• Infrared and Laser Engineering
  • Vol. 50, Issue 5, 20200437 (2021)
Miao Yu1, Mingyang Sun2, Yaolu Zhang2, Yutong He1, and Zhifeng Zheng3
Author Affiliations
  • 1School of Electronic Information Engineering, Zhongshan Institute, University of Electronic Science and Technology of China, Zhongshan 528402, China
  • 2College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130012, China
  • 3Zhuhai Pegasus Optoelectronics Technology Co., Ltd., Zhuhai 519000, China
  • show less
    DOI: 10.3788/IRLA20200437 Cite this Article
    Miao Yu, Mingyang Sun, Yaolu Zhang, Yutong He, Zhifeng Zheng. Phase ambiguity and unwrapping of phase-sensitive optical time-domain reflectometer[J]. Infrared and Laser Engineering, 2021, 50(5): 20200437 Copy Citation Text show less

    Abstract

    The phase ambiguity and unwrapping of phase-sensitive optical time domain reflectometer was investigated. The whole process of phase change introduced by the perturbation was deduced, and the reason for phase ambiguity in the phase demodulation was analyzed. The piezoelectric ceramic was used as the disturbance source, and phase demodulation was performed by digital coherent demodulation. The experimental results show that phase ambiguity exists on each phase demodulation curve and among these curves simultaneously. So it is necessary to perform two phases unwrapping to eliminate phase ambiguity. Meanwhile, the phase disorder in the experiment was analyzed. It was pointed out that the phase unwrapping threshold and the phase drastic change in the disturbance position caused the inaccurate phase unwrapping of the perturbation position. The phase change in the adjacent position following the phase difference peak was used to restore the perturbation. The experimental results show that this method can correctly restore the disturbance signal, can demodulate the disturbance signal in the range of 10 Hz-1.5 kHz accurately, can simultaneously demodulate and respond to multiple perturbations along the optical fiber and the phase change amplitude have a good linear relationship to the disturbances intensity.
    ${E_{{{\rm{R}}}}}\left( t \right) = \sum\limits_{i = 1}^N {r\left( {{\tau _i}} \right)\exp \left( { - \alpha \frac{{c{\tau _i}}}{{{{{n}}_{\rm{f}}}}}} \right)} {\rm{rect}}\left( {\frac{{t - {\tau _i}}}{w}} \right)\cos \left( {\omega \left( {t - {\tau _i}} \right)} \right)$(1)

    View in Article

    ${E_{{{\rm{R}}}}}\left( t \right) = X\left( t \right)\cos \left( {\omega t} \right) + Y\left( t \right)\sin \left( {\omega t} \right)$(2)

    View in Article

    $X\left( t \right) = \sum\limits_{i = 1}^N {r\left( {{\tau _i}} \right)} \exp \left( { - \alpha \frac{{c{\tau _i}}}{{{n_{\rm{f}}}}}} \right){\rm{rect}}\left( {\frac{{t - {\tau _i}}}{w}} \right)\cos \left( {\omega {\tau _i}} \right)$(3)

    View in Article

    $Y\left( t \right) = \sum\limits_{i = 1}^N {r\left( {{\tau _i}} \right)} \exp \left( { - \alpha \frac{{c{\tau _i}}}{{{n_{\rm{f}}}}}} \right){\rm{rect}}\left( {\frac{{t - {\tau _i}}}{w}} \right)\sin \left( {\omega {\tau _i}} \right)$(4)

    View in Article

    ${E_{\rm{R}}}\left( t \right) = {E_s}\left( t \right)\cos \left( {\omega t + \varphi \left( t \right)} \right)$(5)

    View in Article

    ${E_s}\left( t \right) = \sqrt {{X^2}\left( t \right) + {Y^2}\left( t \right)} $(6)

    View in Article

    $\varphi \left( t \right) = - \arctan \left( {{{Y\left( t \right)} / {X\left( t \right)}}} \right)$(7)

    View in Article

    $ \begin{split} \varphi '\left( {{t_0}} \right) = & \arctan \left( {\dfrac{{Y\left( {{t_0}} \right)}}{{X\left( {{t_0}} \right)}}} \right) = \arctan \left( {\dfrac{{ \displaystyle\sum\limits_{i = 1}^N {r\left( {{\tau _i}} \right)\exp \left( { - \alpha \dfrac{{c{\tau _i}}}{{{n_{\rm{f}}}}}} \right){\rm{rect}}\left( {\dfrac{{{t_0} - {\tau _i}}}{w}} \right)\sin \left( {\omega {\tau _i} + {\varphi _v}} \right)} }}{{ \displaystyle\sum\limits_{i = 1}^N {r\left( {{\tau _i}} \right)\exp \left( { - \alpha \dfrac{{c{\tau _i}}}{{{n_{\rm{f}}}}}} \right){\rm{rect}}\left( {\dfrac{{{t_0} - {\tau _i}}}{w}} \right)\cos \left( {\omega {\tau _i} + {\varphi _v}} \right)} }}} \right) = \\ &\arctan \left( {\dfrac{{ \displaystyle\sum\limits_{i = 1}^N {r\left( {{\tau _i}} \right)\exp \left( { - \alpha \dfrac{{c{\tau _i}}}{{{n_{\rm{f}}}}}} \right){\rm{rect}}\left( {\dfrac{{{t_0} - {\tau _i}}}{w}} \right)\left( {\sin \omega {\tau _i}\cos {\varphi _v} + \cos \omega {\tau _i}\sin \varphi } \right)} }}{{ \displaystyle\sum\limits_{i = 1}^N {r\left( {{\tau _i}} \right)\exp \left( { - \alpha \dfrac{{c{\tau _i}}}{{{n_{\rm{f}}}}}} \right){\rm{rect}}\left( {\dfrac{{{t_0} - {\tau _i}}}{w}} \right)\left( {\cos \omega {\tau _i}\cos {\varphi _v} - \sin \omega {\tau _i}\sin \varphi } \right)} }}} \right) = \\ &\arctan \left( {\dfrac{{\sin \left( {\varphi \left( {{t_0}} \right) + {\varphi _v}} \right)}}{{\cos \left( {\varphi \left( {{t_0}} \right) + {\varphi _v}} \right)}}} \right) = \varphi \left( {{t_0}} \right) + {\varphi _v} \\ \end{split}$(8)

    View in Article

    ${E_{\rm{R}}}\left( {{t_0}} \right) = {E_s}\left( {{t_0}} \right)\cos \left( {\omega {t_0} + \varphi \left( {{t_0}} \right) + {\varphi _v}} \right)$(9)

    View in Article

    $ \begin{split} {E_{\rm{R}}}\left( {{t_0}} \right) =& {E_s}\left( {{t_0}} \right)\cos \left( {\omega {t_0} + \phi \left( {{t_0}} \right) + {\phi _v}' + 2k\pi } \right) =\\ & {E_s}\left( {{t_0}} \right)\cos \left( {\omega {t_0} + \phi \left( {{t_0}} \right) + {\phi _v}'} \right) \end{split} $(10)

    View in Article

    ${P_{{\rm{BPD}}}} \propto 2{E_{\rm{R}}}\left( t \right){E_{\rm{L}}}\left( t \right)\cos \left( {2\pi \Delta ft + \varphi \left( t \right)} \right)$(11)

    View in Article

    $\varphi \left( t \right) = \arctan \left( {{Q / I}} \right)$(12)

    View in Article

    $I = {E_{\rm{R}}}\left( t \right){E_{\rm{L}}}\left( t \right)\cos \varphi \left( t \right)$(13)

    View in Article

    $Q = {E_{\rm{R}}}\left( t \right){E_{\rm{L}}}\left( t \right)\sin \varphi \left( t \right)$(14)

    View in Article

    ${\phi _i}(t) = {\phi _i}(t) + 2\pi *Coeffcient$(15)

    View in Article

    $Coeffcient = \left\{ \begin{array}{l} Coeffcient + 1,{\rm{ }}{\phi _i}(t) - {\phi _{i - 1}}(t) < - \pi \\ Coeffcient - 1,{\rm{ }}{\phi _i}(t) - {\phi _{i - 1}}(t) > \pi \end{array} \right.$(16)

    View in Article

    Miao Yu, Mingyang Sun, Yaolu Zhang, Yutong He, Zhifeng Zheng. Phase ambiguity and unwrapping of phase-sensitive optical time-domain reflectometer[J]. Infrared and Laser Engineering, 2021, 50(5): 20200437
    Download Citation