## 6 Conclusions  
In this paper, micro-vibration tests and the two-stage image stabilization of an HPSOP are carried out under disturbances caused by CMGs and cryocoolers. To avoid the disturbance result of simulated flight devices on micro-vibration tests during ground tests, this paper proposes an AQZSSD adjusted by linear motors. The results indicate that the disturbance introduced by the AQZSSD is below 0.4 Hz, which is close to quasi-zero stiffness. Notably, the collaborative test results of CMGs and cryocoolers are lower than the linear superposition due to the coupling of the micro-vibration response. Moreover, this paper also proposes a two-stage image stabilization system, consisting of three passive BVILs and an FSM driven by piezoelectric ceramics, to address the difficulty of image stabilization due to wide-band micro-vibration disturbances. Three passive BVILs and an FSM are used to accomplish the first-order vibration suppression and the second-order vibration suppression. As can be seen from the theoretical analysis, the first-order vibration suppression and the second-order vibration suppression can realize image stabilization by suppressing LOS jitters in the mid-high frequency and low frequency, respectively. The experimental results show that the LOS jitter peak of the HPSOP reduced to 0.276 \(\upmu\)rad from 1.253 \(\upmu\)rad, corresponding to the image point offset amplitude decreasing about 5 pixels (pixel size: 5.5 \(\upmu\)m \(\times\) 5.5 \(\upmu\)m).  
The micro-vibration test platform and two-stage image stabilization system proposed in this paper provide feasible solutions for high-precision micro-vibration testing and image stabilization. Yet, there are still some limitations of the proposed system. For example, since the test object used is a dot target, it is not convenient to evaluate the system's image quality of the complex targets. In addition, by comparing the LOS jitter changes before and after the two-stage image stabilization operation, there is still room for improvement in the jitter suppression. To address the above challenges, future work will concentrate on the following: (a) To evaluate the impact of micro-vibration on the system imaging quality, replace the dot target with an extended target during the micro-vibration test. (b) For higher image stabilization requirements, dual FSMs can be introduced to achieve three-stage image stabilization combined with the vibration isolation legs. (c) During themicro-vibration test, it will be possible and meaningful to restore image details and edges by incorporating machine learning to avoid the risk of image degradation.  
Conceptualization, Z.L., J.G. and B.Q.; methodology, Z.L., J.G. and T.Q.; software, Z.L., T.Q. and J.W.; validation, Z.L., Y.W., J.P. and J.H.; formal analysis, Z.L. and H.Z.; writing--original draft preparation, Z.L., J.G., Z.J. and B.Q.; writing--review and editing, Z.L., J.G. and B.Q. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of China [grant number 62175243].  
Not applicable.  
Data Availability Statement: Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.  
The authors would like to thank [PERSON] et al. from the Shanghai Academy of Spaceflight Technology for their help in measuring the advice. The authors would also like to thank the reviewers for their helpful suggestions for this article.  
The authors declare no conflicts of interest.