An analytical model is derived for the probability of failure (P-fail) to spatially acquire an optical link with a jittering search beam. The analytical model accounts for an arbitrary jitter spectrum and considers the associated correlations between jitter excursions on adjacent tracks of the search spiral. An expression of P-fail in terms of basic transcendental functions is found by linearizing the exact analytical model with respect to the correlation strength. Predictions from the models indicate a strong decrease of P-fail with increasing correlation-strength, which is found to be in excellent agreement to results from Monte Carlo simulations. The dependency of P-fail on track-width and scan speed is investigated, confirming previous assumptions on the impact of correlations. Expressions and applicable constraints are derived for the limits of full and no correlations, and the optimal track width to minimize the acquisition time is computed for a range of scan speeds. The model is applicable to optical terminals equipped with a fast beam steering mirror, as often found for optical communication missions in space.

翻译：推导了一种解析模型，用于描述存在抖动搜索光束时空间获取光学链路的失效概率（P-fail）。该解析模型适用于任意抖动频谱，并考虑了搜索螺旋相邻轨道上抖动偏移之间的关联性。通过对精确解析模型进行关于关联强度的线性化处理，得到了用基本超越函数表示的P-fail表达式。模型预测表明，随着关联强度的增加，P-fail显著降低，这一结果与蒙特卡洛模拟结果高度吻合。研究了P-fail对轨道宽度和扫描速度的依赖性，验证了先前关于关联影响的假设。推导了完全关联和无关联极限情况下的表达式及适用约束条件，并计算了不同扫描速度下最小化获取时间的最优轨道宽度。该模型适用于配备快速光束转向镜的光学终端（常见于空间光通信任务中）。