## 4 Performance Evaluation of the Active Support System for the 4m SiC Primary Mirror
### Correction of the Primary Mirror Surface Shape Errors Caused by Thermal and Wind Loads
#### 4.4.2 Wind Load  
The primary mirrors of modern large telescopes are often directly exposed to air during operation, resulting in a wind load deformation. The wind load exerted on the primary mirror can be divided into two parts: static and dynamic wind load. The static wind load remains static or changes very slowly, whereas the dynamic wind load changes over time with a frequency that can reach several hertz [33].  
Unlike adaptive optics, which corrects for atmospheric turbulence, active optics is used to correct the errors of the telescope itself. The correction object of active optics is the large-aperture primary mirror with a large mass, rather than the small-aperture deformable mirror used in adaptive optics. Therefore, the correction frequency of active optics is generally very low, which is clearly different from that of adaptive optics, whose correction frequency reaches several hundred hertz. Active optics is used to correct manufacturing errors in the primary mirror, surface errors caused by gravity and temperature, and surface  
Figure 21: Zernike distributions of surface before and after correction (axial temperature difference of 0.2 \({}^{\circ}\)C).  
Figure 22: Results of correcting the thermal load deformation of 4m SiC primary mirror with the first 30 orders of bending modes.  
errors caused by telescope movements. The frequency of these errors is below 1 Hz [34]. The calibration frequency of the designed active support system is 1 Hz; therefore, it could not correct the deformation caused by dynamic wind loads. In summary, only the influence and correction of a static wind load were analyzed.  
The effect of the wind load is transmitted through wind pressure [35], which could be expressed as  
\[P=\frac{1}{2}\rho v^{2} \tag{29}\]  
where \(P\) is the wind pressure, \(\rho\) is the air density, and \(v\) is the wind speed. The wind load force could be expressed as  
\[F_{W}=PC_{D}A=\frac{1}{2}\rho v^{2}C_{D}A \tag{30}\]  
where \(F_{W}\) is the force exerted by the wind load on the structure, \(C_{D}\) is the wind-resistance coefficient, and \(A\) is the windward area of the structure.  
An observation station at the National Astronomical Observatory of the Chinese Academy of Sciences was considered as an example. The altitude of the observation station is 900 m. According to the wind speed data from 2007 to 2014, the wind speed was mostly less than 15 m/s, with an average wind speed of approximately 2 m/s [36]. Therefore, in this analysis, the wind speed was set to 15 m/s. The density of air was 1.29 kg/m\({}^{3}\), and the wind pressure was calculated as 145.13 Pa, according to Equation (29).  
In addition, according to Equation (30), the effect of the wind load calculation had to consider the windward area. The angle between the wind direction and the optical axis was set as \(\theta\), as shown in Figure 23. The windward area was inversely proportional to \(\theta\); \(\theta\) was sequentially set to \(0^{\circ}\), \(30^{\circ}\), and \(60^{\circ}\), and the tests were conducted. The surface shape of the 4m SiC primary mirror under the wind load is shown in Figure 24. The first 30 orders of bending modes were used to correct the surface shape, and the results are shown in Figure 25. The surface shape data before and after the correction are listed in Table 5. The rms of the corrected surface shape was less than 2 nm, indicating that the designed system could effectively correct the static wind load deformation of the primary mirror.  
Figure 23: Schematic diagram of the 4m SiC primary mirror under wind load.  
The Zernike polynomial was used to fit the surface shape (\(\theta\) = 0\({}^{\circ}\)) before and after the correction, as shown in Figure 26. The surface correction eliminated the defocus, trefoil aberration, and spherical aberration.