Measuring multi-surface shape by Fourier transform

Jing-wei LI; Chang-lun HOU

doi:10.3788/OPE.20192706.1277

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Measuring multi-surface shape by Fourier transform

Life Science Instrument | 更新时间：2020-08-13

- Measuring multi-surface shape by Fourier transform
- Optics and Precision Engineering Vol. 27, Issue 6, Pages: 1277-1285(2019)
- 作者机构：
  
  杭州电子科技大学电子信息学院，浙江杭州 310000
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20192706.1277
  CLC： O438;TN247
- Received：15 November 2018，
  
  Accepted：07 January 2019，
  
  Published：15 June 2019
- 稿件说明：
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Jing-wei LI, Chang-lun HOU. Measuring multi-surface shape by Fourier transform[J]. Optics and precision engineering, 2019, 27(6): 1277-1285.
DOI：

Jing-wei LI, Chang-lun HOU. Measuring multi-surface shape by Fourier transform[J]. Optics and precision engineering, 2019, 27(6): 1277-1285. DOI： 10.3788/OPE.20192706.1277.

摘要

为了更简便、准确地测量透明平行板，提出了一种基于区域生长算法与傅里叶变换的单幅三表面干涉条纹相位恢复方法。通过傅里叶变化将三表面干涉条纹图由空域变化到频谱域。不同表面的干涉条纹在频谱域中对应的位置不同，通过改变区域生长算法中的参数，提取出合适的区域，最终得到面形。该方法可以由单幅三表面干涉条纹图同时得到透明平行板前后两个表面的面形。分析了由算法求得的表面面形的误差，通过叠加分离的双表面干涉图与原三条纹图进行比较，得到相应的误差分布图，通过误差分布图可以改善算法的精度。将得到的面形与Zygo干涉仪得到的面形进行对比，发现该方法测量精度较高，其相位提取误差PV值小于0.12

，RMS值小于0.065

；重复性得到验证，其重复率可靠度优于

/100。测量到的面形与物体真实面形接近，测量方法更加简便。

Abstract

To measure transparent parallel plates more easily and accurately

a phase recovery method based on the region growing algorithm and Fourier transform for single three-surface interference fringes was proposed. Through the Fourier transform

the three-surface interference fringe pattern was changed from the spatial to the spectral domain. Because the interference fringes of different surfaces have different positions in the spectral domain

the appropriate regions were extracted by changing the parameters in the region-growing algorithm

and the final surface was obtained. By this method

the planar shapes of the front and rear surfaces of the transparent parallel plate can be simultaneously obtained from a single three-surface interference fringe pattern. From an error analysis of the surface shapes obtained by the algorithm

a superimposed and separated double-surface interferogram was compared with the original three-striped graph to obtain the corresponding error distribution graph. The accuracy of the algorithm was improved through the error distribution graph. A comparison of the obtained surface shapes with that obtained by a Zygo interferometer reveals that the method had high measurement accuracy with a phase extraction error PV value of less than 0.12

and a Root Mean Square(RMS) value of less than 0.065

. A verification of the repeatability shows that the repetition rate is reliable

and the degree is better than

/100. The measured surface shape approximated the real surface shape of the object

and the measurement method proved to be simpler than the original method.

关键词

Keywords

references

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