Coherent Wavefront Reconstruction Using Object Statistics

A coherently illuminated diffuse scatterer (object) gives rise to ensemble field statistics at spatial locations in the Fraunhofer plane of the object modeled by circularly complex Gaussian random variables [ref 1]. The joint probability density function for the phase is used to determine the ensemble phase correlation function at two arbitrary spatial locations in the object’s Fraunhofer plane (the entrance pupil plane of a telescope imaging the object). The phase correlation function is used in conjunction with a minimum variance technique to obtain an optimum solution matrix mapping phase difference measurements to phase estimates at arbitrary points in the pupil. Expressions for the expected mean squared phase error are developed for the minimum variance technique and compared with conventional Least Mean Squared reconstructors. Phase estimates using the minimum variance technique and known amplitudes are used to reconstruct the image for simple targets.