Generalized amplitude-phase-shifting interferometry.

Recently, a novel technique was proposed for recovering the complex amplitude of an optical field from a set of interferograms modulated in both visibility and phase steps for the synchronous case, named amplitude-phase-shifting interferometry (APSI). This requirement leads to errors in the accuracy of phase recovery due to miscalibration or the nonlinear response of the device used to generate the phase steps; in the APSI case, these are polarizers. In this paper, we propose to create a generalized model of the APSI technique where the phase steps can be different from each other.

One-shot carrier fringe polarimeter in a double-aperture common-path interferometer.

This paper presents a novel, simple, robust, and very stable polarimeter which is able to measure in a single-shot the state of polarization (SOP) of an optical field. In this proposal, an optical field with an unknown SOP and an optical field with a reference SOP are superposed by using a double aperture common-path interferometer (DACPI), obtaining two interferograms with adjustable carrier frequency in a single shot. Each interferogram has different visibility and phase-step where the information of the unknown SOP is contained.

Self-calibrating phase-shifting interferometry of three unequal phase steps by fitting background light to a polynomial of degree K.

This paper presents a novel non-iterative and robust algorithm in phase-shifting interferometry of three unknown and unequal phase steps. First, the modulation light and the object phase are algebraically eliminated; second, the background light is approximated to a 2-D polynomial of degree K and estimated by applying the least squares method; third the phase steps are obtained, and finally, the object phase is computed. This idea is theoretically described and verified numerically and experimentally for several values of K.

Phase shifting and phase retrieval with a fully automated laser diode system.

A low-cost and fully automated process for phase-shifting interferometry (PSI) by continuously changing the input voltage of a laser diode (LD) under the scheme of an unbalanced Twyman-Green interferometer (TGI) setup is presented. The input signal of a LD is controlled by a data acquisition (NI-DAQ) device that allows it to change its wavelength according to its tunability features. The automation and data analysis will be done using LabVIEW in combination with MATLAB.

Phase retrieval by Euclidean distance in self-calibrating generalized phase-shifting interferometry of three steps.

This paper presents a novel algorithm for phase extraction based on the computation of the Euclidean distance from a point to an ellipse. The idea consists in extracting the intensities from a data row or column in three interferograms to form points of intensity and then fitting them to an ellipse by the method of least squares. The Euclidean distance for each intensity point is computed to find a parametric phase whose value is associated to the object phase.

Fully automated low-cost setup for fringe projection profilometry.

In this paper an alternative low-cost, easy-to-use, and fully automated profilometry setup is proposed. The setup is based on a phase-shifting fringe projection technique with four projected fringe parameters. It uses the well-known triangulation arrangement and low-cost electronic and image acquisition components such as a data acquisition board, a motor controller board, a printer rail, a CMOS webcam, and an LCD projector.

Inhomogeneous phase-visibility modulating interferometry by space on-off non-quadrature amplitude modulation.

A new method in interferometry based on on-off non-quadrature amplitude modulation for object phase retrieval is presented. Although the technique introduces inhomogeneous visibility and phase variations in the interferogram, it is shown that the phase retrieval of a given object is still possible. This method is implemented by using three beams and two Mach-Zehnder interferometers in series.

Phase-shifting interferometry based on the lateral displacement of the light source.

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.

Double aperture common-path phase-shifting interferometry by translating a ruling at the input plane.

A method for introducing phase steps in an interferogram based on translating a ruling at the input plane of a double aperture common-path interferometer is presented. The setup is built on a 4f optical system consisting of two apertures at the input plane and a Ronchi ruling in the Fourier plane, where at each aperture a Ronchi ruling is also placed. By filtering at the Fourier plane a single diffraction order of the spectrum from the rulings in the object plane, we demonstrate that a phase step is generated when one of the rulings in the input plane is translated.

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.

Isotropic edge-enhancement by the Hilbert-transform in optical tomography of phase objects.

In optical tomography, isotropic edge-enhancement of phase-object slices under the refractionless limit approximation can be reconstructed using spatial filtering techniques. The optical Hilbert-transform of the transmittance function leaving the object at projection angles ϕ∈(0°,360°), is one of these techniques with some advantages. The corresponding irradiance of the so modified transmittance is considered as projection data, and is proved that they share two properties with the Radon transform: its symmetry property and its zeroth-moment conservation.

Directional edge enhancement in optical tomography of thin phase objects.

In this paper, we make a proposal to obtain the Hilbert-transform for each entry of the projection data leaving the slice of a thin phase object. These modified projections are stacked in such a way that they form a modified sinogram called Hilbert-sinogram. We prove that the inverse Radon-transform of this sinogram is the directional Hilbert-transform of the slice function, and the reconstructed image is the directional edge enhancement of the distribution function on the slice.

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.

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 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.

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.

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.

Optical tomography of transparent objects with phase-shifting interferometry and stepwise-shifted Ronchi ruling.

An experimental setup for tomographic inspection of phase objects is presented. The system uses a common-path interferometer consisting of two windows in the input plane and a translating grating as its pupil. In the output, interference of the fields associated with replicated windows is achieved by a proper choice of the windows' spacing with respect to the grating period.