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Abstract
A novel technique for improving the dynamic range of slope-assisted Brillouin optical time domain analysis (SA-BOTDA) is proposed. By modulating the pump pulse with a specially designed signal generated using an arbitrary waveform generator, we may manipulate the shape of Brillouin gain spectrum (BGS) to obtain an enlarged strain dynamic range without increasing significant cost on system complexity. In simulation, we realize a 4.8-times improvement by using a 2-tone signal for pump pulse modulation. In experiment, we modulate a 25-ns-width pump pulse with a 2-tone signal whose frequencies are 43 MHz and 86 MHz respectively and achieve a 100-MHz linear slope span, which is about 4.35 times of that in conventional SA-BOTDA technique. Besides, the BGS manipulation technique realizes an efficient utilization of pump power and only introduces a pump power penalty of 3.53 dB, which allows a promising dynamic strain measurement. In the experiment, we successfully measured a sinusoidal strain signal exerted on a 3-m fiber, with a range from −75 με to 875 με and a frequency of 80 Hz. The measured result shows that the suppression ratio of 2nd-order harmonic is 39.35 dB, and the strain measurement accuracy is 5.26 με. The results indicate that the proposed technique has a desirable performance on dynamic strain measurement.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, various fiber-optic sensors have been employed to monitor the deformation and strain of civil structures such as bridges, pipelines and buildings [1]. Among different techniques, the stimulated Brillouin scattering (SBS) based technique has attracted much attention since it is capable of sensing the strain/temperature of the fiber by a truly distributed way with a high spatial resolution [2–5]. It can either achieve a 100-km measurement distance with a 1-m spatial resolution by using Brillouin optical time domain analysis (BOTDA) [6–9] or a 17.5-km measurement range with a 8.8-mm spatial resolution by using a Brillouin optical correlation domain analysis (BOCDA) [10–12]. Generally, in SBS based techniques, the Brillouin gain spectrum (BGS) should be fully scanned by sweeping the frequency offset between the counter-propagating pump- and Stokes-lightwave to obtain the Brillouin frequency shift (BFS) and therefore determine the strain/temperature of the fiber. However, the BGS scanning always leads to a large cost on measurement time and therefore decreases the sampling rate to the strain signal. In order to measure dynamic strains with a sampling rate up to several hundred Hz, the slope-assisted Brillouin optical time domain analysis (SA-BOTDA) technique is proposed [13–15]. In SA-BOTDA scheme, the frequency offset between the pump- and Stokes-lightwave is tuned at the middle of the BGS linear slope. With a strain signal exerted on the fiber, the BGS is spectrally shifted and thus the strain signal can be translated to the intensity change of the Stokes-lightwave. By using this technique, the frequency scanning can be omitted, which provide a capability of dynamic strain measurement. However, the strain dynamic range of SA-BOTDA is determined by the frequency span of BGS linear slope. According to the mechanism of SBS, the frequency span of BGS linear slope is always several tens of MHz, which is not enough in practical applications. Many efforts have been made to enlarge the dynamic range of strain measurement in SA-BOTDA technique. J. Urricelqui et al. introduced the Brillouin phase-shift into SA-BOTDA and used the RF phase-shift as the slope [16, 17]. In [17], a multiple-frequency component pump pulse and a short pump pulse are employed to further enlarge the linear region of the RF phase-shift slope. However, the two technique are limited by the slope nonlinearity and the low signal-to-noise ratio (SNR), respectively. Another technique called multi-slope scheme employs a frequency-agility technique to increase the dynamic range of strain measurement to a considerably large level, which requires a very powerful arbitrary waveform generator (AWG) [18]. Besides, there is also a trade-off problem between the dynamic range and the frequency response of dynamic strain measurement. Recently, we introduced a parameter called Brillouin phase-gain ratio to enlarge the range of dynamic strain measurement to around 100 MHz as well as eliminate the pump-power-dependency [19]. The proposed technique requires a high-frequency single sideband modulation and a large receiving bandwidth, which is unwelcome in practical applications.
In this paper, we propose an enhanced BGS manipulation technique by using a pump pulse modulated by a multi-frequency signal to enlarge the dynamic range of strain measurement. After modulation, each frequency component in pump pulse leads to an individual Brillouin gain and therefore composes a combined BGS. Compared to [17], we carefully designed the power and center frequency of each frequency component to manipulate the shape of BGS for achieving an improved frequency span of linear slope as well as a high pump power efficiency. The proposed technique is cost-effective and does not require any data processing for demodulation. In the experiment, we realize around 100-MHz strain measurement dynamic range by modulating a 25-ns pump pulse, showing a 4.35 times improvement comparing to the method without any modulation. As a demonstration, a dynamic strain signal with a 80-Hz frequency and a range from −75 με to 875 με is exerted on a 3-m fiber. By employing the BGS manipulation technique, the strain signal is accurately obtained with a sampling rate of 1 kHz and a 2nd-order harmonic suppression ratio of 39.35 dB, with a strain measurement standard deviation of 5.26 με.
2. Principle
In a conventional BOTDA, a continuous-wave (CW) Stokes lightwave with an optical frequency of ωS interacts with a count-propagating pump lightwave with an optical frequency of ωP, as shown in Fig. 1. After amplified by the pump pulse, the Stokes lightwave can be expressed as
where ES is the electric field amplitude of Stokes lightwave and GSBS is the Brillouin gain, which can be described as where g0 is the gain coefficient of SBS process, Ep is the electric field amplitude of pump pulse, Δv = ΓB(z) − (ωP − ωS) and ΓB(z) is the BFS of the fiber at the position z. In Eq. (2), we ignore the optical frequency span of pump pulse. Taking the spectrum of pump pulse into consideration, the Brillouin gain can be modified as where P(·) is the spectrum density of the pump pulse. In the conventional SA-BOTDA system, the pump pulse has a rectangular shape. Therefore, with a pump pulse duration time which is larger than the acoustic phonon lifetime in the fiber (∼10 ns), the BGS has a nearly Lorentzian shape and hence a limited frequency span of linear slope. In order to improve the strain dynamic range of SA-BOTDA technique, we may modulate the pump pulse with a carefully designed signal and manipulate the shape of BGS to achieve a large frequency span of linear slope.Taking the complexity of signal generation into consideration, the multi-tone signal is chosen for modulating the pump pulse since it is easy to analyze and generate. Here, we choose a 2-tone modulation with modulation frequencies of f0 and 2f0 respectively, as shown in Fig. 2. The modulated pump pulse can be expressed as
where A(t) is the envelope of the pump pulse, A1 and A2 are the modulation depths of the two tones respectively, φ1 and φ2 are the corresponding modulation phases. Since both the modulation frequency and modulation depth may significantly influence the performance of proposed technique, a simulation based on Eq. (3) is made to investigate the relationship between the achievable linear slope span and different factors. In the simulation, the Brillouin linewidth is set as 30 MHz and the pump pulse is set as a raised-cosine shape with a 25-ns duration time, corresponding to a BGS full-width-of-half-maximum (FWHM) of 60 MHz. Here, we set the flatness tolerance of the linear slope to be 25%. By using the grid searching method, we may determine one group of optimized parameters that f0 is 47 MHz, A1 is 1.23 and A2 is 0.66. The spectrum of the pulse is shown in Fig. 3.With a 2-tone modulation the frequency span is increased to around 250 MHz, which makes a large linear slope span possible. The simulated BGS and corresponding slope are shown in Fig. 4. The linear slope is approximately marked by the thick solid line. Without the modulation, the FWHM of BGS is around 60 MHz and the linear slope span is 25 MHz. However, by modulating the pump pulse, the FWHM of BGS is increased to 156 MHz while the linear slope span is broadened to 120 MHz. The simulation result shows a significant improvement on the linear slope span, which is 4.8 times of that in the conventional SA-BOTDA technique. In order to investigate the sensitivity of the linear slope span to the modulation parameters, the relationship between the linear slope span and these parameters is simulated and shown in Fig. 5. It can be observed from Fig. 5(a) that with the modulation frequency varying from 42.5 MHz to 49.5 MHz, the variation of linear slope span is less than 10 MHz, which implies that the linear slope span is not very sensitive to the modulation frequency. Furthermore, Fig. 5(b) shows that the proposed technique also has a good tolerance to the variation of the modulation depth. Even the modulation depth varies in a large range, the linear slope span can be kept at a high level. Therefore, the simulation results show that the proposed technique can significantly increase the dynamic range of SA-BOTDA with a high reliability.
Fig. 5 The relationship between linear slope span and (a) modulation frequency; (b) modulation depth when modulation frequency is 48 MHz.
3. Experiment and results
The experimental setup is shown in Fig. 6. A fiber laser with an output power of 16 dBm is used as the light source. The lightwave from the fiber laser is then divided into two beams by using a 3dB optical coupler. On the upper branch, an intensity modulator (IM) and a microwave synthesizer are employed to generate a double-side-band (DSB) modulated lightwave with around 11-GHz modulation frequency. An optical band-pass filter is used to cut the upper sideband and obtain the Stokes lightwave. After passing through an optical isolator, the Stokes lightwave is injected into the fiber under test (FUT), which is a standard single-mode fiber with a length of 400 m. In the experiment, the power of probe lightwave injected into FUT is measured to be −10.8 dBm. On the lower branch, another IM is used to perform a modulation, and an acousto-optic modulator (AOM) is used to generate the pump pulse. An AWG is used to provide the designed modulation signals to the IM and AOM. The pump pulse repetition rate is 250 kHz. A polarization scrambler (PS) is employed to scramble polarization state of the pump pulses with a frequency of 700 kHz to solve the polarization fading problem. The pump pulses are then amplified by an Erbium-doped fiber amplifier (EDFA) to a level just below the nonlinear threshold and then injected into FUT through an optical circulator. After SBS interaction, another OBPF is used to cut the Rayleigh backscattering lightwave of the pump pulse. A photo-detector (PD) with a 200-MHz bandwidth is employed to detect the Stokes lightwave. The output signal of PD is filtered by a low-pass filter with a 120-MHz cutoff frequency and then sampled by an analog-to-digital converter (ADC) with a 250-MS/s sampling rate and a 14-bit accuracy. To improve the SNR and solve the polarization fading problem, every 250 traces are averaged to be one trace, which means that the sampling rate to strain is 1 kS/s.
Fig. 6 The experimental setup. IM: intensity modulator; OBPF: optical band-pass filter; FUT: fiber under test; AOM: acousto-optic modulator; PS: polarization scrambler; EDFA: erbium-doped fiber amplifier; AWG: arbitrary waveform generator; DAQ: data acquisition system; PD: photo-detector.
To investigate the performance of the proposed technique, we compared the dynamic range of SA-BOTDA system using 3 types of pump pulse: the 25-ns pump pulse without modulation, the 25-ns pump pulse with 2-tone modulation and the 4-ns short pump pulse. Here, we set the modulation frequency f0 to be 43 MHz, which may not reach a best performance but is expected to provide a stable improvement and a better linearity. It should be noted that the power of pump pulses is limited by the nonlinear effect in FUT, including modulation instability (MI), four wave mixing (FWM) and pump power depletion. In order to prevent the influence of nonlinear effect, the peak power of the 25-ns pump pulse with and without modulation is set to be 30.5 dBm and 30 dBm respectively, while the peak power of 4-ns pump pulse is 31.5 dBm. The major limitation for the pump pulse with 2-tone modulation is pump power depletion, while that for the 4-ns pump pulse is MI. The spectra of different pump pulses before and after passing through FUT are shown in Fig. 7, respectively. It is obvious that the spectral range is much extended by modulating the pump pulse. Only the 4-ns pump pulse shows a slight distortion due to the nonlinear effect. The BGS obtained by using different pump pulses are shown in Fig. 8(a), and the linear slope span is approximately marked by the thick solid line. It can be observed that the manipulated BGS has the largest linear slope span. The 2-tone modulation on the pump pulse results in a power penalty of 3.53 dB, which could degrade the strain measurement accuracy. For comparison, the power penalty using a 4-ns pump pulse is 8.55 dB since the acoustic field cannot be built up effectively within the pulse duration. We calculate the slope of BGS using different pump pulses and determine the dynamic range of strain measurement, as shown in Fig. 8(b). Here, the tolerance of the slope linearity is set to be 25%, which means that the variation of BGS slope in the linear slope region should be less than 25%. The conventional SA-BOTDA technique can only achieve a 23-MHz linear slope span, corresponding to a dynamic range of around 460 με. Thanks to the 2-tone modulation method, the linear slope span is enlarged to 100 MHz, which is around 4.35 times of the conventional technique. The corresponding dynamic range is around 2000 με, which is a desirable performance for the dynamic strain measurement. On the other hand, the largest linear slope span of the BGS with a 4-ns pump pulse is 85 MHz, as marked out in Fig. 8(b). As a conclusion, the proposed BGS manipulation technique can achieve a remarkably improvement on the dynamic range without causing a significant power penalty.
Fig. 8 (a) The BGS obtained by using different pump pulses. (b) The slope of BGS with different pump pulses.
A dynamic strain is exerted on the far end of the fiber for validating the effectiveness of the proposed method by using an exciter, as shown in Fig. 9(a). To achieve a large dynamic range in measurement, the frequency offset is locked at the middle point of the linear slope, and the available dynamic range with modulation may be around 2000 με. Since the exciter has a limited vibration amplitude, we set a strain offset of around 400 με on the fiber and a sinusoidal dynamic strain with a 475-με amplitude and a 80-Hz frequency. The time-domain measurement results using different pump pulses are shown in Fig. 9(b). Without modulation, the dynamic range is limited, which leads to a severe distortion in strain measurement. On the other hand, with 2-tone modulation, a dynamic range of around 2000 με is achieved and therefore the strain can be accurately measured. By using a 4-ns pump pulse, the dynamic strain can also be measured. However, the measurement result is noisy, due to the large power penalty. The normalized spectra of measurement results are shown in Fig. 9(c), with a frequency resolution of 5 Hz. It can be observed that without modulation the measurement result may be heavily influenced by high-order harmonics, while the spectrum noise raises clearly when using a 4-ns pump pulse. Thanks to the 2-tone modulation, the spectrum of dynamic strain is accurately measured with a high SNR and a desirable 2nd-order harmonic suppression ratio of 39.35 dB, which indicates an excellent linearity of the slope. The measurement result shows that the proposed technique has a good performance in dynamic strain measurement.
Fig. 9 (a) The schematic to exert dynamic strain to FUT. (b) The time-domain dynamic strain measurement result and (c) corresponding spectrum.
Actually, there is a trade-off relationship between the slope span and BFS measurement accuracy. A pump power penalty will be introduced by a short pump pulse or using 2-tone modulation on pump pulse. Besides, the BGS slope decreases with the increase of the linear slope span. As both the Brillouin gain and the slope become smaller, the detected noise in the measurement process to measure the probe lightwave power may result in a larger BFS/strain measurement error, as illustrated in Fig. 10(a). We experimentally obtain the strain measurement error of SA-BOTDA system using different pump pulses, as shown in Fig. 10(b). It can be observed that without modulation, the standard deviation of strain measurement error is only 1.37 με. However, the standard deviation of strain measurement error increases to 5.26 με with modulation, due to the change of BGS shape. For comparison, the error using a 4-ns pump pulse significantly increases to 25.93 με. The experiment results indicate that the BGS manipulation technique using a 25-ns pump pulse can achieve a improved strain dynamic range with a much better accuracy compared with that using a 4-ns pump pulse.
Fig. 10 (a) The relationship between the BGS shape and BFS measurement error. (b) The strain measurement error with different pump pulses.
4. Conclusion
In this paper, we proposed a novel technique to remarkably improve the dynamic range of SA-BOTDA without significantly degrading the measurement accuracy. By modulating the pump pulse with a designed signal, we may manipulate the BGS shape and thus enlarge the linear slope span of BGS with an acceptable pump power penalty. Besides, the proposed technique is cost-effective without increasing any complexity on data processing. In simulation, by modulating the pump pulse with a 2-tone signal, the linear slope span of BGS can be enlarged to 4.8 times compared with conventional SA-BOTDA technique. By modulating a 25-ns pump pulse, we also experimentally realized a 100-MHz linear slope span, which is about 4.35 times of that in conventional SA-BOTDA technique, with a pump power penalty of 3.53 dB. The BGS manipulation technique realizes a more efficient utilization of pump power, compared with other technique such as short pump pulse. In dynamic strain measurement, we successfully measure a sinusoidal strain signal with a range from −75 με to 875 με and a frequency of 80 Hz. The measured spectrum shows that the suppression ratio of 2nd-order harmonic is 39.35 dB. Meanwhile, the strain measurement accuracy is 5.26 με which indicates a good performance for dynamic strain measurement.
Funding
This work was supported by the National Natural Science Foundation of China (NSFC) Grant 61775132, 61735015, 61620106015, 61327812, and the State Grid Corporation of China Grant No. 5455HT170031.
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