# Beam Scanning and Capture of Micro Laser Communication Terminal Based on MEMS Microm mirrors
## 5 Scan Capture Simulation Experiment  
Due to the small divergence angle of the communication light that MEMS micromirrors use for laser communication scanning and capturing, the beam jitter impact is significant. Moreover, the system operates in an open-loop state during scanning, without error correction, which can cause the scanning beam to deviate from its intended trajectory, leading to excessive overlap or missed scanning spots. Ultimately, this results in decreased coverage of the scanning beam over the uncertain area. Line-of-sight (LOS) jitter is caused mainly by the vibration of the platform. Therefore, this paper proposes mitigating the effect of optical axis jitter by introducing an additional overlap factor during scanning. In general, LOS jitter follows a Rayleigh distribution in the radial direction, and its probability density function can be expressed as  
\[f(\alpha)=\frac{\alpha}{\varphi^{2}}\exp(-\frac{\alpha^{2}}{2\varphi^{2}}). \tag{26}\]  
During scanning, \(\alpha\) is the angular deviation of the scanning-beam jitter \(\varphi\) is the standard deviation of the beam. When the angular deviation \(\alpha\) of the jitter exceeds a certain threshold in the azimuth and elevation directions, there is a gap between the scanning spots, resulting in an uncovered scanning area. This phenomenon is known as \"missed  
Figure 5: The relationship between the laser beam scanning time and the size of the uncertain region. scanning\". Let's designate the threshold angle for missed scanning as \(\gamma\) and the probability of missed scanning as \(P_{l}\). The expression for \(P_{l}\) is  
\[P_{l}=\int_{\gamma}^{\infty}f(\alpha)d\alpha=\int_{\gamma}^{\infty}\frac{\alpha} {\varphi^{2}}\exp(-\frac{\alpha^{2}}{2\varphi^{2}})d\alpha=\exp(-\frac{\gamma^ {2}}{2\varphi^{2}}). \tag{27}\]  
Therefore, the coverage \(P_{s}\) of the scanning beam of the communication light on the capture uncertainty region is shown by Equation (28). \[P_{s}=1-P_{l}=1-\exp(-\frac{\gamma^{2}}{2\varphi^{2}}). \tag{28}\]  
From this, the expression of the missed scan-limit angle \(\gamma\) can be deduced as  
\[\gamma=\varphi\sqrt{-2\ln(1-P_{s})}. \tag{29}\]  
To eliminate the missed scan and meet the scanning beam coverage requirements \(P_{s}\) of the uncertain region, an additional overlap factor \(k_{0}\) was introduced, as shown in Equation (30):  
\[k_{0}=\frac{2\gamma}{\theta_{b}}=\frac{2\varphi\sqrt{-2\ln(1-P_{s})}}{\theta_{ b}}. \tag{30}\]  
To further analyze and validate the impact of factors such as beam divergence angle, overlap factor, size of the uncertain region and possible microvibrations on the performance of laser communication scanning capture, experimental studies were conducted using computer simulations. For this purpose, a GUI experimental interface was designed as shown in Figure 6. This software program allows the flexible adjustment of parameters such as beam divergence angle, overlap factor, detector response time, size of the uncertain region, and standard deviation of microvibrations. By changing the values of these parameters, the scanning trajectory of the spot and its coverage of the uncertain region can be observed in the interface, enabling simulation-based calculations of the time required to complete the scanning of the uncertain region. First, the simulation program analyzed the scanning coverage of the same uncertain region for different beam divergence angles. The results, shown in Figure 7, indicated that when the system was affected by microvibrations to some extent, certain areas exhibited missed scanning. This observation was consistent with the previous analysis. As the beam divergence angle increased, the time required to scan the entire uncertain region gradually decreased. It was observed that while the microvibrations were kept constant, a larger beam divergence angle led to a smaller area of missed scanning, suggesting that increasing the beam divergence angle had a certain effect on reducing the impact of microvibrations. Figure 6: Laser beam scanning capture simulation experiment interface.