Spatial carrier interferometry from M temporal phase shifted interferograms: Squeezing Interferometry

Abstract

Abstract: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.

Squeezed Carrier Interferogram for Wavelet Phase Recovery

“…The princip le of squeezing interfero metry [12] is based on transforming M temporal-spatial phase shifted fringe patterns by a blending technique into a single carrier fringe pattern and then demodulating this carrier interferogram to retrieve the phase.…”

“…The aim of this work is to determine optical phase distribution from spatial carrier interferogram named squeezed interferogram in the wavelet do main. The squeezing interfero metry technique [12] g en erates a s q u eezed in ter fero g ra m b y n u me r ical co mb in atio n o f M s h ifted frin g es p atterns . Sev eral techniques have been used successfully in fringe pattern d emo d u lation [13].…”

Squeezing Interferometry for Optical Phase Extraction in Digital Speckle Pattern Interferometry

“…In our work, we will generate numerically multiple interferograms with arbitrary phase-shift amount between them from only two interferograms shifted by π/2. The cosine fringe pattern is (9) The π/2 shifted fringe pattern is (10) After removing the background A(x,y) by a highpass filter, the resultant fringe patterns are: (11) (12) We propose to combine numerically the interferogram and its quadrature with cos(β) and sin(β) respectively which leads to the β shifted fringe pattern.…”

“…The principle of squeezing interferometry [11] is based on transforming M temporal-spatial phase shifted fringe patterns by a blending technique into a single carrier fringe pattern and then demodulating this carrier interferogram to retrieve the phase.…”

“…The aim of this paper is to use the Squeezing interferometry Technique [11] to retrieve a phase mapping from only two π/2 shifted speckle fringe patterns without any speckle denoising filtring. The principle of squeezing interferometry is based on transforming N phase shifted fringe patterns by a blending technique into a single carrier fringe pattern and then demodulating this carrier interferogram with a Gabor filter [12].…”