Automatic real-time generalized phase-shifting interferometry to process interferograms with spatio-temporal visibility Rigoberto Juarez-Salazar, Carlos Robledo-Sanchez, Cruz Meneses-Fabian, Gustavo Rodriguez-Zurita, Fermin Guerrero Sanchez, and Antonio Barcelata-Pinzon Facultad de Ciencias F´ ısico-Matem´ aticas, Benem´ erita Universidad Aut´ onoma de Puebla, Apdo Postal 1152 Ciudad Universitaria, 72000 Puebla, M´ exico ABSTRACT A faster and robust generalized phase-shifting interferometry suitable to automatic real-time applications is presented. The proposal is based on the parameter estimation by the least squares method. The algorithm can retrieve the wrapped phase from two or more phase shifted interferograms with unknown phase steps between 0 and π rad. Moreover, by the multiple or single parameter estimation approach of this algorithm, interferograms with variable visibility both spatial and temporally can be processed, overcoming the restrictions and drawbacks from usual variable spatial visibility approaches. By both computer simulation and a optical experiment, the algorithm’s feasibility is illustrated. Keywords: Generalized phase-shifting interferometry, Phase measurement, Fringe analysis, Automatic, Real- time 1. INTRODUCTION Phase-Shifting Interferometry (PSI) has become a powerful tool for high accurate wavefront measurement in various fields of science and engineering. 1 In its standard form, the PSI techniques are based on two main assumptions: the background and modulation light are time-invariant (i.e. the visibility varies spatially only), and the phase shift is a linear function (i.e. all phase step are equals). Fortunately, the most commonly used interferometers practically satisfy the above assumptions. 2 This is due to the illumination conditions can hold near fixed and, by an appropriate calibration of the phase shifter, the phase shift is very close to the nominal values. 3 However, due to the rise of new industrial applications, the requirements on the PSI techniques are increas- ing. 4–7 Some desirable PSI requirements are: a reduced number of phase shifted interferograms necessary for phase demodulation, ability to process interferograms with spatio-temporal visibility, automated real-time data analysis, and simple, robust and inexpensive setups. In response to this, several advanced phase demodulation algorithms and novel interferometric setups have been reported. 8–11 Some recent optical setups provide us a high versatility and simplicity of the measurement procedures such as the electronic speckle pattern interferometry 12 (ESPI) and the PSI by amplitude wave modulation. 13 This optical setups are attractive due to its versatility, robustness and low cost. However, in this particular cases, the illumination’s conditions can not be fixed; this deal to spatio-temporal visibility. Besides, if the shifter calibration is missed or the shifter is controlled manually (by translating a grating with a micrometric screw, for example), the phase shift will be arbitrary and unknown. This conditions are very significant inconveniences because the standard PSI algorithms are not applicable. The Generalized Phase Shifting Interferometry (GPSI) was proposed as a solution to arbitrary unknown phase shift and miscalibration problems although the spatio-temporal visibility is not attended. 14, 15 Recently, a GPSI algorithm by parameter estimation was proposed where interferograms with spatio-temporal visibility can be processed as well. 16 In addition, this algorithm works with only two or more interferograms, is robust, not iterative and not requires user intervention. Thus, it is suitable for automatic real-time applications. Further author information: (Send correspondence to Rigoberto Juarez-Salazar) Rigoberto Juarez-Salazar: E-mail: rjuarezsalazar@gmail.com, Telephone: +52 222 2295500 8th Iberoamerican Optics Meeting and 11th Latin American Meeting on Optics, Lasers, and Applications, edited by Manuel Filipe P. C. Martins Costa, Proc. of SPIE Vol. 8785, 878542 © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2026103 Proc. of SPIE Vol. 8785 878542-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/26/2013 Terms of Use: http://spiedl.org/terms