Laser & Optoelectronics Progress, Volume. 60, Issue 23, 2312001(2023)

Absolute Measurement of Rectangular Flat Mirrors Using a Unidirectional Multi-Shifted Method

Guang Zhou1,3, Weizheng Lei2, Xiaohao Dong1,2、*, and Jie Wang1,2
Author Affiliations
  • 1Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China
  • 2Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China
  • 3University of Chinese Academy of Sciences, Beijing 100049, China
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    With the development of advanced light sources, surface smoothness is becoming crucial for large-sized and high-precision mirrors. In this study, a two-dimensional (2D) absolute metrology method is developed that is based on the laser interferometer translational shear method for high aspect ratio rectangular flat mirrors used in X-rays. In this method, translational measurements in orthogonal directions are replaced with multiple shifted measurements in a single direction. In addition, a multi-matrix augmented zonal method reconstruction algorithm is derived to obtain the absolute surface shape of high-precision rectangular flat mirrors. Through simulations, the root mean square (RMS) of the residuals between the reconstructed absolute surface shape and initial surface shape is 0.03 nm (~λ/20000) without considering noise. Surface shape recovery under different numbers of translations and translation distances when considering Gaussian noise is then simulated and analyzed, and an experimental verification is performed for a rectangular plane mirror of 120 mm×40 mm. The measured absolute surface shape recovery is determined as 1.07 nm (λ/591) using the RMS of the absolute surface shape residual obtained by the three-plane method. Both simulations and experiments show that the proposed method can effectively obtain the 2D absolute surface shape of a high-precision rectangular planar mirror. Unidirectional translation thus lays the foundation for establishing multi-aperture stitching measurements based on absolute measurements.

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    Guang Zhou, Weizheng Lei, Xiaohao Dong, Jie Wang. Absolute Measurement of Rectangular Flat Mirrors Using a Unidirectional Multi-Shifted Method[J]. Laser & Optoelectronics Progress, 2023, 60(23): 2312001

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    Paper Information

    Category: Instrumentation, Measurement and Metrology

    Received: Nov. 8, 2022

    Accepted: Dec. 29, 2022

    Published Online: Dec. 8, 2023

    The Author Email: Dong Xiaohao (dongxiaohao@zjlab.org.cn)

    DOI:10.3788/LOP222992

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