# Recent Advances in Brillouin Optical Correlation-Domain Reflectometry
## 4 Development of Slope-Assisted BOCDR
### Beyond-Nominal-Resolution Effect  
One fundamental issue that must be solved to characterize the slope-assisted BOCDR operation is the correspondence between the final system output (i.e., power-change distribution) and the actual BFS distribution. In standard BOCDR based on frequency information, these two distributions have been proven to be identical in principle; however, in slope-assisted BOCDR based on power information, no report has been made. Here, we theoretically and experimentally show that the final system output of slope-assisted BOCDR is generally different from the actual BFS distribution. We also show that, even when the strained section is shorter than the nominal resolution, some shift in the power change can be observed. This feature is unique to the slope-assisted BOCDR and useful for practical applications. To start with, we simulated the system output of slope-assisted BOCDR. We assumed that one section of the FUT was uniformly strained. The magnitude of the strain was assumed to constantly lie below the upper limit of the linear region (\(\sim\)2000 \(\mu\epsilon\)). The lengths of the strained section were set to 0.25R, 0.5R, 0.75R, \(R\), 2R, 5R, and 10R, where \(R\) indicates the nominal spatial resolution calculated using Equation (2). First, the simulation results for the strain distributions acquired using the standard  
Figure 8: (**a**) Structure of the FUT. (**b**) Measured \(P_{\mathrm{B0}}\) change distribution. Reproduced with permission from [59]. Copyright (2016) IEEE. BOCDR (deduced from the BFS distributions using the linear BFS-to-strain relationship) are shown in Figure 9a, which completely reproduce the actual BFS distributions. Next, the simulation results for the strain distributions obtained from the slope-assisted BOCDR (also deduced from the final power-change distributions simply based on the linear power-to-strain relationship) are shown in Figure 9b (strained: 0.5\(R\), \(R\), 2\(R\), 5\(R\), and 10_R_) and Figure 9c (strained: 0.25\(R\), 0.5\(R\), 0.75\(R\), and _R_). Here, for simplicity, we neglected both the complicated longitudinal shape of the correlation peak and the influence of its sidelobes [65]; that is, the longitudinal shape of the correlation peak was approximated by a rectangular profile with a length of \(R\). At the ends of the strained section (i.e., the boundaries between the strained and non-strained sections), the power change varied linearly with the length of \(R\); consequently, each whole power-change distribution showed a trapezoidal shape (including triangular). Thus, we see that when the strained section is sufficiently longer than \(R\), the power-change distribution almost reproduces the actual BFS distribution. In contrast, when the length of the strained section is approximately \(R\) or only a few times longer than \(R\), the correct BFS distribution cannot be directly obtained (under the assumption that the strain is uniformly applied; however, the correct information can be easily derived). What is notable here is that, even when the strained section is shorter than \(R\), we can observe a trapezoidal-shaped shift in the power change and thereby obtain the information that some irregularity has occurred at that point. For instance, when the length of the strained section is 0.5\(R\), a trapezoidal shape with a maximal power-change shift (corresponding to half the amount obtained with a strained section longer than _R_) is observed. Subsequently, the aforementioned simulation results including this \"beyond-nominal-resolution\" effect are experimentally verified (note that with this effect, we cannot distinguish two hot spots of which the distance is smaller than the nominal resolution, as the two hot spots are broadened; we can just detect an extremely short hot spot, and in this meaning, the spatial resolution of the system is not enhanced with this effect).