Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns

Abstract

Abstract 3D tomographic phase retrieval under the Born approximation for discrete objects supported on a n × n × n grid is analyzed. It is proved that n projections are sufficient and necessary for unique determination by computed tomography with full projected field measurements and that n + 1 coded projected diffraction patterns are sufficient for unique determination, up to a global phase factor, in tomographic phase retrieval. Hence n + 1 is nearly, if not exactly, the minimum number of diffractions patterns needed for 3D tomographic phase retrieval under the Born approximation.