基于面形斜率的光学自由曲面表征  

Characterization of freeform optical surfaces based on surface slope

作　　者：赵星[1] 郑义[1] 张赞[1] 张娟[1] 王灵杰[2] 伍雁雄[2] 

机构地区：[1]南开大学现代光学研究所光学信息技术科学教育部重点实验室,天津300071 [2]中国科学院长春光学精密机械与物理研究所光学系统先进制造技术中国科学院重点实验室,吉林长春130033

出　　处：《光学精密工程》2015年第7期1957-1964,共8页Optics and Precision Engineering

基　　金：中国科学院科技创新基金重点项目;国家自然科学基金资助项目(No.61108046;No.11474169)

摘　　要：对光学自由曲面设计的关键问题——光学自由曲面的表征模型进行了研究。在传统高斯径向基模型的基础上,通过改善基函数的分布特性以及基于面形斜率调整基函数的形状因子,建立了基于面形斜率的高斯径向基表征模型。利用建立的模型、传统径向基模型和Zernike多项式模型拟合了不同类型的自由曲面,并进行了分析比较。结果证实了文中提出的模型较传统径向基模型的面形拟合精度提高了1~2个数量级,具有较强的面形表征能力。应用该模型进行了离轴三反系统的设计,结果显示设计的三反系统的全视场平均调制传递函数（MTF）达到80%以上。与传统面形表征模型相比,该模型的应用提高了系统的像差平衡能力,改善了系统的成像质量。综合分析表明,该模型适用于表征具有显著非对称性的、面形矢高带有显著局域性变化的自由曲面,有望应用于具有大离轴量和大视场的光学系统设计中。This paper focuses on the optical freeform surface model in optical design of freeform optical surfaces. Based on the model of conventional Gaussian Radial Basis Function（RBF）, a model of Gaussian Radial Basis Function based on slope （Gaussian RBF-BS） was proposed by improving the distribution of basis function and changing the shape factor of basis function. The different types of freeform surfaces were fitted and compared by using models of Gaussian RBF-BS, Gaussian RBF and Zernike polynomials. The results demonstrate that the surface fitting ability of the proposed model is stronger than those of the conventional Gaussian RBF model by 1-2 orders, and it has a stronger surface characteristic ability. Then, the proposed model was used to design a Three Mirror Anastigmat （TMA） system, where the average Modulation Transfer Function（MTF） in whole field of view has reached over 80O//oo. As compared with that of the conventional model based on the RBF, the proposed model enhances the aberration balance ability and improves the image quality of the system. Further analysis indicates that RBF-BS model is much suitable for the characterization of the freeform surface with significant asymmetry and local variation. It is expected to be applied to the design of optical systems with large off-axis magnitudes and fields of view.

关 键 词：光学自由曲面 面形拟合 面形斜率 高斯径向基 ZERNIKE多项式 

分 类 号：TH703[机械工程—仪器科学与技术]