Phase retrieval for arbitrary complex-valued objects using structured illumination

A method to solve of the phase retrieval problem in a non-convex formulation for complex-valued objects with a support constraint is proposed. It is shown that two coded diffraction patterns (CDPs) obtained in the same Fresnel or Fraunhofer diffraction plane by masking an object with two, direct and inverse, random binary amplitude masks, are sufficient to reconstruct an arbitrary complex-valued object up to the global phase. The general solution of the problem was found as the sum of two mutually phase-consistent partial solutions obtained by applying the modified error-reduction or hybrid input-output algorithm to each of two "mask+CDP" pairs. The results of model experiments confirmed the possibility of noise-resistant and high-accuracy retrieval of complex-valued objects of various types with the oversampling ratio σ ≥ 2 making use of a small number of iterations. The method is applicable to coherent radiation of any kind.