## 4 Results and Discussion  
In testing the vibration sensitivity, frequency and acceleration variations of the FP cavity are shown in Figure 7. Figure 7a shows the acceleration of the FP cavity in the Z, Y, and X directions sequentially. For example, in the detail area of the 0-1 s display, an acceleration of about 25 mg was applied in the Z direction, and a micro-vibration of 5 mg still occurred in the other two directions. Figure 7b shows the frequency variation caused by the change in acceleration. Frequency variation attributed to acceleration in the Z direction (direction of the optical axis of the FP cavity) is higher than both the X and Y directions. The vibration sensitivity of the FP cavity was calculated according to the method of literature [26]. The vibration sensitivities of the FP cavity in the Z, X, and Y directions are calculated to be 1.73 \(\times\) 10\({}^{-10}\)/g, \(-\)2.09 \(\times\) 10\({}^{-11}\)/g, and \(-\)2.13 \(\times\) 10\({}^{-11}\)/g, respectively. Experimental results are compared with the simulation results as shown in Figure 8a. The experimental results agree with the trend of the simulation results of both methods. However, compared to the first constraint setting method in the simulation, the experi  
Figure 6: Schematic diagram of the experiment optical path for the reinforced-support FP cavity. Figure 7: The acceleration applied to the FP cavity and the frequency variation: (**a**) The applied acceleration; (**b**) The frequency variation. mental results are different in the Z direction. The vibration sensitivity in the simulation presents 0 in the Z direction, while the experimental results indicate the vibration sensitivity is 1.73 \(\times\) 10\({}^{-10}\)/g. The vibration sensitivities of the FP cavity in the X and Y directions are comparable to the simulation results. The simulation and experimental results are in the order of 10\({}^{-11}\)/g. Compared to the second constraint setting method in the simulation, the experimental results agree with the simulation results in the Z direction. In the X and Y directions, the simulations are in the order of 10\({}^{-12}\)/g, which is different from the experimental results. According to our analysis, there are several possible reasons for the difference between the simulation and experimental results. Firstly, the parameters of the simulated materials may differ from the actual materials. For example, differences in [PERSON]'s modulus and Poisson's ratio can lead to the difference between the simulation and experimental results. the Young's modulus of the ULE used in the simulation is 69.6 GPa (data from Corning's Model 7973 ULE glass), and different batches of material may differ from this value in practice. Therefore, the results of the simulation can provide certain reference for the vibration sensitivity analysis. Secondly, the existence of machining and mounting errors makes the FP cavity size deviate from the theoretical design. These deviations lead to inconsistency between experimental and simulation results. For example, the preload on the contact surface between the polyimide shim and the FP cavity may be unbalanced due to the angle of the screw threads; Owing to machining errors, the position of the support points is offset from the design position, etc. In addition, the test results of vibration sensitivity also have errors. In any case, the trends of the simulation and experimental results are in line. The experimental results show that the maximum value of the vibration sensitivity of the FP cavity is 10\({}^{-10}\)/g magnitude in the Z direction, which is in line with the simulation results. Vibration sensitivity of the reinforced-support FP cavity and the four-point support type reported in the literature [26] were compared.