In this paper, the close-form functions of estimation variances on the elements of the measured Mueller matrix for a dual-rotating-retarder Mueller matrix polarimeter with a rotating frequency ratio of 5ω:Nω (N = 1, 2, 3, 4, 6, 7, 8, 9) are addressed by theoretical analysis and simulations in the presence of additive Gaussian noise and signal-dependent Poisson shot noise, which are two dominant types of noise in the most commonly used detectors. The results provide a clear insight into the estimation precision of each Mueller matrix element. It is found that (1) estimation variances on each element of the Mueller matrix are heavily dependent on the retardances of the retarders and inversely proportional to the number of measurements; (2) for Gaussian noise, estimation variances are independent of rotating frequency ratio and dual 130.18° retardances can minimize the total variance of the 16 estimated Mueller matrix elements at a fixed number of measurements; (3) for Poisson noise, the estimation variances are only dependent on four elements of the Mueller matrix under test when the rotating frequency ratio of 5ω:7ω is used; (4) the retardance in the range from 126.43°–133.54° can result in a nearly-minimum total variance for both Gaussian and Poisson noise, whatever the observed Mueller matrix. These results are important for designing dual-rotating-retarder Mueller matrix polarimeters aimed at different types of applications and for assessing their performance.
A Stokes channeled interference imaging spectropolarimeter with full-resolution spectra and aliasing reduction is presented. The sensor uses a Wollaston prism, a Savart polariscope, and a linear analyzer as a birefringent interferometer, along with two high-order retarders to incorporate channeled polarimetry employing a tempo-spatially mixed modulated mode with no internal moving parts and offering a robust system. The performance of the system is verified through laboratory tests. Compared with the previous sensors, the most significant advantage of the described instrument is that the reconstructed spectra retain the resolution of the interferometer, and the errors in the reconstructed spectral resolved polarization state caused by aliasing between the interference channels are suppressed effectively. Additionally, the advantages of the interferometer are maintained, such as compact structure and high optical throughput.
This paper presents a snapshot spectroscopic Mueller matrix polarimetry based on spectral modulation. The polarization state generator consists of a linear polarizer in front of two high-order retarders, and the polarization state analyzer is formed by two non-polarization beam splitters incorporated with three high-order retarder/linear analyzer pairs. It can simultaneously generate three modulated spectra used for reconstructing the 16 spectroscopic Mueller elements of the sample. Since each of the modulated spectra produces seven separate channels equally spaced in the Fourier domain, the channel bandwidth can be enhanced efficiently compared with the conventional spectrally modulated spectroscopic Mueller matrix polarimetry. The feasibility of the proposed spectroscopic Mueller matrix polarimetry is demonstrated by the experimental measurement of an achromatic quarter-wave plate.
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