1. Introduction

Brillouin scattering-based distributed optical fiber sensors are highly attractive for multiple applications such as geotechnical engineering and structural health monitoring, since it offers the capacity to measure temperature and strain along the fiber. So far, Brillouin-based distributed fiber sensors can be realized by three ways [1–5]: Brillouin optical time domain analysis/reflectometry (BOTDA/R), Brillouin optical correlation domain analysis/ reflectometry (BOCDA/R) and Brillouin optical frequency domain analysis/reflectometry (BOFDA/R). Among them, the BOTDA has been intensively investigated and widely applied due to its high spatial resolution and long sensing range [5–7].

The working mechanism of the conventional BOTDA is based on the stimulated Brillouin scattering (SBS) process between a pulsed pump and a counter-propagating frequency-sweeping continuous-wave (CW) probe. In this way, Brillouin gain spectrum (BGS) can be detected and further utilized to extract Brillouin frequency shift (BFS) which exhibits a linear relationship with the temperature and strain. Typically, the sensing speed of the BOTDA is confined by four main factors [3,8,9]: 1) Frequency sweeping process: Due to the wide sweeping range, high sweeping granularity and slow frequency switching of conventional microwave generator, the BGS acquisition via frequency sweeping is normally time-consuming [8,9]. 2) Trace averaging: Due to the inherent fiber loss, measurement certainty is reduced along the fiber due to the signal-to-noise (SNR) degradation. Brillouin gain trace averaging is a common method to improve the SNR, but with reduced sensing speed [8,9]. 3) Polarization fading: The SNR could also be degraded due to polarization fading effect. The polarization scrambling method is possible to eliminate such effect, but it requires large average number [3]. 4) Fiber length: To avoid crosstalk between adjacent pump pulses, the pump pulse interval must be larger than the round-trip time of flight in the fiber. With the increasing fiber length, the pulse interval must be increased with reduced maximal sampling rate [8,9], the pump and probe power also need to be decreased to avoid detrimental nonlinear or non-local effects [10,11], resulting in SNR degradation or larger average number. Confined by above factors, the BOTDA is usually considered to be a good sensor for static rather than dynamic measurement.

Presently, to realize fast dynamic sensing, lots of studies have been done to improve the dynamic sampling rate of the BOTDA sensor [8]: 1) Fast-frequency-switching based on an arbitrary waveform generator can significantly reduce the time consumed in the frequency-sweeping process [9,12,31]. Furthermore, slope-assisted [13–21], optical frequency-comb [22,23] or optical chirp chain [24,25] methods can avoid the frequency-sweeping process. 2) Optical pulse coding method can largely improve the SNR and thus reduce averaging time [26–28]. 3) The use of polarization diversity technology or polarization-maintaining fiber can effectively eliminate the polarization fading without large average number [12,16,17,24,28–31]. Foreseeably, by combining these techniques, the sampling rate of the sensor can be largely enhanced and only limited by the fiber length [8,9]. It is expected that Brillouin-based long-distance dynamic sensors should not only offer the capability to break through the limit of fiber length to the sampling rate, but also be robust to the detrimental nonlinear and non-local effects.

In this paper, a new Brillouin optical time domain collider (BOTDC) is proposed and experimentally demonstrated to break through the limit of fiber length to the sampling rate. In the BOTDC, the pulsed pump and CW probe are both frequency-hopping optical signals. The frequency relationships between the pump and probe lights are delicately designed, i.e., each pump pulse with a specific frequency only interacts with a relevant-frequency probe wave segment through the SBS. Therefore, the crosstalk is avoided even through the pulse interval is shorter than the round-trip time of flight in the fiber. Consequently, the sampling rate is enhanced and higher than the one determined by the fiber length. Meanwhile, since the SBS interaction periodically occurs at a specific fiber region, the SBS interaction length is reduced, which alleviates the non-local effect caused by pump depletion. This indicates that the probe wave with higher power can be employed to enhance the SNR and thus reduce the averaging time. Moreover, dynamic signals measured by the BOTDC can be extracted by employing direct detection with a low sample-rate data acquisition card, which leads to low data volume and potentially high real-time capability. In the experiment, by employing the 4- and 10-frequency BOTDC, periodic mechanical vibrations with a 19.75-Hz fundamental frequency and a 39.49-Hz harmonic frequency are measured at the sampling rates of 19.6 kHz and 49 kHz which are 4 and 10 times higher than that in the conventional BOTDA sensor, respectively.

2. Principle

In the conventional BOTDA, the energy transfer between the pulsed pump and the CW probe through the SBS will happen when their frequency offset falls within the BGS [3]. In order to avoid the sensing information-crosstalk between adjacent pump pulses, the pulse interval (T_p, equivalent to the sampling interval T_sample) must be larger than the round-trip time of flight in the fiber (T_round-trip), as described in Eq. (1) [9]:

For breaking through the limit of fiber length to the sampling rate, a new BOTDC is proposed. Compared with the conventional BOTDA, the pump and probe lights are both frequency-hopping optical signals in the BOTDC. Figure 1(a) illustrates the principle of a 4-frequency BOTDC. In the time range of 0 to 2nL/c (the round-trip time of flight in the fiber), four pump pulses with the frequencies of f₁, f₂, f₃, f₄ and four probe segments with the frequencies of f₁-f_s, f₂-f_s, f₃-f_s, f₄-f_s are injected into the fiber simultaneously. Here, as depicted in Fig. 1(b), f₁<f₂<f₃<f₄, and the frequency spacing between any two adjacent hopping frequencies (e.g., f₂-f₁) is much larger than the overall frequency range of the BGS (determined by the dynamic measurement range). f_s (∼11 GHz) denotes the frequency offset between the pump and probe waves, which makes the Brillouin gain located at the slope of BGS (i.e., incorporating with the Brillouin gain-based slope-assisted method [13]). In this way, after pump-probe colliding at the center of the fiber, each pump pulse with a specific frequency only interacts with the relevant frequency probe wave segment through the SBS. For instance, the pump pulse f₁ only interacts with the probe wave segment f₁-f_s. Consequently, the crosstalk between adjacent pump pulses is avoided even through the pump pulse interval is a quarter of the round-trip time in the fiber. This means that the sampling rate is improved by 4 times. It is worth noting that the sampling rate can be further enhanced by increasing the number of frequencies. Meanwhile, since the SBS interaction is controlled to periodically occur at a specific fiber region, subsequently the SBS interaction length is reduced by 4 times, which alleviates the non-local effect caused by pump depletion [32].

 

Fig. 1. (a) Schematic diagram and (b) frequency relationship of a 4-frequency BOTDC.

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Moreover, to shift the collision area (sensing area) location rapidly and flexibly, a method based on adjusting pump’s frequency-coding rule and delay to change the pump-probe relative delay is proposed. Take the 4-frequency BOTDC for instance, for a fixed frequency coding rule of the probe wave [f₁-f_s, f₂-f_s, f₃-f_s, f₄-f_s], if the pump’s frequency coding rule is [f₁, f₂, f₃, f₄], then the collision area is located from L/2 to 3L/4, as depicted in Fig. 1 (the fiber region marked in red). If the coding rules are [f₂, f₃, f₄, f₁], [f₃, f₄, f₁, f₂] and [f₄, f₁, f₂, f₃], then the collision areas are located from 3L/4 to L, 0 to L/4 and L/4 to L/2, respectively. Besides, to locate the collision area from L/8 to 3L/8, the coding rule and delay of the pump are [f₄, f₁, f₂, f₃] and nL/4c, respectively. It should be noted that the BOTDC with higher levels (e.g., 10-frequency BOTDC) can shift the collision area location in similar ways.

3. Experimental setup

The experimental setup of the BOTDC is shown in Fig. 2. The CW light from a narrow linewidth (∼100 kHz) external cavity laser (ECL) is split into two branches by a 50:50 coupler. In the lower branch, the frequency-hopping pump pulses (the pulse width is 30 ns) are generated by a high extinction-ratio (35 dB) electro-optic modulator (EOM1) with the carrier-suppressed mode and driven by frequency-hopping electric pulses. The electric pulses with specific frequencies are sequentially generated by an arbitrary waveform generator’s (AWG’s) channel (Ch1) and amplified by a low-noise amplifier (LNA1). After amplified by an erbium-doped fiber amplifier (EDFA1), the state of the polarization (SOP) of the pump pulses is adjusted by a polarization controller (PC2) to align to SOP of the probe wave. Then, the pump pulses are injected into the fiber under test (FUT, 1-km polarization-maintaining fiber (PMF)) through a circulator. The BFS of the FUT is ∼10.88 GHz. The peak power of the pump pulse is ∼25.5 dBm. Since the states of polarization (SOPs) of the pump and probe waves are always aligned in the PMF, the polarization fading is avoided, which leads to higher SNR, higher sampling rate and simplified system configuration. The dynamic strain (periodic mechanical vibration) is applied on the stretched fiber section at the end of the FUT by an eccentric wheel, as shown in the inset of the Fig. 2. In the upper branch, a carrier-suppressed double-sideband (CS-DSB) frequency-hopping probe wave is generated by the EOM2 driven by a frequency-hopping electric signal. The electric signal generated by the AWG’s Ch2 is up-converted by using the combination of frequency mixing and band-pass filtering (BPF). After being amplified by the EDFA2, anti-Stokes component of the probe is removed by using a fiber Bragg grating (FBG). Then, the SOP of the probe wave is adjusted by PC4 to align to the slow axis of the FUT. Before injecting into the FUT, the probe wave is spilt into two branches by an 80:20 coupler. The 80% of the probe is injected into the FUT and then sent to the receiver by a circulator. The probe power is ∼-3 dBm. The 20% of the probe is directly sent to the receiver.

 

Fig. 2. Experimental setup of BOTDC. ECL: external cavity laser; PC: polarization controller; EOM: acousto-optic modulator; AWG: arbitrary waveform generator; MG: microwave generator; LNA: low-noise amplifier; BPF: bandpass filter; EDFA: erbium-doped fiber amplifier; FUT: fiber under test; FB: fixed base; FBG: fiber Bragg grating; PD: photodiode; VOA: variable optical attenuator; OSC: oscilloscope; Log. N.: logarithmic normalization.

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At the receiver, the 80% of the probe wave with Brillouin amplification is detected by a 350-MHz photodetector (PD2). Since the responses of the frequency-mixer, LNA, BPF and EOM2 to the microwave signals with different frequencies are not the same, the intensity the probe wave may fluctuate with varied frequencies, as shown in Fig. 2 (the red curve after the PD2: the BGS is mixed with the probe bias fluctuation.). Generally, in the conventional BOTDA, the pulse interval is set to be slightly larger than the round-trip time in the fiber. Thus, the DC component corresponding to the CW probe reaching the fiber near end without Brillouin amplification can be acquired. Then, after the Brillouin signal (from PD2) being divided by the mean value of the DC component, the bias fluctuation can be eliminated. Finally, precise BGS distribution along the FUT can be obtained through logarithmic normalization [27]. However, as shown in Fig. 1(a), the probe light is continuously amplified by the pump pulses in the BOTDC and the DC component (without Brillouin amplification) does not exist anymore. To obtain the precise BGS distribution in the BOTDC, a new probe bias tracking-based (i.e. probe-based) logarithmic normalization method is proposed. Specifically, as described in Fig. 2, 20% of the probe without Brillouin amplification is detected by a 75-MHz PD1 and used as the reference signal to track the bias of the probe. After the Brillouin signal (from PD2) being divided by the reference signal (from PD1), the probe bias fluctuation can be eliminated and the precise BGS distribution can be acquired using logarithmic normalization. Here, the pulse interval is set as 12 μs for the BOTDA configuration, while the interval between pulses with the same hopping frequency is set as 10.2 μs for the BOTDC.

Similarly, the responses of the AWG, LNA1 and EOM1 (in Fig. 2) to microwave pulses with different frequencies are not the same. If the AWG’s imported digital pulses with different frequencies have the same amplitude, the generated optical pulses with different hopping frequencies will actually have different peak power, resulting in Brillouin gain differences between different hopping frequencies and thus the degradation of dynamic measurement accuracies when the BGS-fitting-based [8,9,12,22–24,28,31] or slope-assisted methods [8,13–21] are used. To solve this issue, a digital feedback method is applied. Specifically, the digital pulses’ amplitudes are reversely adjusted according to the differences between the generated optical pump pulses’ amplitudes.

The frequency scanning range of the microwave generator (MG) is from 9.76 to 10.04 GHz with 4-MHz step size. In the 4-frequency BOTDC, AWG’s Ch1 (for the pump) generates electric pulses with hopping frequencies of 1 GHz, 1.4 GHz, 1.8 GHz and 2.2 GHz, and AWG’s Ch2 (for the probe) generates CW electric signals with hopping frequencies of 2 GHz, 2.4 GHz, 2.8 GHz and 3.2 GHz. After passing through the electric bandpass filter (BPF, 11∼15 GHz), only the signals with frequencies from 11.76 (9.76 + 2) GHz to 13.24 (10.04 + 3.2) GHz exist. Similarly, in the 10-frequency BOTDC, electric pulses’ hopping frequencies (AWG’s Ch1) are 1 GHz, 1.25 GHz, 1.5 GHz, 1.75 GHz, 2 GHz, 2.25 GHz, 2.5 GHz, 2.75 GHz, 3 GHz and 3.25 GHz. Meanwhile, the CW electric signal’s hopping frequencies (AWG’s Ch2) are 2 GHz, 2.25 GHz, 2.5 GHz, 2.75 GHz, 3 GHz, 3.25 GHz, 3.5 GHz, 3.75 GHz, 4 GHz and 4.25 GHz. Thus, only the signals with frequencies from 11.76 (9.76 + 2) GHz to 14.29 (10.04 + 4.25) GHz exist.

4. Experimental results

Figure 3(a1) illustrates the BGS distribution along the fiber in the conventional BOTDA when the proposed probe bias tracking-based logarithmic normalization method is employed. It can be seen that the probe bias fluctuation is effectively eliminated. For the 1-km sensing fiber, the round-trip time of flight in the fiber is 10 μs. Therefore, the pulse interval must be larger than 10 μs (a 10.2-μs pulse interval is used). The BGS distribution along the fiber has the following properties: 1) there are significant variations from 0 to 300 m and 2) the stretched 5-m fiber section at the end of the FUT leads to significant BGS distribution change. Moreover, a 200-MHz frequency range can fully cover the overall range of the BGSs, which means that if the frequency spacing between any two adjacent frequencies is larger than 200 MHz, the BOTDC can work properly. The peak Brillouin gain and number of averages are ∼10% and 128, respectively. Figure 3(a2) compares the BGSs at 100 m when the traditional DC-based (blue line) [27] and the proposed probe-based logarithmic normalization methods (red line) are used, indicating that the method can effectively eliminate the bias fluctuation of the probe.

 

Fig. 3. (a1) The BGS distribution along the fiber in the conventional BOTDA when the probe-based logarithmic normalization method is employed. (a2) The extracted BGS at 100 m when the traditional DC-based and the proposed probe-based logarithmic normalization methods are employed. The BGS distribution from (b1) 0 to 245 m, (b2) 95 to 350 m and (b3) 755 to 1000 m in the 4-frequency BOTDC. The BGS distribution from (c1) 0 to 92 m, (c2) 92 to 194 m and (c3) 908 to 1000 m in the 10-frequency BOTDC.

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For the 4-frequency BOTDC, the frequency coding rule of the CW electric signal in the AWG’s Ch2 (for the probe) is fixed at [2, 2.4, 2.8, 3.2] GHz. By setting the frequency coding rules and delays of the electric pulses in the AWG’s Ch1 (for the pump) as 1) [1.8, 2.2, 1, 1.4] GHz and 0 μs, 2) [2.2, 1, 1.4, 1.8] GHz and 1.5 μs and 3) [1.4, 1.8, 2.2, 1] GHz and 0 μs, the corresponding collision areas are located from 1) 0 to 245 m, 2) 95 to 350 m and 3) 755 to 1000 m, respectively, as shown in Figs. 3(b1)–3(b3). It can be seen that the sensing information (BGS distributions) from 0 to 245 m, 95 to 350 m and 755 to 1000 m is periodically repeated by 4 times, illustrating a 4-time improvement of the sampling rate. Meanwhile, by using the similar method, the collision area can be located at any fiber region rapidly and flexibly. It is worth noting that the difference of the pump peak power between different hopping frequencies are cancelled by using the digital feedback method. As shown in Figs. 3(b1)–3(b3), the BGS distributions related to different hopping frequencies has almost the same Brillouin gains, which is beneficial to high-quality dynamic measurements when incorporating with the slope-assisted method.

Furthermore, for the 10-frequency BOTDC, the frequency coding rule of the CW electric signal in AWG’s Ch2 (for the probe) is fixed at [2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.25] GHz. By setting the frequency coding rules of the electric pulses in the AWG’s Ch1(for the pump) as [2.25, 2.5, 2.75, 3, 3.25, 1, 1.25, 1.5, 1.75, 2] GHz, [2.5, 2.75, 3, 3.25, 1, 1.25, 1.5, 1.75, 2, 2.25] GHz and [2, 2.25, 2.5, 2.75, 3, 3.25, 1, 1.25, 1.5, 1.75] GHz (no pump delay), the collision areas are located from 0 to 92 m, 92 to 194 m and 908 to 1000 m, respectively, as shown in Figs. 3(c1)–3(c3). Similarly, the sensing information is repeated by 10 times in 10.2 μs and the collision area can be located at any specific fiber region, indicating a 10-time sampling rate enhancement.

As mentioned above, the frequency sweeping process is time-consuming. Thus, to measure the dynamic strain, we apply the slope-assisted method [13] in the BOTDC to further enhance the sampling rate. The BGSs corresponding to the stretched fiber section (at the end of the fiber) in the conventional BOTDA (magenta line), this proposed 4- (red line) and 10-frequency (blue line) BOTDC are shown in Fig. 4(a). The BGSs in the three cases are almost the same with the peak Brillouin gain of ∼9.5%. Figure 4(b) depicts the detail of Fig. 4(a) from 10.952 GHz to 10.992 GHz. By adopting linear fitting method, the linear region is found to be from 10.96 GHz to 10.984 GHz, as marked in the orange area. According to the 1 MHz/20 μɛ strain-to-frequency conversion factor, the dynamic strain measurement range is ∼480 μɛ [13]. Moreover, the linearities related to the three cases are 0.993, 0.9937 and 0.9972, respectively.

 

Fig. 4. (a) Measured BGS at 100 m and (b) the detail from 10.952 to 10.992 GHz when the conventional BOTDA, the proposed 4- and 10-frequency BOTDC are employed.

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Subsequently, the dynamic strain measurement by the eccentric wheel is performed. Figure 5(a) illustrates the dynamic strain signal measured by the conventional BOTDA (magenta line), the proposed 4- (red line) and 10-frequency (blue line) BOTDC, respectively. A 20-points moving average is employed to enhance the SNR (i.e., the number of averages is 20.). By converting the Brillouin gain variation to the BFS variation, the maximal BFS change due to the dynamic strain is ∼13 MHz. According to the 1 MHz/20 μɛ strain-to-frequency conversion factor, the maximal dynamic strain variation is 260 μɛ. Figure 5(b) shows the details of Fig. 5(a) from 10 to 30 μs. It can be seen that, compared with the conventional BOTDA, the sampling rates are improved by 4 and 10 times for the 4- and 10-frequency BOTDC, respectively. The sampling rates of the conventional BOTDA, the 4- and 10-frequency BOTDC are 4.17 kHz (1/12μs/20), 19.61 kHz (1/2.55μs/20) and 49.02 kHz (1/1.02μs/20), respectively.

 

Fig. 5. (a) The measured dynamic strain signal and (b) the detail from 10 to 30 μs when the conventional BOTDA, the proposed 4- and 10-frequency BOTDC are employed.

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Finally, frequency spectra of measured dynamic strain signals shown in Fig. 5(a) are obtained through fast Fourier transform, as illustrated in Fig. 6. It can be found that the frequency spectra in above three cases (conventional BOTDA in magenta, 4- and 10-frequency BOTDC in red and blue, respectively) are almost the same. Moreover, the frequency spectrums contain a 19.75-Hz fundamental frequency and a 39.49-Hz harmonic frequency.

 

Fig. 6. The frequency spectra of the measured dynamic strain signals.

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5. Discussion and conclusion

Although the proposed BOTDC can break through the limit of fiber length to the sampling rate, there is still a trade-off between the sampling rate and measurement range. If a N-frequency BOTDC (N denotes the number of hopping frequencies) is employed, the dynamic sampling rate is enhanced by N times, meanwhile, 1/N of the fiber length is probed in a single shot. Therefore, the sampling rate improvement should be properly chosen according to the required measurement range. In addition, compared with the conventional BOTDA, the total measurement time to probe overall fiber is the same, while the probe wave with higher power can be employed to enhance the SNR. The BOTDC scheme could also be applied to measure physical parameters (e.g. temperature or strain) at specific areas or locations with improved sampling rate. It is also possible to achieve optimal measurements for the objects with different characteristics by utilizing arbitrary frequencies.

In summary, a new BOTDC is proposed to break through the fiber length-limited dynamic sampling rate. This proposal relies on that the pump and probe are both frequency hopping signals and the frequency relationships between the pump and probe lights are delicately designed. Therefore, the SBS is controlled to periodically occur at specific fiber regions and the sampling rate can be improved by eliminating the sensing information-crosstalk. In order to shift the location of collision area rapidly and flexibly, a method based on altering the relative delay between the pump and probe waves is presented. In addition, the probe-based logarithmic normalization and digital feedback methods are proposed to reduce the fluctuation of the probe bias and the difference of the pump peak power, respectively. Experimental results demonstrate that, compared with the conventional BOTDA, the sampling rates are improved by 4 and 10 times by employing the 4- and 10-frequency BOTDC, respectively.