Optimal processing of shift interferograms obtained on observation of coherently illuminated objects through a randomly inhomogeneous medium

A coherently illuminated extended object of unknown shape is observed through a randomly inhomogeneous medium. The optimal estimates of the amplitude and phase of the wavefront of the reflected object field are deduced from a series of short-exposure interferograms of the transverse shift for an arbitrary signal/noise ratio. An algorithm for practical estimates is proposed: these estimates are used to synthesize the complex amplitude of the object field and thus construct the image of the object.