# On-Orbit Polarization Calibration for Multichannel Polarimetric Camera
## 2 The Multichannel Polarimetric Camera and Main Polarization Elements
### Polarizing Effects of the Solar Diffuser  
There are numerous micro-surfaces on the solar diffuser. Ideally, the sunlight is reflected quite diffusely, and the reflected light is unpolarized light. However, the solar diffuser is not an ideal Lambertian source, especially in the case of the aluminium solar diffuser. The aluminium solar diffuser is often used for space remote sensing detection, as its high stability and low cost.  
There are some polarizing effects for the aluminium solar diffuser. When the incent light is unpolarized light, the light reflected from the solar diffuser is partially polarized light. According to the Poincare sphere [21], the Stokes parameters of the reflected light can be described by  
Figure 6: Schematic of on-orbit polarization calibration.  
\(\mathbf{S}_{in}^{\prime}(DoLP_{0},\sigma_{0})=I^{\prime}\big{[}1 DoLP_{0}\cos 2 \sigma_{0}DoLP_{0}\sin 2\sigma_{0}\big{]}^{T}\), where \(DoLP_{0}\) represents the polarization degree of the light reflected from the solar diffuser and \(\sigma_{0}\) represents the polarization angle of the light.  
The Stokes parameters of light received by each channel is \(\mathbf{S}_{out}^{\prime}(P_{0},\sigma_{0})=T_{i}\mathbf{M}_{\mathrm{P}} \big{(}E_{i},\theta\big{)}\times\mathbf{M}_{\mathrm{R}}(\theta_{1},\varepsilon _{1},\omega,\varphi)\times\mathbf{S}_{in}^{\prime}(DoLP_{0},\sigma_{0})\), and its radiance intensity can be calculated as  
\[\frac{I_{out}^{\prime}(DoLP_{0},\sigma_{0})=}{4}\left\{\begin{array}{c}[1+E_ {i}+(1-E_{i})\varepsilon_{1}\cos 2(\theta^{\prime}-\theta_{1})]+\varepsilon_{1} DoLP_{0}\cos 2\sigma_{0}(1+E_{i})(\cos 2\theta_{1}+\sin 2\theta_{1}\tan 2 \sigma_{0})+\\ (1-\sqrt{1-\varepsilon_{1}^{2}})DoLP_{0}\cos 2\sigma_{0}\cos 2\theta_{1}\sin 2 \theta_{1}(1-E_{i})(\sin 2\theta^{\prime}+\cos 2\theta^{\prime}\tan 2 \sigma_{0})+\\ DoLP_{0}\cos 2\sigma_{0}\cos 2\theta^{\prime}(1-E_{i})(\cos^{2}2\theta_{1}+\sqrt{1- \varepsilon_{1}^{2}}\sin^{2}2\theta_{1})+\\ DoLP_{0}\cos 2\sigma_{0}\sin 2\theta^{\prime}(1-E_{i})(\sin^{2}2\theta_{1}+\sqrt{1- \varepsilon_{1}^{2}}\cos^{2}2\theta_{1})\end{array}\right\}. \tag{15}\]  
We can analyze the relative deviation of the radiance intensity between an ideal Lambertian source and an actual aluminium solar diffuser from Equation (15). In the development process of this instrument, the physical production process has been optimized by physical grinding and chemical etching. However, there is still no guarantee that the roughness is consistent with the ideal Lambertian body, which leads to the polarization effect. Here, we assume the angle of linear polarization of the diattenuation for the optical system as \(\theta_{1}=30^{\circ}\), the polarization angle of the solar diffuser as \(\sigma_{0}=60^{\circ}\), the polarizer axis angle of the linear analyzer as \(\theta^{\prime}=20^{\circ}\), the range of the extinction ratio as \(E_{i}=0\)-\(1/100\), the range of the diattenuation of the optical system as \(\varepsilon_{1}=0\)-\(10\%\), and the range of the polarization degree of the solar diffuser as \(DoLP_{0}=0\)-\(4\%\). The analysis result of the relative deviation \(\delta(DoLP_{0})\) is shown in Figure 7.  
We can see from Figure 8 that the relative deviation \(\delta(DoLP_{0})\) rises as the increase of the polarization degree of the solar diffuser \(DoLP_{0}\). When the polarization degree of the solar diffuser \(DoLP_{0}\) is small (less than the restriction of the accuracy of the calibration), we can use Equation (10) for polarization calibration. Otherwise, we should use Equation (11) for polarization calibration.  
Figure 7: Schematic of the reflection on the solar diffuser.