Pixelated phase-mask dynamic interferometers,” in Fringe 2005

Fringe 2005, 2006

We demonstrate a new type of spatial phase-shifting, dynamic interferometer that can acquire phase-shifted interferograms in a single camera frame. The interferometer is constructed with a pixelated phase-mask aligned to a detector array. The phase-mask encodes a high-frequency spatial interference pattern on two collinear and orthogonally polarized reference and test beams. The phase-difference between the two beams can be calculated using conventional N-bucket algorithms or by spatial convolution. The wide spectral response of the mask and true commonpath design permits operation with a wide variety of interferometer front ends, and with virtually any light source including white-light.

Applied Optics, 2009

It is well known that spatial phase shifting interferometry (SPSI) may be used to demodulate twodimensional (2D) spatial-carrier interferograms. In these cases the application of SPSI is straightforward because the modulating phase is a monotonic increasing function of space. However, this is not true when we apply SPSI to demodulate a single-image interferogram containing closed fringes. This is because using these algorithms, one would obtain a wrongly demodulated monotonic phase all over the 2D space. We present a technique to overcome this drawback and to allow any SPSI algorithm to be used as a single-image fringe pattern demodulator containing closed fringes. We make use of the 2D spatial orientation direction of the fringes to steer (orient) the one-dimensional SPSI algorithm in order to correctly demodulate the nonmonotonic 2D phase all over the interferogram.

Optics Letters, 2008

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.

Journal of Modern Optics, 1995

Optics Communications, 2006

An experimental setup for phase extraction of 2D phase distributions is presented. The system uses a common-path interferometer consisting of two windows in the input plane and a translating grating as spatial filter. In the output, interference of the fields associated with replicated images of the input windows is achieved by a proper choice of the windows spacing with respect to the grating period, the focal length of the transforming lens and the wavelength of the coherent illumination employed. Because in this type of grating interferometer a grating is placed as a spatial filter, the phase changes which are needed for phase-shifting interferometry can be easily performed with translations of the grating driven by a linear actuator. Some experimental results are shown.

arXiv: Signal Processing, 2019

We present a high-precision temporal-spatial phase-demodulation algorithm for phase-shifting interferometry (PSI) affected by random/systematic phase-stepping errors. Laser interferometers in standard optical-shops suffer from several error sources including random phase-shift deviations. Even calibrated phase-shifters do not achieve floating-point linear accuracy, as routinely obtained in multimedia video-projectors for fringe-projection profilometry. In standard optical-shops, calibrated phase-shifting interferometers suffer from nonlinearities due to vibrations, turbulence, and environmental fluctuations (temperature, pressure, humidity, air composition) still under controlled laboratory conditions. These random phase-step errors (even if they are small), increases the uncertainty of the phase measurement. This is particularly significant if the wavefront tolerance is tightened to high precision optics. We show that these phase-step errors precludes high-precision wavefront measu...

Optics Express, 2013

A simple and inexpensive optical setup to phase-shifting interferometry is proposed. This optical setup is based on the Twyman-Green Interferometer where the phase shift is induced by the lateral displacement of the point laser source. A theoretical explanation of the induced phase by this alternative method is given. The experimental results are consistent with the theoretical expectations. Both, the phase shift and the wrapped phase are recovered by a generalized phase-shifting algorithm from two or more interferograms with arbitrary and unknown phase shift. The experimental and theoretical results show the feasibility of this unused phase-shifting technique.

Applied Optics, 2006

In both temporal and spatial carrier phase shifting interferometry, the primary source of phase calculation error results from an error in the relative phase shift between sample points. In spatial carrier phase shifting interferometry, this phase shifting error is caused directly by the wavefront under test and is unavoidable. In order to minimize the phase shifting error, a pixelated spatial carrier phase shifting technique has been developed by 4D technologies. This new technique allows for the grouping of phase shifted pixels together around a single point in two dimensions, minimizing the phase shift change due to the spatial variation in the test wavefront. A formula for the phase calculation error in spatial carrier phase shifting interferometry is derived. The error associated with the use of linear N-point averaging algorithms is presented and compared with those of the pixelated spatial carrier technique.

Optics Communications, 2009

A method to reduce the number of captures needed in phase-shifting interferometry is proposed on the basis of grating interferometry and modulation of linear polarization. The case of four interferograms is considered. A common-path interferometer is used with two windows in the object plane and a Ronchi grating as the pupil, thus forming several replicated images of each window over the image plane. The replicated images, under proper matching conditions, superpose in such a way so that they produce interference patterns. Orders 0 and +1 and À1 and 0 form useful patterns to extract the optical phase differences associated to the windows. A phase of p is introduced between these orders using linear polarizing filters placed in the windows and also in the replicated windows, so two p-shifted patterns can be captured in one shot. An unknown translation is then applied to the grating in order to produce another shift in the each pattern. A second and final shot captures these last patterns. The actual grating displacement and the phase shift can be determined according to the method proposed by Kreis before applying proper phase-shifting techniques to finally calculate the phase difference distribution between windows. Related simulations and experimental results are given.