光电工程, 2016, 43 (12): 104, 网络出版: 2016-12-30
矩形孔径主动自由曲面变形数据拟合
Deformation Data Fitting of Active Free-form Surface with Rectangular Aperture
Zernike 多项式 矩形孔径 正交多项式 折反射式光刻物镜 Zernike polynomial rectangle pupil orthogonal polynomial catadipotric lithography objective
摘要
折反式深紫外光刻物镜采用反射镜为主动自由曲面,补偿系统热像差。一些物镜系统要求反射镜的通光孔径为矩形。出于描述反射镜主动变形的目的,需要采用矩形区域正交的多项式拟合变形数据。高精度的拟合要求需要获得高阶的多项式表达式。本文根据正交多项式的性质,推导了矩形正交多项式的通式并列出前36 项多项式的表达式。应用该多项式对主动自由曲面的变形数据进行拟合。结果表明,变形均方根值(RMS)在2 nm~5 nm 范围内,最小拟合残差可达0.024 nm。根据拟合残差面形的特点,可以对主动自由曲面的结构设计改进。
Abstract
Catadioptic deep ultraviolet lithography objective took the mirror as active free-form surface to compensate thermal aberration. Mirror in compliance with the requirements of the system optical path had a rectangular aperture. For the purpose of describing the active deformation of mirror, it’s necessary for orthogonal polynomials in rectangle zone to fit the deformation data. For high accuracy of fitting surface deformation, it was needed to obtain higher order polynomial expressions. According to the properties of orthogonal polynomials, rectangular orthogonal polynomials formula was derived and the first 36 polynomial expressions were listed. And the polynomials were applied to fit the deformation data of active free-surface. The results showed that the minimum fitting residual error RMS is 0.024 nm when the deformation is 2 nm~5 nm in RMS. According to the characteristic of fitting residual map, the structure design of the active free surface could be improved.
周超, 邢廷文. 矩形孔径主动自由曲面变形数据拟合[J]. 光电工程, 2016, 43(12): 104. ZHOU Chao, XING Tingwen. Deformation Data Fitting of Active Free-form Surface with Rectangular Aperture[J]. Opto-Electronic Engineering, 2016, 43(12): 104.