Zernike圆域多项式镜面拟合仿真与精度研究

郭良贤; 卫俊杰; 唐培

光学与光电技术, 2018, 16 (6): 56, 网络出版: 2018-12-17

Zernike圆域多项式镜面拟合仿真与精度研究

Fitting Simulation and Precision of Mirror Surface With Zernike Circular Polynomial

论文大纲

郭良贤 ^1,*卫俊杰 ²唐培 ¹

作者单位

¹ 华中光电技术研究所—武汉光电国家研究中心, 湖北武汉 430223

² 上海航天控制技术研究所, 上海 201109

摘要

引入光机热集成分析利于综合考虑红外光学系统在多种物理场综合作用下的性能变化,Zernike圆域多项式作为光机热集成分析中的数据转换接口,是实现光、机、热各分析软件间数据有效传递的重要手段。采用不完全归纳法,针对常见的三种镜面面形(二次曲面、球面、自由曲面)研究了采样点数目和Zernike圆域多项式项数对拟合曲面的精度影响。仿真结果表明：不同曲面类型所需要的多项式项数不同,多项式项数对曲面拟合精度的影响权重要大于采样点数目,过多的多项式项数会导致拟合精度下降甚至出现病态矩阵。最后通过设计实例对Zernike圆域多项式拟合算法和精度进行了验证。

Abstract

The thermal/structural/optical(TSO) integrated analysis will be propitious to evaluate the performance change of infrared optical system under the multi-physical field influence. Zernike circular polynomial is an important means which can implement data effective transmission among thermal, structural and optical analysis program. The method of inadequate induction is used to obtain the relation between sampling point number, Zernike circular polynomial term number and fitting precision, according to three common surfaces (quadric, sphere, free-form surface). The simulated results show that different polynomial terms are required for different surface types. The influence of polynomial terms on surface fitting precision is greater than the number of sampling points. Too many polynomial terms will lead to the decrease of fitting precision and even the appearance of ill-conditioned matrix. Finally, the algorithm and accuracy of Zernike circular polynomial fitting are verified by a design example.

参考文献

[1] 武耀, 徐明明, 陈素娟, 等. 光机热集成分析在高光谱成像仪紫外镜头中的应用［J］. 应用光学, 2016, 37(2): 262-266.

WU Yao, XU Ming-ming, CHEN Su-juan, et al. Application of thermal/structural/optical integrated analysis to ultraviolet lens of hyperspectral imaging spectrometer［J］. Journal of Applied Optics, 2016, 37(2): 262-266.

[2] 左滕, 吴耀. 中波红外镜头光机热集成设计分析研究［J］. 光学与光电技术, 2016, 14(3): 67-72.

ZUO Teng, WU Yao. Integrated opto-mechanical-thermal design and analysis of mid-wave infrared lens［J］. Optics & Optoelectronic Technology, 2016, 14(3): 67-72.

[3] 陈驰, 董亭亭, 潘海俊. 光致热效应的光机热集成分析方法［J］. 光学与光电技术, 2015, 13(3): 64-70.

CHEN Chi, DONG Ting-ting, PAN Hai-jun. Opto-thermal-mechanicial integrated analysis method for opto-thermal effects［J］. Optics & Optoelectronic Technology, 2015, 13(3): 64-70.

[4] 李彪, 潘海俊. 基于半导体非均匀内热源的工程求解分析［J］. 光学与光电技术, 2016, 14(2): 18-21.

LI Biao, PAN Hai-jun. Engineering analysis on nonuniform internal generation based on thermocouple［J］. Optics & Optoelecronic Technology, 2016, 14(2): 18-21.

[5] R R Shannon, J C Wyant. Applied Optics and Optical Engineering VIII［M］. San Diego: Academic Press, 1980.

[6] R J Noll. Zernike polynomials and atmospheric turbulence［J］. J. Opt. Soc. Am., 1976, 66(3): 207-211.

[7] G W Forbes. Characterizing the shape of freeform optics［J］. Opt. Express, 2012, 20(3): 2483-2499.

[8] O Cakmakci, Sophie Vo, H Foroosh, et al. Application of radial basis functions to shape description in a dual-element off-axis magnifier［J］. Opt. Lett., 2008, 33(11): 1237-1239.

[9] 叶井飞, 高志山, 刘晓莉, 等. 基于Zernike多项式和径向基函数的自由曲面重构方法［J］. 光学学报, 2014, 34(8): 08822003-1-9.

YE Jing-fei, GAO Zhi-shan, LIU Xiao-li, et al. Freeform surfaces reconstruction based on Zernike polynomials and radial basis function［J］. Acta Optica Sinca, 2014, 34(8): 08822003-1-9.

[10] 张齐元, 韩森, 唐寿鸿, 等. 透射波前Zernike系数与波长的函数关系研究［J］. 光学学报, 2018, 38(2): 0212002-1-8.

ZHANG Qi-yuan, HAN Sen, TANG Shou-hong, et al. . Study on functional relationship between transmitted wavefront Zernike coefficients and wavelengths［J］. Acta Optica Sinica, 2018, 38(2): 0212002-1-8.

[11] 王永伟, 艾华, 卓仁善, 等. 干涉测量波面重构DCT算法研究［J］. 中国光学, 2014, 7(6): 1012-1018.

WANG Yong-wei, AI Hua, ZHUO Ren-shan, et al. Wavefront reconstruction of interferometry by DCT algorithm［J］. Chinese Optics, 2014, 7(6): 1012-1018.

[12] 徐广州, 阮萍. 光机集成仿真前处理中点云边界检测技术［J］. 红外与激光工程, 2016, 45(4): 0428001-1-6.

XU Guang-zhou, RUAN Ping. Point cloud boundary detection in preprocessor of optical-mechanical integrated simulation［J］. Infrared and Laser Engineering, 2016, 45(4): 0428001-1-6.

[13] 杨怿, 张伟, 陈时锦. 光机热集成分析中数据转换接口的研究［J］. 宇航学报, 2005, 26(2): 202-205.

YANG Yi, ZHANG Wei, CHEN Shi-jin. Study on data transmission tool for thermal/structural/optical integrated analysis［J］. Journal of Astronautics, 2005, 26(2): 202-205.

[14] 冯婕, 白瑜, 邢廷文. 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 Jie, BAI Yu, XING Ting-wen. Fitting accuracy of wavefront using Zernike polynomials［J］. Electro-Optic Technology Application, 2011, 26(2): 31-34.

郭良贤, 卫俊杰, 唐培. Zernike圆域多项式镜面拟合仿真与精度研究[J]. 光学与光电技术, 2018, 16(6): 56. GUO Liang-xian, WEI Jun-jie, TANG Pei. Fitting Simulation and Precision of Mirror Surface With Zernike Circular Polynomial[J]. OPTICS & OPTOELECTRONIC TECHNOLOGY, 2018, 16(6): 56.

Zernike圆域多项式镜面拟合仿真与精度研究

关于本站 Cookie 的使用提示

全站搜索

Zernike圆域多项式镜面拟合仿真与精度研究

相关论文

相关资讯

关于本站 Cookie 的使用提示

全站搜索