The space-based full-Stokes imaging polarimeter places the polarizing beam splitting prisms and retarders in front of the focal plane of the objective to achieve simultaneous polarimetric measurement. It can obtain not only the light intensity information of the target but also the degree of polarization, azimuth of polarization, and external contour and thus is used to enhance ground target detection and restore haze images. In order to meet the needs of high spatial resolution, large field of view, and wide spectrum, the telescope objective adopts a silver-coated off-axis three-mirror system. The metal reflective film makes the objective to exhibit diattenuation and retardance effects, which affect the ideal measurement matrix of the imaging polarimeter. For the sake of the accuracy of the imaging polarimeter measurement, the Mueller matrix of the objective needs to be measured accurately.

In this study, the Muller matrix of the off-axis three-mirror telescope objective is measured by a dual-rotating retarder. To begin with, the transmission axis of the Glan-Taylor prism as a polarizer is adjusted to horizontal with a theodolite. Then the optical axis of two waveplates and an analyzer are adjusted horizontally based on the Glan-Taylor prism. After that, two waveplates rotate one cycle at an angular rate of 1∶5. The Fourier amplitude is measured by performing a discrete Fourier transform of the light intensity, and 16 elements of the Mueller matrix are determined. Specifically, the test is divided into two stages. Firstly, the straight-through device measures five system parameters, including the retardation of two waveplates, the azimuth of the two waveplates, and the analyzer relative to the polarizer. The straight-through device is operated with no sample, and five system parameters are deduced through the identity matrix. By changing the ambient temperature, the retardation of two waveplates is measured by equations of the temperature. Secondly, the V-structure device measures the Mueller matrix of the objective. The polarizer, two waveplates, and analyzer are moved to the V-structure device. The temperature of the waveplate is monitored during the measurement of the dual-rotating waveplate, so the retardation at the current temperature of the waveplate is obtained through the equations. Finally, the five system parameters and Fourier amplitude are used to calculate the Mueller matrix of the objective.

A Mueller matrix measurement system for a large-aperture reflective objective is built, and a mathematical model of the temperature effect of the measurement system is established. The equations for the retardation of the waveplates and temperature are obtained by least squares fitting (Fig. 3), and the accuracy of Muller matrix measurement of the objective is improved obviously. When the temperature changes by 1 ℃, the accuracy of Mueller matrix elements m₁₂, m₂₁, m₂₂, and m₃₃ increases theoretically by 0.0014, 0.0016, 0.0030, and 0.0030, respectively. The experiment shows that the measurement error of Mueller matrix elements m₁₂, m₂₁, m₂₂, and m₃₃ of the objective is no more than 0.0011 after temperature compensation. The measured results are basically consistent with the theoretical values of CODE V simulation, with the diattenuation and retardation of the objective having a difference of 0.0002 and 0.5211°. The extended uncertainty of the measured Mueller matrix of the objective is 0.0006 at a confidence of 95%, which has an effect of ≤0.0038@p=1 on the accuracy of the degree of polarization, degree of linear polarization, and degree of circular polarization (Fig. 7). It can be used as a high-precision polarization calibration method.

In this paper, a Mueller matrix measurement system for a reflective objective is designed and established based on the dual-rotating retarder method, which solves the requirements for large-aperture and full-Stokes measurement for the polarization calibration of an off-axis three-mirror objective. In terms of measurement principle, the temperature characteristics of the waveplates are considered and added to the measurement model. The temperature compensation of the waveplate retardation is carried out by the Mueller matrix measurement formula. The equations of the retardation of waveplates with temperature are obtained during the calibration of the five system parameters. After temperature compensation, the measurement error of Mueller matrix elements m12, m21, m22, and m33 of the objective is no more than 0.0011. By pole decomposition of the Mueller matrix, the diattenuation and retardation are basically consistent with the CODE V simulation results, with a difference of 0.0002 and 0.5211°, respectively. The Mueller matrix elements m12 and m13 obtained by rotating the polarizer differ from the dual-rotating retarder method by 0.0002 and 0.0001. The uncertainty of the Mueller matrix measurement results and the influence on the accuracy of polarization measurement are also evaluated. The polarization measurement accuracy is better than 0.0038@p=1 when the incident light is input under the condition of different degrees of polarization, azimuths of polarization, and angles of ellipticity. In conclusion, the measurement method shows excellent polarization calibration accuracy.