## 3 Experiment and Results  
Figure 1a describes the experimental setup of the phase-sensitive OTDR for vibration sensing [11,12]. A continuous-wave (cw) light launched from a highly coherent laser source (\(\lambda\) -1554.2 nm) with ultra-narrow line width (-6 kHz) was modulated into the light pulses using the semiconductor amplifier (SOA) functioning as a switch. An isolator was installed between the laser and SOA to protect the laser from unwanted light reflections from the SOA, and optical features of the light pulse were optimized using a polarization controller (PC). Using an erbium-doped fiber amplifier (EDFA), the optical light pulse was amplified and the undesired ASE light was filtered out. Subsequently, a band-pass filter (BPF), made by an optical circulator and a fiber Bragg grating (FBG) (\(\lambda\) -1554 nm, \(\Delta\lambda\) -0.32 nm, reflectivity \(\sim\)30 dB) filtered out the undesired ASE light. Before entering into FUT, the input optical power should be controlled to be \(\leq\)23 dBm using a variable optical attenuator (VOA) to evade the possible nonlinear effects in the silica optical fiber. Then, the optical pulse was fed into the FUT and the coherent Rayleigh backscattering reflection was detected at the photodiode (PD) via the optical fiber circulator. Finally, the analog electrical signal was digitized using a high-speed data acquisition (DAQ) card, and analyzed by the computer. Figure 1b,c illustrates the vibration actuation setups, which are made by the mechanical actuator and the sound-speaker, respectively. A fiber loop of length 9 m was attached firmly on the setups using a removable tape at the particular position of \(\sim\)1245 m of the FUT. The vibration setups were driven by a function generator, whose frequency can be controlled from several Hz to kHz range. In the experiment, we set the pulse width to 90 ns and the pulse repetition rate to 10 kHz (pulse duration = 100 \(\mu\)s), which means that the \(\Phi\)-OTDR had a spatial resolution of 9 m and a detection range of 10 km. Using a DAQ module, we acquired 610 raw traces of the RBS signal using the setup given in Figure 1b, and 800 raw traces of the RBS signal using the setup given in Figure 1c; thus, the total data-acquisition times were 61 and 80 ms, respectively. During data acquisition, the sampling speed of the DAQ was 50.2 MS/s. Figure 2a shows the plot of the 610 consecutive raw Rayleigh backscattering traces along the length of the FUT. The plot contains the coherent amplitude modulation at specific positions caused by the fiber loop when subjected to a weak vibration event of 102 Hz using the mechanical actuator shown in Figure 1b. The Rayleigh backscattering traces were created by the coherent superposition of the light from multiple scattering centers along the FUT within the duration of optical pulse. The raw Rayleigh backscattering traces show the overall amplitude fluctuation. The fluctuation could be due to phase noise of the laser, random polarization causing partial interferometric issue, or background and electrical noises (thermal noise and shot noise). Moreover, amplitude-fading also exists in the signal after 1500 m. This is thought to be due to the input power of pulse light, which is slightly larger than the nonlinearity limit of the single-mode fiber used as the FUT. Thus, it was difficult to determine the location information and the frequency of the vibration event in the backscattering traces, which are badly affected by the random noises. Figure 2b shows a transformation of the amplitude data of the 610 raw Rayleigh backscattering traces (given in Figure 2a) to a density plot (gray image); the horizontal axis shows the spatial information and the vertical axis shows the temporal information of the dataset. The weak periodic change in the amplitude, which can be seen in the inset at the FUT location of 1245 m, was caused by the external vibration event (102 Hz).