Speckle propagation through atmospheric turbulence: Effects of a random phase screen at the source

By using ABCD ray matrix theory and a random phase screen located near the source, analytic expressions are developed for the mutual coherence function and scintillation index of a Gaussian-beam wave propagating through weak atmospheric turbulence in both the pupil plane and image plane of a receiving system. The phase screen model that we use is based on a previous double-pass analysis by the authors for analyzing speckle propagation from a rough target in a lidar system. In the present context,. it serves as a model for a partially coherent Gaussian-beam wave that is currently used in laser communications. The effect of partial coherence (induced by a diffuser) on the scintillation index of the beam in the presence of weak atmospheric turbulence is investigated as a function of the correlation length of the diffuser and the propagation distance.