Iterative algorithm for phase extraction from tilt phase-shift interferograms with inhomogeneous background

An iterative algorithm for tilt phase-shift interferograms with inhomogeneous background is proposed in this paper. The regional integration results of the interferograms are fitted with a cosine curve in the time domain to obtain the iterative initial values, then the stepwise iterative optimization is carried out for wavefront phase, background, x-direction tilt shift, and y-direction tilt shift by the least-squares method, respectively, and the phase distribution can be obtained after several rounds of iterations. Feasibility of the algorithm is verified through simulations and experiments. Factors affecting the accuracy of phase calculation are analyzed, and the results show that the proposed method is insensitive to the background light intensity distribution, and there is almost no limit on the number of fringes. The algorithm can accept tilt-shift error with vibration amplitude less than 0.86 π rad and translational-shift error with vibration amplitude less than 0.43 π rad.