Abstract
The phase change of back-scattered light due to external perturbations is retrieved in coherent Rayleigh-based distributed sensors by estimating the frequency shift (FS) between the traces of different measurements. The uncertainty associated with the estimator, due to the presence of system noises, can lead to an inaccurate evaluation of the FS. Additionally, in coherent Rayleigh-based sensors, the calculation of the signal-to-noise ratio (SNR) from the jagged back-scattered intensity trace using the statistical estimators can cause an erroneous determination of the absolute value of the SNR. In this work, a method to accurately evaluate the non-uniform SNR caused by the stochastic variation of the back-scattered light intensity along the fibre is presented and validated. Furthermore, an analytical expression to evaluate the uncertainty in the FS estimation using one of the standard estimators, namely cross-correlation, is presented. A direct-detection frequency-scanned phase-sensitive optical time-domain reflectometer (φ-OTDR) is employed for the experimental verification of the expression as a function of two crucial system parameters: the SNR and the spatial resolution. The performance of various distributed sensing system configurations utilising cross-correlation for determining the FS occurring due to the external perturbations can be properly predicted hereafter with the aid of the analytical expression presented in this study.
Highlights
Over the past 50 years, distributed optical fibre sensors (DOFS) have received unprecedented attention owing to their benefits in terms of long-haul detection, intrinsic safety, flexibility, immunity to electromagnetic interference, and low cost [1,2]
Several approaches have been discussed in the literature with the goal of optimising the performance of DOFS based on coherent Rayleigh scattering through the ultimate parameter, the signal-to-noise ratio (SNR)
This study presents a method to calculate the absolute value of the SNR from the jagged φ-OTDR intensity trace, which turns out to be critical to make solid predictions and to require a peculiar methodology
Summary
Over the past 50 years, distributed optical fibre sensors (DOFS) have received unprecedented attention owing to their benefits in terms of long-haul detection, intrinsic safety, flexibility, immunity to electromagnetic interference, and low cost [1,2]. An analytical expression based on the concept of time-delay estimation using cross-correlation in radar and sonar systems [21,22,23] is well adapted to the present scenario and evaluated for determining the accuracy of the FS estimation employing cross-correlation in φ-OTDR. It will be shown and experimentally validated that this inverse proportionality remains valid in coherent Rayleigh distributed sensors, while the spatial resolution impacts twice on the accuracy through the SNR and the correlation peak spectral width, resulting in an inverse squared dependence of the uncertainty on the spatial resolution. The analytical expression can be applied to any system wherein the measurand is quantified through cross-correlation
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