## Electromagnetic Scintillation: Volume 2, Weak ScatteringElectromagnetic Scintillation describes the phase and amplitude fluctuations imposed on signals that travel through the atmosphere. These volumes provide a modern reference and comprehensive tutorial for this subject, treating both optical and microwave propagation. Measurements and predictions are integrated at each step of the development. The first volume dealt with phase and angle-of-arrival measurement errors, which are accurately described by geometrical optics. This second volume concentrates on amplitude and intensity fluctuations of the received signal. |

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### Contents

1 | |

2 The Rytov Approximation | 10 |

3 Amplitude Variance | 33 |

4 Spatial Covariance | 122 |

5 The Power Spectrum and Autocorrelation | 167 |

6 Frequency Correlations | 188 |

7 Phase Fluctuations | 214 |

8 Double Scattering | 247 |

Appendix D Bessel Functions | 390 |

Appendix E Probability Distributions | 400 |

Appendix F Delta Functions | 408 |

Appendix G Kummer Functions | 414 |

Appendix H Hypergeometric Functions | 416 |

Appendix I Aperture Averaging | 418 |

Appendix J Vector Relations | 421 |

Appendix K The Gamma Function | 422 |

9 Fieldstrength Moments | 278 |

10 Amplitude Distributions | 316 |

11 Changes in Polarization | 359 |

12 The Validity of the Rytov Approximation | 367 |

Appendix A Glossary of Symbols | 375 |

Appendix B Integrals of Elementary Functions | 384 |

Appendix C Integrals of Gaussian Functions | 388 |

Appendix L Greens Function | 425 |

Appendix M The Method of Cumulant Analysis | 427 |

Appendix N Diffraction Integrals | 429 |

Appendix O Feynman Formulas | 430 |

431 | |

435 | |

### Common terms and phrases

amplitude fluctuations amplitude variance aperture averaging astronomical atmosphere beam waves Bessel functions calculate coordinates defined depends describe diffraction eddies electromagnetic equation estimate experiments expression field strength Fresnel length Gaussian geometrical optics influence inner scale length ionosphere irregularities Journal Kolmogorov model line-of-sight log-normal distribution logarithmic amplitude measured microwave mutual coherence function observations Optical Society ofAmerica outer scale length parameter paraxial approximation path length phase and amplitude phase fluctuations phase variance plane and spherical plane wave plane-wave plotted in Figure power spectrum Poynting vector predicted Radio random medium receiver refractive-index reproduced in Figure result Rytov approximation Rytov solution satellite scintillation scintillation level second-order spatial correlation spatial covariance spherical waves structure function telescope terrestrial troposphere turbulence spectrum V. I. Tatarskii values variable vector Wave Propagation wavelength wavenumber weak scattering weak-scattering weighting function zenith angle δε