K-distributed spatial intensity derivatives in monochromatic speckle patterns

In a monochromatic speckle pattern the spatial derivative of the intensity obeys a laplacian distribution density. When the intensity derivative is measured with a detector of finite area, the measured distribution departs from the ideal laplacian form. Exact expressions are given for the mean and the variance of the measured signal and an approximate form for the probability density is derived consisting of a K-distribution form.