One-Shot Phase-Shifting Interferometry with Phase-Gratings and Modulation of Polarization Using N≥4 Interferograms

Abstract

Phase-shifting interferometry requires (PSI) of several interferograms of the same optical field with similar characteristics but shifted by certain phase values to retrieve the optical phase. This task has been usually performed by stages with great success and requires of a series of sequential shots [Meneses et al., 2006a]. However, time-varying phase distributions are excluded from this schema. Several efforts for single-shot phase-shifting interferometry have been tested successfully [Novak et al.,2005 ;Rodriguez et al., 2008a], but some of them require of non-standard components and they need to be modified in some important respects in order to get more than four interferograms. Two-windows grating interferometry, on the other hand, has been proved to be an attractive technique because of its mechanical stability as a common-path interferometer [Arrizon and De La Llave 2004]. Moreover, gratings can be used as convenient phase modulators because they introduce phase shifts through lateral displacements. In this regard, phase gratings offer more multiplexing capabilities than absorption gratings (more useful diffraction orders because higher diffraction efficiencies can be achieved). Furthermore, with two phase gratings with their vector gratings at 90° (grids) there appear even more useful diffraction orders[Toto et al., 2008]. Modulation of polarization can be independently applied to each diffraction order to introduce a desired phase-shift in each interference pattern instead of using lateral translations. These properties combine to enable phase-shifting interferometric systems that require of only a single-shot, thus enabling phase inspection of moving subjects. Also, more than four interferograms can be acquired that way. A simple interferogram processing enables the use of interference fringes with different fringe modulations and intensities. In this chapter, the basic properties of two-windows phase grating interferometry (TWPGI) and modulation of polarization is reviewed on the basis of the far-field diffraction properties of phase gratings and grids. Phase shifts in the diffraction orders can be used as an advantage because they simplify the needed polarization filter distributions. It is finally remarked, that these interferometers are compatible with interference fringes exhibiting spatial frequencies of relative low values and, therefore, no great loss of resolution is related with several interferograms when simultaneously using the same image field of the camera. To extract optical phase distributions which evolve in time, the capture of the n shifted