# Non-Local Effects in Brillouin Optical Time-Domain Analysis Sensors
## 3 Mitigation of Non-Local Effects
### Mitigation of Second-Order Non-Local Effects
The final Brillouin spectra is obtained after a post-processing of the measurement to compensate the frequency shift introduced to the probe wave at each location due to the FM modulation. To do this, all measured data are introduced in a matrix, so the trace measured for each pulse delay is stored in a different row of the matrix. The method is simply to apply a shift to the elements of the columns of the matrix containing the probe wave samples (rows) for each relative delay between the FM modulation and the pump pulses [14]. A side benefit of this probe dithering method is that the optical frequency modulation of the probe waves allows to overcome the Brillouin threshold limit of the fiber, by means of reducing the effective amplification of spontaneous Brillouin scattering [22]. Therefore, a very large probe power can be deployed to enhance the SNR in detection, which in turn leads to an enhancement of the measurement precision and/or the measurement time of the BOTDA sensor. Indeed, up to 15 dBm of probe wave power [4] injected into a long-range BOTDA has been demonstrated experimentally [4], which, to the best of our knowledge, is the largest probe power ever deployed in a BOTDA setup. An important caveat of both methods to mitigate second-order non-local effects, the alternative sweep and our probe dithering technique, is that they assume that the BFS profile of the fiber does not significantly deviate from uniformity [23]. As was mentioned before, the alternative sweep method requires the frequency difference between both probe waves during the scanning process to be constant and equal to the BFS of the fiber. However, if the BFS of the fiber changes, the gain and loss spectra generated by both probe waves no longer overlap, and second-order non-local effects reappear. Similarly, our probe dithering method is also affected by variations of the BFS along the fiber because perfect compensation of the gain and loss spectra induced upon the pulse requires a nearly uniform BFS. Figure 4: Fundamentals of the probe dithering technique for mitigation of second-order non-local effects: (**a**) Brillouin interaction on the pump pulse and (**b**) frequency scanning method based on the temporal delay change (\(t_{p1}\) and \(t_{p2}\)) between probe and pump waves. However, the technique is much less sensitive to this effect than the alternative sweep method because the gain and loss spectra are broadened by the FM modulation process. In any case, the assumption of uniform BFS along the fiber is somewhat not realistic in many practical applications because in a sensing link we may have fiber from several manufacturers with slightly different nominal BFS or different fiber sections subjected to different environmental conditions. However, we have devised a technique that solves this issue. It is based on introducing an additional wavelength modulation to the probe wave so as to track the BFS changes along the sensing fiber link [23]. This technique has been demonstrated in a 120-km fiber sensing link deploying three types of single-mode fibers with different nominal BFS. The use of a 15 dBm probe wave power provided 3-m resolution and 2-MHz precision BFS measurement in the worst-contrast position.