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Abstract
Gain-profile tracing (GPT) is a useful strategy of distributed sensing in BOTDA technique for achieving high spatial resolution, which has not been used for the dynamic strain measurement previously. In this paper, we propose a modified gain-profile tracing (MGPT) technique for fast dynamic strain measurement while maintaining the advantage of high spatial resolution. This technique is based on a modified pump pulse modulation scheme and the slope-assisted demodulation method. The time consumption using MGPT technique for a single pump pulse measurement of dynamic strain is less by 25% than the conventional GPT technique. The spatial resolution of our BOTDA system using MGPT technique is 50cm and maximal frequency of dynamic strain detection could be up to 53.5 Hz for 248m sensing length. In the experiments, we measure two vibration events spacing 50 cm with the frequency of 14.0 Hz and 17.0 Hz in a 248 m single-mode fiber. The proposed method is a potential real-time dynamic alternative for distributed structural health monitoring.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Brillouin optical time domain analysis (BOTDA) has been extensively investigated in the last three decades [1] and widely deployed in perimeter security, petrochemical industry, bridge and tunnel safety, to meet the requirements of strain/temperature sensing [2–4] with high spatial resolution (SR) [5–8] and long distance [9–11]. In the BOTDA system, two counter-propagating lights, a continuous-wave (CW) probe signal and a pump pulse, interact with each other all along the fiber under test (FUT). When the optical frequency difference between the pump and probe waves equals Brillouin frequency shift (BFS), the power transfer efficiency between the two beams reaches the maximum. Based on that principle, temperature and strain sensing can be realized through the measurement of BFS by sweeping the Brillouin gain spectrum (BGS).
Sweeping the BGS is a commonly used technology in BOTDA to determine the BFS at each point along the fiber and locate the gain peak. However, the shortage of long time consumption in frequency-swept confines their applications majorly in static measurement. Several alternative schemes have been proposed for dynamic measurements. In 2012, J. Urricelqui et al. proposed a novel dynamic BOTDA sensor which combines the usage of the Brillouin phase-shift and the conventional Brillouin gain for realizing 1.66 kHz measurement rate over a 160 m sensing fiber with 1 m SR [12]. Y. Peled et al. proposed a frequency-agile method based on a pre-programming arbitrary wave generator (AWG) to realize fast BOTDA (F-BOTDA), and demonstrated ~10 kHz sampling rate in a 100m long fiber with 1.3m SR [13]. However, the SR of the two approaches discussed above is limited by the phonon lifetime, which is about 10 ns and results in the SR limitation of larger than 1 m. Meanwhile, a shorter pulse in the pump beam will decrease the Brillouin response and lead to a low signal-to-noise ratio (SNR). In 2013, a high-spatial-resolution F-BOTDA based on differential double-pulse (DDP) and second-order sideband modulation had been introduced to realize the measurement of 50-Hz vibration over a 50-m polarization maintaining (PM) fiber with a SR of 20cm [14]. Due to the cost of PM fiber, it is not suitable for long distance sensing applications.
Another commonly used method for dynamic measurement is slope-assisted BOTDA (SA-BOTDA), which takes advantage of the Brillouin gain variations of the probe wave for fast demodulation of the strain [15,16]. For example, a slope-assisted BOTDA sensing scheme has been proven to obtain two vibrations with the frequency of 7.00 Hz and 10 Hz in 10.6km sensing fiber with 3m SR [17]. However, this scheme employs the short pump pulse as the conventional scheme, and the SR is still limited by the pulse width. Theoretically, the slope-assisted technique not only can be used in the short pulse scheme, but also maintains compatibility with the novel pulse schemes for high SR. Gain-profile tracing (GPT) technique is proposed with cm-order SR. The technique is based on a single long pump pulse for acoustic excitation, and the falling-edge of the pump pulse is used to extract the Brillouin response along the fiber. As a result, the SR is limited by the fall-time of the pump modulation [8]. However, first, the pre-excitation of the acoustic field is generated throughout the sensing fiber, then, the falling-edge starts to detect the Brillouin response of the sensing fiber. It results that a single time-domain trace of the Brillouin gain profile over the FUT is relatively long.
In this paper, we propose a modified gain-profile tracing (MGPT) technique to improve detection speed. This technique takes advantage of the modified pump pulse scheme which employs the falling-edge and rising-edge of a single long pump pulse and the slope-assisted demodulation method. In order to improve detection efficiency of the pump pulse, the modified pump pulse scheme uses the rising-edge to detect the Brillouin response of the first half of the sensing fiber (near the pump pulse input end) and falling-edge to detect the second half of the sensing fiber (near the pump pulse output end). The slope-assisted demodulation method uses a single pump pulse to measure the dynamic strain along the whole FUT. We demonstrate the MGPT technique has a considerable performance for dynamic strain measurement in experiments.
2. Method
2.1 Working Principles of modified gain-profile tracing
When the rising-edge and falling-edge respectively detect the 1/2 length of FUT, the time consumption in a single measurement is shortest. Considering the 1/2 factor for the round-trip time in any BOTDA scheme, the required width of a single long pump pulse is ΔT = L/vg in MGPT technique (L is sensing fiber length, vg is optical group velocity in fiber). It must be indicated that the width of pump pulse cannot be less than the ΔT. Otherwise the Brillouin gain along the whole FUT cannot be completely measured. Figure 1 illustrates the working principle of the proposed MGPT technique. Pump light is injected into the FUT from the input end as shown in Fig. 1(a). After the pump pulse reaches the first half of the FUT, the probe light experiences Brillouin interaction at the position of its meeting with the pump pulse as depicted in Fig. 1(b). The detected power difference of the probe between this state as shown in Fig. 1(b) and the previous state as shown in Fig. 1(a) represents the integral of the Brillouin gain at the red shadowed regions in the FUT. When the rising edge of the pump pulse transmits from the fiber input end to the midpoint, we can obtain the Brillouin gain profile of the first half FUT. Whereas, the second half gain profile can be gotten by repeating the differential process using the falling edge of the pump pulse, which travels from the midpoint to the fiber output end (FOE) as shown in Figs. 1(c) and 1(d).
Fig. 1 Principle of the MGPT-BOTDA measurement. (a) The pump pulse injects into the FUT. (b) The rising edge of pump pulse moves to the midpoint of the fiber. (c) The falling edge of the pump pulse moves to the midpoint of the FUT. (d) The falling edge of the pump pulse travels the second half of the FUT. The power difference Δpower in (b) and (d) equals the integral of the Brillouin gain where the rising edge travels from the position of (a) to that of (b) and the falling edge travels from position of (c) to that of (d).
According to the GPT model [8], we can formulate the Brillouin interaction in our proposed MGPT technique. For the fixed optical frequencies of pump and probe wave, the power of the probe wave along the Brillouin interaction length is described by the following equation. In order to depict the two processes of the transmission of pump pulse in FUT, we divide the equation into two parts:
In the experiment, a photo detector at FIE has been used to monitor the probe beam after passing through the FUT. The pump power is injected into the FUT at the moment of t = 0. By converting Eq. (1) into time-domain, we derive another three formula to describe the power detected by the photodetector at any later moment of t>0:
In Eq. (2), vg is the group velocity of pump/probe light in the fiber. The local slope at any point represents the Brillouin gain of that point. The derivative of the logarithm of the probe signal is linearly proportional to the Brillouin gain, which is given by:
The SR of the MGPT technique is limited by the rising/fall-time of the pump modulation:
According to the Eq. (4), the MGPT technique maintains the advantage of the high SR of the GPT technique.
In Fig.. 2, the numerical simulation results are shown using MGPT and GPT techniques respectively. The length of the sensing fiber in simulation is 300m. The optical frequency difference between pump pulse and probe wave is set to be equal to the theoretical BFS (10.719GHz), and the widths of the pump pulses are 1.5μs and 3μs, for MGPT and GPT techniques respectively. The solid line and the dotted line represent the probe power traces of the MGPT and GPT technique. As clearly shown by the dotted line, the two segments, separately indicate the incident period, starting from the pump pulse reaching the input end of FUT until being completely in the fiber, and the exit period, corresponding to the pump pulse withdrawing from the fiber output end.
Fig. 2 Comparison of the time-domain trace of probe light using MGPT and GPT techniques respectively.
The solid line of the MGPT can be divided into three time segments. The first part corresponds to the rising edge of the pump pulse injecting and traveling through the first half of the FUT, during which the probe light experiences increased stimulated Brillouin scattering at the same time. In the second segment, the pump pulse completely enters and transmits through FUT until the rising edge reaches the fiber output end. During the third segment, the probe light experiences the Brillouin response of the second half of the FUT again when the falling edge of the pump light transmits from the midpoint to the fiber input end. Therefore, both the first and the third time segments involve in effective sensing. The pulse width of the GPT usually sets larger than the time span that light passes through the whole fiber, whereas the pulse width of the MGPT sets to half of that in GPT technique. As a result, the sampling time of the MGPT technique is decreased to three quarters of the GPT for the same sensing system. Obviously shown in Fig. 2, the sampling time of the MGPT is a quarter shorter than the GPT. The period of the pulse is effectively shortened using MGPT technique.
2.2 Dynamic strain demodulation
The Brillouin gain has an expression under a dynamic strain as:
where, fpp is the optical frequency difference between the pump and probe waves. ΓB is the Brillouin natural linewidth. g0 is the Brillouin gain at the peak of the Brillouin gain spectrum (BGS).
Setting ΓB to 40MHz in our experiment, we plot the Brillouin gain spectra under strain of 0με and 400με in Fig. 3(a), correspondingly, νB(t,z) is 10.719GHz for 0με and 10.739GHz for 400με, respectively. In figure. 3(a), the vertical upward arrow marks the fixed optical frequency difference between the probe and pump. When no strain exists, the optical frequency difference between the pump and probe waves are set to match the frequency at the peak of the BGS, where the Brillouin gain reaches the maximum. When 400με strain is introduced, the BGS shifts towards higher frequency, which leads to the Brillouin gain decrease. The BFS can be described as a function of the strain along the fiber:
Fig. 3 (a) Brillouin gain spectrum under the strain of 0με and 400με. (b) The gain to strain curve with the fixed optical frequency difference between the pump and probe waves (10.719GHz).
where ε(t,z) denotes the dynamic strain at a specific position z of the FUT. k is frequency shift coefficient and υ0 is the Brillouin frequency at a specific temperature without strain. Substituting equation. (5) into equation. (6) and setting υ0, k to 10.719GHz and 0.05MHz/με, we get the Brillouin gain G as a function of the strain as shown in Fig. 3(b), which indicates that the Brillouin gain decreases with the increase of the strain. The gain to strain curve has the same trend as the falling edge of a Lorentzian. Thus, we are able to demodulate strain through the measurement of the Brillouin gain.
3. Experiments and results
The experimental step of the proposed dynamic strain sensing scheme is shown in Fig. 4.
Fig. 4 Experimental setup: EOM: electro optic modulator, EDFA: erbium doped fiber amplifier, PS: polarization scrambler, FUT: fiber under test, PC: polarization controller, CIR: circulator, ATT: attenuator, PD: photodiode, DAQ: data acquisition
The light source is a distributed feedback (DFB) laser of 1550nm with a line width of 3MHz, which is split and separately incident into the pump and the probe arm through a 3-dB coupler. The pump light is modulated by an electro-optic modulator (EOM), which is driven by a pulse generator and a RF source to generate a 1.24μs pulse. The EOM generates two sidebands, the upper sideband works as the pump (with Brillouin frequency of 10.719GHz) and the lower one discarded by a tunable filter. The pump pulse is scrambled by a polarization scrambler (PS), which is amplified by an Erbium doped fiber amplifier (EDFA) and finally transmits into the FUT through port 1 of a circulator (CIR). In the probe arm, the probe light passes through a polarization controller (PC), an isolator and an attenuator before transmitting into the other end of the FUT through port 2 of the circulator. After the interaction with the pump light in the FUT, the probe light is finally received by the photo-detector through port 3 of the circulator.
We get the time management of GPT and the proposed MGPT technique without strain in a fiber (G652.D) with length of 248 m. The optical frequency difference between the probe and pump is fixed at 10.719GHz, and the pump pulse width are set to 2.48μs using GPT technique (dotted line) and 1.24μs using MGPT technique (solid line). As the experimental curves of the time-domain probe signals of the GPT and MGPT techniques shown in Fig. 5(a), 25% of the time consumption has been reduced in our proposed MGPT technique. In addition, both of the up and down slopes of the probe in MGPT technique are steeper than those in GPT technique. The duty cycle of the pump pulse in MGPT is 0.25, as compared to 0.5 in GPT, which brings about 2dB gain in pump light amplification by the EDFA in MGPT than in GPT, and results in 25% larger change rate of the probe power calculated by Eq. (3) in MGPT as shown in Fig. 5(a)
Fig. 5 (a) Time-domain trace for probe light employ MGPT technique and GPT technique. (b) Experimental curves of Brillouin gain to strain (G-ε).
We also carry out several sets of experiments to measure the response of the Brillouin gain under various strains from 0με to 800με with a step of 50με. The strain is obtained by a travel translation stage with the accuracy of ± 5με. The Brillouin gain along the fiber is resolved from the time-domain probe signal according to Eq. (3). The experimental results are presented in Fig. 5(b), and the solid red curve is obtained by a linear fitting. The residue sum of squares of the Brillouin gain to strain curve is better than 0.99. According to the slope of the fitted curve, the detected strain resolution of 27με depends on the resolution of the Brillouin gain. The resolution of Brillouin gain refers to the photo-current resolution of 110nA of the photodiode amplifies (PDA).
To demonstrate the proposed strategy in dynamic strain sensing with high resolution, two sections of fiber with length of 1 meter are fixed and periodically stretched by a home-built setup with double elliptical wheels as shown in Fig. 6. The two vibration events are taken place in the fiber segment from 10 m to 35 m (counted from the input end of the FUT). The maximum strain is determined by the cam altitude, and the preloaded strain on the left section is larger than that on the right section. It should be mentioned that the vibration frequency of fiber simulated by rotating cam is twice of the frequency of the rotating cams, due to the double stretching of fiber for each rotation of the cam. The rotating speed of the cams of 420 rounds per minute (RPM) and 510 RPM correspond to vibration frequencies of 14.0 Hz and 17.0 Hz, respectively. In addition, the period of the pump pulse is 3.72 μs, and the average number is 2500 for a high SNR. One full measurement (100 collected time-domain traces of dynamic strain) over 248 m fiber is completed within 0.93 s.
Fig. 6 The layout of the fiber sections applied dynamic strain: 248m FUT, comprising 3 sections of the SMF fiber. The first section is a 231m spool. Two vibration events of 1m lengths with 0.5m spacing are generated by two motor-driven elliptical cams. The minimum or maximum of the strain are obtained when the cam is parallel with or perpendicular to the optical fiber. Length of the last fiber section is 14.5m.
As the Brillouin gain profile upon the variation of time shown in Fig. 7(a), two dynamic strain events can be clearly distinguished. In addition, we can also conclude that the two dynamic strain evens have different amplitude and frequency. In order to demonstrate the SR of the sensor, we plot a single trace of the Brillouin gain profile over the fiber segment measured between 10 m and 35 m as shown in Fig. 7(b), and two dips at 15 m and 17 m corresponds to the two vibration events on the fixed fiber with 1 m length. Meanwhile, the distinguishable length between the two vibration events is 0.5m, which is consistent with our experimental setup. Through substituting the time-domain Brillouin gain signals at 15 m and 17 m into Eqs. (5) and (6), the dynamic strain to time curves are plotted as a square marked red curve (at 17 m) and a circle marked blue curve (at 15 m) in Fig. 7(c), whose period and the maximal strain are calculated to be 0.070s, 783με and 0.060s, 513με, respectively. After applying FFT on the time domain data of the two events, the frequency domain spectra are shown in Fig. 7(d), which indicate the two frequencies of 14.0 Hz and 17.0 Hz obtained from the red square and blue circle marked curve. Those results are high consistent with the experimental rotation speeds of the two cams.
Fig. 7 (a) The 100 collected time-domain traces of the dynamic strain, indicated by color axis (in arbitrary units). (b) A single trace of the Brillouin gain profile in a 25m fiber segment (10m to 35m from the input end of the FUT). (c) The time traces of the vibration point with two different amplitudes and frequencies. (d) The frequency-domain amplitude spectrum of the dynamic strain.
4. Discussion
4.1 Spatial resolution
In practice, the SR of this system is determined by the largest among the three factors: the rising/falling-time of the pump pulse (tedge), the sampling rate (Δfsample) and the bandwidth of the photo-detector (Δfdet):
In our sensing system, the electric pulse generated from pulse generator is measured by a 20GSa/s oscilloscope (Agilent Technologies,DSO09254A) as shown in Fig. 8. The pulse width is 1.24μs, and the rise/fall-time (10%-90%) of the pulse are 730ps/770ps, which decides the effective SR of 7.3/7.7cm. The bandwidth of the photo-detector should be large enough to support that the received signals reproduce the profile of the vibration on the condition of (2ΔZΔfdet)/vg = 1. The bandwidth of photo-detector is 200MHz in our experiment, which meets the requirement of a SR of 50 cm. The third parameter, the sampling rate of the DAQ is set at 200MS/s, which corresponds to 50cm/point. Taking over all consideration of the three parameters, the system SR of 50cm is primarily determined by the detector bandwidth and the sampling rate of the DAQ. This result could be upgraded if higher bandwidth of photo-detector and sampling rate of DAQ were employed. Based on our estimation, the SR of the system by adopting 1GHz bandwidth detector and 1GS/s DAQ can be improved to 10cm through our proposed MGPT method.
Fig. 8 Pulse waveforms of 1.24μs pulse generated from the pulse generator with a rise-time of 730ps and a fall-time of 780ps.
4.2 Dynamic range
Employing slop-assisted method, the variation of the BFS resulted from different strain will be performed by the intensity variation of the Brillouin gain (see Fig. 3). Amplitude of dynamic strain is obtained simply from the linear relation in Fig. 6(b) from the measured Brillouin gain within a relatively small dynamic range. A conversion coefficient of the strain to BFS of 23με/MHz is measured using traditional frequency-scanning method. The linewidth of BGS measured by GPT method and MGPT method are same and equals 39MHz. The maximum strain of 783με using slope-assisted method is corresponding to a 34MHz BFS, which is sufficiently smaller than the BGS linewidth of 39MHz in the FUT.
To extend the measurement range of the dynamic strain, the MGPT technique can be combined with some modified slope-assisted method. Multi-slope assisted fast BOTDA employs a frequency-agile method to generate a multi-tone probe wave, which forms multiple slopes of the BGS in the FUT and extends the measurement range of the strain from single slope to several slopes [18,19]. Another alternative is to employ armored fiber with metal jackets to reduce the strain sensitivity of the fiber. Such method may reduce the measurement accuracy, but realizes a larger dynamic strain range.
4.3 Dynamic strain measurement
In order to measure the fast dynamic strain, the minimal period of pump pulse equals to the time consumption of a single tracing of Brillouin gain profile over the whole fiber. The DDP technique obtains the differential Brillouin signal by two successive short pump pulses. A single tracing of Brillouin gain consumes 4L/vg in DDP technique. L is the length of the fiber and vg is optical group velocity in fiber. The widths of pump pulse in GPT and MGPT technique are 2L/vg and L/vg respectively. A single tracing of Brillouin gain consumes 4L/vg in GPT technique and 3L/vg in MGPT technique. The pulse modulated period of the MGPT is 25% shorter than the DPP and GPT technique as shown in Fig. 9.
Fig. 9 Scheme of the probe wave and pump pulses sequence for a high-spatial-resolution BOTDA. (i.e. differential double-pulse, gain profile tracing, modified gain profile tracing)
When we measure the dynamic strain through the scan of the BGS, the time consumption of a single trace of dynamic strain using GPT is given by:
where Navg is average times and Nfreq is the number of scan of the BGS. If we use the MGPT technique, the time consumption of a single trace of dynamic strain is:
We define a coefficient R to compare the time consumption using the MGPT technique with the one using GPT technique:
In order to precisely measure the BFS within the dynamic range of the BGS (34MHz), the granularity of scanning the BGS is set to 0.5MHz, and the Nfreq equals 68. Under the same condition of the average time, the R is less than 1/90. It is observed that the time consumption using MGPT technique is much less than the GPT technique.
According to the Nyquist sampling theorem, the maximum frequency of the dynamic strain measured by our technique is described as:
In the experiments, a single time-domain trace of dynamic strain requires an average over 2500 successive pulses for the high SNR. The time consumption of a single time-domain trace of dynamic strain in a 248m FUT is 9.3ms calculated by Eq. (10), which results in a maximum dynamic strain of 53.5Hz calculated by Eq. (11).
5. Conclusion
This paper proposes and demonstrates a dynamic BOTDA sensor with sub-meter resolution, based on MGPT technique, which reduces much measurement time compared with the GPT technique and keeps the advantage of the high SR. In the experiments, a dynamic strain range of measurement from 27με to 783με is achieved. The frequency maximum of the vibrations of 17.0Hz is reached limited by the cam speed. Resolutions of the space between two adjacent strain issues and the strain amplitude are respectively 0.5m and 27με in a 248m length fiber. The proposed MGPT technique is a potential application-type scheme for real-time distributed structural health monitoring with high SR.
Funding
National Natural Science Foundation of China (NSFC) (11704293); Natural Science Foundation of Hubei Province (2017CFB286); Fundamental Research Funds for the Central Universities (2018IB008, 2018IB010).
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