Practical implementation of a direct method for coherent diffractive imaging

We experimentally implement a direct, non-iterative method for recovering the complex wave in the exit-surface plane of a coherently illuminated object. The form of illumination is subject to certain conditions. By satisfying these conditions, the complex exit-surface wave is directly recovered from a single far-field intensity pattern, by solving a set of linear equations. These linear equations, whose coefficients depend on the incident illumination, are obtained by analyzing the autocorrelation function of the exit-surface wave. This autocorrelation is constructed by taking the inverse Fourier transform of the diffraction pattern. We introduce a preconditioning step, for the system of linear equations, which improves the robustness of the method to noise. While the present experimental proof of concept has been performed using a visible-light laser, the method is applicable to diffractive imaging using coherent X-ray and electron sources.