## 4 Experiment Analysis
### Influence of Ambient Temperature and Air Content on the Support Height of Support Cylinder  
The FSS is composed of 36 support cylinders. It is not easy to measure 36 support cylinders at the same time when the support height of the support cylinder is affected by ambient temperature change. Therefore, only one support cylinder was tested to determine the change in the support shaft height of the support cylinder. During the experiment, hydraulic oil with unfiltered air and filtered air were injected into the support cylinder. Then, the constant temperature controller in the laboratory was turned off so that \begin{table}
\begin{tabular}{c c c c} \hline
**Number** & **Name** & **Model** & **Accuracy** \\ \hline
1 & Laser micrometer & LG-2 mm & 7.6 nm \\
2 & Pressure sensors & MIK-P3000 & 0.075\% \\
3 & Force sensor & LKC-20 kg & 0.1\% F.S. \\
4 & Temperature sensor & ML X 9016 & 0.02 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table} 
Table 4: The main measuring equipment used in the experiment. Figure 7: Flexible support system. the laboratory temperature would change with ambient temperature. At the same time, the change in the height of the support shaft under different ambient temperatures was measured by a laser micrometer. At the beginning of the experiment, the support pressure of the FSS was raised to 0.65 MPa and the measured laboratory ambient temperature was 25.1 \({}^{\circ}\)C. The measured experimental data are shown in Figure 8. When the unfiltered hydraulic oil was injected, the change in the support height of the support cylinder with the change in ambient temperature was the same as the theoretical trend obtained by the simulation of the established mathematical model. However, the support height error of the support cylinder was lower than the theoretical value and was mostly lower than zero, ranging from \(-\)0.018 to 0.0012 mm. This is because it is difficult to determine the actual air volume fraction in hydraulic oil, and the theoretical value of the air volume fraction was 2% as a reference. Therefore, the accuracy of the established mathematical model can be determined within the allowable range of error. The filtered hydraulic oil was injected into the FSS and the error in the support height of the support cylinder with the change in ambient temperature is shown in Figure 9. It can be seen from the figure that when the laboratory temperature changed, the changes in the support height of the support cylinder were roughly the same as the theoretical value trend of the established mathematical model. The difference between the experimental and theoretical values is basically within \(\pm\)0.008 mm, and the error is relatively large at individual moments. On the one hand, there may be a large error in the reading of the laser micrometer due to the presence of vibration during the measurement process. On the other hand, the measurement process lasts for a certain period, and the leakage phenomenon of the support cylinder under time space causes the support height error to change. Within the allowable range of error, the established mathematical model can accurately reflect the dynamic relationship between the performance parameters of the FSS and the ambient temperature and air content. It provides a theoretical basis for the subsequent research on the three-dimensional reconstruction of the spatial position of the optical mirror surface through the support points of the FSS, and also provides control parameters for height control during the processing. Figure 8: Support height error when injecting hydraulic oil with unfiltered air. Influence of Different Ambient Temperature and Air Content on the Pressure of Upper and Lower Chambers of FSS  
To determine the change pressure values of the upper and lower chambers of the FSS, pressure sensors were installed in the upper and lower chambers of the FSS to collect the pressure values in real time.