Non-linear iterative phase retrieval based on Frechet derivative and projection operators

Phase retrieval from Fresnel diffraction patterns is a nonlinear ill-posed inverse problem of paramount importance in various areas of applied physics. Recently a new non-linear iterative algorithm based on a Landweber method with an analytic calculation of the Frechet derivative adjoint has been proposed. In this work, we refine this scheme by introducing Fienup projectors in the algorithm. The new method was tested on noisy simulated data. Our method outperforms the approaches based on the linearization of the relation between the phase shift induced by the object and the diffracted intensity and the former non linear algorithm with no projectors.