## 4 Evaluation of the Variation of Backscattered Light of the Taiji Telescope in Orbit  
The space environment where the Taiji Telescope is located is not completely clean; there are many high-speed flying particles called micrometeoroids. The high-speed impact of micrometeoroids will cause damage to the unobstructed mirror. Since the primary mirror M1 of the Taiji Telescope is directly facing the space environment, it is likely to be damaged. Meanwhile, the primary mirror is planned to be made of Zerdour, which is a typical brittle and thick material, and its damage is mainly in the form of corrosive pitting. The scattering level of the primary mirror will change significantly after pitting [39], which will cause changes in the PST of the Taiji telescope. Therefore, it is necessary to study the effect of micrometeoroids on the scattering level of the primary mirror of the Taiji telescope.  
The NASA SSP30425B model is a commonly used micrometeoroid environment model, which demonstrates the relationships between interstellar micrometeoroid flux and mass [40]. Combining the orbital data of the Taiji Telescope (Lagrange orbit), we can get the predicted value of the number of impacts of micrometeoroids, as shown in Figure 8. It is estimated that the number of micrometeoroid (mass greater than \(10\times 10^{-12}\) g) impacts on the telescope will reach 308 in 4 years, which will increase to 769 in 10 years.  
The optical surface is pitted after being impacted by micrometeoroids. [PERSON] et al. [41] proposed a BSDF modeling method for scratches and digs, and this method can also be used for the BSDF modeling of the surface impacted by micrometeoroids. The BSDF of the optical surface is related to the number of impacts \(u_{D}\) and diameter of pits \(D\) (as shown in Equation (22)). The diameter \(D\) is described by Equation (23), and the values of the parameters in Equation (23) are shown in Table 7[42]. The BSDF calculated by Equations (22) and (23) is shown in Figure 9. Here, we use the ABg model to describe the BSDF.  
\[\text{BSDF}(\theta)=\frac{u_{D}D^{2}}{4}\times\left\{1+\frac{\pi^{2}D^{2}}{4 \lambda^{2}}\left[1+\frac{\sin^{2}(\theta)}{\left(\frac{4}{\pi^{4}}\right)^{ \frac{3}{2}}\left(\frac{\lambda}{\mathcal{D}}\right)^{2}}\right]^{\frac{-3}{2} }\right\} \tag{22}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Cleanliness Level (CC1264)** & **PST** \\ \hline
100 & \(3.73\times 10^{-14}\) \\
200 & \(5.89\times 10^{-13}\) \\
300 & \(3.55\times 10^{-12}\) \\
500 & \(4.15\times 10^{-11}\) \\
1000 & \(1.46\times 10^{-9}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: PST analysis results of optical surfaces at different cleanliness levels.  
Figure 7: Light intensity distribution diagram of the detector when the cleanliness level is 300.  
\[D_{max}=K_{1}K_{c}d_{\mu}^{\xi}\rho_{\mu}^{\beta}\
u^{\gamma}\rho_{t}^{\kappa} \tag{23}\]  
The PST results obtained by assigning the above calculation results to the M1 and maintaining the other mirrors in the ideal optical surface state are shown in Table 8. According to the analysis results, the PST of the optical system is two orders of magnitude lower than the required value, regardless of whether the service life is 4 or 10 years. Therefore, it can be considered that the variation of the scattering level caused by the damage of micrometeoroids can be ignored.  
\begin{table}
\begin{tabular}{c c c} \hline Model Characteristic Factor \(K_{1}\) & Mean Density of Micrometeoroids \(a\)- & \(f\) \\ \hline
6.0 & 2.5 g/cm\({}^{2}\) & 0.71 \\ \hline Pit factor \(K_{c}\) & Reflector density \(\rho_{t}\) & \(\gamma\) \\ \hline
10 & 2.53 g/cm\({}^{2}\) & 0.755 \\ \hline Impact velocity \(v\) & \(\xi\) & \(\kappa\) \\ \hline
20 km/s & 1.13 & \(-0.5\) \\ \hline \end{tabular}
\end{table}
Table 7: Values of parameters in Equation (23).  
Figure 8: Prediction of the number of micrometeoroid impacts. The number of impacts is 308 for 4 years and 769 for 7 years.  
Figure 9: BSDF of the primary mirror after 4 and 10 years of telescope service.