连续镜面可变形镜面形的正交多项式描述

李舒阳; 郝群; 程雪岷

doi:10.3788/OPE.20152313.0008

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连续镜面可变形镜面形的正交多项式描述

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- 连续镜面可变形镜面形的正交多项式描述
- Description of continuous surface deformable mirrors by using orthogonal polynomials
- 光学精密工程 2015年23卷第10z期页码：8-15
- 作者机构：
  
  1. 北京理工大学光电学院北京,中国,100081
  2. 清华大学深圳研究生院,广东深圳,518055
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(No.61275003,No.51327005)()
- DOI：10.3788/OPE.20152313.0008
  中图分类号： TH703;TP302.7
- 收稿日期：2015-06-22，
  
  修回日期：2015-07-10，
  
  纸质出版日期：2015-11-14
- 稿件说明：
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李舒阳, 郝群, 程雪岷. 连续镜面可变形镜面形的正交多项式描述[J]. 光学精密工程, 2015,23(10z): 8-15

LI Shu-yang, HAO Qun, CHENG Xue-min. Description of continuous surface deformable mirrors by using orthogonal polynomials[J]. Editorial Office of Optics and Precision Engineering, 2015,23(10z): 8-15
李舒阳, 郝群, 程雪岷. 连续镜面可变形镜面形的正交多项式描述[J]. 光学精密工程, 2015,23(10z): 8-15 DOI： 10.3788/OPE.20152313.0008.

LI Shu-yang, HAO Qun, CHENG Xue-min. Description of continuous surface deformable mirrors by using orthogonal polynomials[J]. Editorial Office of Optics and Precision Engineering, 2015,23(10z): 8-15 DOI： 10.3788/OPE.20152313.0008.

摘要

以压电可变形镜(PDM)和微机械薄膜可变形镜(MMDM)为例

讨论了准确描述连续镜面面形的方法。比较了基于Zernike多项式和

多项式的面形描述方法在不同参数条件下的准确度

探讨了高阶项对于提升拟合精度的作用。令单个或多个驱动器作用

分别获得了PDM和MMDM的面形数据各5组。然后

以采样点数和多项式阶数为变量

采用5种采样点阵的分布形式

分别用Zernike多项式和

多项式对获得的10组面形进行最小二乘拟合。实验结果显示:与其他4种均布采样形式相比

边缘聚类采样更有利于提升拟合精度;与Zernike多项式拟合相比

多项式在超过40阶的拟合中残差更小;添加20至80阶多项式用于拟合时

残差的均方根(RMS)值保持在1×10

-5

mm数量级

而靠近孔径中心的区域的残差明显降低。得到的结论有助于在变形镜应用中选取拟合参数

以便准确描述面形

提高波前控制精度。

Abstract

By taking a piezoelectric Deformable Mirror (PDM) and a Micromachined Membrane Deformable Mirror (MMDM) as examples

a method to accurately characterize the surface of continuous surface deformable mirrors was discussed. The description characteristics of Zernike polynomial and

polynomial methods using different fitting parameters were compared and the influence of higher polynomial terms on fitting accuracy was researched. By activating one or more actuators

the two groups of five surface data were obtained for PDM and MMDM respectively. Then

the number of sampling points and the number of polynomial orders were set as variables. The ten surface data were fitted using the least square method based on five types of sampling grids;either the Zernike polynomial and

polynomial were adopted. The experimental results show that the edge-clustered sampling grid outperforms the four uniform grids in terms of fitting accuracy. The

-polynomial fits produce smaller fitting residuals than Zernike fits when the polynomial order goes beyond 40. Moreover

the RMS(Root-Mean-Square)of fitting residuals stays in the 1×10

-5

mm order of magnitude when the polynomial order increases from 10 to 80

while the residuals away from the aperture edge decrease significantly. The above results can guide the choice of fitting parameters in deformable mirror applications

describe the surface characteristics of deformable mirrors and improve wavefront control accuracy.

关键词

Keywords

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