Statistical distributions of partially developed speckle based on a small number of constant scatterers with random phase

The speckle phenomenon is observed in coherent imaging systems such as synthetic aperture radar. The authors deal with situations in which the speckle arises from a small random number of constant amplitude scattering points within the resolution cell. Speckle in this context is referred to as partially developed. They first model the surface scattering statistics as a marked point process. They then derive closed form expressions and accurate approximations for the intensity probability density function of single look and multilook speckle using an orthogonal Gram-Charlier type series expansion having gamma-weighted generalized Laguerre polynomials as the basis functions. Using the Kolmogorov-Smirnov test, they show that the series expansions are a good approximation to the actual pdfs