Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The Rytov Approximation
- 3 Amplitude Variance
- 4 Spatial Covariance
- 5 The Power Spectrum and Autocorrelation
- 6 Frequency Correlations
- 7 Phase Fluctuations
- 8 Double Scattering
- 9 Field-strength Moments
- 10 Amplitude Distributions
- 11 Changes in Polarization
- 12 The Validity of the Rytov Approximation
- Appendix A Glossary of Symbols
- Appendix B Integrals of Elementary Functions
- Appendix C Integrals of Gaussian Functions
- Appendix D Bessel Functions
- Appendix E Probability Distributions
- Appendix F Delta Functions
- Appendix G Kummer Functions
- Appendix H Hypergeometric Functions
- Appendix I Aperture Averaging
- Appendix J Vector Relations
- Appendix K The Gamma Function
- Appendix L Green's Function
- Appendix M The Method of Cumulant Analysis
- Appendix N Diffraction Integrals
- Appendix O Feynman Formulas
- Author Index
- Subject Index
4 - Spatial Covariance
Published online by Cambridge University Press: 15 December 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The Rytov Approximation
- 3 Amplitude Variance
- 4 Spatial Covariance
- 5 The Power Spectrum and Autocorrelation
- 6 Frequency Correlations
- 7 Phase Fluctuations
- 8 Double Scattering
- 9 Field-strength Moments
- 10 Amplitude Distributions
- 11 Changes in Polarization
- 12 The Validity of the Rytov Approximation
- Appendix A Glossary of Symbols
- Appendix B Integrals of Elementary Functions
- Appendix C Integrals of Gaussian Functions
- Appendix D Bessel Functions
- Appendix E Probability Distributions
- Appendix F Delta Functions
- Appendix G Kummer Functions
- Appendix H Hypergeometric Functions
- Appendix I Aperture Averaging
- Appendix J Vector Relations
- Appendix K The Gamma Function
- Appendix L Green's Function
- Appendix M The Method of Cumulant Analysis
- Appendix N Diffraction Integrals
- Appendix O Feynman Formulas
- Author Index
- Subject Index
Summary
The similarity of signals measured at adjacent receivers is an important feature of electromagnetic scintillation. The way in which their correlation decreases with their separation provides a powerful insight into such phenomena. We discussed the correlation of phase fluctuations measured at nearby receivers in Volume 1. We found there that the phase difference defines the angular accuracy of direction-finding systems and the resolution of interferometric imaging techniques.
In this chapter we will investigate the correlation of signal amplitudes and intensities measured at adjacent receivers. This type of experiment played a crucial role in the development of scintillation physics. Optical measurements of intensity correlation on short paths first validated the description based on Rytov's approximation and Kolmogorov's model of atmospheric turbulence. These experiments were later replicated with microwave and millimeter-wave signals on longer paths.
Diffraction patterns are created on the ground when starlight is scattered by tropospheric irregularities. These patterns are correlated over tens of centimeters and are sometimes visually apparent at the onset of solar eclipses. Astronomical signals are thus spatially correlated over distances that are smaller than most telescope openings. This means that the arriving field is coherent over only a modest portion of the reflector surface. The light-gathering power of astronomical telescopes is limited by this effect unless modern speckle-interferometry techniques are used to reconstruct the original wave-front.
- Type
- Chapter
- Information
- Electromagnetic Scintillation , pp. 122 - 166Publisher: Cambridge University PressPrint publication year: 2003