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

M Servin¹, M Cywiak, D Malacara-Hernandez

¹Centro de Investigaciones en Optica A.C., Loma del Bosque 115, C.P. 37000, León, Guanajuato, México. mservin@cio.mx

|June 26, 2008

Summary

This study introduces a novel "squeezing" phase shifting method to demodulate interferograms. It enables the use of higher-order quadrature filters, improving phase demodulation accuracy and harmonic rejection from fewer images.

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Area of Science:

Optical metrology
Interferometry
Signal processing

Background:

Traditional phase shifting (PS) interferometry with limited steps (e.g., 3) restricts algorithm choices for frequency spectrum, detuning, and harmonic robustness.
Existing methods often require a number of phase-shifted interferograms equal to the steps in the chosen algorithm (M-steps) to fully utilize available information.

Purpose of the Study:

To propose and demonstrate a method for demodulating M-steps phase shifting images using a quadrature filter with a real-valued spatial spread, even when the filter spread exceeds M.
To enable more flexible and robust phase demodulation from a limited number of temporal interferograms.

Main Methods:

Introduced the 'squeezing' phase shifting method to consolidate information from M phase-shifted fringe patterns into a single carrier frequency interferogram (spatio-temporal fringe image).
Applied two-dimensional quadrature filters, specifically Gabor quadrature filters with real-valued spatial spreads, for demodulating the synthesized spatio-temporal fringe image.
Designed Gabor filters to control frequency response squeezing along desired spatio-temporal dimensions.

Main Results:

Successfully demonstrated the demodulation of phase-shifted images using quadrature filters with spatial spreads higher than the number of phase steps (M).
Achieved improved signal-to-noise ratio (SNR) in the demodulated phase.
Showcased enhanced rejection of harmonic noise in the estimated phase.

Conclusions:

The proposed 'squeezing' phase shifting method offers a significant advancement in phase demodulation flexibility and performance.
Utilizing higher-than-M spread quadrature filters, particularly Gabor filters, provides superior harmonic robustness and SNR compared to traditional M-step algorithms.
This technique expands the possibilities for phase demodulation in applications with limited temporal interferograms.