Wave Propagation and Scattering in Random Media

Wave Propagation and Scattering in Random Media, Volume 1: Single Scattering and Transport Theory presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner, as well as useful approximation techniques applicable to a variety of different situations. The emphasis is on single scattering theory and transport theory. The reader is introduced to the fundamental concepts and useful results of the statistical wave propagation theory. This volume is comprised of 13 chapters, organized around three themes: waves in random scatterers, waves in random continua, and rough surface scattering. The first part deals with the scattering and propagation of waves in a tenuous distribution of scatterers, using the single scattering theory and its slight extension to explain the fundamentals of wave fluctuations in random media without undue mathematical complexities. Many practical problems of wave propagation and scattering in the atmosphere, oceans, and other random media are discussed. The second part examines transport theory, also known as the theory of radiative transfer, and includes chapters on wave propagation in random particles, isotropic scattering, and the plane-parallel problem.
This monograph is intended for engineers and scientists interested in optical, acoustic, and microwave propagation and scattering in atmospheres, oceans, and biological media.

Preface

Acknowledgments

Contents of Volume 2

Chapter 1 □ Introduction

Part I □ Scattering and Propagation of Waves in a Tenuous Distribution of Scatterers: Single Scattering Approximation

Chapter 2 □ Scattering and Absorption of a Wave by a Single Particle

2-1 Cross Sections and Scattering Amplitude

2-2 General Properties of Cross Sections

2-3 Forward Scattering Theorem

2-4 Integral Representations of Scattering Amplitude and Absorption Cross Section

2-5 Rayleigh Scattering

2-6 Rayleigh-Debye Scattering (Born Approximation)

2-7 WKB Interior Wave Number Approximation

2-8 Mie Theory

2-9 Elliptic Polarization and the Stokes Parameters

2-10 Partial Polarization and Natural Light

2-11 Addition of Independent Waves

2-12 Scattering Amplitude Functions f1l, f12, f21, and f22 and the Stokes Matrix

2-13 Transformation of the Stokes Parameters for Rotation about the Axis

2-14 Particle Size Distribution

2-15 Acoustic Waves

2-16 Acoustic Scattering

Chapter 3 □ Characteristics of Discrete Scatterers in the Atmosphere, Ocean, and Biological Materials

3-1 Weather Radar, Clutter, and Interference

3-2 Aerosols and Hydrometeors

3-3 Optical Scattering in Seawater (Hydrooptics)

3-4 Underwater Acoustic Scattering (Hydroacoustics)

3-5 Scattering from Biological Materials

Chapter 4 □ Scattering of Waves from the Tenuous Distribution of Particles

4-1 Single Scattering Approximation for Average Scattered Power

4-2 First Order Multiple Scattering Representation of Scattered Power

4-3 Narrow Beam Equation

4-4 Coherent and Incoherent Fields

4-5 Time-Correlated Scattering Cross Section of a Moving Particle

4-6 Temporal Correlation Function and Temporal Frequency Spectrum of Scattered Fields

4-7 Spatial Correlation of Scattered Fields

4-8 Correlation with a Moving Receiver

4-9 Probability Distributions of Scattered Fields

Chapter 5 □ Scattering of Pulse Waves from a Random Distribution of Particles

5-1 General Formulation of Pulse Propagation and Scattering in a Time-Varying Random Medium

5-2 Two-Frequency Correlation Function and Correlation of the Output Pulse

5-3 Coherence Time and Coherence Bandwidth

5-4 Scattering of a Narrow Band Pulse

5-5 Backscattering of a Pulse from a Narrow Beam Transmitter

5-6 Backscattering of a Train of Short Pulses

5-7 Backscattering of a Pulse from a Transmitter with a Broad Beam

5-8 Bistatic Scattering of a Pulse

5-9 Ambiguity Function Representation

5-10 Pulse Doppler Radar

Chapter 6 □ Line-of-Sight Propagation through Tenuous Distribution of Particles

6-1 Coherent and Incoherent Intensities and Spatial Correlation of Fluctuation of a Plane Wave

6-2 Temporal Correlation and Frequency Spectrum of a Plane Wave

6-3 Line-of-Sight Propagation of a Plane-Wave Pulse

6-4 Line-of-Sight Propagation between a Transmitter and a Receiver

6-5 Pulse Propagation between a Transmitter and a Receiver

6-6 Rytov Solution for Amplitude and Phase Fluctuations

6-7 Rytov Solution for a Plane Wave Case

6-8 Temporal Correlation and Frequency Spectra of Log-Amplitude and Phase Fluctuations of a Plane Wave

6-9 Rytov Solution Which Includes Transmitter and Receiver Characteristics

Part II □ Transport Theory of Waves in Randomly Distributed Scatterers

Chapter 7 □ Transport Theory of Wave Propagation in Random Particles

7-1 Specific Intensity, Flux, and Energy Density

7-2 Specific Intensity in Free Space and at Boundaries between Homogeneous Media

7-3 Differential Equation for Specific Intensity

7-4 Reduced Incident Intensity, Diffuse Intensity, Boundary Condition, and Source Function

7-5 Integral Equation Formulation

7-6 Receiving Cross Section and Received Power

7-7 Transport Equation for a Partially Polarized Electromagnetic Wave

7-8 Relationship between Specific Intensity and Pointing Vector

Chapter 8 □ Approximate Solutions for Tenuous Medium

8-1 Specific Intensity in the First Order Multiple Scattering Approximation

8-2 Plane Wave Incidence on a Plane-Parallel Medium

8-3 Collimated Beam Incident on a Plane-Parallel Medium

Chapter 9 □ Diffusion Approximation

9-1 Derivation of the Diffusion Equation

9-2 Boundary Conditions

9-3 Collimated Beam Incident upon a Slab of Particles

9-4 Solution for a Plane Wave Incident upon a Slab of Particles

9-5 Solution for a Collimated Beam of a Finite Width Incident upon a Slab of Particles

9-6 Diffusion from a Point Source

9-7 Two-Fiber Reflectance

9-8 The Fiberoptic Oximeter Catheter

Chapter 10 □ Two and Four Flux Theory

10-1 Kubelka-Munk Two Flux Theory

10-2 Coefficients K and S for the Two Flux Theory

10-3 Four Flux Theory

Appendix 10A

Chapter 11 □ Plane-Parallel Problem

11-1 Plane Wave Normally Incident upon a Plane-Parallel Slab

11-2 Typical Phase Functions

11-3 Gauss's Quadrature Formula

11-4 General Solution

11-5 Semi-Infinite Medium

11-6 Oblique Incidence and Other Techniques

11-7 Layered Parallel-Plane Medium

11-8 Some Related Problems

Chapter 12 □ Isotropic Scattering

12-1 Fourier Transform Method for Isotropic Scattering

12-2 Diffusion and near Field Phenomena

12-3 Radiation from an Arbitrary Incident Intensity

12-4 Radiation from Incident Spherical Wave with Angular Variations

12-5 Radiation from an Arbitrary Source Distribution

12-6 Isotropic Scattering in Finite Volume and the Milne Problem

Chapter 13 □ Approximation for Large Particles

13-1 Derivation of Differential Equation for Small Angle Approximation

13-2 General Solution

13-3 Approximate Solution When the Diffuse Intensity is a Slowly Varying Function of Angle

References

Index