Spatial carrier interferometry from M temporal phase shifted interferograms: Squeezing Interferometry.
It is well known that having 3 temporal phase shifting (PS) interferograms we do not have many possibilities of using an algorithm with a desired frequency spectrum, detuning, and harmonic robustness. This imposes severe restrictions on the possibilities to demodulate such set of temporal interferograms. It would be nice to apply for example a 7 step PS algorithm to these 3 images in order to have more possibilities to phase demodulate them; even further, it would be even better to apply a quadrature filter having a spatial spread given by a real number to these 3 interferograms. In this paper we propose to do just that; namely we show how to demodulate a set of M-steps phase shifting images with a quadrature filter having a real-number as spatial spread. The interesting thing in this paper is to use a higher than M spread quadrature filter to demodulate our interferograms; in traditional PS interferometry one is stuck to the use of M step phase shifting formula to obtain the searched phase. Using a less than M PS formula is not interesting at all given that we would not use all the available information. The main idea behind the "squeezing" phase shifting method is to re-arrange the information of the M phase shifted fringe patterns in such a way to obtain a single carrier frequency interferogram (a spatio-temporal fringe image) and use any two dimensional quadrature filter to demodulate it. In particular we propose the use of Gabor quadrature filters with a spread given by real-numbers along the spatial coordinates. The Gabor filter may be designed in such way that we may squeeze the frequency response of the filter along any desired spatio-temporal dimension, and obtain better signal to noise demodulation ratio, and better harmonic rejection on the estimated phase.
Centro de Investigaciones en Optica A.C., Loma del Bosque 115, C.P. 37000, León, Guanajuato, México. mservin@cio.mx
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M
Servin
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M
Cywiak
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Malacara-Hernandez
J C
JC
Estrada
J A
JA
Quiroga
D000465:Algorithms; D003198:Computer Simulation; D004867:Equipment Design; D019544:Equipment Failure Analysis; D007368:Interferometry / Q000295:instrumentation* / Q000379:methods*; D008027:Light; D008962:Models, Theoretical; D012031:Refractometry / Q000295:instrumentation* / Q000379:methods*; D012542:Scattering, Radiation