## 5 Brillouin Optical Correlation Domain Reflectometry
### BOCDR Systems with Performance Improvement Schemes
Recently, a BOCDR system has been formed, in which the four performance improvement schemes are introduced [86]. The \"intensity modulation scheme\" [87] and the \"phase modulation scheme\" [84] are set in the system to reduce the background spectrum. The \"temporal gating scheme\" [87] and the \"double modulation scheme\" [84] elongate the measurement range. Figure 36a-c show synthesized coherence functions for the FM frequency of \(f_{0}\), 4\(f_{0}\), and \(f_{0}\) with 4\(f_{0}\), respectively [55]. As shown in Figure 36c, the double FM using the two frequencies that have the ratio of an integer can  
Figure 33: Experimental results of the distributed BFS measurement at the five-cm DSF section with one-cm spatial resolution [83]. The DSF section can be recognized due to the intensity modulation scheme. elongate the main peak interval while keeping the width of the main peak, which corresponds to the spatial resolution. In Ref. [86], BOCDR simulations were performed to confirm the validity of the simultaneous use of the four schemes. For example, it is shown in the simulation that the double-modulation scheme introduces the additional background noise spectrum. However, the intensity modulation can also reduce the additional noise components. Figure 37 shows an example of the BFS distribution measured by this BOCDR system [86]. In this measurement, the double-modulation scheme elongates the range by eight times, and the temporal  
Figure 34: Schematic drawing of background spectrum reduction by the phase modulation scheme [84]. Two cases are shown; measurement at the strained portion (DSF section) and at the non-strained portion (SMF section). (**a,b**) shows BGS obtained without and with the PM scheme, respectively; (**c**) Background spectrum reduction by subtracting (**b**) from (**a**). Figure 35: Experimental results of the BOCDR outputs (**a**) without the PM and (**b**) with the PM, respectively [84]; (**c**) Subtracted spectra; signal spectrum for the DSF section and the SMF section is clearly shown by the red and the blue curves, respectively. gating scheme additionally elongates by 31 times. Then, the total elongation is 248 times. The FUT length was 5280 m, and the spatial resolution was 3.94 cm. The ratio between the range and the resolution is 134,000, which is the largest ratio that is realized in the BOCDR systems [86]. A larger ratio has been demonstrated in a BOCDA system, thanks to a higher S/N ratio obtained by the larger Brillouin scattering power, compared with the BOCDR systems. Upon introducing the \"double modulation scheme\", \"temporal gating scheme\", and the \"differential modulation scheme\", the ratio of 1,000,000 was demonstrated [88]. This is the highest value demonstrated by all of the correlation domain techniques. As for \"the phase modulation scheme\" in the BOCDR systems, quite a simple way to realize the background spectrum suppression has recently been proposed. In a process to derive the formula that describes the background spectrum reduction with the phase modulation scheme, it has been found that the reduction can also be realized by simply calculating a convolution between the output spectrum of the basic BOCDR system without any PM modulator with a filtering function. This filtering function can simply be formed from the spectrum shape corresponding to the PM modulation. This can simplify the BOCDR system while keeping the background reduction function [89]. Figure 36: Simplified explanation of the double modulation scheme to elongate the measurement range [55]. (**a–c**) show, respectively, the synthesized coherence functions for the FM frequency of \(f_{0}\), \(4f_{0}\), and \(f_{0}\) with \(4f_{0}\). Figure 37: BFS distribution measured by the BOCDR system having the four performance improvement schemes [86]. The measurement range and the spatial resolution is 3.94 cm and 5280 m, respectively. The ratio between these is 134,000.