# Recent Advances in Brillouin Optical Correlation-Domain Reflectometry
## 4 Development of Slope-Assisted BOCDR
### Principle and Fundamental Operation  
In the standard configuration of BOCDR, the BFS at a single sensing point is derived after acquiring the whole BGS. In contrast, the slope-assisted BOCDR provides the BFS information using the BGS slope. This idea has been already proposed for BOTDA [62; 63; 64]. As depicted in Figure 5a, the BFS is in one-to-one correspondence with the spectral power \(P_{\text{B0}}\) at a certain frequency \(\
u_{\text{B0}}\), which is set at the high-frequency point in the linear region (lower-frequency side) of the BGS slope. Then, when the BFS slightly shifts to higher frequency by strain, etc., \(P_{\text{B0}}\) decreases linearly; when the slight loss occurs in the FUT, the spectral power of the BGS entirely decreases, also leading to the reduction of \(P_{\text{B0}}\). Even if the BFS change is so large that \(\
u_{\text{B0}}\) gets out of the linear region, so long as \(P_{\text{B0}}\) is in one-to-one correspondence with the BFS, this system operates properly (with a reduced sensitivity) by simple nonlinear compensation. One may point out that the noise floor of correlation-domain techniques is influenced by the sidelobes of the correlation peak and that the slope-assisted configuration does not work properly in principle, but this issue can be mitigated if we accept the deterioration of the spatial resolution to some extent just in the same manner as in the phase-detected BOCDR [56]. Figure 5b,c schematically show the changes in the \(P_{\text{B0}}\) distributions when strain (or heat) and loss are locally applied, respectively. The strain and temperature effects cannot be separated in this method, but the loss effect can be discriminated from the locally applied strain (or temperature change) in most cases, because the decreased \(P_{\text{B0}}\) value does not return to the initial value. The \(P_{\text{B0}}\) change distributions (calculated by substituting the resultant \(P_{\text{B0}}\) distributions (solid curves) from their initial distributions (dotted lines)) are used as final measurement data. To evaluate the optimal \(\
u_{\text{B0}}\) value and the bandwidth of the linear region, we analyzed a raw BGS with a BFS of 10.89 GHz (see Figure 6a), which was experimentally obtained when the FUT length \(L\) and experimental conditions (such as the modulation frequency \(f_{\text{m}}\) and amplitude \(\Delta f\)) were set to  
Figure 5: Schematic illustrations of the operating principle of slope-assisted BOCDR. (**a**) One-to-one correspondence between the BFS and the spectral power \(P_{\text{B0}}\) at frequency \(\
u_{\text{B0}}\). The dotted curve is the initial BGS, and the solid curve is the BGS shifted to higher frequency because of strain and/or heat. (**b**) \(P_{\text{B0}}\) distributions along the FUT with (solid curve) and without (dotted line) partial strain and heat. (**c**) \(P_{\text{B0}}\) distributions along the FUT with (solid curve) and without (dotted line) a point loss. Reproduced with permission from [59]. Copyright (2016) IEEE. the same values as those for the initial experiment (\(L\) = 5.0 m,\(f_{\text{m}}\) = 8.0 MHz, \(\Delta f\) = 1.4 GHz) [59]. Here, we defined the linear region as the region where the change in the BGS slope was suppressed within 20% compared to its maximum. Based on the slope (i.e., differential coefficient) dependence on the frequency (Figure 6b) obtained by differentiating the BGS with respect to frequency, the optimal \(\
u_{\text{B0}}\) value to widen the linear region was found to be 10.85 GHz. The bandwidth of the linear region was approximately 50 MHz, which corresponds to the strain of up to \(\sim\)1035 \(\upmu\varepsilon\) and the temperature change of \(\sim\)45 K. In this linear region, the theoretical strain and temperature dependence coefficients were calculated to be 2.1 \(\times\) 10\({}^{-4}\) dB/\(\upmu\varepsilon\) and 4.3 \(\times\) 10\({}^{-3}\) dB/K, respectively. The FUT employed in the initial experiment was a 5.0-m-long silica SMF with a BFS of 10.89 GHz at 1.55 \(\upmu\)m at room temperature.