# Design of Parabolic Off-Axis Reflector Optical System for Large Aperture Single Star Simulators
## 4 Parabolic Off-Axis Reflective Optical System Design
### Tolerance Analysis  
For an optical system, the actual processing and mounting processes will introduce certain errors, which will reduce the overall imaging performance compared to the theoretical value. Therefore, to ensure that the image quality still meets the requirements after the  
Figure 8: Field curvature and distortion of the optical system. Figure 10: Wave aberration diagram of the optical system. Figure 9: MTF curve of the optical system. system is processed and mounted, it is necessary to analyze the tolerance of the completed optical system to assess the feasibility of actual mounting. Optical system tolerances are mainly manufacturing tolerances and mechanical assembly tolerances, and the tolerances of the optical system are assigned according to the requirements of the measurement accuracy index of the large aperture single star simulator, as shown in Table 3.  
The MTF is used as the evaluation standard to analyze the sensitivity of this optical system. From the analysis, it can be seen that the first six tolerances affecting the MTF value of the optical transfer function of the system are shown in Table 4. TETY is the element Y-direction tilt tolerance, TETX is the element X-direction tilt tolerance, and TTHI is the element thickness and air spacing tolerance. From the results of the tolerance sensitivity analysis, the corresponding parameter structures of the MTF of the tolerance-influenced system are the distance L between the planar mirror M1 and the parabolic mirror M2, the X-direction and Y-direction tilting of the planar mirror M1, and the X-direction tilting of the parabolic mirror M2, which are mainly caused by the relative positions of the two mirrors. All of the above tolerances are related to assembly and need to be guaranteed by assembly accuracy. Finally, the Monte Carlo analysis method is used to evaluate the tolerance and analyze the comprehensive performance of the optical system. After analyzing 1000 Monte Carlo samples, each of which is a simulation of an actual optical system after machining and mounting, the statistical results of MTF are obtained, as shown in Table 5. The analysis results show that according to the tolerance assignment in Table 3, after processing and mounting, the MTF of more than 98% of the optical system is greater than 0.6966, the MTF of more than 90% of the optical system is greater than 0.7113, the MTF of more than 80% of the optical system is greater than 0.7193, the MTF of more than 50% of the optical system is greater than 0.7302, the MTF of more than 20% of the optical system is greater than 0.7372, the MTF of more than 10% optical system is greater than 0.7396, and the MTF of more than 2% optical system is greater than 0.7418. With this tolerance assignment, the image quality meets the technical requirements of the system design, and the tolerance assignment is reasonable, which can be realized by engineering. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Object** & **Value/mm** & **Standard** & **Change** \\ \hline TFTY & M1 & 0.0056 & 0.727816 & \(-\)0.014788 \\ TETY & M1 & \(-\)0.0056 & 0.727816 & \(-\)0.014788 \\ TETX & M1 & \(-\)0.0056 & 0.730761 & \(-\)0.011843 \\ TETX & M1 & 0.0056 & 0.733467 & \(-\)0.009136 \\ TETX & M2 & 0.0028 & 0.738468 & \(-\)0.004136 \\ TTHI & L & \(-\)0.0200 & 0.739386 & \(-\)0.003218 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Influence of tolerance on MTF.