Statistics of spatially integrated speckle intensity difference

We consider the statistics of the spatially integrated speckle intensity difference obtained from two separated finite collecting apertures. For fully developed speckle, closed-form analytic solutions for both the probability density function and the cumulative distribution function are derived here for both arbitrary values of the mean number of speckles contained within an aperture and the degree of coherence of the optical field.

Additionally, closed-form expressions are obtained for the corresponding nth statistical moments.