Non linear phase retrieval from fresnel diffraction patterns using the frechet derivative

Several methods of phase retrieval for in line phase tomography have already been investigated based on the linearization of the relation between the phase shift induced by the object and the diffracted intensity. They use the Transport Intensity Equation (TIE) or the Contrast Transfer Function (CTF), or mixed approaches. In this work, we present a non linear iterative approach using the Frechet derivative of the intensity recorded at a few number of propagation distances. The inverse problem is regularized with the smoothing L₂ norm of the phase gradient. The evaluation of the method was performed using a simple phase map, both with and without noise. Our approach outerperforms the linear methods on simulated noisy data up to high noise levels.