Optimal phase retrieval from multiple observations with Gaussian noise: augmented Lagrangian algorithm for phase objects

A novel iterative phase-retrieval algorithm is developed for reconstruction of phase objects. We propose a constrained variational formulation of the phase-retrieval problem with the forward wave field propagation from the object to the measurement planes as constraints. It is assumed that noisy intensity-only observations are given at measurement planes parallel to the object plane, and the additive noise in the observations is zero-mean Gaussian. This algorithm is derived from the maximum likelihood approach what enables an optimal solution for the phase reconstruction. The advanced performance of the algorithm is demonstrated by numerical simulations.