Radial polarizing phase-shifting interferometry with applications to single-shot n interferogram measurements and...

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.