非旋转对称相位函数的拟合方法研究+Forbes函数
关键词 自由曲面 拟合相位 最小二乘法 Gram-Schmidt正交法 Forbes函数
毕业设计说明书（论文）外文摘要
Title The research of Fitting method for Non-rotationally unsymmetric Phase function
Abstract
In recent years, the asphere has be a wide range of applications, as it’s unparalleled performance. But the difficulty for this free-form surface machining and inspenction is much larger than usual symmetric non-spherical. This paper mainly to solve the description of a free surface. The work I have done is to research the fitting algorithm to fit the free surface, use these algorithms model to fit the non-rotationally unsymmetric phase function, and then use the result of the to analyze the advantages and disadvantages of these method. There are three method, the least squares method, the Gram-Schmidt orthogonalization and Forbes function, which focus on the Forbes function. This project has a conclusion as a least squares method for precision is not very high and the free surface of the central error of less demanding. Gram-Schmidt orthogonal method is also applicable to the surface accuracy is not high, Forbes function of the relative accuracy is much higher, but the algorithm is relatively complex, precision controlled, with the change of the number of items the location of the maximum error will appear to drift.
Keywords Free-form surface, fitting phase polynomial, least squares method, the Gram-Schmidt orthogonalization method, Forbes function
目 次
1绪论 1
1.1课题的来源与背景 1
1.3本课题研究的内容 3
2自由曲面技术以及曲线拟合方法 4
2.1自由曲面简介 4
2.2自由曲面的定义 4
2.3曲线拟合方法 5
2.4 Zernike多项式[16-18] 5
3自由曲面面形的描述方法 8
3.1最小二乘法 8
3.2 Gram-Schmidt正交法 14
4Forbes函数[19-29] 19
4.1 Forbes函数的提出 19
4.2 Forbes函数的意义 19
4.3 Forbes函数的描述方法 19
5对于自由曲面面形的几种描述方法的比较 33
5.1最小二乘法的拟合结果 33
5.2 Gram-Schmidt正交基的拟合结果 34
5.3 Forbes函数的拟合结果 35
5.4 本章小结 36
结论 38
致谢 39
参考文献 40
1绪论
1.1课题的来源与背景