Evaluating and overcoming the impact of second echo in Brillouin echoes distributed sensing

The detrimental impact of the second echo phenomenon that commonly exists in Brillouin echoes distributed sensing (BEDS) methods is thoroughly investigated by further developing the analytical model of the Brillouin gain on the probe wave. The presented analysis not only points out that the most severe impact imposed by the second echo occurs when the length of the heated/stressed fiber section is exactly equal to the spatial resolution, but also quantifies the systematic error on the estimated Brillouin frequency shift, the maximum of which could reach up to 8.5 MHz. A novel parabolic-amplitude four-section pulse is proposed, which can compensate the impact of the second echo optically, without using extra measurement time and post-processing. The key parameters of the proposed pulse are optimized by combining an upgraded mathematical model and the iterative algorithm. The experimental results show a good agreement with the analysis about the behavior of the second echo, and demonstrate that the proposed technique is capable of providing sub-meter spatial resolution and the natural linewidth of Brillouin gain spectrum simultaneously, while completely eliminating the impact of the second echo.