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

Abstract

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.

A two steps phase-shifting demodulation method using the VU factorization

“…To demonstrate the capabilities of our method on experimental results, we implemented our method on fringe patterns obtained from a Parallel Radial Shear Interferometer (PRSI) as the one proposed in [15]. We used a λ = 532nm laser to illuminate the sample, the shifts are generated by a polarizer array which allows us to capture two steps simultaneously.…”

“…We used a λ = 532nm laser to illuminate the sample, the shifts are generated by a polarizer array which allows us to capture two steps simultaneously. The patterns were captured by a 2048 × 1536 CCD camera and the estimated phase step is define by the rotation of the polarizers (for more details of the arrangement please refer to [15]).…”

Facile Morphological Qualification of Transferred Graphene by Phase‐Shifting Interferometry

“…[57] One of the most common method originates from polarization heterodyne interferometry, [58] where a combination of a waveplate and a rotating polarizer is used to capture a specific phase shift between test and reference beams. Modern implementation of such single-shot PSI utilizes polarizer array [59][60][61] or a pixelated polarizer [62] to simultaneously capture interferograms with desired phase shifts.…”

The comparison of multi-stepping algorithms for real-time thickness measurement of transparent thin films using polarization settings

“…An automatic phase-shifting scheme was also developed by tilting the mirror coupled to a piezoelectric transducer (PZT) to produce a path length difference [3] as the analyzer was oriented and fixed at the angle θ respective to the reference plane. However, the nonlinearity and unstable signals were the potential sources of systematic inaccuracies in the phase production [4]. Several methods for achieving automated phase shift have been published using a PZT [5][6][7].…”