# Polarization Radiometric Calibration in Laboratory for a Channeled Spectropolarimeter
## 4 Verification by Simulation Experiment
The reference beam at central FOV is shined on the system along the optical axis at the center of the aperture, therefore, the effect of polarization properties on calibration results can be ignored. The validity of the self-correction method for alignment errors and retardation calibration has been demonstrated by experiment [17]. According to the calibration results of the alignment errors \(\varepsilon_{1}\), \(\varepsilon_{2}\) and retardation \(\varphi_{2}(\sigma)\) of the PSIM module, we could decouple the radiometric calibration coefficient \(A^{k}(\sigma,\theta)\) and diattenuation of fore-optics \(D_{fore}(\sigma,\theta)\) from modulated radiometric calibration coefficient \(A^{k^{\prime}}(\sigma,\theta)\). Figure 5 gives the magnitude of the autocorrelation function of \(A^{k^{\prime}}(\sigma,\theta)\), which is at the edge FOV, the modulation channels of other FOV are consistent with this, only the amplitude is different. The figure only shows the values of channels 0 and 1, and the values of other channels are too small. Fortunately, only channels 0 and 1 are needed in the decoupling of \(A^{k}(\sigma,\theta)\) and \(D_{fore}(\sigma,\theta)\). The input values and calibration results of diattenuation of the fore-optics at different field of view are shown in Figure 6. And the maximum relative error of the calibration results of \(D_{fore}(\sigma,\theta)\) is less than 0.07% by using  
Figure 4: Input values and calibration results of \(\varphi_{2}(\sigma)\)  
Figure 3: Quantum Efficiency curve of the detector. the presented method, while its maximum relative error is 63.57% by using the traditional calibration method. Figures 7 and 8 give the input values and calibration results of the retardation \(\varphi_{1}(\sigma,\theta)\) and retardance of the fore-optics \(\delta_{fore}(\sigma,\theta)\) at different fields of view. In order to facilitate quantitative analysis of the calibration results, we calculate \(\varphi_{1}(\sigma,\theta)\) from \(\exp[-i[\varphi_{1}(\sigma,\theta)+\varphi_{2}(\sigma)]]\) by using the calibration results \(\varphi_{2}(\sigma)\) and a phase unwrapping algorithm. The calibration results of \(\varphi_{1}(\sigma,\theta)\) and \(\delta_{fore}(\sigma,\theta)\) of two methods are overlapped well with the input values, and the maximum residual errors are less than \(1.0\times 10^{-4}\) rad. It can be seen that, compared with the traditional calibration method, the presented method can achieve more accurate calibration when calibrating diattenuation of the fore-optics. For the calibration of alignment errors, phase retardances in the PSIM module, and retardance of the fore-optics, the two methods can both get good calibration results. Figure 5: Magnitude of the autocorrelation function of \(A^{k\prime}(\sigma,1)\)  
Figure 6: Input values and calibration results of the diattenuation of the fore-optics. After calibrating the parameters in the polarization radiometric calibration model, we substitute these calibration results into Equations (12)-(15) to reconstruct the Stokes parameters of the target light. In the simulation, we employ a 30\({}^{\circ}\) linearly polarized beam as the target light, whose theoretical values of normalized Stokes vectors are \(S_{1}/S_{0}=0.5\), \(S_{2}/S_{0}=0.866\), and \(S_{3}/S_{0}=0\), respectively. Figure 9a-c give the normalized Stokes vectors reconstructed by two methods, wherein the solid and broken line respectively represent the presented calibration method and the traditional calibration method, and the different colors represent reconstruction results at different field of view. Through contrastive analysis, the deviations of the Stokes parameters reconstruction results obtained by the traditional calibration method from the input values are large, and they are different with the change of field of view. While the reconstruction results obtained by the presented method are closer to the input values and overlapped well with different field of view.