Generalized phase-shifting interferometry by parameter estimation with the least squares method

• Published in: Optics and lasers in engineering Vol. 51; no. 5; pp. 626 - 632
• Main Authors: Juarez-Salazar, Rigoberto, Robledo-Sánchez, Carlos, Meneses-Fabian, Cruz, Guerrero-Sánchez, Fermin, Arévalo Aguilar, L.M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-05-2013
• Subjects: Algorithms; Computing time; Fringe analysis; Interferometry; Least squares method; Mathematical models; Modulation; Phase measurement; Proposals; Visibility; Fringe analysis; Phase measurement; Interferometry
• ISSN: 0143-8166; 1873-0302
• DOI: 10.1016/j.optlaseng.2012.12.020

A simple non-iterative algorithm for generalized phase-shifting interferometry is proposed. This algorithm recovers the wrapped phase from two or more interferograms with unknown phase steps between 0 and π rad. The proposal is based on the least squares method to calculate four parameters: background and modulation light, phase steps and wrapped phase distribution. This algorithm, by a new interferogram normalization procedure, can handle interferograms with variable spatiotemporal visibility overcoming the restriction and drawbacks from usual variable spatial visibility approaches. The algorithm works very well for processing interferograms which include many fringes. This behaviour will be explicated and discussed. The effectiveness and robustness of this algorithm are supported by numerical simulation and by the evaluation of experimental interferograms. The phase-shift estimation quality is verified by two different techniques. By the properties of this algorithm, such as the low computing time and free of user intervention, we believe it could be used in automatic real-time applications.
► GPSI based on the parameter estimation by least squares method is proposed. ► A new interferogram normalization method by polynomial surfaces fitting is introduced. ► The algorithm work with two or more interferograms with spatio-temporal visibility. ► Simulated and experimental data are processed to verify the algorithm's feasibility. ► This algorithm could be used in automatic real-time applications.