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.
In this work, we present an accurate polarization reconstruction method based on the coherence demodulation technique, which is different from the previous windowing method operating in the optical path difference domain. The proposed method uses a signal multiplier and a low-pass filter to reconstruct Stokes parameters without performing any Fourier transform. Because this method does not require a Fourier transform, the Stokes reconstruction could be finished in the spectral domain. For calibrating the waveplate phase error, coherence demodulation allows for establishing an analytical model to describe the influence of waveplate imperfections on the polarization measurement process. The phase error will result in a channel shift and Fourier broadening, both of which cause serious errors during Stokes reconstruction. With the model, a method based on a linear polarizer was proposed for calibrating the phase deviation of waveplate. After that, the accurate reconstruction of polarization parameters could be achieved. An experiment was performed to check the ability of the proposed method. The experimental result showed that it has the same excellent performance of reconstructing Stokes parameters using the traditional windowing method. Finally, a series of simulations was carried out to verify the robustness of this method, which showed that the reconstruction technique is robust to misalignment and additional noise.
Channeled Mueller matrix spectropolarimeters (CMMSPs) have gained increasing popularity in recent years due to no moving parts. However, in order to obtain more accurate measurements, thorough studies on the influence and correction of their systematic errors are still needed. This paper presents a novel perspective for CMMSPs based on a signal processing technique, and propose a coherence demodulation method to extract channel signals in the modulated intensity. From theoretical analysis, the influence of phase deviation resulting from the imperfection of retarders is pinpointed. Meanwhile, the mechanism of phase deviation is described in theory and visually displayed by simulation. To mitigate the interference of retarder phase deviation, this work proposes a way for correction utilizing a vacuum and polarizer as determinant samples. Noticeably, the phase deviations are treated as a whole and represented by polynomials during correction. The reverse process of error mechanism is used to correct the influence. Finally, this means is proved by a series of simulation validations with a detector noise of 30 dB and retarder misalignment errors of 0.5°.
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