The multiple scattering of waves in irregular media. II. Spatial autocorrelation functions

When a wave passes through a large thickness of a non-absorbing medium containing weak random irregularities of refractive index, large amplitude and phase fluctuations of the wave field can develop. In a previous paper it was shown how to calculate the probability distributions and average values of these fluctuations. An essential feature of the treatment was that it took into account waves which have been scattered many times (multiple scatter). The present paper considers the spatial autocorrelation functions of the intensity and phase fluctuations in a plane parallel to the wave front of the incident wave for conditions of multiple scatter. These autocorrelation functions are important since they are used in studying the scintillation of radio signals from stellar sources, and yield information about the scattering medium causing the scintillations. The autocorrelation functions of the field quantities depend on the moment matrix of a four-dimensional joint probability distribution. The moments, which are elements of the matrix, are certain average values of the scattered field. A set of integro-differential equations is formulated for the moments and solved analytically for some special cases. General solutions for the moments are obtained by numerical integration, in the case where the irregularities of refractive index have a Gaussian autocorrelation function. Curves for the spatial autocorrelation functions of intensity and phase in this case are given for different distances in the medium.

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