## 5 Experiments and Discussion
### Micro-Vibration Suppression and Image Stabilization Analysis  
As can be seen from Section 5.1, the LOS jitter caused by the CMGs and cryocoolers together is more than 1 \(\upmu\)rad. Hence, it is necessary to introduce a vibration reduction system to suppress the micro-vibration and stabilize the image point. Section 4 proposes a two-stage image stabilization system composed of BVILs and the FSM to reduce the image offset. During the test, the BVILs are unlocked to suppress the disturbances in the mid-high frequency, and then the FSM is collaboratively controlled to compensate for the LOS errors existing in low frequency. The image point offsets under different states are as follows:  
As shown in Figure 20, the image offsets increase by about 2 pixels along the X-axis, decreasing by 0.5 pixels along the Y-axis after unlocking BVILs in the first-order vibration suppression. Then, the image point offsets along the X-axis dropped to 2.31 pixels from 9.59 pixels, and the offsets along the Y-axis dropped to 3.63 pixels from 4.63 pixels after the FSM was in closed-loop control. According to the analysis in Section 4.1, it can be seen that BVILs will introduce the amplification of low-frequency responses around 2 Hz. The pixel offset becoming larger after unlocking BVILs may be the result of the amplification in the low-frequency being higher than the reduction in the mid-high frequency. On the contrary, the offset amplitude of the image decreased significantly because of the compensation for the LOS jitter in the low frequency when the FSM is controlled. Furthermore, the amplitude-frequency response of the LOS jitter after two-stage stabilization is shown in Figure 21. After unlocking BVILs, the amplitude response above 4 Hz decreased, but the LOS jitter near 2 Hz rose a lot due to the amplification characteristics of BVILs in low frequency. Notably, the amplification in the low frequency is larger than the attenuation in the mid-high frequency, which explains the increase in the pixel offset in Figure 20 after the passive vibration isolation in the first stage. Fortunately, the LOS jitters, no matter in the mid-high frequency above 4 Hz or in the low frequency below 4 Hz, are both decreased significantly by opening the FSM and unlocking BVILs together. This shows the possibility of integrating the passive vibration isolation platform and FSM to achieve wide-band image stabilization. Finally, to evaluate the LOS jitter of the HPSOP quantitatively, the root mean square error (RMS) of the jitter angles along the X-axis and the Y-axis are summarized in Table 3. Compared with the case without vibration reduction, after unlocking the first-stage BVILs, the LOS jitters in both directions increase due to the amplification caused by the vibration  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**LOS Jitter Around the X-Axis (Hz, \(\upmu\)rad)** & **LOS Jitter Around the Y-Axis (Hz, \(\upmu\)rad)** \\
**Linear Superposition** **Collaborative Test** & **Linear Superposition** & **Collaborative Test** \\ \hline (8.74, 0.267) & (8.74, 0.038) & (5.18, 0.164) & (5.18, 0.088) \\ (16.53, 0.133) & (16.53, 0.038) & (6.30, 0.177) & (6.30, 0.079) \\ (16.85, 0.060) & (16.85, 0.045) & (8.05, 0.194) & (8.05, 0.057) \\ (75.54, 0.0 isolation legs. On the contrary, the RMSs in the two directions were reduced to 0.257 \(\upmu\)rad and 0.317 \(\upmu\)rad by the two-stage image stabilization platform with BVILs and FSM. The experiment in this paper demonstrates the feasibility of building HPSOPs that require sub-micro-radian pointing accuracy. In addition, to further compare the superiority of the proposed solution \"FSM + VILs\", we compared it with the image stabilization research of dual FSMs conducted by [PERSON] et al. [36], and the results are shown in the following table (Table 4). Obviously, as shown in Table 4 compared with the dual FSM scheme, the two-stage vibration isolation and image stabilization based on FSM and VILs performs better.