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摘要:为了实现大口径椭圆形光学平面镜的高精度面形测量，提升大口径望远镜系统的像质，本文对椭圆形平面反射镜面形的绝对检测算法进行了研究。首先，对椭圆形镜面进行了多项式正交化拟合研究。接着，对绝对检测算法进行了理论研究，利用正交化绝对检测算法可以有效分离参考镜与待测镜的面形误差，从而实现待测椭圆形平面镜面的高精度面形重构。为了证明上述方法的实际检测精度，本文对250 mm×300 mm的椭圆形镜面进行了绝对检测模拟与检测实验。对参考镜面形精度不高的情况进行了仿真计算，实验中利用光阑在Zygo300 mm口径标准平面镜头中选取250 mm×300 mm椭圆形检测区域，采用150 mm口径Zygo干涉仪对上述椭圆形区域完成绝对检测，并基于上述正交化绝对检测算法对椭圆形平面镜实现了面形重构。实验结果表明，利用本文所述方法可以实现参考镜与椭圆形待测镜面的面形误差分离，绝对检测结果的残差图RMS（Root-mean square）值为0.29 nm，证明了本文所述方法的可行性。利用上述方法可以实现椭圆形平面反射镜的高精度面形重构。Abstract:In order to realize the high-precision surface measurement of large-diameter elliptical optical flat mirrors and improve the image quality of large-aperture telescope systems, the absolute measurement algorithm for flat elliptical mirrors is studied in this paper. Firstly, the orthogonal polynomials fitting of an elliptical optical flat mirror is studied. Then, the absolute testing algorithm is studied theoretically. The orthogonal absolute testing algorithm can effectively separate the surface error of the reference mirror from the mirror to be measured, which can realize the high-precision surface reconstruction of the elliptical flat mirror to be measured. To verify the actual testing accuracy of the above method, we carried out an absolute testing simulation and experiment on a 250 mm×300 mm mirror. In the simulation, the possibility that the reference surface error is high was considered. In the experiment, a 250 mm×300 mm elliptical testing area was selected in the Zygo300 mm standard flat surface. The above-mentioned elliptical area was tested by the 150 mm Zygo interferometer, and the surface reconstruction was realized based on the above-mentioned orthogonal absolute testing algorithm. The experimental results show that the surface error separation between the reference mirror and the elliptical mirror can be achieved by using the method described in this paper, and the residual RMS (Root-Mean Square) value of the absolute testing result is 0.29 nm, which proves the feasibility and accuracy of the method described in this paper. The high-precision surface reconstruction of the elliptical flat mirror can be achieved using the above method.
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图 12子孔径检测结果与拼接结果残差图
Figure 12.Difference maps between each subaperture map and its corresponding stitching map
图 14传统算法测试镜面形重构结果
Figure 14.Reconstructed testing elliptic surface map with the standard Zernike polynomials fitting method
图 15传统算法参考镜面形重构结果
Figure 15.Reconstructed reference surface map with the standard Zernike polynomials fitting method
图 16子孔径检测结果与传统绝对检测结果残差图
Figure 16.Difference maps between each subaperture map and its corresponding stitching map using the traditional method
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