Wave Propagation and Scattering in Random Media: (IEEE Press Series on Electromagnetic Wave Theory)

A volume in the IEEE/OUP Series on Electromagnetic Wave Theory Donald G. Dudley, Series Editor This IEEE Classic Reissue presents a unified introduction to the fundamental theories and applications of wave propagation and scattering in random media. Now for the first time, the two volumes of Wave Propagation and Scattering in Random Media previously published by Academic Press in 1978 are combined into one comprehensive volume. This book presents a clear picture of how waves interact with the atmosphere, terrain, ocean, turbulence, aerosols, rain, snow, biological tissues, composite material, and other media. The theories presented will enable you to solve a variety of problems relating to clutter, interference, imaging, object detection, and communication theory for various media. This book is expressly designed for engineers and scientists who have an interest in optical, microwave, or acoustic wave propagation and scattering. Topics covered include: 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 Kubelka--Munk flux theory and plane-parallel 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 long-term 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.

Table of Contents:
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 2-1 Cross Sections and Scattering Amplitude 9 2-2 General Properties of Cross Sections 12 2-3 Forward Scattering Theorem 14 2-4 Integral Representations of Scattering Amplitude and Absorption Cross Section 15 2-5 Rayleigh Scattering 18 2-6 Rayleigh-Debye Scattering (Born Approximation) 22 2-7 WKB Interior Wave Number Approximation 25 2-8 Mie Theory 27 2-9 Elliptic Polarization and the Stokes Parameters 30 2-10 Partial Polarization and Natural Light 32 2-11 Addition of Independent Waves 33 2-12 Scattering Amplitude Functions/11,/12,/21, and/22 and the Stokes Matrix 33 2-13 Transformation of the Stokes Parameters for Rotation about the Axis 35 2-14 Particle Size Distribution 36 2-15 Acoustic Waves 37 2-16 Acoustic Scattering 39 CHAPTER 3 CHARACTERISTICS OF DISCRETE SCATTERERS IN THE ATMOSPHERE, OCEAN, AND BIOLOGICAL MATERIALS 41 3-1 Weather Radar, Clutter, and Interference 41 3-2 Aerosols and Hydrometeors 43 3-2-1 Rain 43 3-2-2 Clouds, Fog, Haze, and Smog 49 3-2-3 Snow and Hail 50 3-3 Optical Scattering in Seawater (Hydrooptics) 52 3-4 Underwater Acoustic Scattering (Hydroacoustics) 55 3-4-1 Scattering from Air Bubbles 58 3-4-2 Scattering from Fish 60 3-5 Scattering from Biological Materials 62 3-5-1 Bioelectromagnetics 62 3-5-2 Biooptics 63 3-5-3 Bioacoustics 67 CHAPTER 4 SCATTERING OF WAVES FROM THE TENUOUS DISTRIBUTION OF PARTICLES 69 4-1 Single Scattering Approximation for Average Scattered Power 71 4-2 First Order Multiple Scattering Representation of Scattered Power 73 4-3 Narrow Beam Equation 74 4-4 Coherent and Incoherent Fields 77 4-5 Time-Correlated Scattering Cross Section of a Moving Particle 80 4-6 Temporal Correlation Function and Temporal Frequency Spectrum of Scattered Fields 85 4-7 Spatial Correlation of Scattered Fields 86 4-8 Correlation with a Moving Receiver 88 4-9 Probability Distributions of Scattered Fields 89 CHAPTER 5 SCATTERING OF PULSE WAVES FROM A RANDOM DISTRIBUTION OF PARTICLES 93 5-1 General Formulation of Pulse Propagation and Scattering in a Time-Varying Random Medium 93 5-2 Two-Frequency Correlation Function and Correlation of the Output Pulse 96 5-3 Coherence Time and Coherence Bandwidth 97 5-4 Scattering of a Narrow Band Pulse 98 5-5 Backscattering of a Pulse from a Narrow Beam Transmitter 101 5-6 Backscattering of a Train of Short Pulses 106 5-7 Backscattering of a Pulse from a Transmitter with a Broad Beam 108 5-8 Bistatic Scattering of a Pulse 109 5-9 Ambiguity Function Representation 110 5-10 Pulse Doppler Radar 112 CHAPTER 6 LINE-OF-SIGHT PROPAGATION THROUGH TENUOUS DISTRIBUTION OF PARTICLES 116 6-1 Coherent and Incoherent Intensities and Spatial Correlation of Fluctuation of a Plane Wave 118 6-2 Temporal Correlation and Frequency Spectrum of a Plane Wave 123 6-3 Line-of-Sight Propagation of a Plane-Wave Pulse 124 6-4 Line-of-Sight Propagation between a Transmitter and a Receiver 126 6-5 Pulse Propagation between a Transmitter and a Receiver 131 6-6 Rytov Solution for Amplitude and Phase Fluctuations 134 6-7 Rytov Solution for a Plane Wave Case 136 6-8 Temporal Correlation and Frequency Spectra of Log-Amplitude and Phase Fluctuations of a Plane Wave 139 6-9 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 7-1 Specific Intensity, Flux, and Energy Density 148 7-2 Specific Intensity in Free Space and at Boundaries between Homogeneous Media 152 7-3 Differential Equation for Specific Intensity 155 7-4 Reduced Incident Intensity, Diffuse Intensity, Boundary Condition, and Source Function 158 7-5 Integral Equation Formulation 160 7-6 Receiving Cross Section and Received Power 163 7-7 Transport Equation for a Partially Polarized Electromagnetic Wave 164 7-8 Relationship between Specific Intensity and Poynting Vector 166 CHAPTER 8 APPROXIMATE SOLUTIONS FOR TENUOUS MEDIUM 168 8-1 Specific Intensity in the First Order Multiple Scattering Approximation 168 8-2 Plane Wave Incidence on a Plane-Parallel Medium 170 8-3 Collimated Beam Incident on a Plane-Parallel Medium 173 CHAPTER 9 DIFFUSION APPROXIMATION 175 9-1 Derivation of the Diffusion Equation 175 9-2 Boundary Conditions 179 9-3 Collimated Beam Incident upon a Slab of Particles 181 9-4 Solution for a Plane Wave Incident upon a Slab of Particles 182 9-5 Solution for a Collimated Beam of a Finite Width Incident upon a Slab of Particles 184 9-6 Diffusion from a Point Source 185 9-7 Two-Fiber Reflectance 186 9-8 The Fiberoptic Oximeter Catheter 188 CHAPTER 10 TWO AND FOUR FLUX THEORY 191 10-1 Kubelka-Munk Two Flux Theory 191 10-2 Coefficients K and S for the Two Flux Theory 195 10-3 Four Flux Theory 196 Appendix 10A 199 CHAPTER 11 PLANE-PARALLEL PROBLEM 202 11-1 Plane Wave Normally Incident upon a Plane-Parallel Slab 203 11-2 Typical Phase Functions 205 11-3 Gauss's Quadrature Formula 205 11-4 General Solution 208 11-5 Semi-Infinite Medium 215 11-6 Oblique Incidence and Other Techniques 216 11-7 Layered Parallel-Plane Medium 216 11-8 Some Related Problems 219 CHAPTER 12 ISOTROPIC SCATTERING 220 12-1 Fourier Transform Method for Isotropic Scattering 221 12-2 Diffusion and Near Field Phenomena 225 12-3 Radiation from an Arbitrary Incident Intensity 227 12-4 Radiation from Incident Spherical Wave with Angular Variations 228 12-5 Radiation from an Arbitrary Source Distribution 230 12-6 Isotropic Scattering in Finite Volume and the Milne Problem 232 CHAPTER 13 APPROXIMATION FOR LARGE PARTICLES 234 13-1 Derivation of Differential Equation for Small Angle Approximation 234 13-2 General Solution 236 13-3 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 14-1 Multiple Scattering Process Contained in Twersky's Theory 246 14-2 Statistical Averages for Discrete Scatterers 251 14-3 Foldy-Twersky's Integral Equation for the Coherent Field 253 14-4 Twersky's Integral Equation for the Correlation Function 255 14-5 Coherent Field 257 14-6 Plane Wave Incidence on a Slab of Scatterers—"Total Intensity" 260 14-7 Relationship between Multiple Scattering Theory and Transport Theory 266 14-8 Approximate Integral and Differential Equations for the Correlation Function 268 14-9 Fundamental Equations for Moving Particles 271 14-10 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 15-1 Fundamental Equations for Moving Scatterers 287 15-2 Correlation Function, Angular Spectrum, and Frequency Spectrum in the Small Angle Approximation 288 15-3 Plane Wave Solution 290 15-4 Limitation on Image Resolution Imposed by Randomly Distributed Scatterers 293 15-5 Output from Receiver in Randomly Distributed Scatterers 298 15-6 Spherical Wave in Randomly Distributed Particles 300 15-7 Backscattering from Randomly Distributed Scatterers 300 15-8 Pulse Propagation in Randomly Distributed Scatterers 305 15-9 Integral and Differential Equations for Two-Frequency Mutual Coherence Function in Randomly Distributed Scatterers 306 15-10 Two-Frequency Mutual Coherence Function for the Plane Wave Case 308 15-11 Weak Fluctuation Solution of a Plane Pulse Wave 310 15-12 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 16-1 Single Scattering Approximation and Received Power 321 16-2 Scattering Cross Section per Unit Volume of the Stationary Random Medium 323 16-3 Booker-Gordon Formula 326 16-4 Gaussian Model and Kolmogorov Spectrum 328 16-5 Anisotropic Random Medium 330 16-6 Temporal Fluctuation of Scattered Fields due to a Time-Varying Random Medium 331 16-7 Strong Fluctuations 334 16-8 Scattering of a Pulse by a Random Medium 335 16-9 Acoustic Scattering Cross Section per Unit Volume 336 16-10 Narrow Beam Equation 337 CHAPTER 17 LINE-OF-SIGHT PROPAGATION OF A PLANE WAVE THROUGH A RANDOM MEDIUM-WEAK FLUCTUATION CASE 338 17-1 Maxwell's Equations for a Fluctuating Medium 339 17-2 Born and Rytov Methods 341 17-2-1 Born Approximation 341 17-2-2 Rytov Transformation 341 17-3 Log-Amplitude and Phase Fluctuations 343 17-4 Plane Wave Formulation 343 17-5 Direct Method and Spectral Method 344 17-6 Spectral Representation of the Amplitude and Phase Fluctuations 345 17-7 Amplitude and Phase Correlation Functions 347 17-8 Amplitude and Phase Structure Functions 350 17-9 Spectral and Spatial Filter Functions 350 17-9-1 Spectral Filter Function 3 51 17-9-2 Spatial Filter Function 352 17-10 Homogeneous Random Media and Spectral Filter Function 352 17-11 Geometric Optical Region L < < 12/X 353 17-12 The Region in Which L > > 12/X 356 17-13 General Characteristics of the Fluctuations in a Homogeneous Random Medium 357 17-14 Homogeneous Random Medium with Gaussian Correlation Function 358 17-15 Homogeneous and Locally Homogeneous Turbulence 359 17-15-1 WhenL < < /02/A 361 17-15-2 When /02/A < < L < < L02/X 362 17-16 Inhomogeneous Random Medium with Gaussian Correlation Function and the Spatial Filter Function 363 17-17 Variations of the Intensity of Turbulence along the Propagation Path 365 17-18 Range of Validity of the Weak Fluctuation Theory 366 17-19 Related Problems 366 CHAPTER 18 LINE-OF-SIGHT PROPAGATION OF SPHERICAL AND BEAM WAVES THROUGH A RANDOM MEDIUM-WEAK FLUCTUATION CASE 368 18-1 Rytov Solution for the Spherical Wave 368 18-2 Variance for the Kolmogorov Spectrum 370 18-3 Correlation and Structure Functions for the Kolmogorov Spectrum 372 18-4 Beam Wave 372 18-5 Variance for a Beam Wave and the Validity of the Rytov Solution 375 18-6 Remote Probing of Planetary Atmospheres 376 18-7 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 19-1 Temporal Frequency Spectra of a Plane Wave 380 19-2 When the Average Wind Velocity U Is Transverse and the Wind Fluctuation V/ls Negligible 381 19-3 Temporal Spectra due to Average and Fluctuating Wind Velocities 385 19-4 Temporal Frequency Spectra of a Spherical Wave 386 19-5 Two-Frequency Correlation Function 388 19-6 Crossed Beams 391 19-7 Wave Fluctuations in an Inhomogeneous Random Medium 393 19-8 Wave Fluctuations in a Localized Smoothly Varying Random Medium 394 CHAPTER 20 STRONG FLUCTUATION THEORY 399 20-1 Parabolic Equation 400 20-2 Assumption for the Refractive Index Fluctuations 401 20-3 Equation for the Average Field and General Solution 402 20-4 Parabolic Equation for the Mutual Coherence Function 404 20-5 Solutions for the Mutual Coherence Function 406 20-6 Examples of Mutual Coherence Functions 410 20-7 Mutual Coherence Function in a Turbulent Medium 412 20-8 Temporal Frequency Spectra 414 20-9 Two-Frequency Correlation Function 416 20-10 Plane Wave Solution for the Two-Frequency Mutual Coherence Function 417 20-11 Pulse Shape 420 20-12 Angular and Temporal Frequency Spectra 421 20-13 Fourth Order Moments 423 20-14 Thin Screen Theory 426 20-15 Approximate Solution for the Thin Screen Theory 430 20-16 Thin Screen Theory for Spherical Waves 432 20-17 Extended Sources 432 20-18 Extended Medium 434 20-19 Optical Propagation in a Turbulent Medium 436 20-20 Modulation Transfer Function of a Random Medium 440 20-21 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 21-1 Received Power and Scattering Cross Section per Unit Area of Rough Surface 457 21-2 First Order Perturbation Solution for Horizontally Polarized Incident Wave 459 21-3 Derivation of the First Order Scattering Cross Section per Unit Area 465 21-4 Statistical Description of a Rough Surface 468 21-5 Bistatic Cross Section of a Rough Surface 469 21-6 Effect of Temporal Variation of a Rough Surface 473 21-7 Ocean Wave Spectra 474 21-8 Other Related Problems 475 21-9 Kirchhoff Approximation—Scattering of Sound Waves from a Rough Surface 476 21-10 Coherent Field in the Kirchhoff Approximation 479 21-11 Scattering Cross Section per Unit Area of Rough Surface 480 21-12 Probability Distribution of a Scattered Field 483 CHAPTER 22 REMOTE SENSING AND INVERSION TECHNIQUES 485 22-1 Remote Sensing of the Troposphere 485 22-2 Remote Sensing of the Average Structure Constant Cn over the Path 487 22-3 Remote Sensing of the Average Wind Velocity over the Path 488 22-4 Remote Sensing of the Profile of the Structure Constant and the Ill-Posed Problem 492 22-5 Inverse Problem 496 22-6 Smoothing (Regularization) Method 496 22-7 Statistical Inversion Technique 497 22-8 Backus-Gilbert Inversion Technique 500 22-9 Remote Sensing of Observables in Geophysics 504 APPENDIX A SPECTRAL REPRESENTATIONS OF A RANDOM FUNCTION 505 A-l Stationary Complex Random Function 505 A-2 Stationary Real Random Function 507 A-3 Homogeneous Complex Random Function 507 A-4 Homogeneous and Isotropic Random Function 508 A-5 Homogeneous and Real Random Function 510 A-6 Stationary and Homogeneous Random Function 510 A-7 "Frozen-In" Random Function 511 APPENDIX B STRUCTURE FUNCTIONS 512 B-l Structure Function and Random Process with Stationary Increments 512 B-2 Spectral Representation of the Structure Function 514 B-3 Locally Homogeneous and Isotropic Random Function 515 B-4 Kolmogorov Spectrum 517 APPENDIX C TURBULENCE AND REFRACTIVE INDEX FLUCTUATIONS 520 C-l Laminar Flow and Turbulence 520 C-2 Developed Turbulence 521 C-3 Scalar Quantities Conserved in a Turbulence and Neutral, Stable, and Unstable Atmosphere 523 C-4 Fluctuations of the Index of Refraction 526 C-5 Structure Functions of a Conservative Scalar and the Index of Refraction Fluctuation 526 C-6 The Energy Dissipation Rate e and the Energy Budget of Atmospheric Turbulence 528 C-7 The Rate of Dissipation of the Fluctuation N 529 C-8 Calculation of the Structure Constant 530 C-9 Boundary Layer, Free Atmosphere, Large- and Small-Scale Turbulence 531 C-10 The Structure Constant for the Index of Refraction in the Boundary Layer 531 C-ll The Structure Constant Cn for Free Atmosphere 533 C-l2 Relation between the Structure Constant Cn and the Variance of the Index of Refraction Fluctuation 534 APPENDIX D SOME USEFUL MATHEMATICAL FORMULAS 536 D-l Kummer Function 536 D-2 Confluent Hypergeometric Function 536 D-3 Other Integrals 537 REFERENCES 539 INDEX 561 ABOUT THE AUTHOR 573

About the Author :
Akira Ishimaru is Boeing Martin Professor in the College of Engineering, University of Washington. He has conducted studies in many areas of antennas and propagation, including pattern synthesis, unequally spaced arrays, leaky waves, periodic structures, anisotropic media, and waves in random media, and has contributed to a number of volumes in the field. Dr. Ishimaru is a Fellow of the IEEE and a Fellow of the OSA. He has served as chairman of Commission B of USNC/URSI. He is the founding editor of the journal, Waves in Random Media, Institute of Physics, United Kingdom. He received the 1968 IEEE Region VI Achievement Award, the IEEE Centennial Medal in 1984, and the Distinguished Achievement Award from the IEEE Antennas and Propagation Society in 1995. He is a member of the National Academy of Engineering.