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.
Servin
M
M
Centro de Investigaciones en Optica A.C., Loma del Bosque 115, C.P. 37000, León, Guanajuato, México. mservin@cio.mx
Cywiak
M
M
Malacara-Hernandez
D
D
Estrada
J C
JC
Quiroga
J A
JA
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