| 基于一阶泰勒展开式的迭代最小二乘相移新算法 |
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| 引用本文： | 郭红卫,陈明仪,韦春龙. 基于一阶泰勒展开式的迭代最小二乘相移新算法[J]. 光学学报, 2001, 21(1) |
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| 作者姓名： | 郭红卫 陈明仪 韦春龙 |
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| 作者单位： | 1. 上海大学(延长校区)精密机械工程系， 上海 200072
2. 上海大学(延长校区)通信工程系， 上海 200072 |
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| 摘 要： | 提出了一种新的最小二乘迭代算法 ,能有效消除因相移器存在导向误差面使相移平面倾斜从而导致的相移误差。当相移器存在的相移误差包括位移误差与倾斜误差时 ,同一幅干涉图诸像素点的相移并不同步 ,但其相移量在同一平面上。求解此平面 ,即可消除相移误差。通过求解由一阶泰勒展开式得到的线性方程组 ,避免了为求解此平面而求解非线性方程组最小二乘解的过程 ,使算法简化。利用迭代法 ,保证求解的精度。并通过数值模拟 ,验证了这种算法在消除较大的相移器倾斜及位移误差影响上具有良好的效果。
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| 关 键 词： | 相移干涉术 相移误差 最小二乘解 迭代法 |
A New Algorithm by Iterative Least-Squares Fitting Based on the First Order Taylor Series Expansion in Phase Shifting Interferometry |
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| Guo Hongwei ) Chen Mingyi ) Wei Chunlong ) ),Precision Mechanical Engineering Department,Shanghai University,Shanghai ),Telecommunication Engineering Department,Shanghai University,Shanghai. A New Algorithm by Iterative Least-Squares Fitting Based on the First Order Taylor Series Expansion in Phase Shifting Interferometry[J]. Acta Optica Sinica, 2001, 21(1) |
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| Authors: | Guo Hongwei ) Chen Mingyi ) Wei Chunlong ) ) Precision Mechanical Engineering Department Shanghai University Shanghai ) Telecommunication Engineering Department Shanghai University Shanghai |
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| Affiliation: | Guo Hongwei 1) Chen Mingyi 1) Wei Chunlong 2) 1),Precision Mechanical Engineering Department,Shanghai University,Shanghai 200072 2),Telecommunication Engineering Department,Shanghai University,Shanghai 200072 |
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| Abstract: | A new algorithm by iterative least squares fitting in phase shifting interferometry is presented. If the reference mirror has tilt and piston errors caused by phase shifting, the phase shifts of the pixels along the same interferogram are not a constant, but they are still kept on the same plane. So solving this plane can eliminate the errors. The first order Taylor series expansion replaces the non linear equation used in solving this plane, and thus simplifies the algorithm. By iterative, the accuracy can be guarantied. The validity of this algorithm has been examined by means of computer simulation. |
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| Keywords: | phase shifting interferometry phase shifting errors least squares fitting iterative |
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