Blind Ptychography: Uniqueness and Ambiguities

Abstract: Ptychography with an unknown mask and object is analyzed for general ptychographic measurement schemes that are strongly connected and possess an anchor. Under a mild constraint on the mask phase, it is proved that the masked object estimate must be the product of a block phase factor and the true masked object. This local uniqueness manifests itself in the phase drift equation that determines the ambiguity at different locations connected by ptychographic shifts. The proposed mixing schemes effectively connects the ambiguity throughout the whole domain such that a distinct ambiguity profile arises and consequently possess the global uniqueness that the block phases have an affine profile and that the object and mask can be simultaneously recovered up to a constant scaling factor and an affine phase factor.