Fig. 1. Schematic diagrams of three DFOS schemes. (a) Schematic diagram of the backscattering-based DFOS scheme. The sensing mechanism uses laser pulses to sample information along the fiber cable. Only after the previous pulse has traveled round trips along the whole fiber can the latter pulse emit sense vibrations in the next period. This rule leads to a limited repetition rate frep=c/2nL (c is the light speed, n is the refractive index of the fiber, and L is the sensing fiber length). (b) Schematic diagram of the forward-transmission laser interferometer scheme. The sensing mechanism uses the CW laser to obtain the integrated vibration information over the entire fiber link. This process makes vibration localization difficult. (c) Schematic diagram of the MI-correlation-enabled DSL interferometer scheme. It can find the true time delay between two overlapped original signals, simultaneously localize multiple vibrations, and be applied in distributed sensing fields (earthquake, traffic events, excavation, border intrusion, etc.).

Fig. 2. Conceptual diagram of the MI-correlation method and its principle. (a) MI-correlation can recover the hidden original signals from the detected composite signals. In the mirror-image process, two original signals will be extended step by step; finally, their true time delay will be obtained. (b) Principle of the MI-correlation method. Using different estimated time delays τ, the corresponding error marks are introduced and obtained. When the real τ0 is applied, the MI-correlation process will not induce an error mark.

Fig. 3. Experimental setup of the laser interferometer and processing of the MI-correlation method. (a) The system is deployed in the local size and only needs a loop-back at the far end. Laser: NKT Koheras BASIK X15; line-width <100Hz. AOM, acousto-optic modulator; OC, optical coupler; PD, photodiode; DAQ, data acquisition module to demodulate the phase-changing signal. (b) Initially detected signal, which is composed of two original parts, with a time delay τ0 of ∼750μs (vibration at point A). (c) The two original signals separated after m=336 mirror-image operations with a wrong time delay τ=1007μs. The mark error is shown as high-frequency noise. (d) The two original signals separated after m=336 mirror-image operations with the true time delay τ0=743μs. (e) The PSD plot of the signal in (c). Mark error appears at frequency 1/2τ=497Hz, with a higher MI-correlation indicator value M(τ)=12.4dB. (f) PSD plot of the signal in (d). The mark error appears at frequency 1/2τ0=673Hz with a lower indicator value M(τ0)=0.6dB. (g) MI-correlation indicator M(τ) of the 20 Hz single vibration with different times of mirror-image operations m. On the blue curve (m=336), the two red points correspond to a wrong time delay of τ=1007μs and the true time delay of τ0=743μs, respectively. The pink curve corresponds to m=10 case, which is used in practice. (h) Waterfall plot of the detected vibration in the time-space domain and its effective strain.

Fig. 4. Error mark power in three different stages. (a) In stage 1, the MI-correlation is performed on background noise, and the error mark power P0(τ) maintains at a low power level. A vibration-like minimum point will appear at τN≈626μs, corresponding to the midpoint of the sensing distance. (b) In stage 2, a beginning segment of the vibration signal has a complex spectrum, and the error mark power P(τ) is coherently enhanced to a high power level by the MI-correlation method, except point P(τ0) corresponding to the real-time delay τ0=743μs. (c) In stage 3, vibration becomes stationary and the error mark power goes back to a low level, which is similar to P0(τ) in stage 1.

Fig. 5. The sensing results of hammer-knock vibrations. (a) The hammer knocks occur at point A, which consists of seven knocks within 3 s. (b) The waterfall plot of hammer-knock vibration detection. These knocks are all localized at point A, ∼74.3km away from the far end. (c) The hammer knocks are distributed at points A, B, and C. Their vibration signals overlap with each other and are hard to be recognized. (d) The waterfall plot of multipoint hammer-knock vibration detection. It shows the knocks’ time–space localization and effective strain.

Fig. 6. The sensing results of urban traffic vibrations. (a) The diagram of sensing fiber link. It travels along an ∼32km urban fiber link and an ∼50km fiber spool in the lab, then loops back. Two main vibration sources are found at the road speed bump on campus (red position) and a pedestrian underpass on the fourth ring road in Beijing (green position). (b) The detected traffic vibration signal when vibrations at red and green positions are not overlapped. (c) The detected traffic vibration signal when vibrations at red and green positions overlap each other. (d) The waterfall plot of the traffic vibration signal in (b). It shows the time–space localization of traffic events at red and green positions separately. (e) The waterfall plot of the traffic vibration signal in (c). It distinguishes the time–space localization of traffic events at red and green positions separately.

Fig. 7. Distributed sensing results of three vibrations happened simultaneously. (a) The detected vibration signal of three FST-induced vibrations. Their waveform overlaps each other in the time domain. (b) Fourier transform plot of the 20-Hz vibration at point A. (c) Localizing distribution of the 20-Hz vibration at point A. (d) Fourier transform plot of the strong vibration at point B. (e) Localizing distribution of the strong vibration at point B. (f) Fourier transform plot of the 50-kHz vibration at point C. (g) Localizing distribution of the 50-kHz vibration at point C. In (c), (e), and (g), the circle points represent the discrete frequency distribution and the red lines are the fitted probability density curves.