## 2 Distributed Optical Fibre Sensors
### Brillouin-Based Distributed Sensing  
Spontaneous Brillouin scattering is another inelastic process occurring in optical fibres. The interaction between the incident light wave and the thermally-induced material-density fluctuations (acoustic phonons) travelling along the fibre at the speed of sound is the phenomenon that underlies the scattering process. Due to the stress-optical effect, a modulation of the refractive index propagates along the fibre at the same speed [12]. In this interaction, the wavelength matching among longitudinal acoustic phonons and input probe optical wavelength generates two additional signals at wavelengths on either side of the probe, as occurs for Raman scattering [65]. Frequency shift and intensity of the generated signals are sensitive to both strain and temperature, and this dependence is exploited in Brillouin-based DOFS, whose early proposals are dated at the end of the 1980s [66; 67; 68]. To the aim of DOFS implementation, spontaneous Brillouin scattering is similar to spontaneous Raman scattering. The most simple approach for detecting spontaneous Brillouin scattering is in fact the same as for Raman-based OTDR, and the term Brillouin optical time-domain reflectometer (BOTDR) refers properly to the time domain interrogation of back-propagating spontaneous Brillouin scattering. With respect to Raman, the bands generated are very narrow (approx. 30 MHz vs. 6 THz for Raman scattering) and the frequency shift is small (approx. 10 GHz vs. 13 THz). Finally, as mentioned above, the intensity of backscatter signal is substantially stronger in spontaneous Brillouin than Raman, although less sensitive to temperature, making the detection less critical. Typical sensitivity coefficients of Brillouin frequency shift vs. strain and temperature in step index single-mode fibres are 0.046 MHz/\(\upmu\varepsilon\) and 1.07 MHz/\({}^{\circ}\)C, respectively. Regarding the intensity, we have instead \(-0.0008\%/\upmu\varepsilon\) and 0.36%/\({}^{\circ}\)C, correspondingly [69; 70]. Figure 4: Typical deployment and calibration configurations for Raman-DTSs: (**a**) Simple single-ended configuration; (**b**) Duplexed single-ended configuration; (**c**) Double-ended configuration. Up to three calibration zones at known temperatures, \(T_{1}\), \(T_{2}\), and \(T_{3}\) (\(T_{1}\
eq T_{2}\)) are recommended, depending on the layout. Please note that double-ended and duplexed single-ended configurations enable redundancy of measurement and are more robust with respect to the event of cable failing at some point. After [64]. Over the years, all these features promoted Brillouin scattering as the most widespread and studied distributed sensing platform in many practical applications. In fact, the very narrow bandwidth of Brillouin scattering drove the implementation of heterodyne techniques with high SNR over long distance [70; 71], also supported by the viability of optical amplification [72; 73] and optical pulse coding [74; 75]. Furthermore, specific implementations of Brillouin-based DOFSs allow the discrimination of temperature from strain, either by measuring the spontaneous Brillouin intensity and Brillouin frequency shift simultaneously [70; 76] or by measuring multi-peak Brillouin spectrum in dispersion-shifted fibres [77]. Nonetheless, to our knowledge, only one of the commercial interrogators existing at the moment has implemented this option by exploiting the first of the two techniques mentioned above. Ultimately, a range of several tens of kilometres with spatial resolution on the order of 1 m is attainable with BOTDR schemes. A typical BOTDR setup with a coherent detection stage is represented in Figure 5.  
Towards the aim of distributed sensing, another Brillouin scattering process can be exploited; namely, the stimulated Brillouin scattering (SBS) [79]. When two counter-propagating waves separated by the Brillouin frequency are launched at the two ends of the fibre, they interact with each other, resulting in a stimulation of the scattering process.