Another study in [37] introduces a method using a long beacon light and one-dimensional scanning to reduce acquisition time and failure probability by approximately 40% and 30%, respectively, improving the efficiency of LEO-GEO laser communication links. In [38], an improved hexagonal honeycomb scanning method based on hexagonal spiral scanning is proposed, increasing capture probability by 3% compared to traditional methods, providing a new solution for target acquisition in laser communication and radar systems. The work in [39] establishes a theoretical model for the field of uncertainty (FOU) and analyzes capture probability, proposing a scanning step model and spiral scanning paths, and comparing the performance of ADRC and PI control for gimbal mirror tracking, demonstrating ADRC's superior control in reducing scanning errors. In [40], a MEMS micromirror-based laser scanning-capture model with an overlap factor is presented to improve capture probability under microvibrations, validated through experimental analysis for microspace laser communication. The work in [41] explores acquisition technology for satellite-ground laser links using a raster-spiral scanning scheme, analyzing the impact of offset errors, scanning step, and speed on acquisition probability and time, and optimizing performance through numerical and experimental analyses. Finally, in [42], the impact of satellite vibrations on acquisition time in laser inter-satellite links (ISLs) is investigated, deriving an analytic expression for acquisition time and the optimal beam divergence angle, with results validated through simulations and experiments, highlighting the importance of adaptive beam divergence. As mentioned earlier, previous studies have primarily focused on optimizing the pointing and tracking phases of the APT system, with limited attention given to enhancing the acquisition phase. Specifically, the optimization of scanning parameters during the acquisition step, aimed at reducing acquisition time and improving acquisition probability in the presence of satellite vibrations, has not been thoroughly explored. This study addressed this by investigating the impact of satellite vibrations on the acquisition process and proposing methods to optimize scan parameters for improved and more reliable acquisition under such conditions. The research presented here offers a probabilistic approach to the characterization of different scanning paths, which can effectively balance acquisition time and acquisition probability, even under challenging vibration-induced disturbances. The remainder of this paper is organized as follows: Section 2 describes the APT system in inter-satellite laser communication links, with subsections on acquisition schemes and target satellite probability density functions in the presence of jitter. Section 3 presents various scanning methods. Section 4 introduces the satellite platform vibration spectrum model and the maximum likelihood estimation (MLE) method. Section 5 discusses different scan parameters and their influence on acquisition performance. Section 6 presents simulation results and discusses their implications. Finally, Section 7 concludes the paper