## 3 Active Optics Correction of the 4m SiC Primary Mirror
### Pose Correction of the 4m SiC Primary Mirror
(**a**) Mechanism in the initial pose; (**b**) mechanism in the state after pose adjustment. The designed primary mirror support system corrected the pose of the primary mirror by adjusting the length of the hardpoints. The required amount of the adjustment could be calculated using Equation (12); the calculated results are shown in Figure 10. Owing to the symmetry of the spatial arrangement of the six hardpoints, the adjustment amounts of the two symmetrical hardpoints were similar. In addition, as the elevation angle increased, the adjustment amounts of all the hardpoints tended to be similar. When the elevation angle was 90\({}^{\circ}\), the adjustment amounts of all the hardpoints were almost similar, because when the optical axis pointed towards the zenith, the primary mirror only had a position error in the direction of the optical axis, and there was no attitude error. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Number of**} & \multicolumn{3}{c}{**Elevation Angle of 45\({}^{\circ}\)**} & \multicolumn{3}{c}{**Elevation Angle of 90\({}^{\circ}\)**} \\ \cline{2-7}  & **d\(x\)/\(\mu\)m** & **d\(y\)/\(\mu\)m** & **d\(z\)/\(\mu\)m** & **d\(x\)/\(\mu\)m** & **d\(y\)/\(\mu\)m** & **d\(z\)/\(\mu\)m** \\ \hline
1 & \(-\)6.37 & 0.96 & \(-\)13.77 & \(-\)1.86 & 1.41 & \(-\)19.54 \\
2 & \(-\)6.36 & \(-\)1.04 & \(-\)13.74 & \(-\)1.61 & \(-\)0.39 & \(-\)18.92 \\
3 & \(-\)5.00 & \(-\)1.72 & \(-\)17.00 & \(-\)0.67 & \(-\)1.06 & \(-\)19.79 \\
4 & \(-\)3.96 & \(-\)0.30 & \(-\)22.35 & 0.88 & \(-\)0.05 & \(-\)19.66 \\
5 & \(-\)3.97 & 0.23 & \(-\)22.53 & 0.87 & 1.01 & \(-\)19.55 \\
6 & \(-\)5.01 & 1.63 & \(-\)17.13 & \(-\)0.77 & 2.17 & \(-\)19.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Displacement at the fixed point between the hardpoint and mirror cell. Figure 10: Adjustment amount of hardpoint length required to correct the primary mirror pose error. Figure 9: Relationship between the pose error of the primary mirror and elevation angle. Influence of Force on Hardpoints on the Surface Shape of the 4m SiC Primary Mirror and Compensation Methods  
In the designed active support system, the pneumatic surface control actuators were not only used to correct the surface shape, but also to support the weight of the primary mirror. The above scheme was to avoid force being applied on the hardpoints, thereby improving surface accuracy. However, we found that the hardpoints were still subjected to a force for other reasons, resulting in a decrease in the surface shape accuracy of the primary mirror. We evaluated the reasons for the force on the hardpoints and proposed a method to solve this problem. The force of the hardpoints caused obvious protrusions and dents to remain in the corrected surface shape, as shown in Figure 11. These surface defects were high-frequency errors in space, which are difficult to correct with active optics. The reasons for the force on the hardpoints were multifaceted. First, the pneumatic actuators provided an axial force to balance the axial component of the primary mirror gravity, while the two-axis actuators provided a radial force to balance the radial component. The magnitude of the resultant force \(\mathbf{F}_{G}\) of the axial and radial forces was the same as the gravity \(\mathbf{G}_{PM}\) of the primary mirror, whereas the direction was opposite. However, \(\mathbf{F}_{G}\) and \(\mathbf{G}_{PM}\) may not be collinear, resulting in the primary mirror being subjected to a moment, which, in turn, led to a force being exerted on the hardpoints. In addition, the primary mirror and entire system were subjected to thermal loads, wind loads, and inertial forces, which could also induce a force on the hardpoints. Due to the severe surface defects caused by the force on the hardpoints, compensation had to be provided for the force. Our approach used pneumatic actuators to output a certain force onto the primary mirror to compensate for the force on the hardpoints before correcting the surface shape.