Absolute interferometric testing of mid-spatial frequency wavefront by rotation and displacement technique

QUAN Qun; GAO Zhi-shan; ZHANG Cong-yang; CHENG Jin-long; ZHU Bo

doi:10.3788/OPE.20132103.0652

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Absolute interferometric testing of mid-spatial frequency wavefront by rotation and displacement technique

更新时间：2020-08-12

- Absolute interferometric testing of mid-spatial frequency wavefront by rotation and displacement technique
- Optics and Precision Engineering Vol. 21, Issue 3, Pages: 652-663(2013)
- 作者机构：
  
  南京理工大学电子工程与光电技术学院
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20132103.0652
  CLC： O436.1
- Received：24 August 2012，
  
  Revised：15 November 2012，
  
  Published Online：20 March 2013，
  
  Published：15 March 2013
- 稿件说明：
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袁群高志山张聪旸成金龙朱波. 中频波面的旋转平移法干涉绝对检验[J]. 光学精密工程, 2013,21(3): 652-663

QUAN Qun GAO Zhi-shan ZHANG Cong-yang CHENG Jin-long ZHU Bo. Absolute interferometric testing of mid-spatial frequency wavefront by rotation and displacement technique[J]. Editorial Office of Optics and Precision Engineering, 2013,21(3): 652-663
袁群高志山张聪旸成金龙朱波. 中频波面的旋转平移法干涉绝对检验[J]. 光学精密工程, 2013,21(3): 652-663 DOI： 10.3788/OPE.20132103.0652.

QUAN Qun GAO Zhi-shan ZHANG Cong-yang CHENG Jin-long ZHU Bo. Absolute interferometric testing of mid-spatial frequency wavefront by rotation and displacement technique[J]. Editorial Office of Optics and Precision Engineering, 2013,21(3): 652-663 DOI： 10.3788/OPE.20132103.0652.

摘要

基于Zernike多项式拟合的传统干涉绝对检验方法由于平滑了波面和丢失了中频成分，仅可以实现面形误差的绝对检验。本文提出利用旋转平移法来实现中频波面的干涉绝对检验。将被测波面分解成旋转对称成分和旋转非对称成分，通过N次旋转被测件，求解波面中的旋转非对称成分；通过平移被测件实现伪剪切，求解波面中的旋转对称成分。与传统绝对检验方法相比，该方法既能够恢复整个波面，又不需要对整个波面进行Zernike多项式拟合；由于仅对旋转对称成分用偶次多项式进行提取，提升了计算速度，降低了拟合误差，保留了中频成分

数值仿真显示其比传统方法优越，测量精度可达到1 nm rms。在ZYGO干涉仪上完成了平面元件的干涉绝对检验测量。采用改变伪剪切比和更换标准镜两种方案，分别实现了实验数据的自比对；将测试结果与经典三面互检法得到的水平和垂直方向的一维轮廓数据进行比对，验证了旋转平移法的准确性。

Abstract

Traditional absolute interferometric testing methods are all based on Zernikes polynomial fitting of tested wavefront

where the wavefront is smoothed and the mid-frequency element is lost

so they can only get the real figure of test optics. This paper adopts the rotation and displacement technique to the absolute interferometric testing of mid-frequency wavefront. The real wavefront of the test optic is separated into a rotationally symmetric component and a rotationally asymmetric component. The rotationally asymmetric component is determined by rotating the test optics for N times

while the rotationally symmetric component is determined by the pseudo shearing data through displacing the test optics. As compared with traditional absolute interferometric testing methods

there is no need to fit the wavefront of test optics with Zernikes polynomials and can preserve whole wavefront with the proposed method. Because the rotationally symmetric component is retrieved using the even polynomials

the computation speed is enhanced and the fitting error is reduced with the mid-frequency element retained. The numerical simulation shows that the proposed method has much superiority than the traditional method and can achieve the nanometer accuracy. An experimental measurement for a flat surface is carried on with a ZYGO interferometer. The self-comparison of the experimental data is implemented by changing the pseudo shearing ratio and substituting the standard lens and the experimental data is also compared with the horizontal and vertical profiles derived from three-flat testing. Obtained results prove the accuracy of the rotation and displacement technique.

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references

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