### Spie Press Book

Field Guide to Atmospheric OpticsPages: 112

Volume: FG02

- Glossary of Symbols / v
- Atmospheric Structure / 1
- Atmospheric Structure with Altitude / 2
- Absorption and Scattering / 3
- Transmittance, Optical Depth, and Visibility / 4
- Meteorological Phenomena / 5
- Kolmogorov Theory of Turbulence / 6
- Classical Turbulence / 7
- Velocity Fluctuations / 8
- Temperature Fluctuations / 9
- Optical Turbulence / 10
- Structure Parameter and Inner Scale / 11
- Cn2 Profile Models / 12
- Power Spectrum Models / 13
- Optical Wave Models / 14
- Paraxial Wave Equation / 15
- Plane Wave and Spherical Wave Models / 16
- Gaussian-beam Wave at Transmitter / 17
- Gaussian-beam Wave at Receiver / 18
- Hermite-Gaussian Beam Wave / 19
- Laguerre-Gaussian Beam Wave / 20
- Example / 21
- Atmospheric Propagation: Second-order Statistics / 22
- Rytov Approximation / 23
- Extended Huygens-Fresnel Principle / 24
- Parabolic Equation Method / 25
- Mean Irradiance and Beam Spreading / 26
- Beam Wander / 27
- Spatial Coherence Radius: Plane Wave / 28
- Spatial Coherence Radius: Spherical Wave / 29
- Spatial Coherence Radius: Gaussian-Beam Wave / 30
- Fried's Parameter and the Phase Structure Function / 31
- Angle of Arrival and Image Jitter / 32
- Examples / 33
- Atmospheric Propagation: Fourth-order Statistics / 35
- Rytov Approximation: Fourth-order Specializations / 36
- Scintillation Index: Theory / 37
- Scintillation Index: Plane Wave / 38
- Scintillation Index: Spherical Wave / 39
- Scintillation Index: Gaussian-beam Wave / 40
- Covariance Function: Plane Wave / 41
- Temporal Power Spectrum: Plane Wave / 42
- Aperture Averaging: Plane Wave / 43
- Aperture Averaging: Spherical Wave / 44
- Example / 45
- Imaging Systems and Adaptive Optics / 46
- Fried's Atmospheric Parameter and Greenwood's Time Constant 47
- Point Spread Function and Modulation Transfer Function / 48
- Spatial Resolution / 49
- Strehl Ratio and Image Resolving Power / 50
- Isoplanatic Angle and Point-ahead Angle / 51
- Zernike Polynomials and Wave Front Representation / 52
- Zernike Polynomials for Atmospheric Imaging / 53
- Modal Expansion and Aperture Filter Functions / 54
- Zernike Tilt, Piston, and Angle-of-Arrival Jitter / 55
- Free Space Optical Communication Systems / 56
- Direct Detection System / 57
- Threshold Detection / 58
- Signal-to-noise Ratio: Direct Detection / 59
- Bit Error-rate / 60
- Coherent Detection System / 61
- Signal-to-noise Ratio: Coherent Detection / 62
- Probability of Fade: Lognormal Model / 63
- Probability of Fade: Gamma-Gamma Model / 64
- Lasersatcom: Mean Irradiance and Beam Spreading / 65
- Lasersatcom: Uplink Scintillation under Weak Fluctuations / 66
- Lasersatcom: Downlink Scintillation under Weak Fluctuations / 67
- Lasersatcom: General Theory for Uplink/Downlink Scintillation / 68
- Lasersatcom: General Theory for Downlink Covariance and Correlation Width / 69
- Laser Radar and Optical Remote Sensing / 70
- Basic Radar Principles / 71
- Statistical Characteristics of Echo Beam / 72
- Enhanced Backscatter: Spherical Wave / 73
- Enhanced Backscatter: Gaussian-beam Wave / 74
- Spatial Coherence / 75
- Scintillation Index: Spherical Wave and Point Target / 76
- Scintillation Index: Gaussian-beam Wave and Point Target / 77
- Scintillation Index: Smooth Target / 78
- Scintillation Index: Diffuse Target I / 79
- Scintillation Index: Diffuse Target II / 80
- Appendix / 81
- Equation Summary / 81
- Notes / 87
- Bibliography / 89
- Index / 91

#### PREFACE

The material in this Field Guide is a condensed version of similar material found in two textbooks: "Laser Beam Propagation through Random Media" by L. C. Andrews and R. L. Phillips and "Laser Beam Scintillation with Applications" by L. C. Andrews, R. L. Phillips, and C. Y. Hopen. Both books are SPIE Press publications.

Topics chosen for this volume include a review of classical Kolmogorov turbulence theory, Gaussian-beam waves in free space, and atmospheric effects on a propagating optical wave. These atmospheric effects have great importance in a variety of applications like imaging, free space optical communications, laser radar, and remote sensing. Specifically, we present tractable mathematical models from which the practitioner can readily determine beam spreading, beam wander, spatial coherence radius (Fried's parameter), angle of arrival fluctuations, scintillation, aperture averaging effects, fade probabilities, bit error-rates, and enhanced backscatter effects, among others.

Notation used in this field guide is largely based on common usage found in propagation studies but may be different from that commonly used in related areas. For example, the symbol "I" is used here for irradiance. In the radiometry community, the symbol "E" is commonly used for irradiance (W/m^2) and the symbol "I" is reserved for intensity (W/sr).

The foundational material for atmospheric optics has generally been widely dispersed throughout the journal literature over many years, making it difficult for researchers to update their knowledge and for newcomers to the field to compile and understand this difficult subject area. It is hoped that this Field Guide will serve a useful purpose for practicing engineers and scientists who wish to have access to such material in a single concise presentation.

Larry C. Andrews

University of Central Florida

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