采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响

武鹏飞; 张赞; 郑义; 张娟; 王尧尧; 赵星; 王灵杰; 伍雁雄

doi:10.3788/OPE.20162407.1564

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采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响

现代应用光学 | 更新时间：2020-08-13

- 采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响
- Influence of sampling point distribution in freeform surfaces fitting with radial based function model
- 光学精密工程 2016年24卷第7期页码：1564-1572
- 作者机构：
  
  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
- 作者简介：
  
  [ "武鹏飞(1968-), 男, 辽宁兴城人, 博士, 教授, 1996年于南开大学获得博士学位, 主要从事光学信息处理等方面的研究。E-mail:pwu@nankai.edu.cn" ]
  赵星(1980-), 男, 北京人, 博士, 副教授, 2007年于南开大学获得博士学位, 主要从事光学信息处理以及光学系统设计等领域的研究工作。E-mail:zhaoxingtjnk@nankai.edu.cn E-mail:zhaoxingtjnk@nankai.edu.cn
- 基金信息：
  
  国家自然科学基金资助项目(11474169);中科院科技创新基金重点项目；天津市应用基础与前沿技术研究计划资助项目(15JCYBJC16900)
- DOI：10.3788/OPE.20162407.1564
  中图分类号： TH703
- 收稿日期：2016-03-04，
  
  录用日期：2016-4-29，
  
  纸质出版日期：2016-07
- 稿件说明：
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武鹏飞, 张赞, 郑义, 等. 采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响[J]. 光学精密工程, 2016,24(7):1564-1572.

Peng-fei WU, Zan ZHANG, Yi ZHENG, et al. Influence of sampling point distribution in freeform surfaces fitting with radial based function model[J]. Optics and precision engineering, 2016, 24(7): 1564-1572.
武鹏飞, 张赞, 郑义, 等. 采样点分布对基于面形斜率径向基模型的自由曲面拟合精度的影响[J]. 光学精密工程, 2016,24(7):1564-1572. DOI： 10.3788/OPE.20162407.1564.

Peng-fei WU, Zan ZHANG, Yi ZHENG, et al. Influence of sampling point distribution in freeform surfaces fitting with radial based function model[J]. Optics and precision engineering, 2016, 24(7): 1564-1572. DOI： 10.3788/OPE.20162407.1564.

摘要

鉴于自由曲面模型的面形拟合精度在自由曲面表征以及面形初始结构选取等研究中的重要性，本文针对基于面形斜率的高斯径向基表征模型，研究了不同的采样点分布类型对该模型面形拟合精度的影响。采用不同采样点分布拟合离轴二次曲面和带凸起的抛物面，结果表明采用均匀随机分布的采样点有利于实现高精度的面形拟合，且达到一定的拟合精度后，采样点的数目对拟合精度的影响有限。以离轴三反系统为设计实例，对比了由不同采样方式生成初始面形后系统的像质优化结果。结果显示，采用均匀随机型采样方式得到的初始面形进行系统优化，最终全视场平均调制传递函数(MTF)可以达到0.72以上

远高于由边缘集中采样方式生成初始面形后系统像质的优化结果，从而印证了理论研究结果。

Abstract

In view of the importance of surface shape fitting precision of free-form surface model in researches such as free-form surface representation and selection of initiating structure of surface shape

the influence of different sampling point distribution patterns on surface shape fitting precision of the Gaussian Radial Basis Function Based on Slope(Gaussian RBF-BS) model was investigated. An off-axis quadric surface and an bumpy paraboloid were fitted with different sampling point distributions which were uniformly random points and edged-clustered points. The results show that the uniformly random grid is better for surface shape fitting due to the high precision. The influence of sampling point quantity on fitting precision remains constant when certain fitting precision is reached. The off-axis Three Mirror Anastigmat(TMA) system was optimized experimentally by using initial surface shapes generated with different sampling methods. The results show that

by using initial surface shape generated from uniformly random sampling method for the system optimization

the average Modulation Transfer Function (MTF) of whole field of view is more than 0.72

which is much higher than that by using surface shape generated by edge cluster sampling points. Thus the theoretical research results were verified.

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references

THOMPSON K P, ROLLAND J P. Freeform optical surfaces:a revolution in imaging optical design[J]. Opt. Pho. News, 2012, 23(6):30-35.

FUERSCHBACH K, JANNICK P R, KEVIN P T. A new family of optical systems employingφ-polynomial surfaces[J]. Opt. Express, 2011, 19(22):21919-21928.

ILHAN K, KEVIN P T, JANNICK P R. Edge clustered fitting grids forφ-polynomial characterization of freeform optical surfaces[J]. Optical Express, 2011, 19(27):26962-26974.

ILHAN K, KEVIN P T, JANNICK P R. 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. http://cdmd.cnki.com.cn/article/cdmd-80139-1014263819.htm

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)

OZAN C, ILHAN K, GREGORY E F, et al.. Application of radial basis functions to represent optical freeform surfaces[J]. SPIE-OSA, 2010, 7652:76520A-1.

OZAN C, GREGORY E F, HASSAN F, et al.. Meshfree approximation methods for free-form surface representation in optical design with applications to head-worn displays[J]. SPIE, 7061:70610D.

OZAN C, BRENDAN M, HASSAN F, et al.. Optimal local shape description for rotationally non-symmetric optical surface design and analysis[J]. Optical Express, 2008, 16(3):1583-1589.

OZAN C, SOPHIE V, HASSAN F, et al.. Application of radial basis functions to shape description in a dual-element off-axis magnifier[J]. Optical Letter, 2008, 33(11):1237-1239.

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):1954-1964.

ZHAO X, ZHENG Y, ZHANG Z, et al.. Characterization of freeform optical surfaces based on surface slope[J]. Opt. Precision Eng., 2015, 23(7):1954-1964.(in Chinese)

张博, 王凌, 常伟军, 等.头盔显示器自由曲面光学组件的优化设计[J].应用光学, 2014, 35(2):193-197.

ZHANG B, WANG L, CCHANG W J, et al.. Optimal design of free-form-surface optical component in helmet mounted display[J].Journal of Applied Optics, 2014, 35(2):193-197.(in Chinese)

晏蕾, 贾平, 洪永丰.红外双视场光学系统的初始结构求解[J].红外, 2011, 32(1):23-26.

YANG L, JIA P, HONG Y F. Design of initial structure of infrared dual field-of-view optical system[J]. Infrared, 2011, 32(1):23-26.(in Chinese)

崔恩坤, 张葆, 洪永丰, 等. PW法对连续变焦光学系统初始结构的求解[J].应用光学, 2014(4):586-591.

CUI E K, ZHANG B, HONG Y F, et al.. Design of initial structure of infrared zoom optical system with PW solution[J]. Journal of Applied Optics, 2014(4):586-591.(in Chinese)

冯婕, 白瑜, 邢廷文, 等. Zernike多项式波面拟合精度研究[J].光电技术应用, 2011, 26(2):31-34.

FENG J, BAI Y, XING T W, et al..Fitting accuracy of wavefront using Zernike polynomials[J]. Electro-Optic Technology Application, 2011, 26(2):31-34.(in Chinese)

孙学真, 苏显渝, 荆海龙, 等.抽样点对基于Zernike多项式曲面拟合精度的影响[J].光学仪器, 2008, 30(4):6-10.

SUN X ZH, SU X Y, XING H L, et al.. The influence of sampling points on the precision of curved surface fitting based on Zernike polynomials[J]. Optical Instruments, 2008, 30(4):6-10.(in Chinese)

谢苏隆. Zernike多项式拟合曲面中拟合精度与采样点数目研究[J].应用光学, 2010, 31(6):943-949.

XIE S L. Sampling point number in curved surface fitting with Zernike polynomials[J]. Journal of Applied Optics, 2010, 31(6):943-949.(in Chinese)

FORBES G W. Shape specification for axially symmetric optical surfaces[J].Opt. Express, 2007, 15:5218-5226.

FORBES G W. Robust, efficient computational methods for axially symmetric optical aspheres[J]. Opt. Express, 2010, 18:19700-19712.

OZAN C, BRENDAN M, HASSAN F, et al.. Optimal local shape description for rotationally non-symmetric optical surface design and analysis[J]. Optical Express, 2008, 16(3):1583-1589.

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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