# Design of Parabolic Off-Axis Reflector Optical System for Large Aperture Single Star Simulators
## 4 Parabolic Off-Axis Reflective Optical System Design
### Optical System Image Quality Evaluation  
The single star simulator optical system design should satisfy the design requirements of smaller image plane dispersion spots, higher energy concentration, larger transfer func  
Figure 3: Structure of the optical system. tion values, and smaller wave aberration [28; 29]. The evaluation criteria of its imaging quality include spot diagrams, field curves and distortion, MTF curves, energy concentration curves, system wave aberration plots, and so on. The spot diagram of the optical system is shown in Figure 4, and the RMS radius and geometric radius of the point-list diagram for each field of view are given in Table 2. From Table 2, it can be seen that the diameter of the diffuse spot in each field of view is small, and the diameter of the diffuse spot increases with the increase of the field of view angle, and the diameter of the diffuse spot in the 0\({}^{\circ}\) center field of view is always smaller than that of the diffuse spot in each other field of view. In the full field of view, the maximum RMS radius is 2.604 \(\upmu\)m, which is much smaller than the Airy spot radius of 7.677 \(\upmu\)m.  
Combining the point spread function of the optical system (shown in Figure 5), the radiant energy distribution map (shown in Figure 6), and the geometric energy concentration curve (shown in Figure 7) provides insight into issues such as the energy of the star-spot like the image of the optical system, the shape distribution, and the diffraction situation. The point diffraction function describes the spatial distribution of the spot like light source after propagation in the optical system (spatial mode). As can be seen in Figure 6, the energy center of a standard single star is mainly affected by the diffraction situation. Combined with Figure 7, it can be seen that the energy concentration of each field of view is greater than 85% in a region with a diameter of 20 \(\upmu\)m, which meets the requirements for use. The field curvature aberration of the system reflects the degree of curvature of the imaging surface, indicating that light rays emitted from different fields of view cannot converge on the same plane. Therefore, excessive field curvature will lead to blurred imaging of the system, and the field curvature and distortion of the optical system are shown in Figure 8. The field curvature of the system is very small and negligible. In addition, the distortion of the system is much less than 0.002% and does not affect the actual measurement. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Field/(\({}^{\circ}\))** & **Geometric Radius/\(\upmu\)m** & **RMS Radius/\(\upmu\)m** \\ \hline
0 & 1.032 & 0.766 \\
0.003 & 1.607 & 0.915 \\
0.005 & 2.795 & 1.630 \\ \(-\)0.003 & 3.310 & 1.820 \\ \(-\)0.005 & 4.834 & 2.604 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Spot radius in point diagram of the optical system. Figure 4: Spot diagram of the optical system. The transfer function curve of the optical system is shown in Figure 9. The MTF of the optical design is an important index to analyze the excellent or bad imaging quality of the system, and the larger the MTF is, the better the imaging quality of the system is. As can be seen from the figure, the optical transfer function of each field of view of the system is more concentrated, and the line is smooth and close to the diffraction limit. The wave aberration diagram of the optical system is shown in Figure 10. The wave aberration of the system is no more than \(0.0324\lambda\) in the entire field of view, which meets the requirement of wave aberration of less than \(1/25\lambda\), and the imaging quality of the optical system is good. Figure 5: Point spread function of the optical system. Figure 6: Radiant energy distribution of the optical system. Figure 7: Energy concentration curve of the optical system. In summary, this paper realizes the design of a parabolic off-axis reflective optical system with an aperture of \(\Phi\)500 mm, a focal length of 5000 mm, and a spectral range of 450 nm\(\sim\)850 nm.