应用泽尼克多项式自由曲面的成像物镜设计  

Design of reflective lens with Zernike polynomial free form surfaces

作　　者：郑臻荣[1] 孙旭涛[1] 缪盈盈[1] 顾培夫[1] 刘旭[1] 

机构地区：[1]浙江大学现代光学仪器国家重点实验室,浙江杭州310027

出　　处：《浙江大学学报（工学版）》2008年第12期2202-2206,共5页Journal of Zhejiang University：Engineering Science

基　　金：浙江省自然科学基金资助项目(R104096)

摘　　要：为了解决自由曲面难以应用于成像系统设计的问题,通过对泽尼克多项式自由曲面的波像差的分析,对一种采用泽尼克多项式自由曲面的成像物镜进行研究.在对非球面离轴反射型成像物镜研究的基础上,应用泽尼克多项式归一化描述光学系统的波前边界,建立与赛得和像差之间的对应关系,推导出采用泽尼克多项式自由面替代偶次非球面的方法.设计采用三片泽尼克多项式自由曲面反射镜组成设计成像物镜,在100倍放大倍数、视场角为130°、相对孔径为2.5的条件下,调制传递函数实现100 lp/mm 60%以上,畸变小于2.0%.研究结果表明,应用泽尼克多项式自由曲面可以减小离轴光学系统像差,达到提高清晰度、简化光学系统结构的作用.In order to study the problem that free form surfaces are hard to be applied in the design of image system, an off-axis reflective lens composed with Zernike polynomials free form mirrors was designed by the wave-front analysis for Zernike polynomials free form surfaces. Based on the analysis of aspheric off- axis lens, Zernike polynomials was used to describe the free form shape mirror, and the aberration which was analyzed to match with Seidel aberration was used to design the free form reflective lens. A reflective projection lens was constructed with three Zernike polynomials free form shape mirrors, with layout of ＂concave -convex-convex＂, and the lens was telecentric in object space. Furthermore, the lens＇s performance was analyzed, under the condition of relative aperture of 2.5 and angle of view of 130°, the module transfer function （MTF） was over 60% at 100 lp/mm on magnification side, and the distortion was less than 2M. Design result showed that using Zernike polynomials free form surface can dramatically decrease the aberration of off-axis lens, simplify the configuration and increase the definition of image system.

关 键 词：光学设计 泽尼克多项式 成像物镜 反射 

分 类 号：O439[机械工程—光学工程]