## 2 Distributed Optical Fibre Sensors
### Raman-Based Distributed Sensing
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Type** & **Fibre** & **Sensing** & **Spatial** & **Measurand** & **Measurand** & **Acquisition Time** \\  & **Type** & **Range** & **Resolution** & **Resolution** & **Resolution** & **Acquisition Time** \\ \hline \multirow{2}{*}{\(\
u\)-OTDR (*)} & SMF/ & \multirow{2}{*}{40 km (SMF)} & \multirow{2}{*}{10 cm} & \multirow{2}{*}{n/a} & \multirow{2}{*}{n/a} & \multirow{2}{*}{minutes} \\  & MMF/POF & & & & & \\ \hline \multirow{2}{*}{\(\phi\)-OTDR} & SMF & 100 km & 5 m & & & \\  & SMF & up to 40 km & 4 m & & & \\ \hline \multirow{4}{*}{OFDR} & SMF & 30/70 m (\(\dagger\)) & 1 cm & & 0.1 °C/1 \(\mu\) & from 10 to 20 s \\  & SMF & 2 km (\(\dagger\)) & 3 cm & Temperature & \textgreater{}0.5 °C/\textgreater{}4.1 \(\mu\) & 6.5 s \\ \cline{1-1}  & SMF & 10 m & 5.2 mm & / & \textless{}0.1 °C/\textless{}1 \(\mu\) & 0.1 s \\ \cline{1-1}  & SMF & 2 m & 5.2 mm & Strain & \textless{}0.1 °C/\textless{}1 \(\mu\) & 4 ms \\ \cline{1-1}  & SMF & 10 m & 1.3 mm & & \textless{}0.1 °C/\textless{}1 \(\mu\) & 42 ms \\ \hline \multicolumn{2}{l}{POFDR (**)} & SMF & 100 m & 2 mm & n/a & n/a & n/a \\ \hline \hline \end{tabular}  
* The device can directly sense strain in polymer optical fibre (POF), where an increase in the backscatter level with strain is observed [47]; ** The device performs a space resolved measurement of birefringence (transverse stress) and reflection. \(\
u\)-OTDR: photon-counting OTDR; \(\phi\)-OTDR: phase-OTDR; MMF: multi-mode fibre; POFDR: polarisation-sensitive OFDR; SMF: single-mode fibre; \(\ddagger\) These rows refer to the two different modes of operation of the same device.  
\end{table} 
Table 1: Performances of some commercial Rayleigh-based interrogators (sources: producers’ datasheets, technical notes, and scientific papers). In Raman-DTS exploiting the ratio of the anti-Stokes signal to the Stokes one, the directional coupler consists of a large bandwidth wavelength division multiplexer or a dichroic coupler, capable of routing the backscattered Stokes and anti-Stokes bands onto separate detectors. Please note that Rayleigh scattering is the strongest among the three different kinds of scattered light, followed by Brillouin scattering (15-20 dB weaker), and Raman is the weakest at 10 dB weaker than Brillouin. Therefore, Raman-DTSs require many backscattered pulses to be collected and averaged to reach an adequate SNR level. Other implementations are also possible; for example, a less-demanding hardware setup replaces the coupler with a simple circulator or coupler, with only one receiver channel equipped with an optical filter. This filter is mechanically switched to separate the anti-Stokes from the Stokes component, and the light is directed to a single photodetector. In principle, Raman scattering is generated at any wavelength of the input probe light. Nonetheless, the kind of fibre that is used poses some practical limitations: in case of multimode fibres (currently the most common choice in Raman-DTSs), the main limitation is due to the intermodal dispersion that broadens the impulse, degrading the spatial resolution. Instead, single mode fibres require the anti-Stokes signal to be at a wavelength longer than the fibre cut-off wavelength (i.e., the wavelength below which the second transverse mode propagates) that for standard single mode fibres is usually around 1300 nm. Other considerations deal with the power available at the anti-Stokes photodetector and with the availability of high-power sources and detectors at the operative wavelengths. Overall, practical implementations of Raman-DTSs are conveniently distinguished according to the working range. In this regard, short-range Raman-DTSs, operating with multimode fibres, laser sources at 850-910 nm, and standard silicon avalanche photodetectors, are limited to a distance range up to 5 km, mainly due to the low emitted power and poor launching efficiency.