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

We consider the reconstruction of a complex-valued object that is coherently illuminated and then viewed through a random-phase screen. The reconstruction involves a phase retrieval based on two intensity measurements. The first is a measurement of the long-exposure averaged intensity of a Fourier transform of the image; it yields full information on the magnitude of the object Fourier transform but noi nformation on its phase. The second measurement is made with the image field modulated by an exponential function. This modulation has the effect of shifting the Fourier-transform function along the imaginary axis of the complex plane of its argument, thus making its intensity dependent on the unknown object phase. This method is capable of reconstructing the object except for an inherent ambiguity corresponding to a simple displacement. The effects of the noise arising from averaging over finite, instead of infinite, exposure times and the quantum noise were assessed. A computer-simulated example of reconstru ting a two-dimensional object demonstrated that the reconstruction is robust. The reconstruction error increases with an increase of the variance of the random-phase function and with a decrease of its correlation length.