## 4 Experiment and Results Discussion  
### Experimental Set-Up  
The experimental set-up is shown in Figure 1. The pulse laser (PL) generates probe pulse light with a pulse width of 20 ns, which is launched into the wavelength division multiplexer (WDM). Through the output port of the WDM, the light pulse comes into the FUT, which is a multi-mode fiber (MMF) of type OM1 62.5/125. The MMF is silica fiber with a gradient index distribution; the fiber core's group refractive index is approximately 1.496 at 1550 nm, and the refractive index of the cladding is approximately 1.472. The wavelength of the PL source is 1550.12 nm. The peak power of the pulse light is approximately 33 dBm. The back-scattered Raman anti-Stokes light goes through the WDM, and it is de-multiplexed in the 1450 nm channel. Following this, the Raman anti-Stokes light is converted to an electric signal by the APD. The data acquisition card (DAQ) with a sampling rate of 100 Msps collects and averages the corresponding voltage signal from the APD. The OTDR trace was obtained with an average of 10,000 times and is shown in Figure 2. The two peaks in Figure 2 correspond to the fiber front end and the fiber back end because a strong reflection phenomenon occurs when the pulse light interacts with the fiber ends. As the peaks represent the fiber's front end and back end, respectively, they are generally adopted to correct the walk-off effect in the traditional double-channel-based temperature demodulation method for positional marking. The personal computer (PC) also controls the PL and sets the parameters for the probe's pulse, such as the pulse width and the peak pulse power. The calibration zone is set within a range of approximately 100 m at the fiber front end. The function of the calibration zone is to obtain reference data at a known temperature \(T_{c}\) (21.2 \({}^{\circ}\)C) for temperature demodulation along each position in the FUT. In addition, it helps to correct the variance caused by changes to the output power of the PL and the gain factor fluctuation of the APD. In the experiment, a thermometer is used to record temperature information in the calibration zone, so the data \(P_{a}(L_{c},T_{c})\) and \(P_{a}^{R}(L_{c},T_{1})\) in Formulas (11) and (13) can be obtained, whereupon the correction coefficient R can be computed by Formula (15). In Figure 1, a heating zone is set at the end of the FUT for measuring temperature within a certain range. In the heating zone, a fiber section with a length of approximately 50 m is wound into a bundle and soaked in hot water. Another thermometer is set in the heating zone to record the water temperature. The temperature values recorded are then compared with the values measured by the sensing system to estimate its performance. To analyze the dynamic range (DR) of the Raman anti-Stokes temperature sensing system, the unit of the signal power information (in volts) is converted to logarithmic units in dB, as shown in Figure 3. It can be seen from Figure 3 that the DR is approximately 24 dB and the fiber attenuation coefficient is 0.703 dB/km. The fiber attenuation coefficient corresponds to the factor \((\alpha_{R}+\alpha_{a})\) in formula (11). It consists of two processes: the first is the attenuation of the light pulse propagation, which corresponds to the Rayleigh light attenuation coefficient \(\alpha_{R}\) as the wavelength of the pulse light is the same with Rayleigh light; and the second is the Raman anti-Stokes light back-propagation, which relates to the attenuation coefficient of the Raman anti-Stokes light \(\alpha_{a}\). In addition, an MMF with a larger fiber core can be adapted to work with fiber scattering spectra-based distributed optical fiber sensing technology, and the modal attenuation and mode coupling should be analyzed before its application [29]. measurement is a very important parameter.