### Spie Press Book

Laser Beam Propagation through Random Media, Second EditionFormat | Member Price | Non-Member Price |
---|---|---|

Pages: 808

ISBN: 9780819459480

Volume: PM152

- Preface to Second Edition xi
- Preface to First Edition xv
- Symbols and Notation xix

- 1 Prologue 3
- 1.1 Introduction 4
- 1.2 Historical Background of Light 5
- 1.3 Optical Wave Models 8
- 1.4 Atmospheric Effects 9
- 1.5 Application Areas 15
- 1.6 A Brief Review of Communication Systems 22
- 1.7 Summary and Overview of the Book 26
- References 32
- 2 Random Processes and Random Fields 35
- 2.1 Introduction 36
- 2.2 Probabilistic Description of Random Process 37
- 2.3 Ensemble Averages 38
- 2.4 Time Averages and Ergodicity 41
- 2.5 Power Spectral Density Functions 42
- 2.6 Random Fields 45
- 2.7 Summary and Discussion 49
- 2.8 Worked Examples 51
- Problems 53
- References 56
- 3 Optical Turbulence in the Atmosphere 57
- 3.1 Introduction 58
- 3.2 Kolmogorov Theory of Turbulence 58
- 3.3 Power Spectrum Models for Refractive-Index Fluctuations 66
- 3.4 Atmospheric Temporal Statistics 72
- 3.5 Summary and Discussion 73
- 3.6 Worked Examples 74
- Problems 77
- References 80
- 4 Free-Space Propagation of Gaussian-Beam Waves 83
- 4.1 Introduction 84
- 4.2 Paraxial Wave Equation 85
- 4.3 Optical Wave Models 87
- 4.4 Diffractive Properties of Gaussian-Beam Waves 91
- 4.5 Geometrical Interpretations�Part I 96
- 4.6 Geometrical Interpretations�Part II 99
- 4.7 Higher-Order Gaussian-Beam Modes 101
- 4.8 ABCD Ray-Matrix Representations 107
- 4.9 Single Element Optical System 112
- 4.10 Summary and Discussion 118
- 4.11 Worked Examples 122
- Problems 127
- References 133
- 5 Classical Theory for Propagation Through Random Media 135
- 5.1 Introduction 137
- 5.2 Stochastic Wave Equation 137
- 5.3 Born Approximation 141
- 5.4 Rytov Approximation 143
- 5.5 Linear Systems Analogy 151
- 5.6 Rytov Approximation for ABCD Optical Systems 152
- 5.7 Classical Distribution Models 154
- 5.8 Other Methods of Analysis 157
- 5.9 Extended Rytov Theory 159
- 5.10 Summary and Discussion 165
- 5.11 Worked Examples 167
- Problems 170
- References 177
- 6 Second-Order Statistics: Weak Fluctuation Theory 179
- 6.1 Introduction 181
- 6.2 Basic Concepts 182
- 6.3 Mutual Coherence Function 187
- 6.4 Spatial Coherence Radius 192
- 6.5 Angle-of-Arrival Fluctuations 199
- 6.6 Beam Wander 201
- 6.7 Angular and Temporal Frequency Spectra 206
- 6.8 Slant Paths 207
- 6.9 Summary and Discussion 210
- 6.10 Worked Examples 214
- Problems 219
- References 227
- 7 Second-Order Statistics: Strong Fluctuation Theory 229
- 7.1 Introduction 230
- 7.2 Parabolic Equation Method 231
- 7.3 Extended Huygens-Fresnel Principle 234
- 7.4 Method of Effective Beam Parameters 241
- 7.5 Summary and Discussion 247
- 7.6 Worked Examples 250
- Problems 252
- References 255
- 8 Fourth-Order Statistics: Weak Fluctuation Theory 257
- 8.1 Introduction 259
- 8.2 Scintillation Index 261
- 8.3 Beam Wander and Scintillation 269
- 8.4 Covariance Function of Irradiance 279
- 8.5 Temporal Spectrum of Irradiance 282
- 8.6 Phase Fluctuations 288
- 8.7 Slant Paths 299
- 8.8 Summary and Discussion 302
- 8.9 Worked Examples 308
- Problems 313
- References 318
- 9 Fourth-Order Statistics: Strong Fluctuation Theory 321
- 9.1 Introduction 322
- 9.2 Modeling Optical Scintillation 323
- 9.3 Asymptotic Theory 330
- 9.4 Scintillation Theory: Plane Wave Model 333
- 9.5 Scintillation Theory: Spherical Wave Model 341
- 9.6 Scintillation Theory: Gaussian-Beam Wave Model 349
- 9.7 Covariance Function of Irradiance 361
- 9.8 Temporal Spectrum of Irradiance 364
- 9.9 Distribution Models for the Irradiance 367
- 9.10 Gamma-Gamma Distribution 369
- 9.11 Summary and Discussion 379
- 9.12 Worked Examples 384
- Problems 387
- References 390
- 10 Propagation Through Complex Paraxial ABCD Optical Systems 495
- 10.1 Introduction 396
- 10.2 Single Element Optical System 396
- 10.3 Aperture Averaging 409
- 10.4 Optical Systems with Several Optical Elements 425
- 10.5 Summary and Discussion 430
- 10.6 Worked Examples 431
- Problems 433
- References 438

- 11 Free-Space Optical Communication Systems 441
- 11.1 Introduction 442
- 11.2 Direct Detection Optical Receivers 444
- 11.3 Fade Statistics�Part I 449
- 11.4 Fade Statistics�Part II 457
- 11.5 Spatial Diversity Receivers 465
- 11.6 Summary and Discussion 471
- 11.7 Worked Examples 472
- Problems 474
- References 475
- 12 Laser Satellite Communication Systems 477
- 12.1 Introduction 478
- 12.2 Atmospheric Channels 479
- 12.3 Background 484
- 12.4 Second-Order Statistics 490
- 12.5 Irradiance Statistics: Downlink Channel 493
- 12.6 Irradiance Statistics: Uplink Channel 500
- 12.7 Fade Statistics: Downlink Channels 510
- 12.8 Fade Statistics: Uplink Channels 516
- 12.9 Summary and Discussion 520
- 12.10 Worked Examples 524
- Problems 526
- References 529
- 13 Double-Passage Problems: Laser Radar Systems 533
- 13.1 Introduction 534
- 13.2 Laser Radar Configuration 536
- 13.3 Modeling the Backscattered Wave 540
- 13.4 Finite Smooth Target�Part I 547
- 13.5 Finite Smooth Target�Part II 559
- 13.6 Finite Smooth Reflector�Part III 570
- 13.7 Unresolved (Point) Target 575
- 13.8 Diffuse Target 589
- 13.9 Summary and Discussion 596
- 13.10 Worked Examples 597
- Problems 599
- References 604
- 14 Imaging Systems Analysis 607
- 14.1 Introduction 608
- 14.2 Coherent Imaging Systems 610
- 14.3 Incoherent Imaging Systems 614
- 14.4 Laser Imaging Radar 624
- 14.5 Zernike Polynomials 628
- 14.6 Summary and Discussion 636
- 14.7 Worked Examples 637
- Problems 639
- References 642

- 15 Propagation Through Random Phase Screens 647
- 15.1 Introduction 648
- 15.2 Random Phase Screen Models 649
- 15.3 Mutual Coherence Function 653
- 15.4 Scintillation Index and Covariance Function 656
- 15.5 Multiple Phase Screens 659
- 15.6 Summary and Discussion 662
- Problems 664
- References 666
- 16 Partially Coherent Beams 667
- 16.1 Introduction 668
- 16.2 Basic Beam Parameters 669
- 16.3 Mutual Coherence Function�Part I 671
- 16.4 Mutual Coherence Function�Part II 673
- 16.5 Scintillation Index�Part I 680
- 16.6 Scintillation Index�Part II 684
- 16.7 FSO Communication Systems 689
- 16.8 Ladar Model in Free Space 693
- 16.9 Ladar Model in Optical Turbulence 699
- 16.10 Summary and Discussion 704
- 16.11 Worked Examples 704
- Problems 706
- References 710
- 17 Other Beam Shapes 713
- 17.1 Introduction 714
- 17.2 Beam Spreading: Higher-Order Gaussian Beams 714
- 17.3 Annular Beam 720
- 17.4 Other Beams 729
- 17.5 Summary and Discussion 733
- Problems 734
- References 736
- 18 Pulse Propagation 737
- 18.1 Introduction 737
- 18.2 Background 738
- 18.3 Two-Frequency Mutual Coherence Function 740
- 18.4 Four-Frequency Cross-Coherence Function 746
- 18.5 Summary and Discussion 749
- Problems 750
- References 752
- Appendix I: Special Functions 755
- Appendix II: Integral Table 763
- Appendix III: Tables of Beam Statistics 765
- Index 775

### PREFACE to Second Edition

Since publication of the first edition of this text in 1998 there have been several new and important developments in the theory of beam wave propagation through a random medium that we have incorporated into this second edition. Also, there were some topics excluded in the first edition that are now included. Nonetheless, we recognize that the general field of wave propagation through random media has grown in the last several years beyond what we can adequately cover in this one volume. For that reason, the reader should not consider this text an exhaustive treatment of propagation through turbulence.

One specific change in notation introduced here is the use of sigma_R^2 for the Rytov variance in place of sigma_1^2 (except in Chapter 13) to avoid confusion of the latter with the scintillation index sigma_I^2. Other changes/additions that now appear include the following:

- more worked examples and expanded sets of exercise problems
- models for the scintillation index under moderate-to-strong irradiance fluctuations
- models for aperture averaging based on ABCD ray matrices
- beam wander and its effects on scintillation
- theory of partial coherence of the source
- models of rough targets (other than Lambertian) for ladar applications
- phase fluctuations
- analysis of other beam shapes
- expanded analysis of free-space optical communication systems
- expanded imaging systems analysis

Foremost among the new theoretical developments is the extension of the Rytov theory from regimes of weak irradiance fluctuations into moderate-to-strong fluctuation regimes. Although much of this theory has been published in a companion text by the authors and C. Y. Hopen, called LASER BEAM SCINTILLATION WITH APPLICATIONS (SPIE Press, 2001), we present it here in a somewhat more complete treatment along with the standard Rytov theory that formed the basis for the first edition. Another topic in this second edition concerns the effects of beam wander on the scintillation index associated with an untracked beam. Conventional theory predicts that the on-axis scintillation associated with a focused beam along a horizontal path and that for a collimated beam on an uplink path to space will experience a substantial reduction (by orders of magnitude) as transmitter beam size increases provided there is limited beam wander. In the case of an untracked beam, however, the predicted reduction in scintillation will not occur. Also included in this second edition is a treatment of phase fluctuations, incorporating the phase variance, structure function, covariance, and temporal power spectrum. Among other topics, we introduce models for and discuss the role of partial coherence (spatially) of the source beam in reducing scintillation for example, in a free-space optical communication system. The same partial- coherence model can also be employed to describe the reflected radiation from a rough target like that which occurs in many laser radar applications.

In preparing this second edition, each chapter of the first edition was carefully examined for clarity and content, and most chapters have had some alteration in such cases the material is either broadened or simply rearranged, or both. As a consequence, the second edition has expanded the original twelve chapters of the first edition into eighteen chapters divided into three fundamental areas:

Part I: Basic Theory 1 PROLOGUE contains a brief discussion of fundamental concepts and application areas. It is basically the same as in the first edition, but now contains updated information on some of the application areas.

2 RANDOM PROCESSES AND RANDOM FIELDS contains a brief introduction to random processes and random fields. Only minor changes appear from first edition.

3 OPTICAL TURBULENCE IN THE ATMOSPHERE introduces Kolmogorov theory and various spectral models. Only minor changes appear from first edition.

4 FREE SPACE PROPAGATION OF GAUSSIAN-BEAM WAVES the introduction of higher- order Gaussian beam modes has been expanded from first edition and we have also moved the free-space propagation through optical elements by the use of ABCD ray matrices to this chapter.

5 CLASSICAL THEORY FOR PROPAGATION THROUGH RANDOM MEDIA introduces the Rytov approximation and other basic theories of wave propagation through random media. The treatment of Rytov theory for ABCD optical systems now appears in this chapter as well as the extended version of the Rytov theory that permits its use in regimes of strong irradiance fluctuations.

6 SECOND-ORDER STATISTICS: WEAK FLUCTUATION THEORY the second edition expands Chapter 6 from the first edition into Chapters 6 and 7. The discussion concerning the second-order field moment (mutual coherence function) is restricted to weak fluctuations but includes a new treatment of beam wander and slant path formulations in addition to the original horizontal path treatment.

7 SECOND-ORDER STATISTICS: STRONG FLUCTUATION THEORY the parabolic equation method and extended Huygens-Fresnel principle are introduced as theories used for calculating the mutual coherence function under strong irradiance fluctuations. The method of effective beam parameters is also introduced for calculating the spatial coherence radius of a beam and the variance of beam wander displacements.

8 FOURTH-ORDER STATISTICS: WEAK FLUCTUATION THEORY the second edition expands Chapter 7 from the first edition into Chapters 8 and 9. Here we discuss scintillation models and the effect of beam wander on scintillation of both collimated and focused beams. Other new topics included here are a discussion of phase fluctuations and scintillation along a slant path.

9 FOURTH-ORDER STATISTICS: STRONG FLUCTUATION THEORY scintillation models for plane waves, spherical waves, and Gaussian-beam waves are separately developed based on the extended Rytov theory for the strong fluctuation regime. The gamma-gamma distribution for irradiance fluctuations is also introduced in this chapter, illustrating how the parameters of this model are completely determined by atmospheric conditions (refractive-index structure constant, inner scale, and outer scale).

10 PROPAGATION THROUGH COMPLEX PARAXIAL ABCD OPTICAL SYSTEMS the propagation of a Gaussian beam wave through complex paraxial ABCD optical systems in the presence of atmospheric turbulence is featured here. In particular, we use the ABCD method to calculate the effect of a large-aperture receiver (aperture averaging) on the irradiance flux variance in the plane of a detector.

Part II: Applications

11 FREE SPACE OPTICAL COMMUNICATION SYSTEMS here we examine the impact of scintillation on free-space optical communication systems that operate along a horizontal path. Various fade statistics are introduced, including the probability of fade and mean fade time.

12 LASER SATELLITE COMMUNICATION SYSTEMS we extend the treatment from Chapter 11 to examine laser satellite communication systems. Various second-order and fourth-order statistics are developed. Beam-wander-induced scintillation caused in an untracked uplink collimated beam is discussed in detail and several comparisons with recent simulation results are included.

13 DOUBLE-PASSAGE PROBLEMS: LASER RADAR SYSTEMS the double-pass propagation problem associated with a laser radar system is treated here, which includes some new models developed since the first edition was published.

14 IMAGING SYSTEMS ANALYSIS a brief treatment on performance measures of imaging systems is presented. Both coherent and incoherent systems are discussed. We also introduce the Zernike polynomials and related filter functions used in adaptive optics systems.

Part III: Related Topics

15 PROPAGATION THROUGH RANDOM PHASE SCREENS the propagation of a beam wave through a random phase screen is taken up here, calculating the statistical quantities introduced in Chapters 6 and 8. The phase screen model also forms the basis for developing the (spatially) partial coherent beam analysis in Chapter 16.

16 PARTIALLY COHERENT BEAMS the notion of transmitter aperture averaging is presented for a partially coherent source and its impact on a free-space optical communication system. The same idea is used to model a rough target in a laser radar system.

17 OTHER BEAM SHAPES here we examine a few effects of atmospheric turbulence on higher-order Gaussian beams and annular beam shapes.

18 PULSE PROPAGATION this chapter briefly covers some aspects (beam spreading and scintillation) on the propagation of ultra-short pulses.

The second edition contains three appendices at the end of the book: (I) a review of properties associated with some of the special functions; (II) a short table of integrals for easy reference purposes; and (III) tables of tractable formulas for the wave structure function, spatial coherence radius, and scintillation index as predicted by various theories and atmospheric spectrum models.

Last, we value the constructive comments made by several users of the first edition that helped to guide us in developing this second edition.

Larry C. Andrews

Ronald L. Phillips

Orlando, FL

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