Simultaneous recovery of phase and defocus from coherent through-focus intensity images

Phase retrieval methods have been proposed to recover phase from through-focus intensity images measured on a microscope. It requires measuring the defocus distances of intensity images, usually by a z-axis translation stage. However, it complicates the experiment, adds expense, and suffers from error in the z-stage measurement. In this paper, we propose an algorithm to recover phase from only through-focus intensity images without measuring extra parameters such as defocus, wavelength and pixel size. We formulate the phase retrieval as a least-square error optimization problem and propose an alternating update scheme to solve the nonconvex optimization problem. We validate the algorithm with simulation and experiment.