Easily implemented approach for the calibration of alignment and retardation errors in a channeled spectropolarimeter

Learnable sparse dictionary compressed sensing for channeled spectropolarimeter

Channeled spectropolarimetry enables real-time measurement of the polarimetric spectral information of the target. A crucial aspect of this technology is the accurate reconstruction of Stokes parameters spectra from the modulated spectra obtained through snapshot measurements. In this paper, a learnable sparse dictionary compressed sensing method is proposed for channeled spectropolarimeter (CSP) spectral reconstruction. Grounded in the compressive sensing framework, this method defines a variable sparse dictionary. It can learn prior knowledge from the measured modulated spectra, continuously optimizing its own structure and parameters iteratively by removing redundant basis functions and refining the matched basis functions. The learned sparse dictionary, post-training, can provide a more accurate sparse representation of the Stokes parameters spectra, enabling the proposed method to achieve more precise reconstruction results. To assess the efficacy of the proposed method, simulations and experiments were conducted, both of which consistently demonstrated the superior performance of the proposed approach. The suggested method is well-positioned to enhance the efficiency and accuracy of polarimetric spectral information retrieval in CSP applications.

Derivation and calibration of spectral response for a channeled spectropolarimeter

The channeled spectropolarimeter (CSP) measures the spectrally-resolved Stokes vector from a snapshot by employing spectral modulation. The spectral modulation transfer function (SMTF) of the spectrometer preferentially suppresses the high-frequency channel amplitude in CSP, resulting in reduced measurement accuracy. This paper rigorously derives the SMTF theory and proposes an efficient calibration method for SMTF via channel shifting in a CSP. The SMTF value, obtained by channel shifting, is used to correct the high-frequency channel amplitude. Moreover, alignment and phase errors, as well as nonlinear dispersion, are compensated in situ. Other than rotating the retarder twice, no additional instruments or algorithms are required in the proposed method. In simulations and experiments, the proposed method shows high accuracy, with a maximum root-mean-square error (RMSE) of the reconstructed Stokes spectrum below 0.01, demonstrating its potential for enhancing the simplicity and practicability of Stokes CSP.

Characteristics of spatial heterodyne spectroscopy for polarization measurement

In this paper, a spatial static polarization modulation interference spectrum technique is proposed, which combines polarimetric spectral intensity modulation (PSIM) technology and spatial heterodyne spectroscopy (SHS), and can obtain the total Stokes parameters of the target light simultaneously. Moreover, there are no moving parts or electronically controlled modulation parts. In this paper, the mathematical model of the modulation process and demodulation process of spatial static polarization modulation interference spectroscopy is deduced, a computer simulation is carried out, the principle prototype is developed, and a verification experiment is carried out. Simulation and experimental results show that the combination of PSIM and SHS can achieve high-precision static synchronous measurement of high spectral resolution, high time resolution, and continuous band complete polarization information.

Channeled spectropolarimeter with arbitrary retarder orientation settings

A channeled spectropolarimeter can simultaneously obtain intensity, spectral, and polarization information. In the traditional model, the retarders must be oriented at specific angles. However, misalignments of the retarders are inevitable during assembly, and the status of the retarders is sensitive to environmental perturbations, which affects the performance of the channeled spectropolarimeter. In this study, a general channeled spectropolarimeter model was derived, in which the retarder orientations can be arbitrary and unknown. Meanwhile, the system is unaffected by environmental perturbation because it can self-calibrate to avoid fluctuations in the retarder orientations and phase retardations. The effectiveness and robustness of the model were verified through simulations and experiments.

Reconstruction and calibration methods for a Mueller channeled spectropolarimeter

Channeled spectropolarimeter (CSP) measures spectrally resolved Stokes vector of light and Mueller matrix of sample from a snapshot. While reconstruction and calibration methods for Stokes CSP have been well established, their Mueller CSP counterparts are lacking. In this paper, we propose methods for Mueller spectrum reconstruction and Mueller CSP calibration. Mueller CSP is modeled as a modulation matrix, linking the Mueller spectrum to be measured and the modulated spectrum from the spectrometer. We describe an optimization problem to solve the Mueller spectrum, where both the regularizer and the residual threshold constrain the result, making our reconstruction accurate, efficient, and noise-robust. The Stokes spectrum generated by polarization state generator and the analyzing vector of polarization state analyzer are measured in situ, the convolution of which construct the calibrated modulation matrix of Mueller CSP. Total polarimetric errors and spectroscopic errors are treated as a whole and represented by the calibrated modulation matrix. Both imaging and non-imaging Mueller CSP are experimentally calibrated. Reconstruction results show high accuracy with a root-mean-square error (RMSE) of 0.0371. The proposed methods help make Mueller CSP practical and have the potential to be general reconstruction and calibration methods for imaging and non-imaging Stokes-Mueller CSP.

Analysis of experimental errors in Mueller matrix channeled polarimeters

This work analyzes the effect of experimental errors and measurement noise on Mueller matrix channeled spectropolarimeters. The main advantage of this type of polarimeter is the independence on temporal resolution, as it can be used as a snapshot polarimeter. The simulation of the polarimeters with experimental errors and two published extraction methods of the sample Mueller matrix are also presented. The Mueller matrix channeled spectropolarimeter (MMCS) setup consists of a mirrored Stokes channeled spectropolarimeter (SCS) as the polarization states generator (PSG) and a SCS as the polarization states analyzer (PSA). The SCS setup comprises two thick birefringent retarders followed by a horizontal linear polarizer. The effects of the thickness ratio of the retarders, the global retardance factor, retardance errors, axes alignment errors, and additive Gaussian noise are further studied to optimize the MMCS setups. In this work, we do not include a calibration procedure to improve the measured Mueller matrix parameters, but we study the sensitivity of the polarimeter to different configurations and error sources.

Error analysis of channeled Stokes polarimeters

This work presents an analysis of passive polarimeters with spectral channeling, referred to as Stokes channeled spectropolarimeters (SCS). The SCS setup comprises two thick birefringent retarders, followed by a horizontal linear polarizer. The simulation of these polarimeters and two extraction methods for the incident Stokes vector is presented as well. The effects of different retarders thickness ratios, the global retardance factor, retardance errors, axes alignment error, and Gaussian noise on root mean square (RMS) errors of the recovered Stokes parameters are described. Furthermore, two different, previously published data extraction methods are presented and compared. We found the best polarimeter configurations from the cases studied, and our results suggest that a mixed extraction process, using different extraction methods for different Stokes parameters, could give better results by reducing RMS errors by about a factor of 5. It is worth mentioning that although calibration is needed to account for the effect of errors, this is out of the scope of this work.

Efficient calibration method of total polarimetric errors in a channeled spectropolarimeter

An efficient calibration method of total polarimetric errors in a channeled spectropolarimeter (CSP) is proposed and experimentally demonstrated. Total polarimetric errors, including alignment and retardance errors as well as those caused by nonideal retarders and the polarizer in CSP, are considered and calibrated. We first construct the calibrated modulation matrix of CSP by directly measuring the Mueller matrix spectrum of the polarization module in CSP. Compared to previously reported calibration works that required 1074 measurements, our calibration requires only 16 individual measurements, which reduces the measurement time by 67-fold while ensuring high accuracy with a maximum rms error less than 0.02. Further experimental test on three types of different CSP systems confirms the efficiency, reliability, and accuracy of the proposed calibration method.