• Photonics Research
  • Vol. 10, Issue 2, 433 (2022)
Guan Wang1、2、†, Zhongwang Pang1、2、†, Bohan Zhang1, Fangmin Wang1、2, Yufeng Chen1、2, Hongfei Dai1、2, Bo Wang1、2、*, and Lijun Wang1、2
Author Affiliations
  • 1State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China
  • 2Key Laboratory of Photonic Control Technology (Tsinghua University), Ministry of Education, Beijing 100084, China
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    DOI: 10.1364/PRJ.443019 Cite this Article Set citation alerts
    Guan Wang, Zhongwang Pang, Bohan Zhang, Fangmin Wang, Yufeng Chen, Hongfei Dai, Bo Wang, Lijun Wang. Time shifting deviation method enhanced laser interferometry: ultrahigh precision localizing of traffic vibration using an urban fiber link[J]. Photonics Research, 2022, 10(2): 433 Copy Citation Text show less

    Abstract

    Using a fiber network as a huge sensing system will enrich monitoring methods of public infrastructures and geological disasters. With the traditional cross-correlation method, a laser interferometer has been used to detect and localize the vibration event. However, the random error induced by the cross-correlation method limits the localization accuracy and makes it not suitable for ultrahigh precision localizing applications. We propose a novel time shifting deviation (TSDEV) method, which has advantages over the cross-correlation method in practicability and localization accuracy. Three experiments are carried out to demonstrate the novelty of the TSDEV method. In a lab test, vibration localization accuracy of 2.5 m is realized. In field tests, TSDEV method enhanced interferometry is applied to monitor the urban fiber link. Traffic vibration events on the campus road and Beijing ring road have been precisely localized and analyzed, respectively. The proposed technique will extend the function of the existing urban fiber network, and better serve the future smart city.
    Δ1=12(Δc·τ0).

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    TSDEV(τ)=σ[x1(t)x2(t+τ)]=1Ttwtw+T{x1(t)x2(t+τ)E[x1(t)x2(t+τ)]}2dt.

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    TSDEV2(τ)=1Ttwtw+T[x1(t)x2(t+τ)C(τ)]2dt=1Ttwtw+T{sin(ωt)sin[ω(t+τ)]C(τ)}2dt=D(τ)·sin2(12ωτ)+G(τ)·sin(12ωτ)+C2(τ),

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    xcorr(τ)=1Ttwtw+Tx1(t)·x2(t+τ)dt=1Ttwtw+Tsin(ωt)·sin[ω(t+τ)]dt=12cos(ωτ)12ωTsin(ωT)·cos(2ωtw+ωT+ωτ).(A1)

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    tan(ωτ)=sin(ωT)·sin(2ωtw+ωT)ωTsin(ωT)·cos(2ωtw+ωT).(A2)

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    s(t)=a0+n=1ansin(nω0t+φn),t(twτ0,tw+T).(A3)

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    s1(t)=a0+n=1ansin(nω0t+φn),t(tw,tw+T),(A4)

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    s2(t)=a0+n=1ansin[nω0(tτ0)+φn],t(tw,tw+T).(A5)

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    xcorr(τ)=1Tbtbtb+Tbs1(t)·s2(t+τ)dt=1Tbtbtb+Tb[a0+n=1ansin(nω0t+φn)]·{a0+n=1ansin[nω0(tτ0+τ)+φn]}dt=1Tbtbtb+Tbk=0n=0{aksin(kω0t+φk)·ansin[nω0(tτ0+τ)+φn]}dt.(A6)

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    xcorr(τ)=1Tbtbtb+Tbaksin(kω0t+φk)·ansin[nω0(tτ0+τ)+φn]dt=akanTb{A(Tb)cos[nω0(τ0τ)]+B(Tb)sin[nω0(τ0τ)]},(A7)

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    tan[nω0(τ0τ)]=B(Tb)A(Tb),n=0,1,2.(A8)

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    s1(t)=x1(t)+ns(t)+nr1(t),s2(t)=x1(tτ0)+ns(tτs)+nr2(t).(B1)

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    TSDEV(τ)=σ[s1(t)s2(t+τ)]σ[s1(t)s2(t+τ)]={σ[x1(t)x1(tτ0+τ)]+σ[ns(t)ns(tτs+τ)]+σ[nr1(t)]+σ[nr2(t+τ)]}{σ[ns(t)ns(tτs+τ)]+σ[nr1(t)]+σ[nr2(t+τ)]}σ[x1(t)x1(tτ0+τ)].(B2)

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    Guan Wang, Zhongwang Pang, Bohan Zhang, Fangmin Wang, Yufeng Chen, Hongfei Dai, Bo Wang, Lijun Wang. Time shifting deviation method enhanced laser interferometry: ultrahigh precision localizing of traffic vibration using an urban fiber link[J]. Photonics Research, 2022, 10(2): 433
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