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Generalized algorithm for phase shifting interferometry

A new generalized algorithm for phase extraction from interferograms recorded sequentially at different phase shifts is proposed. It is developed from the principle of least-square fining with a weight function. This algorithm removes many of the restrictions imposed by conventional phase-measuring algorithms, such as requiring a constant phase shift between consecutive interferograms. This algorithm can estimate phase from a series of sample interferograms with arbitrary phase shift, as long as the phase shifts between these interferograms are known. By introducing the proper weight function, the proposed algorithm is able to estimate the phase with a high degree of tolerance to common error sources including phase-shift mis-estimation and detector nonlinearity. Consequently, this technique may offer improved phase estimation relative to unweighted generalized algorithms using the same number of intensity frames. Theoretical analysis and results supported by numerical simulation and experiments are presented. Keywords: phase shifting interferometry, optical metrology, phase-measuring algorithms.