21 June 2015 Fourier analysis of quadratic phase interferograms
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A phase demodulation method from a single interferogram with a quadratic phase term is developed. The fringe pattern being analysed may contain circular, elliptic or astigmatic fringes. The Fourier transform of such interferograms is seen to be also a sine or a cosine of a second order polynomial in both the real and imaginary parts. In this work we take a discrete Fourier transform of the fringe patterns and then we take separate inverse discrete transforms of the real and imaginary parts of the frequency spectrum. This results in two new interferograms corresponding to the sine and cosine of the quadratic term of the phase modulated by the sine and cosine of the linear term. The linear term of these interferograms may be recovered with similar procedures of fringe analysis from open fringe interferograms. Once the linear term is retrieved the quadratic phase of the interferogram being analysed can also be calculated. The present approach is also being investigated for interferograms with nearly circularly symmetry given that the phase contains some tilt. The described procedure of Fourier analysis from quadratic phase interferograms of nearly symmetric interferograms could be used instead of complex and time consuming algorithms for phase recovery from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.
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Jesús Muñoz-Maciel, Jesús Muñoz-Maciel, Miguel Mora-González, Miguel Mora-González, Francisco J. Casillas-Rodríguez, Francisco J. Casillas-Rodríguez, Francisco G. Peña-Lecona, Francisco G. Peña-Lecona, } "Fourier analysis of quadratic phase interferograms", Proc. SPIE 9526, Modeling Aspects in Optical Metrology V, 952612 (21 June 2015); doi: 10.1117/12.2184889; https://doi.org/10.1117/12.2184889

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