摘要传统的接触式轮廓仪在测量非球面表面轮廓时扫描探针会与非球面镜表面直接接触，存在划伤待测元件表面的风险且探针的直径会引入测量误差。为实现非球面镜表面轮廓的非接触式测量，本文研究了基于白光干涉显微镜的非接触式非球面轮廓测量技术，以光学探头扫描非球面镜轮廓并获得各采样点曲率值，从而重建非球面的面形轮廓。
第一，研究了白光干涉显微镜测量曲率半径值的准确性，提出了用最小二乘法拟合面形轮廓的计算方法，测量了标准球面镜等一些具有相应代表性的光学元件的曲率半径值。结果表明，用白光干涉显微镜测量曲率半径值的方法是可靠的。26420
第二，基于白光干涉显微镜测量曲率值，设计了非接触扫描式非球面镜轮廓测量方案。提出了基于曲率半径值使用拟合法进行面形恢复的面形恢复方案，并通过仿真和实验加以验证。
毕业论文关键词：扫描式轮廓检测，非球面镜，白光干涉 毕业设计说明书外文摘要
Title Research on profilometry for asphere with scanning method
Abstract
Contact probe in traditional profilometer may possibly damage aspheric surface and introduce measurement error because of its tip size. In order to measure asphere without contacting aspheric surface, non-contact optical probe based on white-light interferometric microscope was proposed. Scanning the sampling points on the outline to obtain their curvatures so as to reconstruct surface profiles from curvature values.
Firstly, the accuracy of curvature measured by white-light interferometric microscope was studied. Least squares calculation method was proposed to fit the 3D surface profile. Different radius of curvature (ROC) of standard spherical mirrors and probe which is used on profilometer were measured. The test results indicate that ROC measured by white-light interferometric microscope is accurate.
Secondly, non-contact profilometry based on white-light interferometric microscope was proposed. Abscissa values of sampling points on surface profile were modified with coordinate compensation method while surface profile was reconstructed with integral method or fitting method according to curvature values and their abscissa values.
Keywords scanning profilometry， asphere, white-light interferometric
目 次
1 绪论 1
1.1 论文研究背景与意义 1
1.2 国内外研究现状 1
1.2.1 直角坐标轮廓检测 1
1.2.2 摆臂式轮廓测量系统 2
1.2.3 基于曲率测量的非球面轮廓检测 4
1.3 论文主要研究内容及工作 5
2 基于扫描法的非球面轮廓测量方案系统的设计 6
2.1 垂直扫描白光干涉法（VSI）测量原理 6
2.2 基于扫描法的非球面轮廓测量原理 7
2.3 干涉显微镜测量曲率半径值的准确性的研究 8
2.4 本章小结 10
3 实验仿真 11
3.1 仿真综述 11
3.2 由最小二乘法球面拟合求取曲率的仿真 11
3.2.1 最小二乘法拟合 11
3.2.2 最小二乘法算法拟合仿真 13
3.3 由曲率值恢复非球面轮廓的仿真 13
3.3.1 拟合面形恢复算法 14
3.3.2 拟合法面形恢复仿真 14 基于扫描法的非球面轮廓测试研究:http://www.751com.cn/tongxin/lunwen_20604.html