• Laser & Optoelectronics Progress
  • Vol. 62, Issue 9, 0912004 (2025)
Zijin Deng1,2,3, Changwei Li1,2,3, and Sijiong Zhang1,2,3,*
Author Affiliations
  • 1Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, Jiangsu , China
  • 2Key Laboratory of Astronomical Optics & Technology, Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, Jiangsu , China
  • 3University of Chinese Academy of Sciences, Beijing 100049, China
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    DOI: 10.3788/LOP242091 Cite this Article Set citation alerts
    Zijin Deng, Changwei Li, Sijiong Zhang. Measurement of Lens Parameters Using a Shack-Hartmann Wavefront Sensor[J]. Laser & Optoelectronics Progress, 2025, 62(9): 0912004 Copy Citation Text show less

    Abstract

    The focal length, curvature radius, and refractive index of a lens are important parameters that characterize the lens’ performance and are essential for selecting lenses in optical design. This study proposes a lens parameter measurement method based on the Shack-Hartmann wavefront sensor (SHS). First, the reference point for measuring the focal length of the lens under test is determined by evaluating a function that calculates the sum of the least squares of the centroid offsets of the light spots formed by the SHS (LSSCS). The focal length of the lens can then be obtained by measuring the curvature radii of two spherical waves at two different distances from the reference point. The curvature radius of the lens surface is then calculated by determining the coordinate difference between two specific positions. These positions correspond to the points at which the reflected light beam on the lens surface becomes parallel to the incident beam, as determined by the LSSCS evaluation function. Finally, for thin lenses, the refractive index of the tested lens material is calculated using the lens manufacturer’s formula based on the measured focal length and surface curvature radius. The experimental results demonstrate that the lens parameters measured by the proposed method are in excellent agreement with the nominal values. The proposed method offers several advantages, including simplicity, accuracy, and resistance to interference, while eliminating the need for wavefront reconstruction.
    Δx=xc-xrΔy=yc-yr
    LSSCS=m,nΔxm,n2+Δym,n2
    ϕx,y=Rϕ-Rϕ1-x2+y2Rϕ2
    xϕx,y=xRϕ1-x2+y2Rϕ2yϕx,y=yRϕ1-x2+y2Rϕ2
    Rϕ,m,n=xr2+yr2fMLA2Δxm,n2+Δym,n2+xr2+yr2
    Rϕ=m,nRϕ,m,nM×N
    Rϕ'=Rϕ+d1+d2
    f=Rϕ'1-Rϕ'2Δf1Δf2Δf2-Δf1=Rϕ1-Rϕ2Δf1Δf2Δf2-Δf1
    Rl=zb-za
    n=1+R1R2fR2-R1
    n=1+R1f
    δn=nf2δf2+nR12δR12=-R1f22δf2+1f2δR12
    Δfmin=f2DfMLA22δxc2+D24
    δf=fΔf1δΔf12+fΔf2δΔf22+fRϕ1δRϕ12+fRϕ2δRϕ22
    fΔf1=Rϕ1-Rϕ2Δf2Δf2-Δf1+Rϕ1-Rϕ2Δf1Δf22Δf2-Δf12Rϕ1-Rϕ2Δf1Δf2Δf2-Δf1
    fRϕ1=Δf1Δf22Δf2-Δf1Rϕ1-Rϕ2Δf1Δf2Δf2-Δf1
    δRϕ,m,n=Rϕ,m,nfMLAδfMLA2+Rϕ,m,nxc,m,nδxc,m,n2+Rϕ,m,nyc,m,nδyc,m,n2
    Rϕ,m,nfMLA=xr2+yr2fMLAΔxm,n2+Δym,n2xr2+yr2fMLA2Δxm,n2+Δym,n2+xr2+yr2
    Rϕ,m,nΔxm,n=xr2+yr2fMLA2-2Δxm,nΔxm,n2+Δym,n222xr2+yr2fMLA2Δxm,n2+Δym,n2+xr2+yr2
    1f=n-11R1-1R2+n-12tnR1R2
    n=e2+1f+e2+1f2-4te1e32e1
    e1=R2-R1+tR1R2
    e2=R2-R1+2tR1R2
    e3=1R1R2
    nR1=2e1a1-2e32e4e2+1f+e2+1f2-4te1e32e12
    nt=2a2e1-2e3e2+1f+e2+1f2-4te1e32e12
    nf=a32e1
    a1=2e32e5+2e32e5e2+1f-2e33e4t+2e1e3tR1e2+1f2-4te1e3
    a2=2e3+2e3e2+1f-2e3e1+te3e2+1f2-4te1e3
    a3=-1f2+e2+1f-1f2e2+1f2-4te1e3
    e4=-R22-R2t
    e5=-R22-2R2t
    Z=x¯-y¯s12n1+u2
    Δfmax=f2D24arctan2d2fMLA+D24-f
    Δffocal length measurementf20.01fMLAD22δxc-f
    Zijin Deng, Changwei Li, Sijiong Zhang. Measurement of Lens Parameters Using a Shack-Hartmann Wavefront Sensor[J]. Laser & Optoelectronics Progress, 2025, 62(9): 0912004
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