# Space Object and Background Polarization Models and Detectability Analysis
## 4 Imaging Contrast Simulation Analysis  
Simulation work was carried out for the National Astronomical Observatory of the Chinese Academy of Sciences Changchun Satellite Observatory (43\({}^{\circ}\)8\({}^{\prime}\) N, 125\({}^{\circ}\)32\({}^{\prime}\) E) on 16 December 2020, at 11:42 a.m. under specific space target relative position conditions, where the solar zenith angle \(\theta_{o}\) and azimuth angle are 29\({}^{\circ}\)30\({}^{\prime}\) and \(-\)04\({}^{\circ}\)32\({}^{\prime}\), respectively. Based on the simulation work, the analysis of the effect of ground-based polarization imaging of the space target in this paper will be continued with the following settings. As shown in Figure 8, it is assumed that the polyimide film, solar panel, aluminum plate and #54 black backplane are on the same flat plate, in the same plane with the sun and the ground-based optical system, and the relative azimuth of the sun and the ground-based optical system and the space target in this plane is 180\({}^{\circ}\). Figure 7: 2–D polarization distribution characteristics of sky complex spherical projection, (**a**) Polarization degree (**b**) Polarization angle. The sun is at 180\({}^{\circ}\) relative azimuth to both the space target and the ground-based optical system. The sun is regarded to be a parallel light source, and the incident parallel light angle \(\theta_{i}\) on the surface of the space target is set to 30\({}^{\circ}\) in this paper, and the ground-based polarization imaging effect of the satellite observation angle \(\theta_{r}\) under different altitude angle conditions is analyzed under the above conditions. The simulation of polarization of four materials, namely polyimide film, solar panel, aluminum panel and #54 black backsheet, is carried out first. By substituting the above conditions \(\theta_{i}=30^{\circ}\), \(\Delta\theta=180^{\circ}\) and the physical parameters of the materials obtained by inversion into the pBRDF model established in this paper, the relationship of \(\theta_{r}\) and their degree of polarization can be obtained, as shown in Figure 9.  
Next, the solar zenith angle \(\theta_{o}=29^{\circ}30^{\prime}\) and azimuth angle \(-04^{\circ}32^{\prime}\), the space target azimuth angle \(101^{\circ}28^{\prime}\) is substituted into the sky background Rayleigh scattering model, and the simulation of the sky background polarization value under this condition can be obtained as follows:  
In Figure 10, B represents the Babinet neutral point, \(O_{m}\) represents the zenith center of the sky, and the black line represents the plane including the Sun, the ground-based optical system, and the space target. The distribution curve of the polarization value of the sky background of the space target with the zenith angle into the relative azimuth of the sun is represented by the line segment over \(O_{m}\) and the sun, from which we can obtain the polarization value of the sky background of the space target at any zenith angle at this time, and the space targets at 10\({}^{\circ}\) and 60\({}^{\circ}\) zenith angles are analyzed and discussed in this paper. Figure 8: Geometric angle diagram of the detection time of the space target on the ground. Figure 9: The relationship of DOP and \(\theta_{r}\) of four satellite surface materials.