Distributed optical fiber dynamic strain sensors, also known as distributed vibration sensors (DVS), have been used in a wide range of applications, from monitoring the condition of high-voltage subsea cables to structural health monitoring of pipelines and mapping terrestrial seismic activities [1–4]. For all these applications, the length of the sensing fiber is of vital importance, since a greater sensing range means that a larger structure or a wider area can be monitored with a single sensing system. As a result, recent research has focused on increasing the DVS sensing range. In 2014, Wang et al. reported a sensing system with a 175 km sensing range and 25 m spatial resolution that uses a hybrid distributed amplification [5]. The proposed setup used a combination of co-pumping second-order Raman amplification and counter-pumping first-order Raman and Brillouin amplification to achieve this sensing range. Similar long-range phase-sensitive optical time-domain reflectometer ($\varphi$-OTDR) systems based on the Raman amplification have also been reported as capable of detecting vibrations at distances over 100 km [1,6].

Although all these systems can detect vibrations over a long range, they are not capable of quantifying the vibration magnitude. To fully quantify the dynamic strains along the sensing fiber, the differential phase of the backscattered Rayleigh light needs to be employed [7]. In 2017, Pastor-Graells et al. have demonstrated a long-range DVS system based on a linearly chirped probe pulse with the 75 km sensing range using bidirectional first-order Raman amplification [8]. This system achieved a 10 m spatial resolution and 1 nϵ strain resolution. This technique was later combined with time-gated digital optical frequency domain reflectometry to achieve a 108 km sensing range with a spatial resolution of 5 m and a strain sensitivity of $220\mathrm{p}ϵ/\sqrt{\mathrm{Hz}}$ [9]. However, both techniques required access to both ends of the sensing fiber due to the use of bidirectional amplification, a requirement that may not be feasible for some implementations. Recently, Zhang et al. have demonstrated a single-ended DVS with an 80 km range [10]. This sensing range was achieved through nonlinear modulation of the probe pulse frequency and without the help of distributed amplification. The interrogation setup used to control the pulse chirp, however, was quite elaborate, and extracting the strain information required a complex signal processing.

To extend the sensing range of DVS systems, a different approach was adopted by Cameron et al. [11]. In this approach, a standard single-mode fiber (SSMF) was spliced to an ultra-low loss fiber with a 0.155 dB/km attenuation at one end and an enhanced backscattered fiber at the other end to achieve a maximum sensing range of 125 km without the use of inline amplification. However, the study did not disclose the operating principle of the system and the strain sensitivity of the setup. In addition, the spatial resolution of the sensor was limited to 10 m.

In 2005, Cho et al. have proposed a technique to increase the sensing range of distributed optical fiber sensors beyond the 50 km limit of the first-order Raman in-line amplifiers [12]. In this study, a 1480 nm laser was used as both a Raman inline amplifier and a pump for an Erbium-doped fiber situated 50 km from the front end of the sensing fiber. Cho et al. showed that by remotely pumping a 2-m-long Erbium-doped fiber, the sensing range of their Brillouin optical time domain reflectometry setup could be extended to 88 km. In this study, the same concept proposed in Ref. [12] is used to demonstrate a single-ended DVS system with a 100 km sensing range.

The sensing principle of the DVS setup used in this study is based on analyzing the phase of the Rayleigh backscattered light from adjacent points on the sensing fiber [13]. Briefly, the variation in the length of a given section of an optical fiber can be measured by analyzing the phase difference between the Rayleigh backscattered light from the two ends of that section. The relationship between the phase difference, $\mathrm{\Delta }\varphi$, and the length, $l$, is given by [14]

In this study, an imbalanced Mach–Zehnder interferometer (IMZI) was used to monitor $\mathrm{\Delta }\varphi$. The path imbalance of the IMZI creates a temporal shift between the light traveling in its arms. The gauge length of the sensor is determined by the length of the delay fiber in the IMZI. To avoid signal fading, a symmetric $3\times 3$ coupler was used at the output of the IMZI to create three outputs with a phase shift of $2\pi /3$ between them. Using phase demodulation algorithms, the phase shift and, subsequently, the dynamic strain, can then be measured from the three outputs.

To increase the sensing range of the DVS, two forms of amplifications were utilized. The first form was an in-line Raman optical amplifier. In a Raman optical amplifier, stimulated Raman scattering (SRS) energy from a higher-frequency pump is transmitted to lower-frequency signals. In this setup, a 1480 nm pump was used to amplify 1550 nm photons through SRS. Although 1450 nm would be the ideal wavelength to use for amplifying the 1550 nm light, a 1480 nm laser can also be used due to the broad gain spectrum of Raman amplifiers [the full width at half maximum (FWHM) is around 50 nm at 1550 nm].

The second form of amplification used was a remotely pumped Erbium-doped fiber amplifier (EDFA). This amplifier was implemented by splicing a short piece of an Er-doped fiber at the end of a long stretch of standard single-mode sensing fiber and pumping it with the residual power from the 1480 nm laser.

The experimental setup is shown in Fig. 1. The output of a 1550 nm distributed feedback laser with a 50 kHz linewidth was modulated by an electro-optic modulator to generate a 20 ns probe pulse with the 4 mW peak power. An EDFA (EDFA1) was used to increase the peak power to 100 mW. A dense wavelength division multiplexing (DWDM) filter with a 100 GHz bandwidth was used to reduce the amplified spontaneous emission (ASE) from EDFA1. The amplified pulse was then picked by an acousto-optic modulator with a 50 dB extinction ratio to eliminate any ASE within the bandpass of the DWDM filter from leaking into the sensing fiber.

 

Fig. 1. Experimental setup for a long-range DVS with two remotely pumped EDFAs. EOM, electro-optic modulator; ISO, isolator; EDFA, erbium-doped fiber amplifier; DWDM, dense wavelength division multiplexing; AOM, acousto-optic modulator; WDM, wavelength division multiplexer; PZT, Piezo-electric actuator; FBG, fiber Bragg grating; C, circulator; IMZI, imbalance Mach–Zehnder interferometer; PD, photodetector.

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The probe pulse with the 40 mW peak power was combined with the 500 mW of continuous wave (CW) 1480 nm pump at the front-end of the sensing fiber by a 1480 nm/1550 nm wavelength division multiplexer (WDM) and launched into the sensing fiber. The power of the 1480 nm laser pump and the peak power of the probe pulse were adjusted to avoid the onset of non-linear effects such as self-phase modulation [15].

The sensing fiber consisted of seven sections. The first five sections included three SSMF fibers that were 48 km, 25 km, and 26 km in length, joined to one another by 2 m and 2.5 m of Er-doped fibers. The length of the two Er-doped fibers was chosen to provide the 8 dB and 9 dB amplification, respectively. The end of the last fiber was spliced to a 10-m-long standard single mode fiber (SMF-28), wrapped around a piezoelectric (PZT) actuator. Finally, the fiber on the PZT was spliced to a 500-m-long fiber to separate it from the far end of the sensing fiber.

The backscattered Rayleigh light was collected by the circulator C1 and filtered by another DWDM filter with a 100 GHz bandwidth to remove the majority of Raman backscattered light from the 1480 nm pump. The filtered light was then amplified by an optical amplifier (EDFA2) and further filtered by a fiber Bragg grating [${\lambda }_B=1550.1$, $\mathrm{\Delta }\lambda =6\mathrm{GHz}$ (0.05 nm), reflectivity, 70%] to remove the ASE from the optical amplifier, as well as to reduce the contribution of Raman backscattered light. The amplified backscattered light was fed into a thermally insulated Mach–Zehnder interferometer (MZI) with a 4-m-path imbalance. Three amplified photodetectors ($BW=600\mathrm{MHz}$, $\mathrm{\Omega }=80\mathrm{V}/\mathrm{mA}$) were used to sample the backscattered light from the $3\times 3$ coupler at the output of the MZI. The photodetectors were sampled at 625 MSa/s with a 1 GHz bandwidth digitizer.

Using the attenuation of the SSMF fiber and the absorption of Er-doped fiber at 1480 nm, the power of the pump laser before and after both EDFAs was calculated. Table 1 provides an overview of the pump power along the fiber and the amplification of the probe signal by the two EDFAs.

Table 1. Pump Power Along the Fiber and Amplification of the Main Signal by the Two EDFAs

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In Fig. 2, two OTDR traces are compared. The first (blue) used both Raman amplification and EDFA. For this OTDR trace, the pulse peak power and the 1480 nm CW pump power were 40 mW and 500 mW, respectively. The second OTDR trace (orange) did not have any optical amplification but had a higher launched probe power of 220 mW. The launching power was set to 220 mW below the threshold of the non-linear effects such as stimulated Raman scattering, stimulated Brillouin scattering, and self-phase modulation. From the trace with optical amplification, three different zones can be identified. The first zone is the first 48 km of the fiber, where the Raman amplification is used; the second zone, which can be identified by the peak at 48 km, where the first section of the Er-doped fiber is installed and ends at 73 km; and the third zone from the peak at 73 km, where the second section of the Er-doped fiber is installed and ends at 100 km. Without optical amplification, it can be seen that the power exponentially decays along the fiber and reaches below the level of the amplified trace within 35 km, even when a higher power probe pulse is used. From Fig. 2, it can be seen that with the two optical amplifiers, the Rayleigh backscattered signal is clearly visible at 100 km. Without the optical amplification, the signal-to-noise ratio fell to unity at approximately 50 km for the probe pulse with the 220 mW launch power.

 

Fig. 2. Measured Rayleigh backscattered signal (blue) with a combined EDFA and Raman amplification using a launched power of 40 mW combined with a 500 mW 1480 nm pump; (orange) without the use of optical amplification with the 220 mW launched power.

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Figure 3 shows the results of the processed signals. Figure 3(a) shows the top-view map of the strain level in the time domain. The location of the strain and its periodic profile can be seen in this figure. The color-bar next to this diagram represents the strain level in μϵ. The fast Fourier transform (FFT) of the strain level is shown in the 3D diagram of Fig. 3(b) where the horizontal axes show the distance and the frequency components of vibrations along the fiber, while the vertical axis indicates the magnitude of the vibration. The data used for this FFT were captured over 10 s. The peak in this figure corresponds to the location of the perturbation. The magnitude and frequency of the vibration applied by the PZT to the fiber is measured as 0.85 μϵ and 10 Hz, respectively, at the distance of 99.3 km from the front end of the sensing fiber.

 

Fig. 3. 3D map of the strain distribution along the sensing fiber as a function of (a) time and distance and (b) frequency and distance.

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Two-dimensional (2D) cross-sections of the three-dimensional (3D) diagrams in Fig. 3 are shown in Fig. 4. Figure 4(a) depicts the cross-section of the 3D time-domain plot at 99.3 km, showing the strain variation at a fixed point on the fiber as a function of time. The strain is periodic (sinusoidal) and has slight variation in amplitude due to noises in the system, such as laser phase noise. The average value of the strain amplitude is 0.85 μϵ. Figure 4(b) shows a 2D cross section of the frequency domain results at fixed point on the fiber as a function of frequency. This plot can be used to verify the frequency and magnitude of the vibration at a fixed point. It can also be used to measure the noise floor of the setup as a function of frequency at that position. Figure 4(c) depicts a 2D cross-section of the frequency domain plot [Fig. 3(b)] at a fixed frequency as a function of distance. The analysis of this plot demonstrates that the 10%/90% spatial resolution of the system is 2.6 m, which is close to the theoretical limit of 2 m. The discrepancy between the theoretical and experimental values of the spatial resolution is due to the temporal and spatial data averaging, which was implemented to improve the signal-to-noise ratio.

 

Fig. 4. 2D cross-section of the 3D diagram of Fig. 3 at a specific location on the sensing fiber where strain is applied (99.3 km). (a) 2D cross-section in time domain, (b) 2D cross-section in the frequency domain at fixed position on the fiber, and (c) 2D cross-section in the frequency domain at fixed frequency.

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Figure 5 shows the strain level on the fiber measured by the DVS as a function of the input voltage to the PZT. For this test, different strain levels were exerted on the fiber by the PZT at a fixed frequency. This figure shows a linear relationship between the applied and measured strain on the sensing fiber. Due to the laser phase noise, drift in IMZI path imbalance, detector noise, and digitization level of the data acquisition card used in the setup, the minimum detectable strain at 99.3 km was measured to be 100 nϵ for a 10 Hz oscillation corresponding to a power spectral density noise of $7\mathrm{n}ϵ/\sqrt{\mathrm{Hz}}$ within the 5–500 Hz frequency band. It should be pointed out that the noise floor of the sensing system depends on the amplitude of the coherent Rayleigh noise (CRN). The sections of the OTDR trace where the amplitude of the CRN is closer to zero have a higher noise level since the phase demodulation algorithm rely on weak backscattered light to extract the phase information. The 100 nϵ noise floor reported in this study was obtained by analyzing the strain level at the unperturbed section of the sensing fiber. By comparing the strain response profile of the PZT at 10 Hz that was measured separately, it can be concluded that the proposed sensing arrangement is capable of quantifying the frequency, amplitude, and location of dynamic perturbations anywhere along a 100-km-long sensing fiber.

 

Fig. 5. Strain response of the fiber to the PZT input voltage for 10 Hz sinusoidal signal measured by the DVS.

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In summary, a long-range distributed vibration sensor with inline Raman amplification and remotely pumped EDFA is demonstrated in this Letter. It was shown that by combining these two amplification techniques, the DVS system can accurately measure the location, frequency, and amplitude of the perturbation applied to the sensing fiber at the far end of the 100-km-long SSMF from a single end of the fiber. The system showed a spatial and strain resolution of 2.6 m and 100 nϵ, respectively.