For data processing in conventional phase shifting interferometry, Fourier transform, and least-squares-fitting techniques, a whole interferometric data series is required. We propose a new interferometric data processing methodology based on a recurrent nonlinear procedure. The signal value is predicted from the previous step to the next step, and the prediction error is used for nonlinear correction of an a priori estimate of the parameters phase, visibility, or frequency of interference fringes. Such a recurrent procedure is correct on the condition that the noise component be a Markov stochastic process realization. The accuracy and stability of the recurrent Markov nonlinear filtering algorithm were verified by computer simulations. It was discovered that the main advantages of the proposed methodology are dynamic data processing, phase error minimization, and high noise immunity against the influence of non-Gaussian noise correlated with the signal and the automatic solution of the phase unwrapping problem.
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