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Hilbert transform algorithm for fringe-pattern evaluation

The Gabor analytic signal is constructed by means of the Hilbert transform. This linear operator gives the single-valued determination of the envelope and phase of a 1D signal with the support from infinity to infinity. But the wave field has four arguments and the interferogram is a 2D function. Moreover, these functions can be measured only in a restricted domain. These problems are discussed in this paper. In addition, the errors estimation of phase recovering are considered. The results of numerical experiments on the interferogram inversion are given.