• Photonics Research
  • Vol. 12, Issue 9, 1877 (2024)
Chen Zhang1,2,3, Yisi Dong1,2,3,*, Pengcheng Hu1,2,3,5, Haijin Fu1,2,3..., Hongxing Yang1,2,3, Ruitao Yang1,2,3, Yongkang Dong3,4, Limin Zou1,2 and Jiubin Tan1,2|Show fewer author(s)
Author Affiliations
  • 1Center of Ultra-precision Optoelectronic Instrument, Harbin Institute of Technology, Harbin 150080, China
  • 2Key Laboratory of Ultra-precision Intelligent Instrumentation, Harbin Institute of Technology, Harbin 150080, China
  • 3Zhengzhou Research Institute, Harbin Institute of Technology, Zhengzhou 450000, China
  • 4National Key Laboratory of Science and Technology on Tunable Laser, Harbin Institute of Technology, Harbin 150001, China
  • 5e-mail: hupc@hit.edu.cn
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    DOI: 10.1364/PRJ.525667 Cite this Article Set citation alerts
    Chen Zhang, Yisi Dong, Pengcheng Hu, Haijin Fu, Hongxing Yang, Ruitao Yang, Yongkang Dong, Limin Zou, Jiubin Tan, "Large-range displacement measurement in narrow space scenarios: fiber microprobe sensor with subnanometer accuracy," Photonics Res. 12, 1877 (2024) Copy Citation Text show less

    Abstract

    The embedded ultra-precision displacement measurement is of great interest in developing high-end equipment as well as precision metrology. However, conventional interferometers only focus on measurement accuracy neglecting the sensor volume and requirement of embedded measurement, thus hindering their broad applications. Here we present a new sensing method for realizing large-range displacement measurement in narrow space scenarios based on the combination of a fiber microprobe interference-sensing model and precision phase-generated carrier. This is achieved by microprobe tilted-axis Gaussian optical field diffraction and high-order carrier demodulation to realize large-range displacement sensing. It is uncovered that the microprobe element misalignment and phase demodulation means play pivotal roles in the interference signal and the accuracy of large-range displacement sensing. The analysis shows that the proposed interference-sensing method can effectively reduce the nonlinearities. Experimental results illustrate that the measurement range extends from 0 to 700 mm. Furthermore, the maximum nonlinear error is reduced from tens of nanometers to 0.82 nm over the full range, allowing subnanometer accuracy for embedded measurements in the hundreds of millimeters range.
    E(x0,y0)=E0exp(x02+y02w02),

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    E(x1,y1)=E0w0w1exp((x12+y12)(1w12+ik2R1)+iarctan(λL0πw02)ikL0),

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    E(x1*,y1*)=E0w0w1exp(((x1*+d)2+y1*2)(1w12+ik2R1)+iφ1ik(L0+x1*sinθ)),

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    E(x2*,y2*)=E0w0w2*exp(((x2*bgsinθ+dag)2+y2*2)(1w2*2+ik2R2*)+i(φ1+φ2))×exp(ik(L0+n0Lg))×exp(ik2(bgdgsin2θ2dgsinθx2*+2dcgx2*+d2agcg2bgcgdsinθ)),

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    M21=(agbgcgdg)=(cos(gLg)sin(gLg)/gn0gn0sin(gLg)cos(gLg)),

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    E(x2,y2)=E0w0w2exp(((x2+d1bgsinθ+dag)2+y22)(1w22+ik2R2)+i(φ1+φ2))×exp(ik(L0+n0Lg)+ikx2(sinθdgsinθ+dcg)+ikd1sinθ)×exp(ik2K1),

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    E(x8,y8)=E0w0w8exp(((x8bssinΦ1+d)2+y82)(1w82+ik2R8)+i(φ1+φ2+φ8))×exp(ik(L0+n0Lg+2p+2n1dt+2Zwd)+ikd1sinθ)×exp(ik2(K1+bssin2Φ12sinΦ1x8)),

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    ES(xs,ys)=E0w0w10exp(((xsL0sinΦ3+ds*)2+ys2)(1w102+ik2R10)+iφs)×exp(ikL+ik(d1+d)sinθ)×exp(ik2(K1+K2+K3+L0sin2Φ32sinΦ3xs)),

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    sinΦ3=sinθ+dgsinΦ2cgd˜s,

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    ds*=agd˜sdbgsinΦ2,

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    ER(xr,yr)=E0w0w10exp(((xrL0sinΦ3+dr*)2+yr2)(1w102+ik2R10)+iφr)×exp(ikL+ik(d1+d)sinθ)×exp(ik2(K1+K2+K3+L0sin2Φ32sinΦ3xr)),

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    ηs=|2w0w10Qsexp(iψs)exp(Ps24QsOs4Qs)|2,

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    ηr=|2w0w10Qrexp(iψr)exp(Pr24QrOr4Qr)|2,

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    I=Is+Ir+2IsIrcos(2πλ(LL)+φ0),

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    v=2IsIrIs+Ir=2|ES|2δs2Rsηs|ER|2δr2Rrηr|ES|2δs2Rsηs+|ER|2δr2Rrηr.

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    s(t)=(1+mcos(wct)+φm)  ×(A+Bcos(Zcos(wct)+φ(t))).

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    s1(t)=Bm24cos2φm(J0(Z)J2(Z))2+J12(Z)sin(φ(t)θ1)+mA12cosφm,

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    s2(t)=Bm24cos2φm(J1(Z)J3(Z))2+J22(Z)cos(φ(t)θ2),

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    φ(t)=Phauw(arctans1(t)s2(t))=Phauw(arctansinφ(t)cosφ(t))+φerror,

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    s3(t)=Bm24cos2φm(J2(Z)J4(Z))2+J32(Z)sin(φ(t)θ3),

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    s2(t)=2cos(θ3θ22+π4)cos(φ(t)(θ3+θ22+π4)),

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    s3(t)=2sin(θ3θ22+π4)sin(φ(t)(θ3+θ22+π4)).

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    s2(t)=cos(φ(t)(θ3+θ22+π4)),

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    s3(t)=sin(φ(t)(θ3+θ22+π4)).

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    Chen Zhang, Yisi Dong, Pengcheng Hu, Haijin Fu, Hongxing Yang, Ruitao Yang, Yongkang Dong, Limin Zou, Jiubin Tan, "Large-range displacement measurement in narrow space scenarios: fiber microprobe sensor with subnanometer accuracy," Photonics Res. 12, 1877 (2024)
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