Wen Ming, Han Chengshan, Ma Hongcai
Appl Opt. 2021 Feb 20;60(6):1790-1800. doi: 10.1364/AO.414596.
This paper presents an active compensation strategy for RMS wavefront error of perturbed off-axis telescopes in the framework of nodal aberration theory. First, the orthogonalized expression of the wave aberration function in the vector form for perturbed off-axis telescopes is derived by using RMS normalization. The orthogonalized aberration function is applied to analytically describe the RMS wavefront error in perturbed off-axis telescopes with circular apertures. Then, the system compensation model for perturbed off-axis telescopes is established. The compensation model takes the weighted square sum of the RMS wavefront errors at representative field points as the objective function, which is minimized to obtain the optimal compensation solution of off-axis systems with perturbation constraints. The compensation model is solved by using a particle swarm optimization algorithm. Then, the off-axis three-mirror anastigmatic telescope is taken as an example, and the system compensations for the misaligned tertiary mirror and deformed primary mirror are discussed. After compensation, the average RMS wavefront errors in the perturbed off-axis systems are greatly reduced, which can well meet the system requirements. Finally, Monte Carlo simulations of the optimal compensation method and sensitivity table method are carried out to demonstrate the correctness and accuracy of the proposed method.
本文在节点像差理论框架下提出了一种针对受扰离轴望远镜均方根（RMS）波前误差的主动补偿策略。首先，通过RMS归一化推导了受扰离轴望远镜波像差函数在矢量形式下的正交化表达式。将正交化像差函数应用于解析描述具有圆形孔径的受扰离轴望远镜中的RMS波前误差。然后，建立了受扰离轴望远镜的系统补偿模型。该补偿模型以代表性视场点处RMS波前误差的加权平方和为目标函数，通过最小化该目标函数来获得具有扰动约束的离轴系统的最优补偿解。利用粒子群优化算法求解补偿模型。接着，以离轴三镜消像散望远镜为例，讨论了第三镜失调和主镜变形情况下的系统补偿。补偿后，受扰离轴系统中的平均RMS波前误差大幅降低，能够很好地满足系统要求。最后，对最优补偿方法和灵敏度表方法进行了蒙特卡罗模拟，以证明所提方法的正确性和准确性。
