Raster Grid Pathology and Other Ambiguities in Blind Ptychography
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Blind ptychography is a phase retrieval method using multiple diffraction patterns from different, overlapping parts of the unknown object illuminated with an unknown probe. Uniqueness problem for blind ptychography is analyzed rigorously for the raster scan and its variants. The block phases are shown to form an arithmetic progression and the complete characterization of the raster scan ambiguities is given, including: First, the periodic raster grid pathology of degrees of freedom proportional to the squared step size and, second, a non-periodic, arithmetically progressing phase shift from block to block. Finally a simple modification to the raster scan is introduced and demonstrated to remove all ambiguities other than the scaling factor and the affine phase ambiguity which are inherent to any blind ptychography.
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