Wang Jinxin, He Xu, Luo Jing, Zhang Xiaohui, Xu Tianxiao
Opt Express. 2022 Apr 11;30(8):13159-13183. doi: 10.1364/OE.453005.
For pupil-offset off-axis reflective astronomical telescopes with designed tilts and decenters, owing to the absence of symmetry, axial and lateral misalignments exhibit strong coupling. The astigmatic and coma aberration fields of the misaligned optical systems are not only effected by lateral misalignments but also closely related to axial misalignments. However, the traditional misalignment algorithm based on nodal aberration theory (NAT) usually ignore the effect of axial misalignments on the aberration fields of optical systems when constructing calculation models. As a result, the presence of axial misalignments in pupil-offset off-axis telescopes with designed tilts and decenters will invalidate the traditional NAT-based lateral misalignment algorithm, which makes it difficult to be applied to actual computer-aided alignment experiments. In order to solve this issue, on the framework of modified NAT, third-order astigmatic, third-order coma, and third-order spherical net aberration fields of pupil-offset off-axis systems with designed tilts and decenters induced by axial and lateral misalignments are separated from the total aberration fields, and their inherent relations are analytically expressed. On this basis, in order to construct a solution model that can simultaneously and quantitatively calculate the axial and lateral misalignments, a method is proposed to fit the partial derivative coefficient matrix of misalignments according to field dependence of the net aberrations induced by misalignments. The simulation and actual alignment experiments were performed on a real wide-field off-axis three-mirror telescope using the constructed solution model, which proved the feasibility of the proposed method. Simulation experiments show that for different misalignment conditions generated randomly, both axial and lateral misalignments have achieved convergent solution results. In the actual alignment experiment, the average RMS wavefront errors of the nine field of views is corrected from 1.9 λ to 0.12 λ (λ = 632.8nm) through 3-5 iterations.
对于具有设计倾斜和偏心的光瞳偏移离轴反射天文望远镜，由于缺乏对称性，轴向和横向失准呈现出强烈的耦合。失准光学系统的像散和彗差像差场不仅受到横向失准的影响，还与轴向失准密切相关。然而，传统的基于节点像差理论（NAT）的失准算法在构建计算模型时，通常忽略轴向失准对光学系统像差场的影响。因此，在具有设计倾斜和偏心的光瞳偏移离轴望远镜中，轴向失准的存在将使传统的基于NAT的横向失准算法失效，这使得该算法难以应用于实际的计算机辅助对准实验。为了解决这个问题，在改进的NAT框架下，将由轴向和横向失准引起的具有设计倾斜和偏心的光瞳偏移离轴系统的三阶像散、三阶彗差和三阶球面净像差场从总像差场中分离出来，并解析表达它们的内在关系。在此基础上，为了构建一个能够同时定量计算轴向和横向失准的求解模型，提出了一种根据失准引起的净像差的场依赖性来拟合失准偏导数系数矩阵的方法。利用构建的求解模型在一台实际的宽视场离轴三镜望远镜上进行了模拟和实际对准实验，证明了所提方法的可行性。模拟实验表明，对于随机产生的不同失准条件，轴向和横向失准均获得了收敛的求解结果。在实际对准实验中，通过3至5次迭代，九个视场的平均RMS波前误差从1.9λ校正到了0.12λ（λ = 632.8nm）。
