## 5 Brillouin Optical Correlation Domain Reflectometry
### Discriminative and Distributed Measurement of Strain and Temperature with BDG-BOCDA Systems  
Figure 41 shows the strain and temperature dependence of the BFS and the BDG Bragg frequency [106]. The BDG Bragg frequency is caused by the birefringence of the PMF. It is shown in Figure 41 that the strain dependence of the two parameters shows the same sign, but the temperature dependence shows different signs, with respect to each other. This is a nice relation to calculate the strain and temperature from the two parameters. The relation between the two parameters and the strain/temperature are expressed by using a \(2\times 2\) matrix. Due to the dependence shown in Figure 41, the matrix has good characteristics when calculating the inverse matrix. The strain change \(\delta\epsilon\) and the temperature change \(\delta T\) are expressed as [106]:  
\[\left( \begin{array}{c}\delta\epsilon\\ \delta T\end{array} \right)=\frac{1}{C_{v}^{\ast}C_{f}^{\ast}-C_{v}^{T}C_{f}^{ \ast}}\left( \begin{array}{cc}C_{f}^{T}&-C_{v}^{T}\\ -C_{f}^{\ast}&C_{v}^{\ast}\end{array} \right)\left( \begin{array}{c}\delta v _{B}\\ \delta fyx\end{array} \right) \tag{5}\]  
Figure 40: Brillouin dynamic grating (BDG) generation in a polarization-maintaining optical fiber (PMF). (**a**) Schematic drawing of the mechanism for the BDG generation; (**b**) experimental result of BDG reflection spectra measurement [20]. where the four coefficients are the strain and the temperature dependence of the two physical parameters calculated from the data shown in Figure 41.  
Figure 42 shows a BOCDA system to measure the strain and the temperature distribution discriminatively along a PMF while also measuring the BDG reflection [18]. The upper part is the same as the basic BOCDA-distributed sensing system. In the lower part, another light source, LD2, is set to launch the reading lightwave in the orthogonal polarization axis of the PMF through a polarization beam splitter (PMF). The distributed measurement function is introduced by the BOCDA technique. It is important to also modulate the LD2 with the same FM waveform as the LD1 to have a fine reflection spectrum, due to the dispersion of the acoustic wave [107]. Figure 43a shows the distribution of the two physical parameters, the BFS and the birefringence-induced Bragg frequency difference [18]. In the first measurement shown in the blue squares, the B, D, E, F, and H sections are heated, but no strain is applied. In the second measurement shown in the red dots, the temperature distribution is the same as the first one, but strain is applied at the E section. Figure 43b shows the strain and temperature change calculated by Equation (5). The distribution of the applied strain and the temperature are clearly recognized [18]. Figure 41: Strain and temperature dependence of the BFS and the BDG Bragg reflection frequency in a polarization-maintaining optical fiber [106]. Strain dependence (**a**) and temperature dependence (**b**) of the BFS and the BDG Bragg reflection frequency. Figure 42: BOCDA system to measure strain and temperature distribution discriminatively along a PMF while measuring both the BFS and the BDG reflection [90]. As for the spatial resolution, that for the BFS-distributed measurement shows a good coincidence with the BOCDA theory, namely Equation (3). However, the spatial resolution for the distributed measurement of the BDG Bragg reflection frequency is worth about 10 times more than the BOCDA theory, which is clearly shown in the experiments [18]. To clarify the degradation of the spatial resolution, a simulation technique for the BDG-distributed measurement based on the BOCDA technique has been developed. Figure 44 shows the simulation results [108]. In the upper portion of Figure 44, the fiber sample that was used in the simulations is shown. At the center portion, a strain-applied section is set, whose length is changed as \(n\times d_{z}\), where n is an integer and \(d_{z}\) is the spatial resolution calculated by Equation (3).