Compensation of astigmatism in coordinate measurement for optical aspheric elements

Xiao-ming FAN; Ci-jin LUO; Xue-ke XU; Ling-qi WU; Chen HU

doi:10.3788/OPE.20162412.3012

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Compensation of astigmatism in coordinate measurement for optical aspheric elements

High Power Laser Optical Componets | 更新时间：2020-08-13

- Compensation of astigmatism in coordinate measurement for optical aspheric elements
- Optics and Precision Engineering Vol. 24, Issue 12, Pages: 3012-3019(2016)
- 作者机构：
  
  1.武汉理工大学材料科学与工程学院, 湖北武汉 430070
  2.中国科学院上海光学精密机械研究所强激光材料重点实验室, 上海 201800
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20162412.3012
  CLC： TH703;TH721
- Received：13 October 2016，
  
  Accepted：17 November 2016，
  
  Published：25 December 2016
- 稿件说明：
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Xiao-ming FAN, Ci-jin LUO, Xue-ke XU, et al. Compensation of astigmatism in coordinate measurement for optical aspheric elements[J]. Optics and precision engineering, 2016, 24(12): 3012-3019.
DOI：

Xiao-ming FAN, Ci-jin LUO, Xue-ke XU, et al. Compensation of astigmatism in coordinate measurement for optical aspheric elements[J]. Optics and precision engineering, 2016, 24(12): 3012-3019. DOI： 10.3788/OPE.20162412.3012.

摘要

利用三坐标测量仪在光学非球面镜研磨与粗抛阶段进行面形检测时，测量结果常由于补偿程序不完善而出现像散误差。本文分析了非球面三坐标测量得到的数据，指出测量结果中出现像散误差是测头半径补偿不准确所致。然后，提出了一种离线数据处理方法对测量数据进行补偿来消除像散误差。该方法通过计算网格排列的测头中心点行和列方向的切向量得出曲面上每个点的法向矢量；根据测头半径计算出测头球心到接触点的偏移量，从而实现三坐标测量仪的三维测头半径补偿。球面样板实验显示这种方法可以将该样板测量中的像散峰谷值（PV）由4.921 9

m减小到0.065 2

m，基本消除了测量结果中的像散误差，提高了三坐标测量结果的准确度。实验结果验证了提出的三维测头半径补偿程序的有效性。

Abstract

When a three Coordinate Measurement Machine is used to test the surface shape of an aspheric element in grinding and polishing

obtained result often shows astigmatism errors due to an imperfect compensation programming. This paper analyzes these measurement data

and points out that the astigmatism errors comes from the imprecise compensation programming for the radius of three-dimensional probe in the CMM. Then

It presents an off-line data processing method to compensate the measurement data and to eliminate the astigmatism. By calculation of the tangent vectors of row and column at the meshed central point

the normal vector of each point on the surface is obtained. By calculation of the offsets between the centers of probe and the contact points

the radius of the tree-dimensional probe in the CMM is compensated. The experiment of a standard sphere show that this method decreases the astigmatism PV (Peak-to-Valley) of the measurement result from 4.921 9 μm to 0.065 2 μm

eliminating basically the astigmatism errors and improving the accuracy of the coordinate measurement. Obtained results verify the effectiveness of the proposed compensation programming for the radius of tree-dimensional probe in the CMM.

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references

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