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A differential pulse-width pair Brillouin optical time domain analysis (DPP-BOTDA) for centimeter spatial resolution sensing using meter equivalent pulses is proposed. This scheme uses the time domain waveform subtraction at the same scanned Brillouin frequency obtained from pulse lights with different pulse-widths (e.g. 50ns and 49ns) to form the differential Brillouin gain spectrum (BGS) at each fiber location. The spatial resolution is defined by the average of the rise and fall time equivalent fiber length for a small stress section rather than the pulse-width difference equivalent length. The spatial resolution of 0.18m for the 50/49ns pulse pair and 0.15m for 20/19ns pulse pair over 1km sensing length with Brillouin frequency shift accuracy of 2.6MHz are demonstrated.
©2008 Optical Society of America
1. Introduction
Stimulated Brillouin scattering (SBS) based fiber optic distributed sensors, such as Brillouin optical time-domain analysis (BOTDA), have been used for structural deformation and strain measurement for civil structural health monitoring [1, 2], as they have the unique capability of truly distributed sensing of strain with high spatial resolution. It is known that the spatial resolution in conventional BOTDA system is the spatial coverage of the pulse-width equivalent fiber length, and the shorter pulse-width represents higher spatial resolution. However the short pulse-width also represents short SBS interaction length which results in weaker Brillouin gain signal and the requirement of the broadband electronics for optical pulse generation, hence low signal to noise ratio. The Brillouin gain spectrum (BGS) broadens rapidly beyond 100MHz as the pulse-width is shorter than 10ns (corresponds to a 1-m spatial resolution), because the BGS is formed by the convolution of the optical pulse spectrum and the Brillouin spectrum of the fiber. The broaden BGS results in low pumping efficiency over the natural Brillouin spectral width of ~30MHz, thus high pumping power is required. On the other hand the high pump power may introduce Brillouin gain saturation at the resonant Brillouin frequency and distorted Brillouin spectrum. The trade-off between spatial resolution and Brillouin frequency-shift resolution makes it difficult to achieve high spatial resolution and high strain or temperature resolution over the kilometer sensing length simultaneously in BOTDA or BOTDR systems.
Recently it was reported that, when a combination of cw pre-pumping light and pulsed light (the probe beam) interacts with a cw light (the pump beam), the pre-pumping light amplifies the phonon field to give a strong Stokes signal. This technique is used to develop BOTDA system with a centimetre spatial resolution using 1.5ns probe pulse [3, 4]. The cw pre-pulsed portion of the probe signal interacts with the pump beam over the entire sensing length without spatial information, whereas the interaction of the pump with the pulsed portion of the probe signal provides the location information which is added coherently to the pre-pumping enhanced Brillouin signal for strain or temperature measurement. However, when the sensing length is very long (a few kilometers), and it will be difficult to control the amount of the DC portion for the probe signal. As the pre-pumping induced Brillouin signal from the entire sensing length of the DC level forms the background Brillouin gain spectrum, which is much larger than the Brillouin spectrum contribution from small stressed fiber section. Thus the strain or temperature induced Brillouin signal must overcome the pre-pumping from the DC level induced Brillouin gain spectrum so that it can be detected and spatially resolved. This sets the limit of the minimum detectable stress or temperature section, for the kilometer sensing length the pulse extinction ratio must be very high (>20–30dB).
In this paper, a novel DPP-BOTDA system for high spatial resolution sensing to detect small strain or temperature changes over centimeter fiber section by using long duration pulses (tens of nanosecond) over kilometer sensing length is proposed. This scheme employs the differential waveform subtraction at each scanned Brillouin frequency between the BGS pulse pair obtained by injecting two separated probe pulses with different pulse-widths, τ and τ +δτ (τ >10 nanosecond and δτ <<τ) to the sensing fiber. The deferential BGS has much higher spatial resolution than those obtained by using probe pulse with pulse-width τ orτ +δτ, which is related to the difference between the two pulse-widthsδτ, the rise and fall time of the pulse used and the detection system bandwidth. The proposed DPP-BOTDA system has following advantages over conventional BOTDA: 1) BGS with narrow line-width (<30MHz) is obtained which enhances the accuracy of the Brillouin frequency shift measurement because of the long duration probe pulses; 2) high extinction ratio (>30dB) pulses can be used without the need of the pre-pumping for long optical fiber length (kilometers), thus the cross-talk due to the cw component leakage [5] is reduced. By carefully choosing τ andτ +δτ values, a spatial resolution of <0.2m and accuracy of 2–3MHz for 1km fiber length is demonstrated. The working principle of the DPP-BOTDA and experimental setup and results will be presented in following sections.
2. Background
The theoretical model of SBS in single mode fiber can be described by the coupled wave equations for the pump and Stokes waves with the field amplitudes Ep (z, t) and Es (z, t), respectively, interacting with the acoustic wave Q̄(z,t) [6]:
where n is the refractive index, c is the velocity of light in vacuum, and gB is gain factor. Γ is the damping constant of the acoustic wave and Γ=Γ1+iΓ2, Γ1 is the damping time of the phonon field and Γ1=1 2τ ph, τ ph ~10ns for silica fiber, and Γ2 is the detuning angular frequency Γ2=2π(ν-ν B),ν is the beat frequency between the pump and probe wave in which the pump laser is tuned. ν B is the local Brillouin frequency of the fiber. Equations (1) to (3) can be solved numerically to calculate Ep (z, t) and Es (z, t) respectively, for the boundary condition of pulsed Stokes wave at z=0 and the cw pump wave at z=L. In the calculation, the optical pulse takes 20th-order super-Gaussian shape and the stressed fiber profile is a 0.2m-long square shape. From Eq. (3), the general solution of the phonon field Q̄ can be expressed as
By setting z=0 and normalizing above equation yields the intensity of the phonon field:
If the dc component of the pulsed Stokes light is neglected as we take the extinction ratio to be >30dB, the above equation can be re-written as
Where |E s0|2 is the optical power of the pulsed Stokes beam, f (t,t 0,τp) denotes a m-th order super-Gaussian pulse of width τ p centered at t 0, i.e.f(t,t 0,τp)=exp{-ln 2[2(t-t 0)/τp]m}.
As the enhanced phonon field generated by the pump and probe wave interaction at any position, the intensity of the phonon field at z=0 expressed in Eq. (6) described such a process which is measured by the intensity of the cw pump wave at z=0. The calculation shows that during the time period between the pulse leading edge and the pulse center entered the stressed fiber section, the temporal Brillouin gain signal experiences an exponential growth and is modulated by the damping time of the phonon fieldΓ. As the pulse center starts to leave the stressed section, the temporal Brillouin gain signal decays rapidly with damping constant governed by the pulse fall time and phonon relaxation time. When two temporal Brillouin gain signals are obtained by injecting a pair of pulsed light with different pulse-width,τ andτ+δτ to the fiber, the subtraction of those two signals removes the common term, such as equal temperature or stress portion, and retains the difference as we detect the differential Brillouin gain caused by the pulse-width difference rather than the Brillouin gain cause by long period pulses. This differential processing is shown schematically in Fig. 1, in which I (0,t,τ) and I(0, t,τ+δτ) denote the temporal Brillouin gain signals obtained at z=0 by using a pair of pulsed lights with different pulse-widths, τ andτ+δτ at a particular detuning frequency, and I (0,δτ) denotes the difference between them. For a small stressed fiber section at position z, its relative position within the pulse-widths ofτ and τ+δτ is different, as well as the Brillouin gain. Thus the subtraction of the Brillouin signals allows the detection of such a difference at zero background, as shown in Fig. 1. Therefore DPP-BOTDA is able to detect the small stress or temperature section for the pulse coverage lengthδz=cδτ/2. By tuning the frequency difference ν-ν B and repeating the measurement of the temporal Brillouin gain signals and taking the waveform difference, the differential BGS can be mapped along the fiber with resolution determined by the difference of the two pulse-widths and rise time of the pulse.
Fig. 1. The principle of DPP-BOTDA is to use a pulse pair with different pulse-widths to obtain high spatial resolution determined by the difference of the two pulse-widths and rise and fall time of the pulses.
The 3D curves of conventional BOTDA and proposed DPP-BOTDA based on simulations are shown in Figs. 2(a) and 2(b) as a function of frequency shift ν-ν B ranging from 12780 to 12880MHz. The pulse-width used in conventional BOTDA system is 50ns and the pulse-width pair used in DPP-BOTDA is 50 and 49ns. The length of the stressed fiber section is 0.2m with Brillouin frequency shift at 12860MHz (the Brillouin frequency of the un-stressed fiber is 12800MHz). It can be seen in Fig. 2(a) that the BOTDA curve shows the stressed fiber section centered at location of 6m covered by 5m sensing length, which matches with 50ns pulse. In Fig. 2(b), the DPP-BOTDA curve locates the stressed fiber section with much narrow coverage and higher spatial resolution, which can be calculated as 0.85m. There is a location offset of about a half pulse-width in DPP-BOTDA curve, comparing to BOTDA curve which is introduce by differential processing and can be calibrated. The spatial resolution can be further improved by smaller rise/fall time. Obviously DPP-BOTDA has much better spatial resolution and frequency shift measurement accuracy than conventional BOTDA.
Figure 3 shows the varied stressed length for the calculated DPP-BOTDA signal using pulse pair of 50 and 49ns at the Brillouin frequency shift of 12860MHz. The spatial resolution in all cases is around 1m, limited by the phonon lifetime. It can be seen that the center of the stressed fiber section of the DPP-BOTDA gain signals is offset from that of the conventional BOTDA gain signal by about cτ/4, which is the half of the pulse length. In the calculation the strain is varied between two Brillouin frequencies of ν=12860MHz and ν B=12800MHz over the stressed fiber section. We assume that the strain profile takes square shape and the strain changing length to be 0.02m. This explains the similar spatial resolution of ~0.85m in Fig. 3. Although the pulse-width is tens of nanoseconds, the phonon relaxation time is effectively reduced because of the detection of the differential Brillouin gain over the smaller stressed fiber section and higher spatial resolution can be achieved, which will be demonstrated in the following experimental results.
Fig. 2. The 3D BOTDA spectra along the sensing fiber for a 0.2m length fiber section with 60MHz Brillouin frequency shift from 12800MHz. (a) Conventional BOTDA using 50ns pulse light and, (b) DPP-BOTDA using 50 and 49ns pulse pair.
Fig. 3. The calculated conventional BOTDA for 50ns pulse light (solid) and DPP-BOTDA for the 50/49ns pulse pairs at peak Brillouin frequency shift of 12860MHz for various stress section length of 0.2m (dash), 1.0m (point) and 1.5m (dash-point).
It is notable that the subtraction of differential waveform of DPP-BOTDA shows some analogy to the effect of a high-pass filter in which the slow varying components are removed as they represent the same Brillouin gain for both pulses of τ and τ+δτ, and the fast varying components amplified in differential signal. The fast varying components in temporal Brillouin gain signals may be introduced via the non-resonant Brillouin frequency mismatching [6].
Also it can be seen in DPP-BOTDA that the larger the difference between the two pulse-widths, the stronger the differential signal and the higher measurement accuracy of the Brillouin frequency shift; On the other hand, the smaller the difference between the two pulse-widths, the higher spatial resolution and lower measurement accuracy of the frequency shift. In addition, the rise/fall time of the pulse pair should be selected shorter than the equivalent pulse-width difference δτ and the inverse of the detection bandwidth to achieve minimum spatial resolution.
3. Experimental results
The DPP-BOTDA experiment is shown in Fig. 4, which is based on BOTDA-type system. Pulsed Stokes beam is injected into a sensing fiber and experiences Brillouin amplification at the expense of the counter-propagating cw pump beam. The resultant power drops in the pump beam are measured while the frequency difference between the lasers is scanned across Brillouin loss spectrum. With the use of a pair of the pulsed beam to probe the fiber and perform DPP-BOTDA processing, the Brillouin shift of the fiber is determined from the differential spectrum and is used to calculate the strain or the temperature of the sensing fiber.
Fig. 4. Configuration of the DPP-BOTDA sensing system. PD: photo-detectors, FUT: fiber under test, EOM: electro-optic modulator. The pulse width is controlled by pulse generator.
The laser sources are Nd:YAG lasers operating at 1320 nm. The peak pulsed power is approximately 12mW, and the probe power is 4mW. The rise/fall time of the pulsed Stokes is 5ns. The time-domain signals are monitored with a 1-GHz bandwidth AC-coupled photo-detector, and 4000 averages are taken at each frequency step. The time-domain signals are recorded at intervals of 2MHz to produce the Brillouin gain spectra. The fiber under test is 1km long, including two stressed sections of 0.5m, separated by 1m loose fiber, as schematically shown in Fig. 5(a). The strains applied to the two sections are around 2,000 and 3,000 micro-strains, respectively. Figure 5(b) shows the recorded 3D graph of the BGS obtained by a conventional BOTDA using 50ns pulse as versus distance and the Brillouin frequency. It can be seen that the two 0.5m stress fiber sections occurring at 5m location overlaps each other over a distance of ~9m. Thus the 1m loose fiber in the middle is not spatially resolved due to the limitation of 5m spatial resolution. The line-width of the BGS is about 30MHz.
Figure 6 shows the 3D graphs of the BGS obtained with DPP-BOTDA for 50/45ns pulse pair (a) and 50/48ns pulse pair (b). As shown in the graphs, the two 0.5m stressed fiber sections and the 1m loose fiber are clearly resolved, even though the pulse-widths are 50, 48 and 45ns, which are much longer than the stressed length. The double peak of the stressed section at 58m is caused by the extra strain induced by two stretched points at large strains where the glues do not hold fiber well.
Fig. 5. (a). The sensing fiber layout with two stress sections of 2,000 and 3,000 micro-strains separated by 1m loose fiber. (b). 3D graph of the BGS from a conventional BOTDA using 50ns pulse.
Fig. 6. The 3D graphs of the BGS by DPP-BOTDA using (a) 50/45ns pulse pair and (b) 50/48ns pulse pair. The later shows better spatial resolution and finer fiber feature.
As shown in Fig. 6, the DPP-BOTDA precisely resolves the length of the stressed fiber sections of 0.5m, and the loose fiber section of 1m, with much higher spatial resolution than the calculated resolution of 0.85m as shown in Fig. 3. As mentioned in earlier section, the theoretical calculation shows the smallest detectable fiber length of about 0.85, which is limited by the phonon relaxation time. In experiment, however, it is not the case because that within the pulse length only the small fraction of the Brillouin gain is kept while the majority of the Brillouin interaction is removed by the differential process of DPP-BOTDA, as well as the slow varying phonon lifetime effect. The bandwidth of the photo-detector used and its amplification system is ~1GHz, which is capable to resolve 0.1m spatial modulation in time-domain analysis.
The 3D BGS curves obtained by BOTDA alone with the use of pulse-widths of 50ns, 45ns and 48ns have their similar signal-to-noise ratios (SNR), while the SNR of the resultant DPP-BOTDA with uses of 50/45ns and 50/48ns pulse pair are slightly different with their SNR values of 26dB and 18dB, respectively, as shown in Figs. 6(a) and 6(b). However the later case has its better spatial resolution and shows finer feature of the sensing fiber, as shown in Fig. 6(b). In the experiment, the time-domain signals are recorded at frequency intervals of 2MHz over 400MHz range and 4,000 averages are taken at each frequency step. With the use of high speed Acquris DC 240 data acquisition board and Labview 8.2 control interface, it only takes 4 to 5 minutes to complete the whole measurement.
The impact of the pulse light rise/fall time of the pulse light τ r to the spatial resolution of the DPP-BOTDA is also studied. The experimental setup is described in Ref. [7], where the two laser sources are two DFB lasers at wavelength of 1550nm. A 5m polarization maintaining fiber (PMF) is used as FUT with a 0.2m stressed section in the middle of PMF. The Brillouin frequency of the loose PMF is ~10590MHz at room temperature, while the stressed section has the equivalent Brillouin frequency shift of ~10690MHz. The pump power is 5mW, and the pulse peak power is ~2.4mW. The pulse pair of 20/19ns with different rise/fall time of, τr=0.67ns and τr=2ns is used to obtain DPP-BOTDA curves as a function of position and frequency and their top view are shown in Figs. 7(a) and 7(b). Similarly, DPP_BOTDA for the pulse pair of 20/15ns with the rise time of τr=0.67ns and τr=2ns are shown in Figs. 7(c) and 7(d), respectively. Apparently the differential gain using 20/15ns pulse pair has stronger signal than that of using 20/19ns pulse pair. Although the pulse-width difference is the same as that of 50/49 pulse pair in Fig. 6, the spatial resolution has been improved with shorter rise time. The larger τr corresponds to smaller bandwidth and less noise in the signal, hence higher SNR and higher strain accuracy. According to our experiment, the optimized parameter of rise/fall time τr=0.2~0.4δτ is selected to achieve 0.2m spatial resolution.
Fig. 7. Comparison of different DPP-BOTDA using pulse pair with various rise/fall times of the pulses: (a) 20/19ns pulse pair with=r τ 0.67ns and (b)=r τ 2ns, (c) 20/15ns pulse pair with=r τ 0.67ns and (d)=r τ 2ns.
The spatial resolution of the DPP-BOTDA can be calculated by the average of the rise and fall time equivalent length in meter for the stressed fiber section with DPP-BOTDA time domain signal for the Brillouin frequency shift of 12900MHz, correspond to the first stressed fiber section. As shown in Fig. 8, a spatial resolution of ~0.35m is achieved using DPP-BOTDA with 50/45ns pulse-width pair. In the cases of 50/48ns and 50/49ns pulse-width pair, the spatial resolution are 0.25m and 0.18m, respectively, which is equivalent to 2.5ns and 1.8ns pulse-width used in conventional BOTDA. Note that the Brillouin spectral line-width in DPP-BOTDA maintained at 30MHz due to the large pulses (~50ns). In the current experiment the combined bandwidth of the photo-detector, the post-amplifier and the data acquisition digitizer is ~1GHz. Although the bandwidth of detection system and the optical power levels of the pump and Stokes lights are maintained the same, the resultant SNR of the DPP-BOTDA are different. This is because that the stimulated Brillouin scattering (SBS) interaction between pump and Stokes wave over different interaction lengths produces different Brillouin gain (or loss). Therefore the measurement frequency resolution is the highest for the 50/45ns pulse pair, which is 1.7MHz. On the other hand, the SNR is the lowest for 50/49ns pulse pair due to the smallest difference in DPP-BOTDA comparing to the pulse-width pairs of 50/48ns and 50/45ns. This gives the 3.4MHz frequency accuracy, as shown in Table 1. The Brillouin frequency accuracy is calculated by δνB=ΔνB/(√2 SNR1/4) [8], where ΔνB=30MHz, which is the Brillouin spectral line-width calculated based on the least squares fit to the measured Brillouin gain spectrum at the fiber locations, and SNR is the electrical signal-to-noise power ratio.
Fig. 8. Evaluation of the spatial resolution for DPP-BOTDA with 50/45ns pulse pair based on (rise time+fall time)/2, in the time-domain DPP-BOTDA signal at the Brillouin frequency shift of 12900MHz.
Table 1. Spatial and Brillouin frequency resolution of DPP-BOTDA
4. Conclusions
A novel DPP-BOTDA sensing system is proposed for measuring distributed strain and temperature with high spatial resolution of 0.18m over kilometer long fiber using pulse of tens nanoseconds. The advantages of this DPP-BOTDA approach are: 1, The narrow BGS of 30MHz is obtained due to long pulses; 2, DPP-BOTDA based BGS has higher signal-to-noise ratio (SNR) than the BGS obtained using conventional BOTDA with pulse-width of δτ due to the nonlinear amplification of long duration pulses. 3, The large pulse-width difference gives stronger differential gain and shorter averaging time; 4, The long pulse-width reduce the broadband requirements on the pulse generator and electro-optic modulator (EOM) for optical pulses and higher extinction ratio can be easily achieved for kilometers fiber length; 5, The long sensing length can be achieved with much lower optical power and less depletion and gain saturation effects. By choosing proper pulse-width pairτ and τ+δτ, as well as their rise/fall time, a spatial resolution of <0.2m and Brillouin frequency accuracy of 2–3MHz for a km length fiber is demonstrated. The proposed technique is suitable for static and quasi-static measurement such as civil structural health monitoring and perimeter applications that require high measurement and spatial resolution over long sensing length.
Acknowledgment
The experimental work is supported by Natural Science and Engineering Research Council of Canada via Discovery Grant and Intelligence Sensing for Innovative Structures - a National Center of Excellence Program in Canada.
References and links
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