Off-axis three-mirror anastigmatic (TMA) telescopes with designed decenters and tilts, have many misalignment degrees of freedom and strong coupling between each misalignment degree of freedom. Therefore, it is difficult to establish misalignment equations only using A222 and A131 in nodal aberration theory (NAT). In addition, for off-axis TMA optical systems with designed decenters and tilts, the robustness of the existing fifth-order NAT misalignment calculation algorithm based on high-order Zernike coefficients and boresight errors decreases, so it is difficult to realize its engineering application. To solve the issue of insufficient practicality of the existing misalignment algorithm based on fifth-order NAT, a third-order NAT calculation algorithm based on quadratic aberration field decenter vectors is derived and established. Two concepts of inherent aberration field decenter vector and misalignment aberration field decenter vector are proposed. Taking an off-axis TMA optical system with 6-m focal length as the research object, simulations, and alignment verification experiments were carried out. Compared with the existing fifth-order NAT misalignment algorithm, the results show that when measurement noise is not considered, the two methods can both obtain convergent calculation results, and the average RMS wavefront errors (WFE) of the optical system are both corrected to be below 0.0574 waves. When different levels of measurement noise are introduced, the robustness of the fifth-order NAT misalignment algorithm decreases, and there are even cases where the optical system completely fails to be corrected. However, the algorithm based on quadratic aberration field decenter vectors shows better robustness. Under different levels of measurement noise, this algorithm could correct the average RMS WFE of the optical system to around 0.0574 waves.

中文翻译：

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基于三阶二次节点像差理论的宽视场巡天望远镜失准算法

具有设计偏心和倾斜度的离轴三反像散 (TMA) 望远镜具有许多错位自由度和每个错位自由度之间的强耦合。因此，在节点像差理论（NAT）中仅使用 A222 和 A131 很难建立错位方程。此外，对于设计偏心和倾斜的离轴TMA光学系统，现有的基于高阶Zernike系数和视轴误差的五阶NAT错位计算算法的鲁棒性降低，难以实现其工程应用。针对现有基于五阶NAT的错位算法实用性不足的问题，推导并建立了一种基于二次像差场偏心向量的三阶NAT计算算法。提出了固有像差场偏心向量和未对准像差场偏心向量两个概念。以焦距6米的离轴TMA光学系统为研究对象，进行了仿真和对准验证实验。结果表明，与现有的五阶NAT错位算法相比，在不考虑测量噪声的情况下，两种方法均能得到收敛的计算结果，光学系统的平均RMS波前误差（WFE）均修正为低于 0.0574 波。当引入不同级别的测量噪声时，五阶NAT错位算法的鲁棒性下降，甚至出现光系统完全无法校正的情况。然而，基于二次像差场偏心向量的算法具有较好的鲁棒性。在不同的测量噪声水平下，该算法可以将光学系统的平均 RMS WFE 校正到 0.0574 波左右。