## 2 Sensing Principle  
When light transmits in an optical fiber, the light waves will be scattered to different degrees under the influence of medium molecules, resulting in a scattering spectrum with different frequencies [28]. Thus, the elastic scattering (Rayleigh scattering) and inelastic scattering (Brillouin scattering and Raman scattering) can be identified according to their frequency (Figure 1). While Raman scattering, including two different frequency parts, has been discovered to have a strong temperature sensitivity among these scattered lights, especially in its high frequency region. When light propagates through the fiber, the luminous flux of Stokes Raman scattering generated by each light pulse [29] is presented in Equation (1):  
\[\Phi_{S}=K_{S}\cdot S\cdot v_{S}^{4}\cdot\phi_{e}\cdot R_{S}(T)\cdot\exp[-( \alpha_{0}+\alpha_{S})\cdot L] \tag{1}\]  
The luminous flux of anti-Stokes Raman scattering can be expressed as Equation (2):  
\[\Phi_{AS}=K_{AS}\cdot S\cdot v_{AS}^{4}\cdot\phi_{e}\cdot R_{AS}(T)\cdot\exp[- (\alpha_{0}+\alpha_{AS})\cdot L] \tag{2}\]  
where \(K_{S}\) and \(K_{AS}\) are the cross-section coefficients of optical fiber related to Stokes scattering and anti-Stokes scattering, respectively; \(S\) is the backscattering factor of the fiber; \(v_{S}\) and \(v_{AS}\) are the frequencies of Stokes and anti-Stokes scattering photons; \(\phi_{e}\) is the number of incident laser pulse photons; \(\alpha_{0}\), \(\alpha_{S}\) and \(\alpha_{AS}\) are the average propagation loss factors of incident light, Stokes scattering  
Figure 1: Spontaneous scattering in optical fiber. light and anti-Stokes scattering light, respectively; \(L\) is the distance between the incident end of fiber and the measured point; and \(R_{S}(T)\) and \(R_{AS}(T)\) are the corresponding coefficients, related to the particle distribution of fiber molecules at different energy levels, which act as the temperature modulation functions of Stokes Raman scattering and anti-Stokes Raman scattering [30], as shown in Equations (3) and (4):  
\[R_{S}(T)=\left[1-\exp(-h\Delta v/kT)\right]^{-1} \tag{3}\]  
\[R_{AS}(T)=\left[\exp(h\Delta v/kT)-1\right]^{-1} \tag{4}\]  
where \(h\) is the Planck constant (\(h\) = 6.626 \(\times\) 10\({}^{-34}\) J-s); \(\Delta v\) is the Raman phonon frequency (\(\Delta v\) = 1.32 \(\times\) 10\({}^{13}\) Hz); \(k\) is the Boltzmann constant (\(k\) = 1.38 \(\times\) 10\({}^{-23}\) J-K\({}^{-1}\)); and \(T\) is the thermodynamic temperature. As the anti-Stokes Raman scattering has an obvious temperature sensitivity, it can be further used as the signal channel. Also, the temperature field can be obtained through the demodulation of these two scatterings from their ratio, as shown in Equation (5):  
\[ \begin{split}\Phi_{AS}(T)/\Phi_{S}(T)=K_{AS}/K_{S}\cdot(v_{AS}/v_ {S})^{4}\\ \cdot R_{AS}(T)/R_{S}(T)\cdot\exp[-(\alpha_{AS}-\alpha_{S})\cdot L ]\end{split}  \tag{5}\]  
It can be further displayed as Equation (6) when substituting Equations (3) and (4) into the above formula at the temperature of \(T_{0}\). \[ \begin{split}\Phi_{AS}(T_{0})/\Phi_{S}(T_{0})=K_{AS}/K_{S}\cdot(v _{AS}/v_{S})^{4}\\ \cdot\exp[(\alpha_{S}-\alpha_{AS})\cdot L-h\Delta v/kT_{0}]\end{split}  \tag{6}\]  
In order to perform temperature calibration, some front sections of the fiber sensor are selected as the calibration fiber, which will be placed in a thermostatic bath at temperature \(T_{0}\)[29].