为了解决长条形镜面面形拟合中各项不正交, 无法在调整中利用像差指导计算机辅助装调的问题, 本文建立了一套合理的拟合模型。该模型以矩阵求解正交化Zernike多项式系数为基础, 将离散的数据点作为定义域, 对已选取的Zernike项进行定义域内正交化计算, 并以获得的各正交项为基底, 实现对长条形镜面及其他异形光学镜面的正交化多项式拟合求解。进而确定在干涉检测中加工误差与装调误差的分离, 为光学镜面的最终面形收敛提供保障。根据本文实验结果, 对一口径600 mm×260 mm, PV与RMS值分别为5889λ及1002λ的长条形光学镜面进行拟合, 利用Metropro去像散后, 面形未得到收敛, PV与RMS值分别变为7448λ及1725λ。而采用本文算法处理后, 其PV与RMS值分别收敛为4666λ及0679λ, 验证了本文方法对于长条形镜面拟合的正确性。

In order to solve the non-orthogonal problems in the surface fitting to rectangular mirror, and realize the computer aided adjustment based on aberration, a reasonable fitting model is established in this paper. The model is based on the method by using matrix to solve the orthogonal Zernike polynomial coefficients, through the matrix solving method, and using the discrete data points as the domain, the orthogonalization calculation is performed on the selected Zernike term, and the orthogonal terms obtained are used as the basis to realize the orthogonal polynomial fitting solution for the rectangular mirror and other irregular optical mirrors to determine the separation of the machining error and the alignment error in the interference detection, thus guaranteeing convergence of the final shape of the optical mirror. According to the experimental results, a rectangular mirror with size of 600 mm×260 mm and PV and RMS values of 5889λ and 1002λ is fitted. After anastigmatism with Metropro, the surface shape is not converged, and the PV and RMS values become 7448λ and 1725λ respectively. But according to the algorithm described in this paper, the PV and RMS values converge to 4666λ and 0679λ respectively, which verifies the correctness of the proposed method for rectangular mirror surface fitting.