Wave Propagation and Scattering in Random MediaISBN: 9780780347175
600 pages
February 1999, WileyIEEE Press

 Wave characteristics in aerosols and hydrometeors
 Optical and acoustic scattering in sea water
 Scattering from biological materials
 Pulse scattering and beam wave propagation in such media
 Optical diffusion in tissues and blood
 Transport and radiative transfer theory
 KubelkaMunk flux theory and planeparallel problem
 Multiple scattering theory
 Wave fluctuations in turbulence
 Strong fluctuation theory
 Rough surface scattering
 Remote sensing and inversion techniques
 Imaging through various media
About the IEEE/OUP Series on Electromagnetic Wave Theory Formerly the IEEE Press Series on Electromagnetic Waves, this joint series between IEEE Press and Oxford University Press offers outstanding coverage of the field with new titles as well as reprintings and revisions of recognized classics that maintain longterm archival significance in electromagnetic waves and applications. Designed specifically for graduate students, practicing engineers, and researchers, this series provides affordable volumes that explore electromagnetic waves and applications beyond the undergraduate level. See page il of the front matter for a listing of books in this series.
FOREWORD xix
PREFACE xxi
ACKNOWLEDGMENTS xxv
CHAPTER 1 INTRODUCTION 1
PART I SCATTERING AND PROPAGATION OF WAVES IN A TENUOUS DISTRIBUTION OF SCATTERERS: SINGLE SCATTERING APPROXIMATION 7
CHAPTER 2 SCATTERING AND ABSORPTION OF A WAVE BY A SINGLE PARTICLE 9
21 Cross Sections and Scattering Amplitude 9
22 General Properties of Cross Sections 12
23 Forward Scattering Theorem 14
24 Integral Representations of Scattering Amplitude and Absorption Cross Section 15
25 Rayleigh Scattering 18
26 RayleighDebye Scattering (Born Approximation) 22
27 WKB Interior Wave Number Approximation 25
28 Mie Theory 27
29 Elliptic Polarization and the Stokes Parameters 30
210 Partial Polarization and Natural Light 32
211 Addition of Independent Waves 33
212 Scattering Amplitude Functions/11,/12,/21, and/22 and the Stokes Matrix 33
213 Transformation of the Stokes Parameters for Rotation about the Axis 35
214 Particle Size Distribution 36
215 Acoustic Waves 37
216 Acoustic Scattering 39
CHAPTER 3 CHARACTERISTICS OF DISCRETE SCATTERERS IN THE ATMOSPHERE, OCEAN, AND BIOLOGICAL MATERIALS 41
31 Weather Radar, Clutter, and Interference 41
32 Aerosols and Hydrometeors 43
321 Rain 43
322 Clouds, Fog, Haze, and Smog 49
323 Snow and Hail 50
33 Optical Scattering in Seawater (Hydrooptics) 52
34 Underwater Acoustic Scattering (Hydroacoustics) 55
341 Scattering from Air Bubbles 58
342 Scattering from Fish 60
35 Scattering from Biological Materials 62
351 Bioelectromagnetics 62
352 Biooptics 63
353 Bioacoustics 67
CHAPTER 4 SCATTERING OF WAVES FROM THE TENUOUS DISTRIBUTION OF PARTICLES 69
41 Single Scattering Approximation for Average Scattered Power 71
42 First Order Multiple Scattering Representation of Scattered Power 73
43 Narrow Beam Equation 74
44 Coherent and Incoherent Fields 77
45 TimeCorrelated Scattering Cross Section of a Moving Particle 80
46 Temporal Correlation Function and Temporal Frequency Spectrum of Scattered Fields 85
47 Spatial Correlation of Scattered Fields 86
48 Correlation with a Moving Receiver 88
49 Probability Distributions of Scattered Fields 89
CHAPTER 5 SCATTERING OF PULSE WAVES FROM A RANDOM DISTRIBUTION OF PARTICLES 93
51 General Formulation of Pulse Propagation and Scattering in a TimeVarying Random Medium 93
52 TwoFrequency Correlation Function and Correlation of the Output Pulse 96
53 Coherence Time and Coherence Bandwidth 97
54 Scattering of a Narrow Band Pulse 98
55 Backscattering of a Pulse from a Narrow Beam Transmitter 101
56 Backscattering of a Train of Short Pulses 106
57 Backscattering of a Pulse from a Transmitter with a Broad Beam 108
58 Bistatic Scattering of a Pulse 109
59 Ambiguity Function Representation 110
510 Pulse Doppler Radar 112
CHAPTER 6 LINEOFSIGHT PROPAGATION THROUGH TENUOUS DISTRIBUTION OF PARTICLES 116
61 Coherent and Incoherent Intensities and Spatial Correlation of Fluctuation of a Plane Wave 118
62 Temporal Correlation and Frequency Spectrum of a Plane Wave 123
63 LineofSight Propagation of a PlaneWave Pulse 124
64 LineofSight Propagation between a Transmitter and a Receiver 126
65 Pulse Propagation between a Transmitter and a Receiver 131
66 Rytov Solution for Amplitude and Phase Fluctuations 134
67 Rytov Solution for a Plane Wave Case 136
68 Temporal Correlation and Frequency Spectra of LogAmplitude and Phase Fluctuations of a Plane Wave 139
69 Rytov Solution Which Includes Transmitter and Receiver Characteristics 141
PART II TRANSPORT THEORY OF WAVES IN RANDOMLY DISTRIBUTED SCATTERERS 145
CHAPTER 7 TRANSPORT THEORY OF WAVE PROPAGATION IN RANDOM PARTICLES 147
71 Specific Intensity, Flux, and Energy Density 148
72 Specific Intensity in Free Space and at Boundaries between Homogeneous Media 152
73 Differential Equation for Specific Intensity 155
74 Reduced Incident Intensity, Diffuse Intensity, Boundary Condition, and Source Function 158
75 Integral Equation Formulation 160
76 Receiving Cross Section and Received Power 163
77 Transport Equation for a Partially Polarized Electromagnetic Wave 164
78 Relationship between Specific Intensity and Poynting Vector 166
CHAPTER 8 APPROXIMATE SOLUTIONS FOR TENUOUS MEDIUM 168
81 Specific Intensity in the First Order Multiple Scattering Approximation 168
82 Plane Wave Incidence on a PlaneParallel Medium 170
83 Collimated Beam Incident on a PlaneParallel Medium 173
CHAPTER 9 DIFFUSION APPROXIMATION 175
91 Derivation of the Diffusion Equation 175
92 Boundary Conditions 179
93 Collimated Beam Incident upon a Slab of Particles 181
94 Solution for a Plane Wave Incident upon a Slab of Particles 182
95 Solution for a Collimated Beam of a Finite Width Incident upon a Slab of Particles 184
96 Diffusion from a Point Source 185
97 TwoFiber Reflectance 186
98 The Fiberoptic Oximeter Catheter 188
CHAPTER 10 TWO AND FOUR FLUX THEORY 191
101 KubelkaMunk Two Flux Theory 191
102 Coefficients K and S for the Two Flux Theory 195
103 Four Flux Theory 196
Appendix 10A 199
CHAPTER 11 PLANEPARALLEL PROBLEM 202
111 Plane Wave Normally Incident upon a PlaneParallel Slab 203
112 Typical Phase Functions 205
113 Gauss's Quadrature Formula 205
114 General Solution 208
115 SemiInfinite Medium 215
116 Oblique Incidence and Other Techniques 216
117 Layered ParallelPlane Medium 216
118 Some Related Problems 219
CHAPTER 12 ISOTROPIC SCATTERING 220
121 Fourier Transform Method for Isotropic Scattering 221
122 Diffusion and Near Field Phenomena 225
123 Radiation from an Arbitrary Incident Intensity 227
124 Radiation from Incident Spherical Wave with Angular Variations 228
125 Radiation from an Arbitrary Source Distribution 230
126 Isotropic Scattering in Finite Volume and the Milne Problem 232
CHAPTER 13 APPROXIMATION FOR LARGE PARTICLES 234
131 Derivation of Differential Equation for Small Angle Approximation 234
132 General Solution 236
133 Approximate Solution When the Diffuse Intensity Is a Slowly Varying Function of Angle 239
PART III MULTIPLE SCATTERING THEORY 243
CHAPTER 14 MULTIPLE SCATTERING THEORY OF WAVES IN STATIONARY AND MOVING SCATTERERS AND ITS RELATIONSHIP WITH TRANSPORT THEORY 245
141 Multiple Scattering Process Contained in Twersky's Theory 246
142 Statistical Averages for Discrete Scatterers 251
143 FoldyTwersky's Integral Equation for the Coherent Field 253
144 Twersky's Integral Equation for the Correlation Function 255
145 Coherent Field 257
146 Plane Wave Incidence on a Slab of Scatterers—"Total Intensity" 260
147 Relationship between Multiple Scattering Theory and Transport Theory 266
148 Approximate Integral and Differential Equations for the Correlation Function 268
149 Fundamental Equations for Moving Particles 271
1410 Fluctuations due to the Size Distribution 277
Appendix 14A Example of Twersky's Scattering Process When N = 3 278
Appendix 14B Stationary Phase Evaluation of a Multiple Integral / 279
Appendix 14C Forward Scattering Theorem 284
CHAPTER 15 MULTIPLE SCATTERING THEORY OF WAVE FLUCTUATIONS AND PULSE PROPAGATION IN RANDOMLY DISTRIBUTED SCATTERERS 285
151 Fundamental Equations for Moving Scatterers 287
152 Correlation Function, Angular Spectrum, and Frequency Spectrum in the Small Angle Approximation 288
153 Plane Wave Solution 290
154 Limitation on Image Resolution Imposed by Randomly Distributed Scatterers 293
155 Output from Receiver in Randomly Distributed Scatterers 298
156 Spherical Wave in Randomly Distributed Particles 300
157 Backscattering from Randomly Distributed Scatterers 300
158 Pulse Propagation in Randomly Distributed Scatterers 305
159 Integral and Differential Equations for TwoFrequency Mutual Coherence Function in Randomly Distributed Scatterers 306
1510 TwoFrequency Mutual Coherence Function for the Plane Wave Case 308
1511 Weak Fluctuation Solution of a Plane Pulse Wave 310
1512 Strong Fluctuation Solution of a Plane Pulse Wave 313
PART IV WAVES IN RANDOM CONTINUUM AND TURBULENCE 319
CHAPTER 16 SCATTERING OF WAVES FROM RANDOM CONTINUUM AND TURBULENT MEDIA 321
161 Single Scattering Approximation and Received Power 321
162 Scattering Cross Section per Unit Volume of the Stationary Random Medium 323
163 BookerGordon Formula 326
164 Gaussian Model and Kolmogorov Spectrum 328
165 Anisotropic Random Medium 330
166 Temporal Fluctuation of Scattered Fields due to a TimeVarying Random Medium 331
167 Strong Fluctuations 334
168 Scattering of a Pulse by a Random Medium 335
169 Acoustic Scattering Cross Section per Unit Volume 336
1610 Narrow Beam Equation 337
CHAPTER 17 LINEOFSIGHT PROPAGATION OF A PLANE WAVE THROUGH A RANDOM MEDIUMWEAK FLUCTUATION CASE 338
171 Maxwell's Equations for a Fluctuating Medium 339
172 Born and Rytov Methods 341
1721 Born Approximation 341
1722 Rytov Transformation 341
173 LogAmplitude and Phase Fluctuations 343
174 Plane Wave Formulation 343
175 Direct Method and Spectral Method 344
176 Spectral Representation of the Amplitude and Phase Fluctuations 345
177 Amplitude and Phase Correlation Functions 347
178 Amplitude and Phase Structure Functions 350
179 Spectral and Spatial Filter Functions 350
1791 Spectral Filter Function 3 51
1792 Spatial Filter Function 352
1710 Homogeneous Random Media and Spectral Filter Function 352
1711 Geometric Optical Region L < < 12/X 353
1712 The Region in Which L > > 12/X 356
1713 General Characteristics of the Fluctuations in a Homogeneous Random Medium 357
1714 Homogeneous Random Medium with Gaussian Correlation Function 358
1715 Homogeneous and Locally Homogeneous Turbulence 359
17151 WhenL < < /02/A 361
17152 When /02/A < < L < < L02/X 362
1716 Inhomogeneous Random Medium with Gaussian Correlation Function and the Spatial Filter Function 363
1717 Variations of the Intensity of Turbulence along the Propagation Path 365
1718 Range of Validity of the Weak Fluctuation Theory 366
1719 Related Problems 366
CHAPTER 18 LINEOFSIGHT PROPAGATION OF SPHERICAL AND BEAM WAVES THROUGH A RANDOM MEDIUMWEAK FLUCTUATION CASE 368
181 Rytov Solution for the Spherical Wave 368
182 Variance for the Kolmogorov Spectrum 370
183 Correlation and Structure Functions for the Kolmogorov Spectrum 372
184 Beam Wave 372
185 Variance for a Beam Wave and the Validity of the Rytov Solution 375
186 Remote Probing of Planetary Atmospheres 376
187 Some Related Problems 377
CHAPTER 19 TEMPORAL CORRELATION AND FREQUENCY SPECTRA OF WAVE FLUCTUATIONS IN A RANDOM MEDIUM AND THE EFFECTS OF AN INHOMOGENEOUS RANDOM MEDIUM 380
191 Temporal Frequency Spectra of a Plane Wave 380
192 When the Average Wind Velocity U Is Transverse and the Wind Fluctuation V/ls Negligible 381
193 Temporal Spectra due to Average and Fluctuating Wind Velocities 385
194 Temporal Frequency Spectra of a Spherical Wave 386
195 TwoFrequency Correlation Function 388
196 Crossed Beams 391
197 Wave Fluctuations in an Inhomogeneous Random Medium 393
198 Wave Fluctuations in a Localized Smoothly Varying Random Medium 394
CHAPTER 20 STRONG FLUCTUATION THEORY 399
201 Parabolic Equation 400
202 Assumption for the Refractive Index Fluctuations 401
203 Equation for the Average Field and General Solution 402
204 Parabolic Equation for the Mutual Coherence Function 404
205 Solutions for the Mutual Coherence Function 406
206 Examples of Mutual Coherence Functions 410
207 Mutual Coherence Function in a Turbulent Medium 412
208 Temporal Frequency Spectra 414
209 TwoFrequency Correlation Function 416
2010 Plane Wave Solution for the TwoFrequency Mutual Coherence Function 417
2011 Pulse Shape 420
2012 Angular and Temporal Frequency Spectra 421
2013 Fourth Order Moments 423
2014 Thin Screen Theory 426
2015 Approximate Solution for the Thin Screen Theory 430
2016 Thin Screen Theory for Spherical Waves 432
2017 Extended Sources 432
2018 Extended Medium 434
2019 Optical Propagation in a Turbulent Medium 436
2020 Modulation Transfer Function of a Random Medium 440
2021 Adaptive Optics 446
Appendix 20A 448
Appendix 20B 449
Appendix 20C 450
PART V ROUGH SURFACE SCATTERING AND REMOTE SENSING 453
CHAPTER 21 ROUGH SURFACE SCATTERING 455
211 Received Power and Scattering Cross Section per Unit Area of Rough Surface 457
212 First Order Perturbation Solution for Horizontally Polarized Incident Wave 459
213 Derivation of the First Order Scattering Cross Section per Unit Area 465
214 Statistical Description of a Rough Surface 468
215 Bistatic Cross Section of a Rough Surface 469
216 Effect of Temporal Variation of a Rough Surface 473
217 Ocean Wave Spectra 474
218 Other Related Problems 475
219 Kirchhoff Approximation—Scattering of Sound Waves from a Rough Surface 476
2110 Coherent Field in the Kirchhoff Approximation 479
2111 Scattering Cross Section per Unit Area of Rough Surface 480
2112 Probability Distribution of a Scattered Field 483
CHAPTER 22 REMOTE SENSING AND INVERSION TECHNIQUES 485
221 Remote Sensing of the Troposphere 485
222 Remote Sensing of the Average Structure Constant Cn over the Path 487
223 Remote Sensing of the Average Wind Velocity over the Path 488
224 Remote Sensing of the Profile of the Structure Constant and the IllPosed Problem 492
225 Inverse Problem 496
226 Smoothing (Regularization) Method 496
227 Statistical Inversion Technique 497
228 BackusGilbert Inversion Technique 500
229 Remote Sensing of Observables in Geophysics 504
APPENDIX A SPECTRAL REPRESENTATIONS OF A RANDOM FUNCTION 505
Al Stationary Complex Random Function 505
A2 Stationary Real Random Function 507
A3 Homogeneous Complex Random Function 507
A4 Homogeneous and Isotropic Random Function 508
A5 Homogeneous and Real Random Function 510
A6 Stationary and Homogeneous Random Function 510
A7 "FrozenIn" Random Function 511
APPENDIX B STRUCTURE FUNCTIONS 512
Bl Structure Function and Random Process with Stationary Increments 512
B2 Spectral Representation of the Structure Function 514
B3 Locally Homogeneous and Isotropic Random Function 515
B4 Kolmogorov Spectrum 517
APPENDIX C TURBULENCE AND REFRACTIVE INDEX FLUCTUATIONS 520
Cl Laminar Flow and Turbulence 520
C2 Developed Turbulence 521
C3 Scalar Quantities Conserved in a Turbulence and Neutral, Stable, and Unstable Atmosphere 523
C4 Fluctuations of the Index of Refraction 526
C5 Structure Functions of a Conservative Scalar and the Index of Refraction Fluctuation 526
C6 The Energy Dissipation Rate e and the Energy Budget of Atmospheric Turbulence 528
C7 The Rate of Dissipation of the Fluctuation N 529
C8 Calculation of the Structure Constant 530
C9 Boundary Layer, Free Atmosphere, Large and SmallScale Turbulence 531
C10 The Structure Constant for the Index of Refraction in the Boundary Layer 531
Cll The Structure Constant Cn for Free Atmosphere 533
Cl2 Relation between the Structure Constant Cn and the Variance of the Index of Refraction Fluctuation 534
APPENDIX D SOME USEFUL MATHEMATICAL FORMULAS 536
Dl Kummer Function 536
D2 Confluent Hypergeometric Function 536
D3 Other Integrals 537
REFERENCES 539
INDEX 561
ABOUT THE AUTHOR 573