## 4 Brillouin Optical Correlation Domain Analysis: BOCDA  
### Brillouin Scattering-Based Distributed Fiber Sensing  
Before describing the BOCDA technology, Brillouin scattering-based distributed optical fiber sensing is briefly discussed, which clarifies the features of BOCDA technology. Figure 17 shows a schematic description of the Brillouin scattering in an optical fiber. The scattering is acoustic phonon-related. In a schematic description, thermal vibration of the material  
Figure 16: Experimental results of the lateral force distribution measurement along a polarization-maintaining optical fiber [33]. System output (**a**) for no lateral force applied, and (**b**) for lateral force applied at three points along the fiber. Figure 15: Optical setup for distributed lateral force measurement along a polarization-maintaining optical fiber utilizing polarization modes coupling and the SOCF technology [32]. (**a,b**) show, respectively, the FM waveform to synthesize the delta-function-like optical coherence function and PM waveform to shift the synthesized optical coherence function along the optical fiber. molecules creates an ultrasonic wave that propagates along the fiber, which creates periodical refractive index change. This can act as a grating for the incident lightwave. When the wavelength of the lightwave \(\lambda\) in the fiber and the period of the grating \(d\) meet the Bragg condition with respect to each other, that is \(d=\lambda/2\), the incident lightwave makes a so-called Bragg reflection. As the grating is a moving one, the Brillouin scattering has a down-shifted and an up-shifted frequency, due to the Doppler shift. The former scattering is called the Stokes wave, and the latter is called the anti-Stokes wave, respectively. The Stokes wave is used mainly for the measurement. In silica optical fibers, the Bragg condition is satisfied when the ultrasonic frequency is around 11 GHz for an incident wavelength of 1.5 \(\upmu\)m.  
Then, the spectral relation shown in Figure 17c is obtained. The spectral broadening of around 30 MHz is observed in the Brillouin gain spectrum (BGS), which corresponds to the phonon lifetime. The down-shifted frequency \(f_{\mathrm{B}}\) is called the Brillouin frequency shift (BFS). The BFS shows a linear relationship to the strain change and/or temperature change that are introduced to the fiber. This is the sensing mechanism of the Brillouin scattering for strain and/or temperature. As shown in Figure 17a, spontaneous Brillouin scattering takes place by simply launching the pump lightwave at one end of the fiber. On the contrary, by additionally launching the probe lightwave at the opposite fiber end, which has the frequency difference of \(-f_{\mathrm{B}}\) from the pump, stimulated Brillouin scattering can be induced. The former setup is simple, but the scattering power is tiny. On the other hand, the latter setup is rather complicated, but the scattering power is enhanced by several orders. Figure 18a shows a setup for the distributed sensing with using a pulsed lightwave as the pump. When the spontaneous scattering is used with the one-end access configuration, the setup is called \"reflectometry\" in this field. Then, this configuration is called \"Brillouin optical time-domain  
Figure 17: Schematic drawing of Brillouin scattering caused along an optical fiber and its dependences on applied longitudinal strain and temperature change. (**a**) Spontaneous Brillouin scattering; (**b**) stimulated Brillouin scattering; (**c**) Brillouin gain spectrum (BGS) having the down-shifted frequency compared with the incident pump lightwave; and (**d**) dependence of Brillouin frequency shift on strain and temperature. The BGS of silica optical fibers has a spectrum width of about 30 MHz, which is related to the phonon lifetime. reflectometry (BOTDR)\" [5]. When the stimulated Brillouin scattering is used with the two-end access configuration, the setup is called \"Brillouin optical time-domain analysis (BOTDA)\" [4].