• Laser & Optoelectronics Progress
  • Vol. 60, Issue 23, 2312001 (2023)
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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    DOI: 10.3788/LOP222992 Cite this Article Set citation alerts
    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 Copy Citation Text show less

    Abstract

    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.
    M0x+p0,y=S0(x+p0,y)+R0(x,y)M1x+p1,y=S1(x+p1,y)+R1(x,y)M2x+p2,y=S2(x+p2,y)+R2(x,y)MNx+pN,y=SN(x+pN,y)+RN(x,y)
    M=M0M1M2MNT=R1,1+S1,1R1,m+S1,mRn,1+Sn,1Rn,m+Sn,mR1,2+S1,1R1,m+S1,m-1Rn,2+Sn,1Rn,m+Sn,m-1R1,m+S1,1Rn,m+Sn,1T
    C[KW+(m+1)W,KW+W]=1C[KW+(m+1)W,KW+m]=1KW=1,2,,m-W ,
    CZ=M,Z=RS
    100010000100010000100010000100010000000001001000001000000001001000011000R1,1R1,2R1,n-1R1,nR2,1R2,2R2,n-1R2,nRm,1Rm,2Rm,n-1Rm,nS1,1S1,2S1,n-1S1,nS2,1S2,2S2,n-1S2,nSm-1,1Sm-1,2Sm-1,n-1Sm-1,nSm,1Sm,2Sm,n-1Sm,n=M1,1M1,2M1,n-1M1,nM2,1M2,2M2,n-1M2,nMm-1,1Mm-1,2Mm-1,n-1Mm-1,nMm,1Mm,2Mm,n-1Mm,nM1,1M1,2M1,n-1M1,nMm-1,1Mm-1,2Mm-1,n-1Mm-1,nM1,1M1,2M1,n-1M1,nMm-2,1Mm-2,2Mm-2,n-1Mm-2,mM1,1M1,1M1,1M1,1M2,1M2,2M2,n-1M2,nM1,1M1,2M1,n-1M1,n
    Z=CTC-1CTM
    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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