Fast Reference Phase Extraction and Wave-front Reconstruction for Generalized Phase-shifting Interferometry

Abstract

An important approach of complex wave reconstruction in generalized phase-shifting interferometry (GPSI) with arbitraryu nknown phase shifts is the combination of two (a conventional and an inverse) least square methods (LSMs), where the conventional LSM requires the calculation of solving a set of least square equations for each pixel in each iteration,g iving riset o a heavy computation burden.H ere a much-simplified algorithm is suggested to extract reference phasea nd then reconstruct object wave-front by replacing the conventional LSM in above process with our specially derived wave reconstruction formulae for GPSI. In this method, only one least-square equation is needed in each iteration to retrieve the reference phase, andthe object phasecan be calculated analyticallyand simultaneously.The feasibility and effectiveness of this algorithm have been verified by computer simulations with both the smooth and diffusing objects. The results show that this innovation can save computing time by about 20 times compared with previous two-LSM algorithm while still ensures its high precision. This approach can be used for GPSI with three or more frames in the wide range of unknown positive or negative phase shifts. Optical experiments havea lso made with satisfactory results.