Leung Tsang, Jin Au Kong, Kung-Hau Ding
Scattering of Electromagnetic Waves
Theories and Applications
By Leung Tsang, Jin Au Kong and Kung-Hau Ding
Leung Tsang, Jin Au Kong, Kung-Hau Ding
Scattering of Electromagnetic Waves
Theories and Applications
By Leung Tsang, Jin Au Kong and Kung-Hau Ding
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A timely and authoritative guide to the state of the art of wave scattering Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces. Written by leading scientists who have made important contributions to wave scattering over three decades, this new work explains the principles, methods, and applications of this rapidly expanding, interdisciplinary field. It covers both introductory and advanced material and provides students and researchers in remote sensing as well as imaging, optics,…mehr
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A timely and authoritative guide to the state of the art of wave scattering
Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces. Written by leading scientists who have made important contributions to wave scattering over three decades, this new work explains the principles, methods, and applications of this rapidly expanding, interdisciplinary field. It covers both introductory and advanced material and provides students and researchers in remote sensing as well as imaging, optics, and electromagnetic theory with a one-stop reference to a wealth of current research results. Plus, Scattering of Electromagnetic Waves contains detailed discussions of both analytical and numerical methods, including cutting-edge techniques for the recovery of earth/land parametric information.
The three volumes are entitled respectively Theories and Applications, Numerical Simulation,and Advanced Topics. In the first volume, Theories and Applications, Leung Tsang (University of Washington) Jin Au Kong (MIT), and Kung-Hau Ding (Air Force Research Lab) cover:
_ Basic theory of electromagnetic scattering
_ Fundamentals of random scattering
_ Characteristics of discrete scatterers and rough surfaces
_ Scattering and emission by layered media
_ Single scattering and applications
_ Radiative transfer theory and solution techniques
_ One-dimensional random rough surface scattering
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces. Written by leading scientists who have made important contributions to wave scattering over three decades, this new work explains the principles, methods, and applications of this rapidly expanding, interdisciplinary field. It covers both introductory and advanced material and provides students and researchers in remote sensing as well as imaging, optics, and electromagnetic theory with a one-stop reference to a wealth of current research results. Plus, Scattering of Electromagnetic Waves contains detailed discussions of both analytical and numerical methods, including cutting-edge techniques for the recovery of earth/land parametric information.
The three volumes are entitled respectively Theories and Applications, Numerical Simulation,and Advanced Topics. In the first volume, Theories and Applications, Leung Tsang (University of Washington) Jin Au Kong (MIT), and Kung-Hau Ding (Air Force Research Lab) cover:
_ Basic theory of electromagnetic scattering
_ Fundamentals of random scattering
_ Characteristics of discrete scatterers and rough surfaces
_ Scattering and emission by layered media
_ Single scattering and applications
_ Radiative transfer theory and solution techniques
_ One-dimensional random rough surface scattering
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Wiley Series in Remote Sensing and Image Processing 1
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 440
- Erscheinungstermin: 31. Juli 2000
- Englisch
- Abmessung: 240mm x 161mm x 28mm
- Gewicht: 709g
- ISBN-13: 9780471387992
- ISBN-10: 0471387991
- Artikelnr.: 14920035
- Wiley Series in Remote Sensing and Image Processing 1
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 440
- Erscheinungstermin: 31. Juli 2000
- Englisch
- Abmessung: 240mm x 161mm x 28mm
- Gewicht: 709g
- ISBN-13: 9780471387992
- ISBN-10: 0471387991
- Artikelnr.: 14920035
Leung Tsang is the author of Scattering of Electromagnetic Waves: Theories and Applications, published by Wiley. Jin Au Kong was an American expert in applied electromagnetics. He was a 74th-generation lineal descendent of the famous Chinese philosopher Confucius.
PREFACE xi
CHAPTER 1 INTRODUCTION TO ELECTROMAGNETIC SCATTERING BY A SINGLE PARTICLE 1
1 Basic Scattering Parameters 2
1.1 Scattering Amplitudes and Cross Sections 2
1.2 Scattering Amplitude Matrix 6
2 Rayleigh Scattering 9
2.1 Rayleigh Scattering by a Small Particle 9
2.2 Rayleigh Scattering by a Sphere 10
2.3 Rayleigh Scattering by an Ellipsoid 12
2.4 Scattering Dyads 14
3 Integral Representations of Scattering and Born Approximation 16
3.1 Integral Expression for Scattering Amplitude 16
3.2 Born Approximation 18
4 Plane Waves, Cylindrical Waves, and Spherical Waves 21
4.1 Cartesian Coordinates: Plane Waves 21
4.2 Cylindrical Waves 22
4.3 Spherical Waves 24
5 Acoustic Scattering 30
6 Scattering by Spheres, Cylinders, and Disks 32
6.1 Mie Scattering 32
6.2 Scattering by a Finite Length Cylinder Using the Infinite Cylinder
Approximation 41
6.3 Scattering by a Disk Based on the Infinite Disk Approximation 46
References and Additional Readings 52
CHAPTER 2 BASIC THEORY OF ELECTROMAGNETIC SCATTERING 53
1 Dyadic Green's Function 54
1.1 Green's Functions 54
1.2 Plane Wave Representation 55
1.3 Cylindrical Waves 57
1.4 Spherical Waves 59
2 Huygens' Principle and Extinction Theorem 60
3 Active Remote Sensing and Bistatic Scattering Coefficients 66
4 Optical Theorem 68
5 Reciprocity and Symmetry 73
5.1 Reciprocity 73
5.2 Reciprocal Relations for Bistatic Scattering Coefficients and
Scattering Amplitudes 75
5.3 Symmetry Relations for Dyadic Green's Function 79
6 Eulerian Angles of Rotation 81
7 T-Matrix 83
7.1 T-Matrix and Relation to Scattering Amplitudes 83
7.2 Unitarity and Symmetry 88
8 Extended Boundary Condition 91
8.1 Extended Boundary Condition Technique 91
8.2 Spheres 97
8.2.1 Scattering and Absorption for Arbitrary Excitation 100
8.2.2 Mie Scattering of Coated Sphere 102
8.3 Spheroids 104
References and Additional Readings 106
CHAPTER 3 FUNDAMENTALS OF RANDOM SCATTERING 107
1 Radar Equation for Conglomeration of Scatterers 108
2 Stokes Parameters and Phase Matrices 116
2.1 Elliptical Polarization, Stokes Parameters, Partial Polarization 116
2.2 Stokes Matrix 123
2.3 Scattering per Unit Volume and Phase Matrix 124
2.4 Rayleigh Phase Matrix 127
2.5 Phase Matrix of Random Media 129
3 Fluctuating Fields 131
3.1 Coherent and Incoherent Fields 131
3.2 Probability Distribution of Scattered Fields and Polarimetric
Description 132
4 Specific Intensity 140
5 Passive Remote Sensing 145
5.1 Planck's Radiation Law and Brightness Temperature 145
5.2 KirchhofT's Law 149
5.3 Fluctuation Dissipation Theorem 152
5.4 Emissivity of Four Stokes Parameters 155
6 Correlation Function of Fields 161
References and Additional Readings 165
CHAPTER 4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES 167
1 Ice 168
2 Snow 170
3 Vegetation 171
4 Atmosphere 172
5 Correlation Function and Pair Distribution Function 173
5.1 Correlation Function 174
5.2 Pair Distribution Function 176
6 Gaussian Rough Surface and Spectral Density 179
7 Soil and Rocky Surfaces 184
8 Ocean Surface 185
References and Additional Readings 195
CHAPTER 5 SCATTERING AND EMISSION BY LAYERED MEDIA 199
1 Incoherent Approach of Radiative Transfer 200
2 Wave Approach 203
2.1 Reflection and Transmission 203
2.2 Dyadic Green's Function for Stratified Medium 207
2.3 Brightness Temperatures for a Stratified Medium with Temperature
Distribution 212
3 Comparison Between Incoherent Approach and Coherent Approach 217
4 Applications to Passive Remote Sensing of Soil 220
References and Additional Readings 229
CHAPTER 6 SINGLE SCATTERING AND APPLICATIONS 231
1 Single Scattering and Particle Position Correlation 232
2 Applications of Single Scattering 237
2.1 Synthetic Aperture Radar 237
2.2 Interferometric SAR 248
2.3 Active Remote Sensing of Half-Space Random Media 252
References and Additional Readings 258
CHAPTER 7 RADIATIVE TRANSFER THEORY 259
1 Scalar Radiative Transfer Theory 260
2 Vector Radiative Transfer Theory 269
2.1 Phase Matrix of Independent Scattering 269
2.2 Extinction Matrix 272
2.3 Emission Vector 275
2.4 Boundary Conditions 283
References and Additional Readings 286
CHAPTER 8 SOLUTION TECHNIQUES OF RADIATIVE TRANSFER THEORY 287
1 Iterative Method 288
1.1 Iterative Procedure 288
1.2 Integral Equation for Scattering Problems 293
1.3 Active Remote Sensing of a Half-Space of Spherical Particles 298
1.4 Active Remote Sensing of a Layer of Nonspherical Particles 303
1.4.1 Numerical Illustrations with Finite Dielectric Cylinders 310
1.5 Second-Order Scattering from Isotropic Point Scatterers 322
2 Discrete Ordinate-Eigenanalysis Method 324
2.1 Radiative Transfer Solution for Laminar Structures 324
2.2 Numerical Procedure of Discrete Ordinate Method: Normal Incidence 328
2.3 Active Remote Sensing: Oblique Incidence 337
2.4 Discrete Ordinate Method for Passive Remote Sensing 343
2.5 Passive Remote Sensing of a Three-Dimensional Random Medium 349
2.6 Passive Remote Sensing of a Layer of Mie Scatterers Overlying a
Dielectric Half-Space 352
3 Invariant Imbedding 362
3.1 One-Dimensional Problem 363
3.2 Passive Remote Sensing of a Three-Dimensional Scattering Medium with
Inhomogeneous Profiles 370
3.3 Passive Remote Sensing of a Three-Dimensional Random Medium 373
3.4 Thermal Emission of Layers of Spherical Scatterers in the Presence of
Inhomogeneous Absorption and Temperature Profiles 374
4 Diffusion Approximation 380
References and Additional Readings 386
CHAPTER 9 ONE-DIMENSIONAL RANDOM ROUGH SURFACE SCATTERING 389
1 Introduction 390
2 Statistics of Random Rough Surface 392
2.1 Statistics, Correlation Function and Spectral Density 392
2.2 Characteristic Functions 396
3 Small Perturbation Method 397
3.1 Dirichlet Problem for One-Dimensional Surface 397
3.2 Neumann Problem for One-Dimensional Surface 403
4 Kirchhoff Approach 407
4.1 Dirichlet Problem for One-Dimensional Surface 408
4.2 Neumann Problem for One-Dimensional Surface 415
References and Additional Readings 417
INDEX 419
CHAPTER 1 INTRODUCTION TO ELECTROMAGNETIC SCATTERING BY A SINGLE PARTICLE 1
1 Basic Scattering Parameters 2
1.1 Scattering Amplitudes and Cross Sections 2
1.2 Scattering Amplitude Matrix 6
2 Rayleigh Scattering 9
2.1 Rayleigh Scattering by a Small Particle 9
2.2 Rayleigh Scattering by a Sphere 10
2.3 Rayleigh Scattering by an Ellipsoid 12
2.4 Scattering Dyads 14
3 Integral Representations of Scattering and Born Approximation 16
3.1 Integral Expression for Scattering Amplitude 16
3.2 Born Approximation 18
4 Plane Waves, Cylindrical Waves, and Spherical Waves 21
4.1 Cartesian Coordinates: Plane Waves 21
4.2 Cylindrical Waves 22
4.3 Spherical Waves 24
5 Acoustic Scattering 30
6 Scattering by Spheres, Cylinders, and Disks 32
6.1 Mie Scattering 32
6.2 Scattering by a Finite Length Cylinder Using the Infinite Cylinder
Approximation 41
6.3 Scattering by a Disk Based on the Infinite Disk Approximation 46
References and Additional Readings 52
CHAPTER 2 BASIC THEORY OF ELECTROMAGNETIC SCATTERING 53
1 Dyadic Green's Function 54
1.1 Green's Functions 54
1.2 Plane Wave Representation 55
1.3 Cylindrical Waves 57
1.4 Spherical Waves 59
2 Huygens' Principle and Extinction Theorem 60
3 Active Remote Sensing and Bistatic Scattering Coefficients 66
4 Optical Theorem 68
5 Reciprocity and Symmetry 73
5.1 Reciprocity 73
5.2 Reciprocal Relations for Bistatic Scattering Coefficients and
Scattering Amplitudes 75
5.3 Symmetry Relations for Dyadic Green's Function 79
6 Eulerian Angles of Rotation 81
7 T-Matrix 83
7.1 T-Matrix and Relation to Scattering Amplitudes 83
7.2 Unitarity and Symmetry 88
8 Extended Boundary Condition 91
8.1 Extended Boundary Condition Technique 91
8.2 Spheres 97
8.2.1 Scattering and Absorption for Arbitrary Excitation 100
8.2.2 Mie Scattering of Coated Sphere 102
8.3 Spheroids 104
References and Additional Readings 106
CHAPTER 3 FUNDAMENTALS OF RANDOM SCATTERING 107
1 Radar Equation for Conglomeration of Scatterers 108
2 Stokes Parameters and Phase Matrices 116
2.1 Elliptical Polarization, Stokes Parameters, Partial Polarization 116
2.2 Stokes Matrix 123
2.3 Scattering per Unit Volume and Phase Matrix 124
2.4 Rayleigh Phase Matrix 127
2.5 Phase Matrix of Random Media 129
3 Fluctuating Fields 131
3.1 Coherent and Incoherent Fields 131
3.2 Probability Distribution of Scattered Fields and Polarimetric
Description 132
4 Specific Intensity 140
5 Passive Remote Sensing 145
5.1 Planck's Radiation Law and Brightness Temperature 145
5.2 KirchhofT's Law 149
5.3 Fluctuation Dissipation Theorem 152
5.4 Emissivity of Four Stokes Parameters 155
6 Correlation Function of Fields 161
References and Additional Readings 165
CHAPTER 4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES 167
1 Ice 168
2 Snow 170
3 Vegetation 171
4 Atmosphere 172
5 Correlation Function and Pair Distribution Function 173
5.1 Correlation Function 174
5.2 Pair Distribution Function 176
6 Gaussian Rough Surface and Spectral Density 179
7 Soil and Rocky Surfaces 184
8 Ocean Surface 185
References and Additional Readings 195
CHAPTER 5 SCATTERING AND EMISSION BY LAYERED MEDIA 199
1 Incoherent Approach of Radiative Transfer 200
2 Wave Approach 203
2.1 Reflection and Transmission 203
2.2 Dyadic Green's Function for Stratified Medium 207
2.3 Brightness Temperatures for a Stratified Medium with Temperature
Distribution 212
3 Comparison Between Incoherent Approach and Coherent Approach 217
4 Applications to Passive Remote Sensing of Soil 220
References and Additional Readings 229
CHAPTER 6 SINGLE SCATTERING AND APPLICATIONS 231
1 Single Scattering and Particle Position Correlation 232
2 Applications of Single Scattering 237
2.1 Synthetic Aperture Radar 237
2.2 Interferometric SAR 248
2.3 Active Remote Sensing of Half-Space Random Media 252
References and Additional Readings 258
CHAPTER 7 RADIATIVE TRANSFER THEORY 259
1 Scalar Radiative Transfer Theory 260
2 Vector Radiative Transfer Theory 269
2.1 Phase Matrix of Independent Scattering 269
2.2 Extinction Matrix 272
2.3 Emission Vector 275
2.4 Boundary Conditions 283
References and Additional Readings 286
CHAPTER 8 SOLUTION TECHNIQUES OF RADIATIVE TRANSFER THEORY 287
1 Iterative Method 288
1.1 Iterative Procedure 288
1.2 Integral Equation for Scattering Problems 293
1.3 Active Remote Sensing of a Half-Space of Spherical Particles 298
1.4 Active Remote Sensing of a Layer of Nonspherical Particles 303
1.4.1 Numerical Illustrations with Finite Dielectric Cylinders 310
1.5 Second-Order Scattering from Isotropic Point Scatterers 322
2 Discrete Ordinate-Eigenanalysis Method 324
2.1 Radiative Transfer Solution for Laminar Structures 324
2.2 Numerical Procedure of Discrete Ordinate Method: Normal Incidence 328
2.3 Active Remote Sensing: Oblique Incidence 337
2.4 Discrete Ordinate Method for Passive Remote Sensing 343
2.5 Passive Remote Sensing of a Three-Dimensional Random Medium 349
2.6 Passive Remote Sensing of a Layer of Mie Scatterers Overlying a
Dielectric Half-Space 352
3 Invariant Imbedding 362
3.1 One-Dimensional Problem 363
3.2 Passive Remote Sensing of a Three-Dimensional Scattering Medium with
Inhomogeneous Profiles 370
3.3 Passive Remote Sensing of a Three-Dimensional Random Medium 373
3.4 Thermal Emission of Layers of Spherical Scatterers in the Presence of
Inhomogeneous Absorption and Temperature Profiles 374
4 Diffusion Approximation 380
References and Additional Readings 386
CHAPTER 9 ONE-DIMENSIONAL RANDOM ROUGH SURFACE SCATTERING 389
1 Introduction 390
2 Statistics of Random Rough Surface 392
2.1 Statistics, Correlation Function and Spectral Density 392
2.2 Characteristic Functions 396
3 Small Perturbation Method 397
3.1 Dirichlet Problem for One-Dimensional Surface 397
3.2 Neumann Problem for One-Dimensional Surface 403
4 Kirchhoff Approach 407
4.1 Dirichlet Problem for One-Dimensional Surface 408
4.2 Neumann Problem for One-Dimensional Surface 415
References and Additional Readings 417
INDEX 419
PREFACE xi
CHAPTER 1 INTRODUCTION TO ELECTROMAGNETIC SCATTERING BY A SINGLE PARTICLE 1
1 Basic Scattering Parameters 2
1.1 Scattering Amplitudes and Cross Sections 2
1.2 Scattering Amplitude Matrix 6
2 Rayleigh Scattering 9
2.1 Rayleigh Scattering by a Small Particle 9
2.2 Rayleigh Scattering by a Sphere 10
2.3 Rayleigh Scattering by an Ellipsoid 12
2.4 Scattering Dyads 14
3 Integral Representations of Scattering and Born Approximation 16
3.1 Integral Expression for Scattering Amplitude 16
3.2 Born Approximation 18
4 Plane Waves, Cylindrical Waves, and Spherical Waves 21
4.1 Cartesian Coordinates: Plane Waves 21
4.2 Cylindrical Waves 22
4.3 Spherical Waves 24
5 Acoustic Scattering 30
6 Scattering by Spheres, Cylinders, and Disks 32
6.1 Mie Scattering 32
6.2 Scattering by a Finite Length Cylinder Using the Infinite Cylinder
Approximation 41
6.3 Scattering by a Disk Based on the Infinite Disk Approximation 46
References and Additional Readings 52
CHAPTER 2 BASIC THEORY OF ELECTROMAGNETIC SCATTERING 53
1 Dyadic Green's Function 54
1.1 Green's Functions 54
1.2 Plane Wave Representation 55
1.3 Cylindrical Waves 57
1.4 Spherical Waves 59
2 Huygens' Principle and Extinction Theorem 60
3 Active Remote Sensing and Bistatic Scattering Coefficients 66
4 Optical Theorem 68
5 Reciprocity and Symmetry 73
5.1 Reciprocity 73
5.2 Reciprocal Relations for Bistatic Scattering Coefficients and
Scattering Amplitudes 75
5.3 Symmetry Relations for Dyadic Green's Function 79
6 Eulerian Angles of Rotation 81
7 T-Matrix 83
7.1 T-Matrix and Relation to Scattering Amplitudes 83
7.2 Unitarity and Symmetry 88
8 Extended Boundary Condition 91
8.1 Extended Boundary Condition Technique 91
8.2 Spheres 97
8.2.1 Scattering and Absorption for Arbitrary Excitation 100
8.2.2 Mie Scattering of Coated Sphere 102
8.3 Spheroids 104
References and Additional Readings 106
CHAPTER 3 FUNDAMENTALS OF RANDOM SCATTERING 107
1 Radar Equation for Conglomeration of Scatterers 108
2 Stokes Parameters and Phase Matrices 116
2.1 Elliptical Polarization, Stokes Parameters, Partial Polarization 116
2.2 Stokes Matrix 123
2.3 Scattering per Unit Volume and Phase Matrix 124
2.4 Rayleigh Phase Matrix 127
2.5 Phase Matrix of Random Media 129
3 Fluctuating Fields 131
3.1 Coherent and Incoherent Fields 131
3.2 Probability Distribution of Scattered Fields and Polarimetric
Description 132
4 Specific Intensity 140
5 Passive Remote Sensing 145
5.1 Planck's Radiation Law and Brightness Temperature 145
5.2 KirchhofT's Law 149
5.3 Fluctuation Dissipation Theorem 152
5.4 Emissivity of Four Stokes Parameters 155
6 Correlation Function of Fields 161
References and Additional Readings 165
CHAPTER 4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES 167
1 Ice 168
2 Snow 170
3 Vegetation 171
4 Atmosphere 172
5 Correlation Function and Pair Distribution Function 173
5.1 Correlation Function 174
5.2 Pair Distribution Function 176
6 Gaussian Rough Surface and Spectral Density 179
7 Soil and Rocky Surfaces 184
8 Ocean Surface 185
References and Additional Readings 195
CHAPTER 5 SCATTERING AND EMISSION BY LAYERED MEDIA 199
1 Incoherent Approach of Radiative Transfer 200
2 Wave Approach 203
2.1 Reflection and Transmission 203
2.2 Dyadic Green's Function for Stratified Medium 207
2.3 Brightness Temperatures for a Stratified Medium with Temperature
Distribution 212
3 Comparison Between Incoherent Approach and Coherent Approach 217
4 Applications to Passive Remote Sensing of Soil 220
References and Additional Readings 229
CHAPTER 6 SINGLE SCATTERING AND APPLICATIONS 231
1 Single Scattering and Particle Position Correlation 232
2 Applications of Single Scattering 237
2.1 Synthetic Aperture Radar 237
2.2 Interferometric SAR 248
2.3 Active Remote Sensing of Half-Space Random Media 252
References and Additional Readings 258
CHAPTER 7 RADIATIVE TRANSFER THEORY 259
1 Scalar Radiative Transfer Theory 260
2 Vector Radiative Transfer Theory 269
2.1 Phase Matrix of Independent Scattering 269
2.2 Extinction Matrix 272
2.3 Emission Vector 275
2.4 Boundary Conditions 283
References and Additional Readings 286
CHAPTER 8 SOLUTION TECHNIQUES OF RADIATIVE TRANSFER THEORY 287
1 Iterative Method 288
1.1 Iterative Procedure 288
1.2 Integral Equation for Scattering Problems 293
1.3 Active Remote Sensing of a Half-Space of Spherical Particles 298
1.4 Active Remote Sensing of a Layer of Nonspherical Particles 303
1.4.1 Numerical Illustrations with Finite Dielectric Cylinders 310
1.5 Second-Order Scattering from Isotropic Point Scatterers 322
2 Discrete Ordinate-Eigenanalysis Method 324
2.1 Radiative Transfer Solution for Laminar Structures 324
2.2 Numerical Procedure of Discrete Ordinate Method: Normal Incidence 328
2.3 Active Remote Sensing: Oblique Incidence 337
2.4 Discrete Ordinate Method for Passive Remote Sensing 343
2.5 Passive Remote Sensing of a Three-Dimensional Random Medium 349
2.6 Passive Remote Sensing of a Layer of Mie Scatterers Overlying a
Dielectric Half-Space 352
3 Invariant Imbedding 362
3.1 One-Dimensional Problem 363
3.2 Passive Remote Sensing of a Three-Dimensional Scattering Medium with
Inhomogeneous Profiles 370
3.3 Passive Remote Sensing of a Three-Dimensional Random Medium 373
3.4 Thermal Emission of Layers of Spherical Scatterers in the Presence of
Inhomogeneous Absorption and Temperature Profiles 374
4 Diffusion Approximation 380
References and Additional Readings 386
CHAPTER 9 ONE-DIMENSIONAL RANDOM ROUGH SURFACE SCATTERING 389
1 Introduction 390
2 Statistics of Random Rough Surface 392
2.1 Statistics, Correlation Function and Spectral Density 392
2.2 Characteristic Functions 396
3 Small Perturbation Method 397
3.1 Dirichlet Problem for One-Dimensional Surface 397
3.2 Neumann Problem for One-Dimensional Surface 403
4 Kirchhoff Approach 407
4.1 Dirichlet Problem for One-Dimensional Surface 408
4.2 Neumann Problem for One-Dimensional Surface 415
References and Additional Readings 417
INDEX 419
CHAPTER 1 INTRODUCTION TO ELECTROMAGNETIC SCATTERING BY A SINGLE PARTICLE 1
1 Basic Scattering Parameters 2
1.1 Scattering Amplitudes and Cross Sections 2
1.2 Scattering Amplitude Matrix 6
2 Rayleigh Scattering 9
2.1 Rayleigh Scattering by a Small Particle 9
2.2 Rayleigh Scattering by a Sphere 10
2.3 Rayleigh Scattering by an Ellipsoid 12
2.4 Scattering Dyads 14
3 Integral Representations of Scattering and Born Approximation 16
3.1 Integral Expression for Scattering Amplitude 16
3.2 Born Approximation 18
4 Plane Waves, Cylindrical Waves, and Spherical Waves 21
4.1 Cartesian Coordinates: Plane Waves 21
4.2 Cylindrical Waves 22
4.3 Spherical Waves 24
5 Acoustic Scattering 30
6 Scattering by Spheres, Cylinders, and Disks 32
6.1 Mie Scattering 32
6.2 Scattering by a Finite Length Cylinder Using the Infinite Cylinder
Approximation 41
6.3 Scattering by a Disk Based on the Infinite Disk Approximation 46
References and Additional Readings 52
CHAPTER 2 BASIC THEORY OF ELECTROMAGNETIC SCATTERING 53
1 Dyadic Green's Function 54
1.1 Green's Functions 54
1.2 Plane Wave Representation 55
1.3 Cylindrical Waves 57
1.4 Spherical Waves 59
2 Huygens' Principle and Extinction Theorem 60
3 Active Remote Sensing and Bistatic Scattering Coefficients 66
4 Optical Theorem 68
5 Reciprocity and Symmetry 73
5.1 Reciprocity 73
5.2 Reciprocal Relations for Bistatic Scattering Coefficients and
Scattering Amplitudes 75
5.3 Symmetry Relations for Dyadic Green's Function 79
6 Eulerian Angles of Rotation 81
7 T-Matrix 83
7.1 T-Matrix and Relation to Scattering Amplitudes 83
7.2 Unitarity and Symmetry 88
8 Extended Boundary Condition 91
8.1 Extended Boundary Condition Technique 91
8.2 Spheres 97
8.2.1 Scattering and Absorption for Arbitrary Excitation 100
8.2.2 Mie Scattering of Coated Sphere 102
8.3 Spheroids 104
References and Additional Readings 106
CHAPTER 3 FUNDAMENTALS OF RANDOM SCATTERING 107
1 Radar Equation for Conglomeration of Scatterers 108
2 Stokes Parameters and Phase Matrices 116
2.1 Elliptical Polarization, Stokes Parameters, Partial Polarization 116
2.2 Stokes Matrix 123
2.3 Scattering per Unit Volume and Phase Matrix 124
2.4 Rayleigh Phase Matrix 127
2.5 Phase Matrix of Random Media 129
3 Fluctuating Fields 131
3.1 Coherent and Incoherent Fields 131
3.2 Probability Distribution of Scattered Fields and Polarimetric
Description 132
4 Specific Intensity 140
5 Passive Remote Sensing 145
5.1 Planck's Radiation Law and Brightness Temperature 145
5.2 KirchhofT's Law 149
5.3 Fluctuation Dissipation Theorem 152
5.4 Emissivity of Four Stokes Parameters 155
6 Correlation Function of Fields 161
References and Additional Readings 165
CHAPTER 4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES 167
1 Ice 168
2 Snow 170
3 Vegetation 171
4 Atmosphere 172
5 Correlation Function and Pair Distribution Function 173
5.1 Correlation Function 174
5.2 Pair Distribution Function 176
6 Gaussian Rough Surface and Spectral Density 179
7 Soil and Rocky Surfaces 184
8 Ocean Surface 185
References and Additional Readings 195
CHAPTER 5 SCATTERING AND EMISSION BY LAYERED MEDIA 199
1 Incoherent Approach of Radiative Transfer 200
2 Wave Approach 203
2.1 Reflection and Transmission 203
2.2 Dyadic Green's Function for Stratified Medium 207
2.3 Brightness Temperatures for a Stratified Medium with Temperature
Distribution 212
3 Comparison Between Incoherent Approach and Coherent Approach 217
4 Applications to Passive Remote Sensing of Soil 220
References and Additional Readings 229
CHAPTER 6 SINGLE SCATTERING AND APPLICATIONS 231
1 Single Scattering and Particle Position Correlation 232
2 Applications of Single Scattering 237
2.1 Synthetic Aperture Radar 237
2.2 Interferometric SAR 248
2.3 Active Remote Sensing of Half-Space Random Media 252
References and Additional Readings 258
CHAPTER 7 RADIATIVE TRANSFER THEORY 259
1 Scalar Radiative Transfer Theory 260
2 Vector Radiative Transfer Theory 269
2.1 Phase Matrix of Independent Scattering 269
2.2 Extinction Matrix 272
2.3 Emission Vector 275
2.4 Boundary Conditions 283
References and Additional Readings 286
CHAPTER 8 SOLUTION TECHNIQUES OF RADIATIVE TRANSFER THEORY 287
1 Iterative Method 288
1.1 Iterative Procedure 288
1.2 Integral Equation for Scattering Problems 293
1.3 Active Remote Sensing of a Half-Space of Spherical Particles 298
1.4 Active Remote Sensing of a Layer of Nonspherical Particles 303
1.4.1 Numerical Illustrations with Finite Dielectric Cylinders 310
1.5 Second-Order Scattering from Isotropic Point Scatterers 322
2 Discrete Ordinate-Eigenanalysis Method 324
2.1 Radiative Transfer Solution for Laminar Structures 324
2.2 Numerical Procedure of Discrete Ordinate Method: Normal Incidence 328
2.3 Active Remote Sensing: Oblique Incidence 337
2.4 Discrete Ordinate Method for Passive Remote Sensing 343
2.5 Passive Remote Sensing of a Three-Dimensional Random Medium 349
2.6 Passive Remote Sensing of a Layer of Mie Scatterers Overlying a
Dielectric Half-Space 352
3 Invariant Imbedding 362
3.1 One-Dimensional Problem 363
3.2 Passive Remote Sensing of a Three-Dimensional Scattering Medium with
Inhomogeneous Profiles 370
3.3 Passive Remote Sensing of a Three-Dimensional Random Medium 373
3.4 Thermal Emission of Layers of Spherical Scatterers in the Presence of
Inhomogeneous Absorption and Temperature Profiles 374
4 Diffusion Approximation 380
References and Additional Readings 386
CHAPTER 9 ONE-DIMENSIONAL RANDOM ROUGH SURFACE SCATTERING 389
1 Introduction 390
2 Statistics of Random Rough Surface 392
2.1 Statistics, Correlation Function and Spectral Density 392
2.2 Characteristic Functions 396
3 Small Perturbation Method 397
3.1 Dirichlet Problem for One-Dimensional Surface 397
3.2 Neumann Problem for One-Dimensional Surface 403
4 Kirchhoff Approach 407
4.1 Dirichlet Problem for One-Dimensional Surface 408
4.2 Neumann Problem for One-Dimensional Surface 415
References and Additional Readings 417
INDEX 419