Tilt shift determinations with spatial-carrier phase-shift method in temporal phase-shift interferometry

An algorithm is proposed to deal with tilt-shift errors in temporal phase-shift interferometry (PSI). In the algorithm, the tilt shifts are detected with the spatial-carrier phase-shift (SCPS) method and then the tilt shifts are applied as priori information to the least-squares fittings of phase retrieval. The algorithm combines the best features of the SCPS and the temporal PSI. The algorithm could be applied to interferograms of arbitrary aperture without data extrapolation for the Fourier transform is not involved. Simulations and experiments demonstrate the effectiveness of the algorithm. The statistics of simulation results show a satisfied accuracy in detecting tilt-shift errors. Comparisons of the measurements with and without environmental vibration show that the proposed algorithm could compensate tilt-shift errors and retrieve wavefront phase accurately. The algorithm provides an approach to retrieve wavefront phase for the temporal PSI in vibrating environment.