  3D tomographic phase retrieval under the Born approximation for discrete
objects supported on a $n\times n\times n$ grid is analyzed. It is proved that
$n$ projections are sufficient and necessary for unique determination by
computed tomography (CT) 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.
