## 3 Results and Discussion  
### The Influence of Excitation on the Peak Value of Output Light Angle Response  
In actual conditions, the different amplitude, frequency, or phase of the two support trusses will affect the vibration response of the Optomechanical structure, and then affect the beam pointing stability of the spatial filter. After the Optomechanical structure design is completed, the influence of different working conditions is studied, and the system is optimized according to the influence degree, and the long-term stability of the beam direction is improved. In this paper, a harmonic signal is used as the source of excitation, and the influence of amplitude ratio \(\alpha\), frequency difference \(\Delta\omega\), and phase difference \(\Delta\phi\) on the directional stability of the spatial filter is analyzed to determine the control parameters of the system. Equation (17) is the expression of amplitude ratio, frequency difference, and phase difference. \[\alpha=\frac{A_{2}}{A_{1}},\Delta\omega=\omega_{1}-\omega_{2},\Delta\phi=\phi _{1}-\phi_{2} \tag{17}\]  
By substituting Equation (17) into Equation (16), the expression of the peak value of the output light angle response of the spatial filter can be rewritten as  
\[\Theta=\frac{G(s)}{mf_{1}}\sqrt{A_{1}^{2}+\alpha^{2}A_{1}^{2}-2\alpha A_{1}^{ 2}\cos[\Delta\omega t+\Delta\phi]} \tag{18}\]  
where, without control, the transfer rate is \(G(s)=15.7\), \(mf_{1}=16m\). * When the frequency difference is zero (\(\Delta\omega=0\)), the peak value of output light angle response is non-time-varying. The influence of excitation amplitude ratio and phase difference on the peak value of output light angle response of the Optomechanical coupling system is analyzed. It can be seen from Figure 8 that the influence of the excitation amplitude ratio on the peak value of the output light angle response should be analyzed according to the size of the phase difference. When the phase difference is within the range of \([0,\pi/2)\) and the phase difference is constant, the peak value of the angle response first decreases and then increases with the increase of the amplitude ratio, and there is a minimum point. When the phase difference is zero, and the amplitude ratio is 1, the peak value of the angle response is 0. At this time, there is no dynamic drift or jitter in the beam pointing, and  
2. Influence of excitation frequency difference on beam pointing accuracy given \(\alpha=5\), \(\Delta\phi=\pi\); It can be seen from Figure 10 that the change of frequency ratio makes the peak value of angle response change periodically in the range of 3.9-5.8 \(\upmu\)rad, and the upper and lower limits of the peak value of angular response do not change. 3. Influence of excitation phase difference on beam pointing accuracy given \(\alpha=5\), \(\Delta\omega=5\); It can be seen from Figure 11 that the change of phase difference makes the peak value of angle response change periodically in the range of 3.9-5.8 \(\upmu\)rad, and the upper and lower limits of the peak value of angular response do not change. From the above analysis, it can be seen that the excitation amplitude ratio has the greatest influence on the peak value of the output light angle response, which is the main factor. When the amplitude ratio is fixed, the frequency ratio and phase difference will make the peak value of the output light angle response change periodically in a fixed  
Figure 11: Given \(\alpha=5,\Delta\omega=5\), the influence of phase difference on the peak value of output light angle response: (**a**) The amplitude variation of output light angle response under phase difference, and time variable; (**b**) the amplitude variation of angular response of phase difference output light.