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基于Forbes多项式的光学自由曲面面形描述方法研究

时间:2018-08-07 20:51来源:毕业论文
针对拟合误差主要在曲面边缘的问题,在归一化半径中引入修正因子,提高了面形描述能力;提出用协方差矩阵法完成 Forbes多项式系数的拟合,提高了运算效率;提出用二阶算子梯度变

与传统光学元件相比,自由曲面光学元件能有效校正几乎所有像差,而且还能减轻光学系统的结构,显著提升了光学系统的性能。光学自由曲面是非旋转对称的,其表面梯度变化比较复杂,对其面形的准确描述比较困难。本文将基于 Forbes 多项式研究光学自由曲面面形描述方法。26724
本文针对拟合误差主要在曲面边缘的问题,在归一化半径中引入修正因子,提高了面形描述能力;提出用协方差矩阵法完成 Forbes多项式系数的拟合,提高了运算效率;提出用二阶算子梯度变化率 pv值作为曲面面形的评价指标,通过仿真分析得出了Forbes多项式的适应性。  
重庆时时彩的规律关键词  自由曲面  曲面拟合  Forbes 多项式   协方差矩阵法
Title        Characterizing the shape of freeform optics based on Forbes polynomial
 Abstract
Compared with the traditional optical element, freeform optical element can
correct almost all image aberrations effectively as well as relieve  optical
system structure, and it significantly improve the performance of optical
system. The freeform optical surface is non-rotationally symmetric, its surface
gradient changes intricately, so it is difficult to characterize its surface.
In the paper, I  will research the method of characterizing the shape of freeform
optical surface based on Forbes polynomial.
Because the  fitting error is mainly on the edge of the surface, the paper
introduces a correction factor into the normalized radius to enhance the ability
of shape description.  Then covariance matrix method is taken to fit Forbes
polynomial, and it improves the operation efficiency. Finally, the second-order 源自:六-维!论*文`网.加7位QQ3249`114 重庆时时彩的规律 www.mamitama.com
operator that the peak-valley value of gradient change rate is proposed to be
the evaluation index of surface, and the adaptability is obtained by simulation analysis.   
Keywords    freeform surface    curve fitting    Forbes polynomial  covariance matrix method
 目   次  
1  绪论  1
1.1   研究的目的与意义  1
1.2   光学自由曲面描述方法  1
1.3   论文的主要内容  3
2  对Forbes多项式的研究与改进  4
2.1    Forbes多项式结构模型   4
2.2    Forbes 多项式各参数的计算  5
2.3    Forbes 多项式的改进   7
2.4   本章小结  9
3    Forbes多项式系数拟合算法研究   10
3.1   最小二乘法  10
3.2    Gram-Schmidt 正交法11
3.3   协方差矩阵法  11
3.4    Householder 变换法  12
3.5   拟合算法的优化  13
3.6  本章小结  14
4    Forbes 多项式的适应性分析  15
4.1    适应性分析  15
4.2    仿真试验分析  17
4.3    本章小结  20
结论    21
致谢    22
参考文献23
 1  绪论
1.1  研究的目的与意义
近年来,光学系统飞速发展,传统的光学曲面元件已越来越无法满足人们对光学系统性
能的要求。与传统的球面、非球面光学元件相比,自由曲面光学元件能为光学设计人员提供
更多的“自由度”,能消除几乎所有像差,并且使得系统结构简化,被广泛地应用于照明、显 源自:六-维!论*文`网.加7位QQ3249`114 重庆时时彩的规律 www.mamitama.com
示和生物医学等各种领域[1-4]
。然而,与上述应用相比,在更能体现光学技术价值的成像领域, 基于Forbes多项式的光学自由曲面面形描述方法研究:重庆时时彩的规律/a/wuli/20180807/20989.html
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