Analysis and Compensation of Vibration Induced Beat Frequency Shift in OFDR Based Fiber-Optic Distributed Acoustic Sensor

Abstract

Optical frequency domain reflectometry (OFDR) is an attractive locating technology for distributed acoustic sensor (DAS) due to its high spatial resolution, but the detectable bandwidth of vibration is very limited up to date, because high frequency vibration will induce time-variant beat frequency shift within the probe, which can deteriorate or even invalidate the demodulation algorithm. In this work, the influence of vibration induced beat frequency shift in OFDR is analyzed and assessed by the crosstalk power spectral density (PSD). Then an adaptive two-dimensional cross-correlation algorithm is proposed for beat frequency shift compensation, in which the instantaneous beat frequency shift within the probe is estimated and compensated for precise strain demodulation. In the experiment, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$18 \text{-}kHz$</tex-math></inline-formula> vibration signal is successfully detected with spatial resolution of 12 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rm cm$</tex-math></inline-formula> and strain resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$594\;\rm p\varepsilon/\sqrt{Hz}$</tex-math></inline-formula> , whose frequency is an order of magnitude higher than previous works. The proposed beat frequency shift compensation algorithm is evaluated in different conditions, and a suppression of crosstalk PSD up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$40.5\rm \ dB$</tex-math></inline-formula> is proved.