David-Ignacio Serrano-García

Parallel two-step phase shifting interferometry using a double cyclic shear interferometer.

A parallel two-step polarizing phase shifting interferometer based on a Double Cyclic Shear Interferometer (DCSI) is proposed in this paper for quantitative phase imaging. The system has the advantage of retrieving the derivative phase data map directly. Due to its configuration, it presents better stability against external configurations than other types of interferometers. The DCSI generates two π-shifted interferograms, which are recorded by the CCD camera in a single-shot. The separation between parallel interferograms can be varied in the two axes for convenience. To obtain the optical phase data map, a parallel phase shift between interferograms is obtained by rotating a half wave plate retarder. We analyzed the cases of four patterns with shifts of π/2 captured in two shots; the optical phase was processed by a four-step algorithm. Related experimental results obtained for microscopic transparent samples are presented.

Adjustable-window grating interferometer based on a Mach-Zehnder configuration for phase profile measurements of transparent samples

This communication describes some details of polarization modulation that are useful in phase-shifting interferometry when applied to phase profile measurements of phase objects. Since non-destructive optical techniques allow surface measurement with high accuracy, a Mach-Zehnder configuration coupled to a 4-f arrangement using phase gratings placed on the Fourier plane was implemented to analyze phase objects. Each beam of the interferometer goes through a birefringent wave plate in order to achieve nearly circular polarization of opposite rotations, with respect to each other. The interference of the fields associated with replicated beams, centered on each diffraction order, is achieved varying the spacing of windows with respect to the grating period. Experimental results are presented for cases of four and nine simultaneously captured interferograms.

Single shot interferometry using a two-interferogram phase shifting algorithm

Abstract An interferometer capable of retrieving the phase information in a single shot was implemented, the system was made by taking into account the double interferogram output obtained in a Mach Zehnder interferometer and then retrieving the phase information using a two-step algorithm already encountered in the literature. By controlling the polarization properties of the system, a new polarization phase shifting technique was implemented based upon the rotation of two quarter wave retarders placed in each of the arms of the interferometer. We present the analytical model taking into account the necessary conditions presented by the demodulation method. The configuration presented does not require micro-polarizer arrays or diffraction gratings presenting the advantage of avoiding the use of conventional polarizing filters to control the phase shift. Experimental results are presented.

Slope measurement of a phase object

An interferometric method to measure the slope of phase objects is presented. The analysis was performed by implementing of a polarizing phase shifting cyclic shear interferometer coupled to a grating interferometer. This system can obtain four interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope of a phase object, is analyzed the optical phase applying the classical method of phase extraction.

Simultaneous phase shifting interferometry based in a Mach Zehnder interferometer for measurement of transparent samples

A Mach Zehnder (MZ) interferometer was implemented to analyze a phase object using polarization phase-shifting interferometry. The Mach Zehnder interferometer produces two beams with circular polarization of opposite rotations one respect to the other. The system is coupled to a 4-f system with phase grating in the Fourier plane, interference of the fields associated with replicated beams centered on the diffraction orders is achieved by a proper choice of the beams spacing with respect to the gratings period. The optical configuration allows obtaining n-interferograms in one shot. The configuration presented does not require micro-polarizer arrays or additional software to eliminate noise caused by vibration, as the system is stable itself and uses conventional polarizing filters. Considering the object under study a thin phase object, experimental results are presented.

Simultaneous Phase Shifting Shearing Interferometry for Measurement of Static and Dynamic Phase Objects

Through the use of non-destructive optical techniques to measure the surface with high accuracy, two shearing interferometers were implemented to analyze the slope of phase objects using simultaneous phase-shifting shearing interferometry [Toto et al., 2010]. These optical configurations allow obtaining n-shearograms simultaneously to retrieve the optical phase data map with higher accuracy [Rodriguez et al., 2009; Toto et al 2009].

Experimental π Phase-Shifts Observed in the Fourier Spectra of Phase Gratings and Applications in Simultaneous PSI

As it 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 π at certain diffraction orders. Because of this, an almost trivial fact seems to have been overlooked in the literature regarding its practical implications.

Parallel phase shifting interferometry using a double cyclic shear interferometer

In this work we present a parallel polarizing phase shifting interferometer based in a Double Cyclic Interferometer (DCSI) to analyze transparent samples. This system has the advantage of generating four beams that can interfere properly; this can reduce the number of captures needed in phase shifting interferometry. The interferometric system generates two π-shifted interferograms, which are recorded by the CCD camera in a single-shot. For the processing of the optical phase data map, a parallel phase shift can be generated by placing a linear polarizer covering two patterns. We analyze the cases of four patterns with arbitrary shifts captured in two shots. The unwrapped phase is processed by Kreis methods. Experimental results obtained by the proposed interferometer are presented.

Single shot phase shifting interferometry for measurement of transparent samples

Due to non-destructive optical techniques allows surface measurement with high accuracy, a Common Path interferometer based on a Michelson configuration was implemented to analyze phase objects by using polarization simultaneous phase-shifting interferometry. Each beam of the interferometer has a birefringent wave plate attached in order to achieve nearly circular polarization of opposite rotations one respect to the other. The system is coupled to a 4-f arrangement with Bi-Ronchi gratings collocated in the Fourier plane. The interference of the fields associated with replicated beams, centered on each diffraction orders, is achieved varying the beams spacing with respect to the grating period. The optical configuration allows obtaining n-interferograms simultaneously. The phase reconstruction is performing by a three steps phase shifting algorithm. Experimental results are present for a phase object.

Radial slope measurements of transparent samples using phase shifting interferometry by polarization

We present experimental results obtained by using phase-shifting interferometry by polarization to measure the radial slope of transparent samples, by implementing a Radial-Shear interferometer and using a grating to replicate the interference patterns modulated by polarization; the interferometer is capable to process the optical phase data by obtaining four interferograms in one-shot. The experimental results for transparent samples are presented in this research.