NLSF算法非线性最小二乘法测量球面曲率半径的研究
摘要：光学检测技术的迅猛发展大大促进了光学元器件性能的提高。球面是光学元件常见的一种面形，曲率半径无疑又是决定球面元件性能的一个重要参量。本文阐述了曲率半径的几种常用测量方法以及他们的优缺点，并在此基础上研究和论述了基于单幅干涉图进行球面曲率半径测量的非线性最小二乘拟合（Non-linear least square fitting，NLSF）算法。实验采用牛顿环装置，通过CCD和视频图像卡记录单幅数字化干涉图，并根据NLSF算法对采样得到的条纹离散极值点进行处理，由此得到一次测量结果。实验进行了三次重复测量，所得最终结果的相对误差为2%。结果表明，采用NLSF算法测量曲率半径不仅是可行的，更有利于提高单幅干涉图下测量的准确度。67119
毕业论文关键词 ：牛顿环 最小二乘法 曲率半径
毕业设计说明书（论文）外文摘要
Title Measurement the radius of the curvature of a spherical surface based on the non-linear least square fitting
Abstract: The rapid development of modern optical test techniques has greatly promoted the properties of optical components Spherical optical element is one with a common surface shape The radius of curvature of an optical element is undoubtedly an important parameter affecting the performance of the optical element This article describes the radius of curvature of several common measurement methods and their advantages and disadvantages, and after that introduces an algorithm of non-linear least square fitting (NLSF) for measuring the radius of curvature of a spherical surface based on a single interferogram During the measurement, a Newton Ring set-up is used With a CCD and an image card, a single digital interferogram is obtained, and is then processed with NLSF Thus a measurement result is obtained All in all three measurements are conducted, with the relative error of the final result as 2% This result indicates that, the NLSF algorithm is not only applicable to the measurement of the radius of the spherical surface, but also advantageous to raising the accuracy in the case of single interferogram measurement
Keywords ：Newton rings least square fitting radius of curvature
目次
1 引言 1
11 本文的研究背景与意义 1
12 球面曲率半径测量方法综述 2
121 环式球径仪测量球面的曲率半径 2
122 自准直显微镜法测量球面的曲率半径 3
123 基于干涉测量的零条纹法 4
124 球面样板法 5
125 移相干涉法 6
126 虚光栅移相莫尔条纹法 6
127 其它测量方法 7
13 本文采用的方法及所做的工作 8
2 实验原理 9
21 非线性最小二乘法拟合的数学模型 9
211 非线性最小二乘法模型 9
212牛顿-高斯迭代法 9
22 牛顿环干涉测量球面曲率半径的原理 10
3 实验装置和调节步骤 14
31 CCD图像采集系统 14
32 实验装置与调节步骤 16
4 实验数据及处理结果