Wave Propagation and Scattering in Random Media

Wave Propagation and Scattering in Random Media

Multiple Scattering, Turbulence, Rough Surfaces, and Remote Sensing

1st Edition - May 28, 1978

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  • Author: Akira Ishimaru
  • eBook ISBN: 9781483273150

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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


Product details

  • No. of pages: 339
  • Language: English
  • Copyright: © Academic Press 1978
  • Published: May 28, 1978
  • Imprint: Academic Press
  • eBook ISBN: 9781483273150

About the Author

Akira Ishimaru

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