Improvement of Differential Method for Estimating the Axial Intensity Derivative in the Transport-of-Intensity Equation

Phase retrieval is an important problem in many areas of physics while transport-of-intensity Equation (TIE) is a traditional method for recovering phases by intensity detection. Derivative of axial intensity is an important parameter in TIE and usually obtained by finite difference (FD) method. However, nonlinearity error is unavoidable in these FD methods. We suggest a method for eliminating this error by setting an axial smoothing filter, and the width of smoothing window varies with the parameters of the observation point. Simulation and experimental results of reconstructed wave-front phase with this filter are shown in this paper for demonstrating the performance of this technique.