Deep Learning to Overcome Non-Local Effect in Brillouin Optical Time-Domain Analysis

Detrimental non-local effect (NLE) causes fatal measurement errors and limits the allowed optical power in long-range Brillouin optical time-domain analysis (BOTDA) sensing system. NLE occurs in both the single-sideband BOTDA (SSB-BOTDA) and dual-sideband BOTDA (DSB-BOTDA), namely the 1st-order NLE and 2nd-order NLE, respectively. Conventional methods to overcome NLE usually require modification of system setup which greatly increases the system complexity and cost. Here we have proposed a BOTDA system powered by deep learning method, i.e., deep neural network (DNN), to overcome both the 1st-order NLE and 2nd-order NLE without any system modification. Analytical expressions of Brillouin gain spectrum (BGS) profile under the 1st-order NLE and 2nd-order NLE are derived, respectively, which are used to generate training dataset for DNN training. A single DNN model has been successfully demonstrated to be capable of accurately extracting the Brillouin frequency shift (BFS) from the normal BGS and distorted BGS, no matter whether NLE exists or not in the system. Through both simulation and experiment, the performance of the proposed DNN is verified and compared with that of conventional Lorentzian curve fitting (LCF) method. Under strong 1st-order NLE in the SSB-BOTDA, the use of our DNN reduces the temperature root mean square error (RMSE) by 6.5 times, and the maximum allowed probe power is increased by 16.5 dB. Under strong 2nd-order NLE in the DSB-BOTDA with 50 km sensing distance, the DNN reduces the temperature error by 6.1 times, and the maximum allowed probe power per sideband is increased by 11 dB. The DNN model does not need any prior knowledge on whether the data has NLE or not, thus a single DNN model is enough to accurately extract BFS under both conditions without and with NLE, which makes the scheme practical and can greatly improve the system tolerance to NLE with low cost.