## 1 Introduction  
As space exploration and optical communication advance into deep space, high-precision space optical payloads (HPSOPs) with sub-micro-radian precision have emergedas a focal point in space science and advanced optical research [1; 2]. However, the line-of-sight (LOS) jitters induced by moving components, such as flywheels, control moment gyros (CMGs), and cryocoolers, may lead to image degradation and communication interruptions [3; 4]. Consequently, conducting high-precision micro-vibration tests and image stabilization studies on these optical payloads has become both a challenging and imperative task [5; 6; 7]. The primary challenges associated with high-precision micro-vibration testing are the design of gravity unloading equipment with robustness against environmental disturbances and the accurate assessment of effects caused by various disturbance sources [3; 8; 9; 10; 11]. Gravity unloading equipment design can be categorized into four types based on differences in elastic elements, such as linear springs, disc springs, parallel mechanisms with positive and negative stiffness, and air springs. Among these, suspension systems with linear springs have been widely used in ground tests due to their safety, adjustability, and simplicity [9; 12; 13; 14; 15]. For instance, [PERSON] et al. proposed a quasi-zero stiffness suspension device (QZSSD) based on linear springs adjusted by bidirectional bolts to study the image point offset of a 0.1\({}^{\prime\prime}\) space pointing measuring instrument [9]. Nevertheless, achieving the desired accuracy remains a challenge. To address this, an automated quasi-zero stiffness suspension device (AQZSSD) adjusted by linear motors is proposed in this paper to enhance precision in gravity unloading. In addition, for analyzing the effects caused by different micro-vibration sources accurately, the test and mechanism research of independent disturbance sources has always been the focus in the past years [13; 17; 18; 19; 20]. Combining high-precision acceleration sensors, [PERSON] et al. predicted the image offset (refers to the movements of the image point) caused by flywheels [13]. [PERSON] et al. found that the energy resolution of the detector would reduce because of the micro-vibration caused by cryocoolers during testing the energy changes in the detector on the HITOMI [20]. However, the LOS jitter (refers to the line-of-sight jitter, a different concept from image offset) caused by multiple disturbance sources may be coupled and nonlinearly amplified, simultaneously [9]. Some researchers have begun to study the micro-vibration response caused by multi-disturbance sources [3; 9; 21; 22; 23]. For example, [PERSON] studied the micro-vibration effects caused by the flywheel and antenna pointing mechanism on the satellite SSTL 300 S1 [22]. [PERSON] studied the micro-vibration energy transfer characteristics when two flywheels work simultaneously [23]. By contrast, few studies have reported on the micro-vibrations caused by the CMGs and cryocoolers together. To address this research gap, CMGs and cryocoolers were chosen as the micro-vibration sources for our study. In addition to addressing the high-precision micro-vibration testing, the suppression of LOS jitters constitutes another core challenge, necessitating effective image stabilization strategies [3]. Owing to micro-vibration ranging from 0.01 Hz to kHz, the design of vibration isolation systems has always been critical in image stabilization [24]. Typically, micro-vibration isolation systems can be classified into passive isolation, active-passive hybrid isolation, and semi-active isolation. Among these, passive isolation has garnered significant attention due to its high reliability and absence of energy transfer [24; 25; 26; 27; 28]. For example, [PERSON] et al. designed a vibration isolator by optimizing the structure and introducing dampers to isolate the micro-vibration of the satellite platform above 10 Hz [27]. [PERSON] et al.