Numerical optimization algorithms for wavefront phase retrieval from multiple measurements

Wavefront phase retrieval from a set of intensity measurements can be formulated as an optimization problem. Two nonconvex models (MLP and its variant LS) based on maximum likelihood estimation are investigated in this paper. We derive numerical optimization algorithms for real-valued function of complex variables and apply them to solve the wavefront phase retrieval problem efficiently. Numerical simulation is given with application to three test examples. The LS model shows better numerical performance than that of the MLP model. An explanation for this is that the distribution of the eigenvalues of Hessian matrix of the LS model is more clustered than that of the MLP model. We find that the LBFGS method shows more robust performance and takes fewer calculations than other line search methods for this problem.