## 4 Results and Discussion
The comparison results are shown in Figure 8b and Table 2. After taking the absolute value of the vibration sensitivity of the reinforced-support results (regardless of the direction of the FP cavity deformation), the FP cavity of the reinforced-support is consistent with the vibration sensitivity of four-point support reported in the literature. In the Z, X and Y directions, the FP cavity vibration sensitivities reported in the literature [26] are 2.3 \(\times\) 10\({}^{-10}\)/g, 2 \(\times\) 10\({}^{-11}\)/g, and 7 \(\times\) 10\({}^{-11}\)/g, respectively. The measured vibration sensitivities for the reinforced-support are 1.73 \(\times\) 10\({}^{-10}\)/g, 2.09 \(\times\) 10\({}^{-11}\)/g, and 2.13 \(\times\) 10\({}^{-11}\)/g, respectively. The FP cavity vibra  
Figure 8: Analysis of experimental results: (**a**) Comparison of experimental and simulation results; (**b**) Comparison between four-point support [26] and reinforced-support. tion sensitivities for both support methods are below \(2.5\times 10^{-10}/\)g in the Z direction and below \(1\times 10^{-10}/\)g in the X and Y directions. This indicates that the reinforced-support FP cavity can achieve the same level of vibration sensitivity as the four-point support FP cavity. In addition to vibration sensitivity, zero-expansion temperature of the reinforced-support FP cavity was also tested. Figure 9 shows the measurement results of zero-expansion temperature. The fitted curves were plotted according to the method of literature [6]. The fitting result shows that the zero-expansion temperature of the reinforced-support FP cavity is about 29.5 \({}^{\circ}\)C. However, the zero-expansion temperatures of the FP cavity with and without reinforced-support are not compared because accurate zero-expansion temperature data is not obtained when purchased. The zero-expansion temperature of ULE glass is in the range of \(30\pm 5\)\({}^{\circ}\)C according to the information provided by the manufacturer. The experimental result of the zero-expansion temperature of the FP cavity is in line with this range. Therefore, according to the experimental and simulation results for zero-expansion temperature, although the exact value of the zero-expansion temperature being affected is not known, the reinforced-support method has limited effect on the zero-expansion temperature of the FP cavity. Although the reinforced-support FP cavity has the same level of vibration sensitivity as the four-point support FP cavity, several obvious disadvantages exist. Compared to the four-point support method, the number of support points is increased from four to eight. The increase in the number of support points will result in assembly stresses. The presence of assembly stresses will affect the length stability of the FP cavity. In addition, the increase in the number of support points and the increase in support area will affect the heat transfer between the support structure and the FP cavity. The temperature transfer from the support structure to the FP cavity will be faster, which will also affect the stability of the cavity length. \begin{table}
\begin{tabular}{c c c c} \hline
**Support Method** & **Z** & **X** & **Y** \\ \hline [PERSON] et al. 2023 [26] & \(2.3\times 10^{-10}/\)g & \(2\times 10^{-11}/\)g & \(7\times 10^{-11}/\)g \\ The reinforced-support FP cavity & \(1.73\times 10^{-10}/\)g & \(2.09\times 10^{-11}/\)g & \(2.13\times 10^{-11}/\)g \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison with vibration sensitivity reported by [PERSON] et al. 2023 [26]. Figure 9: Zero expansion temperature test results.