# Polarization Radiometric Calibration in Laboratory for a Channeled Spectropolarimeter
## 4 Verification by Simulation Experiment  
To verify the feasibility and advantages of the presented method, simulations experiment for the calibration of parameters in the polarization radiometric calibration model and reconstruction of Stokes parameters are performed. In the simulations, we use a fieldable CDISP designed for airborne remote sensing in advance, whose schematic layout is shown in Figure 2. It operates over 13,000-18,000 cm\({}^{-1}\), the FOV is 40\({}^{\circ}\) and the F-number is 4. R\({}_{1}\) and R\({}_{2}\) are made of quartz, whose birefringence in the selected wave band can be referred to Ref. [21], and their thicknesses are 6 mm and 2 mm, respectively. We analyze the polarization properties of each sub-modules through polarization ray tracing [22; 23] and calculate the phase retardations of R\({}_{2}\) and R\({}_{1}\) at different field of view. These results are used as the input values of the simulations. We compare the calibration results of parameters in the polarization radiometric calibration model and reconstructed Stokes parameters with two methods, i.e., the presented method in this paper, and the traditional calibration method of spectropolarimeter. Both methods take into account the alignment errors of polarization module and the variation of the retardations at different field of view in the process of radiometric calibration. The only difference is that in the radiometric calibration, the presented method considers the influence of polarization properties of optical system and decouples it, while the traditional calibration method does not consider its influence. We first simulate the process of radiometric calibration of the fieldable CDISP. The detector uses SARNOFF's CAM512 CCD as an example, whose area array is \(512\times 512\), the pixel size is \(18\)\(\upmu\)m \(\times 18\)\(\upmu\)m, the frame frequency is 100 _fps_, and the quantum efficiency curve is shown in Figure 3. According to the imaging chain analysis of the radiance from optical system entrance pupil to detector, the DN recorded by detector can be obtained by simulation. Using the radiance of the optical system entrance pupil and the simulated DN of detector, the dark current response \(C(\sigma,\theta)\) and modulated radiometric calibration coefficient \(A^{K^{\prime}}(\sigma,\theta)\) can be obtained on the basis of the classical radiometric calibration principle. Next, we calibrate the alignment errors \(\varepsilon_{1}\), \(\varepsilon_{2}\) and retardation \(\varphi_{2}(\sigma)\) of the PSIM module by using the self-correction method. The alignment errors of R\({}_{1}\) and R\({}_{2}\) are \(\varepsilon_{1}=-0.5^{\circ}\), \(\varepsilon_{2}=0.5^{\circ}\), respectively. Because the alignment errors are independent of wavenumber, we can use the averages of the calculated values in different wavenumbers as the final determination results, which are both \(-0.5029^{\circ}\)and \(0.5007^{\circ}\) by the presented method and the traditional calibration method. The input values and calibration results of \(\varphi_{2}(\sigma)\) at different field of view is shown in Figure 4. The field of view is normalized and the wavenumber is 16,000 cm\({}^{-1}\). In order to facilitate quantitative analysis of the calibration results, we calculate \(\varphi_{2}(\sigma)\) from \(\exp[i\varphi_{2}(\sigma)]\) by using a phase unwrapping algorithm, though it is not needed in the calibration and reconstruction. The maximum residual error of \(\varphi_{2}(\sigma)\) is less than \(1.0\times 10^{-3}\) rad. These calibration results indicate that the self-correction method is applicative for the fieldable CDISP. Since \(\varepsilon_{1}\), \(\varepsilon_{2}\), and \(\varphi_{2}(\sigma)\) do not change with the field of view, it is feasible to calibrate them only by  
Figure 2: Schematic layout of the fieldable CDISP. using the data at central FOV.