Electromagnetic Scintillation: Volume 1, Geometrical Optics: Geometrical Optics Vol 1 (Electromagnetic scintillation)

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
How it began......Page 13
Understanding the phenomenon......Page 14
The second wave of applications......Page 15
The origin of the present volumes......Page 17
Approach and intended users......Page 18
Acknowledgments......Page 20
1 Introduction......Page 21
References......Page 23
2 Waves in Random Media......Page 25
2.1 Maxwell’s Equations in Random Media......Page 26
2.2 Describing Random Media......Page 31
2.2.1 Stationary Random Processes......Page 32
2.2.2 Ensemble Averages......Page 33
2.2.3 The Spatial Covariance Description......Page 35
2.2.4 The Structure-function Description......Page 38
2.2.5.1 Simplification of Propagation Calculations......Page 41
2.2.5.2 Interpretation of the Wavenumber......Page 43
2.2.5.3 Relation to Measured Quantities......Page 44
2.2.6 The Wavenumber Spectrum of Irregularities......Page 47
2.2.6.1 The Inertial Range......Page 50
2.2.6.2 The Energy-loss Region......Page 53
2.2.6.3 The Energy-input Region......Page 57
2.2.7 Describing Anisotropic Irregularities......Page 67
2.2.8 Inhomogeneous Random Media......Page 71
2.3.1 Refractive-index Expressions......Page 73
2.3.2 Values of C Near the Surface......Page 74
2.3.2.1 Microwave Values of C Near the Surface......Page 75
2.3.2.2 Optical Values of C Near the Surface......Page 77
2.3.3.1 Vertical Profiles of Microwave Values for C......Page 82
2.3.3.2 Vertical Profiles of Optical Values for C......Page 90
2.3.4 Inner-scale Measurements......Page 94
2.3.5 Anisotropy and the Outer Scale Length......Page 98
2.3.5.1 The Outer Scale Length Near the Surface......Page 99
2.3.5.2 The Outer Scale Length in the Free Atmosphere......Page 100
2.3.5.3 A Composite Picture of Atmospheric Anisotropy......Page 103
2.4 Ionospheric Properties......Page 104
2.4.1 The Ambient Ionosphere......Page 106
2.4.2.1 Locating the Source of Scintillations......Page 110
2.4.2.3 Measuring the Structure of Plasma Irregularities......Page 111
2.4.3.1 The Wavenumber-spectrum Description......Page 113
2.4.3.2 The Spectrum of Electron-density Fluctuations......Page 114
Problem 1......Page 118
Problem 2......Page 119
References......Page 120
3 Geometrical Optics Expressions......Page 129
3.1 Solutions of the Eikonal Equation......Page 131
3.2 Nominal Ray Paths......Page 132
3.3 The Signal Phase......Page 136
3.4 The Signal Amplitude......Page 138
3.5 The Angle of Arrival......Page 141
3.6 Validity Conditions......Page 143
3.6.1 The Smooth-medium Condition......Page 144
3.6.2 The Caustic Condition......Page 146
3.6.3 The Diffraction Condition......Page 150
Problem 2......Page 153
References......Page 154
4 The Single-path Phase Variance......Page 156
4.1.1 Microwave Phase Measurements......Page 158
4.1.2 Optical Phase Measurements......Page 160
4.1.3 A Basic Expression for the Phase Variance......Page 161
4.1.4 Frequency Scaling......Page 163
4.1.5 Phase-variance Estimates......Page 164
4.1.5.2 Microwave Link Estimates......Page 165
4.1.6 Anisotropic Media and Distance Scaling......Page 167
4.1.7 Phase Trends and the Sample-length Effect......Page 171
4.1.8 Receiver-aperture Averaging......Page 176
4.2 Satellite Signals......Page 180
4.2.1 GPS Range Errors......Page 182
4.2.2 The Ionospheric Influence......Page 190
References......Page 195
5 The Phase Structure Function......Page 199
5.1.1 Spherical Waves on Horizontal Paths......Page 201
5.1.1.1 A Basic Expression for the Phase Structure Function......Page 202
5.1.1.2 Results for the Kolmogorov Spectrum......Page 204
5.1.1.3 Microwave Measurements......Page 208
5.1.1.4 Optical Measurements......Page 210
5.1.2.1 A Basic Description of the Phase Structure Function......Page 211
5.1.2.2 Results for the Kolmogorov Spectrum......Page 213
5.1.2.3 Results for the von Karman Spectrum......Page 214
5.1.2.4 Optical Phase-difference Measurements......Page 216
5.1.3 The Effect of Atmospheric Anisotropy......Page 217
5.1.4 Beam Waves on Horizontal Paths......Page 220
5.2 Microwave Interferometry......Page 221
5.2.1 D(Rho) for Atmospheric Transmission......Page 224
5.2.1.1 D(Rho) for Oblique Paths......Page 226
5.2.1.2 D(Rho) Based on the Structure Function of n......Page 229
5.2.2.1 The Long-baseline Approximation......Page 230
5.2.2.2 The Baseline Normal to the Plane of Propagation......Page 231
5.2.3 The Influence of the Sample Length......Page 233
5.2.4.1 VLA Structure-function Measurements......Page 239
5.2.4.2 VLBI Structure-function Measurements......Page 244
5.2.4.4 A Perspective......Page 245
5.3 Optical Interferometry......Page 246
5.3.1 Optical Interferometer Installations......Page 248
5.3.2.1 Optical Measurements of D(Rho)......Page 249
5.3.2.2 A Theoretical Description......Page 250
Problem 2......Page 254
References......Page 255
6.1 Atmospheric Variability......Page 260
6.1.1 Atmospheric Wind Fields......Page 261
6.1.2 Taylor’s Frozen-random-medium Hypothesis......Page 262
6.1.3 The Locally Frozen Random-medium Approximation......Page 266
6.1.4 More General Descriptions......Page 269
6.2 The Single-path Variability of Phase......Page 270
6.2.1 Autocorrelation of Phase......Page 271
6.2.1.1 Optical Measurements of Autocorrelation......Page 272
6.2.1.2 Microwave Measurements of Autocorrelation......Page 273
6.2.2 The Temporal Structure Function......Page 276
6.2.3 The Phase Power Spectrum......Page 277
6.2.3.1 A Basic Description of the Power Spectrum......Page 278
6.2.3.2 The Influence of the Sample Length on the Power Spectrum......Page 280
6.2.3.3 Microwave Measurements of the Power Spectrum......Page 282
6.2.3.4 Optical Measurements of the Power Spectrum......Page 284
6.2.4 Wind-speed Variations......Page 286
6.2.4.1 The Gaussian Distribution of Wind Speeds......Page 287
6.2.4.2 The Zero-wind Problem......Page 288
6.2.5 The Influence of Phase Trends......Page 292
6.2.6 The Allan Variance......Page 293
6.3 The Phase Difference for Spherical Waves......Page 294
6.3.1.1 Paths Close to the Surface......Page 295
6.3.1.2 Microwave Autocorrelation Measurements on Elevated Paths......Page 298
6.3.2.1 A Basic Expression for Paths Close to the Surface......Page 300
6.3.2.2 Experimental Confirmations......Page 302
6.4.1 The Autocorrelation of the Phase Difference......Page 304
6.4.2 Phase-difference Power Spectra......Page 306
6.5 Astronomical Interferometry......Page 307
6.5.1 The Time-shifte Phase Structure Function......Page 308
6.5.3 The Allan Variance for Interferometric Data......Page 310
6.5.3.1 An Analytical Description for A(Tau, Rho)......Page 312
6.5.3.2 Measurements of A(Tau, Rho)......Page 315
6.5.4 The Frequency Stability of Arriving Signals......Page 316
6.5.5 Interferometric Power-spectrum Measurements......Page 318
6.5.5.1 The Influence of the Sample Length......Page 319
6.5.5.2 The Single-path Phase Power Spectrum for Atmospheric Transmission......Page 320
6.5.5.3 Interferometric Measurements of Power Spectra......Page 324
6.5.5.4 The Applicability of Taylor’s Hypothesis......Page 327
Problem 2......Page 328
Problem 5......Page 329
Problem 6......Page 330
Problem 7......Page 331
References......Page 332
7 Angle-of-arrival Fluctuations......Page 337
7.1 Measurement Considerations......Page 338
7.1.1 Interferometers......Page 339
7.1.2 Centroid Trackers......Page 341
7.2.1 Plane Waves......Page 342
7.2.2 Spherical Waves......Page 343
7.2.3 Aperture Averaging......Page 344
7.2.4 Beam Waves......Page 348
7.3 Optical Astronomical Signals......Page 353
7.3.1 Angular Position Errors......Page 354
7.3.2 The Spatial Correlation of Angular Errors......Page 358
7.3.3 The Angular-error Correlation for Adjacent Stars......Page 364
7.3.4 Angular-error Averaging by Extended Sources......Page 366
7.3.5 The Influence of Anisotropy......Page 369
7.4 Microwave Tracking of Satellites......Page 372
7.5 Radio Astronomy......Page 376
7.5.1 Ionospheric Influences......Page 377
7.5.2 Tropospheric Influences......Page 382
Problem 2......Page 383
Problem 3......Page 384
References......Page 385
8.1 The Single-path Phase Distribution......Page 390
8.1.2 DeltaEpsilon Non-Gaussian......Page 391
8.1.3 The Effect of Phase Trends......Page 392
8.1.4 Experimental Results......Page 394
8.2.1 The Predicted Distribution......Page 396
8.2.2 Experimental Confirmations......Page 397
8.3 The Angle-of-arrival Distribution......Page 399
8.4 Temporal Distributions......Page 401
References......Page 402
9.1 The Average Field Strength......Page 404
9.2 The Mutual Coherence Function......Page 406
9.3 Frequency Coherence......Page 407
9.4 Shortcomings......Page 408
Problem 2......Page 409
References......Page 410
Appendix A Glossary of Symbols......Page 411
Appendix B Integrals of Elementary Functions......Page 417
Appendix C Integrals of Gaussian Functions......Page 421
D.1 Ordinary Bessel Functions......Page 423
Weber’s integrals......Page 429
Series of Bessel functions......Page 430
D.2 Modified Bessel Functions......Page 431
E.1 The Gaussian Distribution......Page 434
E.2 The Bivariate Gaussian Distribution......Page 436
Appendix F Delta Functions......Page 440
Appendix G Kummer Functions......Page 446
Appendix H Hypergeometric Functions......Page 449
Appendix I Aperture Averaging......Page 452
Appendix J Vector Relations......Page 455
Appendix K The Gamma Function......Page 457
Author Index......Page 461
Subject Index......Page 467