• Chinese Optics Letters
  • Vol. 19, Issue 10, 101402 (2021)
Xiufang Wang1, Lina Feng1, Peng Chen1、*, Zhen Huang2, and Ye Yuan3
Author Affiliations
  • 1College of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China
  • 2School of Physics Science and Technology, Lingnan Normal University, Zhanjiang 524048, China
  • 3School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
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    DOI: 10.3788/COL202119.101402 Cite this Article Set citation alerts
    Xiufang Wang, Lina Feng, Peng Chen, Zhen Huang, Ye Yuan. Micro displacement reconstruction of self-mixing grating interferometer based on Littrow structure[J]. Chinese Optics Letters, 2021, 19(10): 101402 Copy Citation Text show less

    Abstract

    An improved self-mixing grating interferometer based on the Littrow structure has been proposed in this Letter to measure displacement. The grating is integrated inside the interferometer to reduce the impact on the vibration parameters of the object caused by the grating attached to the vibrating object. The +1st diffracted light returns to the laser cavity after being reflected by the target object, and self-mixing interference occurs. The displacement can be reconstructed by processing the self-mixing signals. The feasibility of the proposed interferometer is demonstrated by experimental measurements, and results show that it can achieve micro displacement measurement with the maximum absolute errors of less than 50 nm.
    φ0(t)=φF(t)+Csin[φF(t)+arctanα],

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    P=P0{1+ξcos[φ0(t)]},

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    d(sinθm+sinθi)=mλ,m=0,±1,±2,±3…,

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    θm=θi.

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    sinθi=mλ2d.

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    m=+1,θi=θ1.

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    fA=f0(1+vsinθ11c),

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    f1=fA(1+vsinθ12c),

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    f1=f0(1+vsinθ11c)(1+vsinθ12c)=f0c2[c2+cv(sinθ11+sinθ12)+v2sinθ11sinθ12].

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    f1=f0+vλ(sinθ11+sinθ12).

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    f1=f0+vλ2sinθ1.

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    f1=f0+vd.

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    Δf=f1f0=vd.

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    φg=2πΔft=4πtanθ1x(t)d.

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    φL=4πΔLλ=8πx(t)λcosθ1,

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    λ=2dsinθ1.

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    φL=8πx(t)2dsinθ1cosθ1.

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    φ(t)=φL+φg=4πx(t)dtanθ1=4πx(t)dtanθi.

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    x(t)=dtanθi4πφ(t).

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    |Δx(t)|=dtanθi4π|φ(t)|+φ(t)tanθi4π|Δd|+dφ(t)4π(secθi)2|Δθi|.

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    Xiufang Wang, Lina Feng, Peng Chen, Zhen Huang, Ye Yuan. Micro displacement reconstruction of self-mixing grating interferometer based on Littrow structure[J]. Chinese Optics Letters, 2021, 19(10): 101402
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