随望远镜口径的不断增大, 其结构和热变形所导致的光学系统失调而造成图像质量下降问题越来越显著。为了估计望远镜的失调误差, 建立结构力学模型, 并对失调误差计算方法及补偿进行研究。对望远镜结构进行简化并采用有限元方法建立结构力学模型。然后, 以望远镜主次镜镜面节点的当前位置为输入, 提出了基于非线性最小二乘拟合的主次镜失调误差计算方法。以主镜当前光轴为基准, 以补偿失调误差为目标, 即主次镜光轴重合且无间隔误差, 提出了基于空间坐标变换来确定Hexapod平台支杆长度的计算方法。以2 m口径望远镜为例, 对重力及热变形所致的失调误差进行模拟, 并在此基础上利用Hexapod平台调整次镜位置来补偿失调误差。数值仿真结果表明: 重力变形和热变形均会导致光学系统出现明显的失调误差, 弥散斑最大达到了1 473 μm和557 μm, 经过次镜位置补偿, 弥散斑半径下降到32 μm以下。本文提出的失调误差以及Hexapod平台支杆长度计算方法可应用于实际望远镜标定和装调过程中。

As the diameter of a ground-based telescope increases, the image quality will significantly degrade because of optical misalignment, which is caused by gravity and thermal deformations of the telescope structure. To accurately estimate the misalignment error, a mechanical model of a telescope was established, and the computation method and compensation process were investigated. According the structural components of the telescope, the structural model was simplified, and then the mechanical model was established using the finite element method. Based on nonlinear least square fitting, a method was presented to compute the misalignment error between the primary and secondary mirrors in which the inputs were the current node position of the primary and secondary mirror surfaces. Thereafter, a method in which the optical axis of the primary mirror used as the benchmark were adopted to determine the length of the hexapod leg with the objective of compensating for the misalignment error. Finally, numerical examples of a ground-based telescope with a diameter of 2 m were presented to verify the presented methods and the corresponding theories. The simulation results show that there are obvious misalignment errors because of gravity and thermal deformations, with maximum root mean square (RMS) radii of the optical spots being 1 473 and 557 μm, respectively. After the secondary mirror compensation, the RMS radii of the spots are decreased significantly, with all of them being <32 μm. The results verify the misalignment error and the hexapod leg length computation methods.