Phase extraction from a single closed interferogram with a quadratic phase plays an important role in optical interferometry. Based on the energy of the interference images of this type is concentrated in a very narrow range around a point in the fractional Fourier transform (FRFT) domain under matched angle, the FRFT technique is a useful parameter estimator for the fringe pattern, but it has not been used to retrieve the desired phase from the fringe pattern. Thus, the parameter estimation approach based on FRFT is extended to the extract phase. The phase extraction can be done without using a phase unwrapping algorithm. Moreover, for ensuring both the estimation precision and speed, a coarse-to-fine searching strategy that includes a direct searching process implemented with a large step size and an iterative searching based on quasi-Newton method is presented in this paper to implement the FRFT method. The feasibility and applicability of the proposed approach are demonstrated using simulation and experimental results. The experimental results show that the proposed method is robust to noise and obstacles.
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