Modeling Fluctuations in Scattered Waves: 1st Edition (Hardback) book cover

Modeling Fluctuations in Scattered Waves

1st Edition

By E. Jakeman, K. D. Ridley

CRC Press

336 pages | 145 B/W Illus.

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pub: 2006-06-19
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Description

Fluctuations in scattered waves limit the performance of imaging and remote sensing systems that operate on all wavelengths of the electromagnetic spectrum. To better understand these fluctuations, Modeling Fluctuations in Scattered Waves provides a practical guide to the phenomenology, mathematics, and simulation of non-Gaussian noise models and discusses how they can be used to characterize the statistics of scattered waves.

Through their discussion of mathematical models, the authors demonstrate the development of new sensing techniques as well as offer intelligent choices that can be made for system analysis. Using experimental results and numerical simulation, the book illustrates the properties and applications of these models. The first two chapters introduce statistical tools and the properties of Gaussian noise, including results on phase statistics. The following chapters describe Gaussian processes and the random walk model, address multiple scattering effects and propagation through an extended medium, and explore scattering vector waves and polarization fluctuations. Finally, the authors examine the generation of random processes and the simulation of wave propagation.

Although scattered wave fluctuations are sources of information, they can hinder the performance of imaging and remote sensing systems. By providing experimental data and numerical models, this volume aids you in evaluating and improving upon the performance of your own systems.

Table of Contents

STATISTICAL PRELIMINARIES

Introduction

Random Variables

Transformation of Variables

Wiener-Khinchin Theorem

The Karhunen-Loeve Expansion

Statistical Independence

Characteristic Functions and Generating Functions

Detection

References

THE GAUSSIAN PROCESS

Introduction

Independent Gaussian Variables

Correlated Gaussian Variables

Higher-Order Correlations

Gaussian Processes

Complex Gaussian Processes

Joint Statistical Properties

Properties of the Derivative of a Complex Gaussian Process

Joint Phase Derivative Statistics

References

PROCESSES DERIVED FROM GAUSSIAN NOTES

Introduction

Rice Variables

Rice Processes

Gamma Variables

Gamma Processes

Statistics of the Derivative of a Gamma Process

Compound Variables

Other Commonly Encountered Distributions

References

SCATTERING BY A COLLECTION OF DISCRETE OBJECTS: THE RANDOM WALK MODEL

Introduction

The Incident Wave

Moments of the Field Scattered by a Fixed Number of Small Particles

The Probability Distribution of the Scattered Wave

Variations in Step Length: Illumination by a Gaussian Beam

The Effect of Variations in Step Number

Intensity Correlation

Partially Developed Speckle

References

SCATTERING BY CONTINUOUS MEDIA: PHASE SCREEN MODELS

Introduction

Scattering Geometries

Time-Dependent Scattering

Scattering into the Fresnel Region

Fraunhofer Scattering

Scattering in Non-Gaussian Regimes

Surface Scattering

References

SCATTERING BY SMOOTHLY VARYING PHASE SCREENS

Introduction

"Smooth" Models for the Phase Correlation Function

Qualitative Features of Scattering by Smoothly Varying Phase Screens

Calculation of the Scintillation Index in the Fresnel Region

Predicted Behavior of the Scintillation Index in the Fresnel Region

Higher-Order Statistics in the Fresnel Region

Spatial Coherence Properties in the Fresnel Region

Calculation of the Scintillation Index in the Fraunhofer Region

Predicted Behavior of the Scintillation Index in the Far Field

Higher-Order Statistical Properties in the Far Field

Coherence Properties in the Far Field

Phase Statistics

References

SCATTERING BY FRACTAL PHASE SCREENS

Introduction

Scattering into the Fresnel Region by a Fractal Phase Screen

Scattering into the Fraunhofer Region by a Fractal

Phase Screen

Subfractal Phase Screens

Ray Density Fluctuations beyond a Subfractal Phase Screen

Coherence Properties of the Intensity Beyond a Subfractal Screen

Outer Scale Effects

Scattering into the Fraunhofer Region by a Subfractal Screen

Concluding Remarks

References

OTHER PHASE SCREEN MODELS

Introduction

Scattering by Smoothly Varying Gamma Distributed Phase Screens

Scattering by Fractal Gamma Distributed Phase Screens

Telegraph Wave Phase Screens

Scattering by Telegraph Wave Phase Screens

Phase Statistics

Concluding Remarks

References

PROPAGATION THROUGH EXTENDED INHOMOGENEOUS MEDIA

Introduction

Single Phase Screen Approximation

Power-Law Models for the Refractive Index Spectrum

Multiple Phase Screens

Propagation of Electromagnetic Waves through Turbulence

Intensity Fluctuations

References

MULTIPLE SCATTERING: FLUCTUATIONS IN DOUBLE PASSAGE AND MULTIPATH SCATTERING GEOMETRIES

Introduction

Multiple Scattering in Particulates

Enhanced Backscattering through Continuous Media

A Phase Screen Model for Enhanced Backscattering

Fluctuations in Double Passage Configurations

Multipath Near Surfaces

References

VECTOR SCATTERING: POLARIZATION FLUCTUATIONS

Introduction

The Polarization Characteristics of Gaussian Speckle

Non-Gaussian Polarization Effects in Scattering by Particles

Correlation of Stokes Parameters in Particle Scattering

Scattering from Particles Near an Interface

Polarization Fluctuations: Particles Near an Interface

References

K-DISTRIBUTED NOISE

Introduction

Experimental Evidence

A Population Model for Scatterer Number Fluctuations

Properties of the Scattered Intensity

Related Distributions

Statistical Mechanics

References

MEASUREMENT AND DETECTION

Introduction

Temporal Averaging of a Gamma-Lorentzian Process

Approximations for the Effect of Temporal and Spatial Integration

Averaging Signals with More than One Scale

Enhancement of Fluctuations Caused by Filtering

The Effect of Finite Dynamic Range

The Effect of Finite Measurement Time

Noise in Frequency Demodulation

Detection

Quantum Limited Measurements

References

NUMERICAL TECHNIQUES

Introduction

The Transformation of Random Numbers

Gaussian Random Numbers

The Telegraph Wave

The Gaussian Random Process

Non-Gaussian Processes

Simulation of Wave Propagation

Multiple Phase Screens

References

About the Series

Series in Optics and Optoelectronics

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Subject Categories

BISAC Subject Codes/Headings:
SCI053000
SCIENCE / Optics
TEC019000
TECHNOLOGY & ENGINEERING / Lasers & Photonics