Wave Propagation in a Random Medium
This monograph by a prominent Russian expert was a ground-breaking contribution to the literature on the theory of wave propagation in randomly inhomogeneous media. Since the publication of the first English translation in 1960, the systematic treatment has been widely used by scientists, engineers, and advanced undergraduate students in such fields as acoustics, radio-wave physics, and optics.
The three-part treatment begins with a study of the problem of wave propagation using the ray approximation, followed by the second part's examination of the diffraction theory of wave propagation. The final part explores the question of how fluctuations in the incident wave affect the diffraction image formed by a focusing system, a question of considerable interest in hydroacoustics and astronomical optics. Some of the theoretical deductions are compared with experimental data, and two appendixes contain more elaborate calculations. This edition serves as a companion volume to Wave Propagation in a Turbulent Medium, also available from Dover Publications.
"1124688980"
Wave Propagation in a Random Medium
This monograph by a prominent Russian expert was a ground-breaking contribution to the literature on the theory of wave propagation in randomly inhomogeneous media. Since the publication of the first English translation in 1960, the systematic treatment has been widely used by scientists, engineers, and advanced undergraduate students in such fields as acoustics, radio-wave physics, and optics.
The three-part treatment begins with a study of the problem of wave propagation using the ray approximation, followed by the second part's examination of the diffraction theory of wave propagation. The final part explores the question of how fluctuations in the incident wave affect the diffraction image formed by a focusing system, a question of considerable interest in hydroacoustics and astronomical optics. Some of the theoretical deductions are compared with experimental data, and two appendixes contain more elaborate calculations. This edition serves as a companion volume to Wave Propagation in a Turbulent Medium, also available from Dover Publications.
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Wave Propagation in a Random Medium

Wave Propagation in a Random Medium

Wave Propagation in a Random Medium

Wave Propagation in a Random Medium

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Overview

This monograph by a prominent Russian expert was a ground-breaking contribution to the literature on the theory of wave propagation in randomly inhomogeneous media. Since the publication of the first English translation in 1960, the systematic treatment has been widely used by scientists, engineers, and advanced undergraduate students in such fields as acoustics, radio-wave physics, and optics.
The three-part treatment begins with a study of the problem of wave propagation using the ray approximation, followed by the second part's examination of the diffraction theory of wave propagation. The final part explores the question of how fluctuations in the incident wave affect the diffraction image formed by a focusing system, a question of considerable interest in hydroacoustics and astronomical optics. Some of the theoretical deductions are compared with experimental data, and two appendixes contain more elaborate calculations. This edition serves as a companion volume to Wave Propagation in a Turbulent Medium, also available from Dover Publications.

Product Details

ISBN-13: 9780486812236
Publisher: Dover Publications
Publication date: 05/17/2017
Series: Dover Books on Physics
Pages: 176
Product dimensions: 7.00(w) x 10.00(h) x (d)

About the Author

Lev Aleksandrovich Chernov (1911–81) was on the faculty of the Yaroslavl Pedagogical Institute (now the Yaroslavl Demidov State University) in Yaroslavl, Russia, from 1940–58. He was afterward affiliated with the Acoustics Institute of Moscow.

Table of Contents

Translator's preface iii

Author's preface v

Introduction 1

Part I Ray Theory

Chapter I Statistical Characteristics of the Medium 5

1 The Correlation Function 6

2 Determination of the Form of the Correlation Function 7

Chapter II Ray Statistics 12

3 The Ray Equation 12

4 The Ray Diffusion Coefficient 15

5 The Angular Distribution of Rays. The Einstein-Fokker-Kolmogorov Equation 18

6 The Mean Ray Displacement 22

7 Fluctuations of the Transit Time and Intensity of the Rays 28

Part II Diffraction Theory

Chapter III The Wave Equation 35

8 Derivation of the Wave Equation for an Inhomogeneous Medium 35

9 The Wave Equation for a Multi-Component Medium 38

Chapter IV Scattering By Inhomogeneities 41

10 The Method of Small Perturbations 41

11 The Scattering Formula 43

12 The Scattering Coefficient 55

13 Applicability of the Scattering Formula 55

14 Attenuation of an Acoustic Bundle due to Scattering 56

Chapter V Fluctuations 58

15 The Method of Small Perturbations 58

16 Rytov'a Method 61

17 Comparison of the Methods 65

18 The Fresnel Approximation 66

19 Amplitude and Phase Fluctuations 68

20 The Region of Large Values of the Wave Parameter (Fraunhofer Diffraction) 74

21 The Region of Small Values of the Wave Parameter 77

22 The Region of Intermediate Values of the Wave Parameter 82

Chapter VI Correlation of Fluctuations 84

23 Correlation of the Amplitude and Phase Fluctuations at the Receiver 85

24 Longitudinal Autocorrelation of the Amplitude (or Phase) Fluctuations 89

25 Transverse Autocorrelation of the Amplitude and Phase Fluctuations 95

26 The Quasi-Static Condition 111

27 The Time Autocorrelation of the Amplitude Fluctuations 112

28 Comparison with Experiment 117

Part III The Influence of Fluctuations on the Diffraction Image of a Focusing System

Introductory Remarks 125

Chapter VII General Formulas 126

29 The Debye Formula 126

30 Statistical Averaging 128

31 Various Special Cases 135

Chapter VIII The Mean Distribution Near the Focus 137

32 The Mean Distribution in the Focal Plane 138

33 The Mean Distribution along the Principal Axis 143

Chapter IX Fluctuations Behind the Lens 147

34 The Distribution of Fluctuations 147

35 Fluctuations at the Focus 149

Appendix I 155

Appendix II 160

References 166

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