基于面形斜率的光学自由曲面表征

赵星; 郑义; 张赞; 张娟; 王灵杰; 伍雁雄

doi:10.3788/OPE.20152307.1957

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基于面形斜率的光学自由曲面表征

现代应用光学 | 更新时间：2020-08-12

- 基于面形斜率的光学自由曲面表征
- Characterization of freeform optical surfaces based on surface slope
- 光学精密工程 2015年23卷第7期页码：1957-1964
- 作者机构：
  
  1. 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
  2. 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
- 作者简介：
- 基金信息：
  
  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)()
- DOI：10.3788/OPE.20152307.1957
  中图分类号： TH703
- 收稿日期：2015-01-20，
  
  修回日期：2015-03-20，
  
  纸质出版日期：2015-07-25
- 稿件说明：
移动端阅览
赵星, 郑义, 张赞等. 基于面形斜率的光学自由曲面表征[J]. 光学精密工程, 2015,23(7): 1957-1964

ZHAO Xing, ZHENG Yi, ZHANG Zan etc. Characterization of freeform optical surfaces based on surface slope[J]. Editorial Office of Optics and Precision Engineering, 2015,23(7): 1957-1964
赵星, 郑义, 张赞等. 基于面形斜率的光学自由曲面表征[J]. 光学精密工程, 2015,23(7): 1957-1964 DOI： 10.3788/OPE.20152307.1957.

ZHAO Xing, ZHENG Yi, ZHANG Zan etc. Characterization of freeform optical surfaces based on surface slope[J]. Editorial Office of Optics and Precision Engineering, 2015,23(7): 1957-1964 DOI： 10.3788/OPE.20152307.1957.

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。

Abstract

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 80%. 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

Keywords

references

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FUERSCHBACH K, ROLLAND J P, THOMPSON K P. A new family of optical systems employing φ-polynomial surfaces[J]. Opt. Express, 2011,19(22): 21919-21928.

薛栋林,郑立功,张峰. 基于光学自由曲面的离轴三反光学系统[J]. 光学精密工程, 2011,19(12):2813-2820. XUE D L, ZHENG L G, ZHANG F. Off-axis three mirror system based on freeform mirror[J]. Opt. Precision Eng., 2011,19(12): 2813-2820. (in Chinese)

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KAYA I, THOMPSON K P, ROLLAND J P. Comparative assessment of freeform polynomials as optical surface descriptions[J]. Opt. Express, 2012,20(20): 22683-22691.

王超. 自由曲面表征函数及其应用研究[D]. 长春:中国科学院长春光学精密机械与物理研究所, 2014. WANG CH. Research on Characterization Function and Application of free-form Surface[D]. Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2014. (in Chinese)

黄冬民,潘泉,梁新华. 基于随机化Halton序列的粒子滤波算法研究[J]. 计算机应用研究,2011,28(1): 91-94. HUANG D M, PAN Q,LIANG X H.Research of particle filter algorithm based on randomized Halton sequences[J].Application Research of Computers,2011,28(1): 91-94. (in Chinese)

鄢静舟,雷凡,周必方,等.用Zernike多项式进行波面拟合的几种算法[J]. 光学精密工程,1999,7(5): 119-128. YAN J ZH, LEI F, ZHOU B F, et al. Several algorithms for wavefront fitting using Zernike polynomails[J]. Opt. Precision Eng., 1999,7(5): 119-128. (in Chinese)

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