Polarizing white light interferometry for phase measurements using two simultaneous interferograms.

Our research introduces a design for a polarization phase-shifting white light interferometric system (PPS-WLIS) that operates in a transmissive mode for measuring the slope phase of transparent objects. It comprises a cyclic path interferometer (lateral shear interferometer) coupled with a multiplexing Michelson interferometer. The system uses polarization to produce two parallel interferograms with polarization modulated with relative shifts simultaneously. To determine the optical phase, we used a two-step algorithm for phase demodulation that does not necessitate precise phase shifts, making the system more straightforward to operate. As a result, we could observe variations in the object associated with optical phase changes. Furthermore, our method simplifies the phase-shift interferometry process by requiring only one capture, making it an effective way to examine objects at dynamic events. As an illustration, we demonstrated the temperature measurement generated by a section of a candle flame.

Dynamic parallel phase-shifting electronic speckle pattern interferometer.

Methods for measuring variations in diffuse surfaces using electronic speckle pattern interferometry (ESPI) are widely used and well known. In this research, we present an out-of-plane ESPI system coupled to a Michelson configuration to generate simultaneous parallel interferograms with different phase shifts. The system uses circular polarization states to generate parallel phase shifted interferograms. Due to the polarization states, the fringes do not experience a contrast reduction, thus avoiding measurement errors that affect spatial or temporal phase-shifting in interferometry. The basic operating principle of polarization modulation is described, and results that represent the temporal evolution of an aluminum plate are presented. The generation of two simultaneous patterns allows one to track the dynamic performance of the plate.

Radial polarizing phase-shifting interferometry with applications to single-shot n interferogram measurements and potential usage for white light interferogram analysis.

In this research, we present an interferometric system to analyze transparent samples using interferograms generated by a phase-shifting radial shear grating interferometer for two cases: the first obtaining n simultaneous phase-shifting interferograms using a coherent light source and the second one using sequential phase steps with a white light source. For the first case, the simultaneous interferograms are generated using two optical systems: the first one generates the polarized pattern while the second one consists of a 4f system creating replicas of the output interferograms. By using a 2D sinusoidal phase grating, we have the advantage of obtaining up to nine replicated interferograms, all of them with comparable intensities and having amplitudes modulated by the 2D sinusoidal phase grating diffraction orders as zero-order Bessel's functions. To obtain the optical phase map, several phase shifts are generated by placing a polarizing filter covering each replicated interferogram. We highlight the advantage of using n simultaneous interferograms by comparing resulting optical phases processed by a conventional four-step algorithm against those obtained by an implemented n=N+1 method, reducing errors with noisy interferograms. Results for n=7 and n=9 cases are presented. In addition, we have tested the setup with white light interference techniques by employing the polarizer radial shearing interferometer; for this case, the optical phase is calculated with the four-step and the three-step algorithms. Results of testing the developed system to examine static and dynamic phase objects are also included.

Parallel phase shifting radial shear interferometry with complex fringes and unknown phase shift.

We present an interferometric method to analyze transparent samples using complex fringes generated by a parallel phase shifting radial shear interferometer using two coupled interferometers. Parallel interferograms are generated using two interferometers: the first one generates the polarized base pattern, and the second system is used to generate parallel interferograms allowing the adjustment of the x-y positions of the parallel interferograms. To obtain the optical phase map, parallel phase shift is generated by collocating polarizing filters at the output of the system; the polarizers are placed at arbitrary angles since they do not require adjustment because of the phase-recovery algorithm. The optical phase was processed using a two-step algorithm based on a modified Gram-Schmidt orthogonalization method. Such an algorithm has the advantage of not being iterative and is robust to amplitude modulation. The proposed method reduces the number of captures needed in phase-shifting interferometry. We applied the developed system to examine static and dynamics phase objects.

Multiwavelength wavefront detection based on a lateral shear interferometer and polarization phase-shifting techniques.

We present a multiwavelength analysis of a wavefront detected by a color camera and a lateral shear interferometer. The system employs polarization phase-shifting techniques by rotating a linear polarizer at the output and detecting the phase information through a frequency demodulation algorithm. By considering the phase modulation obtained by rotating the analyzer, a frequency filter centered on the desired peak carries the phase and amplitude information of the detected wavefront. Theoretical approach, the consideration of Jones matrices of each element, and experimental results show the feasibility of the implementation.

Dynamic phase imaging of microscopic measurements using parallel interferograms generated from a cyclic shear interferometer.

We present a technique which allows us to generate two parallel interferograms with phase shifts of π/2 using a Cyclic Shear Interferometer (CSI) and a polarizing splitter. Because of the use of a CSI, we obtain the derivative phase data map directly, due to its configuration, it is immune to vibrations because the reference wavefront and the object wavefront have a common path; the shearing interferometer is insensitive to temperature and vibration. To obtain the optical phase data map, two interferograms are generated by collocating a polarizing device at the output of the CSI. The optical phase was processed using a Vargas-Quiroga algorithm. Related experimental results obtained for dynamic microscopic transparent samples are presented.

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.

Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer.

An interferometric method to measure the slope of phase objects is presented. The analysis was performed by implementing a polarizing phase-shifting cyclic shear interferometer coupled to a 4-f Fourier imaging system with crossed high-frequency Ronchi gratings. This system can obtain nine interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope of a phase object, it is only analyzed using four patterns obtained in a single shot, and applying the classical method of phase extraction.

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.