# Research on Micro-Vibration Analysis of Segmented Telescope Based on Opto-Mechanical Integration
## 4 Opto-Mechanical Integration Analysis
### Imaging Quality of Optical Systems Under Micro-Vibration  
The results of opto-mechanical integration analysis under micro-vibration show that the WFE RMS is satisfied to be less than 0.061\(\lambda\) for the vast majority of the moments in 4 s, and the RMS is satisfied to be less than 0.071\(\lambda\) for the whole time period. The wavefront diagrams of 10 consecutive moments are taken as shown in Figure 13, where (a) shows the initial system WFE at 0 s. The scale on the right of the figure can directly see the PV value of the WFE at this moment. The micro-vibration source input \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Characteristic Frequency/Hz** & **Vibration Pattern** \\ \hline
1 & 7.56 & X-direction vibration of the secondary mirror \\
2 & 9.50 & Y-direction vibration of the secondary mirror \\
3 & 128 & Secondary mirror Z-axis rotation \\
4 & 174 & Z-direction vibration of the whole machine \\
5 & 191 & Y-direction vibration of the secondary mirror \\
6 & 194 & X-direction vibration of the secondary mirror \\ \hline \hline \end{tabular}
\end{table} 
Table 2: First 6 orders of modal shapes. signal of micro-vibration has randomness in the time domain, and the micro-vibration signal is transmitted to the primary mirror of the optical system causing the position change of the sub-mirror to have a certain degree of randomness. By establishing the sensitivity matrix of the relationship between the WFE and the position of the primary mirror, the positional attitude of the primary mirror can be deduced from the detected wavefront, which provides ideas for the mounting of the primary mirror of the segmented mirror. When the optical system is under long exposure time, its actual imaging effect is the energy accumulation under the uniform time interval, and the PSF of the optical system under long exposure time is the superposition of the PSF obtained at each moment in the integration time. Under the action of micro-vibration, the shift of the system's optic axis will lead to the shift of the center position of the PSF. Secondly, due to the change of the position between the sub-mirrors caused by the change in the shape of the primary mirror, so that the energy distribution of the PSF is also changed accordingly, and the joint effect of the two will make the system PSF fuzzy. As shown in Figure 14, the PSF of the center field of view under the initial moment of the optical system (taking the log value), due to the symmetric arrangement of the primary mirror's sub-mirrors, the PSF of the system also has a symmetric distribution about the X and Y axis. At this moment, the PSF has obvious main peaks and side flaps, and the impact on the imaging quality of the optical system is small due to the small magnitude of the micro-vibration amplitude. In order to study the influence of micro-vibration on the imaging quality characteristics under different exposure times, the X and Y-axis cross-sections of PSF images with exposure times of 0.25 s, 0.5 s, 0.75 s, 1 s and 2 s were taken respectively, and the actual imaging effect under the long exposure time is the accumulation of energy under the uniform time interval, so the longer the exposure time is, the greater the PSF intensity is. The above exposure time starts from the initial moment of the Micro-vibration source signal in Figure 10, and the PSF with center intensity shifts are accumulated for each moment. The PSF intensity under different exposure times is normalized by taking the positive direction of X and Y axes as shown in Figure 15, respectively (taking the log value), in which (a) is the X-axis cross-section, (b) is the local magnification at the sub-peak of the X-axis cross-section, (c) is the Y-axis cross-section, and (d) is the local magnification at the sub-peak of the Y-axis cross-section. Under the action of micro-vibration, the secondary peak and the third peak of PSF with different exposure times are gradually separated. The spatial distribution of PSF is related to the resolution ability of the optical system.