Uniqueness theorems for tomographic phase retrieval with few coded diffraction patterns

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