|
|
|
Published by SPIE—The International Society for Optical Engineering P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1 360 676 3290 Fax: +1 360 647 1445 Email: spie@spie.org Web: http://spie.org The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. Printed in the United States of America. Second printing 2007.
Introduction to the SeriesWelcome to the SPIE Field Guides! This volume is one of the first in a new series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series. Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field. The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at fieldguides@SPIE.org. The Field Guide seriesKeep information at your fingertips with all of the titles in the Field Guide Series: Field Guide to Geometrical Optics, John E. Greivenkamp (FG01) Field Guide to Atmospheric Optics, Larry C. Andrews (FG02) Field Guide to Adaptive Optics, Robert K. Tyson and Benjamin W. Frazier (FG03) Field Guide to Visual and Ophthalmic Optics, Jim Schwiegerling (FG04) Field Guide to Polarization, Edward Collett (FG05) Field Guide to Optical Lithography, Chris A. Mack (FG06) Field Guide to Optical Thin Films, Ronald R. Willey (FG07) Field Guide to Spectroscopy, David W. Ball (FG08) Field Guide to Infrared Systems, Arnold Daniels (FG09) Field Guide to Interferometric Optical Testing, Eric P. Goodwin and James C. Wyant (FG10) Field Guide to Atmospheric OpticsThe 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 fluc-tuations, 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/m2) 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. Table of ContentsGlossary of Symbols x Atmospheric Structure 1 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 Kolmogorov Theory of Turbulence 6 Classical Turbulence 7 Velocity Fluctuations 8 Temperature Fluctuations 9 Optical Turbulence 10 Structure Parameter and Inner Scale 11 Profile Models 12 Power Spectrum Models 13 Optical Wave Models in Free Space 14 Optical Wave Models in Free Space 14 Par axial 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 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 Example 33 Example 34 Atmospheric Propagation: Fourth-Order Statistics 35 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 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 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 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 Glossary of SymbolsA Aperture averaging factor bI(ρ, L) Normalized covariance function of irradiance BER Bit error rate BI(r1, r2, L), BI(ρ) Covariance function of irradiance (r, L) Correlation function associated with amplitude enhancement of reflected wave c Speed of light (= 3 × 108 m/s) , Refractive-index structure parameter Velocity structure parameter Temperature structure parameter CNR Carrier-to-noise ratio d Normalized lens diameter D Diameter of collecting lens DOC Modulus of the complex degree of coherence D(r1, r2, L), D (ρ, L) Wave structure function Ds(ρ, L) Phase structure function Dn(R) Index of refraction structure function DRR(R) Velocity structure function DT(R) Temperature structure function E Electric field erf(x), erfc(x) Error functions EBS Enhanced backscatter EG Equal gain coherent detection scheme EO Electro-optics F Phase front radius of curvature of beam at receiver FAR False alarm rate FG Effective focal length of Gaussian lens FT Fade level (in dB) below the mean on-axis irradiance F0 Phase front radius of curvature of beam at transmitter pFq Generalized hypergeometric function G(s, r; L) Green’s function h Altitude h0 Altitude of transmitter/receiver H Altitude of receiver/transmitter Hn(x) Hermite polynomial of degree n H−V5/7 Hufnagle-Valley C2n(h) model iIF Intermediate frequency (IF) signal current iS Signal current in a receiver iN Shot noise current in a receiver iT Current threshold in a receiver I0(r, L) Irradiance of beam in free space I(r, L) Irradiance of beam in random medium Iv(x) Modified Bessel function of order v Jv(x) Bessel function of order v k Wave number of beam wave (= 2π/λ) Kv(x) Modified Bessel function of order v l0 Inner scale of turbulence L Propagation path length LO Local oscillator L0 Outer scale of turbulence Ln(m)(x) Associated Laguerre polynomial MCF Mutual coherence function MTF Modulation transfer function n(R) Index of refraction n1(R), n1(r, z) Random fluctuation in index of refraction OTF Optical transfer function p Transverse vector between two observation points pI(I) Probability density function of irradiance PSF Point spread function Prd Probability of detection Prfa Probability of false alarm Pr(E) Probability of error Ps Signal power q Strength of turbulence parameter (= L/k) Ql Nondimensional inner-scale parameter (= L/k) Q0 Nondimensional outer-scale parameter (= L/k) r Transverse position of observation point r0 Atmospheric coherence length (Fried’s parameter) R Position vector in three dimensions Re Reynolds number S(r, L) Random phase SI(ω) Power spectral density of irradiance SNR Signal-to-noise ratio SR Strehl ratio TEMmn Transverse electromagnetic mode U0(r, z) Complex amplitude of the field in free space U(r, z) Complex amplitude of the field in random medium W0 Beam radius at transmitter W Beam radius in free space at receiver WB Beam radius in free space at the waist We Effective beam radius in random medium at receiver WG Radius of Gaussian lens WR Radius of target (reflector) surface WSF Wave structure function zB Distance to beam waist from transmitter (r, θ), Zi[m, n] Zernike polynomials α(L) Extinction coefficient α, β Parameters of the gamma-gamma distribution Rytov variance for a spherical wave Γ(x) Gamma function Γ2 (r1, r2, L) Mutual coherence function Γ4(r1, r2, r3, r4, L) Fourth-order moment of the field θ0 Isoplanatic angle Θ0 Beam curvature parameter at transmitter Θ Beam curvature parameter at receiver κ Scalar spatial wave number κl Inner-scale wave number parameter (= 3.3/l0) κm Inner-scale wave number parameter (= 5.92/l0) κ0 Outer-scale wave number parameter (= 2π/L0) λ Wavelength Λ0 Fresnel ratio of beam at transmitter Λ Fresnel ratio of beam at receiver ρ Scalar separation distance between two observation points ρc Correlation width of irradiance fluctuations ρ0 Transverse spatial coherence radius Rytov variance for a plane wave Rytov variance for a Gaussian-beam wave Scintillation associated with reflected wave from a diffuse target Scintillation index (normalized irradiance variance) Irradiance flux variance for a collecting aperture of diameter D Total noise power in detector current Φn(κ) Three-dimensional spatial power spectrum of refractive index ΦRR(κ) Three-dimensional spatial power spectrum of velocity ΦT(κ) Three-dimensional spatial power spectrum of temperature χ(r, L) Random log-amplitude ψ1(r, L), ψ2(r, L) Complex phase perturbations of Rytov approximation ψ1(r, s), ψ2(r, s) Complex phase perturbations of extended Huygens-Fresnel principle Ωf Focusing parameter for geometric focus ΩG Fresnel ratio characterizing radius of Gaussian lens ΩR Fresnel ratio characterizing radius of reflector target ζ Zenith angle ∇2 Laplacian operator ∇2T1 Laplacian operator with respect to r1 ∇2T2 Laplacian operator with respect to r2 〈 〉 Ensemble average |
CITATIONS
Atmospheric optics
Scintillation
Atmospheric modeling
Adaptive optics
Atmospheric propagation
Imaging systems
Statistical modeling
