave scanning-beam Doppler radar designed for the detection of moving humans from a moving platform; the system block diagram is given in Figure 1.8(b), and Figure 1.8(c) shows a plot in the timefrequency domain of the radar return signal of three walking people. The rotation rate of the sensor was approximately 1 rad·s–1. The continuous oscillatory line is the return signal from the stationary environment, an artifact of rotation of the sensor, while the point responses are the Doppler-shifted returns from the people walking around the sensor. The background signal is due to the movement of the platform and the rotation rate of the pedestal; it is deterministic, and filtering it out results in the isolation of the responses from the people only. The antenna beamwidth was

1.4

Examples of Remote Security Sensors

15

Figure 1.8 (a) A 36-GHz continuous-wave Doppler radar for detecting moving people from a moving platform. (© IEEE 2009 [41].) (b) System diagram. (c) Signal response from three walking people as the sensors rotates atop a moving platform. The point responses are due to walking people, while the oscillation is due to the stationary environment. Filtering the environmental response isolates the responses from the moving humans.

16

Microwave and Millimeter-Wave Remote Sensing for Security Applications

3.5º, and the system had a Doppler frequency resolution of 16 Hz. Figure 1.9(a) shows a 27.4-GHz radiometer for detecting people from a moving platform. The system consisted of both total power and correlation detection modes on a rotator with a 1 rad·s–1 rotation rate. The total power radiometers had radiometric temperature sensitivities of 0.5 K, while the correlation mode had a sensitivity of 0.27 K. Figure 1.9(b) shows the signal response of a total power radiometer and a correlation radiometer scanning across a stationary human and a pillar constructed of metal and concrete [39]. The large peaks are due to the thermal radiation emitted by the human. It can be seen that the correlation mode responds to the human, but not the pillar; this is due to the lower coherence of the radiation from the

(a)

0.6 0.4 pillar 0.2 0 −0.2

Amplitude

0.6 human 0.4 0.2 0 −0.2

Amplitude

70

75

80

85

145 150 155 160 165

1

1

0

0

−1 70

75

θ

80

85

Total power response

Correlation response

−1 145 150 155 160 165 θ (b)

Figure 1.9 (a) A 27.4-GHz radiometer system atop a mobile robotic platform. The sensor included both total power and correlation detection modes. (b) Signal response of a total power radiometer and a correlation radiometer in an outdoor environment scanning across a stationary human and a pillar constructed of concrete and metal. (© IEEE 2008 [39].)

Examples of Remote Security Sensors

Figure 1.10 (a) Measured and (b) simulated micro-Doppler signature of a walking human from a 2.4-GHz radar. (c) Simulated micro-Doppler signature of a walking human with a 12-GHz radar. (© IEEE 2008 [53], courtesy of H. Ling.)

1.4 17

18

Microwave and Millimeter-Wave Remote Sensing for Security Applications

pillar, which is largely reflected, relative to that of the human, which is intrinsically generated and has higher spatial coherence. 1.4.4

Discrimination of Humans and Classification of Human Activity

Upon detection, it is important to determine that a nonhuman, such as an animal, has not been inaccurately determined to be a human. Furthermore, it is desirable to classify the type of activity the person is engaged in to determine whether the person represents a threat. Of the various signatures that may be analyzed for these purposes, the micro-Doppler signature present in the radar returns of humans and animals is a prominent feature, and it has been the focus of target discrimination and activity classification using microwave and millimeter-wave Doppler radar systems [47–62]. The micro-Doppler signature arises from the dynamic motion of the various parts of the body, such as the different velocities of the torso, arms, and legs. The arms and legs also move in a periodic fashion that lends itself to classification. Through micro-Doppler signal classification, humans can be discriminated from vehicles and animals, and various human activities can be classified. Figures 1.10(a) and 1.10(b) show measured and simulated micro-Doppler signatures of a walking human in the time-frequency domain, from a 2.4-GHz radar [53]. The large oscillations are due to the motion of the legs, and the dominant signal with little oscillation variability at the center of the signature is due to the torso. Figure 1.10(c) shows a simulated micro-Doppler signature of a walking human from a 12-GHz radar that has increased frequency resolution. The frequency responses of the foot, leg, lower arm, and torso are more visible [53].

2.5 Reflecting plates

range (m)

2

1.5 Wall

1

0.5 0

0.5

1

2 1.5 cross−range (m)

2.5

3

Figure 1.11 Ultra-wideband through-wall radar image of two reflecting plates. The bright spots in the wall are metal pylons. (© IEEE 2009 [74].)

1.4

Examples of Remote Security Sensors

1.4.5

19

Through-Wall Detection

Detection of humans and objects through walls is difficult due to attenuation of electromagnetic waves in wall material, but it can be accomplished using either radar or radiometer systems [60, 63–78]. Losses due to most wall materials increase

Figure 1.12 (a) Block diagram of a Ka-band continuous-wave radar for biological signal measurements. (b) Heartbeat and respiration detection in the frequency domain, plotted as a function of heartbeat rate, taken from the front and back of the body from a distance of 1.5 m. (© IEEE 2006 [79].)

20

Microwave and Millimeter-Wave Remote Sensing for Security Applications

with frequency, and thus most through-wall sensors are operated at low microwave frequencies, often 10 GHz or less. In order to achieve reasonable angular resolution, the required aperture sizes are thus physically large, which generally rules out high-resolution imaging techniques. However, the bulk movement of people can be detected, and micro-Doppler signatures can also be measured. Figure 1.11 shows a measured cross-range and down-range plot of a 5-GHz ultra-wideband throughwall radar with 6 GHz of bandwidth, showing the wall material and two reflecting plates behind the wall [74]. The longitudinal resolution was 2.5 cm. Images with this system were formed by placing the antennas on a mobile robotic platform that moved down the length of the wall, generating a synthetic aperture. 1.4.6

Biological Signature Detection

Radar systems with high frequency resolution can be used to detect and measure minute biological movements of the human body, including movement of the torso due to respiration and heartbeat [79–85]. The Doppler frequency shift is proportional to the carrier frequency and the velocity of the object; therefore, sensing of this type requires high carrier frequencies to measure the relatively small frequency shifts. Figure 1.12(a) shows the diagram of a Ka-band continuous-wave radar for the detection of respiration and heartbeat. Figure 12(b) shows a plot of the measured frequency response of a human on the front and back of the torso from a Ka-band radar [79]. The axis shows the Doppler frequency as the heartbeat rate in beats per minute.

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Millimeter-Wave Imaging Applications,” Instrumentation and Measurement, IEEE Transactions on, Vol. 60, 2011, pp. 186–197. Sato, H., K. Sawaya, K. Mizuno, J. Uemura, M. Takeda, et al., “Passive Millimeter-Wave Imaging for Security and Safety Applications,” in Proceedings of the SPIE, Orlando, FL, 2010, p. 76710V-11. Sato, H., K. Sawaya, K. Mizuno, J. Uemura, M. Takeda, et al., “Development of 77 GHz Millimeter Wave Passive Imaging Camera,” Sensors, 2009 IEEE, 2009, pp. 1632–1635. Hua-Mei, C., L. Seungsin, R. M. Rao, M. A. Slamani, and P. K. Varshney, “Imaging for Concealed Weapon Detection: A Tutorial Overview of Development in Imaging Sensors and Processing,” Signal Processing Magazine, IEEE, Vol. 22, 2005, pp. 52–61. Salmon, N. A., R. Macpherson, A. Harvey, P. Hall, S. Hayward, et al., “First Video Rate Imagery from a 32-Channel 22-GHz Aperture Synthesis Passive Millimetre Wave Imager,” Proceedings of the SPIE, Prague, Czech Republic, 2011, pp. 818, 805–818, 812. Salmon, N. A., I. Mason, P. Wilkinson, C. Taylor, and P. Scicluna, “First Imagery Generated by Near-Field Real-Time Aperture Synthesis Passive Millimetre Wave Imagers at 94 GHz and 183 GHz,” Proceedings of the SPIE, Vol. 7837, 2010, p. 78370I. Dill, S., M. Peichl, and H. Suss, “Study of Passive MMW Personnel Imaging with Respect to Suspicious and Common Concealed Objects for Security Applications,” Proceedings of the SPIE, Vol. 7117, 2008, p. 71170C. Brenda, A. K., “Selected Systems for the Detection of Human Stowaways in Air Cargo Containers,” Carnahan Conferences Security Technology, Proceedings 2006 40th Annual IEEE International, 2006, pp. 26–29. Nanzer, J. A., and R. L. Rogers, “Human Presence Detection Using Millimeter-Wave Radiometry,” Microwave Theory and Techniques, IEEE Transactions on, Vol. 55, 2007, pp. 2727–2733. Nanzer, J. A., and R. L. Rogers, “A Ka-Band Correlation Radiometer for Human Presence Detection from a Moving Platform,” Microwave Symposium, 2007, IEEE/MTT-S International, 2007, pp. 385–388. Nanzer, J. A., and R. L. Rogers, “Applying Millimeter-Wave Correlation Radiometry to the Detection of Self-Luminous Objects at Close Range,” Microwave Theory and Techniques, IEEE Transactions on, Vol. 56, 2008, pp. 2054–2061. Nanzer, J. A., and R. L. Rogers, “A Simple Model of Human Thermal Millimeter-Wave Radiation for Radiometric Human Presence Detection,” 2009 USNC/URSI National Radio Science Meeting, 2009. Nanzer, J. A., M. G. Anderson, T. M. Josserand, L. Kuan, G. A. Olinger, et al., “Detection of Moving Intruders from a Moving Platform Using a Ka-Band Continuous-Wave Doppler Radar,” Antennas and Propagation Society International Symposium, 2009, APSURSI ‘09, IEEE, 2009, pp. 1–4. SangHyun, C., N. Mitsumoto, and J. W. Burdick, “An Algorithm for UWB Radar-Based Human Detection,” Radar Conference, 2009 IEEE, 2009, pp. 1–6. Nanzer, J. A., E. Popova, and R. L. Rogers, “Applying Correlation Radiometry to Human Presence Detection in Multiple Outdoor Environments,” 2010 CNC/USNC/URSI National Radio Science Meeting, 2010. Nanzer, J. A., E. Popova, and R. L. Rogers, “Analysis of the Detection Modes of a Human Presence Detection Millimeter-Wave Radiometer,” Antennas and Propagation Society International Symposium (APSURSI), 2010 IEEE, 2010, pp. 1–4. SangHyun, C., M. Wolf, and J. W. Burdick, “Human Detection and Tracking via UltraWideband (UWB) Radar,” Robotics and Automation (ICRA), 2010 IEEE International Conference on, 2010, pp. 452–457. Nanzer, J. A., and R. L. Rogers, “Frequency Estimation of Human Presence Detection Signals From a Scanning-Beam Millimeter-Wave Correlation Radiometer,” Geoscience and Remote Sensing Letters, IEEE, Vol. 8, 2011, pp. 78–82.

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Examples of Remote Security Sensors

23

[47] van Dorp, P., and F. C. A. Groen, “Human Walking Estimation with Radar,” Radar, Sonar and Navigation, IEE Proceedings, Vol. 150, 2003, pp. 356–365. [48] Thayaparan, T., S. Abrol, E. Riseborough, L. Stankovic, D. Lamothe, et al., “Analysis of Radar Micro-Doppler Signatures from Experimental Helicopter and Human Data,” Radar, Sonar & Navigation, IET, Vol. 1, 2007, pp. 289–299. [49] Chen, V. C., “Detection and Analysis of Human Motion by Radar,” Radar Conference, 2008, RADAR ‘08. IEEE, 2008, pp. 1–4. [50] Smith, G. E., K. Woodbridge, and C. J. Baker, “Multistatic Micro-Doppler Signature of Personnel,” Radar Conference, 2008, RADAR ‘08, IEEE, 2008, pp. 1–6. [51] Anderson, M. G., “Design of Multiple Frequency Continuous Wave Radar Hardware and Micro-Doppler Based Detection and Classification Algorithms,” Ph.D. Thesis, University of Texas at Austin, 2008. [52] Youngwook, K., and L. Hao, “Human Activity Classification Based on Micro-Doppler Signatures Using an Artificial Neural Network,” Antennas and Propagation Society International Symposium, 2008, AP-S 2008, IEEE, 2008, pp. 1–4. [53] Sundar Ram, S., and L. Hao, “Simulation of Human MicroDopplers Using Computer Animation Data,” Radar Conference, 2008, RADAR ‘08, IEEE, 2008, pp. 1–6. [54] Zhaonian, Z., and A. G. Andreou, “Human Identification Experiments Using Acoustic Micro-Doppler Signatures,” Micro-Nanoelectronics, Technology and Applications, 2008, EAMTA 2008, Argentine School of, 2008, pp. 81–86. [55] Nanzer, J. A., and R. L. Rogers, “Bayesian Classification of Humans and Vehicles Using Micro-Doppler Signals from a Scanning-Beam Radar,” Microwave and Wireless Components Letters, IEEE, Vol. 19, 2009, pp. 338–340. [56] Youngwook, K., and L. Hao, “Human Activity Classification Based on Micro-Doppler Signatures Using a Support Vector Machine,” Geoscience and Remote Sensing, IEEE Transactions on, Vol. 47, 2009, pp. 1328–1337. [57] Tahmoush, D., and J. Silvious, “Angle, Elevation, PRF, and Illumination in Radar MicroDoppler for Security Applications,” Antennas and Propagation Society International Symposium, 2009, APSURSI ‘09, IEEE, 2009, pp. 1–4. [58] Vignaud, L., A. Ghaleb, J. Le Kernec, and J. M. Nicolas, “Radar High Resolution Range & Micro-Doppler Analysis of Human Motions,” Radar Conference—Surveillance for a Safer World, 2009, RADAR. International, 2009, pp. 1–6. [59] Silvious, J., J. Clark, T. Pizzillo, and D. Tahmoush, “Micro-Doppler Phenomenology of Humans at UHF and Ku-Band for Biometric Characterization,” Proceedings of the SPIE, Orlando, FL, 2009, pp. 73080X-9. [60] Ram, S. S., C. Christianson, Y. Kim, and H. Ling, “Simulation and Analysis of Human Micro-Dopplers in Through-Wall Environments,” Geoscience and Remote Sensing, IEEE Transactions on, Vol. 48, 2010, pp. 2015–2023. [61] Moulton, M. C., M. L. Bischoff, C. Benton, and D. T. Petkie, “Micro-Doppler Radar Signatures of Human Activity,” in Proceedings of the SPIE, 2010, p. 78370L. [62] Chen, V. C., The Micro-Doppler Effect in Radar, Norwood, MA: Artech House, 2011. [63] Frazier, L., “Surveillance Through Walls and Other Opaque Materials,” Proc. SPIE, Vol. 2497, 1995, p. 115. [64] Venkatasubramanian, V., and H. Leung, “A Novel Chaos-Based High-Resolution Imaging Technique and Its Application to Through-the-Wall Imaging,” Signal Processing Letters, IEEE, Vol. 12, 2005, pp. 528–531. [65] Ram, S. S., and H. Ling, “Through-Wall Tracking of Human Movers Using Joint Doppler and Array Processing,” Geoscience and Remote Sensing Letters, IEEE, Vol. 5, 2008, pp. 537–541. [66] Nilsson, S., A. Janis, M. Gustafsson, J. Kjellgren, and A. Sume, “Through-the-Wall HighResolution Imaging of a Human and Experimental Characterization of the Transmission of Wall Materials,” Proceedings of the SPIE, Vol. 7117, 2008, p. 71170L.

24

Microwave and Millimeter-Wave Remote Sensing for Security Applications [67] Chi-Wei, W., and H. Zi-Yu, “Using the Phase Change of a Reflected Microwave to Detect a Human Subject Behind a Barrier,” Biomedical Engineering, IEEE Transactions on, Vol. 55, 2008, pp. 267–272. [68] Narayanan, R. M., “Through-Wall Radar Imaging Using UWB Noise Waveforms,” Journal of the Franklin Institute, Vol. 345, 2008, pp. 659–678. [69] Dehmollaian, M., and K. Sarabandi, “Refocusing Through Building Walls Using Synthetic Aperture Radar,” Geoscience and Remote Sensing, IEEE Transactions on, Vol. 46, 2008, pp. 1589–1599. [70] Johnson, J. T., M. A. Demir, and N. Majurec, “Through-Wall Sensing with Multifrequency Microwave Radiometry: A Proof-of-Concept Demonstration,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 47, 2009, pp. 1281–1288. [71] Gonzalez-Partida, J. T., P. Almorox-Gonzalez, M. Burgos-Garcia, B. P. Dorta-Naranjo, and J. I. Alonso, “Through-the-Wall Surveillance with Millimeter-Wave LFMCW Radars,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 47, 2009, pp. 1796–1805. [72] Venkatasubramanian, V., H. Leung, and L. Xiaoxiang, “Chaos UWB Radar for Throughthe-Wall Imaging,” IEEE Transactions on Image Processing, Vol. 18, 2009, pp. 1255– 1265. [73] Hong, W., R. M. Narayanan, and Z. Zheng Ou, “Through-Wall Imaging of Moving Targets Using UWB Random Noise Radar,” Antennas and Wireless Propagation Letters, IEEE, Vol. 8, 2009, pp. 802–805. [74] Braga, A. J., and C. Gentile, “An Ultra-Wideband Radar System for Through-the-Wall Imaging Using a Mobile Robot,” IEEE International Conference on Communications, 2009, ICC ‘09, 2009, pp. 1–6. [75] Solimene, R., F. Soldovieri, G. Prisco, and R. Pierri, “Three-Dimensional Through-Wall Imaging Under Ambiguous Wall Parameters,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 47, 2009, pp. 1310–1317. [76] Lianlin, L., Z. Wenji, and L. Fang, “A Novel Autofocusing Approach for Real-Time Through-Wall Imaging Under Unknown Wall Characteristics,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, 2010, pp. 423–431. [77] Chieh-Ping, L., and R. M. Narayanan, “Ultrawideband Random Noise Radar Design for Through-Wall Surveillance,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 46, 2010, pp. 1716–1730. [78] Qiong, H., Q. Lele, W. Bingheng, and F. Guangyou, “UWB Through-Wall Imaging Based on Compressive Sensing,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, 2010, pp. 1408–1415. [79] Yanming, X., L. Jenshan, O. Boric-Lubecke, and V. M. Lubecke, “A Ka-Band Low Power Doppler Radar System for Remote Detection of Cardiopulmonary Motion,” 27th Annual International Conference of the Engineering in Medicine and Biology Society, 2005, IEEEEMBS 2005, 2005, pp. 7151–7154. [80] Yanming, X., L. Changzhi, and L. Jenshan, “Accuracy of a Low-Power Ka-Band NonContact Heartbeat Detector Measured from Four Sides of a Human Body,” Microwave Symposium Digest, 2006, IEEE MTT-S International, 2006, pp. 1576–1579. [81] Jenshan, L., and L. Changzhi, “Wireless Non-Contact Detection of Heartbeat and Respiration Using Low-Power Microwave Radar Sensor,” Microwave Conference, 2007, APMC 2007, Asia-Pacific, 2007, pp. 1–4. [82] Petkie, D. T., E. Bryan, C. Benton, C. Phelps, J. Yoakum, et al., “Remote Respiration and Heart Rate Monitoring with Millimeter-Wave/Terahertz Radars,” Proceedings of the SPIE, 2008, pp. 71170I. [83] Droitcour, A. D., O. Boric-Lubecke, and G. T. A. Kovacs, “Signal-to-Noise Ratio in Doppler Radar System for Heart and Respiratory Rate Measurements,” IEEE Transactions on Microwave Theory and Techniques, Vol. 57, 2009, pp. 2498–2507.

1.4

Examples of Remote Security Sensors

25

[84] Changzhi, L., J. Cummings, J. Lam, E. Graves, and W. Wenhsing, “Radar Remote Monitoring of Vital Signs,” Microwave Magazine, IEEE, Vol. 10, 2009, pp. 47–56. [85] Massagram, W., V. M. Lubecke, A. Host-Madsen, and O. Boric-Lubecke, “Assessment of Heart Rate Variability and Respiratory Sinus Arrhythmia via Doppler Radar,” IEEE Transactions on Microwave Theory and Techniques, Vol. 57, 2009, pp. 2542–2549.

CHAPTER 2

Electromagnetic Plane Wave Fundamentals Remote sensing, whether for security sensing, satellite sensing, or radio astronomy, involves the transport of energy between a sensor and a remote location or object for the purpose of determining some information about the object. When the sensing involves microwave or millimeter-wave electromagnetic radiation, the energy is transported via time-varying electromagnetic fields. Remote sensing of an object is generally facilitated using one of two methods: measuring the intrinsic signals emanating from the remote location or transmitting a predetermined signal and measuring the signal that reflects back from the remote location. As will be shown, these signals take the form of electromagnetic waves. If the distance between the sensor and the remote object is sufficiently large compared to the wavelength of the radiation, the electromagnetic waves can be considered to be planar in that they change only in time and along the direction of propagation; they remain constant in amplitude and phase in a plane orthogonal to the direction of propagation. Such waves are called plane waves, and although they are a theoretical construct in that by definition they extend infinitely in the directions perpendicular to the direction of propagation, they are approximated well in practice by a wave that has travelled a distance from the source that is large relative to the wavelength and the size of the aperture. For example, a spherical wavefront emanating from a point radiator becomes approximately planar at great distances, as illustrated in Figure 2.1, and a receiver far from the source measures a wavefront in the z direction that is very nearly constant in the x and y directions. This specific range is called the far field, and is discussed further in Chapter 4. In practice, the far field is near enough to the sensor for microwave and millimeter-wave frequencies that many remote security sensors can be analyzed using the plane wave approximation. The understanding of the characteristics of plane waves is therefore an important foundation for the understanding of microwave and millimeter-wave remote sensors and their application to security sensing. In this chapter, the equations describing plane electromagnetic waves are derived from Maxwell’s equations. General aspects are covered which describe concepts of plane waves and their characteristics; these are important throughout the rest of the book. More involved treatments of plane waves can be found in most textbooks on electromagnetic waves [1–4].

2.1 Maxwell’s Equations Electromagnetic phenomena are in general described in terms of six basic physical quantities: 27

28

Microwave and Millimeter-Wave Remote Sensing for Security Applications

Planar wavefronts

Spherical wavefronts

. . .

Radiating point source

Figure 2.1 A spherical wavefront emanating from a point radiator is approximately planar after traveling a sufficiently long distance.

· · · · · ·

E (V·m–1), the electric field; H (A·m–1), the magnetic field; D (C·m–2), the electric flux density; B (Wb·m–2), the magnetic flux density; J (A·m–2), the electric current density; ρ (C·m–3), the electric charge density.

The first four terms are electromagnetic field quantities, while the current and charge densities are source quantities. Electromagnetic fields are generated by current and charge, and hence the latter are referred to as current and charge sources; however, the fields are also characterized in the absence of sources, where the fields are assumed to have been generated by sources outside the region of interest. This is the case when considering the propagation of electromagnetic waves in free space. Each quantity is defined in terms of its spatial and temporal dependencies; that is, χ = χ (r, t)

(2.1)

where χ represents one of the vector or scalar quantities, r is the three-dimensional position vector, and t is the time variable. For simplicity, the dependence on r and t will generally be implicitly assumed through the rest of the book and will be explicitly introduced when necessary. The interactions of the field and source quantities are defined by the four Maxwell equations: ¶B ¶t

(2.2)

¶D +J ¶t

(2.3)

Ñ´E = -

Ñ´H =

2.1

Maxwell’s Equations

29

Ñ×D = ρ

(2.4)

Ñ×B = 0

(2.5)

where (2.2) is Faraday’s law, (2.3) is the Ampere-Maxwell law, or simply Ampere’s law, (2.4) is Gauss’s law, and (2.5) is the magnetic Gauss’s law, or simply the absence of magnetic point sources. Taken together, (2.2)–(2.5) are called the Maxwell equations or Maxwell’s equations. The source quantities are interrelated through Ñ× J+

¶ρ =0 ¶t

(2.6)

which is the equation of continuity. This equation is an expression of conservation of charge; it states that the current density diverging from a closed surface must be equal to the negative of the time rate of change of the charge density within the surface. That is, electric charge is neither created nor destroyed. Maxwell’s equations as described by (2.2)–(2.5) are referred to as the Minkowski form of Maxwell’s equations. In this form, however, the equations appear to be imbalanced; the electric field and electric flux density each have magnetic counterparts; however, there are no magnetic complements to the electric current and charge densities. To address this, the following quantities · ·

Jm (V·m–2), the magnetic current density, ρm (Wb·m–3), the magnetic charge density,

were introduced as purely theoretical constructs, since such quantities have not been shown to exist in nature. The magnetic charge density would be a magnetic monopole; however, only magnetic dipoles exist: if a magnetic dipole is split, the result is two smaller magnetic dipoles. Despite their apparently fictitious nature, the magnetic source quantities are often mathematically useful when describing certain problems. For instance, the magnetic current density is used in the discussion of aperture antennas in Chapter 4. Using the magnetic current and charge densities results in: Ñ´E = -

¶B - Jm ¶t

(2.7)

Ñ´H =

¶D +J ¶t

(2.8)

Ñ×D = ρ

(2.9)

Ñ × B = ρm

(2.10)

Discussions on other forms of Maxwell’s equations can be found in [5]. The analyses that proceed throughout this book will generally use the Minkowski form of Maxwell’s equations, with magnetic sources introduced where necessary. Derivations and analyses including the electric sources are easily extended to include

30

Microwave and Millimeter-Wave Remote Sensing for Security Applications

the magnetic sources due to the balanced nature of Maxwell’s equations; derivations generally proceed identically with the electric and magnetic field quantities interchanged. 2.1.1

The Constitutive Parameters

To describe the behavior and characteristics of electromagnetic phenomena within media, some parameters describing relevant aspects of the media and how they interact with the field quantities are required. In general, the electromagnetic flux densities are related to the electromagnetic fields through D = εE

(2.11)

1 B (2.12) µ –1 –1 where ε (F·m ) and µ (H·m ) are the permittivity and permeability of the medium, respectively. In addition, the electric current density is related to the electric field through H=

J =σE

(2.13)

where σ (S·m–1) is the conductivity of the medium. Equations (2.11)–(2.13) are called the constitutive relations and ε, µ, and σ are called the constitutive parameters. In general, the constitutive parameters are complex vector quantities; however, in linear, homogeneous, nondispersive media, they are simple constants. In free space, the conductivity is zero and the permittivity and permeability are ε 0 = 8.854 ´ 10-12 F × m -1

(2.14)

µ0 = 4π ´ 10-7 H × m -1

(2.15)

The permittivity and permeability of media other than free space are generally characterized in terms of the free space values through ε = εrε 0

(2.16)

µ = µ r µ0

(2.17)

where εr and µr are called the relative permittivity and relative permeability, respectively. The permittivity of a medium is never less than that of free space; thus, the relative permittivity is always greater or equal to one, with equality only in the case of free space. Most media have relative permeability values very close to one; ferromagnetic and ferrimagnetic materials are exceptions and can have permeability values much different than that of free space. Relative conductivity values are often used to classify media; materials with very high conductivity are conductors, while those with very low conductivity are dielectrics or insulators. Good conductors, such as metals, are often approximated by σ = ∞, whereas good dielectrics are often approximated by σ = 0; such media are considered in Chapter 3.

2.2

Time-Harmonic Electromagnetic Fields

31

Use of the constitutive relations allow Maxwell’s equations to be cast in terms of the electromagnetic field quantities E and H. Specifically, ¶H ¶t

(2.18)

¶E + σE ¶t

(2.19)

Ñ ´ E = -µ Ñ´H = ε

ρ ε

(2.20)

Ñ×H = 0

(2.21)

Ñ×E =

In this form, the characteristics of the medium are explicitly included through the constitutive parameters.

2.2 Time-Harmonic Electromagnetic Fields Maxwell’s equations as described in the previous section are fairly general in the sense that no assumptions were made about the nature of the field quantities. For remote security sensing, time varying fields are of primary interest—in particular, sinusoidally time-varying or time-harmonic fields, as these are the types of fields that propagate through a medium. In general, a time-harmonic field is given by χ (r, t) = χ (r)e jωt

(2.22)

where χ(r) describes the field in the spatial dimensions and ω = 2πf is the angular frequency of the temporal oscillation of the field. Temporal derivatives of timeharmonic quantities are straightforward; the time-derivative of (2.22) is ¶ χ (r,t ) = jωχ (r)e jωt = jωχ (r, t) ¶t

(2.23)

In terms of the representations described by (2.22), the time-harmonic electric and magnetic fields can be given by E(r, t) = E(r)e jωt

(2.24)

H(r, t) = H(r)e jωt

(2.25)

Using the property (2.23), the time derivatives in Faraday’s and Ampere’s laws (2.18) and (2.19) can be simplified, resulting in Ñ ´ E = - jωµH

(2.26)

Ñ ´ H = jωε E + σ E

(2.27)

32

Microwave and Millimeter-Wave Remote Sensing for Security Applications

2.2.1

The Wave Equation

Time-harmonic fields are governed by wave equations, and therefore time-harmonic electromagnetic fields can be considered to be waves. In this section, the wave equation is derived from Maxwell’s equations; the plane wave solution to the wave equation is considered in the following section. Consider an electromagnetic field in free space, with no sources present; that is, J = 0 and ρ = 0 and the divergence of both the electric and magnetic field quantities are zero. In the absence of sources, Maxwell’s equations thus are given by Ñ ´ E = - jωµH

(2.28)

Ñ ´ H = jωε E

(2.29)

Ñ×E = 0

(2.30)

Ñ×H = 0

(2.31)

Taking the curl of (2.28) results in Ñ ´ (Ñ ´ E ) = - jωµÑ ´ H

(2.32)

Substituting (2.29) for the right-hand side and using the vector identity Ñ ´ Ñ ´ A = Ñ(Ñ × A) - Ñ 2 A

(2.33)

Ñ(Ñ × E) - Ñ 2 E = ω 2 µε E

(2.34)

yields

The first term on the left-hand side is zero due to (2.30), and thus Ñ 2 E + ω 2µε E = 0

(2.35)

A similar derivation follows for Ampere’s law, which results in Ñ2 H + ω 2µε H = 0

(2.36)

Defining the wavenumber k m–1 to be k = ω µε

(2.37)

equations (2.35) and (2.36) become Ñ 2 E + k2 E = 0

(2.38)

Ñ 2 H + k2 H = 0

(2.39)

2.2

Time-Harmonic Electromagnetic Fields

33

Equations (2.38) and (2.39) are vector Helmholtz wave equations for E and H. If the vector fields are separated into their rectangular coordinates, the result is six scalar Helmhotz wave equations of the form ¶χ n + k2 χ n = 0 ¶n

(2.40)

where χ = E, H, and n = x, y, z. 2.2.2

Plane Waves

The simplest solution to the scalar Helmholtz equation can be found by considering a straightforward case where a given field consists of only one coordinate component. Consider an electric field with a component only in the x direction given by E(r, t) = xˆ Ex e jωt

(2.41)

The Laplacian operator is then Ñ2 E =

¶ 2 Ex ¶z 2

(2.42)

and the scalar Helmholtz equation becomes ¶ 2 Ex + k2 Ex = 0 ¶z 2

(2.43)

The solution of (2.43) is of the general form Ex (z) = E1e - jkz + E2 e jkz

(2.44)

which is the superposition of two waves, one traveling in the +z direction, the other traveling the –z direction. Consider a solution consisting of one wave traveling in the +z direction; that is, E2 = 0. The electric field in such a case is E(r, t) = E1e j(ωt -kz)

(2.45)

The phase of this wave is constant over the surface ωt–kz; that is, the wave extends infinitely in both the x and y dimensions and furthermore is constant in both dimensions. The wave therefore changes only in the z direction and in time. Such a wave defines a geometric plane and is thus termed a plane wave. Plane waves are therefore electromagnetic waves that are constant in phase and amplitude in plane orthogonal to the direction of propagation, and, as discussed in the introduction to this chapter, a wave that has travelled a sufficient distance from the source generating the wave can be considered planar. The analysis of plane waves is generally simpler than that of nonplanar waves; thus, approximating a wave as a plane wave eases the computational complexity of wave propagation problems.

34

Microwave and Millimeter-Wave Remote Sensing for Security Applications

The angular frequency ω describes the dependence of the plane wave in the temporal domain, and in a similar way the wavenumber describes the dependence of the wave in the spatial domain along the direction of propagation. The angular frequency can be defined in terms of the temporal oscillation of the field by the relation ω=

2π T

(2.46)

where T is the period of the temporal oscillation, or the time duration between adjacent maxima (or minima) of the sinusoidal temporal oscillation. Similarly, the wavenumber can be defined in terms of the distance between adjacent maxima of the sinusoidal oscillation of the wave in the spatial domain by the relation k=

2π λ

(2.47)

where λ is the wavelength, or the spatial distance between maxima. The relationship between wavenumber and wavelength can also be derived by considering the distance between a point z0 and a point a distance Dz away in the z direction given by z0 + Dz. Since the wavelength is the distance between maxima of the spatial sinusoidal oscillation, setting Dz = λ, (ωt - kz) - [ωt - k(z + λ )] = 2 π

(2.48)

kλ = 2π

(2.49)

or

which is the same as (2.47). 2.2.2.1

Phase Velocity

Electromagnetic waves propagate through a medium at a finite velocity. For a plane wave, the phase is constant in the dimensions perpendicular to the direction of propagation, and thus the velocity of the phase is equal to the velocity of propagation of the wave. The phase velocity is found by the time rate of change of the phase in the spatial domain: vp =

dz dt

(2.50)

By definition of a plane wave, the phase is constant: ωt - kz = const

(2.51)

ωt - const k

(2.52)

or z= and thus vp =

d æ ωt - const ö ω ç ÷= dt è k ø k

(2.53)

2.2

Time-Harmonic Electromagnetic Fields

35

Using the definition of the wavenumber (2.37) results in vp =

1 µε

(2.54)

The phase velocity is therefore determined solely by the constitutive parameters of the medium through which the wave travels. In free space, the phase velocity is c=

1 = 2.9979 × 108 m ⋅ s−1 µ 0ε 0

(2.55)

which is the velocity of light. 2.2.2.2

Relationship Between E and H

Consider an electric field propagating in the z direction and consisting of only a component in the x direction given by E = xˆ Ex e j(ωt -kz)

(2.56)

Using Faraday’s law (2.28), the magnetic field is given by H=j

1 k ε Ñ ´ E = yˆ Ex e j(ωt -kz) = yˆ Ex e j(ωt- kz) ωµ ωµ µ

(2.57)

Thus, the resulting magnetic field consists of only a component in the y direction. As discussed earlier, a plane wave at a fixed point z is constant in both the x and y directions. Therefore, ¶E ¶E = =0 ¶x ¶y

(2.58)

¶H ¶H = =0 ¶x ¶y

(2.59)

and

From Ampere’s law, the z component of the electric field is given by Ez =

1 æ ¶H y ¶H x ç ¶y jω ε è ¶x

ö ÷=0 ø

(2.60)

and similarly from Faraday’s law, Hz = 0

(2.61)

Therefore, the longitudinal components of the electric and magnetic fields are zero; the fields of a plane wave consist of only components perpendicular to the direction of propagation.

36

Microwave and Millimeter-Wave Remote Sensing for Security Applications

Additionally, both the electric and magnetic fields are perpendicular to each other. This can be seen by considering the electric field E = xˆ Ex + yˆ Ey

(2.62)

The magnetic field is then, from (2.57), given by H = -xˆ

k k Ey + yˆ Ex ωµ ωµ

(2.63)

The vector product of the electric and magnetic fields is therefore E×H = -

k k Ex Ey + E E =0 ωµ ωµ x y

(2.64)

The electric and magnetic fields are thus perpendicular to one another and perpendicular to the direction of propagation. Such a wave is referred to as a transverse electromagnetic (TEM) wave. The magnitude of the magnetic field as given by (2.57) is simply the magnitude of the electric field scaled by ε µ . The relationship between the electric and magnetic field components can therefore be given by 1 E η

(2.65)

E µ = ε H

(2.66)

H = where η=

is the intrinsic impedance of the medium, measured in W. Substituting the free-space permittivity and permeability yields the intrinsic impedance of free space η0 =

µ0 » 377 W ε0

(2.67)

Up to this point, only simple fields where the electric or magnetic fields consisted of one component have been considered; however, the analyses are easily extended to fields consisting of components in multiple dimensions. In general, the solution to the vector Helmholtz wave equation (2.38) is given by E (r ) = E0 e ± jk×r

(2.68)

where the wavenumber vector is k = xˆ kx + yˆ ky + zˆ kz

(2.69)

r = xˆ x + yˆ y + zˆ z

(2.70)

and the position vector is

2.2

Time-Harmonic Electromagnetic Fields

37

The magnetic field is given in general by H=

1 k´E ωµ

(2.71)

and similarly the electric field is given in general by E = -ωµk ´ H

2.2.3

(2.72)

Energy and Power

The electric energy density of an electromagnetic wave is ue =

1 E×D 2

(2.73)

1 H×B 2

(2.74)

while the magnetic energy density is um =

The total electromagnetic energy density is the sum of the individual electric and magnetic energy densities. If the electromagnetic wave is propagating through a linear, homogenous, lossless medium, the constitutive parameters are time-invariant, and the total energy density is u = ue + um =

(

)

1 2 2 ε E + µH 2

(2.75)

In order to determine the power carried by the electromagnetic wave, the time rate of change of the energy density is considered. This is given by ¶u ¶E ¶H = εE × + µH × ¶t ¶t ¶t

(2.76)

Using Faraday’s and Ampere’s laws, the time derivatives of the electric and magnetic fields are ¶E 1 = (Ñ ´ H - J) ¶t ε

(2.77)

¶H 1 = - Ñ´E ¶t µ

(2.78)

and

and the time rate of change of the energy density is therefore ¶u = E × (Ñ ´ H) - H × (Ñ ´ E) - E × J ¶t

(2.79)

Now using the vector identity B × (Ñ ´ A) - A × (Ñ ´ B) = Ñ × (A ´ B)

(2.80)

38

Microwave and Millimeter-Wave Remote Sensing for Security Applications

yields ¶u + Ñ × (E ´ H) = -E × J ¶t

(2.81)

Equation (2.81) describes the balance of energy in an electromagnetic system and is referred to as Poynting’s theorem after the physicist J. H. Poynting. The first term on the left-hand side represents the differential change in energy density, while the second term represents the flow of power. The term on the right-hand side, the product of the electric field and the electric current density, represents the work done by the fields on the sources. In the absence of sources, the rate of change of energy density is exactly balanced by the outward flow of power: Ñ×S + where

¶u =0 ¶t

S = E´H

(2.82)

(2.83)

is the Poynting vector, which represents the power carried by the electromagnetic wave. For time-harmonic electromagnetic fields the Poynting vector is given by S=

1 E ´ H* 2

(2.84)

where * indicates the complex conjugate. Equation (2.82) is of the same form as the continuity equation (2.6), and the Poynting theorem is similarly a statement of conservation of energy. The net flow of power through a closed surface must be equal to the rate of change of energy density within the surface.

2.3 Wave Polarization As a time-harmonic wave propagates through time and space, the electric and magnetic field vectors change. The orientation of the electric field vector as a function of time and space is called the polarization of the wave. The orientation may be static or dynamic in time and space. The polarization of the receiving antenna must be matched to that of the incident radiation for maximum signal conversion into the receiver, as discussed in Chapter 4: if the polarization of the antenna and the incident radiation are orthogonal, no signal is transferred to the receiving hardware. In general, the polarization of the incident wave will be different from that of the antenna. In passive radiometric remote sensing, the incident radiation is unpolarized while the antenna can respond to one direction of polarization; thus, only half of the power of the incident radiation can be received by the receiver system. Active systems receive signals transmitted by the system and reflected off an object. The polarization is thus well matched; however, some depolarization, however minimal, generally occurs on the reflected signal in practice.

2.3

Wave Polarization

39

y |E|

Ey

φ z Figure 2.2

2.3.1

x

Ex

Linearly polarized electric field vector.

Linear Polarization

In the simplest case, the electric field vector is oriented in a single direction in the x-y plane, which is called linear polarization. A linearly polarized wave can be described by E = (xˆ Ex + yˆ Ey )e j(ωt -kz)

(2.85)

The magnitude of this field traces out a line in the x-y plane with magnitude E = Ex2 + Ey2

(2.86)

as indicated by Figure 2.2. The angle separating the field vector and the x-axis is given by æ Ey ö φ = tan-1 ç (2.87) ÷ è Ex ø The dynamic nature of the field vector can be seen by considering the real part of (2.85) at an arbitrary fixed location along the z axis; for simplicity, z = 0 is chosen. Then the real part of the field is Re{E} = (xˆ Ex + yˆ Ey )cos(ωt)

(2.88)

Figure 2.3 shows the change in the electric field vector as a function of time. When ωt = 0, the vector has positive magnitude |E| at an angle φ. When ωt = π ⁄ 2, the

Ey

ωt = π

ωt = π/2

ωt = 0 |E|

-Ey Ex

|E|

|E|

Figure 2.3

Linearly polarized electric field vector orientation over time.

-Ex

40

Microwave and Millimeter-Wave Remote Sensing for Security Applications

y x

z

Figure 2.4

Over time (or space) a linearly polarized electric field traces out a sinusoid.

cosine term is zero and the vector has zero magnitude. When ωt = π, the vector has magnitude –|E| at an angle φ + π, in the opposite direction. The vector thus traces out a sinusoid over time, as described in Figure 2.4. If the y component of the electric field is zero (Ey = 0), the magnitude of the vector is Ex and its angle is φ = 0; the field is oriented along the x-axis. Such a wave is linearly polarized along the x direction. Similarly, if Ex = 0, the wave is linearly polarized along the y direction. Note that the same linear behavior arises in both the temporal and spatial domains; the earlier analysis could have alternatively fixed the time variable (conveniently at t = 0) and varied the spatial variable kz with the same sinusoidal response in space. 2.3.2.

Elliptical Polarization

Whereas linear polarization represents the simplest form of wave polarization, the most general form of polarization of a monochromatic plane wave is elliptical polarization, of which other forms of polarization are special cases. Thus, any monochromatic wave can be described in terms of elliptical polarization. Consider an electromagnetic wave given by E = (xˆ Ex + yˆ Ey )

(2.89)

Ex = E1 cos(ω t - kz)

(2.90)

Ey = E2 cos(ωt - kz + δ )

(2.91)

where

The phase δ represents the phase difference between the two waves making up the total wave. In order to more simply analyze the dynamic nature of the wave, take a fixed location in space z = 0. The wave components are then Ex = E1 cos ω t

(2.92)

Ey = E2 cos(ωt + δ ) = E2 (cos ωt cos δ - sin ωt sin δ )

(2.93)

2.3

Wave Polarization

41

or Ex = cos ω t E1

(2.94)

Ey = cosω t cos δ - sinω t sin δ E2

(2.95)

Squaring and adding (2.94) and (2.95) results in 2

2

æ Ex ö æ Ey ö 2 2 2 2 2 ç E ÷ + ç E ÷ = cos ωt + cos ω t cos δ + sin ω t sin δ è 1ø è 2ø

(2.96)

-2 cos ωt sin ωt cos δ sin δ Using the squares of (2.94) and (2.95), the last term on the right-hand side can be written æ E ö æ Ey ö 2 cosω t sinω t cosδ sin δ = 2 cos2 ω t cos2 δ - 2 ç x ÷ ç ÷ cos δ è E1 øè E2 ø

(2.97)

Substituting this into (2.96) yields 2

2

æ Ex ö æ Ey ö æ Ex ö æ Ey ç E ÷ + ç E ÷ - 2ç E ÷ç E è 1ø è 2ø è 1 øè 2

ö 2 ÷ cos δ = sin δ ø

(2.98)

This is the equation of an ellipse, and thus the electric field vector traces out an elliptical shape over time. The wave is therefore said to be elliptically polarized. Equation (2.98) represents the most general form of polarization that a monochromatic wave can take. Other forms of wave polarization are given as special cases of (2.98). When the phase difference between the components is δ = 0 or π, the polarization reduces to linear polarization. In such a case, with δ = 0 and E2 = 0, the resulting wave is linearly polarized in the x-direction. y

ωt = π/2

ωt = 3π/4

ωt = π/4

ωt = 0

ωt = π

x

ωt = 7π/4

ωt = 5π/4 ωt = 3π/2

Figure 2.5

Circularly polarized wave vectors.

42

Microwave and Millimeter-Wave Remote Sensing for Security Applications

A significant special case is found when δ = ±π ⁄ 2 and E1 = E2 = E0. The polarization given by (2.98) then becomes Ex2 + Ey2 = E02 = const

(2.99)

which is the equation of a circle, and the wave is said to be circularly polarized. Consider, for example, the case where δ = π ⁄ 2 and E1 = E2 = E0. Substituting (2.90) and (2.91) into (2.89) then results in E = xˆ E0 cos ωt + yˆ E0 sin ω t

(2.100)

where the wave is analyzed at the point z = 0. As the wave propagates in time the electric field vector traces out a circle, as shown in Figure 2.5. When ωt = 0, the electric field is directed along the x-axis; when ωt = π ⁄ 4 it is at an angle of 45˚ to the x-axis; and when ωt = π ⁄ 2 the electric field is directed along the y-axis. Thus, when δ = π ⁄ 2 the field traces out a circle in the counter-clockwise direction; this is called right-hand circular polarization because it conforms to the right-hand rule along the direction of propagation. When δ = –π ⁄ 2, the electric field vector traces out a circle in the clockwise direction and is known as left-hand circular polarization. It should be noted that in general, there is no unique way of defining the orientation of the electric field vectors in a wave. That is, the axes of the ellipse do not necessarily conform to the axes of the predefined coordinate system, and the ellipse coordinates will be shifted away from the defined coordinates by an angle given by (2.87). This is particularly true for passive systems, which do not transmit a signal; the electromagnetic waves emitted by a source may be of any orientation. However, the precise angle of the wave coordinate system is not generally useful in passive radiometric systems; what is important is the relative angle or relative phase difference between the field components, as this is what determines the type of polarization. In active systems, the polarization of the reflective wave also may not match that of the transmitted wave, as the source may alter the polarization of the incident wave upon reflecting it.

References [1] [2] [3] [4] [5]

Jackson, J. D., Classical Electrodynamics, 3rd ed., Hoboken, NJ: John Wiley & Sons, 1999. Stratton, J. A., Electromagnetic Theory, New York, NY: McGraw-Hill, 1941. Harrington, R. F., Time-Harmonic Electromagnetic Fields, New York, NY: McGraw-Hill, 1961. Balanis, C. A., Advanced Engineering Electromagnetics, Hoboken, NJ: John Wiley & Sons, 1989. Rothwell, E. J., and M. J. Cloud, Electromagnetics. Boca Raton, FL: CRC Press, 2001.

CHAPTER 3

Electromagnetic Waves in Media In the previous chapter, fundamental concepts of electromagnetic wave propagation were introduced for a general lossless media; in this chapter, the focus is on the propagation of electromagnetic waves through media that is lossy due to conductivity, the effect of boundaries between different media, and properties of specific media of interest in remote security sensing. The media encountered by a propagating wave in remote sensing depends on the kind of measurement being performed, as indicated in Figure 3.1. In a radar application, the wave propagates from the radar antenna through the atmosphere and reflects off the object of interest. The reflected wave then propagates back through the atmosphere before impinging on the receiving antenna. In the case of human presence detection, the transmitted wave encounters the clothing being worn by the person and, if a fraction of the wave energy transmits through the clothing, the wave encounters the human skin. If contraband detection is the goal, the wave may also encounter the contraband beneath the clothing. The wave may also transmit through walls between the antenna and the clothing. In a passive, radiometric application, the wave is generated by natural thermal radiation in the object, which then propagates through the atmosphere to the antenna. If a human is the object of interest, the wave propagates through a clothing layer and perhaps through walls before being incident on the antenna. The specific types of media encountered in remote security sensing, as well as their physical makeup such as thickness, depend on the application. In most cases, however, the propagating wave travels through the atmosphere, and in many situations in security sensing a human is present in the measurement as well, either as the object to be detected or as the background to concealed contraband. Propagating waves thus travel through multiple media types, each with different physical and electromagnetic characteristics that affect the amplitude and phase of the propagating waves. Upon encountering a boundary between two media, part of the wave energy will reflect off the new medium, and part of the energy will transmit into it. It is therefore important to understand the effects of lossy media and media boundaries in order to properly design a remote sensor. For example, if contraband detection through walls using radar is the specified application, the transmitted signal must have enough power to transmit through various wall and clothing materials, reflect off the contraband, and then pass again through the clothing and wall materials and still retain enough power to ensure a reasonable signal-to-noise ratio for detection. This chapter begins by deriving the effects on a propagating electromagnetic wave through a general lossy medium. Following this, the interaction of propagating waves and boundaries between different media are discussed. Finally, the chapter concludes by presenting parameters of specific media that are of interest in microwave and millimeter-wave remote security sensing, including atmospheric 43

44

Microwave and Millimeter-Wave Remote Sensing for Security Applications

Radar

Atmosphere Clothing Air Skin

(a) Radiometer

Atmosphere Clothing Air Skin

(b) Figure 3.1 (a) Diagram of the media encountered in the application of radar to contraband detection. (b) Diagram of the media encountered in the application of radiometry to human presence detection.

effects, attenuation through wall and clothing materials, and parameters of different types of human tissue.

3.1 Plane Wave Propagation in Unbounded Media In a general medium, the time-harmonic Faraday’s law and Ampere’s law were shown in Chapter 2 to be Ñ ´ E = - jωµH

(3.1)

Ñ ´ H = (σ + jω ε)E

(3.2)

With nonzero conductivity, the resulting wave equation is of the form σ ö æ Ñ 2 E - ω 2µε ç 1 - j ÷E = 0 ω εø è

(3.3)

In Chapter 2, it was also shown that a plane wave propagating in the z direction has components only in the x and y directions. Consider a plane wave with an electric field component directed along the x-axis. The solution of (3.3) is then Ex (z) = E0 e

- jω µε 1- j

σ z ωε

= E0 e - jkz

(3.4)

where k = ω µε 1 - j

σ σ = kr 1 - j ωε ωε

(3.5)

3.1

Plane Wave Propagation in Unbounded Media

45

is the complex wave number and kr = ω µε

(3.6)

is the noncomplex wavenumber introduced in Chapter 2. For a lossless media, σ = 0, and (3.5) reduces to kr. The effects of the complex wavenumber on the propagation of the wave can be more easily determined by separating the argument of the exponential into real and imaginary parts. That is, let Ex (z) = E0 e - jkz = E0 e -α z e - j β z

(3.7)

jk = α + jβ = -ω 2 µε + jωµσ

(3.8)

where, from (3.5),

The quantity (3.8) is also called the complex phase constant γ = α + jβ, with which the electric field component can be written Ex (z) = E0 e -γ z

(3.9)

Squaring (3.8) and equating the real and imaginary parts yields the relations α 2 - β 2 = -ω 2µε 2

(3.10)


= ωµσ

(3.11)

from which is derived 1

é æ 2 öù 2 1 æ σ ö ÷ú α =ω µε ê ç 1+ ç 1 ÷ ê2 ç ÷ú è ωε ø øû ë è

(3.12)

1

β =ω

é æ 2 öù 2 1ç æ σ ö ê µε 1 + ç ω ε ÷ + 1÷ú ê2 ç ÷ú è ø øû ë è

(3.13)

The first term α is called the attenuation coefficient, or the absorption coefficient, which is measured in Np·m−1, and β is the phase coefficient, measured in rad·m−1. In (3.7), the wave includes an exponential of the attenuation coefficient multiplied by the distance, which results in a reduction of the amplitude of the wave as it propagates further into the medium; the lost energy is converted to thermal energy in the medium. The phase coefficient alters the phase of the wave as it propagates. Note that for a medium with zero conductivity, α=0

(3.14)

β = ω µε = kr

(3.15)

46

Microwave and Millimeter-Wave Remote Sensing for Security Applications

and the wave is given by Ex (z) = E0 e - jkr z

(3.16)

which is the same form that was derived in Chapter 2. Such a wave does not experience attenuation; thus, nonconducting media are lossless. As the wave propagates in a conducting medium, the amplitude is decreased. The distance at which the wave amplitude is decreased to a value of e−1 of the original amplitude is call the skin depth δ, which is found by e -α z e - j β z = e - z

(3.17)

which yields α = 1, or δ =

1 m α

(3.18)

Certain media can be categorized by the relative value of the conductivity to the product of the angular frequency and permittivity. In particular, the loss tangent tanδ can be defined by tan δ =

σ µε

(3.19)

which is present in the definitions of both the attenuation and phase coefficients. Note that the loss tangent tanδ is not the tangent of the skin depth δ. Materials with large loss tangents have high conductivity and high loss, whereas a low loss tangent indicates a low-loss medium. The phase velocity of the wave can be given in terms of the phase constant through v=

ω β

(3.20)

2π β

(3.21)

and the wavelength can be given by λ=

3.1.1

Good Conducting Media

A medium that has high conductivity relative to the product of the permittivity and permeability is considered to be a good conductor. Such a medium also has high loss, as its attenuation will be significant. A good conducting medium is characterized by σ >> 1 µε

(tan δ >> 1)

(3.22)

The argument in the square root of (3.12) and (3.13) can then be approximated by 2

σ σ æ σ ö +1 » = tan δ 1+ ç ÷ +1 » ωε ωε è ωε ø

(3.23)

3.1

Plane Wave Propagation in Unbounded Media

47

and the resulting attenuation and phase coefficients are therefore α » ω µε

1 tan δ = 2

1 ωµσ 2

(3.24)

β » ω µε

1 tanδ = 2

1 ωµσ 2

(3.25)

and the wave is given by Ex (z) = E0 e

-(1+ j)

ω µσ z 2

(3.26)

From (3.18) and (3.24), the skin depth of a good conducting medium is given by 2 ω µσ

δ =

(3.27)

Because σ is large, the skin depth is small. The skin depth for good conductors, such as gold, copper, and aluminum, is on the order of 8 ´ 10−10 m at 10 GHz. Therefore, the majority of the current in a conductor is confined to the surface; the energy dissipates rapidly as the wave propagates into the medium. A perfect conductor has infinite conductivity, and therefore its skin depth is 0, and a propagating wave cannot penetrate into the medium. Thus, no fields can exist within a perfectly conducting medium. 3.1.2

Good Dielectric Media

In contrast to a good conductor, a good dielectric medium is characterized by a relatively low conductivity relative to the product of the permittivity and permeability, and thus relatively low loss, by σ r' and r - r¢ » r - r¢ × rˆ

(4.33)

The free space Green’s function can then be written g(r, r¢) »

e - jkr e jkr¢×rˆ 4π (r - r¢ × rˆ )

(4.34)

92

Microwave and Millimeter-Wave Remote Sensing for Security Applications

p1

z p2

|r-r`| r

r` y x Figure 4.3

Geometry for the calculation of the far fields.

The term in the denominator affects only the amplitude and can further be approximated by 1 1 r¢ × rˆ 1 (4.35) )» » (1 + r - r¢ × rˆ r r r since r is large. The Green’s function is then given by g(r, r¢) » g(r)e jkr¢×rˆ

(4.36)

where g(r) =

e - jkr 4π r

(4.37)

The magnetic vector potential can then be given by A(r) =

e - jkr J(r¢)e jkr¢×rˆ dV ¢ = g(r) ò J(r¢)e jkr¢×rˆ dV ¢ 4π r Vò¢ V¢

(4.38)

The term in the exponential can be rewritten using r¢ = x¢xˆ + y¢yˆ + z¢zˆ

(4.39)

rˆ = sin θ cosφ xˆ + sin θ sin φ yˆ + cosθ zˆ

(4.40)

kr¢ × rˆ = k sin θ cosφ x¢ + k sin θ sinφ y¢ + k cosθ z¢ = kx x¢ + ky y¢ + kz z¢

(4.41)

and

which yields

The magnetic vector potential can then be written A(r) = g(r) ò ò ò J(x¢, y¢, z¢)e x¢ y¢ z¢

j(kx x¢+ ky y¢+kz z¢)

dx¢dy¢dz¢

(4.42)

4.1

Electromagnetic Potentials

93

The integral is simply the three-dimensional Fourier transform of the current density, �J(kx , ky , kz ) =

ò ò ò J(x¢, y¢, z¢)e

j(kx x¢+ ky y¢+kz z¢)

dx¢dy¢dz¢

(4.43)

x¢ y¢ z¢

and thus A(r) = g(r)�J(kx , ky , kz )

(4.44)

The magnetic vector potential is thus found directly in terms of the Fourier transform of the current density. Although the Fourier transform of the current density is a function of the three wavenumbers kx, ky, and kz, the wavenumbers, as defined in (4.41), are functions only of the two spherical coordinates θ and φ, while the Green’s function accounts for the radial dependence. Thus, the vector potential can be described in terms of the Green’s function and a directional function a that is only a function of the tangential spherical coordinates: A(r) = g(r)a(θ , φ)

(4.45)

where the directional function is defined, in rectangular coordinates, as a = �J x xˆ + �J y yˆ + �J z zˆ

(4.46)

In spherical coordinates, the components of a can be found by aθ = θˆ × a = cos θ cos φ �J x + cos θ sin φ �J y - sin θ �J z

(4.47)

aφ = φˆ × a = - sinφ �J x + cos φ �Jy

(4.48)

The electric and magnetic fields in the far field can then be found using (4.6), (4.16), and (4.45), retaining only the terms that are proportional to r–1. The result is E = - jkη g(r)(θˆaθ + φˆaφ)

(4.49)

H = jkg(r)(θˆaφ - φˆ aθ )

(4.50)

The far field electric and magnetic fields therefore contain components only in the θ and φ directions, which are orthogonal to the radial direction of propagation. This corresponds precisely to the orientation of the fields in a plane wave, as derived in Chapter 2. Thus, the waves in the far field generated by current density can be considered to be planar. A similar analysis can be carried out for the fields generated by magnetic current densities, yielding F(r) = g(r)f (θ , φ)

(4.51)

94

Microwave and Millimeter-Wave Remote Sensing for Security Applications

where f is a directional function associated with the electric vector potential, the components of which are given in terms of the Fourier transform of the magnetic current density by fθ = cosθ cos φ �Jmx + cos θ sin φ �Jmy - sin θ �Jmz

(4.52)

fφ = - sin φ �Jmx + cos φ �Jmy

(4.53)

The fields are then given by E = - jkg(r)(θˆfφ - φˆfθ ) H=-

1 jkg(r)(θˆfθ + φˆ fφ ) η

(4.54) (4.55)

If both electric and magnetic current densities are present, the resulting fields are the superposition of the fields generated by the two current densities separately:

4.1.5

E = - jkg(r) éëθˆ(ηaθ + fφ ) + φˆ(ηa φ - fθ )ùû

(4.56)

é 1 1 ù H = jkg(r) êθˆ(aφ - fθ ) - φˆ(a θ + fφ)ú η η û ë

(4.57)

Infinitesimal Dipole Far Field Radiation

Returning to the example of the infinitesimal dipole antenna with electric current density given by (4.26), the Fourier transform of the current is given by j(k x¢+ k y¢+k z¢) �J(kx , ky , kz ) = zˆ ò ò ò Idlδ (x¢)δ (y¢)δ (z¢)e x y z dx¢dy¢dz¢ = zˆ Idl

(4.58)

x¢ y¢ z¢

Then, from (4.47) and (4.48), the components of the directional function are aθ = - sin θ Idl

(4.59)

aφ = 0

(4.60)

because the current density has only a component in the z direction. The radiated fields are then, from (4.49) and (4.50), - jkr

e E = θˆ jkηIdl sinθ 4π r

(4.61)

- jkr

e sin θ H = φˆ jkIdl 4π r

(4.62)

4.2

Antenna Parameters

95

Referring back to the earlier example of the infinitesimal dipole in Section 4.1.3, it can be seen that (4.61) and (4.62) correspond exactly to the components of (4.28) and (4.29) that are dependent on r –1. This formulation is valid for the far field only, while that of the earlier example is valid for all space. Note that, again, the electric and magnetic fields are orthogonal to each other and to the direction of propagation.

4.2 Antenna Parameters A number of parameters are used to describe various aspects of the performance of an antenna, and this section summarizes the more common parameters used to describe microwave and millimeter-wave antennas in remote sensing applications. Many of the parameters derive from the electromagnetic fields in the far field region and are thus interrelated. The IEEE standard definitions of these and other parameters can be found in [3]. 4.2.1

Radiated Power Density and Total Radiated Power

The radiated power density from an antenna is found from the Poynting vector (power density) calculated from the electric and magnetic fields radiated by the antenna 1 (4.63) S = Re E ´ H* 2

{

}

In the far field, the electric and magnetic fields radiated by the antenna are functions only of θ and φ, E = θˆEθ + φˆ Eφ H=

(4.64)

1 1 (rˆ ´ E) = (φˆ Eθ - θˆEφ ) η η

(4.65)

and the magnitude of the power density radiated by the antenna is S=

1 ( Eθ 2η

2

2

+ Eφ )

(4.66)

where S is measured in W·m–2·str–1. The power density can alternatively be written in terms of the directional function a (or f) as S=

η k2 (aθ 32π 2r 2

2

2

+ aφ )

(4.67)

The total radiated power Pr of an antenna is found by integrating the power density over a closed surface encompassing the antenna: Pr =

òò Sds = òò Sr

4π

where Pr has units of W.

4π

2

sinθ dθ d φ

(4.68)

96

Microwave and Millimeter-Wave Remote Sensing for Security Applications

4.2.2

Antenna Pattern

The antenna pattern, or the radiation intensity, is the radiated power per unit solid angle (W·str –1), and is given by A(θ , φ) = r 2 S =

r2 ( Eθ 2η

2

2

+ Eφ ) =

2 η k2 2 (aθ + aφ ) 2 32π

(4.69)

Note that because the definitions of the electric fields include the Green’s function, they are inversely proportional to r, and the antenna pattern is thus independent of the radial dimension and depends only on θ and φ. Due to the reciprocity theorem [2], the antenna pattern describes the spatial distribution of both the radiation pattern of a transmitting antenna and the reception pattern of a receiving antenna. A common practice is to normalize the antenna pattern to its maximum value Amax and define the normalized antenna pattern as AN (θ , φ) =

A(θ , φ) Amax

(4.70)

which is unitless. The normalized antenna pattern is useful in describing various aspects of the antenna pattern in terms of relative levels. Figure 4.4 shows the threedimensional antenna pattern of a rectangular aperture. A number of prominent characteristics of the antenna pattern will affect the performance of a system in which it is used, and other antenna parameters are derived from the antenna pattern; the antenna pattern is thus an important characteristic of the antenna. The main beam of the antenna is the largest peak in the antenna pattern, and it characterizes the direction in which most of the power is radiated. In z

x Figure 4.4

y

Antenna pattern of a square aperture antenna of length 3λ per side.

4.2

Antenna Parameters

97

θHPBW θNNBW

SLL

θNNBW θHPBW Figure 4.5

Definitions of antenna beamwidths and sidelobe levels.

addition to the direction of the peak, an important characteristic of the main beam is its angular width, or beamwidth, which describes the angle over which the power in the main beam is radiated. The antenna pattern also includes a number of secondary peaks, called sidelobes, through which additional power is radiated. Sidelobes are a major concern in antenna design for remote sensing and antenna applications in general, as they represent undesired directions where signals will also be transmitted or received. In an active radar system, the transmitted signal in a sidelobe may reflect off the ground or other nearby objects, causing large reflected signals that may mask small returns from the more distant object in the main beam. The metric describing sidelobes most often used is the sidelobe level, or the difference between the power radiated by the main beam to the power radiated by the sidelobe, typically expressed in decibels. The highest sidelobes often occur directly adjacent to the main beam and are called the first sidelobes, primary sidelobes, or major sidelobes; the other, smaller sidelobes are referred to as secondary sidelobes or minor sidelobes. Figure 4.5 depicts a typical antenna pattern and shows the definition of the sidelobe level (SLL). 4.2.3

Antenna Pattern Beamwidth

The angular width in a given plane between the points where the radiation intensity is half of the maximum radiation intensity is called the half-power beamwidth, or simply the beamwidth and is shown in Figure 4.5. For a symmetric beam, on the φ = 0 plane, the half-power beamwidth in the θ direction θHPBW is found by θ HPBW = 2θ ¢

(4.71)

Amax 2

(4.72)

where A(θ ¢,0) = or AN (θ ¢,0) =

1 2

(4.73)

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

The angle between the first two nulls adjacent to the main beam is called the null-to-null beamwidth. For a symmetric beam, on the φ = 0 plane, the null-to-null beamwidth in the θ direction θNNBW is found by θ NNBW = 2θ ¢¢

(4.74)

A(θ ¢¢,0) = 0

(4.75)

where

is the first null in the pattern. The half-power beamwidth of a line of current with uniform amplitude is given by θ HPBW » 0.886

λ λ = 50.8° d d

(4.76)

where d is the length of the antenna. The null-to-null beamwidth of a line of current is θ NNBW = 2

λ λ » 114.6° d d

(4.77)

These two values will be derived later when discussing radiation from a rectangular aperture. The sidelobe level of the primary sidelobe for the uniform linear current distribution is approximately 13.2 dB below the main beam peak. If the current distribution is sinusoidal, with a maximum in the center of the antenna and tapering to zero at the ends, the half-power beamwidth is given by θ HPBW » 68.8°

λ d

(4.78)

while the null-to-null beamwidth is θ HPBW » 171.8°

λ d

(4.79)

The sidelobe level for the sinusoidal distribution is 23 dB below the main beam peak. Thus, by tapering the current distribution across the aperture of the antenna, the sidelobes can be reduced; however, the drawback is an increase in the beamwidth. It is a rather general construct in antenna engineering that the reduction of sidelobes results in a wider main beam. Sinusoidal current distributions are more representative of the currents present on a real linear antenna; thus, (4.78) and (4.79) can be used as approximations for the beamwidth of a linear antenna. In a rectangular aperture antenna, the distribution can more closely approximate a uniform distribution in a given dimension, in which case (4.76) and (4.77) are more accurate. For instance, the directivity of a horn antenna can be approximated along either principle dimension by considering the current distribution as a line current. The half-power beamwidth and null-to-null beamwidth of a circular aperture with diameter d and uniform current distribution are given by [4] as

4.2

Antenna Parameters

99

θ HPBW » 58.9°

λ d

(4.80)

λ (4.81) d These relationships demonstrate an important characteristic of the performance of antennas in general: antennas of large size compared to wavelength yield narrow, highly directive beams. Antennas with small dimensions compared to wavelength yield wide, less directive beams. θ NNBW » 139.6°

4.2.4

Antenna Solid Angles

In remote sensing applications, it is often useful to describe some characteristics of the antenna pattern in terms of the solid angles into which various fractions of the transmitted power are radiated. Such parameters will be useful in the derivation of received power densities when radiometry is considered in Chapter 6. The pattern solid angle, or beam solid angle, is the solid angle through which all the radiated power would stream if the power per unit solid angle were constant throughout this solid angle and at the maximum value of the radiation intensity. It is defined as the spatial integral of the normalized antenna pattern, WA =

òò AN dW

(4.82)

4π

and has units of steradians. The main beam solid angle is the spatial integral of the normalized antenna pattern over the extent of the main beam, WM =

òò

AN dW

(4.83)

main beam

The extent of the main beam is generally defined as the angle between the first nulls in the pattern. The minor lobe solid angle is the spatial integration of the antenna pattern over the space excluding the main beam; thus, Wm = W A - W M

(4.84)

The ratio of the main beam solid angle to the pattern solid angle is called the main beam efficiency, εM =

WM WA

(4.85)

and is a measure of the amount of power radiated through the main lobe compared to power directed in other, usually undesired, directions. 4.2.5

Directivity

The directivity of an antenna is the ratio of the radiation intensity in a given direction to the radiation intensity averaged over all directions,

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

D(θ , φ) =

4π A(θ , φ)

òò A(θ, φ)dW

=

4π A(θ, φ) Pr

(4.86)

4π

If no direction is specified, the directivity is typically taken along the direction of maximum radiation intensity. The maximum directivity is given in terms of the maximum antenna pattern by Dmax =

4π Amax Pr

(4.87)

In terms of the normalized antenna pattern, Dmax =

4π Amax

òò A(θ, φ)dW

4π

=

4π

òò AN (θ, φ)dW

(4.88)

4π

Thus, from (4.83), the maximum directivity can be written Dmax =

4π WA

(4.89)

Any real antenna is directive; that is, the antenna pattern is not isotropic, or constant over all space. Isotropic antennas are often useful as mathematical constructs in the analysis and design of antennas, such as in the definition of antenna gain; however, they do not exist in practice [5]. For highly directive antennas, most of the radiated power is in the main beam, and the contribution outside the main beam may be considered negligible in some instances. In such a case, the pattern solid angle can be represented by W A » θBW φ BW

(4.90)

where θBW and φBW are the half-power beamwidths of the main beam in the θ and φ dimensions. The maximum directivity can then be approximated by Dmax »

4π θBW φ BW

(4.91)

Dmax »

41, 253 θBW φ BW

(4.92)

which is given in degrees by

This expression is an approximation for a single antenna with uniform illumination; for a planar array, considered later in this chapter, a more accurate approximation given by [6] is 32, 400 Dmax » (4.93) θBW φBW

4.2

Antenna Parameters

4.2.6

101

Gain

The gain of an antenna is the ratio of the radiated power density in a given direction to the power density of an isotropic antenna with the same input power Pin. The gain is a standard metric of antenna performance and is often given simply as the maximum gain along the direction of maximum radiation intensity. The gain can be related to the directivity through the radiation efficiency of the antenna, which is the ratio of the radiated power and the power input to the antenna, εr =

Pr Pin

(4.94)

The lost power Pl is converted into heat in the antenna material. Because Pin = Pr + Pl

(4.95)

the radiated and lost powers can be given in terms of the radiation efficiency by Pr = ε r Pin

(4.96)

Pl = (1 - ε r )Pin

(4.97)

The gain is defined in terms of the radiated power density of an antenna with input power Pin as G(θ , φ) =

S(θ , φ) Si

(4.98)

where Si is the radiated power density of a lossless isotropic antenna with equal input power Pi. Because the isotropic antenna is lossless, the input power is equal to the isotropic radiated power Pri. Thus, from (4.68), Si =

Pri P = in 2 2 4π r 4π r

(4.99)

Using (4.96), the isotropic radiated power can be related to the radiated power of the nonideal antenna under consideration. Thus, Si =

Pr 1 = 2 4πε r 4πεr r

òò S(θ, φ)dW

(4.100)

4π

The gain is therefore G(θ , φ) = 4πε r

S(θ , φ)

òò S(θ, φ)dW

= ε r D(θ , φ)

(4.101)

4π WA

(4.102)

4π

and the maximum gain is Gmax = ε r Dmax = ε r

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

4.2.7

Aperture Area and Pattern Solid Angle

A relationship that will be useful in the discussion of radiometry is that between the pattern solid angle and the effective area of the antenna aperture. The effective aperture Ae is the ratio of the available power PT at the terminals of a receiving antenna to the power flux density of a plane wave incident on the antenna from a given direction, assuming that the polarization of the antenna is matched to the polarization of the incident wave, as discussed in the next section, and is given by Ae =

PT Sinc

(4.103)

The effective area is given in terms of the physical area of the antenna Ap by Ae = ε A Ap

(4.104)

where 0 £ εA £ 1 is the aperture efficiency, which accounts for conduction losses in the antenna and impedance mismatches. The relationship between the effective aperture area and the pattern solid angle can be found by considering the power due to the fields in the aperture 2

Eap Ae

P1 =

2η

(4.105)

and the power at a distance r 2

P2 =

Er 2 r WA 2η

(4.106)

The electric field at r is related to that in the aperture by [7] Er =

Eap Ae rλ

(4.107)

which holds true for a uniformly illuminated aperture. From (4.106) and (4.107), P2 =

Eap

2

2η λ2

Ae2 W A

(4.108)

If the medium through which the waves propagate is lossless, the radiated power P2 must be equal to the aperture power P1. Thus, equating (4.105) and (4.108) yields Ae =

λ2 WA

(4.109)

Thus, the product of the effective aperture area and the pattern solid angle is equal to the square of the wavelength. The maximum directivity can be given in terms of the effective area by substituting (4.109) into (4.89), yielding Dmax =

4π Ae λ2

(4.110)

4.2

Antenna Parameters

103

From (4.101), the gain is thus Gmax = ε r

4π Ae λ2

(4.111)

A useful approximation of the directivity of an antenna is the assumption that for a given antenna, the effective area is equal to the physical area of the aperture. Then, (4.110) can be used to directly calculate the directivity of an antenna at a given wavelength. If the radiation efficiency is known, the gain may then be found by multiplying the directivity by the efficiency. That is, Gmax » ε r

4π Ap λ2

(4.112)

for antennas with good efficiency. A useful example is that of an isotropic antenna with unity gain. For such a radiator, AN = 1, and the antenna solid angle (4.82) is WA = 4π. The effective area of an isotropic antenna is therefore, from (4.109), Ae,isotropic =

λ2 4π

(4.113)

The effective area of an isotropic radiator therefore scales with the square of the wavelength. 4.2.8

Antenna Temperature and Noise Power

Due to movement of electrons within materials, all objects at a nonzero temperature radiate energy, referred to as thermal radiation and discussed in detail in Chapter 6. Antennas thus intrinsically radiate energy that manifests as noise power at the antenna terminals. At microwave and millimeter-wave frequencies, the power of the radiated energy is proportional to the noise temperature of the antenna, called the antenna noise temperature TA, and is given by PA = kTA Df

(4.114)

where k = 1.38 × 10–23 J·K–1 is Boltzmann’s constant and Df is the bandwidth of the signal. Due to the random nature of thermal fluctuations, the noise power has a Gaussian distribution. In a radiometer, the antenna noise temperature is primarily the result of incident thermal radiation, and the antenna noise power represents the signal of interest; this is discussed further in Chapter 6. 4.2.9

Polarization

The polarization of an antenna is given by the polarization of a wave transmitted by the antenna in a given direction. While generally dependent on angle, the polarization of an antenna is typically considered as that of a wave transmitted along the direction of maximum radiation intensity. A measure of how well an antenna is matched to the polarization of an incident wave is given by the polarization loss factor. Given an incident wave

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

Einc = pˆ inc Einc

(4.115)

where pˆ inc is the unit vector of the incident wave polarization, and the wave in the receiving antenna E a = pˆ a Ea

(4.116)

where pˆ a is the antenna polarization, the loss factor is defined as ε p = pˆ inc × pˆ a = cos Y

(4.117)

where Y is the angle between the two waves.

4.3 Properties of Wire Antennas In this section, the concepts covered in the previous sections will be utilized in examples of radiation from an electric current source. As described in the introduction, radiation sources may be either electric current densities on an antenna or equivalent current densities in an aperture. Linear wire antennas fall under the first category, whereas antennas such as horn and microstrip antennas fall under the latter. Earlier, the radiation fields of an infinitesimal dipole antenna were derived. Due to its infinitesimal linear nature, such an antenna may be used as a differential element to calculate the fields of a finite length linear wire antenna. First, some properties of the infinitesimal dipole antenna will be derived. Following this, the radiation fields and the antenna pattern of a long wire dipole antenna will be considered. For a detailed analysis of linear wire antennas, the reader is referred to [8]. 4.3.1

Infinitesimal Dipole

As shown in Section 4.1, the directional function of an infinitesimal dipole is given by aθ = - sin θ Idl (4.118) As defined by (4.67), the radiated power density is therefore S=

ηk2 Idl 32π r

2

2 2

sin2 θ

(4.119)

and the antenna pattern is A(θ) = r S = 2

ηk2 Idl

2

32π 2

sin2 θ

(4.120)

The maximum point in the antenna pattern is found when sin2θ = 1, yielding Amax =

ηk2 Idl 32π 2

2

(4.121)

4.3

Properties of Wire Antennas

105

θ 0 30

30

60

60 0.5

90

1 90

120

120 150

150 180

Figure 4.6

Normalized antenna pattern of an infinitesimal dipole.

The normalized antenna pattern is therefore AN (θ) = sin2 θ

(4.122)

The antenna pattern is plotted in Figure 4.6. It is toroidally shaped, has nulls at θ = 0° and 180, and is maximum at θ = 90°. The peak in the pattern corresponds to the broadside direction, whereas the nulls correspond to the axis along the length of the antenna. Additionally, due to the symmetrical shape of the antenna in the φ direction, the antenna pattern is constant in φ and depends only on θ. The total power radiated by an infinitesimal dipole is found from (4.68); carrying out the integration results in Pr =

2 òò Sr sin θ dθ dφ =

ηk2 Idl

4π

12π 2

2

(4.123)

The directivity is therefore 3 2 sin θ 2

(4.124)

4π Amax 3 = Pr 2

(4.125)

D(θ , φ) = and the maximum directivity is Dmax =

4.3.2

Long Dipole

A finite-length dipole antenna can be considered to be a superposition of infinitesimal dipoles. Figure 4.7 shows a long (compared to wavelength) dipole antenna of length l oriented along the z axis. The current along a center-fed, linear dipole antenna has been shown experimentally to be approximately sinusoidal along the

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

length of the antenna, with nulls at the ends [8, 9]. The current along the length of the antenna can thus be described by é æl öù I = zˆ I0δ (x ¢)δ (y ¢)sin êk ç - z ¢ ÷ ú è øû ë 2

(4.126)

where the current is zero elsewhere. The Fourier transform of the current density is found by integrating over the length of the antenna, �J = zˆ ò

é æl

öù

ò ò I0δ (x¢)δ (y¢)sin êëk çè 2 - z ¢ ÷ø úû e

j(kx x¢ + ky y ¢ + kz z ¢)

dx ¢dy ¢dz ¢

x¢ y ¢ z ¢

= zˆ

l 2

é æl

öù

ò I0 sin êëk çè 2 - z ¢ ÷ø úû e

jkz z ¢

dz ¢

l 2

(4.127)

The wavenumber is kz = kcosθ; thus, �J = zˆ

l 2

é æl

öù

ò I0 sin êëk çè 2 - z ¢ ÷ø úû e

jkz ¢ cos θ

dz ¢

(4.128)

l 2

The directional function is given by substituting (4.128) into (4.47); carrying out the integration yields é æ1 ö æ1 öù cos ç kl cos θ ÷ - cos ç kl ÷ ú ê è ø è2 ø 2I 2 aθ = - 0 ê ú sin θ k ê ú êë úû

(4.129)

The far field electric and magnetic fields are then é æ1 ö æ1 öù cos ç kl cos θ ÷ - cos ç kl ÷ ú è2 ø è2 ø e - jkr ê Eθ = jηI0 ê ú 2π r ê sin θ ú êë úû z dz l y x

Figure 4.7

Long dipole antenna.

(4.130)

4.4

Aperture Antennas

107

l = 1λ 0 90

90

90

90

180

180

l = 3λ 0

l = 4λ 0

90

90 180

Figure 4.8

l = 2λ 0

90

90 180

Normalized antenna patterns of a long linear dipole with l = 1λ, 2λ, 3λ, 4λ.

é æ1 ö æ1 öù cos ç kl cos θ ÷ - cos ç kl ÷ ú ê è2 ø è2 ø e Hφ = jI0 ê ú 2π r ê sinθ ú êë úû - jkr

(4.131)

The radiated power density from the long dipole can be calculated from either the directional function (4.129) or the electric field (4.130); the result is the same in either case, é æ1 ö æ1 öù cos ç kl cos θ ÷ - cos ç kl ÷ ú η I0 ê è2 ø è2 ø S= 2 2ê ú sin θ 8π r ê ú êë úû

2

2

(4.132)

The antenna pattern is found by A = r2S, yielding

A(θ) =

η I0

2

8π 2

é æ1 ö æ1 öù ê cos çè 2 kl cos θ ÷ø - cos çè 2 kl ÷ø ú ê ú sin θ ê ú ëê ûú

2

(4.133)

Due to the symmetry of the antenna, the antenna pattern is only a function of θ. The normalized antenna pattern is plotted in Figure 4.8 for lengths of l = 1λ , 2λ , 3λ , and 4λ.

4.4 Aperture Antennas The simplicity of the method of calculating the radiated fields introduced in Section 4.1 was predicated on the fact that the potentials could be calculated from current densities existing on surface of the antenna. In an aperture antenna, such as a horn antenna, the radiated fields are also ultimately generated by current sources; however, the antenna, where the wave transitions from a guided wave to a propagating

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

wave, is no longer described as a metal region on which current densities reside. The relevant part of the antenna is the aperture, occupied by free space or a dielectric, where electromagnetic fields exist but no physical current densities do. Thus, in order to use the relatively straightforward method of calculating the radiated fields from the electromagnetic potentials, a relation between the potentials and the fields in the aperture must be devised. Such a relation can be made by using the equivalence principle, with which electromagnetic fields can be replaced by equivalent sources that satisfy the boundary conditions. The equivalence principle was originally devised by Schelkunoff [10, 11] as an extension of Huygen’s principle, which states that the points comprising a wavefront can be considered to be individual point sources generating new wavefronts [2]. Using this principle, the fields in the aperture of an antenna can be replaced by equivalent sources and the potentials can then be used to calculate the radiated fields. 4.4.1

Image Theory

The formulation of the equivalence principle for use in aperture antenna analysis requires a discussion of image theory, which can be derived from the evaluation of the fields generated by sources in the presence of a conducting plane [12]. The problem of primary interest will be the boundary value problem, where the conductor is a perfect electric conductor; however, the dual problem with a perfect magnetic conductor is analogous. Consider a current source density in the presence of a perfect electric conducting plane of infinite extent. The boundary conditions state that the tangential components of the electric field on the conducting boundary must be zero. According to image theory, the boundary conditions can be satisfied by replacing the conductor with free space in which an appropriately oriented image source is placed such that the tangential components of the electric field at the location of the boundary are zero. Figure 4.9 shows the required orientation of the image current, given a real current density in the cases of both a perfect electric conductor and a perfect magnetic conductor. In the case of a perfect electric conductor, a tangential current source has associated with it an image that is in the opposite direction, whereas the dd

dd Perfect electric conductor

Perfect magnetic conductor

J

J J

J

Jm

Jm

Jm

Jm Images Figure 4.9

Sources

Images

Sources

Real and image sources in the presence of a conducting plane.

4.4

Aperture Antennas

109

dd Perfect electric conductor

0

J lim d 0 Jm

2Jm

Figure 4.10 Resulting tangential current densities as the spacing between the source and conducting plane approaches zero.

image is in the same direction for a magnetic source. In the case of a perfect magnetic conductor, the orientations of the images are reversed. An important aspect of the equivalence principle is derived from the result obtained when the distance between the plane and the tangential sources approaches zero. In the limit, the current densities become surface current densities; replacing the conductor with free space and image currents results in the superposition of the real and image sources, since they are both on the surface of the boundary. With a perfect electric conductor, the tangential electric currents cancel one another, as shown in Figure 4.10, resulting in a null current on the surface; thus, electric currents do not exist on a perfect electric conductor. The tangential magnetic currents, however, combine to produce a current density that is twice the real current density. 4.4.2

The Equivalence Principle

Consider the fields E1 and H1, generated by the sources J and Jm, which are in free space. As shown in Figure 4.11, a surface s can be defined that completely encompasses the current densities in the volume V0. The fields outside the surface, in the volume V1, are unchanged. The equivalence principle states that the sources and fields within V0 can be replaced by new fields E0 and H0 with current densities Js and Jms on the surface s, which satisfy the boundary conditions J s = nˆ ´ (H1 - H0 ) E 1, H 1

E1, H1

(4.134)

E 1, H 1 V1

V1

Js E 0, H 0 J

Jm

J

s Figure 4.11 Equivalence principle.

Jms

Jm s

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

Jms = - nˆ ´ (E1 - E0 )

(4.135)

With the new fields and surface currents defined such that (4.134) and (4.135) are satisfied, the fields E1 and H1 in the volume V1 will remain unchanged from the original problem. In replacing the volume V0, the implicit assumption is that it is the fields within V1 that are of interest, rather than the fields within V0. Thus, the problem can be simplified by setting the fields within the surface to be zero. The boundary conditions are then J s = nˆ ´ H1

(4.136)

Jms = - nˆ ´ E1

(4.137)

where E1 and H1 are specified on the surface. The equivalent current densities are now specified in terms of only the fields at the surface s. If the surface is defined to enclose an antenna, such as a horn, and is coincident with the aperture, the fields E1 and H1 are the fields present in the antenna aperture. Thus, equivalent currents can be formed in the aperture using (4.136) and (4.137), and the electromagnetic potentials can be used to calculate the radiated fields. Consider an open-ended waveguide in an infinite ground plane, as shown in Figure 4.12. The aperture contains the electric field Ea and no magnetic field. Using the equivalence principle, a surface s can be defined to be coincident with the ground plane and the aperture, and the field in the aperture can be replaced by an equivalent magnetic current density. The tangential electric fields on the ground plane are zero; thus, no equivalent magnetic current exists outside of the aperture. The magnetic fields outside of the aperture are undefined; therefore, an equivalent electric current can exist on the surface s. Because the fields in the volume of the ground plane (left of the surface) are not of interest, the volume can be replaced by an arbitrary medium. For the analysis of aperture antennas, it is convenient to replace the volume with a perfect electric conductor. Image currents are then generated by the equivalent magnetic current density in the aperture, as well as by the equivalent electric current density on s.

PEC ^ n

Ea

Js=0 ^ Jms=-nxE a

Jms Jms

^ Jms=-2nxE a

Figure 4.12 Equivalence principle for an open-ended waveguide in an infinite ground plane.

4.4

Aperture Antennas

111

Because these are all surface currents, the image of the equivalent electric current density is in the opposite direction, nulling the equivalent current. The image current of the equivalent magnetic current density in the aperture is in the same direction, adding to the equivalent current density. Thus, the result is that the equivalent electric current densities are zero everywhere, and the equivalent magnetic current density is zero outside of the aperture, and in the aperture is Jms = -2nˆ ´ E a

(4.138)

The resulting equivalent problem is that of a magnetic current density (representing the aperture) in free space. From Jms the electric vector potential F can be calculated using (4.51), from which the radiated fields can be calculated using (4.18) and (4.22), or they can be calculated directly using (4.52)–(4.55). In many cases, the antenna under consideration will not be flush with a ground plane, and may be surrounded by free space. The typical approach in such a case is to define the surface s in the plane of the aperture (as if there were a ground plane) and simply assume that the electric and magnetic fields are zero outside of the aperture. Thus, the equivalent currents will only be nonzero within the antenna aperture, and the analysis proceeds as described in the previous example. Although an approximation, this approach provides results that closely match measured data and is highly accurate for the antenna main beam [2]. 4.4.3

Radiation from a Rectangular Aperture

Rectangular apertures are commonly implemented in microwave and millimeterwave remote sensing in the form of horn antennas, waveguide slot antennas, and microstrip antennas, among others. The results from analyzing a general rectangular aperture can be applied as an approximation to most rectangular antenna apertures. Consider a rectangular aperture of dimensions a × b on a ground plane, as shown in Figure 4.13. In the aperture is an electric field given by E a = yˆ E 0

(4.139)

The aperture contains no magnetic field, and the fields outside the aperture are also zero. By the equivalence principle, the field in the aperture can be replace by an equivalent magnetic current density given by Jm = -2nˆ ´ E a = 2xˆ E0

(4.140)

The current exists only within the region –a/2 £ x £ a/2, –b/2 £ y £ b/2. Taking the Fourier transform thus yields �Jmx = 2abE0sinc æç akx ö÷ sinc çæ bky ÷ö è 2 ø è 2 ø

(4.141)

where sinc(α ) =

sin α α

(4.142)

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

z

Ea PEC

PEC a

y

b x Figure 4.13 Rectangular aperture in a ground plane.

The components of the magnetic directional function f are found using (4.52) and (4.53), and are given by æ bky ö æ ak ö fθ = 2abE0cosθ cosφsinc ç x ÷ sinc ç è 2 ø è 2 ÷ø

(4.143)

æ bky ö æ ak ö fφ = -2abE0 sinφ sinc ç x ÷ sinc ç è 2 ø è 2 ÷ø

(4.144)

From (4.54), the electric field components are then given by æ bky ö æ ak ö Eθ = jk2abE0 g(r)sinφ sinc ç x ÷ sinc ç è 2 ø è 2 ÷ø

(4.145)

æ bky ö æ ak ö Eφ = jk2abE0 g(r)cos θ cosφ sinc ç x ÷ sinc ç è 2 ø è 2 ÷ø

(4.146)

The antenna pattern is calculated in terms of the electric field components by (4.69), which yields A(θ , φ) =

1 (abk E0 )2 2 8ηπ

é æ ak ö æ bk ö sinθ sinφ ÷ ´ êsin2 φsinc 2 ç sin θ cos φ ÷ sinc 2 ç è ø è ø 2 2 ë

(4.147)

æ ak ö æ bk öù sinθ sinφ ÷ ú + cos2 θ cos2 φ sinc 2 ç sinθ cosφ ÷ sinc 2 ç è 2 ø è 2 øû where the wavenumbers have been expanded. The maximum value of the term in brackets in (4.147) is 1; thus, the normalized antenna pattern is

Aperture Antennas

113

æ ak ö æ bk ö AN (θ , φ) = sin2 φ sinc 2 ç sinθ cosφ ÷ sinc 2 ç sinθ sinφ ÷ è 2 ø è 2 ø

(4.148)

æ ak ö æ bk ö + cos2 θ cos2 φ sinc 2 ç sinθ cosφ ÷ sinc 2 ç sinθ sinφ ÷ è 2 ø è 2 ø and is plotted in Figure 4.14(a) for the parameters a = 4l, b = 3l. It is often convenient to examine the antenna pattern as a two-dimensional function along a plane through the origin. The logical planes to consider are the x-z z

4λ

3λ x

y

(a) 0

E−plane H−plane

−5 −10 dB

4.4

−15 −20 −25 −30 −1.5

−1

−0.5

0 θ (rad) (b)

0.5

1

1.5

Figure 4.14 (a) Normalized antenna pattern and (b) E-plane and H-plane patterns of a rectangular aperture with a = 4λ, b = 3λ.

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Microwave and Millimeter-Wave Remote Sensing for Security Applications

plane and the y-z plane, as they align with the geometry of the aperture. The y-z plane is oriented along the direction of the electric field, and thus the antenna pattern on this plane is called the E-plane pattern. Similarly, the pattern along the x-z plane aligns with the magnetic field and is called the H-plane pattern. The E-plane pattern is found by evaluating the normalized antenna pattern at the angle φ = π/2, which yields æ bk ö AE (θ) = AN (θ ,φ = π /2) = sinc 2 ç sinθ ÷ è 2 ø

(4.149)

The H-plane pattern is found by setting φ = 0, which results in æ ak ö AH (θ) = AN (θ ,φ = 0) = cos2 θ sinc 2 ç sinθ ÷ è 2 ø

(4.150)

The E-plane and H-plane antenna patterns are plotted in Figure 4.14(b). The half-power beamwidth of the E-plane pattern is found in terms of the angle where the normalized antenna pattern in the main beam is equal to 0.5, æ bk ö sinc 2 ç sin θ H ÷ = 0.5 è 2 ø

(4.151)

This occurs when the argument of the sinc function is equal to approximately 1.391. Thus, bk sin θ H = 1.391 2

(4.152)

λö æ 2.782 ö æ θ H = sin -1 ç = sin -1 ç 0.443 ÷ è kb ÷ø è bø

(4.153)

or

The half-power beamwidth is thus λö æ θ HPBW = 2sin -1 ç 0.443 ÷ è bø

(4.154)

For large apertures where b >> λ, the argument of (4.154) is small, and thus θ HPBW » 0.886

λ b

(4.155)

The null-to-null beamwidth of the E-plane pattern is found in terms of the angle where the pattern reaches its first zero, which occurs when bk sin θ N = π 2

(4.156)

æ 2π ö æ λö θ N = sin -1 ç ÷ = sin -1 ç ÷ è kb ø è bø

(4.157)

Thus,

and the null-to-null beamwidth is æ λö θ NNBW = 2sin -1 ç ÷ è bø

(4.158)

4.4

Aperture Antennas

115

For large apertures where b >> λ, the beamwidth is approximated by θ NNBW » 2

4.4.4

λ b

(4.159)

Radiation from a Circular Aperture

Although rectangular apertures are the most commonly implemented antenna shapes, circular apertures are also commonly used, for instance, in cylindrical horn antennas with circular apertures, and reflector and lens antenna systems. As with a rectangular aperture, the results from the analysis of a general circular aperture may be applied as an approximation to an antenna or antenna system with a circular aperture. Consider the circular aperture of radius a in an infinite ground plane in Figure 4.15(a). The field in the aperture is given by E = yˆ E0

(4.160)

Jm = xˆ 2E0

(4.161)

and the current is thus

for ρ £ a, and is zero elsewhere. The calculation of the radiated fields follows the same procedure as before; however, for the circular aperture the analysis is more easily accomplished using cylindrical coordinates (e.g., see [2]). The resulting electric fields are é J (ak sin θ) ù Eθ = jk4π a2 E0 g(r)sin φ ê2 1 ak sin θ úû ë

(4.162)

é J (ak sin θ) ù Eφ = jk4π a2 E0 g(r)cos θ cos φ ê2 1 ak sin θ úû ë

(4.163)

where J1(x) is the first-order Bessel function of the first kind (see, e.g., [13]). The normalized antenna pattern is é J (ak sin θ) ù AN (θ , φ) = (sin2 φ + cos2 θ cos2 φ ) ê2 1 ak sin θ úû ë

2

(4.164)

and is plotted in Figure 4.15(b) for a = 2λ. The E-plane pattern of the circular aperture is given by é J (ak sin θ) ù AE (θ) = AN (θ , φ = π 2) = ê2 1 ak sin θ úû ë

2

(4.165)

and the H-plane pattern is é J (ak sin θ) ù AH (θ) = AN (θ , φ = 0) = cos2θ ê2 1 ak sin θ úû ë

2

(4.166)

The E-plane and H-plane antenna patterns are plotted in Figure 4.15(c) for a = 3λ. The half-power beamwidth of the E-plane pattern is found in terms of the angle where (4.165) is equal to 0.5, or

Microwave and Millimeter-Wave Remote Sensing for Security Applications z

a

PEC

PEC y

Ea

x

(a) z

2λ x

y

(b) 0 E−plane H−plane

−5 −10 dB

116

−15 −20 −25 −30 −1.5

−1

−0.5

0 θ (rad) (c)

0.5

1

1.5

Figure 4.15 (a) Circular aperture in a ground plane. (b) Normalized antenna pattern and (c) Eplane and H-plane patterns of a circular aperture with a = 2l.

4.5

Antenna Arrays

117

J1(ak sin θ) = 0.3535 ak sin θ

(4.167)

which is satisfied when aksinθ » 1.6, and thus λö æ 1.6 ö æ θ H = sin -1 ç = sin -1 ç 0.25 ÷ è ak ÷ø è aø

(4.168)

The half-power beamwidth is therefore λö æ θ HPBW = 2θH = 2sin -1 ç 0.25 ÷ è aø

(4.169)

which for large apertures (a >> λ) reduces to θ HPBW »

λ 2a

(4.170)

The null-to-null beamwidth is found when J1(ak sin θ) =0 ak sin θ

(4.171)

which is satisfied when ak sin θ » 3.825. Therefore, λö æ 3.825 ö æ θ N = sin -1 ç = sin -1 ç 0.61 ÷ ÷ è ak ø è aø

(4.172)

λö æ θ NNBW = 2sin -1 ç 0.61 ÷ è aø

(4.173)

and

For large apertures, this simplifies to θ NNBW » 1.22

λ a

(4.174)

4.5 Antenna Arrays An antenna array may be described as an antenna comprised of a number of radiating elements whose inputs or outputs are combined to obtain one or more prescribed radiation patterns. The individual elements of an array need not be identical; however, it simplifies the analysis of arrays to consider identical elements. As seen in the previous sections, the directional characteristics of antennas, such as the beamwidth, are dependent on the antenna dimensions; larger antenna dimensions result in narrower beams. Arrays are widely used due to the ability to increase the gain of an antenna and simulate a large aperture using smaller, cheaper discrete elements. However, due to the increase in hardware required in an array, the cost can be prohibitive for some applications, particularly at millimeter-wave frequencies where component costs are greater. Additionally, the discrete nature of such an antenna causes aliasing effects that manifest as additional highly directive beams, called grating lobes, which must be addressed to remove spatial ambiguities. Array elements can also be individually addressed to steer the main beam for scanning.

118

Microwave and Millimeter-Wave Remote Sensing for Security Applications

4.5.1

Linear Array Theory

An antenna array can be considered to be a single large antenna comprised of a number of smaller antennas that are physically separated from one another. Figure 4.16 shows a linear array comprised of N infinitesimal dipoles separated by a distance d, which can be seen to be a discretely sampled version of the long linear dipole antenna considered earlier. The current density along the array is given by

J = zˆ

N -1 2

å

n =-

In dlδ (x ¢)δ (y ¢)δ (z ¢ - nd)

(4.175)

N -1 2

The current is thus a summation of delta functions spaced along the z axis in increments of length d. The Fourier transform of the current density is then �J = zˆ

N -1 2

å ò ò ò In dlδ (x ¢)δ(y ¢)δ(z ¢ - nd)e j(k x¢ +k y¢ +k z ¢)dx ¢dy ¢dz ¢ N -1

n =-

= zˆ

x

y

z

x¢ y¢ z ¢

2

N -1 2

å

In dle jknd cos θ

å

In dle jkz nd = zˆ

N -1 n =2

(4.176)

N -1 2 N -1 n =2

If the current on each antenna element is identical, the Fourier transform of the current density is �J = zˆ Idl

N -1 2

å

e jknd cos θ = zˆ IdlAF(θ)

(4.177)

N -1 n =2

where AF(θ) is called the array factor. A more compact form of the array factor is found by first letting ψ = kdcosθ; the array factor is then

z d

y x

Figure 4.16 Linear array consisting of infinitesimal dipole antennas.

4.5

Antenna Arrays

119

N -1 2

å

AF =

n =-

=e

e jn ψ

N -1 2

(4.178)

æ N -1ö - jç ψ è 2 ø÷

+e

æ N -3ö - jç ψ è 2 ø÷

+…+ e

- jψ

+1+ e

jψ

+…+ e

æ N -3ö jç ψ è 2 ø÷

+e

æ N -1ö jç ψ è 2 ø÷

Multiplying the array factor by ejψ yields AFe

jψ

=e

æ N -3ö ψ - jç è 2 ÷ø

+…+ e

-jψ

+1+ e

jψ

+ …+ e

æ N -1ö ψ jç è 2 ÷ø

+e

æ N +1ö ψ jç è 2 ÷ø

(4.179)

Subtracting (4.178) from (4.179) gives AFe jψ - AF = AF(e j ψ - 1) = e

æ N +1ö jç ψ è 2 ÷ø

-e

æ N -1ö - jç ψ è 2 ÷ø

(4.180)

or

AF =

e

æ N +1 ö ψ jç è 2 ÷ø

æ N -1ö - jç ψ è 2 ÷ø

-e jψ e -1

=

e

j

1 ψ 2

1 j ψ e2

1 æ j 1 Nψ - j Nψ -e 2 çe 2 1 ç j1ψ -j ψ çè e 2 -e 2

ö 1 ÷ sin 2 Nψ ÷ = sin 1 ψ ÷ø 2

(

( )

)

(4.181)

The current (4.177) is therefore given by æ1 ö sin ç Nkd cos θ ÷ è ø 2 �Jz = Idl æ1 ö sin ç kd cos θ ÷ è2 ø

(4.182)

The electric field is then derived from the directional function a using (4.47), resulting in æ1 ö sin ç Nkd cos θ ÷ è2 ø Eθ = jkηIdlg(r)sinθ æ1 ö (4.183) sin ç kd cos θ ÷ è2 ø The electric field of the uniform linear array (4.183) is similar to that derived for the long dipole, however with an additional function that is the ration of two sine functions. As given by (4.183), the maximum value of the array factor is N, the number of elements. It is customary to normalize the array factor by N so that its maximum value is unity; thus, æ1 ö sin ç Nkd cos θ ÷ è2 ø AF(θ) = æ1 ö N sin ç kd cos θ ÷ è2 ø and the electric field is given by Eθ = jkηIdlg(r)N sinθ AF(θ ) = N ´ Ee ´ AF

(4.184)

(4.185)

120

Microwave and Millimeter-Wave Remote Sensing for Security Applications

where Ee is the electric field pattern due to one of the identical elements comprising the array. Equation (4.185) is an expression of pattern multiplication for arrays of identical elements, which states that the total field pattern of an array is given by the multiplication of the pattern of the individual antenna elements and the array factor, scaled by the number of elements N. Thus, the pattern due to the array can be evaluated separately from the individual elements. The factor of N accounts for the additional energy due to the total number of elements in the array. The normalized antenna pattern of the array is therefore given by 1  sin2  N kd cosθ 2  = A (θ ) × A F 2(θ ) AN (θ ) = sin2θ e  2 21 N sin  kd cosθ 2 

(4.186)

where Ae is the antenna pattern of the element. The nulls in the array factor are found when the numerator of (4.184) is zero, which corresponds to 1 Nkd cosθn = ±nπ , 2

n = 1, 2,3,…

(4.187)

Thus, the angles of the nulls are æ nλ ö θn = cos -1 ç è Nd ÷ø

(4.188)

The locations of the maxima of the array factor are found when the denominator of (4.184) is zero, which is true when 1 kd cos θm = ± mπ, 2

m = 0,1, 2,…

(4.189)

and thus the maxima are located at the angles æ mλ ö θm = cos -1 ç è d ÷ø

(4.190)

Multiple maxima can therefore be present in the array factor. This arises from the discrete nature of the current density, which results in spatial aliasing in the form of grating lobes in the pattern. Equation (4.190) produces real angles when mλ /d < 1; thus, in order that only the m = 0 maxima is present in the pattern, the element spacing should be d