Phase retrieval with the transport-of-intensity equation in an arbitrarily shaped aperture by iterative discrete cosine transforms.

A transport-of-intensity equation (TIE)-based phase retrieval method is proposed with putting an arbitrarily shaped aperture into the optical wavefield. In this arbitrarily shaped aperture, the TIE can be solved under nonuniform illuminations and even nonhomogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and nonuniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phase distribution under nonuniform illumination and nonhomogeneous boundary conditions within an arbitrarily shaped aperture, which enables the technique of TIE with hard aperture to become a more flexible phase retrieval tool in practical measurements.