  Alternating projection (AP) of various forms, including the Parallel AP
(PAP), Real-constrained AP (RAP) and the Serial AP (SAP), are proposed to solve
phase retrieval with at most two coded diffraction patterns. The proofs of
geometric convergence are given with sharp bounds on the rates of convergence
in terms of a spectral gap condition.
  To compensate for the local nature of convergence, the null initialization is
proposed for initial guess and proved to produce asymptotically accurate
initialization for the case of Gaussian random measurement. Numerical
experiments show that the null initialization produces more accurate initial
guess than the spectral initialization and that AP converges faster to the true
object than other iterative schemes for non-convex optimization such as the
Wirtinger Flow. In numerical experiments, AP with the null initialization
converges globally to the true object.
