## 7 Conclusions  
Optical wireless communication (OWC) has emerged as a key alternative to traditional RF communication, offering a higher bandwidth, faster data rates, and lower power consumption. A line-of-sight (LOS) laser link is established through the acquisition, pointing, and tracking (APT) system to initiate communication, which faces challenges due to satellite vibrations.  
In this study, several scanning paths were evaluated based on their mean acquisition time, and the results showed the following performance ranking: spiral < hexagonal < square spiral < raster. Based on the analysis, spiral scanning is the best method among the discussed techniques. It offers the highest scanning efficiency by starting from the high-probability center region, enabling faster target detection. In addition to selecting the scan path, adjusting scan parameters such as the overlap factor can increase acquisition probability, although it also increases acquisition time. Modifying the beam divergence in the presence of vibrations can reduce scan gaps, whereas changing the uncertainty area size, without altering the overlap factor or beam divergence, does not reduce the scan gaps.  
By optimizing these multiple scan parameters and selecting the appropriate scan path, an effective trade-off between acquisition time and acquisition probability can be achieved, provided that the satellite vibration amplitudes do not exceed the limitations imposed by the scan parameters. Monte Carlo simulations revealed that optimized parameters reduced the need for repeated scans to almost none (1.01 scans on average), compared to 1.23 scans with fixed parameters, and achieved a remarkable 90.6% reduction in scan time (from 9.38 s to 0.88 s). This underscores the effectiveness of parameter optimization in minimizing both scan repetitions and acquisition time under satellite vibrations. The performance of the maximum likelihood estimator was also found to be reliable. Future studies should explore additional scan methods, including Rose and Lissajous paths, and evaluate them using probabilistic approaches. An enhanced estimation of satellite vibrations should be considered to improve the robustness of scan parameter performance in the acquisition phase.  
Conceptualization, W.J.; methodology, M.K.; software, M.K.; validation, W.J., D.L. and L.K.; investigation, M.K.; data curation, M.K.; writing--original draft preparation, M.K.; writing--review and editing, M.K., W.J., D.L. and L.K.; visualization, M.K.; supervision, W.J.; project administration, W.J.; funding acquisition, W.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China (Grant No. 2021 YFB3900100) and the Beijing Municipal Science and Technology (Grant No. Z241100005424008).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The author [PERSON] acknowledges the support of the Alliance of International Science Organizations (ANSO) Scholarship for Young Talents series No. 2021 ANSOP050 during the research for this study.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
ABCAdaptive Beam Control  
LOSLine-of-sight