Nonlinear Optimization Algorithm for Partially Coherent Phase Retrieval and Source Recovery

We propose a new algorithm for recovering both complex field (phase and amplitude) and source distribution (illumination spatial coherence) from a stack of intensity images captured through focus. The joint recovery is formulated as a nonlinear least-square-error optimization problem, which is solved iteratively by a modified Gauss-Newton method. We derive the gradient and Hessian of the cost function and show that our second-order optimization approach outperforms previously proposed phase retrieval algorithms, for datasets taken with both coherent and partially coherent illumination. The method is validated experimentally in a commercial microscope with both Köhler illumination and a programmable light-emitting diode dome.