Random phase retrieval approach using Euclidean matrix norm of sum and difference map and fast least-squares algorithm

Abstract

In order to meet the requirements of the in-situ optical measurement, a random phase retrieval approach using the Euclidean matrix norm of sum and difference map and fast least-squares algorithm (EMNSD&FLSA) is proposed. It can obtain the high accuracy as the iterative algorithm and cost less computational time as the non-iterative algorithm simultaneously. No pre-filtering, iteration and relatively accurate initial phase lead to the high accuracy, fast iterative method and only two phase shifted interferograms lead to the high speed. It can obtain absolutely accurate result when the background intensity and modulation amplitude are perfect. Moreover, it is suitable for different levels of noises. If the high accuracy is required, it would be best to suppress the noise before using EMNSD&FLSA, and the phase shift would be best to far away from 0 rad and π rad, furthermore, the numbers of patterns are best to be more than 2. Last but not least, it is robust for the circular, straight or complex fringes. The simulations and experiments verify the correctness and feasibility of EMNSD&FLSA.