Cruz Meneses-Fabian

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.

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.

Experimental generating the partially coherent and partially polarized electromagnetic source

The technique for generating the partially coherent and partially polarized source starting from the completely coherent and completely polarized laser source is proposed and analyzed. This technique differs from the known ones by the simplicity of its physical realization. The efficiency of the proposed technique is illustrated with the results of physical experiment in which an original technique for characterizing the coherence and polarization properties of the generated source is employed.

Phase-shifting interferometry by wave amplitude modulation.

A new method for phase-shifting interferometry based on wave amplitude modulation is proposed and discussed. This proposal is based on the interference of three waves, where two waves attend as two reference waves and the other wave attends as a probe wave. Thereby, three interference terms are obtained, but because a phase difference of π/2 between the two references is kept constant, one of the three terms will be dropped, while the two remaining will be put in quadrature. Under these conditions, the resulting pattern is mathematically modeled by an interferogram of two waves, where an additional phase is given by the amplitude variations of the reference waves. In this Letter, both a theoretical model and some numerical simulations are presented.

Fourier normalized-fringe analysis by zero-order spectrum suppression using a parameter estimation approach

Abstract. The simple filtering procedure, high spatial resolution, and low computation time benefits of Fourier normalized-fringe analysis are verified. For this, both the fringe-pattern normalization method by parameter estimation using the least squares method and the standard Fourier transform method are implemented. This proposal, or any Fourier normalized-fringe analysis scheme, has the advantage that the filter’s properties are not very critical because the zero-order spectrum is suppressed by the normalization stage. Then, the simple half-plane filter is applied in the filtering procedure which, in addition, increases the spatial resolution. Both a computer simulation and the experimental results show the functionality and feasibility of the suggested scheme.

Carrier fringes in the two-aperture common-path interferometer

We present a method to introduce a linear phase into an interference pattern. This phase is introduced when a grating is placed outside of the Fourier plane of a two-aperture common-path interferometer, which is built using a 4f optical imaging system. Based on an analysis of near-field diffraction, the introduction of the carrier fringes is mathematically justified. It is important to note that no tilt between the two beams is requested to produce this effect, and it turns out to be simpler, easier, and more versatile than other existing methods. The main attributes and advantages of the setup will be discussed and illustrated in detail with experimental fringe patterns.

Adjustable lateral-shear single-shot phase-shifting interferometry for moving phase distributions

A grating interferometer to produce n lateral-sheared phase-shifted interferograms simultaneously in collimated light and with adjustable shear is proposed. It consists of a variable lateral-shear interferometer in conjunction with a grating interferometer. This combination enables the use of phase-shifting techniques for measuring moving wavefront slopes. Several shifted interferograms can be achieved with a single shot using two mutually crossed phase gratings of equal frequency, while the required phase shifts can be performed with modulation of polarization. Results of the proposed method for cases of n = 4, 5 and 7 interferograms are reported.

A single-shot phase-shifting radial-shearing interferometer

A grating interferometer to simultaneously produce n radial-sheared phase-shifted interferograms is proposed. It consists basically of an adaptation of a well known radial-shear interferometer in conjunction with a grating interferometer. This combination enables the use of phase-shifting techniques for measuring phase distributions. Several interferograms can be achieved with a double phase grating of a given frequency, and the required phase shift can be performed with modulation of polarization. Experimental results are presented for cases of n = 4, 5, and 7 interferograms. These results are obtained with two configurations of the system, which are discussed.

A differential formulation of the T-History calorimetric method

We present a differential formulation of the T-History calorimetric method in order to achieve thermodynamic consistency with phase transitions theory and to include the important experimental effect of the speed of the thermal process in calorimetric calculations. To illustrate the applicability of the new formulation, we show some numerical results which give an acceptable description of calorimetric measures.