Lensless coherent imaging by a deterministic phase retrieval method with an aperture-array filter

Recently we have proposed a noniterative and analytic phase retrieval method using the filter of an aperture array to reconstruct a complex-valued object from a diffraction intensity pattern [Phys. Rev. Lett.98, 223901 (2007)], but this method suffers from the restriction of the far-field condition of two distances between the object and the filter and between the filter and the detector for the intensity measurement. An improved method, which extends the adaptable condition of those distances to the region of Fresnel diffraction, is proposed here. In addition, the procedure for reducing the influence of noises on the phase retrieval is presented, in which the phase information contained in multiple groups of sampling data of a single intensity distribution is utilized. The usefulness of this method is shown in computer-simulated examples of the object reconstructions, including an object with phase vortices.