SPECKLE STATISTICS FROM GAMMA-DISTRIBUTED RANDOM-PHASE SCREENS

We study the statistics of speckle produced in the far field by a class of non-Gaussian random-phase screens. These screens introduce phase fluctuations whose first-order statistical properties are described by a gamma distribution. Assuming that the illuminated region contains a large number of independent scattering centers, we derive expressions for various statistical properties of the speckle and analyze their behavior as a function of the point of observation, the number of uncorrelated areas illuminated, and the statistical parameters of the diffuser. Of particular interest are the speckle contrast, the strength of the specular component, and the probability-density functions of intensity and phase. It is found that the speckle contrast is extremely sensitive to the detailed form of the probability-density function of the random phase introduced by the diffuser. This result makes inappropriate the estimation of surface-roughness parameters from measurements of this quantity.