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The second-order statistics for speckle patterns are derived through the use of an integral equation which determines the moment generating function. A specific geometry of apertures is treated as an example of the techniques developed. The inversion problem of determining the field correlation function from measurements of the integrated intensities is examined in the context of singular-value decomposition. The joint probability density function for the integrated intensities is evaluated.
Barakat et al. (1978) studied this question.