Measurement errors resulted from misalignment errors of the retarder in a rotating-retarder complete Stokes polarimeter

Rotatable retarder fixed polarizer (RRFP) Stokes polarimeters, which employ uniformly spaced angles over 180° or 360°, are most commonly used to detect the state of polarization (SOP) of an electromagnetic (EM) wave. The misalignment error of the retarder is one of the major error sources. We suppose that the misalignment errors of the retarder obey a uniform normal distribution and are independent of each other. Then, we derive analytically the covariance matrices of the measurement errors. Based on the covariance matrices derived, we can conclude that 1) the measurement errors are independent of the incident intensity s0, but seriously depend on the Stokes parameters (s1, s2, s3) and the retardance of the retarder δ; 2) for any mean incident SOP, the optimal initial angle and retardance to minimize the measurement error both can be achieved; 3) when N = 5, 10, 12, the initial orienting angle could be used as an added degree of freedom to strengthen the immunity of RRFP Stokes polarimeters to the misalignment error. Finally, a series of simulations are performed to verify these theoretical results.