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.

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.

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. The Hilbert-transform is implemented by a 4f optical Fourier-transform correlator and a spatial filter consisting of a phase step of π radians. One important feature of this proposal is to perform a turn of 180° in the spatial filter at a certain value of the projection angle within the range [0°, 360°]. The desired direction of enhancement can be chosen by the proper selection of such turning angle. We present both the mathematical modeling and numerical results.

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. Accordingly, a modified sinogram able to reconstruct edge-enhanced phase slices is obtained. In this paper, the theoretical model is amply discussed and illustrated both with numerical and experimental results.

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.