Electromagnetic Scintillation: Volume 2, Weak Scattering

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
How It Began......Page 15
Understanding the Phenomenon......Page 16
The Second Wave of Applications......Page 17
Resources for Learning About Scintillation......Page 18
Approach and Intended Users......Page 19
Acknowledgments......Page 21
1 Introduction......Page 23
1.1 The Born Approximation......Page 25
1.2 The Rytov Approximation......Page 26
1.3 The Plan for this Volume......Page 28
References......Page 31
2.1 Rytov’s Transformation......Page 32
2.1.1 The Relation to Riccati’s Equation......Page 34
2.1.2 The Series-expansion Solution......Page 35
2.2 The Basic Rytov Solution......Page 36
2.2.1 Phase and Amplitude Expressions......Page 38
2.2.1.1 Homogeneous Random Media......Page 39
2.2.1.2 Inhomogeneous Random Media......Page 41
2.2.2 Reduction to Geometrical Optics......Page 43
2.3.1 Tatarskii’s Version......Page 45
2.3.2 Yura’s Version......Page 46
2.3.3 The Equivalence of the Two Versions......Page 48
2.4.1 The Third-order Solution......Page 49
2.4.2 The Fourth-order Solution......Page 51
2.5 Problems......Page 52
References......Page 53
3 Amplitude Variance......Page 55
3.1 The Paraxial Approximation......Page 57
3.2 Terrestrial Links......Page 61
3.2.1 Plane Waves......Page 62
3.2.1.2 Amplitude Variance for the Kolmogorov Model......Page 67
3.2.1.3 The Inner-scale Influence......Page 69
3.2.1.4 The Outer-scale Influence......Page 72
3.2.2 Spherical Waves......Page 74
3.2.3 Aperture Averaging of Scintillation......Page 78
3.2.3.1 Plane Waves......Page 80
3.2.3.2 Spherical Waves......Page 83
3.2.3.3 Experimental Tests......Page 84
3.2.4 Wavelength Scaling of the Scintillation Level......Page 85
3.2.4.1 Microwave Measurements......Page 86
3.2.4.2 Optical Measurements......Page 89
3.2.5 Beam Waves......Page 90
3.2.5.1 Vacuum Field Strength for Beam Waves......Page 91
3.2.5.2 The Amplitude-variance Expression......Page 92
3.2.5.3 Graphical Descriptions......Page 97
3.2.6 The Influence of the Sample Length......Page 100
3.2.7 The Influence of Anisotropic Irregularities......Page 103
3.3.1 The Transmission Expression......Page 107
3.3.1.1 The Variance for the Kolmogorov Model......Page 110
3.3.1.2 Aperture Averaging......Page 111
3.3.3 Wavelength Scaling......Page 117
3.3.4 Zenith-angle Scaling......Page 120
3.3.5 Source Averaging......Page 122
3.3.5.1 Scintillation Correlation of Adjacent Sources......Page 123
3.3.5.2 Averaging for a Planet or Extended Source......Page 124
3.4 The Ionospheric Influence......Page 126
3.4.1 A General Description......Page 127
3.4.2 Frequency Scaling......Page 131
3.4.2.1 Radio-astronomy Observations......Page 132
3.4.2.2 Satellite-signal Observations......Page 133
3.4.3 Zenith-angle Scaling......Page 135
3.5 Problems......Page 136
References......Page 137
4 Spatial Covariance......Page 144
4.1.1.1 The Covariance Expression......Page 145
4.1.2 Spherical Waves......Page 150
4.1.3 Experimental Confirmations......Page 154
4.1.4 The Influence of Aperture Averaging......Page 156
4.1.5 The Inner-scale Influence......Page 158
4.1.6 Beam Waves......Page 159
4.2 Optical Astronomy......Page 160
4.2.1 Describing the Spatial Covariance......Page 162
4.2.2 Atmospheric Modeling......Page 164
4.2.3 Experimental Confirmations......Page 166
4.3 Inversion of Shadow Patterns......Page 169
4.3.2 Series-solution Inversion......Page 170
4.3.3 The Exact Solution for Point Receivers......Page 172
4.3.4 Inversion Using Spatial Filters......Page 174
4.4.1 The Covariance Expression......Page 178
4.4.2 Experimental Tests......Page 182
4.5 Problems......Page 185
References......Page 186
5 The Power Spectrum and Autocorrelation......Page 189
5.1.1 Autocorrelation of Terrestrial Signals......Page 191
5.1.2 The Power Spectrum for Terrestrial Links......Page 193
5.1.2.1 The Plane-wave Power Spectrum......Page 194
5.1.2.2 The Spherical-wave Power Spectrum......Page 197
5.1.3 Power-spectrum Measurements......Page 198
5.2.1 Autocorrelation of Astronomical Signals......Page 200
5.2.2 The Power Spectrum of Astronomical Signals......Page 203
5.3 The Ionospheric Influence......Page 205
References......Page 208
6 Frequency Correlations......Page 210
6.1 Terrestrial Links......Page 211
6.1.1 The Predicted Frequency Correlation......Page 212
6.1.2 Microwave-link Experiments......Page 215
6.1.2.1 Frequency-correlation Measurements......Page 216
6.1.2.2 Amplitude-coherence Measurements......Page 218
6.1.3 Laser Experiments......Page 219
6.1.3.1 Ignoring Inner-scale Effects......Page 221
6.1.3.2 The Inner-scale Influence......Page 222
6.2 Astronomical Observations......Page 223
6.2.1 Wavelength Correlation of Stellar Scintillation......Page 224
6.2.2 Inversion of Stellar Correlations......Page 226
6.3.1 The Predicted Correlation......Page 228
6.3.2 Radio-astronomy Measurements......Page 230
6.3.3 Observations of Satellite Signals......Page 232
References......Page 233
7 Phase Fluctuations......Page 236
7.1 The Phase Variance......Page 237
7.1.1 The Phase Variance for Plane Waves......Page 238
7.1.1.1 The Sum Rule......Page 240
7.1.1.3 Fraunhofer Scattering......Page 241
7.1.1.4 Intermediate Cases......Page 242
7.1.2 The Phase Variance for Spherical Waves......Page 243
7.1.3 The Phase Variance for Beam Waves......Page 244
7.2 The Phase Structure Function......Page 245
7.2.1 The Plane-wave Structure Function......Page 247
7.2.2 The Spherical-wave Structure Function......Page 251
7.2.3 The Beam-wave Structure Function......Page 252
7.3 The Phase Power Spectrum......Page 254
7.3.1 The Plane-wave Power Spectrum......Page 255
7.3.2 Numerical Results......Page 257
7.4 Correlation of Phase and Amplitude......Page 258
7.4.1 Plane-wave Cross Correlation......Page 259
7.4.2 Spherical-wave Cross Correlation......Page 262
7.4.3 Cross-correlation Measurements......Page 263
7.5.2 The Second-order Phase Distribution......Page 264
7.6 Problems......Page 266
References......Page 267
8.1 Basic Expressions......Page 269
8.1.1 Terrestrial Paths......Page 270
8.1.2 Astronomical Observations......Page 271
8.2 Spherical Waves......Page 272
8.2.1 A General Description......Page 273
8.2.2 Isotropic Random Media......Page 275
8.2.3.1 Wide-angle Scattering......Page 276
8.2.3.3 Microwave Attenuation......Page 277
8.2.3.4 The Influence of Microwave Attenuation......Page 280
8.3 Plane Waves......Page 284
8.3.1 General Description......Page 285
8.3.2 Optical and Infrared Observations......Page 288
8.3.3 Radio and Microwave Observations......Page 289
8.3.4 The Relation to Phase and Amplitude Variances......Page 291
8.4 Beam Waves......Page 292
8.4.1 The Expression for (c + id)......Page 293
8.4.3 The Relation to Phase and Amplitude Variances......Page 296
8.5 Problems......Page 297
References......Page 298
9 Field-strength Moments......Page 300
9.1.1 An Analytical Description......Page 301
9.1.2 The Influence on the Received Signal......Page 303
9.1.3 A Physical Model of Out-scattering......Page 305
9.2 The Mean Irradiance......Page 306
9.2.1 Plane and Spherical Waves......Page 307
9.2.2 Beam Waves......Page 308
9.3.1 A Diagrammatic Demonstration......Page 310
9.3.2 A Description with the Poynting Vector......Page 312
9.3.3 Plane and Spherical Waves......Page 314
9.3.4 Beam Waves......Page 317
9.4 The Mutual Coherence Function......Page 320
9.4.1 The Expression for Plane and Spherical Waves......Page 321
9.4.2 Experimental Confirmations......Page 325
9.4.3 The Beam-wave Expression......Page 327
9.5.1 The Mean Logarithmic Irradiance......Page 329
9.5.2 The Variance of the Logarithmic Irradiance......Page 331
9.6 The Variance of Intensity......Page 333
References......Page 335
10 Amplitude Distributions......Page 338
10.1 The Log-normal Distribution......Page 339
10.1.1 Microwave Confirmations......Page 341
10.1.2 Optical Confirmations......Page 343
10.1.4 The Influence of Aperture Averaging......Page 345
10.2 The Second-order Correction......Page 346
10.2.1 The Predicted Distribution......Page 347
10.2.2 Comparison with Numerical Simulations......Page 351
10.3 Non-stationary Conditions......Page 352
10.4 Intermittency......Page 355
10.5 Astronomical Observations......Page 362
10.6 Satellite Signals......Page 363
10.6.1.1 Transionospheric Signals......Page 364
10.6.1.2 The Rice Distribution......Page 368
10.6.1.3 Experimental Indications......Page 369
10.6.1.4 The Nakagami-m Distribution......Page 371
10.6.2 Communication Satellites......Page 374
10.6.2.2 Synoptic Distributions......Page 375
References......Page 376
11 Changes in Polarization......Page 381
11.1 The Diffraction-theory Description......Page 382
11.2.2 Satellite Signals......Page 385
11.3 The Geometrical-optics Description......Page 386
11.4 Problems......Page 387
References......Page 388
12 The Validity of the Rytov Approximation......Page 389
12.1 A Qualitative Approach......Page 390
12.1.2 Fresnel Scattering......Page 392
12.2 An Analytical Approach......Page 393
12.2.1 The Amplitude Limit......Page 394
12.2.2 The Phase Limit......Page 395
References......Page 396
Appendix A Glossary of Symbols......Page 397
Appendix B Integrals of Elementary Functions......Page 406
Appendix C Integrals of Gaussian Functions......Page 410
D.1 Ordinary Bessel Functions......Page 412
Series of Bessel Functions......Page 418
D.2 Modified Bessel Functions......Page 419
E.1 The Gaussian Distribution......Page 422
E.2 The Log-Normal Distribution......Page 424
E.3 The Nakagami-m Distribution......Page 425
E.4 The Bivariate Gaussian Distribution......Page 427
Appendix F Delta Functions......Page 430
Appendix G Kummer Functions......Page 436
Appendix H Hypergeometric Functions......Page 438
Appendix I Aperture Averaging......Page 440
Appendix J Vector Relations......Page 443
Appendix K The Gamma Function......Page 444
Appendix L Green’s Function......Page 447
Appendix M The Method of Cumulant Analysis......Page 449
Appendix N Diffraction Integrals......Page 451
Appendix O Feynman Formulas......Page 452
Author Index......Page 453
Subject Index......Page 457