• Chinese Optics Letters
  • Vol. 14, Issue 3, 030801 (2016)
Jinggao Zheng*, Qun Wei**, Linyao Yu, Mingda Ge, and Tianyi Zhang
Author Affiliations
  • Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
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    DOI: 10.3788/COL201614.030801 Cite this Article Set citation alerts
    Jinggao Zheng, Qun Wei, Linyao Yu, Mingda Ge, Tianyi Zhang. Simple optical method for small angular displacement measurement based on the astigmatic effect[J]. Chinese Optics Letters, 2016, 14(3): 030801 Copy Citation Text show less

    Abstract

    We propose a novel small-angle measuring optical method based on the astigmatic effect of two orthogonally placed cylindrical lenses. According to the one-to-one correspondence between the laser spot shape and the angle, the angle is determined. We theoretically analyze the measuring range and demonstrate that a longer distance between the rotating axis and the optical axis leads to a smaller measuring range, but better sensitivity. Also, an associated experimental system is established and a measuring range of 0.94 mrad (cubic fit r=0.9993) as well as a good linear range of 0.37 mrad (linear fit r=0.9994) with a resolution of 8 μrad is achieved.
    Δz(d1,d2,fMO,fx,fy)=d1fMO2(fx+fMOd1d2)(fy+fMOd2),(1)

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    Δz=L×tan(Δθ),(2)

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    Δz=L×Δθ.(3)

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    Δθ(L,d1,d2,fMO,fx,fy)=ΔzL=d1fMO2L(fx+fMOd1d2)(fy+fMOd2).(4)

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    FES=E1+E2E3+E4E1+E2+E3+E4,(5)

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    y1=410826.63x13+44588.25x12341.99x121.34,(6)

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    y2=1170.47x237.55,(7)

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    Jinggao Zheng, Qun Wei, Linyao Yu, Mingda Ge, Tianyi Zhang. Simple optical method for small angular displacement measurement based on the astigmatic effect[J]. Chinese Optics Letters, 2016, 14(3): 030801
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