Reconstruction of a complex-valued object in double-passage coherent imaging through a random-phase screen

We consider the reconstruction of a complex-valued object that is coherently illuminated and viewed through the same random-phase screen. The reconstruction is based on two intensity measurements: the intensity of the Fourier transform of the image and the intensity of the Fourier transform of the image when modulated with an exponential filter. The illumination beam has a Gaussian intensity profile of arbitrary width, and the phase screen is assumed to be described by a Gaussian random process of large variance and arbitrary correlation length. Computer-simulated examples of the reconstruction of a two-dimensional complex object demonstrate that the reconstruction is robust.