Alignment errors calibration for 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.

Frequency properties of channeled spectropolarimetry: an information theory perspective

Channeled spectropolarimetry (CSP) has emerged as a notable technique due to its unique capacity to instantaneously measure either the polarization state of light or the Mueller matrix of a sample over a broad spectral range. Leveraging the quasi-linear relation between phase retardances of thick birefringent retarders and wavenumber, the target signal undergoes wavelength encoding. For the first time, we present a theoretical framework for the general CSP from a perspective of information theory. This framework comprehensively addresses the frequency properties of CSP, encompassing signal bandwidth, modulation frequency, sampling relationships, and filter window width during the demodulation process. Drawing from the frequency properties of CSP, we establish a theoretical foundation that informs the design of versatile CSPs and evaluates their measurement capabilities. Simulations for both Stokes CSP and Mueller CSP validate the efficacy of the proposed approach.

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.

Physics-guided neural network for channeled spectropolarimeter spectral reconstruction

A reconstruction method incorporates the complete physical model into a traditional deep neural network (DNN) is proposed for channeled spectropolarimeter (CSP). Unlike traditional DNN-based methods that need to employ training datasets, the method starts from randomly initialized parameters which are constrained by the CSP physical model. It iterates through the gradient descent algorithm to obtain the estimation of the DNN parameters and then to obtain the mapping relationship. As a result, it eliminates the need for thousands of sets of ground truth data, while also leveraging the physical model to achieve high-precision reconstruction. As seen, the physical model participates in the optimization process of DNN parameters, thus achieving physical guidance for the DNN output results. Based on the characteristic of the network, we designate this method as the physics-guided neural network (PGNN). Both simulations and experiments demonstrate the superior performance of the proposed method. Our approach will further promote the practical application of CSP in a wider range of fields.

Polarization property analysis of single lenses

We have studied the basic polarization properties of variously shaped lenses for the on-axis beam in the exit pupil and present the data obtained. The Mueller calculus and three-dimensional polarization calculus methods were applied for polarization ray tracing. The calculation methods were compared on different samples. We have demonstrated that taking into account the shape of lenses when designing lens optical systems contributes to the minimization of the diattenuation magnitude.

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.

Design of channeled spectropolarimeters

I present design and tolerancing guidelines for constructing channeled spectropolarimeter systems employing high-order retarders. The discussion includes how to select appropriate retarder thicknesses, how to accurately align the elements, how to tolerance the retarders, and how to analyze the effect of different polarizer types on the system performance.

Convolutional neural network-based spectrum reconstruction solver for channeled spectropolarimeter

Channeled spectropolarimetry is a snapshot technique for measuring the spectra of Stokes parameters of light by demodulating the measured spectrum. As an indispensable part of the channeled spectropolarimeter, the spectrometer module is far from being perfect to reflect the real modulation spectrum, which further reduces the polarimetric reconstruction accuracy of the channeled spectropolarimeter. Since the modulation spectrum is composed of many continuous narrow-band spectra with high frequency, it is a challenging work to reconstruct it effectively by existing methods. To alleviate this issue, a convolutional neural network (CNN)-based spectral reconstruction solver is proposed for channeled spectropolarimeter. The key idea of the proposed method is to first preprocess the measured spectra using existing traditional methods, so that the preprocessed spectra contain more spectral features of the real spectra, and then these spectral features are employed to train a CNN to learn a map from the preprocessed spectra to the real spectra, so as to further improve the reconstruction quality of the preprocessed spectra. A series of simulation experiments and real experiments were carried out to verify the effect of the proposed method. In simulation experiments, we investigated the spectral reconstruction accuracy and robustness of the proposed method on three synthetic datasets and evaluate the effect of the proposed method on the demodulation results obtained by the Fourier reconstruction method. In real experiments, system matrices are constructed by using measured spectra and reconstructed spectra respectively, and the spectra of Stokes parameters of incident light are estimated by the linear operator method. Several other advanced demodulation methods are also used to demodulate the measured spectrum in both simulation and real experiments. The results show that compared with other methods, the accuracy of the demodulation results can be much more improved by employing the CNN-based solver to reconstruct the measured spectrum.

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.

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.

Spectral-temporal hybrid modulation for channeled spectropolarimetry

Channeled spectropolarimeters (CSPs) are capable of estimating spectrally resolved Stokes parameters from a single modulated spectrum. However, channel crosstalk and subsequent spectral resolution loss reduce the reconstruction accuracy and limit the systems' scope of application. In this paper, we propose a spectral-temporal modulation strategy with the aim of extending channel bandwidth and improving reconstruction accuracy by leveraging the hybrid carriers and allocating channels in the two-dimensional Fourier domain that yield optimal performance. The scheme enables spectral bandwidth and temporal bandwidth to be traded off, and provides flexibility in selecting demodulation strategies based on the features of the input. We present an in-depth comparison of different systems' performances in various input features under the presence of noise. Simulation results show that the hybrid-modulation strategy offers the best comprehensive performance as compared to the conventional CSP and dual-scan techniques.

Alignment precision of polarization components

Recent research publications in the polarization literature have discussed methods of correcting for azimuthal alignment errors of optical elements in postprocessing. However, we show that high angular precision is not difficult to achieve during system alignment, so that postprocessing correction should be unnecessary. We estimate the alignment precision achievable for linear polarizers and waveplates in polarization systems. This shows that using an optical signal model for alignment allows a precision limited by the quality of the optics and detectors rather than the quality of the mechanics, rendering millidegree alignment precision possible with ordinary rotational mounts.

Low crosstalk polarization-difference channeled imaging spectropolarimeter using double-Wollaston prism

A polarization-difference channeled imaging spectropolarimeter (PDCISP) using double-Wollaston prism is presented. It enables simultaneous acquisition of a set of three-channel interferograms corresponding to orthogonal polarization modulation. This brings a large range expanding of optical path difference for useful channels, and the major limitation of channeled spectropolarimetry (CSP), namely the channel crosstalk, can be greatly suppressed by using interferogram difference processing. As a result, full resolution intensity spectrum, as well as high-resolution polarimetric signatures, can be obtained with fewer reconstruction errors, compared to conventional CSP-based systems. The PDCISP is insensitive to alignment errors of retarders and maintains the snapshot feature (1D spatial imaging). The effectiveness of the proposed method is demonstrated by the simulation results.

On-Orbit Polarization Calibration for Multichannel Polarimetric Camera

In this paper, a new on-orbit polarization calibration method for the multichannel polarimetric camera is presented. A polarization calibration model for the polarimetric camera is proposed by taking analysis of the polarization radiation transmission process. In order to get the polarization parameters in the calibration model, an on-orbit measurement scheme is reported, which uses a solar diffuser and a built-in rotatable linear analyzer. The advantages of this scheme are sharing the same calibration assembly with the radiometric calibration and acquiring sufficient polarization accuracy. The influence of the diffuser for the measurement is analyzed. By using a verification experiment, the proposed method can achieve on-orbit polarization calibration. The experimental results show that the relative deviation for the measured degree of linear polarization is 0.8% at 670 nm, which provides a foundation for the accurate application of polarimetric imaging detection.

Channeled compressive imaging spectropolarimeter

A compressive imaging spectropolarimeter is proposed in this paper, capable of simultaneously acquiring full polarization, spatial and spectral information of the object scene. The spectral and polarization information is modulated through a combination of high-order retarders, a dispersion prism and a polarizer filter wheel. Using a random coded aperture, compressive sensing is applied to eliminate the channel crosstalk and resolution limitation of traditional channeled spectropolarimeters. The forward sensing model and inverse problem are developed. Computer simulation results are reported, followed by experimental demonstrations.

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

Calibration of the channeled spectropolarimeter is significant for the quantitative application of this instrument. In current calibration methods for a channeled spectropolarimeter, an absolute angle between the coordinate system of an auxiliary polarizer and the global coordinate system of the instrument is usually indispensable. The effectiveness of calibration depends on the precision of the absolute angle, while it is usually difficult to achieve in a practical calibration process. This paper presents an easily implemented method to simultaneously calibrate the alignment and retardation errors of high-order retarders for a channeled spectropolarimeter. In the presented method, the requirement of an absolute angle between the coordinate system of an auxiliary polarizer and the global coordinate system of the instrument is replaced by only rotating a relative angle in the coordinate system of the auxiliary polarizer itself. First, we theoretically derive the modified reconstruction model considering the alignment errors of high-order retarders. By analyzing and summarizing the modified reconstruction model, the calibration and compensation models of the alignment and retardation errors are further proposed. Then, two linearly polarized beams with a relative angle of 45° between them are utilized to determine the alignment and retardation errors. Based on these results, the alignment and retardation errors can be compensated by a software correction algorithm without any precise mechanical adjustments. The effectiveness and feasibility of the presented method are verified by numerical simulations and experiments. The advantage of easy implementation makes this calibration method more suitable to apply in the laboratory and to be on track for correcting the channeled spectropolarimeter.

Adaptive correction of retardations with immunity to alignment errors for a channeled spectropolarimeter

Retardation errors of high-order retarders will decrease the accuracy of a channeled spectropolarimeter. Taniguchi et al. have proposed a self-calibration method to calibrate the retardations [Opt. Lett.31, 3279 (2006)OPLEDP0146-959210.1364/OL.31.003279]; however, they do not take into account the inevitable alignment errors of high-order retarders. In this paper, an adaptive correction method with immunity to alignment errors is proposed to reduce the effects of temperature variation on retardations. By separating and analyzing the amplitude terms and phase terms contained in the measurement data, the phase terms are utilized to correct the retardations, which makes the effectiveness of this adaptive correction method immune to the inevitable alignment errors of high-order retarders. The adaptive correction process can be accomplished in parallel to the measurement process without any auxiliary resources. The effectiveness and feasibility of this method is verified by simulations and experiments. The convenience and simplicity of the presented method make it extremely suitable for application on track.

Self-correction of alignment errors and retardations for a channeled spectropolarimeter

Alignment errors of birefringent retarders and retardation errors introduced by environmental perturbations can cause significant influences on reconstructed Stokes parameters for the channeled spectropolarimeter. In this paper, we propose what we believe is a novel self-correction model that is independent of input polarization parameters to reduce the effects of alignment errors and environmental perturbations. This self-correction method can realize calibration and compensation of alignment errors and retardations simultaneously by measuring the target light in orbit. Simulation results show that alignment errors and retardations can be calibrated accurately, and the reconstructed Stokes parameters by using the presented method are more precise than by using the traditional method. The validity and feasibility of the presented method are further confirmed through experiments in the presence of alignment errors and environmental perturbations.

Reduction of the effects of angle errors for a channeled spectropolarimeter

Angle errors of high-order retarders will decrease the accuracy of a channeled spectropolarimeter. This paper presents an easily implemented and widely applicable method for reducing the effects of the angle errors. First, we theoretically derive a modified reconstruction model to express and analyze the effects of the angle errors. Based on the modified reconstruction model and current reference beam calibration technique, we put forward the modified reference beam calibration technique to reduce the effects of the angle errors. This method can calculate the angle errors by employing the amplitude terms, which have been ignored in the results of the current reference beam calibration. The effectiveness of the presented method is verified by numerical simulations, which show that the demodulated deviations of polarization parameters have been reduced by one order of magnitude. Experiments are further implemented to validate the proposed method. The convenience and wide applicability of the presented method make it suitable for regular correction of the instrument, especially for the case on track.

Three-dimensional polarization ray tracing calculus for partially polarized light

Calculating the evolution of polarization for all polarization states of light in optical systems, in global coordinates, is an important, yet challenging task. This calculation exists for completely polarized light, but has not yet been developed for partially polarized light. A 3 × 3 coherency matrix for partially polarized light, in global coordinates, is presented to calculate the transformation of its polarization as it passes through an optical system. This matrix is a three-dimensional generalization of the coherency matrix. A new coherency matrix calculus method in three dimensions is suggested and validated for two cases. A double Gauss optical lens is introduced to compare this method's performance with two-dimensional calculus.

Methods of polarimetric calibration and reconstruction for a fieldable channeled dispersive imaging spectropolarimeter

Polarimetric calibration and reconstruction methods for a fieldable channeled dispersive imaging spectropolarimeter (CDISP) are presented. A theoretical model for the polarimetric calibration is derived first. In the polarimetric calibration for the CDISP, the alignment errors of the polarimetric spectral intensity modulation module, and the polarization effects of the optical system and phase factors of the high-order retarders at different viewing angles, are considered and determined independently. Based on the results of the polarimetric calibration, the Stokes vector of the target is reconstructed through the derived reconstruction model. Simulation results with a fieldable CDISP designed for airborne remote sensing indicate that by using the presented polarimetric calibration and reconstruction methods, the measurement accuracy at each viewing angle of the fieldable CDISP can be improved. Experimental results are summarized and analyzed to demonstrate the effectiveness of the presented methods.

Optimal Mueller matrix estimation in the presence of additive and Poisson noise for any number of illumination and analysis states

We investigate the optimal strategies for estimating the Mueller matrix with arbitrary numbers of illumination and analysis states, in the presence of signal-independent additive noise or signal-dependent Poisson shot noise. We demonstrate that the architectures that minimize and equalize the estimation variances for both types of noise sources are based on spherical designs of order 2 or 3, and we provide closed-form expressions of the estimation precision obtained with these optimal measurement strategies. The obtained results are important to design Mueller polarimeters in practice and assess their fundamental limits in terms of estimation precision.