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14 August 2006 Phase recovery from a single interferogram using multiple Fourier transforms
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An algorithm for phase determination from a single interferogram with closed fringes using Fourier transforms is proposed. Traditionally, the Fourier transform method has been used for interferograms containing only open fringes. This is done performing a pass-band filtering of one half of the frequency spectrum and taking the arctangent function of the real and imaginary parts of the filtered spectrum. The proposed method performs multiple pass-band filtering resulting in several wrapped phases with wrong sign changes corresponding to the orientation of the filters. Among the different wrapped phases, regions are expected to have the same sign enabling the correct reconstruction of the phase. The corrections of the sing changes are made by comparing the derivatives of the wrapped phases by means of a modified process of phase unwrapping taking into account small areas of the interferogram field. This is done under the assumption of that adjacent areas won't have abrupt changes in their phase derivatives as corresponding to smooth continuous surfaces. The procedure is robust against noise since low-pass filtering can be easily performed in the calculation of the wrapped maps and during the modified process of phase unwrapping.
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Jesús Muñoz-Maciel, F. Gerardo Lecona-Peña, Cesar Castillo-Quevedo, Franciso J. Casillas-Rodríguez, Víctor Duran-Martínez, and Miguel Mora-González "Phase recovery from a single interferogram using multiple Fourier transforms", Proc. SPIE 6292, Interferometry XIII: Techniques and Analysis, 62920D (14 August 2006);

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