Optical Channels Fibers, Clouds, Water, and the Atmosphere

Applications of Communications Theory Series Editor: R. W. Lucky, AT & T Bell Laboratories

Recent volumes in the series:

COMPUTER COMMUNICATIONS AND NETWORKS John R. Freer

COMPUTER NETWORK ARCHITECTURES AND PROTOCOLS Edited by Paul E. Green, Jr.

DATA TRANSPORTATION AND PROTECTION John E. Hershey and R. K. Rao Yarlagadda

DEEP SPACE TELECOMMUNICATIONS SYSTEMS ENGINEERING Edited by Joseph H. Yuen

DIGITAL PHASE MODULATION John B. Anderson, Tor Autin, and Carl-Erik Sundberg

DIGITAL PICTURES: Representation and Compression Arun N. Netravali and Barry G. Haskell

ERROR~CORRECTION CODING FOR DIGITAL COMMUNICATIONS George C. Clark, Jr., and J. Bibb Cain

FIBER OPTICS: Technology and Applications Stewart D. Personick

FUNDAMENTALS OF DIGITAL SWITCHING Edited by John C. McDonald

MODELING AND ANALYSIS OF COMPUTER COMMUNICATIONS NETWORKS Jeremiah F. Hayes

MODERN TELECOMMUNICATION!S E. Bryan Carne

OPTICAL CHANNELS: Fibers, Clouds, Water, and the Atmosphere Sherman Karp, Robert M. Gagliardi, Steven E. Moran, and Larry B. Stotts

OPTICAL FIBER TRANSMISSION SYSTEMS Stewart D. Personick

PRACTICAL COMPUTER DATA COMMUNICATIONS William J. Barksdale

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Optical Channels Fibers, Clouds, Water, and the Atmosphere

Sherman Karp Lutronix, Inc. San Diego, California

Robert M. Gagliardi University of Southern California Los Angeles, California

Steven E. Moran SAIC San Diego, California

Larry B. Stotts DARPA Arlington, Virginia

Springer Science+Business Media, LLC

Library of Congress Cataloging in Publication Data

Optical channels: fibers, clouds, water, and the atmosphere I Sherman Karp ... [et al.].

p. em.- (Applications of communications theory) Includes bibliographies and index. ISBN 978-1-4899-0808-7 ISBN 978-1-4899-0806-3 (eBook) DOI 10.1007/978-1-4899-0806-3 1. Optical communications. I. Karp, Sherman. II. Series.

TK5103.59.066 1988 621.38'0414-dcl9

© 1988 Springer Science+ Business Media New York Originally published by Plenum Press, New York in 1988 Softcover reprint of the hardcover 1st edition 1988

All rights reserved

88-15063 CIP

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

Preface

When we were first approached by Dr. Lucky to write this book we were very enthusiastic about the prospect, since we had contemplated a similar project for quite some time. The difficulty lay in how best to digest the vast amount of data on optical propagation, reduce it to a book of manageable size, and simultaneously form the transition from the physics of propagation to the engineering of optical channels. This is the intent of Optical Channels. In accomplishing our goal it was necessary to condense the material on optical propagation and, in so doing, we have left a large amount to be handled via references. We have tried to make these decisions in a consistent manner so that the book will be uniform in its treatment of this topic.

We identify four channels for consideration: the free-space channel, which: is characteristic of a tranquil atmosphere or a space-to-space link; the turbulent channel, which is characteristic of the atmospheric channel; the scatter channel in two forms, clouds and water; and the fiber optic channel. For each of these channels we have tried to reduce the applicable propagation theory to a level that can be used for engineering design. This has been done by example, but here again decisions had to be made on which examples to present. We have not tried to present any material on optical components and consequently other references on engineering would be necessary to supplement this book.

We have presented the material on optical propagation from two parallel points of view, radiative transport and Maxwell's equations, and have tried to show the relationship between the two. Since the relationship is complex, most of this discussion has been relegated to an appendix and the references. In Chapter 1 we introduce the concept of sources, both point and distributed, by using the traditional concepts of radiance. The propaga­tion of radiance in the free-space environment is discussed, as are methods for considering distributed and noise sources. In Chapter 2 we introduce the concept of the mutual coherence function and show how it is propagated

v

vi Preface

between source and receiver aperture and then between aperture and detec­tor. In the process we introduce the concept of a linear channel and discuss how this affects the propagation of mutual coherence. In so doing, we discuss the issues of signal narrowbandedness and time-space separability. When the channel is separable we see that all spatial effects can be analyzed by passing the mutual coherence function through a channel transfer func­tion, a process much like that covered by conventional filter theory. This concept is used in Chapter 5 for the turbulence channel, and in parts of Chapter 7 for the scatter channel. In Chapter 3 we present an overview on how to make signal-to-noise calculations when the mutual coherence is also included, for both coherent and incoherent systems. Each type of system is described as necessary. We also discuss how to make bit error calculations, with special focus on the avalanche detector. In Chapter 4 we use results from radiative transport theory to describe the behavior of the fiber optic channel. Generic results are presented wherever possible. In Chapter 5 we present a thorough review of the known results in propagation through turbulent media. These results are then applied to both incoherent and coherent communication systems. In Chapter 6 we present a review of the known physical constituents of the optical scatter channels, e.g., clouds, haze, fog, and water. This chapter brings this material together for the first time in a manner and form that permit us to consider the optical scatter channel in its general systems context. Finally, in Chapter 7 we again present a summary review of the known transmission results for optical scatter channels. Topics discussed include pulse stretching in clouds and blue-green propagation into and through water. Whenever possible, general~ examples are chosen from which insight into the basic problems can be presented.

This book was written to be used primarily as a reference book for engineers working on optical communication systems. Consequently it uses specific individual optical channels for examples. For those interested in fiber optics, Chapter 1 will give some insight into the behavior and charac­terization of optical sources. To understand this topic there is no need for a discussion of mutual coherence, so one would then go to Chapter 3 for a discussion of signal-to-noise ratios and bit error probabilities. In Chapter 4 we cover the effects of scattering, absorption, and pulse stretching as required to size communication links. We have not included information on couplers and other components that would also be needed to design fiber optic networks.

Those interested in designing transatmospheric systems would again start in Chapter 1. However, they would next proceed to Chapter 2 for the required information on the mutual coherence function and channel transfer functions. From there one would proceed to Chapter 3 to learn about calculating communication system signal-to-noise ratios and bit errors.

Preface vii

Finally, one would end at Chapter 5, in which the turbulent channel is discussed with design examples.

Those interested in underwater communications would also proceed through Chapters 1-3, skip to Chapter 6 for information on the scattering properties of water, and go on from there to Chapter 7 for models and examples of the underwater channel.

For those engineers interested in the cloud channel or other similar channels in which use of mutual coherence breaks down, the route would be Chapters 1, 3, 6, and 7. We point out here that Chapter 7 considers models for both the forward-angle scattering channel and the general scattering channel. For the latter, Monte Carlo techniques are also presented.

In summary, we have tried to make this book as useful as possible as a resource for engineers interested in designing communication systems for a variety of optical channels. In the process of doing so, we feel that we have also written a state-of-the-art reference book on optical channels that will be useful for those in other disciplines, such as optical radar systems and lidars. Finally, we feel that because of the breadth of material covered, the volume will also serve as a handy reference book for researchers in the field of optical propagation. We would like to thank Drs. G. M. Lee, P. A Bello and R. F. Lutomirski for their technical insights and advice. We also thank Mrs. Gilda Corley for typing the manuscript.

Sherman Karp Robert M. Gagliardi Steven E. Moran

Larry B. Stotts

Contents

Chapter 1. Introduction

1.1. The Optical Transmission System....................................... 1 1.2. Source Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1. Point Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2. Extended Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.2.1. The Traditional Radiometry............................. 9 1.2.2.2. The Radiant Emittance and Irradiance. . . . . . . . . . . . . . . . . . . . 10 1.2.2.3. The Traditional Radiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1l 1.2.2.4. The Traditional Radiant Intensity . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2.5. The Lambertian Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3. Power Collected by a Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4. Noise Sources........................................................ 14

1.4.1. Blackbody Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4.2. Solar Irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4.3. Daytime Sky Radiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.4. Nighttime Sky Radiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.5. Earthshine Radiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Chapter 2. Coherence Theory and Random Channels

2.1. Field Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2. The Mutual Coherence Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3. The Narrowband Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4. Coherence Separability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5. Partially Coherent and Incoherent Spatial Fields . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.6. System Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.7. Linear Channels...................................................... 42 2.8. Receiver Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.9. Clutter.............................................................. 51 2.10. Summary............................................................ 54

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

ix

X Contents

Chapter 3. Optical Receivers

3.1. The Direct Detection Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2. The Heterodyne (Photomixing) Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3. Signal-to-Noise Ratio in Optical Receivers............................... 70 3.4. The Free-Space Optical Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5. Counting Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.6. Binary Digital Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.6.1. Shot Noise Limited, Ideal Gain.................................. 85 3.6.2. Shot Noise Limited, APD Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.6.3. Thermal Noise-Limited Receivers, APD Gain. . . . . . . . . . . . . . . . . . . . . . 87

3.7. Block-Coded Performance............................................. 92 3.7.1. Multilevel Pulse Amplitude Modulation (MPAM).................. 93 3.7.2. Multislot Pulse-Position Modulation (MPPM) . . . . . . . . . . . . . . . . . . . . . 95

3.8. Digital Signaling with Heterodyne Detection ......... : . . . . . . . . . . . . . . . . . . . 97 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Chapter 4. The Fiber Optic Channel

4.1. The Optical Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2. Attenuation and Dispersion in Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3. Dispersion and Pulse Shaping in Fibers Undergoing Diffusion . . . . . . . . . . . . . 112 4.4. Pulse Stretching in Multimode Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.5. Communications Link Models for the Fiber Channel. . . . . . . . . . . . . . . . . . . . . . 117 4.6. Digital Transmission in Fiber Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.7. Designing Fiber Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Chapter 5. The Turbulence Channel

5.1. Atmospheric Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.1.1. Atmospheric Turbulence Models................................. 132 5.1.2. The Atmospheric Scattering Cross Section......................... 137 5.1.3. Models for the Wavenumber Spectrum Structure Parameter . . . . . . . . . 141

5.2. Optical Propagation through Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 5.2.1. The Rytov Method............................................. 146 5.2.2. The Spectrum of Log-Amplitude and Phase Fluctuations. . . . . . . . . . . . 148 5.2.3. The Log-Amplitude, Phase, and Wave Structure Functions . . . . . . . . . . 150 5.2.4. Spatial Coherence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.2.4.1. Spatial Coherence in Weak Turbulence . . . . . . . . . . . . . . . . . . . 152 5.2.4.2. Spatial Coherence in Strong Turbulence . . . . . . . . . . . . . . . . . . 154

5.2.5. Optical Heterodyne Detection in Atmospheric Turbulence . . . . . . . . . . 173 5.2.6. Scintillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

5.2.6.1. Log-Amplitude and Phase Fluctuations for Kolmogorov Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

5.2.6.2. Scintillation Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5.2.6.3. Aperture Averaging of Scintillation. . . . . . . . . . . . . . . . . . . . . . . 182

5.2.7. Angle-of-Arrival Fluctuations.................................... 188 5.2.8. Beam Spreading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Contents xi

5.3. Optical Propagation in Marine Turbulence............................... 197 5.3.1. ct>"(k) for Marine Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 5.3.2. The Scattered Radiance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

5.4. An Example-Multimode Heterodyne Detection . . . . . . . . . . . . . . . . . . . . . . . . . 204 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Chapter 6. The Optical Scatter Channel and Its Properties

6.1. Mie Scattering Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.2. General Characteristics of the Atmosphere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

6.2.1. Atmospheric Haze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 6.2.2. Atmospheric Fogs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 6.2.3. Atmospheric Clouds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 6.2.4. Atmospheric Rain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

6.3. General Characteristics of the Ocean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 6.4. The Apparent Properties of the Sea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

6.4.1. Reflectance.................................................... 254 6.4.2. Irradiance Attentuation Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 6.4.3. Secchi Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

Chapter 7. Mathematical Models for Energy Propagation in the Optical Scatter Channel

7.1. The Mutual Coherence Function for Multiple-Forward-Scatter Media....... 274 7.1.1. The MCF Model............................................... 274 7.1.2. Discussion of the Particulate MCF and Its Approximate Forms...... 276

7.2. Radiation Transport in Atmospheric and Marine Environments . . . . . . . . . . . . 278 7.2.1. The Theory of Radiative Transfer in Mie Scattering Media.......... 280 7.2.2. Multiple-Forward-Scatter Characterizations Using the Small-Angle

Scattering Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 7.2.2.1. A First-Order Solution for Multiple Forward-Scattered

Irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 7.2.2.2. Over-the-Horizon Propagation from Multiple Forward

Scatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 7.2.2.3. The Green's Function for Multiple Scattering... . . . . . . . . . . . 293 7.2.2.4. The Arnush-Fante Multiple-Forward-Scattering

Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 7.2.2.5. Other Mathematical Approaches . . . . . . . . . . . . . . . . . . . . . . . . . 311 7.2.2.6. Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

7.3. The Air/Sea Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 7.3.1. Geometrical Optics Approach to Channel Coupling . . . . . . . . . . . . . . . . 338 7.3.2. Irradiance Transmittance through the Air/Sea Interface. . . . . . . . . . . . . 343

7.3.2.1. Light Transmittance through Sea Foam................... 346 7.3.3. A Green's Function Approach to Air/Sea Interface Radiance

Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 7.4. System Considerations for the Optical Scatter Channel . . . . . . . . . . . . . . . . . . . . 350

7.4.1. Modulation Format Selection.................................... 351

xii Contents

7.4.2. Noise Considerations........................................... 354 7.4.3. Signal-to-Noise Ratio and Bit Error Probability.................... 356 7.4.4. Link Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 7.4.5. System Design................................................. 360

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

Appendix A. Generalized Radiometry 369

A.l. The Generalized Radiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 A.2. The Mutual Radiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 A.3. The Generalized Radiant Emittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 A.4. The Generalized Radiant Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376

Appendix B. Transport Theory 377

B.l. Heuristic Derivation of the Radiative Transport Equation . . . . . . . . . . . . . . . . . 377 B.2. Radiative Transfer Theory in the Small-Angle Scattering Limit . . . . . . . . . . . . . 379 B.3. Derivation of the Small-Angle Transport Equation from Parabolic Wave Optics

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

Appendix C. Solution of the Small-Angle Transport Equation for the Generalized Radiance and the Mutual Coherence Function 385

Appendix D. Power Flow in Fibers 387

Appendix E. Optical and Physical Thickness Relations for Clouds at Various Locations on the Earth 393

Appendix F. Atmospheric Optical Loss Model 397

Index 401

Optical Channels