Journal ArticlePolarization purity and cross-channel intensity correlationsKestner, Daniel; Kostinski, Alexandernaanon<p>We consider the question of monitoring polarization purity, that is, measuring deviations from orthogonality<italic>δ</italic>_{<italic>τ</italic>}and<italic>δ</italic>_{<italic>ϵ</italic>}of an ostensibly orthogonal polarization basis with a reference channel of ellipticity<italic>ϵ</italic>and tilt<italic>τ</italic>. A simple result was recently derived for a phase-sensitive receiver observing unpolarized radiation [<mixed-citation publication-type='journal'><source>IEEE Trans. Geosci. Remote Sens.</source><volume>62</volume>,<fpage>2003610</fpage>(<year>2024</year>)<pub-id pub-id-type='doi'>10.1109/TGRS.2024.3380531</pub-id></mixed-citation>]: with<italic>ρ</italic>⁽¹⁾denoting the Pearson complex correlation coefficient between channel<italic toggle='yes'>complex fields</italic>, it states that ∓<italic>cos</italic>⁡(2<italic>ϵ</italic>)<italic>δ</italic>_{<italic>τ</italic>}±<italic>i</italic><italic>δ</italic>_{<italic>ϵ</italic>}≈<italic>ρ</italic>⁽¹⁾when<italic>δ</italic>_{<italic>τ</italic>,<italic>ϵ</italic>}≪1. However, phase-sensitive (in-phase and quadrature) data are seldom available at optical frequencies. To that end, here we generalize the result by deriving a new equation for the polarization “alignment” error:<italic>cos</italic>²(2<italic>ϵ</italic>)<italic>δ</italic>_{<italic>τ</italic>}²+<italic>δ</italic>_{<italic>ϵ</italic>}²≈<italic>ρ</italic>⁽²⁾, where<italic>ρ</italic>⁽²⁾is the intensity cross-correlation coefficient. Only the measurement of the<italic toggle='yes'>(real) intensity</italic>cross-correlation coefficient is needed when observing unpolarized light. For the special case of a linearly polarized basis, the tilt error is simply<italic>δ</italic>_{<italic>τ</italic>}≈<italic>ρ</italic>⁽²⁾, and for the circular basis case, with ellipticity deviation<italic>δ</italic>_{<italic>ϵ</italic>}from circular helicity<italic>π</italic>/4 (the reference channel of opposite helicity),<italic>δ</italic>_{<italic>ϵ</italic>}≈<italic>ρ</italic>⁽²⁾. These results provide simple means to gauge the quality of polarimeters and depolarizers.</p>J. Optic. Soc.2025-01-0110631031Journal of the Optical Society of America A42810771084-7529https://doi.org/10.1364/JOSAA.5646962217182polarimetryNational Science Foundation