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Field Guide to Atmospheric Optics, Second Edition
Author(s): Larry C. Andrews
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Book Description

This second edition of the Field Guide to Atmospheric Optics contains several new developments in atmospheric propagation through the atmosphere since publication of the first edition (2004). Some of these new topics include the HAP Cn2 profile model, ABCD ray matrices, beam-wander-induced scintillation, phase fluctuations, round-Earth model, analytic models for enhanced backscatter off of semi-rough targets, and non-Kolmogorov anisotropic models. As in the first edition, this Field Guide includes a review of classical Kolmogorov theory, Gaussian-beam waves in free space, and tractable atmospheric propagation models for the second-order and fourth-order field moments known, respectively, as the mutual coherence function and fourth-order cross-coherence function. Specializations of these general field moments allow the practitioner to easily calculate beam spreading, beam wander, spatial coherence (the Fried parameter), angle-of-arrival fluctuations, scintillation index, aperture-averaging effects, fade probabilities, bit error rates, and enhanced backscatter effects, among others. Knowledge of these mathematical models is important in many applications like imaging, free-space optical communications, and laser radar.


Book Details

Date Published: 4 January 2019
Pages: 182
ISBN: 9781510619371
Volume: FG41

Table of Contents
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Glossary of Symbols

Atmospheric Structure
Atmospheric Structure with Altitude
Absorption and Scattering
Transmittance, Optical Depth, and Visibility
Meteorological Phenomena

Kolmogorov Theory of Turbulence
Classical Turbulence
Velocity Fluctuations
Temperature Fluctuations
Optical Turbulence
Structure Parameter and Inner Scale
Power Spectrum Models

Optical Wave Models in Free Space
Paraxial Wave Equation
Plane Wave and Spherical Wave Models
Gaussian-beam Wave at the Transmitter
Gaussian-beam Wave at the Receiver
Hermite–Gaussian Beam Wave
Laguerre–Gaussian Beam Wave
Annular Beam
ABCD-Ray-Matrix Representation
Single Gaussian Lens
Propagation Off of a Smooth Reflector
Example: Free-Space Gaussian Beam
Example: ABCD Propagation

Atmospheric Propagation: Second-Order Statistics
Second Moment of the Field
Free-Space Mutual Coherence Function
Rytov Approximation
Mutual Coherence Function
Mean Irradiance and Beam Spreading
Beam Wander and Short-Term Beam Radius
Beam Wander: Graphs
Spatial Coherence Radius: Plane Wave
Spatial Coherence Radius: Spherical Wave
Spatial Coherence Radius: Gaussian-Beam Wave
Graph of Spatial Coherence Radius and the Fried Parameter
Angle of Arrival and Image Jitter
Example: Spot Size and Beam Wander
Angular and Temporal Frequency Spectra

Atmospheric Propagation: Fourth-Order Statistics
Fourth-Order Field Moment
Rytov Approximation: Fourth-Order Specializations
Scintillation Index: General Theory
Scintillation Index: Plane Wave
Scintillation Index: Spherical Wave
Scintillation Index: Gaussian-Beam Wave
Scintillation Index: Graphs
Beam-Wander-Induced Scintillation Index
Beam-Wander-Induced Scintillation Index: Graphs
Aperture Averaging: Plane Wave
Aperture Averaging: Spherical Wave
Aperture Averaging: Gaussian-Beam Wave
Example: Scintillation and Aperture Averaging
Covariance Function: Plane Wave
Covariance Function: Spherical Wave
Covariance Function: Gaussian-Beam Wave
Temporal Power Spectrum: Plane Wave
Phase Fluctuations: Plane Wave
Temporal Power Spectrum of Phase

Imaging Systems and Adaptive Optics
Fried Parameter and Greenwood Time Constant
Point Spread Function and Modulation Transfer Function
Spatial Resolution in Free Space
Strehl Ratio and Image-Resolving Power
Isoplanatic Angle and Point-Ahead Angle
Zernike Polynomials and Wavefront Representation
Zernike Polynomials for Atmospheric Imaging
Modal Expansion and Aperture Filter Functions
Zernike Tilt, Piston, and Angle-of-Arrival Jitter
Tilt Anisoplanatism: Plane Wave
Tilt Anisoplanatism: Spherical Wave

Free-Space Optical Communication Systems
FSOC Overview
Direct-Detection System
Performance Measure: Strehl Ratio
Performance Measure: Optical Power
Performance Measure: Signal-to-Noise Ratio
Threshold Detection: Free Space
Bit Error Rate
Irradiance Probability Density Function (PDF) Models
Statistical Models of Fade and BER
Coherent Detection System
Coherent Detection: Signal-to-Noise Ratio

Laser Satellite Communication Systems
Satellite Orbits
HV (Hufnagel–Valley) Cn2 Profile Model
HAP (Hufnagel–Andrews–Phillips) Cn2 Profile Model
Comparison of Cn2 Profile Models
Spatial Coherence Radius and the Fried Parameter
Angle of Arrival and Isoplanatic Angle
Irradiance Statistics: Downlink Path—Weak Fluctuations
Irradiance Statistics: Downlink Path—Deep Turbulence
Fade Statistics: Downlink Path
Beam Size and Beam Wander: Uplink Path
Scintillation Index: Uplink Path
Uplink Scintillation Index: Graphs
Round-Earth Model
PDF Models for the Uplink Beam
Untracked Uplink Beam: Graphs
Tracked Uplink Beam: Graphs
Fade Statistics: Uplink Path and Round-Earth Model
Risk Analysis: Probability of Surge

Laser Radar and Optical Remote Sensing
Basic Radar Principles
Statistical Characteristics of Echo Beam
Gaussian-Beam Parameters for a Smooth Target
Smooth Target: Mean Irradiance and Beam Spot Size
On-Axis BSAE: Spherical Wave
Mirror BSAE: Weak Fluctuations
Retroreflector BSAE: Weak Fluctuations
BSAE: Graphs
Retroreflector BSAE: Deep Turbulence
Retroreflector BSAE: Deep-Turbulence Graphs
Semi-rough Target: Free-Space Analysis
Semi-rough Target BSAE: Weak Fluctuations
Diffuse Target BSAE: Weak Fluctuations
Spatial Coherence Radius: Weak Fluctuations
Far-Field Scintillation Index: Weak Fluctuations
Far-Field Scintillation Index: Deep Turbulence
Diffuse Target: Scintillation Index: I
Diffuse Target: Scintillation Index: II

Non-Kolmogorov Atmospheric Turbulence
Non-Kolmogorov Anisotropic Structure
Non-Kolmogorov Spectral Models
Generalized Rytov Variance
Mean Irradiance and Beam Spot Size
Spatial Coherence Radius
Scintillation Index: Weak Fluctuations
Scintillation Index: Graphs

Equation Summary
Bibliography
Index

Preface to Second Edition

There have been a number of new model developments in atmospheric propagation of a laser beam since the publication of the first edition of this Field Guide to Atmospheric Optics, many of which are included in this second edition. Some of the new mathematical models were introduced in Laser Beam Propagation through Random Media by L. C. Andrews and R. L. Phillips (SPIE 2005), but others have been developed since the publication of that text owing to the fact that this is still an active area of research.

Some changes/additions and previous omissions that are included in this second edition of the Field Guide are the following:

      • Connection between visibility and transmittance
      • HAP Cn2 profile model
      • Annular beams
      • ABCD ray matrices
      • New expressions for beam wander
      • Angular and temporal frequency spectra
      • Inclusion of inner-/outer-scale effects in the scintillation index
      • Beam-wander-induced scintillation
      • Phase fluctuations
      • Temporal power spectrum of phase
      • Performance measures of FSOC systems
      • Round-Earth model
      • New probability density function models for tracked and untracked uplink paths
      • New models for EBS from smooth and semi-rough targets
      • Non-Kolmogorov anisotropic models

The subject of atmospheric optics is more extensive than what is presented here. For example, most treatments of the subject matter concentrate heavily on the scattering and absorption by the molecular gases, particulates, and aerosols in the atmosphere. This usually also includes a detailed analysis of the wind, temperature, and pressure, particularly as a function of altitude. Another area of concentration in many treatments of the subject takes into account meteorological optics, which is a fascinating area all of its own. The subject of optical phenomena is often presented in great detail covering rainbows, halos, mirages, red sunsets, and so on.

We touch on most of the above-mentioned areas of Atmospheric Optics in this Field Guide, but some only briefly. As in the first edition, our treatment of Atmospheric Optics concentrates more heavily on the propagation of optical waves through optical turbulence and the mathematical models used to describe this phenomenon. In particular, we discuss how the many deleterious effects created by the atmosphere impact various applications that depend on optical wave propagation like free-space optical communications, imaging, and laser radar, among others.

I wish to thank Larry Stotts and two anonymous reviewers for their many useful comments on the first draft of this second edition. Finally, the computer simulation data that appear in some of the figures were provided to me over a period of several years courtesy of the following individuals: Gary J. Baker, Aniceto Belmonte, Federico Dios, Ronald R. Parenti, and Jaume Recolons.

Larry C. Andrews
Professor Emeritus
Townes Laser Institute
CREOL, College of Optics
University of Central Florida


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