Combined nonlinear iterative algorithms for retrieving the complex wave field

Phase retrieval problem has attracted many interests for its wide application in many domains. In this paper we focus on the topic of retrieving the full complex wave field of the object plane from three or more diffraction planes. The iterative Fresnel algorithm always suffers from slow convergence and stagnation problems, while the generalized hybrid-input-output (GHIO) algorithm can effectively accelerate convergence and break stagnation of this kind. Therefore, we combined the two methods into a more efficient algorithm. Each step, the iterative Fresnel algorithm using three or more diffraction intensities is firstly performed to jointly estimate the intensity and the phase of the object plane. Then the GHIO algorithm is adopted to generate a new complex amplitude for the next iteration. It is not necessary to search optimal step size as the conjugate gradient method and can also avoid stagnation, so it is very efficient. This is proved by simulations.