## 4 Simulation Experiment and Analysis of desensitization Optimization
### Analysis of Optimization Results  
This section analyzes the changes of the system during the desensitization process of the method in this paper from three aspects: the layout of the optical system, the relationship between the sensitivity of the aberration term and the field of view, and the results of the large sample Monte-Carlo analysis. Select the solution of NO. 0 (the system without desensitization), the solution of NO. 1 (the optimized system after one-time desensitization), and the solution of NO. 6 (the optimized system after final desensitization) to analyze the changes in the optical structure during the desensitization process. The layout of the optical system is shown in Figure 7. Figure 7a is the solution of NO. 0, Figure 7b is the solution of NO. 1, and Figure 7c is the solution of NO. 6. It can be seen from Figure 7 that, for a single lens, the lens form changes after desensitization. The thickness of the first lens is reduced, the third lens is changed from a plano-concave lens to a bi-concave lens, and the curvature of the fourth lens is increased. For the overall change of the system, the rear group lens of the system after final desensitization bears more optical power and has a more compact structure and the change of the lens form is the performance of the system sensitivity reduction. The root of the reduction of the \(C\) value is the reduction of the sensitivity of the aberration term. The variation of the sensitivity of the aberration term with the field of view  
Figure 7: Layout of the optical system of (**a**) the solution of NO. 0, (**b**) the solution of NO. 1 and (**c**) the solution of NO. 6.  
is shown in Figure 8. A, B and C represent different systems, corresponding to Figure 7a-c. Figure 8a shows the variation of sensitivity with the field of view when the secondary mirror is tilted by \(0.1^{\circ}\) around the x-axis, Figure 8b shows the variation of sensitivity with the field of view when the secondary mirror is tilted by \(-0.1^{\circ}\) around the x-axis, Figure 8c shows the variation of sensitivity with the field of view when the secondary mirror is tilted by \(0.1^{\circ}\) around the y-axis and Figure 8d shows the variation of sensitivity with the field of view when the secondary mirror is tilted by \(-0.1^{\circ}\) around the y-axis. \(\Delta C5\) and \(\Delta C6\) represent the sensitivity of the astigmatism terms, shown as the edges of the filled color in Figure 8; \(\Delta C7\) and \(\Delta C8\) represent the sensitivity of the coma terms, shown as the edges of the filled line in Figure 8.  
It can be seen from Figure 8 that the sensitivity of the coma term is constant in the full field of view, and the sensitivity of the astigmatism term is linearly related to the field of view. When the secondary mirror is tilted around the x-axis, the slopes of \(\Delta C5\) and \(\Delta C6\) are opposite to each other, and \(\Delta C8\) are equal. When the secondary mirror is tilted around the y-axis, the slopes of \(\Delta C5\) and \(\Delta C6\) are equal, and \(\Delta C7\) are equal. This shows that when the absolute value of the tilt angle (the misalignment) is equal, the first-order  
Figure 8: The variation of the sensitivity of the aberration term with the field of view when the secondary mirror is tilted by (**a**) \(0.1^{\circ}\) around the x-axis, (**b**) \(-0.1^{\circ}\) around the x-axis, (**c**) \(0.1^{\circ}\) around the y-axis and (**d**) \(-0.1^{\circ}\) around the y-axis. coefficients of the sensitivity of the astigmatism terms, and the coefficients of the coma terms are equal in absolute values. \(\Delta C5\) and \(\Delta C6\) basically intersect in the central field of view, indicating that the constant term of the sensitivity of the astigmatism terms are equal.