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.

Features:

• Covers practical problems encountered in optical and microwave remote sensing
• Collects scattering results from random phase screens that provide an excellent model for many non-Gaussian scattering systems
• Discusses K-distributed noise, the most widely used non-Gaussian model
• Outlines some of the practical limitations encountered in experimental measurement and how they affect the interpretation of results, detection, and measurement accuracy
• Provides over 130 figures of theoretical predictions as well as real and simulated data, including photographs of optical scattering patterns

Contents

Statistical Preliminaries

• Random Variables
• Transformation of Variables
• Wiener-Khinchin Theorem
• The Karhunen-Loeve Expansion
• Statistical Independence
• Characteristic Functions and Generating Functions
• Detection

The Gaussian Process

• 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

Processes Derived From Gaussian Notes

• Rice Variables
• Rice Processes
• Gamma Variables
• Gamma Processes
• Statistics of the Derivative of a Gamma Process
• Compound Variables
• Other Commonly Encountered Distributions

Scattering by a Collection of Discrete Objects

• 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

Scattering by Continuous Media: Phase Screen Models

• Scattering Geometries
• Time-Dependent Scattering
• Scattering into the Fresnel Region
• Fraunhofer Scattering
• Scattering in Non-Gaussian Regimes
• Surface Scattering

Scattering by Smoothly Varying Phase Screens

• "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

Scattering by Fractal Phase Screens

• 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

Other Phase Screen Models

• 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

Propagation Through Extended Inhomogeneous Media

• Single Phase Screen Approximation
• Power-Law Models for the Refractive Index Spectrum
• Multiple Phase Screens
• Propagation of Electromagnetic Waves through Turbulence
• Intensity Fluctuations

Multiple Scattering: Fluctuations in Double Passage and Multipath Scattering Geometries

• Multiple Scattering in Particulates
• Enhanced Backscattering through Continuous Media
• A Phase Screen Model for Enhanced Backscattering
• Fluctuations in Double Passage Configurations
• Multipath Near Surfaces

Vector Scattering: Polarization Fluctuations

• 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

K-Distributed Noise

• Experimental Evidence
• A Population Model for Scatterer Number Fluctuations
• Properties of the Scattered Intensity
• Related Distributions
• Statistical Mechanics

Measurement and Detection

• 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

Numerical Techniques

• 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

Index

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