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Modeling Fluctuations in Scattered Waves

Modeling Fluctuations in Scattered Waves by E. Jakeman
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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
CRC Press; June 2006
333 pages; ISBN 9781420012163
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Title: Modeling Fluctuations in Scattered Waves
Author: E. Jakeman; K. D. Ridley
 
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