Measurement errors induced by deformation of optical axes of achromatic waveplate retarders in RRFP Stokes polarimeters.

The optical axes of achromatic waveplate retarders (AWR) may deform from ideal linear eigenpolarizations and be frequency-dependent owing to the imperfect design and fabrication. Such deformations result in the ellipticity error and the orientation error of an AWR away from the nominal values. In this paper, we address the measurement errors of Stokes parameters induced by deformation of optical axes of AWRs in roatatable retarder fixed polarizer (RRFP) Stokes polarimeters. A set of theoretical formulas is derived to reveal that such measurement errors actually depend on both retardance and angular orientations of the AWR in use, as well as the state of polarization (SOP) under test. We demonstrate that,by rotating the AWR to N (N≥5) uniformly spaced angles with the angle step of 180°/N or 360°/N, the measurement errors of Stokes parameters induced by the ellipticity error of the AWR can be suppressed compared with the result using any set of four specific angles, especially when the SOP under test is nearly circular. On the other hand, the measurement errors induced by the orientation error of the AWR have more complicated relationships with the angular orientations of the AWR: 1) when the SOP under test is nearly circular, above-mentioned N (N≥5) uniformly spaced angles also lead to much smaller measurement errors than any set of four specific angles; 2) when the SOP under test is nearly linear, N (N≥5) uniformly spaced angles result in smaller or larger measurement errors, depending on the SOP under test, compared with the usually-recommended sets of four specific angles. By theoretical calculations and numerical simulations, we can conclude that the RRFP Stokes polarimeters employing angle sets of N (N≥5) uniformly spaced angles, ( ± 90°, -54°, -18°, 18°, 54°) for instance, can effectively reduce the measurement errors of Stokes parameters induced by the optical axes deformation of the AWR.