## 4 Simulation Experiment and Analysis of desensitization Optimization
### Dessensitization Optimization Based on This Method  
This section starts from the design indicators of the optical system, and desensitizes the optical system after the imaging performance optimization. Figure 3: Flow diagram of catadioptric optical system with low tilt sensitivity of secondary mirror. Since the aerial camera optical system is selected for optimization in this paper, its design indicators must consider various factors. The focal length of an aerial camera is determined by the resolution, flying height and pixel size. The field of view of the optical system is related to the focal length and the size of the detector. The larger the F number of the optical system, the better the signal-to-noise ratio; however, this will increase the weight and volume of the optical system and design will be more difficult. The amount of image shift of an aerial camera is related to many factors such as the speed-to-height ratio, focal length, exposure time, swept angular velocity, and flight attitude of the aircraft. The design index of the aerial camera optical system with image motion compensation of secondary mirror tilt motion is shown in Table 1.  
After the imaging performance is optimized, the system is composed of a front correction lens, a primary and a secondary mirror, and a rear correction lens. The H-K9L and TF3 glass materials are combined to eliminate the secondary spectrum. The system realizes the correction of primary aberration and chromatic aberration. Next, the optical system after imaging performance optimization is used as the system without desensitization, and the tilt sensitivity is optimized. The desensitization function \(C\) is established by macro programming and added to the evaluation function. In the optimization process, it is found that the reduction of the \(C\) value is beneficial to improve the transfer function of the optical system when the secondary mirror is tilted. Therefore, multiple structures with different tilt directions of the secondary mirror are set up, and the transfer function of the optical system when the secondary mirror is tilted at the maximum angle is greater than 0.3 as the value standard for the minimum value of \(C\). The initial \(C\) value is \(127.017\times 10^{-3}\), when the \(C\) value is reduced from 127.017 to 49.856, the transfer function of the optical system is greater than 0.3. When the secondary mirror is tilted by 0.1\({}^{\circ}\) around the x-axis, the MTF of the optical system without desensitization and after final desensitization are shown in Figure 4. \begin{table}
\begin{tabular}{c c} \hline \hline Focal length/mm & 350 \\ F number & 4 \\ Full field of view & 6\({}^{\circ}\) \\ Spectral range/\(\mu\)m & 0.48–0.65 \\ Primary wavelength/\(\mu\)m & 0.58 \\ MTF (68 lp/mm) & \(\geq\)0.30 \\ Maximum tilt angle of secondary mirror & \(\pm\)0.1\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Indexes of the aerial camera. Figure 4: The MTF of the optical system when the secondary mirror is tilted by 0.1\({}^{\circ}\) around the x-axis (**a**) without desensitization, (**b**) after final desensitization. It can be seen from Figure 4 that, when the secondary mirror is tilted to the maximum angle, the MTF of the optical system after final desensitization is greater than 0.3 at 68 lp/mm, which meets the design requirements. Save the systems in the tilt sensitivity optimization process, and perform a small sample Monte-Carlo analysis (sampling of 200) using only the secondary mirror tilt of 0.1\({}^{\circ}\) as the system tolerance. The desensitization optimization process is shown in Figure 5. The abscissa is the optimization times, the left ordinate is the \(C\) value, and the right ordinate is the standard deviation of the system. The standard deviation is an index to measure the sensitivity of the system. The smaller the standard deviation, the lower the sensitivity.