Distributed Dynamic Strain Sensing Based on Brillouin Scattering in Optical Fibers

sensors

Review Distributed Dynamic Strain Sensing Based on Brillouin Scattering in Optical Fibers

Agnese Coscetta *, Aldo Minardo and Luigi Zeni Department of Engineering, University of Campania “Luigi Vanvitelli”, 81031 Via Roma 29, Aversa, Italy; [email protected] (A.M.); [email protected] (L.Z.) * Correspondence: [email protected]

Received: 9 September 2020; Accepted: 28 September 2020; Published: 1 October 2020

Abstract: Over the past three decades, extensive research activity on Brillouin scattering-based distributed optical fiber sensors has led to the availability of commercial instruments capable of measuring the static temperature/strain distribution over kilometer distances and with high spatial resolution, with applications typically covering structural and environmental monitoring. At the same time, the interest in dynamic measurements has rapidly grown due to the relevant number of applications which could benefit from this technology, including structural analysis for defect identification, vibration detection, railway traffic monitoring, shock events detection, and so on. In this paper, we present an overview of the recent advances in Brillouin-based distributed optical fiber sensors for dynamic sensing. The aspects of the Brillouin scattering process relevant in distributed dynamic measurements are analyzed, and the different techniques are compared in terms of performance and hardware complexity.

Keywords: dynamic strain; distributed optical ﬁber sensors; stimulated Brillouin scattering

1. Introduction Recently, research and investment toward the development of distributed optical fiber sensors able to detect dynamic phenomena such as vibrations and sound waves have increased. The growing interest mainly comes from areas such as the oil and gas extraction companies [1], geophysics [2,3], and structural health monitoring [4]. In some applications, such as perimeter control and anti-intrusion, the simple detection of vibrations and their localization is sufficient, and this led to the development of the so-called distributed acoustic sensors (DAS) based on Rayleigh scattering [5,6]. On the other hand, when accurate and reliable measurements of the vibrations is required, sensors based on the Brillouin scattering can represent the right solution. This is especially true when structural analysis in aeronautic and civil applications is required to enable the identification of structural damages and pinpoint defects along large structures. In fact, the availability of an enormous number of spatially resolved data, typical of distributed optical fiber sensors, can make the difference. As an example, the detection of passive or actively induced vibrations in a structure can be exploited for non-destructive testing (i.e., online detection of cracks) without the need to dismantle the structure itself [7]. In addition, damage detection may get enormous advantage from distributed dynamic measurements, because changes in modal shapes may give precise indications on the position and severity of damage [8–10]. Conventional Brillouin scattering-based sensors suffer from a relatively long acquisition time (from seconds to minutes), basically due to two reasons: the first reason is that the intensity of the backward Brillouin scattering is weak, therefore many backscattered traces need to be averaged for adequate signal-to-noise ratio (SNR); the second reason is that the frequency offset between pump and probe beams must be swept, in order to obtain the Brillouin gain spectrum (BGS). Usually, several tens

Sensors 2020, 20, 5629; doi:10.3390/s20195629 www.mdpi.com/journal/sensors Sensors 2020, 20, 5629 2 of 23 of Brillouin gain profiles must be acquired, to recover the temperature or strain distribution along the fiber [11]. In dynamic sensing applications, the acquisition time must be short enough to catch the relevant information. The required acquisition rate is very much dependent on the intended application, ranging from a few Hz in case of e.g., seismic monitoring [12] and wind turbine blade monitoring [13,14], up to several kHz in case of e.g., railway traffic monitoring [15] and pipeline leakage monitoring [16]. To reach an acquisition rate adequate for dynamic sensing applications, several techniques addressing the second aspect have been developed, i.e., they are aimed to eliminate (or at least attenuate) the requirement of scanning the probe frequency. On the other hand, it is clear that any optimization of the experimental configuration that increases the SNR (e.g., based on the use of a narrow linewidth laser [17], optimized detection schemes [18,19], or more sophisticated methods for the suppression of the polarization noise [20]) is also beneficial to dynamic measurements, as it permits the cutting down of the averaging factor. For example, the simple (but costly) adoption of a polarization-maintaining (PM) fiber as the sensing fiber, leads to obvious advantages in terms of acquisition speed, as it eliminates the averaging requirements usually associated with the polarization scrambling of the pump, and required to compensate the Brillouin gain fluctuations due to the fiber birefringence. In this review, we focus our attention on the schemes aimed at reducing the acquisition time associated with the probe frequency sweep, either by reducing the number of swept frequencies, or by accelerating the sweep process. Nonetheless, it is understood that any strategy that leads to an SNR improvement (with consequent reduction or even avoidance of averaging) can be adopted to raise up the acquisition rate, making it compliant to he intended application. The paper is organized as follows: after a brief recall of the Brillouin analysis and the discussion on the main factors limiting its application to dynamic sensing, the main technical solutions that have been devised to overcome the problem will be described along, in some cases, with illustrative experimental achievements.

2. Brillouin Analysis for Distributed Sensing When a pump light in injected into an optical fiber, it interacts with the quantized vibrational modes of molecules in the matter (the so-called acoustic phonons). They can be regarded as acoustic waves, inducing periodic variations in the refractive index of the fiber due to the elasto-optic effect. These traveling refractive index variations act as a diffraction grating, scattering the incident light in all directions. In the backward direction, the frequency of the scattered light is downshifted from that of the incident light, by a quantity equal to the frequency of the acoustic wave (the so-called Brillouin Frequency Shift, BFS). When a probe light, frequency shifted from the pump light by the BFS, is injected from the opposite side of the fiber, an acoustic wave much more intense than those thermally excited is generated by electrostriction, leading to a stronger backscattered signal. The underlying phenomenon is known as stimulated Brillouin scattering (SBS), and has been employed to realize Brillouin lasers [21], amplifiers [22], slow-light systems [23,24], as well as for the implementation of distributed sensors able to sense temperature and strain changes over large distances [25,26]. The dependence of the backscatter amplitude from the frequency shift between pump and probe waves follows a typical Lorentz function (see Figure1), centered at the BFS. The latter is given by:

2ne f f VA BFS = (1) λ where VA is the velocity of the acoustic waves, neff is the effective refractive index, and λ is the optical wavelength. Both VA and neff depend on the temperature and strain of the fiber, therefore the changes in these two parameters can be measured by monitoring the changes in the BFS. The BFS is 10 11 GHz in silica fibers at λ = 1550 nm, while temperature and strain sensitivities are 1 MHz/ C ÷ ∼ ◦ and 50 kHz/µε, respectively. ∼ Sensors 20202020,, 2020,, 5629x FOR PEER REVIEW 33 of of 23

Figure 1.1.Brillouin Brillouin Gain Gain Spectrum Spectrum in a conventionalin a conventional silica ﬁber.silica The fiber. red circlesThe red represent circles therepresent frequencies the acquiredfrequencies for acquired BFS extraction. for BFS extraction.

To getget informationinformation aboutabout thethe distribution distribution of of the the BFS BFS along along the the fiber, fiber, some some form form of of modulation modulation of theof the pump pump light light is is required. required. A A comprehensive comprehensive review review of of the the most most relevantrelevant demodulationdemodulation techniquestechniques for Brillouin sensing sensing can can be be found found in in Ref. Ref. [27]. [27 ].Here, Here, we we briefly briefly recall recall the thethree three main main approaches: approaches: the theBrillouin Brillouin Optical Optical Time-Domain Time-Domain Analysis Analysis (BOTDA), (BOTDA), the the Brillouin Brillouin Optical Frequency-DomainFrequency-Domain Analysis (BOFDA),(BOFDA), andand thethe BrillouinBrillouin OpticalOptical Correlation-DomainCorrelation-Domain AnalysisAnalysis (BOCDA).(BOCDA). The BOTDA makes use of a pulsed pump, therefore it strictly resembles the conventional optical time domain domain reflectometry. reflectometry. The The spatial spatial resolution, resolution, i.e., i.e., the the capability capability to discriminate to discriminate between between the BFS the BFSin adjacent in adjacent positions, positions, is determined is determined by the by temporal the temporal width width of the of pulse the pulse injected injected into the into fiber. the fiber. The Thedetected detected BGS BGSis the is convolution the convolution between between the natura the naturall BGS BGS(with (with a linewidth a linewidth of about of about 30 MHz) 30 MHz) and andthe pulse the pulse spectrum. spectrum. Therefore, Therefore, pulse pulse durations durations less than less thanabout about 10 ns10 led ns to led a broadened to a broadened BGS BGSand, and,consequently, consequently, a less aaccurate less accurate BFS estimate. BFS estimate. When a su Whenbmeter a submeterspatial resolution spatial resolutionis required, is some required, form someof pre-activation form of pre-activation of the acoustic of the wave acoustic is usually wave adopted is usually to adopted measure to the measure BFS with the adequate BFS with adequateaccuracy accuracy[28–31]. As [28 –regards31]. As the regards acquisition the acquisition time, each time, Brillouin each Brillouin gain profile gain profile(i.e., each (i.e., point each pointin the in BGS the BGSfrequency frequency domain) domain) requires requires an (ideal) an (ideal) acquisition acquisition time timeequal equal to the to roundtrip the roundtrip time timeof the of pulse the pulse over 2n overthe fiber the fiberlength, length, i.e., i.e.,𝑇=T = 𝐿, whereg L, where 𝐿 isL theis the fiber fiber length length and and 𝑛 n isis the the group group velocity velocity of of the the pulse. pulse. c g For example, the roundtrip time for a 100-m fiberfiber length is ∼1 µµs,s, unveilingunveiling aa maximummaximum acquisitionacquisition ∼ rate of 1 MHz if nono averagingaveraging nornor probeprobe frequencyfrequency sweepsweep isis performed.performed. The basic basic setup setup for for BOTDA BOTDA measurements measurements is shown is shown in Figure in Figure 2. A single2. A laser single source laser (typically, source (typically,a distributed a distributed feedback feedbackdiode laser), diode is laser),employ ised employed for pump for pumpand probe and probebeam beamgeneration. generation. The Thefrequency-shifted frequency-shifted probe probe is generated is generated through through an el anectro-optic electro-optic modulator modulator (EOM (EOM1)1) biased biased near nearzero zerotransmission transmission point, point, driven driven by a byradiofrequency a radiofrequency signal signal to realize to realize a dual a dualsideband sideband modulation. modulation. The Thepump pump is pulsed is pulsed using using a second a second electro-optic electro-optic modula modulatortor (EOM2), (EOM2), also also biased biased near near zero zero transmission point and driven by an electrical pulse. The fiber fiber Bragg grating in the receiver path acts as a reflection reflection bandpass optical fiber,fiber, selecting one of the two sidebands generated by EOM1 (the one at lower frequency, typically). Finally, Finally, a a polarization polarization scrambler scrambler (PS) (PS) is is inserted inserted into into the the pump pump path path in inorder order to toremove remove (by (by averaging) averaging) the thesignal signal fluctuations fluctuations associated associated with with the dependance the dependance of the of Brillouin the Brillouin gain gainfrom fromthe lightwaves the lightwaves polarization. polarization. The pulse The generator pulse generator acts as a acts trigger as a for trigger data acquisition, for data acquisition, which is whichgenerally is generally carried carriedout in outaverage in average mode mode to reach to reach an anadequate adequate SNR. SNR. The The conventional conventional BOTDA measurement processprocess requires requires the the pump pump/probe/probe frequency frequency shift shift to beto sweptbe swept around around the BFSthe ofBFS the of fiber, the tofiber, reconstruct to reconstruct the BGS the shown BGS shown in Figure in Figure1. This 1. scan This is scan performed is performed step by step step: by thestep: frequency the frequency shift (i.e.,shift the(i.e., radiofrequency the radiofrequency applied applied to EOM1) to EOM1) is set, and is set, then and a certain then a numbercertain number of Brillouin of Brillouin gain profiles gain areprofiles acquired, are acquired, cumulated cumulated (averaged) (averaged) and stored and into stored memory. into memory. Then, a new Then, frequency a new frequency shift is set, shift and is a newset, and collection a new ofcollection Brillouin of gain Brillouin profile gain acquisitions profile acquisitions is done. The is process done. The terminates process when terminates an adequate when numberan adequate of frequency number shiftsof frequency (i.e., data shifts points (i.e., in data the BGS points frequency in the BGS domain) frequency havebeen domain) acquired. have been acquired.

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Figure 2. Conventional BOTDA configuration. conﬁguration. PS: PS: polarization polarization scrambler; scrambler; FBG: FBG: fiber ﬁber Bragg Bragg grating. grating. EOM: Electro-optic modulator. PD: photodetector.

A different different method, working in the frequency domaindomain (the so-called BOFDA), makes use of an intensity- oror phase-modulatedphase-modulated pump pump wave wave [32 –[3234–34].]. Sweeping Sweeping the modulationthe modulation frequency frequency over a over proper a properrange and range a proper and a step proper (which step depend (which on depend the measurement on the measurement range and intendedrange and spatial intended resolution), spatial resolution),the modulation the modulation impressed onimpressed the emerging on the probeemergi waveng probe is captured wave is bycaptur a vectored by network a vector analyzernetwork analyzer(VNA). In (VNA). this case, In thethis datacase, acquired the data byacquired the VNA by must the VNA be inverse must Fourierbe inverse transformed, Fourier transformed, to retrieve the to retrieveBrillouin the gain Brillouin profile gain along profile the fiber. along Cm- the or fiber. even Cm- mm-scale or even spatial mm-scale resolutions spatial areresolutions easily achieved are easily in achievedBOFDA sensors, in BOFDA making sensors, them making especially them attractive especially in attractive the aerospace in the industry aerospace [35 industry,36]. The [35,36]. acquisition The acquisitionof each Brillouin of each gain Brillouin profile gain takes profile a time takes equal a time to the equal inverse to the of inverse the resolution of the resolution bandwidth bandwidth (RBW) of (RBW)the VNA. of the The VNA. RBW The is the RBW bandwidth is the bandwidth of the bandpass of the bandpass filter used filter for data used acquisition for data acquisition and is related and tois relatedthe fiber to length the fiber by length the Nyquist’s by the Nyquist’s theorem. Therefore,theorem. Therefore, the BOFDA the method BOFDA has method theoretically has theoretically the same theperformance same performance as the BOTDA as the method BOTDA in method terms of in acquisition terms of acquisition time. However, time. the However, use of a small-signalthe use of a small-signalmodulation formodulation the pump for implies the pump that an implies adequate that SNR an adequate is usually SNR achieved is usually only byachieved setting anonly RBW by setting(at least) an one RBW order (at of least) magnitude one order narrower of magnitude than that narrower dictated bythan Nyquist, that dictated making by BOFDA Nyquist, sensors making less BOFDAattractive sensors than BOTDA less attractive sensors than for dynamicBOTDA sensingsensors for applications. dynamic sensing applications. Besides time-domain and frequency-domain dete detectionction schemes, a correlation-based technique based on frequency-modulated continuous-wave pump pump and and probe lights has been demonstrated as well [[37].37]. The Brillouin Optical Correlation Analysis (BOCDA) provides excellent spatial resolution capabilities (down (down to to the the mm mm scale), scale), at the at theexpense expense of the of maximum the maximum number number of sensing of sensing points, points,which iswhich typically is typically limited limitedto a few to hundreds. a few hundreds. For exampl Fore, example,a 1-cm spatial a 1-cm resolution spatial resolutionimplies a maximum implies a sensingmaximum length sensing of a few length meters. of a fewThus, meters. the correlation Thus, the method correlation is suitable method in is the suitable monitoring in the of monitoring relatively small-sizedof relatively structures, small-sized such structures, as composite such material as composite parts materialin the automotive, parts in the nautical, automotive, and aerospace nautical, industriesand aerospace [38]. industriesAs regards [38 the]. Asacquisition regards thespeed, acquisition the following speed, argument the following can argumentbe followed: can the be vg followed: the measurement range dm in BOCDA sensors is given by dm = [39], where vg is the measurement range 𝑑 in BOCDA sensors is given by 𝑑 = [39], where2 fm 𝑣 is the group group velocity, and fm is the sine-wave modulation applied to the pump and probe waves for the velocity, and 𝑓 is the sine-wave modulation applied to the pump and probe waves for the synthesis synthesis of a correlation peak. Assuming that the Brillouin gain (i.e., the probe amplification) is of a correlation peak. Assuming that the Brillouin gain (i.e., the probe amplification) is captured by captured by use of a lock-in amplifier with a time constant 50 times larger than the inverse of fm [40], use of a lock-in amplifier with a time constant 50 timesvg larger than the inverse of 𝑓 [40], the the maximum acquisition rate f will be given by to . For example, for a fiber length of 100 m, s 100 dm maximum acquisition rate 𝑓 will be given by to ×. For example, for a fiber length of 100 m, the the maximum acquisition rate is 20 kHz. However,× it must be kept in mind that this rate only refers to maximumthe measurement acquisition over arate single is 20 position kHz. However, of the fiber it undermust testbe kept (FUT). in Measurementmind that this over rate moreonly locationsrefers to theleads measurement to a proportionally over a longer single acquisition position of time. the fiber under test (FUT). Measurement over more locationsIndependently leads to a proportionally of the chosen detectionlonger acquisition scheme (time time. domain, frequency domain, or correlation domain),Independently the need to of scan the the chosen pump–probe detection frequency scheme (time shift overdomain, ~200 frequency frequencies domain, is often or the correlation bottleneck domain), the need to scan the pump–probe frequency shift over ~200 frequencies is often the

Sensors 2020, 20, 5629 5 of 23 Sensors 2020, 20, x FOR PEER REVIEW 5 of 23 bottleneckof the acquisition of the rate.acquisition Consequently, rate. Consequently, methods to overcome methods thisto overcome limitation havethis limitation been devised have and been are deviseddescribed and in are the described following sections.in the following sections.

3. Dynamic Dynamic Sensing Sensing Based on BOCDA Interestingly, the firstfirst report of a relativelyrelatively highhigh acquisitionacquisition rate was demonstrated with a BOCDA configuration configuration [39], [39], which, according according to to what discussed earlier, earlier, is the less favorable for distributed dynamic sensing (due to the necessity to scan the correlation peak over each sensed position). AsAs aa matter matter of of fact, fact, the the method method was was applied applied to detect to detect the dynamic the dynamic strain overstrain a singleover a location. single location.The configuration The configuration is shown inis Figureshown3 .in The Figure scheme 3. implementsThe scheme a implements modified BOCDA a modified configuration, BOCDA configuration,in which the frequency-shifted in which the frequency-shifted probe wave is generated probe wave by switching is generated the laser by frequency, switching rather the laser than frequency,applying an rather external than modulation applying an to external the laser. modula In anytion case, to the this laser. modification In any case, was this only modification intended to wassimplify only theintended experimental to simplify configuration, the experimental having noconfiguration, effect on the having maximum no effect permissible on the acquisitionmaximum permissiblerate. The laser acquisition current waveformrate. The laser was current formed waveform by superimposing was formed a sine-wave by superimposing modulation a sine-wave at a few modulationMHz, required at a tofew localize MHz, therequired SBS interaction to localize the in a SBS specific interaction section in of a thespecific FUT, section to a 100-kHz of the FUT, square to wavea 100-kHz required square to alternate wave required the pump to alternate and probe the frequencies. pump and By probe this method,frequencies. the authorsBy this method, reported the authorsacquisition reported of strain the acquisition over a single of positionstrain over along a single a 20-m position long along FUT, ata 20-m a maximum long FUT, sampling at a maximum rate of 1sampling kHz and rate spatial of 1 resolutionkHz and spatial of 10 cm. resolution of 10 cm.

Figure 3. Experimental setup employed for BOCDA meas measurements;urements; EOM, electr electro-optico-optic modulator; PD, photodiode; FUT, ﬁberfiber underunder testtest (Adapted(Adapted fromfrom Ref.Ref. [[39]).39]).

As discusseddiscussed earlier, earlier, whenever whenever dynamic dynamic sensing sensing over over more more locations locations is required, is required, BOCDA BOCDA systems systemsare not the are best not solution,the best solution, as only one as only position one canpositi beon sensed can be at sensed a time. at In a other time. words, In other the words, sampling the samplingrate is scaled rate down is scaled proportionally down proportionally to the number to ofthe sensed number locations. of sensed More locations. advanced More schemes advanced have schemesbeen demonstrated, have been indemonstrated, which the amplitude in which of the the amp backscatterlitude of signal the backscatter is measured signal in multiple is measured locations in multiplesimultaneously. locations These simultaneously. schemes include These the schemes use of ainclude pulsed the pump, use of to a discriminate pulsed pump, between to discriminate multiple betweencorrelation multiple peaks along correlation the FUT peaks [41], along or multi-tone the FUT modulation [41], or multi-tone of the laser modulation light [42]. of In the the laser latter light case, [42].an electrical In the spectrumlatter case, analyzer an electrical (ESA), lockedspectrum at twice analyzer the modulation (ESA), locked frequency, at twice detects the themodulation Brillouin frequency,gain changes detects in the positionthe Brillouin corresponding gain changes to that in modulation the position frequency. corresponding In Ref. [42 to], thethat measurement modulation frequency.of the dynamic In Ref. strain [42],at the two measurement locations simultaneously, of the dynamic was strain demonstrated at two locations in a simultaneously, 1100 m long ﬁber was at demonstrateda spatial resolution in a 1,100 of 60 m cm. long The fiber time at a required spatial resolution to perform of the 60 BGScm. The acquisition time required in both to positions perform wasthe BGS 210 acquisition ms (in case in of both 3-MHz positions sampling was 210 step ms for (i then case BGS), of 3-MHz or 65 mssampling (in case step of 10-MHzfor the BGS), sampling or 65 msstep) (in (see case Figure of 10-MHz4). Still, sampling the acquisition step) (see rate Figure was rather4). Still, low the (a acquisition few Hz), compared rate was rather to the low inverse (a few of Hz),the roundtrip compared time to the for theinverse given of ﬁber the length,roundtrip suggesting time for athe not given optimized fiber measurementlength, suggesting SNR ofa not the optimizedexperimental measurement scheme. Also, SNR the of methodthe experimental requires anscheme. independent Also, the detection method channelrequires foran independent each sensing detection channel for each sensing location. In other words, two independent ESAs (or two

Sensors 2020, 20, 5629 6 of 23 Sensors 2020, 20, x FOR PEER REVIEW 6 of 23 location.independent In other channels words, of two the independent same ESA) ESAsare requir (or twoed independentfor two correlation channels peaks of the (i.e., same two ESA) sensed are requiredlocations), for making two correlation the method peaks hardly (i.e., scalable. two sensed locations), making the method hardly scalable.

(a) (b)

FigureFigure 4. 4.BOCDA BOCDA measurementsmeasurements atat two two sensing sensing locations locations simultaneously. simultaneously. (a(a)) BGS BGS acquired acquired in in the the locationlocation subjected subjected to to BFS BFS changes. changes. ( b(b)) Corresponding Corresponding BFS BFS changes changes [ 42[42].].

AA didifferentfferent method, method, referredreferred toto as as di differentialfferential frequency frequency modulation modulation BOCDA, BOCDA,has hasbeen beenalso also proposedproposed to to fast fast scan scan the the correlation correlation peak peak (i.e., (i.e., the sensedthe sensed position) position) over theover entire the entire fiber [ 43fiber]. The [43]. setup The issetup very is similar very similar to the one to the shown one inshown Figure in3 ,Figure with the 3, with di fference the difference that the modulationthat the modulation frequency frequency applied duringapplied pump during generation pump generation is slightly is detuned slightly (adetuned few kHz) (a few from kHz) the from modulation the modulation frequency frequency applied duringapplied probe during generation. probe generation. In this way, In this the correlationway, the correlation peak moves peak continuously moves continuously along the fiberalong at the a constantfiber at a speed. constant By applyingspeed. By this applying method, this the meth authorsod, the have authors demonstrated have demonstrated the measurement the measurement of the BFS alongof the the BFS entire along fiber the entire length fiber (100 length m), at a(100 spatial m), at resolution a spatial ofresolution 80 cm and of 80 an cm acquisition and an acquisition rate of 20 Hz.rate Althoughof 20 Hz. the Although method the is e ffmethodective in is moving effective the in sensed moving position the sensed over the position entire fiber,over the acquisitionentire fiber, rate the isacquisition severely impaired, rate is severely compared impaired, to the conventional compared to BOCDA the conventional method with BOCDA a single method sensing with position. a single sensingA successive position. improvement of the BOCDA method, still aimed at increasing the acquisition rate, has beenA successive presented improvement in [44]. Here, of the the authors BOCDA made method, use ofstill a aimed voltage-controlled at increasing oscillatorthe acquisition (VCO) rate, in orderhas been to change presented rapidly in [44]. the frequencyHere, the ofauthors the probe, made reaching use of a in voltage-controlled this way an acquisition oscillator rate (VCO) as high in asorder 5 kHz to overchange a fiber rapidly of 6 the m and frequency at a spatial of the resolution probe, reaching of 3 cm. in However, this way thean measurementacquisition rate was as stillhigh limitedas 5 kHz to maximumover a fiber five of 6 (arbitrarily m and at a selected) spatial resolution sensing locations of 3 cm. simultaneously.However, the measurement was still limited to maximum five (arbitrarily selected) sensing locations simultaneously. 4. Slope-Assisted BOTDA (SA-BOTDA) Methods 4. Slope-AssistedAlthough the methodsBOTDA (SA-BOTDA) discussed in the Methods previous sections still rely on the measurement of the BrillouinAlthough gain at the various methods pump–probe discussed frequency in the previous shifts, sections slope-assisted still rely (SA) on techniques the measurement are based of onthe theBrillouin measurement gain at various of the Brillouin pump–probe gain forfrequency a fixed sh pump–probeifts, slope-assisted frequency (SA) shift, techniques chosen are in orderbased toon liethe within measurement the rising of or the the Brillouin falling slopegain for of thea fixed BGS pump–probe (see Figure5 a).frequency In such shift, a way, chosen the BFS in order temporal to lie changeswithin the are directlyrising or transferred the falling to slope the amplitude of the BGS of (see the backscatteredFigure 5a). In trace, such ata leastway,for the BFS BFS variations temporal smallchanges enough are directly with respect transferred to the BGSto the linewidth. amplitude This of the method backscattered somewhat trace, resembles at least the fordemodulation BFS variations techniquesmall enough used with in fiber respect Bragg to gratingthe BGS (FBG)-based linewidth. This dynamic method sensing, somewhat in which resembles the laser the wavelengthdemodulation is lockedtechnique on the used mid-reflection in fiber Bragg wavelength grating (FBG)-based of the FBG reflection dynamic spectrum sensing, in [45 which]. Of course, the laser the wavelength concept of SAis locked measurements on the mid-reflection can be equally wavelength applied to theof the Brillouin FBG reflection Phase Spectrum spectrum (BPS) [45]. [46 Of– 48course,] (see the Figure concept5b), orof toSA the measurements gain-to-phase can ratio be equally [48,49]. applied Lifting to the the measurementBrillouin Phase process Spectrum from (BPS) the [46–48] need to (see scan Figure the pump–probe5b), or to the frequency, gain-to-phase provides ratio a[48,49]. simple Lifting and eff theective measurement way to speed-up process the from acquisition the need rate to scan (at the the expensepump–probe of the frequency, dynamic range),provides which a simple will and be onlyeffect limitedive way by to thespeed-up fiber length the acquisition and the averagingrate (at the factorexpense [50 of]. the Furthermore, dynamic range), the SA-BOTDA which will be method only li canmited be by paired the fiber with length any acousticand the averaging pre-activation factor method[50]. Furthermore, (such as the the pulse-pair SA-BOTDA differential method method), can be paired in order with to push any theacoustic spatial pre-activation resolution below method to the(such 1-m as limit the setpulse-pair by the phonon differential lifetime method), [51]. in order to push the spatial resolution below to the 1-m limit set by the phonon lifetime [51].

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((aa)) ((bb))

FigureFigure 5. 5. PrinciplePrinciple of of operation operation of of the the SA-BOTDA SA-BOTDA method method:method:: thethe strain-induced strain-induced spsp spectralectralectral shiftsshifts of of the the BGSBGS ( (aa)) or or the the BPS BPSBPS ( ((bb))) can cancan be be regarded regarded as as temporal temporal variatio variationsvariationsns of of the probe frequency around around its its workingworking point. point.

InIn thethe firstfirst first demonstrationdemonstration demonstration ofof of thisthis this idea,idea, idea, thethe the dynadyna dynamicmicmic strainstrain strain waswas was acquiredacquired acquired atat aa at samplingsampling a sampling raterate rate ofof 200200 of Hz200Hz overover Hz over aa fiberfiber a fiber lengthlength length ofof 3030 of m,m, 30 atat m, aa at spatialspatial a spatial resolutionresolution resolution ofof 33 of mm 3 andand m and withwith with aa dynamicdynamic a dynamic resolutionresolution resolution ofof 2727 of 𝜇𝜀27𝜇𝜀⁄⁄µε√√𝐻𝑧𝐻𝑧/ √ [50].Hz[50].[50 AlthoughAlthough]. Although inin thatthat in that casecase case aa pulsedpulsed a pulsed probeprobe probe waswas was letlet let toto to interactinteract interact withwith with aa a counter-propagated counter-propagated pulsedpulsed pump, pump, restricting restricting the the measurement measurement atat aa single single location location atat a a time, time, the the method method can can be be equally equally appliedapplied usingusing aa conventional conventional cwcw probe,probe, allowingallowing simultaneoussimultaneous measurementsmeasurements measurements overover over thethe the wholewhole whole fiber.fiber. fiber. AsAs ananan example exampleexample of ofof truly trulytruly distributed distributeddistributed and dynamicandand dynamicdynamic strain strain measurements,strain measurements,measurements, a modal aa analysis modalmodal ofanalysisanalysis an aluminum ofof anan aluminumbeamaluminum excited beambeam via excitedexcited a magnetic viavia aa shaker magneticmagnetic was shakershaker reported waswas in reported Ref.reported [52] (seeinin Ref.Ref. Figure [52][52]6 ).(see(see The FigureFigure setup 6).6). used TheThe for setupsetup the usedexperimentsused forfor thethe is theexperimentsexperiments conventional isis BOTDAthethe conventionalconventional shown in Figure BOTDABOTDA2. The shownshown SA-BOTDA inin FigureFigure measurement 2.2. TheThe SA-BOTDA wasSA-BOTDA carried measurementoutmeasurement by fixing the waswas probe carriedcarried frequency outout byby shift fixingfixing (i.e., thethe the probeprobe RF frequency freqfrequencyuency applied shiftshift (i.e.,(i.e., to the thethe EOM) RFRF frequencyfrequency in order to appliedapplied lie within toto thethe EOM) risingEOM) (orinin orderorder falling) toto slopelielie withinwithin of the thethe local risingrising BGS. (or(or falling)falling) slopeslope ofof thethe locallocal BGS.BGS.

Figure 6. Cantilever beam used for modal analysis experiments [52]. FigureFigure 6.6. CantileverCantilever beambeam usedused forfor modalmodal analysisanalysis experimentsexperiments [52].[52]. The cantilever beam had a length of 1 m, a width of 3 cm and a thickness of 1cm. The fiber TheThe cantilevercantilever beambeam hadhad aa lengthlength ofof 11 m,m, aa widthwidth ofof 33 cmcm andand aa thicknessthickness ofof 1cm.1cm. TheThe fiberfiber waswas was glued along three parallel directions of the beam, to capture the strains along multiple lines. gluedglued alongalong threethree parallelparallel directionsdirections ofof thethe beambeam,, toto capturecapture thethe strainsstrains alongalong multiplemultiple lines.lines. TheThe The dynamic strain magnitude at 1.7 Hz and 10.8 Hz (corresponding to the first two modes of the dynamicdynamic strainstrain magnitudemagnitude atat 1.71.7 HzHz andand 10.810.8 HzHz (corresponding(corresponding toto thethe firstfirst twotwo modesmodes ofof thethe structure), measured along the middle fiber, are shown in Figure7, together with the results of a structure),structure), measuredmeasured alongalong thethe middlemiddle fiber,fiber, areare shownshown inin FigureFigure 7,7, togethertogether withwith thethe resultsresults ofof aa finite element method (FEM) analysis. Discrepancies between experimental and numerical results finitefinite elementelement methodmethod (FEM)(FEM) analysis.analysis. DiscrepanciesDiscrepancies betweenbetween experimentalexperimental andand numericalnumerical resultsresults areare are mostly attributed to the limited (50 cm) spatial resolution of the measurements. Please note that mostlymostly attributedattributed toto thethe limitedlimited (50(50 cm)cm) spatialspatial resoluresolutiontion ofof thethe measurements.measurements. PleasePlease notenote thatthat eacheach each experimental point in the mode shapes of Figure7 was calculated as the magnitude of the fast experimentalexperimental pointpoint inin thethe modemode shapesshapes ofof FigureFigure 77 wawass calculatedcalculated asas thethe magnitudemagnitude ofof thethe fastfast FourierFourier Fourier transform (FFT) of the dynamic strain signal acquired in that position, over a time period transformtransform (FFT)(FFT) ofof thethe dynamicdynamic strainstrain signalsignal acquiredacquired inin thatthat position,position, overover aa timetime periodperiod ofof 2020 s.s. OfOf of 20 s. Of course, the acquisition of the strain temporal changes over a temporal window of 20 s, course,course, thethe acquisitionacquisition ofof thethe strainstrain temporaltemporal changeschanges overover aa temporaltemporal windowwindow ofof 2020 s,s, underunder constantconstant under constant vibrating conditions, greatly enhances the SNR compared to the capture of a single-shot, vibratingvibrating conditions,conditions, greatlygreatly enhancesenhances thethe SNRSNR compcomparedared toto thethe capturecapture ofof aa single-shot,single-shot, transienttransient transient phenomenon. phenomenon.phenomenon.

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(a) (b)

Figure 7. Dynamic strain amplitude related to the (a) first and (b) second mode of the cantilever beam. Mode frequencies are 1.7 Hz are 10.8 Hz, respectively. The blue lines represent the mode shapes measuredFigure 7.using Dynamic the SA-BOTDAstrain amplitude method, related while to the ( reda) first lines and represent (b) second the mode FEMresult of the [cantilever52]. beam. Mode frequencies are 1.7 Hz are 10.8 Hz, respectively. The blue lines represent the mode shapes Themeasured SA-BOTDA using the method SA-BOTDA was further method, employed while the red by lines the samerepresent authors the FEM for theresult modal [52]. analysis [9] and defect identification [10] of a composite plate, and for railway traffic monitoring [53]. In the latter case, theThe method SA-BOTDA was employedmethod was to further measure employed the strain by induced the same by authors train passage for the alongmodal a analysis rail track, [9] overand adefect distance identif of 60ication m and [10] at of an a composite acquisition plate rate, and of 31 for Hz. railway This wastraffic su monitoringfficient to detect [53]. In the the train latter passagecase, the and method extract was several employed information to measure from the the acquired strain induced data, such by astrain train passage speed, along number a rail of axles, track, interaxleover a distance distances, of and60 m axle and load. at an acquisition rate of 31 Hz. This was sufficient to detect the train passageDespite and its extract advantages, several the information SA-BOTDA from method the acquired has its own data, limitations: such as train first, speed, the method number requires of axles, theinteraxle probe frequency distances to, and lie withinaxle load. the slope of the BGS (or BPS as well). In general, this condition cannot be metDespite in all fiber its positions, advantages, because the each SA-BOTDA position maymethod exhibit has a diitsff erent own BFS limitations: due to strain first,/temperature the method spatialrequires nonuniformities. the probe frequency Another to limitation lie within is thatthe slope even when of the the BGS probe (or frequencyBPS as well). is exactly In general, tuned this to thecondition middle ofcannot the BGS be met linear in all slope, fiber the positions, maximum because strain each variation position is limited may exhibit to about a different a few hundred BFS due µεtofor strain/temperature faithful frequency / spatialamplitude nonuniformities. conversion (see Another Figure 5 limitation). Third, the is systemthat even is more when susceptible the probe tofrequency noise compared is exactly to the tuned conventional to the middle BOTDA of the method, BGS linear in which slope, the the BFS maximum is recovered strain by processingvariation is (e.g.,limited by quadraticto about a fitting)few hundred the entire µε for BGS. faithful For example, frequency/amplitude operating with conversion a typical (see laser Figure linewidth 5). Third, of 1the MHz, system the SA is methodmore susceptible directly translates to noise thecompared laser phase to the noise conventional in a rms strain BOTDA error method, of about in 20 whichµε [54 the]. Finally,BFS is therecovered SA-BOTDA by processing method recovers(e.g., by quadratic the strain fromfitting) the the amplitude entire BGS. (rather For example, than the op frequency)erating with of thea typical backscattered laser linewidth signal, making of 1 MHz it prone, the SA to errorsmethod related directly to laser translates power the variations. laser phase noise in a rms strainAs regardserror of the about first 20 limitation, µε [54]. a Finally, modification the SA of-BOTDA the SA techniquemethod recovers has been the demonstrated strain from in the Ref.amplitude [55], relying (rather on thethan use the of frequency) a specially synthesizedof the backs probecattered wave, signal, whose making frequency it prone is rapidly to errors changed related byto use laser of power an arbitrary variations. waveform generator (AWG) in order to lie along the slope of the BGS in each fiber positionAs regards (see the Figure first 8limitation,). Exploiting a modification this method, of the the SA authors technique have has performed been demonstrated dynamic strain in Ref. measurements[55], relying on over the anuse 85 of m a longspecially fiber synthesized at a spatial resolution probe wave, of 1.5whose m.The frequency dynamic is strainrapidly detected changed inby two use positions, of an arbitrary vibrating waveform at 180 generator Hz and 320 (AWG) Hz, respectively,in order to lie and along with the a slope static of BFS the di BGSffering in each by 120fiber MHz position (thus well (see above Figure the 8). constraint Exploiting imposed this method, by the conventional the authors SA-BOTDAhave performed method), dynamic are shown strain inmeasurements Figure9 (data wereover 1-kHzan 85 m lowpass long fiber filtered at a forspatial SNR resolution enhancement). of 1.5 m. The dynamic strain detected in two positions, vibrating at 180 Hz and 320 Hz, respectively, and with a static BFS differing by 120 MHz (thus well above the constraint imposed by the conventional SA-BOTDA method), are shown in Figure 9 (data were 1-kHz lowpass filtered for SNR enhancement).

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FigureFigure 8.8. FastFast changingchanging thethe probeprobe frequencyfrequency allowsallows thethe latterlatter toto lielie withinwithin thethe slopeslope ofof eacheach locallocal BGS,BGS, eveneven inin casecase ofof spatialspatial nonuniformitiesnonuniformities [ [55].55].

FigureFigure 9.9. ((Top)) BrillouinBrillouin gaingain variationsvariations acquiredacquired along along an an 85-m85-m longlong ﬁberfiber withwith twotwo sectionssections subjectedsubjected toto dynamicdynamic strain. strain. ((BottomBottom)) CorrespondingCorresponding BFSBFS changeschanges inin thethe two two positions positions [ [55].55].

AsAs regardsregards thethe dynamicdynamic rangerange issue,issue, aa simplesimple solutionsolution stemsstems fromfromthe the useuse ofof pumppump pulsespulses shortershorter thanthan the the phonon phonon lifetime lifetime (~10 (~10 ns). ns). In In fact, fact, this this leads leads to a to broadening a broadening of the of BGS the linewidth BGS linewidth (which (which scales withscales the with inverse the inverse of the of pulse the pulse duration), duration), which wh enlargesich enlarges thedynamic the dynamic range range while while also also helping helping in equalizingin equalizing the the dynamic dynamic sensitivity sensitivity along along the the fiber fiber [56 [56].]. This This also also has has a a positive positive e effectffect on on the thespatial spatial resolution.resolution. OnOn thethe otherother hand,hand, shorteningshortening thethe pulsepulse widthwidth reducesreduces thethe backscatteredbackscattered signalsignal amplitudeamplitude andand reducesreduces thethe BGSBGS slopeslope asas well.well. TheseThese twotwo factorsfactors togethertogether maymay eventuallyeventually compromisecompromise thethe measurementmeasurement SNR.SNR. MoreMore sophisticatedsophisticated solutionssolutions havehave beenbeen demonstrated,demonstrated, inin whichwhich thethe pumppump pulsepulse spectrumspectrum is is properly properly engineered engineered for for dynamic dynamic range ra extensionnge extension under under the same the spatialsame spatial resolution resolution [57,58]. [57,58].Finally, as regards the sensitivity to pump power fluctuations, measurement configurations independentFinally, ofas the regards pump the power sensitivity have been to demonstratedpump power asfluctuations, well. In Ref. measurement [47], a configuration configurations capable ofindependent extracting the of the dynamic pump strain power from have the been BPS, demonstrat rather thaned the as well. BGS, In was Ref. demonstrated. [47], a configuration The conceptual capable schemeof extracting is shown the in dynamic Figure 10 .strain from the BPS, rather than the BGS, was demonstrated. The conceptual scheme is shown in Figure 10.

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Figure 10. SBS interaction between a pulsed pump and a phase-modulated probe wave for dynamic Figure 10. SBS interaction between a pulsed pump and a phase-modulated probe wave for dynamic strain measurements [47]. strain measurements [[47].47]. The method makes use of a phase-modulated probe field, whose modulation frequency is much The method makes use of a phase-modulated prob probee field, field, whose modulation frequency is much higher than the BGS bandwidth. In this way, only one modulation sideband falls within the BGS (and higher than than the the BGS BGS bandwidth. bandwidth. In Inthis this way, way, only only one one modulation modulation sideband sideband falls fallswithin within the BGS the (and BGS BPS) generated by the pump. The gain and phase-shift induced by SBS on this sideband modulates (andBPS) BPS)generated generated by the by pump. the pump. The The gain gain and and phasephase-shiftshift induced induced by by SBS SBS on on this this sideband sideband modulates modulates the heterodyne signal produced on a photodetector placed at the fiber output, from which the phase the heterodyne signal produced on a photodetector placed at the fiber fiber output, from which the phase modulation induced by SBS is easily extracted. The use of the BPS, rather than its amplitude modulation inducedinduced by by SBS SBS is easily is easily extracted. extracted. The use The of theuse BPS, of the rather BPS, than rather its amplitude than its counterpart, amplitude counterpart, provides a measurement of the BFS shift (i.e., strain) not affected by pump power providescounterpart, a measurement provides a ofmeasurement the BFS shift of (i.e., the strain) BFS shift not a(i.e.,ffected strain) by pump not affected power variations. by pump The power use variations. The use of the BPS for Brillouin measurements is also beneficial for long-range variations.of the BPS forThe Brillouin use of measurementsthe BPS for isBrillouin also beneficial measurements for long-range is also measurements, beneficial for as long-range it provides measurements, as it provides BFS measurements immune to the nonlocal effects deriving from the measurements,BFS measurements as it immune provides to theBFS nonlocal measurements effects deriving immune from to the the nonlocal frequency-dependent effects deriving depletion from the of frequency-dependent depletion of the pump pulse [59]. The strain acquired at a sampling rate of 1.66 frequency-dependentthe pump pulse [59]. The depletion strain acquiredof the pump at a pulse sampling [59]. rate The of strain 1.66 kHzacquired along at a a piece sampling of fiber rate attached of 1.66 kHz along a piece of fiber attached to a 1-m long cantilever beam subject to vibrations is shown in kHzto a 1-malong long a piece cantilever of fiber beam attached subject to toa 1-m vibrations long cantilever is shown beam in Figure subject 11 (the to vibrations total fiber is length shown was in Figure 11 (the total fiber length was 160 m in this experiment). 160Figure m in11 this (the experiment). total fiber length was 160 m in this experiment).

(a) (b) (a) (b) Figure 11. Experimental demonstration of dynamic strain measurement (b) over a 1-m cantilever Figure 11.11. ExperimentalExperimental demonstrationdemonstration of of dynamic dynamic strain strain measurement measurement (b) over(b) over a 1-m a cantilever1-m cantilever beam beam subjected to vibration (a), carried out using the setup of Figure 10 [47]. beamsubjected subjected to vibration to vibration (a), carried (a), carried out using out theusing setup the ofsetup Figure of Figure 10[47]. 10 [47].

A somewhat similar approach has been reported in Ref. [[60],60], where the phase of the probe beam A somewhat similar approach has been reported in Ref. [60], where the phase of the probe beam was modulated at a much lower frequency. In this case, both carrier and ﬁrst-orderfirst-order sidebands fall was modulated at a much lower frequency. In this case, both carrier and first-order sidebands fall within the BGS and and then then interact interact with with the the pump pump lig lightht (see (see Figure Figure 12). 12 ).Tuning Tuning the the carrier carrier frequency frequency at within the BGS and then interact with the pump light (see Figure 12). Tuning the carrier frequency at atthe the BGS BGS resonance resonance and and setting setting a amodulation modulation freque frequencyncy equal equal to to half half the the BGS BGS linewidth, the two the BGS resonance and setting a modulation frequency equal to half the BGS linewidth, the two sidebands experience the same gaingain butbut oppositeopposite phase-shift.phase-shift. Thus, a partialpartial phase-to-amplitudephase-to-amplitude sidebands experience the same gain but opposite phase-shift. Thus, a partial phase-to-amplitude conversion appears on the emerging probe intensity. In other words, the probe intensity contains a conversion appears on the emerging probe intensity. In other words, the probe intensity contains a self-heterodyne beat note at the same frequencyfrequency ofof thethe phasephase modulation.modulation. self-heterodyne beat note at the same frequency of the phase modulation.

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SensorsSensors 20202020, ,2020, ,x 5629 FOR PEER REVIEW 1111 of of 23 23

Figure 12. Schematic representation of the interactions involved in the heterodyne slope-assisted

method [60]. The BGS and BPS affect both the carrier and the two first-order sidebands of the phase- Figure 12. Schematic representation of the interactions involved in the heterodyne slope-assisted modulatedFigure 12. probe,Schematic leading representation to the appearance of the ofinteractions an RF beat involvednote on the in transmittedthe heterodyne probe slope-assisted intensity. methodmethod [60]. [60]. The The BGS BGS and and BPS BPSaffect aﬀ bothect boththe carri theer carrier and the and two the first-order two ﬁrst-order sidebands sidebands of the phase- of the phase-modulated probe, leading to the appearance of an RF beat note on the transmitted probe intensity. Whenmodulated an external probe, leading perturbation to the appearance (strain) modulaof an RFtes beat the note BFS, on thethe transmitted amplitude probe of this intensity. tone grows linearlyWhen with anthe external applied perturbationstrain. More importantly, (strain) modulates the ratio the between BFS, the the amplitude amplitude of ofthis this tonebeat growsnote, When an external perturbation (strain) modulates the BFS, the amplitude of this tone grows andlinearly the DC with component the applied of the strain. transmitted More importantly, probe wave the is ratio independent between of the the amplitude pump power. of this We beat show note, linearly with the applied strain. More importantly, the ratio between the amplitude of this beat note, inand Figure the DC13a componentthe ac-to-dc of ratio, thetransmitted calculated as probe a function wave isof independent the frequency of detuning the pump from power. resonance, We show and the DC component of the transmitted probe wave is independent of the pump power. We show andin Figurefor a pump 13a the pulse ac-to-dc duration ratio, of calculated10 ns. The plot as a functionreveals that of thetuning frequency the carrier detuning frequency from about resonance, half in Figure 13a the ac-to-dc ratio, calculated as a function of the frequency detuning from resonance, a andBGS for bandwidth a pump pulse away duration from ofthe 10 ns.resonance, The plot revealsa linear that slope tuning is theavailable carrier frequencyfor dynamic about strain half a and for a pump pulse duration of 10 ns. The plot reveals that tuning the carrier frequency about half measurements.BGS bandwidth away from the resonance, a linear slope is available for dynamic strain measurements. a BGS bandwidth away from the resonance, a linear slope is available for dynamic strain measurements.

(a) (b)

FigureFigure 13. 13. (a()a Amplitude) Amplitude(a) of of the the heterodyne heterodyne signal signal normaliz normalizeded to to its its dc dc value, value,(b computed) computed for for a apulse pulse durationduration of of 10 10 ns, ns, as as a function ofof detuningdetuningfrom from resonance resonance (b ()b Dynamic) Dynamic strain strain measured measured on on a 1-m a 1-m long Figure 13. (a) Amplitude of the heterodyne signal normalized to its dc value, computed for a pulse longcantilever cantilever beam beam subjected subjected to vibration. to vibration. (The (The inset inset shows shows the the FFT FFT of theof the acquired acquired waveform waveform [60 [60]).]). duration of 10 ns, as a function of detuning from resonance (b) Dynamic strain measured on a 1-m FigurelongFigure cantilever 13b 13b shows shows beam thethe subjected heterodyne heterodyne to vibration. signal signal converted(The converted inset shows in in strain strain the FFTunits, units, of acquiredthe acquired acquired by by waveform attaching attaching [60]). the the fiber ﬁber onon a acantilever cantilever beam beam vibrating vibrating at at the the frequency frequency of of 1.8 1.8 Hz, Hz, and and with with an an acquisition acquisition rate rate of of 13 13 Hz. Hz. ComparedComparedFigure to 13b to the the shows conventional conventional the heterodyne SA-BOTDA SA-BOTDA signal method, method,converted the the in heterodyne heterodynestrain units, SA-BOTDA SA-BOTDAacquired by method methodattaching provides provides the fiber a a betteronbetter a cantileverSNR SNR thanks thanks beam to to the vibrating the fact fact that that at the the signal signalfrequency is is sh shiftedifted of 1.8 to to Hz,a ahigher higher and withfrequency frequency an acquisition (therefore (therefore rate reducing reducing of 13 theHz. the influenceComparedinﬂuence of of tothe the the low low conventional frequency frequency laser SA-BOTDA laser noise). noise). Furtherm method, Furthermore, ore,the comparedheterodyne compared to toSA-BOTDA Ref. Ref. [47] [47 ]the the method technique technique provides has has the the a advantagebetteradvantage SNR of thanks of not not requiring requiringto the fact the thethat use use the of of signala ahigh-bandwidth high-bandwidth is shifted to a(~ (~higher GHz) GHz) frequencydetector detector for for(therefore the the extraction extraction reducing of of thethe the phaseinfluencephase shift. shift. of the low frequency laser noise). Furthermore, compared to Ref. [47] the technique has the advantageInIn Ref. Ref. of[61] [ 61not ]a arequiringdual dual SA SA method methodthe use hasof has a been beenhigh-bandwidth demonstrated demonstrated (~ for forGHz) pump pump detector power power for independent independent the extraction dynamic dynamic of the strainphasestrain measurements.shift. measurements. In In this this me method,thod, the carrier frequencyfrequency ofof the the probe probe wave wave is is switched switched between between the thetwo twoIn slopes slopesRef. of[61] of the thea BGS,dual BGS, whileSA while method the the useful usefulhas signalbeen signal demonstrated is is calculated calculated asfor as the pumpthe ratio ratio power of of the the measurementsindependent measurements dynamic taken taken on strain measurements. In this method, the carrier frequency of the probe wave is switched between the two slopes of the BGS, while the useful signal is calculated as the ratio of the measurements taken

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Sensorson the 2020 two, 20 slopes, x FOR PEER(see FigureREVIEW 14). Ideally, when no perturbation is applied to the fiber, this 12ratio of 23 is Sensors 2020, 20, 5629 12 of 23 unitary: when a strain is applied, the signals from the two slopes change in opposite way, thus their onratio the changes two slopes as well. (see Instead, Figure 14). when Ideally, the pump when powe no perturbationr changes, both is applied signals scaleto the by fiber, the samethis ratio factor, is unitary:thetherefore two slopeswhen their a (see ratiostrain Figure remains is applied, 14). Ideally,unchanged. the signals when noAlthou from perturbation thegh twothe slopesdual is applied SA change method to thein opposite ﬁber,provides this way, ratio pump thus is unitary: power their ratiowhenindependence, changes a strain isas applied, itwell. does Instead, not the signalsimpact when fromthe the dynamic thepump two powe slopes range,r changes, change which in bothis opposite still signals limited way, scale thusto bya theirfew the ratiohundredsame changes factor, µε. thereforeasFurthermore, well. Instead, their the ratio when necessity remains the pump to unchanged.switch power from changes, Althouone sl bothopegh tothe signals the dual other scale SA reduces bymethod the samethe provides maximum factor, thereforepump acquisition power their independence,ratiorate by remains half. unchanged. it does not Although impact the the dynamic dual SA methodrange, which provides is still pump limited power to independence, a few hundred it does µε. Furthermore,not impact the the dynamic necessity range, to switch which isfrom still one limited slope to ato few the hundredother reducesµε. Furthermore, the maximum the necessityacquisition to rateswitch by fromhalf. one slope to the other reduces the maximum acquisition rate by half.

Figure 14. In the dual slope-assisted BOTDA method, the probe frequency is switched between the

two slopes, while the dynamic strain is extracted from the ratio between the signals acquired from the Figure 14. In the dual slope-assisted BOTDA method, the probe frequency is switched between the Figuretwo slopes 14. In [61]. the dual slope-assisted BOTDA method, the probe frequency is switched between the twotwo slopes, slopes, while while the the dynamic dynamic strain strain is is extracted extracted from from the the ratio ratio betw betweeneen the the signals signals acquired acquired from from the the twotwoAn slopes slopesextension [61]. [61]. of this technique has been demonstrated by Dexin et al. [62], in which the probe frequency is stepped consecutively by a quantity equal to the BGS linewidth (see Figure 15). This An extension of this technique has been demonstrated by Dexin et al. [62], in which the probe methodAn extensionextends the of dynamicthis technique range, has as the been BFS demonstrated is no more bounded by Dexin to etlie al. within [62], thein which slope ofthe a probesingle frequency is stepped consecutively by a quantity equal to the BGS linewidth (see Figure 15). This method frequencyBGS. As withis stepped the dual consecutively slope method, by a thequantity drawba equalck of to the the multipleBGS linewidth slope BOTDA(see Figure method 15). This is a extends the dynamic range, as the BFS is no more bounded to lie within the slope of a single BGS. methodreduction extends of the the maximum dynamic acquisition range, as the rate BFS by is a nofactor more equal bounded to the to number lie within of slopesthe slope employed of a single for As with the dual slope method, the drawback of the multiple slope BOTDA method is a reduction of BGS.the measurement. As with the dual slope method, the drawback of the multiple slope BOTDA method is a reductionthe maximum of the acquisition maximum rate acquisition by a factor rate equal by to a thefactor number equal of to slopes the number employed of slopes for the employed measurement. for the measurement.

FigureFigure 15.15. Extension of the measurement range byby multi-slope-assistedmulti-slope-assisted BOTDABOTDA [[62].62].

5.5. Frequency-SweepFigure 15. Extension Free Methods of the measurement range by multi-slope-assisted BOTDA [62]. The methods discussed in the previous paragraph remove the need to scan the pump–probe 5. Frequency-SweepThe methods discussed Free Methods in the previous paragraph remove the need to scan the pump–probe frequencyfrequency shift,shift, by by probing probing the the Brillouin Brillouin gain gain/phase/phase at only at oneonly (or one a few (orones) a few frequencies. ones) frequencies. A different A approachdifferentThe methodsapproach relies on thediscussed relies use on of athein multi-tone the use previous of a pumpmulti-ton paragr (ande aph/pumpor probe) remove (and/or wave, the probe) inneed such towa ascanve, way in the that such pump–probe the a Brillouinway that frequencygainthe Brillouin is recovered shift, gain by atis recovered diprobingfferent the frequencies at differentBrillouin simultaneously.frequencies gain/phase simultaneously. at only The firstone demonstration(or The a few first ones)demonstration of frequencies. this technique, of this A differentreferredtechnique, toapproach asreferred frequency-sweep relies to as frequency-sweepon the freeuse method,of a multi-ton free has meth beene od,pump reported has (and/or been by reported Voskoboinikprobe) waby ve,Voskoboinik et in al. such [63 ].a Theetway al. basic that[63]. theconceptThe Brillouin basic is concept illustrated gain is is recovered illustrated in Figure at 16differentin .Figure Instead frequencies 16. of In usingstead simultaneously. aof single-frequency using a single-frequency The pulsed first demonstration pump, pulsed the pump, method of this the technique,reliesmethod on relies the referred use on of the ato discrete asus efrequency-sweep of numbera discreteN numberof pumpfree meth N pulses, ofod, pump has equally been pulses, spaced reported equally in theby spaced Voskoboinik frequency in the domain etfrequency al. [63]. by a Thequantitydomain basic by significantly concept a quantity is illustrated larger significantly than in the Figure larger BGS linewidth 16.than In steadthe (100BGS of MHz, usinglinewidth typically).a single-frequency (100 MHz, Each pumptypically). pulsed tone Each generatespump, pump the a methodspectrallytone generates relies shifted on a spectrally BGS.the us Ae numberof shifted a discreteN BGS.of probenumber A number tones N ofN are ofpump simultaneously probe pulses, tones areequally launched simultaneously spaced into in the the launched sensing frequency fiber into domainfrom the by opposite a quantity side. significantly These tones larger are downshifted than the BGS from linewidth the pump (100 tones MHz, by approximatelytypically). Each the pump BFS tone generates a spectrally shifted BGS. A number N of probe tones are simultaneously launched into

Sensors 2020, 20, x FOR PEER REVIEW 13 of 23 Sensors 2020, 20, x FOR PEER REVIEW 13 of 23 Sensorsthe sensing2020, 20, 5629fiber from the opposite side. These tones are downshifted from the pump tones13 of 23by the sensing fiber from the opposite side. These tones are downshifted from the pump tones by approximately the BFS but are spectrally shifted by a slightly larger quantity. As each probe tone lies approximately the BFS but are spectrally shifted by a slightly larger quantity. As each probe tone lies in a different position of its corresponding BGS, the acquisition and spectral analysis of the probe inbut a different are spectrally position shifted of its by corresponding a slightly larger BGS, quantity. the acquisition As each probe and tone spectral liesin analysis a diﬀerent of the position probe of signal intensity at the exit of the FUT permits recovery of the BGS in multiple frequencies signalits corresponding intensity at BGS,the theexit acquisition of the FUT and permits spectral recovery analysis ofof the the probe BGS signal in multiple intensity frequencies at the exit of simultaneously. simultaneously.the FUT permits recovery of the BGS in multiple frequencies simultaneously.

Figure 16. SBS interaction between a multi-tone pump wave and a multi-tone probe wave as done in FigureFigure 16. 16. SBSSBS interaction interaction between between a amulti-tone multi-tone pump pump wave wave and and a amulti-tone multi-tone probe probe wave wave as as done done in in the frequency-sweep free method [63]. thethe frequency-sweep frequency-sweep free free method method [63]. [63]. The experimental setup used in Ref. [63] is reported in Figure 17. The configuration is very TheThe experimental experimental setup usedused inin Ref. Ref. [63 [63]] is reportedis reported in Figurein Figure 17. The17. conﬁgurationThe configuration is very is similarvery similar to the conventional BOTDA scheme, with the only exception that both pump and probe beams similarto the to conventional the conventional BOTDA BOTDA scheme, scheme, with with the only the only exception exception that that both both pump pump and and probe probe beams beams are are now intensity-modulated to realize the multi-tone scheme. arenow now intensity-modulated intensity-modulated to to realize realize the the multi-tone multi-tone scheme. scheme.

FigureFigure 17. 17.Experimental Experimental setup setup employed employed for for sweep-free sweep-free BOTDA BOTDA measurements measurements [63 [63].]. Figure 17. Experimental setup employed for sweep-free BOTDA measurements [63]. Figure 18 shows the BGS profiles acquired along a 2-km FUT, composed by two fiber spools Figure 18 shows the BGS profiles acquired along a 2-km FUT, composed by two fiber spools splicedFigure at 1000-m.18 shows The the figure BGS compares profiles acquired the result alon of theg a sweep-free 2-km FUT, method composed (Figure by 18twoa), fiber implemented spools spliced at 1000-m. The figure compares the result of the sweep-free method (Figure 18a), splicedwith a 30-tonesat 1000-m. frequency The figure comb compares and a frequency the result shift betweenof the sweep-free each pump–probe method pair (Figure differing 18a), by implemented with a 30-tones frequency comb and a frequency shift between each pump–probe pair implemented3 MHz from with thenext a 30-tones one, with frequency the result comb of and the conventionala frequency shift BOTDA between (Figure each 18 pump–probeb) using the pair same differing by 3 MHz from the next one, with the result of the conventional BOTDA (Figure 18b) using differinggranularity by 3 (3MHz MHz). from The the results next one, are with perfectly the re consistent,sult of the whichconventional means thatBOTDA the sweep-free(Figure 18b) method, using the same granularity (3 MHz). The results are perfectly consistent, which means that the sweep-free thein same which granularity a certain number (3 MHz). of The pump–probe results are pairs perfectly is let consistent, to interact duringwhich means each step, that providesthe sweep-free similar method, in which a certain number of pump–probe pairs is let to interact during each step, provides method,performance in which as the a certain conventional number BOTDA, of pump–probe where a single pairs probeis let /toprobe interact pair during interacts each at each step, step, provides with a similar performance as the conventional BOTDA, where a single probe/probe pair interacts at each similarspeed-up performance factor equal as tothe the conventional number of pump–probe BOTDA, wh pairsere a (30,single in thisprobe/probe case), because pair interacts each pair at replaces each step, with a speed-up factor equal to the number of pump–probe pairs (30, in this case), because each step,one with sweeping a speed-up step required factor equal in the to classical the number BOTDA. of pump–probe pairs (30, in this case), because each pair replaces one sweeping step required in the classical BOTDA. pair replaces one sweeping step required in the classical BOTDA.

Sensors 2020, 20, 5629 14 of 23 Sensors 2020, 20, x FOR PEER REVIEW 14 of 23

FigureFigure 18.18. MeasurementMeasurement of of the the BGS BGS along along a 2-km a 2-km FUT FUT using using (a) the (a) frequency-sweep the frequency-sweep method, method, with with30 frequency 30 frequency tones tones spanning spanning 90 MH 90 MHz,z, reconstructed reconstructed at ata aspatial spatial resolution resolution of of 50 50 m; m; or (b) UsingUsing aa classicalclassical BOTDABOTDA withwith 3MHz3MHz sweeping sweeping step step [ 63[63].].

InIn practicalpractical applications,applications, thethe mainmain drawbacksdrawbacks ofof thethe sweep-freesweep-free methodmethod areare aa higherhigher complexitycomplexity ofof thethe measurementmeasurement setup,setup, duedue toto thethe necessitynecessity toto modulatemodulate bothboth pumppump andand probeprobe beamsbeams withwith multifrequencymultifrequency waveforms,waveforms, butbut especiallyespecially thethe factfact thatthat itit addsadds aa trade-otrade-offff between between thethe granularitygranularity inin thethe BGSBGS reconstruction reconstruction and and the the spatial spatial resolution. resolution. In In fact, fact, the the method method requires requires that that the the probe probe signal signal is analyzedis analyzed over over time time windows windows at at least least equal equal to to the th inversee inverse of of the the BGS BGS sampling sampling step: step: this this limitslimits thethe spatialspatial resolution resolution to to a a few few tens tens of of meters meters for for adequate adequate BGS BGS granularity, granularity, independently independently of theof the duration duration of theof the pump pump pulses. pulses. Please Please note note that athat similar a similar limitation limitation afflicts afflicts the techniques the techniques described described in Refs. in [64 Refs.,65], where[64,65], a where single-tone a single-tone pump pulse pump and pulse a multi-tone and a mult probei-tone are probe employed. are employed. For example, For example, in Ref. in [65 Ref.] a frequency[65] a frequency comb composedcomb composed by about by 1000about tones 1000 separated tones separated by 1.95 by MHz, 1.95 wasMHz, employed was employed as the probeas the beam.probe Duebeam. to Due interaction to interaction with a with counter-propagating, a counter-propag single-toneating, single-tone pump pulse,pump eachpulse, tone each in tone the probein the waveprobe experiences wave experiences a different a different Brillouin Brillouin gain, thus gain, the thus frequency the frequency comb is reshapedcomb is reshaped at the exit at of the the exit fiber. of Analyzingthe fiber. Analyzing the transmitted the transmitted probe over successiveprobe over time successive slots, the time BGS slots, related the to BGS each related corresponding to each fibercorresponding portion can fiber be reconstructed. portion can be As reconstructed. the duration of As each the time duration slot is of inversely each time proportional slot is inversely to the BGSproportional frequency to granularity, the BGS frequency a typical granularity, spatial resolution a typical of spatial tens of resolution meters results of tens for of adequately meters results fine spectralfor adequately resolution. fine spectral As an example, resolution. in Ref.As an [65 example,] the actual in Ref. spatial [65] resolutionthe actual spatial was limited resolution to about was 50limited m due to to about the duration 50 m due (500 to ns)the ofduration the time (500 slots ns) employed of the time for demodulatingslots employed the for received demodulating frequency the combs.received In frequency Ref. [66], the combs. same In authors Ref. [66], have the proposed same authors a variant have of thisproposed method, a variant in which of thethis transmitted method, in multi-tonewhich the probetransmitted wave ismulti-tone coherently probe received, wave i.e.,is coherently it is mixed received, with a local i.e., oscillator.it is mixed Compared with a local to theoscillator. method Compared presented into Ref.the [65method] based presented on direct detection,in Ref. [65] the based use of on coherent direct detectiondetection, permits the use the of retrievalcoherent of detection the BPS, permits which has the aretrieval linear shape of the near BPS, the which BFS has (see a Figure linear5 shapeb). Furthermore, near the BFS the (see boost Figure in the5b). detected Furthermore, signal the provided boost in by the coherent detected detection signal provided allowed theby coherent authors todetection perform allowed the measurements the authors withoutto perform averaging, the measurements therefore reachingwithout averaging, an ultimate ther acquisitionefore reaching rate onlyan ultimate limited acquisition by the fiber rate length only (e.g.,limited 10 kHzby the for fiber a 10-km length long (e.g., fiber 10 kHz spool). for Stilla 10-km the main long drawbackfiber spool). is Still the limitedthe main spatial drawback resolution is the (aboutlimited 50 spatial m also resolution in this case). (about 50 m also in this case).

6. Fast Frequency Sweeping Methods 6. Fast Frequency Sweeping Methods Fast frequency sweeping methods provide better acquisition rates compared to the conventional Fast frequency sweeping methods provide better acquisition rates compared to the conventional BOTDA method, as they compress (or eliminate) the settling time required to switch the probe frequency BOTDA method, as they compress (or eliminate) the settling time required to switch the probe during the measurement. In fact, as discussed in Section2, the measurement process in the BOTDA frequency during the measurement. In fact, as discussed in Section 2, the measurement process in the method requires the Brillouin gain profile to be acquired for each preset pump/probe frequency shift. BOTDA method requires the Brillouin gain profile to be acquired for each preset pump/probe Thefrequency time required shift. toThe switch time the required probe frequency to switch between the probe two consecutive frequency measurements between two may consecutive be in the ordermeasurements of milliseconds, may be and in the must order be counted of milliseconds, as many and times must as the be numbercounted ofas scannedmany times probe as frequencies.the number Thus,of scanned it can significantlyprobe frequencies. deteriorate Thus, the it can maximum significantly acquisition deteriorate rate. Thethe maximum first demonstration acquisition of rate. this The first demonstration of this method is by Peled et al. [67]. The authors employed an AWG to fast switch the probe frequency among 100 scanning frequencies. The experimental setup is shown in

Sensors 2020, 20, 5629 15 of 23 methodSensors 2020 is by, 20, Peledx FOR PEER et al. REVIEW [67]. The authors employed an AWG to fast switch the probe frequency15 of 23 among 100 scanning frequencies. The experimental setup is shown in Figure 19a. Compared to Figure 19a. Compared to the conventional BOTDA method, the probe frequency is fast swept through the conventional BOTDA method, the probe frequency is fast swept through a vector-modulated a vector-modulated microwave source, with the in-phase and quadrature modulation signals microwave source, with the in-phase and quadrature modulation signals provided by a two-channel provided by a two-channel AWG pre-loaded with the frequencies chosen to obtain the BGS. An AWG pre-loaded with the frequencies chosen to obtain the BGS. An acquisition rate of 10 kHz was acquisition rate of 10 kHz was demonstrated over a fiber length of 100 m and at a spatial resolution demonstrated over a ﬁber length of 100 m and at a spatial resolution of 1 m (see Figure 19b). of 1 m (see Figure 19b).

(a) (b)

FigureFigure 19. 19.( a(a)) Experimental Experimental setup setup for for fast fast frequency frequency sweeping sweeping BOTDA; BOTDA; ( b(b)) BGS BGS acquired acquired in in one one ﬁxed fixed andand two two vibrating vibrating locations locations of of the the FUT FUT [67 [67].].

AlthoughAlthough e ffeffectiveective in in cutting cutting down down the the acquisition acquisition time, time, this this method method has has the the disadvantage disadvantage of of requiringrequiring a a fast fast AWG AWG to to scan scan thethe probeprobe frequency.frequency. TheThe AWGAWG hashas less stringent requirements requirements when when a asecond-order second-order modulation modulation scheme scheme isis adopted adopted for for th thee frequency-shifting frequency-shifting device, device, i.e., i.e., by bybiasing biasing the theEOM EOM at maximum at maximum transmission transmission and and carefully carefully choosing choosing the theRF RFamplitude amplitude [68]. [68 An]. alternative An alternative (and (andcost-effective) cost-effective) approach approach consists consists of ofsweeping sweeping the the probe probe frequency frequency in in a a linear, linear, rather thanthan step-like,step-like, fashionfashion [ 69[69],], through through the the use use of of a a frequency-agile frequency-agile RF RF generator. generator. In In this this case, case, the the probe probe frequency frequency is is linearlylinearly swept, swept, so so that that at at the the end end of of the the linear linear sweep sweep the the whole whole BGS BGS is is obtained. obtained. The The scan scan rate rate is is so so slowslow that that the the pump pump pulse pulse “sees” “sees” an an almost almost constant constant probe probe frequency frequency during during its its propagation, propagation, so so that that thethe emerging emerging probe probe intensity intensity can can be uniquely be uniquely associated associated with awith single a pointsingle in point BGS frequencyin BGS frequency domain. Compareddomain. Compared to the original to the fast original frequency-sweep fast frequency-sweep method proposed method in proposed Ref. [67], in this Ref. method [67], this is simpler method asisit simpler requires as a it frequency-agile requires a frequency-agile microwave source,microwave instead source, of an instead AWG and of an a microwaveAWG and a source microwave with vectorsource modulation with vector capabilities. modulation Figure capabilities. 20 compares Figure the20 compares frequency the sweep frequency applied sweep to the applied probe in to the the fastprobe BOTDA in the method fast BOTDA proposed method in Ref. proposed [67], with in Ref. one [67], employed with one in Ref. employed [69]. in Ref. [69]. Figure 21a reports the BGS distribution acquired using a linearly swept probe frequency, with a sweep time of 33 ms, a fiber length of 100 m and a spatial resolution of 1 m. In Figure 21b, the quality of the BFS reconstruction is validated against the BFS profile acquired using the conventional BOTDA, with the significant difference that the latter is acquired in a time of about 0.5 s (more than ten times longer), mainly due to the settling time of the microwave source. Fast BOTDA methods can be also combined with the differential pulse-pair method originally proposed in Ref. [29], to enhance the spatial resolution down to the cm-range. In brief, the differential pulse-pair method involves the measurement of the Brillouin gain for two closely spaced pump pulse durations. By subtracting the corresponding Brillouin gain signals, the BGS can be reconstructed at a

spatial resolution determinedprobe frequency by the difference between the durations of the two pulses. Furthermore, the BGS keeps its narrow bandwidth dictated by the acoustic loss (~30 MHz), i.e., it gets rid of the inverse dependence of its bandwidth from the pulse duration as in conventional BOTDA sensors. Although the application of the differential pulse-pair method does not help when trying to reach the maximum acquisition speed (due to the requirement of two consecutive measurements for each pump/probe frequency shift), it is of great benefit when a submeter spatial resolution is required. In Ref. [68], a spatial resolution of 20 cm was achieved thanks to the use of a 52/50 ns pulse pair. Figure 20. Probe frequency sweep used for stepped sweep [67] and linear sweep [69] BOTDA measurements. 𝑇 represents the time slot allocated for the acquisition of each Brillouin gain profile (in the ideal case, e.g., no averaging, 𝑇 corresponds to the roundtrip time of the pump pulse over the fiber length).

Sensors 2020, 20, x FOR PEER REVIEW 15 of 23

Figure 19a. Compared to the conventional BOTDA method, the probe frequency is fast swept through a vector-modulated microwave source, with the in-phase and quadrature modulation signals provided by a two-channel AWG pre-loaded with the frequencies chosen to obtain the BGS. An acquisition rate of 10 kHz was demonstrated over a fiber length of 100 m and at a spatial resolution of 1 m (see Figure 19b).

(a) (b)

Figure 19. (a) Experimental setup for fast frequency sweeping BOTDA; (b) BGS acquired in one fixed and two vibrating locations of the FUT [67].

Although effective in cutting down the acquisition time, this method has the disadvantage of requiring a fast AWG to scan the probe frequency. The AWG has less stringent requirements when a second-order modulation scheme is adopted for the frequency-shifting device, i.e., by biasing the EOM at maximum transmission and carefully choosing the RF amplitude [68]. An alternative (and cost-effective) approach consists of sweeping the probe frequency in a linear, rather than step-like, fashion [69], through the use of a frequency-agile RF generator. In this case, the probe frequency is Sensors 2020, 20, 5629 16 of 23 linearly swept, so that at the end of the linear sweep the whole BGS is obtained. The scan rate is so slow that the pump pulse “sees” an almost constant probe frequency during its propagation, so that Furthermore,the emerging the acquisitionprobe intensity rate overcan be a fiber uniquely length as ofsociated 50 m was with as a high single as 14point kHz, in owingBGS frequency to the use of domain. Compared to the original fast frequency-sweep method proposed in Ref. [67], this method a frequency-agile probe wave and a limited (N = 51) number of frequency steps. We show in Figure 22 is simpler as it requires a frequency-agile microwave source, instead of an AWG and a microwave the Brillouin gain spectra acquired over an 80-cm vibrating fiber with only 5 averages. Despite the Sensorssource 2020 with, 20, xvector FOR PEER modulation REVIEW capabilities. Figure 20 compares the frequency sweep applied16 toof the23 low numberprobe in ofthe averages, fast BOTDA we method can appreciate proposed the in veryRef. [67], good with SNR one of employed these measurements, in Ref. [69]. probably also thanks toFigure the use 21a of reports a PM the fiber. BGS distribution acquired using a linearly swept probe frequency, with a sweep time of 33 ms, a fiber length of 100 m and a spatial resolution of 1 m. In Figure 21b, the quality of the BFS reconstruction is validated against the BFS profile acquired using the conventional BOTDA, with the significant difference that the latter is acquired in a time of about 0.5 s (more than ten times longer), mainly due to the settling time of the microwave source. probe frequency

Sensors 2020, 20, x FOR PEER REVIEW 16 of 23

FigureFigureFigure 20. 20.21aProbe Probe reports frequency frequency the BGS sweep sweep distribution usedused forfor acquired steppedstepped using sweep sweep a linearly[67] [67 ]and and sweptlinear linear probesweep sweep frequency,[69] [69 BOTDA] BOTDA with a sweepmeasurements. time of 33 ms, 𝑇 representsa fiber length the timeof 100 slot m allocated and a spatial for the resolution acquisition of of 1 each m. In Brillouin Figure gain21b, profilethe quality measurements. T represents the time slot allocated for the acquisition of each Brillouin gain proﬁle (inof the (in ideal BFSthe ideal case,reconstruction case, e.g., e.g., no no averaging, averaging,is validatedT 𝑇corresponds corresponds against the to to the theBFS roundtriproundtrip profile timeacquired time of of the the usingpump pump pulsethe pulse conventionalover over the the BOTDA,Figurefiber length).with 21. (a) the BGS significant acquired bydifference using a linearly that the swept latte probr is acquirede frequency, in ina timea sweep of about time of 0.5 33 sms; (more (b) than ﬁber length). ten Comparisontimes longer), of themainly BFS profile due to acquired the settling using time either of the the FAST microwave BOTDA source.method with a linearly swept frequency, or the conventional BOTDA method.

Fast BOTDA methods can be also combined with the differential pulse-pair method originally proposed in Ref. [29], to enhance the spatial resolution down to the cm-range. In brief, the differential pulse-pair method involves the measurement of the Brillouin gain for two closely spaced pump pulse durations. By subtracting the corresponding Brillouin gain signals, the BGS can be reconstructed at a spatial resolution determined by the difference between the durations of the two pulses. Furthermore, the BGS keeps its narrow bandwidth dictated by the acoustic loss (~30 MHz), i.e., it gets rid of the inverse dependence of its bandwidth from the pulse duration as in conventional BOTDA sensors. Although the application of the differential pulse-pair method does not help when trying to reach the maximum acquisition speed (due to the requirement of two consecutive measurements for each pump/probe frequency shift), it is of great benefit when a submeter spatial resolution is required. In Ref. [68], a spatial resolution of 20 cm was achieved thanks to the use of a 52/50 ns pulse pair.

Furthermore, the acquisition rate over a fiber length of 50 m was as high as 14 kHz, owing to the use ofFigure a frequency-agileFigure 21. (a)21. (a)BGS BGS probe acquired acquired wave by by and using using a limited a linearly (N swept= swept51) number prob probee frequency, of frequency, frequency in a insweep steps. a sweep time We showof time 33 ms; ofin 33Figure(b)ms; 22(b the) Comparison ComparisonBrillouin gain of of the the spectra BFSBFS profileprofile acquired acquired over usingan 80-c eith eithermer vibrating the the FAST FAST fiberBOTDA BOTDA with method methodonly 5with averages. with a linearly a linearly Despite swept swept the lowfrequency, numberfrequency, or of the averages, or conventionalthe conventional we can BOTDA appreciate BOTDA method. method. the very good SNR of these measurements, probably also thanks to the use of a PM fiber. Fast BOTDA methods can be also combined with the differential pulse-pair method originally proposed in Ref. [29], to enhance the spatial resolution down to the cm-range. In brief, the differential pulse-pair method involves the measurement of the Brillouin gain for two closely spaced pump pulse durations. By subtracting the corresponding Brillouin gain signals, the BGS can be reconstructed at a spatial resolution determined by the difference between the durations of the two pulses. Furthermore, the BGS keeps its narrow bandwidth dictated by the acoustic loss (~30 MHz), i.e., it gets rid of the inverse dependence of its bandwidth from the pulse duration as in conventional BOTDA sensors. Although the application of the differential pulse-pair method does not help when trying to reach the maximum acquisition speed (due to the requirement of two consecutive measurements for each pump/probe frequency shift), it is of great benefit when a submeter spatial resolution is required. (a) (b) In Ref. [68], a spatial resolution of 20 cm was achieved thanks to the use of a 52/50 ns pulse pair. FigureFurthermore,Figure 22. 22.BGS BGSthe acquired acquisitionacquired using using rate thethe over fastfast a BOTDABOTDAfiber length method method of 50 combined combined m was aswith withhigh the as the differential 14 di kHz,fferential owing pulse-pair pulse-pair to the use techniqueof atechnique frequency-agile [68 [68].]. The The vibrating probe vibrating wave fiber fiber and was was a limited excitedexcited at(N a a= frequency frequency51) number of of ( aof ()a 33.3 )frequency 33.3 Hz Hz or or(b steps.) ( 50b) Hz. 50 We Hz. show in Figure 22 the Brillouin gain spectra acquired over an 80-cm vibrating fiber with only 5 averages. Despite the low number of averages, we can appreciate the very good SNR of these measurements, probably also thanks to the use of a PM fiber.

(a) (b)

Figure 22. BGS acquired using the fast BOTDA method combined with the differential pulse-pair technique [68]. The vibrating fiber was excited at a frequency of (a) 33.3 Hz or (b) 50 Hz.

Sensors 2020, 20, 5629 17 of 23 Sensors 2020, 20, x FOR PEER REVIEW 17 of 23 Sensors 2020, 20, x FOR PEER REVIEW 17 of 23 7. Single-Shot BOTDA 7. Single-Shot BOTDA 7. Single-Shot BOTDA Ultimate performance in terms of probe frequency-sweep rate have been demonstrated in 2018 Ultimate performance in terms of probe frequency-sweep rate have been demonstrated in 2018 by ZhouUltimate et al. performance [70]. In their in work, terms the of authorsprobe frequenc have performedy-sweep rate BGS have measurements been demonstrated using a rapidlyin 2018 by Zhou et al. [70]. In their work, the authors have performed BGS measurements using a rapidly frequency-modulatedby Zhou et al. [70]. In probetheir work, wave, the covering authors a have large performed frequency rangeBGS measur aroundements the Stokes using frequency a rapidly frequency-modulated probe wave, covering a large frequency range around the Stokes frequency withfrequency-modulated respect to the pump probe beam wave, (see covering Figure 23a larg). Comparede frequency to range previous around methods the Stokes also relyingfrequency on with respect to the pump beam (see Figure 23). Compared to previous methods also relying on frequency-agilewith respect to probethe pump waves, beam the present(see Figure method 23). di Comparedﬀers in that to a fastprevious and periodic methods modulation also relying of theon frequency-agile probe waves, the present method differs in that a fast and periodic modulation of the probefrequency-agile frequency probe is performed waves, the with present a period method of a fewdiffers tens in ofthat nanoseconds, a fast and periodic so that modulation the entire BGS of the is probe frequency is performed with a period of a few tens of nanoseconds, so that the entire BGS is real-timeprobe frequency scanned is in performed a time usually with associateda period of with a few a singletens of resolution nanoseconds, cell. so As that the the probe entire frequency BGS is real-time scanned in a time usually associated with a single resolution cell. As the probe frequency followsreal-time a sequencescanned in of a optical time usually chirps, theassociated method with has beena single named resolution optical cell. chirp As chain the probe (OCC) frequency BOTDA. follows a sequence of optical chirps, the method has been named optical chirp chain (OCC) BOTDA. follows a sequence of optical chirps, the method has been named optical chirp chain (OCC) BOTDA.

Figure 23. Principle of operation of the single-shot BOTDA based on the use of an OCC probe wave. FigureFigure 23.23. Principle of operation of the single-shot BOTDABOTDA based on the use of an OCC probe wave. (a) OCC probe wave is composed by several short optical chirp segments (b) Frequency relation ((aa)) OCCOCC probeprobe wavewave isis composedcomposed byby severalseveral shortshort opticaloptical chirpchirp segmentssegments ((bb)) FrequencyFrequency relationrelation between the pump pulse and the probe beam [70]. betweenbetween thethe pumppump pulsepulse andand thethe probeprobe beambeam [[70].70].

PleasePlease note that thethe methodmethod is somewhatsomewhat similarsimilar to the oneone presentedpresented in Ref.Ref. [[69],69], withwith thethe Please note that the method is somewhat similar to the one presented in Ref. [69], with the fundamentalfundamental didifferencefference that the linear sweep of thethe probe wave is compressed in the time domain, fundamental difference that the linear sweep of the probe wave is compressed in the time domain, soso thatthat thethe pumppump pulsepulse interactsinteracts withwith severalseveral frequencyfrequency sweepssweeps of thethe probeprobe duringduring itsits propagationpropagation so that the pump pulse interacts with several frequency sweeps of the probe during its propagation alongalong thethe fiber,fiber, andand thusthus thethe BGSBGS isis acquiredacquired “on“on thethe fly”.fly”. TheThe pumppump pulsepulse durationduration must be shorter along the fiber, and thus the BGS is acquired “on the fly”. The pump pulse duration must be shorter thanthan thethe optical optical chirp chirp segment, segment, to not to deterioratenot deterior theate spatial the spatial resolution. resolution. The transmitted The transmitted probe intensity, probe than the optical chirp segment, to not deteriorate the spatial resolution. The transmitted probe analyzedintensity, inanalyzed the time in domain, the time is domain, shown in is Figureshown 24 in forFigure a sawtooth 24 for a modulationsawtooth modulation of the probe of frequency.the probe intensity, analyzed in the time domain, is shown in Figure 24 for a sawtooth modulation of the probe Thefrequency. plot shows The thatplot theshows probe that intensity the probe waveform intensity presents waveform a sequence presents of a impressedsequence of BGSs, impressed in a number BGSs, frequency. The plot shows that the probe intensity waveform presents a sequence of impressed BGSs, in a number equal to the number of OCCs injected into the FUT during the propagation of the pump equalin a number to the number equal to of the OCCs number injected of OCCs into the injected FUT during into the the FUT propagation during the of propagation the pump over of the the pump entire over the entire fiber length. fiberover length.the entire fiber length.

Figure 24. (a) Transmitted probe power as a function of time, showing a sequence of BGSs impressed Figure 24. (a) Transmitted probe power as a function of time, showing a sequence of BGSs impressed Figureon it due 24. to(a )interaction Transmitted with probe the power pump as pulse. a function (b) Zoomed of time, view showing of the a sequence portion of of the BGSs probe impressed signal on it due to interaction with the pump pulse. (b) Zoomed view of the portion of the probe signal oncorresponding it due to interaction to the segment with the of the pump fiber pulse. subjected ( ) Zoomed to strain. view The ofwaveform the portion has ofbeen the acquired probe signal with correspondingcorresponding toto the the segment segment of of the the ﬁber fiber subjected subjected to to strain. strain. The The waveform waveform has has been been acquired acquired with with an an averaging factor of 200 and a pump pulse duration of 10 ns and an OCC duration of 20 ns [70]. averagingan averaging factor factor of 200 of 200 and and a pump a pump pulse pulse duration duration of 10 of ns10 andns and an OCCan OCC duration duration of 20 of ns 20 [ 70ns]. [70]. Each impressed BGS is followed by a secondary (“ghost”) peak, due to the generation of an EachEach impressedimpressed BGSBGS isis followedfollowed byby aa secondarysecondary (“ghost”)(“ghost”) peak,peak, duedue toto thethe generationgeneration ofof anan equivalent frequency near the BFS when the frequency is decreased from the highest frequency equivalentequivalent frequencyfrequency near the BFSBFS whenwhen thethe frequencyfrequency isis decreaseddecreased fromfrom thethe highesthighest frequencyfrequency component to the lowest frequency component of the sawtooth waveform. The extraction of the BFS componentcomponent toto thethe lowestlowest frequencyfrequency componentcomponent ofof thethe sawtoothsawtooth waveform.waveform. TheThe extractionextraction ofof thethe BFSBFS from each BGS relies on the time delay between each piece of the signal, and the corresponding piece fromfrom eacheach BGSBGS reliesrelies onon thethe timetime delaydelay betweenbetween eacheach piecepiece ofof thethe signal,signal, andand thethe correspondingcorresponding piecepiece of a reference signal previously acquired, which can be conveniently evaluated by cross-correlation ofof aa referencereference signalsignal previouslypreviously acquired,acquired, whichwhich cancan bebe convenientlyconveniently evaluatedevaluated byby cross-correlationcross-correlation techniques (see Figure 25b). Exploiting this method, dynamic strain measurements over a fiber length techniquestechniques (see(see FigureFigure 2525b).b). Exploiting this method,method, dynamic strain measurements overover aa ﬁberfiber lengthlength of 10 m, have been demonstrated at an exceptionally high sampling rate of 6.25 MHz,. Figure 25 ofof 1010 m,m, havehave beenbeen demonstrateddemonstrated atat anan exceptionallyexceptionally highhigh samplingsampling raterate ofof 6.256.25 MHz.MHz,. FigureFigure 2525 shows the time evolution of the BGS in a generic section of the fiber, obtained emulating a periodic, shows the time evolution of the BGS in a generic section of the fiber, obtained emulating a periodic, 20-MHz shift of the BGS though periodical shifting of the frequency sweep applied to the probe. 20-MHz shift of the BGS though periodical shifting of the frequency sweep applied to the probe.

Sensors 2020, 20, 5629 18 of 23 shows the time evolution of the BGS in a generic section of the ﬁber, obtained emulating a periodic, 20-MHz shift of the BGS though periodical shifting of the frequency sweep applied to the probe. Sensors 2020, 20, x FOR PEER REVIEW 18 of 23

Figure 25. TimeTime evolution evolution of of the the BGS BGS acquired acquired over over a 10-m a 10-m long long fiber ﬁber for for(a) averaging (a) averaging 200 200times times and and(b) no (b averaging,) no averaging, where where the BFS the variation BFS variation is simula isted simulated by periodically by periodically switching switchingthe probe frequency- the probe frequency-sweepsweep range. (c) Corresponding range. (c) Corresponding BFS evolution BFS evolutionover time, overwith time, and without with and averaging without averaging [70]. [70].

A successivesuccessive optimization of the OCC method was proposed by the same authors in Ref. [71], [71], whichwhich combinescombines thethe frequency-agile probeprobe withwith thethe difffferentialerential pulse-pairpulse-pair methodmethod [[29],29], andand aa patternpattern recognitionrecognition algorithm. In In such such a case, the didifferenfferentialtial method was not addedadded forfor spatialspatial resolutionresolution enhancement, rather it was used to reducereduce thethe OCCOCC modulationmodulation noisenoise andand avoidavoid thethe self-phaseself-phase modulation (SPM) effect. effect. The The OCC OCC modulation modulation noise noise arises arises from from the the uneven uneven amplitude amplitude response response for fordifferent different frequency frequency components, components, while while SPM SPM distor distortsts the the pump pump pulse pulse waveform waveform in long-rangelong-range measurements. In Ref. [71], [71], the temperature was measured over a fiberfiber length of 100 km at a spatialspatial resolutionresolution ofof 44 m.m. However, the measurement time was 5 s in this case, due to thethe longlong FUTFUT and the relativelyrelatively largelarge averagingaveraging factorfactor ((N𝑁av ==2000). 2000). The mainmain drawbacksdrawbacks of the OCCOCC methodmethod areare thethe needneed forfor sophisticated,sophisticated, highhigh samplingsampling raterate AWGs,AWGs, and the underlying underlying trade-off trade-off betweenbetween spatial spatial resolution, resolution, SNR, SNR, and and dyna dynamicmic range. range. In fact, In fact, the theextension extension of the of thedynamic dynamic range range requires requires the the adopti adoptionon of ofa alonger longer chirp chirp (f (foror a a fixed fixed chirp rate), negatively influencinginfluencing the spatial r6esolution. Similarly, Similarly, the the use of a steeper chirp leads to a timetime compression ofof the the BGS BGS impressed impressed on theon probethe probe intensity, intensity, reducing reducing the accuracy the accuracy of the cross-correlation of the cross- forcorrelation a given for sampling a given rate sampling (unless rate more (unless sophisticated more sophisticated extraction extrac techniquestion techniques such as those such based as those on principalbased on componentprincipal component analysis (PCA) analysis are (P adopted,CA) are asadopted, in Ref. [as71 ]).in Ref. [71]). We finallyfinally observe observe that that an an acquisition acquisition rate rate close clos toe theto the maximum maximum rate rate dictated dictated by the by chosen the chosen fiber lengthfiber length (10 MHz), (10 MHz), as reported as reported in Ref. [in70 ]Ref. for a[70] 10-m for fiber, a 10-m means fiber, that means no averaging that no hasaveraging been performed. has been Inperformed. other words, In other an adequate words, an SNR adequate was achieved SNR was even achieved with single-shot even with acquisitions,single-shot acquisitions, thanks to a carefulthanks optimizationto a careful optimization of the setup (veryof the narrow setup (very linewidth narrow laser, linewidth PM FUT, laser, careful PM choice FUT,of careful the injected choice optical of the powers,injected optical powers, filtering optical of the amplified filtering of spontaneous the amplified emission spontaneous (ASE) emission noise added (ASE) by noise erbium-doped added by fibererbium-doped amplifiers fiber (EDFAs)). amplifiers An optimized (EDFAs)). setup An optimize that doesd setup not require that does averaging, not require is very averaging, fast even is when very employedfast even towhen conduct employed conventional to conduct BOTDA conventi measurements.onal BOTDA For example,measurements for a conventional. For example, BOTDA for a schemeconventional operated BOTDA with scheme no averaging, operated measurement with no averaging, over a measurement 10-m fiber length over a and 10-m with fiber 100 length scanned and frequencieswith 100 scanned gives an frequencies acquisition gives rate of an 100 acquisition kHz, which rate is adequateof 100 kHz, in many which applications. is adequate in many applications. 8. Conclusions 8. Conclusions The measurement of dynamic phenomena and the quantification of strain amplitude is a challenge for distributedThe measurement optical fiber of sensors.dynamic Rayleighphenomena scattering-based and the quantification configurations of strain allow theamplitude detection is ofa vibrationschallenge for and distributed their spectral optical analysis, fiberbut sensors. do not Ra easilyyleigh provide scattering-based reliable quantitative configurations measurements allow the detection of vibrations and their spectral analysis, but do not easily provide reliable quantitative measurements because of their limited linearity range and phase ambiguity [72]. On the other hand, Brillouin-based configurations exhibit an excellent linearity and can measure the absolute strain with an extended range. In this paper, we have reviewed some of the more interesting techniques proposed for dynamic sensing based on Brillouin scattering.

Sensors 2020, 20, 5629 19 of 23 because of their limited linearity range and phase ambiguity [72]. On the other hand, Brillouin-based conﬁgurations exhibit an excellent linearity and can measure the absolute strain with an extended range. In this paper, we have reviewed some of the more interesting techniques proposed for dynamic sensing based on Brillouin scattering. The more relevant aspects inherent performance of the presented methods are summarized in Table1. Please note that the reported values are only indicative, and do not represent the ultimate performance of the various methods.

Table 1. Summary of the main performance of fast Brillouin sensing methods.

Pump Power Fast SA-BOTDA Sweep-Free Single-Shot BOTDA BOCDA [39] Independent BOTDA [50,55] BOTDA [63] [70] SA-BOTDA [67,69] [60,61] Spatial 10 s of cm ~m ~m 10 s of m ~m ~m resolution 0 0 Sensing 10 s of m for high-speed 10 s of m 100 s of m 100 s of m 100 s of m 100 s of m 0 range 0 0 0 0 0 measurements Acquisition ~kHz ~kHz ~kHz ~kHz 10 s of Hz ~MHz rate 0 Dynamic 100 s of 100 s of 100 s of MHz 30 MHz 30 MHz 0 0 100 s of MHz range 0 ∼ ∼ MHz MHz 0 Low dynamic Only one (or a few) range and Low Trade-oﬀ between Main Low spatial Setup simultaneous pump dynamic spatial resolution, SNR, limitation(s) resolution complexity sensing positions power/ range and dynamic range loss dependance

Apart from the specific technique applied, one major factor impacting the capability to perform high-speed measurements is the SNR: an optimized configuration with a higher SNR permits the reduction (or even elimination) of the need for averaging. Thus, it is fundamental to understand and optimize the principal factors influencing the SNR in Brillouin systems [73]. On the other hand, the relatively low strain sensitivity of the BFS ( 50 kHz/µε in conventional fibers), combined with ∼ the BGS intrinsic linewidth ( 30 MHz), makes improbable that Brillouin sensors will reach the nε ∼ sensitivity of Rayleigh-based sensors, even after that all the experimental parameters have been optimized. Therefore, possible future developments in the distributed dynamic sensing field in optical fibers may involve the simultaneous use of Rayleigh and Brillouin scattering into the same fiber [74], combining high sensitivity and adequate dynamic range. Another factor that should be taken into account, is that the present review only refers to configurations based on the SBS. Several configurations for dynamic sensing based on spontaneous Brillouin scattering have been proposed as well (e.g., [75,76]) but they have not been considered in this review, as spontaneous Brillouin scattering is intrinsically much weaker than SBS, which means that much more averages are required to satisfy the same SNR requirements. The use of SBS imposes the access to both ends of the fiber, which may be a limitation in some applications. Single-ended SBS configurations have been proposed as well, but generally are based on the use of some reflector at the end of the fiber [77,78], which means that these configurations are not fault tolerant, as a single breakage along the fiber prevents the measurement on the whole length. A recent demonstration of a truly single-ended BOTDA configuration [79] exploits the non-linear interaction between a Rayleigh-backscattered wave and a forward-traveling optical pump pulse, using sources separated by approximately one BFS. Such a configuration may be also adopted for dynamic sensing, for example by combining it with the SA method discussed in Section4, to realize truly single-ended BOTDA dynamic strain measurements. Sensors 2020, 20, 5629 20 of 23

Author Contributions: Writing—original draft preparation, A.C.; writing—review and editing, A.M.; supervision, L.Z.; All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Università degli Studi della Campania Luigi Vanvitelli (PremialitàValere2018). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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