One-shot phase-shifting interferometry: five, seven, and nine interferograms

Abstract

To extract phase distributions, which evolve in time using phase-shifting interferometry, the simultaneous capture of several interferograms with a prescribed shift has to be done. Previous interferometric systems aimed to fulfill such a task were reported to get only four interferograms. It is pointed out that more than four suitable interferograms can be obtained with an interferometer that uses two windows in the object plane, a phase grid as a pupil, and modulation of polarization for each diffraction orders in the image plane. Experimental results for five, seven, and nine interferograms are given.

Simultaneous Phase Shifting Shearing Interferometry for Measurement of Static and Dynamic Phase Objects

“…(18) shows that the results are replicas of the pattern generated by the CSI displaced to the n th and l th orders of diffraction; each replica of the main pattern maintains an intensity modulated by Fourier Coefficients C n and C l corresponding to each direction. It should be noted that the contrast of the fringes depends on the degree of circular polarization of the interfering beams [Rodriguez, 2008]. In this case, the Ronchi gratings only multiplex the pattern, so the amplitudes of the orders only increase or decrease the intensity of the interference patterns, as it is shown in Fig.…”

“…Previous works have shown that when the interferometer is coupled to a 4-f system using phase grids, it is possible to obtain replicas of the interference pattern, and each one of these replicas can be modulated by polarization [Rodriguez 2008;Serrano, 2011]. A sinusoidal phase grid generated by the multiplication of two sinusoidal phase gratings, whose respective grating vectors are crossed, generates diffraction orders modulated by Bessel functions J q and J r [Rodriguez, 2008;, and the image of the interference pattern generated by the interferometer is found centered around each of them.…”

“…A sinusoidal phase grid generated by the multiplication of two sinusoidal phase gratings, whose respective grating vectors are crossed, generates diffraction orders modulated by Bessel functions J q and J r [Rodriguez, 2008;, and the image of the interference pattern generated by the interferometer is found centered around each of them. …”

“…Several optical systems have been developed to retrieve the optical phase data in a single capture employing polarization, for example, through the use of micro-polarizer arrays [Novak et al,2005], a point diffraction interferometer [Neal, 2003 ], a two-beam grating interferometer [Rodriguez, 2008] and a liquid-crystal spatial modulator [Mercer and Creath, 1996], among others. These systems have been employed in several fields of application, such as optical metrology [Wyant, 2004;Cheng and Wyant, 1984], holography [Yamaguchi and Zhang, 1997;Nomura, 2006], optical tomography [Meneses, 2006], ESPI [Chen, 2010], etc.…”

Phase-shifting interferometry based on induced vibrations

“…a self-reference method is proposed for phase-shifting interferometry when translation and tilt errors exist. Another strategy to deal with this kind of problems can be using a one-shot phase-shifting interferometry method [9]. This approach allows recovering at the same time different interferograms at the camera detector.…”