On the measurement accuracy of coherent Rayleigh-based distributed sensors

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.