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

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.

One-shot phase-shifting phase-grating interferometry with modulation of polarization: case of four interferograms.

An experimental setup for optical phase extraction from 2-D interferograms using a one-shot phase-shifting technique able to achieve four interferograms with 90 degrees phase shifts in between is presented. The system uses a common-path interferometer consisting of two windows in the input plane and a phase grating in Fourier plane as its pupil. Each window has a birefringent wave plate attached in order to achieve nearly circular polarization of opposite rotations one respect to the other after being illuminated with a 45 degrees linear polarized beam. In the output, interference of the fields associated with replicated windows (diffraction orders) is achieved by a proper choice of the windows spacing with respect to the grating period. The phase shifts to achieve four interferograms simultaneously to perform phase-shifting interferometry can be obtained by placing linear polarizers on each diffraction orders before detection at an appropriate angle. Some experimental results are shown.

Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry.

Among several techniques, phase shifting interferometry can be implemented with a grating used as a beam divider to attain several interference patterns around each diffraction order. Because each pattern has to show a different phase-shift, a suitable shifting technique must be employed. Phase gratings are attractive to perform the former task due to their higher diffraction efficiencies. But as is very well known, the Fourier coefficients of only-phase gratings are integer order Bessel functions of the first kind. The values of these real-valued functions oscillate around zero, so they can adopt negative values, thereby introducing phase shifts of pi at certain diffraction orders. Because this almost trivial fact seems to have been overlooked in the literature regarding its practical implications, in this communication such phase shifts are stressed in the description of interference patterns obtained with grating interferometers. These patterns are obtained by placing two windows in the object plane of a 4f system with a sinusoidal grating/grid in the Fourier plane. It is shown that the corresponding experimental observations of the fringe modulation, as well as the corresponding phase measurements, are all in agreement with the proposed description. A one-shot phase shifting interferometer is finally proposed taking into account these properties after proper incorporation of modulation of polarization.