Error Estimation of BFS Extraction With Optimized Neural Network & Frequency Scanning Range

Abstract

We present and investigate a scheme for the error estimation formula derivation of Brillouin frequency shift (BFS) extraction based on an optimized neural network and frequency scanning range for a Brillouin optical time-domain analyzer (BOTDA) system. The system uses a general single mode optical fiber as the sensing medium, and the pump pulse duration is much longer than the phonon lifetime to ensure that the measured gain spectra are close to a Lorentzian shape. The performance of the network for extracting the BFS from f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> to f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> with different frequency scanning ranges is studied in detail, where f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ~f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> is the measurement range needing high precision. The results show that the optimal frequency scanning range is f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> -20~f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> + 20 (MHz). Based on the optimized network, the influences of the signal-to-noise ratio (SNR), linewidth of the gain spectrum (Δv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> ) and frequency step (δ) on the error of BFS extraction are each discussed in detail. The error declines exponentially as the SNR improves and rises linearly as Δv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> increases. The linear interpolation method is used to obtain the desired input data for the network under different frequency steps, and the error shows a linear relationship with δ. Finally, a comprehensive error estimation formula for the BFS extraction of a BOTDA is constructed according to the above three relationships and completed by fitting the errors under various SNRs, Δv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> and δ.