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Abstract
Conventional Brillouin optical time-domain analyzer (BOTDA) with a frequency-modulated probe (FMP) could avoid non-local effects, while still suffering from the acoustic crosstalk between different frequencies. The induced Brillouin frequency shift (BFS) measurement errors over the whole sensing fiber link reduce system certainty subsequently. A BOTDA scheme with a bidirectional frequency-modulated probe (BFMP) is proposed to overcome such an effect. It utilizes BFMP to generate the crosstalk of the same magnitude and opposite direction to compensate each other. Experimental results indicate that the pulse interval of the coded sequence could be reduced to ∼500 ns to improve the measurement efficiency and BFS estimation errors (∼2.2 MHz) over 117.46-km sensor link are eliminated simultaneously.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Brillouin optical time-domain analysis (BOTDA) sensor is widely employed for distributed strain and temperature monitoring over a long optical fiber with a spatial resolution ranging from a few centimeters to several meters [1–8]. The technique is based on the stimulated Brillouin scattering (SBS) process [8] between a pulsed pump and a counter-propagating continuous probe with the acoustic wave serving as a medium for energy transfer between them. The amount of the transferred energy is associated with the pump-probe frequency difference (v) and the Brillouin resonant frequency (vB). The corresponding frequency of peak gain/loss (the probe is amplified/reduced by the pump) is called Brillouin frequency shift (BFS). It is almost linearly related to the temperature and strain [9]. Therefore, distributed temperatures and strains along a sensing fiber can be measured by retrieving the distributed BFSs. The sensor performance is dependent on the measurement signal-to-noise ratio (SNR) [10]. At the conditions of a given spatial resolution and sensing distance, the SNR is proportional to the injected pump and probe power. The pump and probe power are limited at ∼20 dBm and per sideband -6 dBm in a dual-sideband configuration by the modulation instability [11,12] and the non-local effect [13–16], respectively. Therefore, the optical pulse coding (OPC) technique [17–31] is proposed to increase the pump’s total energy while ensuring that the power of a single pulse does not exceed 20 dBm. However, the eventually effective SNR improvement is only ∼7.5 dB, which is again limited by the high-order non-local effect [24,26]. Hence, the frequency-modulated probe(FMP) technique [24,32–34] is put forward to overcome such an effect and to allow the implementation of longer OPC codes to enhance the sensor performance. However, crosstalk between different frequency acoustic waves (named acoustic crosstalk) is parasitized in the FMP. This issue pushes or pulls the Brillouin gain spectrum (BGS), induces BFS measurement errors over the whole fiber link, and then reduces sensor system certainty.
In this paper, a BOTDA scheme with a bidirectional frequency-modulated probe (BFMP) is proposed to compensate the impact of the acoustic crosstalk and narrow the pulse interval of the coded sequence. This method utilizes a bidirectional (i.e., the rising and falling) frequency-modulated probe to generate the crosstalk of the same magnitude and opposite direction to superpose each other to remove the BFS errors. First, a numerical simulation is performed to show temporal and spatial evolutions of the acoustic and probe wave, reveal the parasitized crosstalk, and verify the proposed BFMP’s effectiveness. Second, the proposed scheme is experimentally demonstrated in a 117.46-km sensing fiber with a 2-m spatial resolution. Both simulational and experimental results point out that 1) traditional rising (or falling) FMP pushes (or pulls) the BGS, induces BFS errors over the whole sensing fiber link, and then reduces sensor system certainty. 2) The BFMP method is a simple and robust approach to overcome the acoustic crosstalk and narrow the pulse interval of the coded sequence.
2. Operation principle and simulation
In this section, we first give the final results of the simulation and then elaborate on the simulation process and explain the cause of acoustic crosstalk. Although the modulated frequency is set as symmetric at zero, the rising- and falling- directional FMP pushes and pulls the BGS to be biased towards high and low frequencies, respectively, as shown in Fig. 1. The probe borrowing the acoustic wave built by preceding different frequencies results in this bias and then BFS measurement error. The BFMP method straightforward averages the BGSs from the rising and falling FMP. It uses the rising and falling frequency-modulation to generate the crosstalk of the same magnitude and opposite direction to compensate each other to remove the BFS errors. In the FMP, the measured probe needs to be shifted and reordered to decode the signal and retrieve the BGS [15,24,32]. The final fitted BFSs along a 200-m sensing fiber are shown in Fig. 2. Here, we can observe that the BFS errors from the rising and falling FMP have the same magnitude and opposite direction. Simulational results point out that 1) a single rising or falling FMP induces BFSs measurement errors; 2) By using the BFMP, BFS errors can be compensated. In this part, a numerical theory simulation is performed at the condition of the frequency-modulated probe to get the above final results (i.e., Fig. 1 and 2). The SBS interaction in optical fiber is described by three-wave coupled equations [35,36]:
The simulation parameters: The period of frequency-modulated probe Tperiod = 1000 ns (which is equal to the pulse interval of the coded sequence) and the duration of each frequency Tbit =20 ns; the number of frequencies in a period is N = 50 (N = Tperiod/Tbit); The v is from -98 MHz to +98MHz (i.e., the rising FMP) or from +98 MHz to -98MHz (i.e., the falling FMP) with a step 4 MHz; The ${v_B}$ is placed a hotspot (+25 MHz) at positions from 8 m to 28 m, and other locations’ ${v_B}$ are 0. The pulse width is 20 ns corresponding to $\Delta {v_B}$= 50 MHz.
The acoustic wave at each fiber location starts to build up and decay when the pulse arrives and leaves at the location, as indicated in Fig. 3. A white line in the figure is the motion trajectory of the probe (z = 100 m) light. It mainly gains energy from those crossing points between the white line and the acoustic wave. The figure is an excellent display of the interaction between the probe light and the acoustic wave in the temporal and spatial domain. In order to clearly show the acoustic amplitude changing with the frequency modulation, its cross-sectional view is shown in Fig. 4. Here, as v approaches and leaves ${v_B}$, the acoustic intensity increases (from 100 m to 150 m) and decreases (from 150 m to 200 m), respectively.
Fig. 4. Simulated acoustic wave amplitude corresponding distance after a pump-probe interaction time of 10 ns at each fiber location.
The following Fig. 5 is used to explain the causes of crosstalk. Supposing a small fraction of probe light (marked as a yellow dot in Fig. 5) meets the pulsed pump at z point. Here, the acoustic wave is established by the probe’s frequency fe and the pump, as displayed in Fig. 5(a). When the yellow dot transmits to z-VgT/4 point (where T is the pulse width), (It is worth noting that the pulse encounters the frequency fc of the probe at the z-VgT/4 point for the first time, as shown on the left in Fig. 5(b)), the acoustic wave at this point is established by the probe’s those frequencies fc, fd, fe, and the pump, as exhibited in Fig. 5(b). The acoustic wave at the z-VgT/4 point starts building from the pulse's arrival and lasts to the time of the dot's arrival. And so on, when the yellow dot arrives at z-VgT/2, the acoustic wave corresponds to those frequencies fa, fb, fc, fd, fe as indicated in Fig. 5(c). In other words, the yellow dot transmits from z to z-VgT/2, it relies on the acoustic wave medium built by preceding those frequencies of pulse-width-time for Brillouin amplification. In the FMP, there is no guarantee that the frequency of all points will always remain the same within the pulse width time. Therefore, no matter it is linear or steps frequency-modulated probe, there is the acoustic crosstalk.
3. Experimental setups
Figure 6 shows the experimental setup. A narrow linewidth (∼100 kHz) light source's central wavelength and output power are ∼1550.2 nm and ∼13 dBm, respectively. The output of the light source is divided into two branches by 50:50 optical couplers. The upper branch in the figure works as the Brillouin FMP probe, and the lower branch works as the Brillouin pulsed pump. A polarization controller (PC) is placed at the input of an intensity modulator (IM) to achieve maximum modulation efficiency. The IM biased at Vπ voltage is used to obtain a carrier-suppressed dual-sideband probe wave. The IM is driven by a frequency-modulated signal (i.e., fS). In detail, the fs is modulated in a 4 MHz step and 20 ns duration (Tbit) from 10782 MHz to 10978 MHz (i.e., the rising FMP) or from 10978 MHz to 10782 MHz (i.e., the falling FMP) within the Tperiod = 1000 ns. The next few steps generate the frequency fs signal: 1) The Arbitrary waveform generator(AWG) generates the frequency-modulated signal f1 from 102 MHz to 298 MHz (corresponding to the rising) or from 298 MHz to 102 MHz (corresponding to the falling); 2) A frequency-fixed f2 10680 MHz generated by the microwave generator(MG); 3)The f1 mixes the f2; afterward, a band-pass filters out the f1 + f2 frequency component. The probe light passes through an acousto-optic modulator (AOM1) and isolator into the sensing fiber. The probe power injected into the fiber is -4 dBm/sideband. The use of AOM1 induces the same frequency shift with respect to the pump (i.e., 200 MHz). The probe interacts with the pump in the fiber and then passes through an OC1 toward the erbium-doped fiber amplifier(EDFA). In the lower branch, the light is firstly boosted by a high-power Erbium Ytterbium Doped Fiber Amplifier (EYDFA) with adjustable gain. Then, the amplified light is further gated by an AOM2 with a 60-dB extinction ratio to generate pulse sequence and sent into the sensing fiber as the pump after passing through a polarization scrambler (PS) and an optical circulator (OC1). The use of AOM2 also induces a 200 MHz optical frequency shift for the pump. The probe light is amplified by the EDFA. Its lower sideband is selectly filtered out by a fiber Bragg grating (FBG, optical filter) and sent to a 350-MHz photodetector (PD). The bandwidth, reflectivity, and central wavelength of FBG are 0.134nm, >99%, and 1549.292 nm, respectively. The 512-bit Golay-code is used in this experiment. Note that OPC is applied in the FMP, which requires the frequency modulation period of the probe must be equal to the pulse interval of the coded sequence [24]. Each bit width and bit interval duration of optical pulse are 20 ns and 1000 ns, respectively. It is a return-to-zero (RZ) modulation format [19]. The PD’s outputs are sampled at 100 MSa/s and averaged 256-time (when using the BFMP, the average is 256 times per rising and falling frequency modulation; when using traditional rising (or falling) FMP, the average is 512 times) by an oscilloscope (OSC). Then sampled data are processed to obtain BGS and further retrieve the BFS.
Fig. 6. The experimental setup. DFB: distributed feedback laser; PC: polarization controller; IM: intensity modulator; AWG: arbitrary waveform generator; MG: microwave generator; AOM: acousto-optic modulator; EYDFA: Erbium Ytterbium Doped Fiber Amplifier; PS: polarization scrambler; OC: optical circulator; FUT: fiber under test; EDFA: erbium-doped fiber amplifier; FBG: fiber Bragg grating (optical filter); PD: photodetector; OSC: oscilloscope.
4. Experimental results and discussions
In this section, the BFMP's effectiveness is experimentally demonstrated by comparing BFSs and their relative variation. As the simulation analysis indicated in the principle section, a single rising and falling FMP pushes and pulls the BGS to be biased towards higher and lower frequencies, respectively. The comparisons of absolute and relative BFSs are exhibited in Fig. 7(a) and (b), respectively. Here, we select the near end of the fiber with a hotspot because the near has better SNR than the far end of the fiber, which better solely verifies the impact from the acoustic crosstalk. The Tperiod and Tbit are 1000 ns and 20 ns, respectively. The absolute BFSs (i.e., Fig. 7(a)) agree with the simulated results as indicated in Fig. 2. Here, we also observe that the BFS errors from the rising and falling FMP have the same magnitude and opposite direction. The BFMP can effectively compensate for the BFS errors. In addition, because v and vB decides the acoustic wave together, the errors induced by the acoustic crosstalk are also impacted by the unevenness of the actual fiber BFS, as the inset shown in Fig. 7(b).
Fig. 7. Comparisons of (a) absolute and (b) relative BFSs of a hotspot (∼50 °C) are at the conditions of Tperiod =1000 ns and Tbit = 20 ns.
To investigate the acoustic crosstalk more comprehensively, we change the Tperiod and corresponding Tbit. Figure 8 exhibits the absolute and relative BFSs at Tperiod = 500 ns and Tbit = 10 ns. BFS offset is ∼10 MHz, greater than the result (∼5 MHz) from Tperiod = 1000 ns case. On account of the 20 ns pulse width is double the duration of each frequency duration (10 ns). The crosstalk is more serious than the case in Fig. 7, according to the causes of the acoustic crosstalk in the principle section. Here, the rippling errors superficially disappear due to that the acoustic wave of each position of fiber cannot be built with a uni-frequency. In fact, it overlaps and becomes a more severe measurement error. From the relative results (i.e., Fig. 8(b)), ∼2 MHz BFS errors are compensated by the BFMP method. Figure 9 exhibits the BFSs from longer Tperiod = 1500 ns and Tbit = 30 ns. The offset and the rippling measurement errors are ∼3MHz and ∼2.2 MHz, respectively.
Fig. 8. Comparisons of (a) absolute and (b) relative BFSs of a hotspot (∼50 °C) are at the conditions of Tperiod =500 ns and Tbit = 10 ns.
Fig. 9. Comparisons of (a) absolute and (b) relative BFSs of a hotspot (∼50 °C) are at the conditions of Tperiod =1500 ns and Tbit = 30 ns.
The whole BFSs along the ∼117.46 km sensing fiber are displayed in Fig. 10, which also shows the detailed BFSs at ∼40 km and ∼80 km locations in the insets. From the above experimental results, we can see that: 1) the BFSs from the rising and falling FMP have opposite offset and ripple; 2) the errors caused by the acoustic crosstalk cannot be compensated by calculating its relative variation; 3) the BFMP method effectively compensates for the errors and narrows the pulse interval of the coded sequence toward 500 ns.
Measurement uncertainty along the whole sensing fiber can evaluate the performance of a BOTDA sensor. First, we consecutively measure the BGS by ten times. Then the BGSs are fitted by the Lorentz curve [29] to extract the BFSs’ distributions. By calculating the standard deviation value of the 10 BFSs at each location, the measurement uncertainties are depicted in Fig. 11. The measurement uncertainties with and without the BFMP at the far end are ∼1.56 MHz and ∼2.1 MHz, respectively. Furthermore, measurement uncertainty with the BFMP method is less than the rising or falling case. By the way, a small deviation from 30 km to 80 km (corresponding to the high Brillouin gain range of the trace) is mainly caused by polarization noise [37]. In a word, the BFMP method enhances sensor certainty by 1.28 times.
Fig. 11. Measurement uncertainties are along with the 117.46-km fiber at the conditions of Tperiod =1000 ns and Tbit = 20 ns, where green lines are corresponding exponential fitting.
A ∼22 m testing fiber at the far end of ∼117.46-km fiber is heated up to ∼46 °C, and the remaining fiber is kept at room temperature. The hotspot's BFSs are indicated in Fig. 12. About 2-m spatial resolution (from 10% to 90%) is observed, agreeing well with the 20-ns optical pulse width.
Fig. 12. A hotspot (∼46 °C) is at ∼117.42-km location at the conditions of Tperiod =1000 ns and Tbit = 20 ns.
5. Conclusion
In this work, the crosstalk between acoustic waves of different frequencies is discovered and researched in a BOTDA sensor with the frequency-modulated probe. Moreover, a bidirectional frequency-modulated probe method is proposed to overcome the global unfavorable impact of the acoustic crosstalk. The above experimental and simulational results point out that the BFMP method can effectively compensate for ∼2.2 MHz BFS errors over 117.46-km sensor link and narrow the pulse interval of the coded sequence toward 500 ns. Moreover, the simulation results agree with the experiment.
Funding
National Natural Science Foundation of China (61735015, 62005220).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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