Wave Propagation and Scattering in Random Media

PrefaceAcknowledgments Contents if Volume 1Part III Multiple Scattering Theory Chapter 14 Multiple Scattering Theory of Waves in Stationary and Moving Scatterers and Its Relationship with Transport Theory 14-1 Multiple Scattering Process Contained in Twersky's Theory 14-2 Statistical Averages for Discrete Scatterers 14-3 Foldy-Twersky's Integral Equation for the Coherent Field 14-4 Twersky's Integral Equation for the Correlation Function 14-5 Coherent Field 14-6 Plane Wave Incidence on a Slab of Scatterers—"Total Intensity" 14-7 Relationship between Multiple Scattering Theory and Transport Theory 14-8 Approximate Integral and Differential Equations for the Correlation Function 14-9 Fundamental Equations for Moving Particles 14-10 Fluctuations due to the Size Distribution Appendix 14A Example of Twersky's Scattering Process When N = 3 Appendix 14B Stationary Phase Evaluation of a Multiple Integral I Appendix 14C Forward Scattering Theorem Chapter 15 Multiple Scattering Theory of Wave Fluctuations and Pulse Propagation in Randomly Distributed Scatterers 15-1 Fundamental Equations for Moving Scatterers 15-2 Correlation Function, Angular Spectrum, and Frequency Spectrum in the Small Angle Approximation 15-3 Plane Wave Solution 15-4 Limitation on Image Resolution Imposed by Randomly Distributed Scatterers 15-5 Output from Receiver in Randomly Distributed Scatterers 15-6 Spherical Wave in Randomly Distributed Particles 15-7 Backscattering from Randomly Distributed Scatterers 15-8 Pulse Propagation in Randomly Distributed Scatterers 15-9 Integral and Differential Equations for Two-Frequency Mutual Coherence Function in Randomly Distributed Scatterers 15-10 Two-Frequency Mutual Coherence Function for the Plane Wave Case 15-11 Weak Fluctuation Solution of a Plane Pulse Wave 15-12 Strong Fluctuation Solution of a Plane Pulse WavePart IV Waves in Random Continuum and Turbulence Chapter 16 Scattering of Waves from Random Continuum and Turbulent Media 16-1 Single Scattering Approximation and Received Power 16-2 Scattering Cross Section per Unit Volume of the Stationary Random Medium 16-3 Booker Gordon Formula 16-4 Gaussian Model and Kolmogorov Spectrum 16-5 Anisotropie Random Medium 16-6 Temporal Fluctuation of Scattered Fields due to a Time-Varying Random Medium 16-7 Strong Fluctuations 16-8 Scattering of a Pulse by a Random Medium 16-9 Acoustic Scattering Cross Section per Unit Volume 16-10 Narrow Beam Equation Chapter 17 Line-of-Sight Propagation of a Plane Wave Through a Random Medium—Weak Fluctuation Case 17-1 Maxwell's Equations for a Fluctuating Medium 17-2 Born and Rytov Methods 17-3 Log-Amplitude and Phase Fluctuations 17-4 Plane Wave Formulation 17-5 Direct Method and Spectral Method 17-6 Spectral Representation of the Amplitude and Phase Fluctuations 17-7 Amplitude and Phase Correlation Functions 17-8 Amplitude and Phase Structure Functions 17-9 Spectral and Spatial Filter Functions 17-10 Homogeneous Random Media and Spectral Filter Function 17-11 Geometric Optical Region L < I2/y 17-12 The Region in Which L>I2/y 17-13 General Characteristics of the Fluctuations in a Homogeneous Random Medium 17-14 Homogeneous Random Medium with Gaussian Correlation Function 17-15 Homogeneous and Locally Homogeneous Turbulence 17-16 Inhomogeneous Random Medium with Gaussian Correlation Function and the Spatial Filter Function 17-17 Variations of the Intensity of Turbulence along the Propagation Path 17-18 Range of Validity of the Weak Fluctuation Theory 17-19 Related Problems Chapter 18 Line-of-Sight Propagation of Spherical and Beam Waves Through a Random Medium—Weak Fluctuation Case 18-1 Rytov Solution for the Spherical Wave 18-2 Variance for the Kolmogorov Spectrum 18-3 Correlation and Structure Functions for the Kolmogorov Spectrum 18-4 Beam Wave 18-5 Variance for a Beam Wave and the Validity of the Rytov Solution 18-6 Remote Probing of Planetary Atmospheres 18-7 Some Related Problems Chapter 19 Temporal Correlation and Frequency Spectra of Wave Fluctuations in a Random Medium and the Effects of an Inhomogeneous Random Medium 19-1 Temporal Frequency Spectra of a Plane Wave 19-2 When the Average Wind Velocity U is Transverse and the Wind Fluctuation Vf is Negligible 19-3 Temporal Spectra due to Average and Fluctuating Wind Velocities 19-4 Temporal Frequency Spectra of a Spherical Wave 19-5 Two-Frequency Correlation Function 19-6 Crossed Beams 19-7 Wave Fluctuations in an Inhomogeneous Random Medium 19-8 Wave Fluctuations in a Localized Smoothly Varying Random Medium Chapter 20 Strong Fluctuation Theory 20-1 Parabolic Equation 20-2 Assumption for the Refractive Index Fluctuations 20-3 Equation for the Average Field and General Solution 20-4 Parabolic Equation for the Mutual Coherence Function 20-5 Solutions for the Mutual Coherence Function 20-6 Examples of Mutual Coherence Functions 20-7 Mutual Coherence Function in a Turbulent Medium 20-8 Temporal Frequency Spectra 20-9 Two-Frequency Correlation Function 20-10 Plane Wave Solution for the Two-Frequency Mutual Coherence Function 20-11 Pulse Shape 20-12 Angular and Temporal Frequency Spectra 20-13 Fourth Order Moments 20-14 Thin Screen Theory 20-15 Approximate Solution for the Thin Screen Theory 20-16 Thin Screen Theory for Spherical Waves 20-17 Extended Sources 20-18 Extended Medium 20-19 Optical Propagation in a Turbulent Medium 20-20 Modulation Transfer Function of a Random Medium 20-21 Adaptive OpticsPart V Rough Surface Scattering and Remote Sensing Chapter 21 Rough Surface Scattering 21-1 Received Power and Scattering Cross Section per Unit Area of Rough Surface 21-2 First Order Perturbation Solution for Horizontally Polarized Incident Wave 21-3 Derivation of the First Order Scattering Cross Section per Unit Area 21-4 Statistical Description of a Rough Surface 21-5 Bistatic Cross Section of a Rough Surface 21-6 Effect of Temporal Variation of a Rough Surface 21-7 Ocean Wave Spectra 21-8 Other Related Problems 21-9 Kirchhoff Approximation—Scattering of Sound Waves from a Rough Surface 21-10 Coherent Field in the Kirchhoff Approximation 21-11 Scattering Cross Section per Unit Area of Rough Surface 21-12 Probability Distribution of a Scattered Field Chapter 22 Remote Sensing and Inversion Techniques 22-1 Remote Sensing of the Troposphere 22-2 Remote Sensing of the Average Structure Constant Cn over the Path 22-3 Remote Sensing of the Average Wind Velocity over the Path 496 22-4 Remote Sensing of the Profile of the Structure Constant and the Ill-Posed Problem 22-5 Inverse Problem 22-6 Smoothing (Regularization) Method 22-7 Statistical Inversion Technique 22-8 Backus-Gilbert Inversion Technique 22-9 Remote Sensing of Observables in GeophysicsAppendix A Spectral Representations of a Random Function A-1 Stationary Complex Random Function A-2 Stationary Real Random Function A-3 Homogeneous Complex Random Function A-4 Homogeneous and Isotropie Random Function A-5 Homogeneous and Real Random Function A-6 Stationary and Homogeneous Random Function A-7 "Frozen-In" Random FunctionAppendix B Structure Functions B-l Structure Function and Random Process with Stationary Increments B-2 Spectral Representation of the Structure Function B-3 Locally Homogeneous and Isotropie Random Function B-4 Kolmogorov SpectrumAppendix C Turbulence and Refractive Index Fluctuations C-1 Laminar Flow and Turbulence C-2 Developed Turbulence C-3 Scalar Quantities Conserved in a Turbulence and Neutral, Stable, and Unstable Atmosphere C-4 Fluctuations of the Index of Refraction C-5 Structure Functions of a Conservative Scalar and the Index of Refraction Fluctuation C-6 The Energy Dissipation Rate r. and the Energy Budget of Atmospheric Turbulence C-7 The Rate of Dissipation of the Fluctuation N C-8 Calculation of the Structure Constant C-9 Boundary Layer, Free Atmosphere, Large- and Small-Scale Turbulence C-10 The Structure Constant for the Index of Refraction in the Boundary Layer C-11 The Structure Constant Cn for Free Atmosphere C-12 Relation between The Structure Constant Cn and the Variance of the Index of Refraction FluctuationAppendix D Some Useful Mathematical Formulas D-1 Kummer Function D-2 Confluent Hypergeometric Function D-3 Other IntegralsReferencesIndex