We propose a link acquisition time model deeply involving the process from the transmitted power to received signal-to-noise ratio (SNR) for LEO-to-ground laser communication for the first time. Compared with the conventional acquisition models founded on geometry analysis with divergence angle threshold, utilizing SNR as the decision criterion is more appropriate for practical engineering requirements. Specially, under the combined effects of platform vibration and turbulence, we decouple the parameters of beam divergence angle, spiral pitch, and coverage factor at a fixed transmitted power for a given average received SNR threshold. Then the single-scan acquisition probability is obtained by integrating the field of uncertainty (FOU), probability distribution of coverage factor, and receiver field angle. Consequently, the closed-form analytical expression of acquisition time expectation adopting multi-scan, which ensures acquisition success, with essential reset time between single-scan is derived. The optimizations concerning the beam divergence angle, spiral pitch, and FOU are presented. Moreover, the influence of platform vibration is investigated. All the analytical derivations are confirmed by Monte Carlo simulations. Notably, we provide a theoretical method for designing the minimum divergence angle modulated by the laser, which not only improves the acquisition performance within a certain vibration range, but also achieves a good trade-off with the system complexity.

我们首次提出了一种深度涉及低轨对地激光通信从发射功率到接收信噪比（SNR）过程的链路捕获时间模型。与基于发散角阈值的几何分析的传统采集模型相比，以信噪比作为决策标准更适合实际工程需求。特别是，在平台振动和湍流的综合影响下，我们在给定平均接收信噪比阈值的固定发射功率下解耦波束发散角、螺距和覆盖因子等参数。然后通过综合不确定性场（FOU）、覆盖因子的概率分布和接收器视场角来获得单扫描捕获概率。因此，推导了采用多扫描的采集时间期望的封闭式解析表达式，该表达式确保了采集成功，并且单次扫描之间具有必要的复位时间。提出了有关光束发散角、螺距和 FOU 的优化。此外，还研究了平台振动的影响。所有分析推导均通过蒙特卡罗模拟得到证实。值得注意的是，我们提供了一种设计激光调制的最小发散角的理论方法，不仅提高了一定振动范围内的采集性能，而且与系统复杂性实现了良好的权衡。