Reconstruction and calibration methods for a Mueller channeled spectropolarimeter

Ultrafast polarization characterization with Mueller matrix based on optical time-stretch and spectral encoding

High-speed optical polarization characterization is highly desirable for a wide range of applications, including remote sensing, telecommunication, and medical diagnosis. The utilization of the Mueller matrix provides a superior systematic and comprehensive approach to represent polarization attributes when matter interacts with optical beams. However, the current measurement speed of Mueller matrix is limited to only seconds or milliseconds. In this study, we present an ultrafast Mueller matrix polarimetry (MMP) technique based on optical time-stretch and spectral encoding that enables us to achieve an impressive temporal resolution of 4.83 nanoseconds for accurate Mueller matrix measurements. The unique feature of optical time-stretch technology enables continuous, ultrafast single-shot spectroscopy, resulting in a remarkable speed of up to 207 MHz for spectral encoding Mueller matrix measurement. We have employed an effective Mueller linear reconstruction algorithm based on the measured modulation matrix, accounting for all potential non-ideal effects of polarization components like retardance error and azimuth error. To ensure high precision, prior to the actual measurement, high-order dispersion induced by time-stretch requires adjustment through proper modulation matrix design. Upon such correction, both the results of static and rapid dynamic samples measurements exhibit exceptional accuracy with root-mean-square error (RMSE) approximately equal to 0.04 and 0.07 respectively. This presented ultrafast MMP provides a significant advance over preceding endeavors, enabling superior accuracy and increased speed concurrently.

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.

Efficient acquisition of Mueller matrix via spatially modulated polarimetry at low light field

Mueller polarimetry performed in low light field with high speed and accuracy is important for the diagnosis of living biological tissues. However, efficient acquisition of the Mueller matrix at low light field is challenging owing to the interference of background-noise. In this study, a spatially modulated Mueller polarimeter (SMMP) induced by a zero-order vortex quarter wave retarder is first presented to acquire the Mueller matrix rapidly using only four camera shots rather than 16 shots, as in the state of the art technique. In addition, a momentum gradient ascent algorithm is proposed to accelerate the reconstruction of the Mueller matrix. Subsequently, a novel adaptive hard thresholding filter combined with the spatial distribution characteristics of photons at different low light levels, in addition to a low-pass fast-Fourier-transform filter, is utilized to remove redundant background noise from raw-low intensity distributions. The experimental results illustrate that the proposed method is more robust to noise perturbation, and its precision is almost an order of magnitude higher than that of the classical dual-rotating retarder Mueller polarimetry at low light field.

Analysis and Correction of Polarization Response Calibration Error of Limb Atmosphere Ultraviolet Hyperspectral Detector

A UV hyperspectral instrument was designed with a polarization measurement channel for real-time in-orbit polarization correction to reduce the influence of polarization on the detection accuracy of atmospheric radiation. One of the prerequisites for in-orbit polarization calibration is accurately calibrating the instrument's polarization properties in the laboratory. This study first introduces the calibration method and measuring device of the polarization characteristics of the ultraviolet (UV) hyperspectral detector and conducts a polarization calibration test of the instrument. The two main error sources introduced by the calibration device were emphatically analyzed, and the correction method of the error sources was deduced theoretically. Finally, the polarization calibration results of the UV hyperspectral detector were corrected, and the uncertainty analysis of the corrected calibration results was about 1.4%, which provides effective ground polarization calibration data for the on-orbit polarization correction of the instrument.

Optimal design for a broadband Stokes polarimeter of liquid crystal variable retarders

Liquid crystal variable retarders (LCVRs) are the core component for rapid and high-precision broadband polarization detection. Additionally, the ability to suppress noise greatly affects the results of polarization measurements. In this work, a solving optimal design approach is proposed for building a high-performance broadband Stokes polarimeter based on LCVRs, which greatly reduces the influences of data fluctuation from liquid crystals and dispersion on the experimental results. This method relies on evaluation criteria of the condition number (CN) to build a gradual optimization that includes the following three steps: fixing the fast axis angles, meeting the requirements of a wideband, and ensuring a minimum CN. Additionally, with the method of increasing the measurement analysis vector, we ensure the whole band in the low CN and offer a solution to the problem of the difficulty in optimizing the LCVRs caused by the large change of retardance at 490-700 nm. Finally, the rapid and high-precision Stokes measurement of 490-700 nm wavelengths is achieved. We test the performance of the polarimeter after optimization in our simulation and experiment, which shows that the total RMS error is less than 0.032 and the single point error is small. This work not only reduces the influence of LCVR error on the experimental results but also makes it possible to apply LCVRs to 490-700 nm detection.

Spectrally modulated polarimetry with wavelength domain analysis

Spectrally modulated Stokes polarimeters use a pair of high-order crystal retarders to generate a spectrally dependent modulation of the polarization of light. In these systems, the detected intensity versus wavenumber spectrum is usually referred to as a channeled spectrum, and the Fourier inversion of this spectrum allows the determination of Stokes parameters of light without needing any other mechanical or active device for polarization control. This work proposes a spectrally modulated polarimeter beyond the concept of a channeled wavenumber spectrum, so effectively detaching the spectral modulation from the Fourier analysis technique. The wavelength domain analysis we use is best suited for dispersive spectrometers offering intensity versus wavelength measurements. The technique is illustrated with the measurement of very small optical rotations produced by sucrose solutions. The proposed technique is easily extendable to spectrally modulated Mueller polarimeters.