Scattering of Electromagnetic Waves: Theories and Applications

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