Abstract

In this paper, a general result is given for the coherence of any order of a wave propagating through a random medium, provided that the phase and the logarithm of the amplitude are gaussian random variables. Because theoretical and experimental work concerned with optical waves propagating through the atmosphere are in good agreement with the prediction of a gaussian random variable for these quantities, such an assumption appears reasonable. For this case, all higher-order coherence functions can be expressed in terms of the autocovariance and cross-covariance functions of log amplitude and phase. The general expression for the higher-order coherence function is shown to agree with the results of other workers for the mutual coherence function and the fourth-order coherence function for a plane monochromatic wave in a homogeneous random medium. However, the general expressions given may be applied for any case in which the covariance functions of log amplitude and phase are known, e.g., spherical-wave or beam-wave propagation, or propagation through a random medium with smoothly varying characteristics as a function of space.

© 1970 Optical Society of America

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Equations (27)

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