Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination

The properties of the iterative phase-retrieval ptychographical imaging technique are modelled. We use the multi-slice method to generate a series of diffraction patterns when a small convergent illumination spot is moved across a silicon crystal orientated in the <1 0 0> direction. These are then used to reconstruct the transmission function of the sample by solving the phase of diffraction patterns using the ptychographical iterative engine (PIE) algorithm [H.M.L. Faulkner, J.M. Rodenburg, Physical Review Letters 93 (2004) 023903], which assumes the object is a thin, two-dimensional grating. It is found that to obtain lattice-resolved reconstructions, the thickness of the crystal should be smaller than half of the corresponding extinction distance, the probe should be highly defocused to obtain a planar enough wave front and the movements of the probe should be as small as possible to minimize the changes in the transmission function of the sample for two adjacent illumination positions