Quantitative performance of a polarization diffraction grating polarimeter encoded onto two liquid-crystal-on-silicon displays

We present a quantitative analysis of the performance of a complete snapshot polarimeter based on a polarization diffraction grating (PDGr). The PDGr is generated in a common path polarization interferometer with a Z optical architecture that uses two liquid-crystal on silicon (LCoS) displays to imprint two different phase-only diffraction gratings onto two orthogonal linear states of polarization. As a result, we obtain a programmable PDGr capable to act as a simultaneous polarization state generator (PSG), yielding diffraction orders with different states of polarization. The same system is also shown to operate as a polarization state analyzer (PSA), therefore useful for the realization of a snapshot polarimeter. We analyze its performance using quantitative metrics such as the conditional number, and verify its reliability for the detection of states of polarization.