# Wave Propagation and Scattering in Random Media

## 1st Edition

### Multiple Scattering, Turbulence, Rough Surfaces, and Remote Sensing

**Authors:**Akira Ishimaru

**eBook ISBN:**9781483273150

**Imprint:**Academic Press

**Published Date:**28th May 1978

**Page Count:**339

## Description

Wave Propagation and Scattering in Random Media, Volume 2, presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner. The topics covered in this book may be grouped into three categories: waves in random scatterers, waves in random continua, and rough surface scattering. Random scatterers are random distributions of many particles. Examples are rain, fog, smog, hail, ocean particles, red blood cells, polymers, and other particles in a state of Brownian motion. Random continua are the media whose characteristics vary randomly and continuously in time and space. Examples are clear air turbulence, jet engine exhaust, tropospheric and ionospheric turbulence, ocean turbulence, and biological media such as tissue and muscle. Rough surface examples are the ocean surface, planetary surfaces, interfaces between different biological media, and the surface roughness of an optical fiber. This book is intended for engineers and scientists interested in optical, acoustic, and microwave propagation and scattering in atmospheres, oceans, and biological media, and particularly for those involved in communication through such media and remote sensing of the characteristics of these media.

## Table of Contents

Preface

Acknowledgments

Contents if Volume 1

Part 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 Wave

Part 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 Optics

Part 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 Geophysics

Appendix 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 Function

Appendix 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 Spectrum

Appendix 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 Fluctuation

Appendix D Some Useful Mathematical Formulas

D-1 Kummer Function

D-2 Confluent Hypergeometric Function

D-3 Other Integrals

References

Index

## Details

- No. of pages:
- 339

- Language:
- English

- Copyright:
- © Academic Press 1978

- Published:
- 28th May 1978

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483273150