## 4 Simulation Experiment and Analysis of desensitization Optimization
### Dessitization Optimization Based on Traditional Methods  
The traditional optimization method, also known as the angle-splitting method [23; 24], points out that the system sensitivity is replaced by the root mean square of incident and refracted angles of several rays traced to each surface, as follows:  
\[\theta=\sqrt{\frac{1}{2k}\sum_{s=1}^{k}({i_{s}}^{2}+{r_{s}}^{2})} \tag{11}\]  
In the formula, \(i_{s}\) and \(r_{s}\) are the incident angle and the refracted angle of the light on the s-plane, respectively, and \(k\) is the number of surfaces of the system. In the optimization process, parameters such as thickness, radius, and conic coefficient are set as optimization variables, and the structural size of the optical system is controlled at the same time. The tilt sensitivity of the secondary mirror is reduced by optimizing the incident angle and refracted angle of the secondary mirror. During the angle reduction process, the performance when the secondary mirror is tilted by 0.1\({}^{\circ}\) around the x-axis and standard deviation of the system change as shown in Table 2.  
Figure 5: Dessensitization optimization process diagram. In the process of reducing the angle, the standard deviation of the system and the change of MTF when the secondary mirror is tilted by 0.1\({}^{\circ}\) around the x-axis are shown in Figure 6. R1 is the applicable range of angles obtained by the traditional method; R2 is the applicable range of angles obtained by this method. In general, there is a trade-off relationship between performance and sensitivity, and it is difficult to optimize performance and sensitivity at the same time. The system performance and standard deviation obtained by the traditional method are shown in Figure 6a. In the process of reducing the angle, the reduction of the sensitivity of the solution from NO. 0 to NO. 1 depends on the improvement of the system performance, which reflects the advantage of the corner segmentation method is that the system can achieve the effect of reducing the sensitivity and improving the image quality at the same time. However, the system performance has reached the extreme value in the change of NO. 1 to NO. 3, and the reduction of the angle has no optimization effect on the sensitivity at this time. The performance and sensitivity of NO. 3 to NO. 6 are reduced at the same time, indicating that reducing the angle has no optimization effect on the system performance. By reducing the angle to reduce the sensitivity, it is found that the effective range of its angle is very narrow, only in the range of 0.28\({}^{\circ}\). The system performance and standard deviation obtained by the method in this paper are shown in Figure 6b. The reduction of the sensitivity of the solution from NO. 0 to NO. 2 depends on the improvement of the system performance. The system performance has reached the extreme in the change from the solution NO. 2 to NO. 5, but the sensitivity continues to decrease, indicating that the reduction of the angle is still one of the key factors to reduce the sensitivity at this time. The performance of the solution from NO. 5 to NO. 6 jumps out of the local optimum value, and \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Solution**} & \multirow{2}{*}{**Angle (\(\theta\))**} & **MTF (The Secondary Mirror Is Tilted by 0.1\({}^{\circ}\)** & **Standard Deviation** \\  & & **Around the X-Axis)** & **Standard Deviation** \\ \hline No. 0 & 6.098 & 0.135 & 0.035 \\ No. 1 & 5.928 & 0.208 & 0.032 \\ No. 2 & 5.812 & 0.196 & 0.032 \\ No. 3 & 5.723 & 0.205 & 0.036 \\ No. 4 & 5.625 & 0.176 & 0.036 \\ No. 5 & 5.551 & 0.174 & 0.034 \\ No. 6 & 5.447 & 0.044 & 0.031 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of solutions. Figure 6: Variation of MTF when the secondary mirror is tilted by 0.1\({}^{\circ}\) around the x-axis and standard deviation of system (**a**) traditional method (**b**) this method. the sensitivity decreases.