Speckle propagation through atmospheric turbulence: Effects of partial coherence of the target

Based on ABCD ray matrix theory and a random phase screen model for the target surface, analytic expressions are developed for the normalized mutual coherence function (MCF) of a reflected Gaussian-beam wave from a finite target in the presence of atmospheric turbulence. This analysis features both pupil plane and image plane expressions and includes partial and fully developed speckle from the target. The target model is a combination of a thin random phase screen and limiting aperture stop such that a weak screen corresponds to a mildly-rough target and a strong (or deep) random phase screen corresponds to fully developed speckle. From the normalized MCF, estimates are given for the speckle size in the pupil plane and image plane as a function of transmitted beam wave characteristics, size and roughness of the target, and size of the receiver collecting lens.