# Research on Micro-Vibration Analysis of Segmented Telescope Based on Opto-Mechanical Integration
###### Abstract  
Aiming at the inherent nature and complexity of the influence of in-orbit micro-vibration in the imaging quality of segmented telescopes, a dynamic full-link opto-mechanical integration analysis method is proposed. The method is based on the measured micro-vibration signals of the infrared refrigerator, using the finite element method to perform the transient response analysis of the opto-mechanical system in Patran/Nastran software. The interface tool is written by Matlab to achieve the calculation of rigid body displacement and real-time data interaction with Zemax. The results show that when the working wavelength is 1 \(\mu\)m, the optical system has a wavefront error Root-Mean-Square value of less than 0.071\(\lambda\) in 4 s. Evaluating the effect of micro-vibration on the imaging quality of the system in terms of the peak ratio of the point spread function. When the exposure time was 2 s, the ratio maximum values of 0.4628 and 0.6207 were reached for the X-axis and Y-axis, respectively. The method provides an important reference basis for the evaluation of imaging quality of an optical system under micro-vibration environment with a long exposure time. s 202525, 1901  
24 January  
and a linearized phase diversity algorithm LAPD for the fine-phase modes, with the final ELASTICS state is used as the starting point for fine phasing with LAPD. The on-orbit deployment of JWST makes the JWST co-phase wavefront detection and control system more complex. The final JWST primary mirror integrated surface shape accuracy is 23.2 nm, the sub-mirror Tip & Tilt error correction accuracy can be better than 0.028\({}^{\prime\prime}\), and the Piston error correction accuracy has reached tens of nanometers [15; 16; 17]. When the satellite is in the in-orbit working state, it will be affected by the fluctuation of the space environment and the perturbation of the internal vibration source of the satellite and generate micro-vibration [18; 19; 20]. Aiming at the source of micro-vibration, [PERSON] et al. [21] used the theoretical derivation to represent the structural elasticity and damping of the system by a linear spring and a linear damper, respectively, and considered that the flywheel disturbance mainly originated from the rotor's dynamic imbalance and static imbalance, so as to establish an analytical model. [PERSON] [22] summarized the main reasons for the flywheel disturbance, and carried out the ground disturbance test of the flywheel and the in-orbit test, and established an analytical model based on the statistical analysis of the test data. orbit test, and established the flywheel disturbance model based on the statistical analysis of the test data. [PERSON] [23] analyzed and studied the broadband vibration output during flywheel operation by using quantile statistics to establish the grading standard of flywheel micro-vibration, which can provide a theoretical and engineering basis for the development and screening of super-static flywheel. [PERSON] [24] conducted space measurements of the angular micro-vibration of platform jitter in the ground-star laser communication link of the Optical Communication Engineering Test Satellite (OCETS) and compared the results with those of ground tests. The measurement results provide a reference for the estimation of angular jitter and the design of tracking control loops for space laser communication systems. Micro-vibration is characterised by small energy, broad spectrum, inherent nature and difficult to suppress. It will cause the rigid body displacement and the surface shape change of the optical elements within the optical system, thus directly affecting the imaging quality. Among them, the rigid body displacement of optical elements has the most significant impact on image quality. However, for the segmented primary mirror optical structure, micro-vibration leads to more complex changes in the positional relationship between the sub-mirrors. [PERSON] [25] analyzes the point spread function of a segmented mirror affected by random tilt errors.