Ritchey-Common interferometry using unit-excitation influence matrix's numerical calculation method

Yi-ming LIU; Jin-peng LI; Lei CHEN; Dong-dong LIN; Feng-hua ZHENG

doi:10.3788/OPE.20182604.0771

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Ritchey-Common interferometry using unit-excitation influence matrix's numerical calculation method

Modern Applied Optics | 更新时间：2020-07-05

- Ritchey-Common interferometry using unit-excitation influence matrix's numerical calculation method
- Optics and Precision Engineering Vol. 26, Issue 4, Pages: 771-777(2018)
- 作者机构：
  
  1.南京理工大学电光学院, 江苏南京 210094
  2.中国科学院南京天文仪器有限公司, 江苏南京 210042
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20182604.0771
  CLC： TH741
- Received：06 December 2017，
  
  Accepted：09 January 2018，
  
  Published：25 April 2018
- 稿件说明：
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Yi-ming LIU, Jin-peng LI, Lei CHEN, et al. Ritchey-Common interferometry using unit-excitation influence matrix's numerical calculation method[J]. Optics and precision engineering, 2018, 26(4): 771-777.
DOI：

Yi-ming LIU, Jin-peng LI, Lei CHEN, et al. Ritchey-Common interferometry using unit-excitation influence matrix's numerical calculation method[J]. Optics and precision engineering, 2018, 26(4): 771-777. DOI： 10.3788/OPE.20182604.0771.

摘要

在影响矩阵法瑞奇-康芒检验中，恢复被测面形的关键在于构建被检平面面形误差与系统波像差之间的Zernike系数影响矩阵。为了提高瑞奇-康芒法的检测精度，研究了采用单位激励法来精确计算影响矩阵的方法。分别重构平面镜仅包含某一种Zernike波像差下的系统波像差分布，经Zernike拟合得到该种Zernike像差的影响系数向量；由各Zernike像差的影响系数向量组成影响矩阵，然后用最小二乘拟合出被检平面面形。对口径为90 mm的平面镜进行实际检验，在瑞奇角为26.5°与40.6°的情况下进行波前恢复，得到被检平面镜PV值为0.141 3λ，RMS为0.019 4λ。与直接采用平面参考镜检测相比，瑞奇-康芒法检测误差PV值为0.082 8λ，RMS为0.010 9λ。该方法能够精确生成影响矩阵，抑制了影响矩阵法中对大

数的依赖，可用于精确恢复平面镜面形。

Abstract

Calculating the influence matrix between surface error and wavefront aberration is a key step in the Ritchey-Common test. A method that uses unit-excitation operation to calculate the influence matrix with high accuracy was studied in order to improve the precision of the test. It retrieves the system wavefront aberration when the flat mirror concludes only one kind of Zernike aberration

and obtains the influence coefficient vector through Zernike fitting. The influence matrix is formed from the coefficient vectors of all the Zernike aberrations. Least square fitting is then used to reconstruct the surface shape of the tested mirror. After reconstructing the wavefront with Ritchey angles of 26.5° and 40.5°

the test results show PV and RMS values of 0.1413λ and 0.0194λ respectively for the

90 mm flat mirror. Compared to the results from direct testing

the PV and RMS error in the Ritchey-Common method are 0.0828λ and 0.0109λ

respectively. This method can calculate the influence matrix accurately

eliminate the dependence on the big

-number in traditional influence matrix methods and can reconstruct the surface shape with high precision.

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Keywords

references

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