# Recent Advances in Brillouin Optical Correlation-Domain Reflectometry
## 4 Development of Slope-Assisted BOCDR
### Beyond-Nominal-Resolution Effect
The setup was basically the same as that in Figure 7; the change in the spectral power at 10.81 GHz was sequentially output to the OSC (owing to the difference in the video bandwidth of the ESA). The FUT was a 13.0-m-long silica SMF with a BFS of 10.86 GHz at 1.55 \(\upmu\)m at room temperature (25 \({}^{\circ}\)C). Measurements were performed using two configurations: one for a relatively high spatial resolution and the other for a relatively low resolution (required to  
Figure 9: Deduced strain distributions directly obtained from the final power outputs of (**a**) standard BOCDR and (**b**,**c**) slope-assisted BOCDR. Note that the traces in (**a**) give the correct strain distributions. Reproduced with permission from [60]. Copyright (2016) OSA. investigate the beyond-nominal-resolution effect). In the first configuration with a high resolution, strains of 750 \(\mu\epsilon\) and 1500 \(\mu\epsilon\) were applied to 5-cm-, 10-cm-, 20-cm-, 50-cm-, and 100-cm-long sections of the FUT, as depicted in Figure 10a. The modulation frequency \(f_{\mathrm{m}}\) and amplitude \(\Delta f\) were set to 7.11-7.31 MHz and 1.3 GHz, respectively, corresponding to the measurement range of 14.5 m and the theoretical spatial resolution of 9.5 cm according to Equations (2) and (3). In the second configuration with a low resolution, a strain of 1500 \(\mu\epsilon\) was applied to 5-cm-, 10-cm-, 15-cm-, and 20-cm-long sections of the FUT (see Figure 10b). The modulation frequency \(f_{\mathrm{m}}\) was swept in the same range (7.11-7.31 MHz), thus giving the same measurement range (14.5 m). The modulation amplitude \(\Delta f\) was reduced to 0.7 GHz, corresponding to a theoretical spatial resolution of 19.6 cm. In both configurations, the repetition rate was set to 100 Hz, and averaging was performed 64 times on the OSC to improve the SNR. First, we present the experimental results with a relatively high spatial resolution (9.5 cm). An example of the measured power change distribution (converted into strain) along the whole length of the FUT (with a 1500 \(\mu\epsilon\) strain applied to a 20-cm-long section) is shown in Figure 11a. At this scale, it appears that the correct amount of strain was detected at the correct location. The strain distributions measured when strains of 750 \(\mu\epsilon\) and 1500 \(\mu\epsilon\) were applied (magnified views around the strained sections), simply deduced from the power-change distributions based on the linear power-to-strain relationship, are shown in Figure 11b,c, respectively. Each distribution is shifted by 3000 \(\mu\epsilon\), and the simulated data are indicated by dotted lines. The trends in the measured distributions agree well with the simulation results, including the case where the strained section is half the nominal spatial resolution. This indicates that our relatively rough simulation is almost sufficient to predict the experimental results, which is beneficial from the viewpoint of simulation cost. We then performed similar experiments with a relatively low spatial resolution (19.6 cm) to evaluate the beyond-nominal-resolution effect. The magnified views of the strain distributions (simply deduced from the power-change distributions), measured when a strain of 1500 \(\mu\epsilon\) was applied, are shown in Figure 12. As the strained section becomes shorter, the maximal power-change shift becomes smaller. The trend in the measured distributions is basically in good agreement with the simulation results. As the strained section is shortened further, the signal is buried by the noise. The standard deviation of the noise floor (power fluctuations corresponding to the strain of the non-strained sections) was calculated to be approximately 130 \(\mu\epsilon\) in this measurement. This amount is theoretically obtained as the maximal strain when the strained section is 1.7 cm, which could be regarded as the shortest detectable length.