One of the critical factors affecting acquisition performance is satellite platform vibrations, which can create scan gaps, reduce acquisition probability, and lead to multiple scans of the uncertainty area, thereby increasing the acquisition time. Previous studies have mainly focused on the impact of satellite platform vibrations on the pointing and tracking systems, with minimal attention given to the acquisition phase and the characterization of different scan paths using a probabilistic approach, since satellite vibrations and the resulting errors are inherently random in nature. In [25], a model is proposed that examines optical spatial tracking systems with heterodyne detection, emphasizing reduced noise susceptibility and optimized local oscillator (LO) distributions for improved tracking performance. In another work presented in [26], laser satellite communication systems were studied, comparing feedback and feed-forward control methods for mitigating vibration-induced angular noise in beam pointing. Adaptive transmitter power models were developed for heterodyne laser satellite communication links to compensate for vibration effects on beam pointing and maintain a constant bit error rate (BER). The analysis showed that the required power increases almost exponentially with linear increases in vibration amplitude [27]. The study in [28] developed a detailed simulation to analyze the impact of platform jitter and atmospheric fading on the far-field energy distribution during laser acquisition scans. It also examined the optimization of search parameters using different scanning strategies, including spiral and raster-spiral patterns, to maximize the probability of detection under varying disturbance conditions. The impact of pointing errors on the acquisition process in inter-satellite laser communication systems was studied in [29], where several scan techniques for inter-satellite laser communications were investigated. Numerical simulations identified the spiral scan as the optimal method for improving acquisition success probability by optimizing the overlap factor of the beacon laser beam. An alternative approach, involving processing and acquisition via composite spiral scanning and iterative learning control, is introduced in [30] to enhance tracking accuracy in dynamic target systems. The method achieves tracking precision within \(\pm\)2 \(\upmu\)rad, addressing laser divergence and disturbances. The study in [31] compared different methods for acquiring optical links in space using dedicated acquisition sensors, focusing on single and dual spiral scan approaches. The dual scan method was found to be faster and more robust against beam jitter, while the parallel acquisition of links in a constellation is quicker but more complex to implement. Similarly, in [32], the feasibility of beaconless satellite-to-satellite acquisition is demonstrated using a diffraction-limited beam, and the impact of vibration spectra and scanning algorithms on the process is evaluated. The impact of vibrations on laser beam search patterns in beaconless inter-satellite communication links is analyzed in [33], showing that increasing the scan beam ratio improves hit probability under high vibration levels. Another work presented in [34] analyzed various acquisition methods and scanning patterns, including raster and spiral, and evaluated the influence of satellite vibrations on the acquisition process, proposing a correction algorithm for vibration compensation. In [35], acquisition and tracking times in LEO satellites are analyzed, evaluating scanning methods like raster, spiral, and Lissajous, while addressing vibration effects and proposing a vibration compensation filter. In [36], a hexagonal spiral scanning method with equal internal and external scanning circles is proposed to improve the efficiency and success rate of satellite laser communication link establishment, optimizing scanning time and system performance.