applied sciences

Article The Influence of Linewidth on the Brillouin Shift Frequency Accuracy of BOTDR

Qing Bai 1 , Min Yan 1, Bo Xue 1, Yan Gao 1, Dong Wang 1, Yu Wang 1 , Mingjiang Zhang 1, Hongjuan Zhang 1 and Baoquan Jin 1,2,*

1 Key Laboratory of Advanced Transducers and Intelligent Control Systems (Ministry of Education and Shanxi Province), Taiyuan University of Technology, Taiyuan 030024, China; [email protected] (Q.B.); [email protected] (M.Y.); [email protected] (B.X.); [email protected] (Y.G.); [email protected] (D.W.); [email protected] (Y.W.); [email protected] (M.Z.); [email protected] (H.Z.) 2 State Key Laboratory of Coal and CBM Co-mining, Shanxi Jincheng Anthracite Ming Group Co., Ltd., Jincheng 048000, China * Correspondence: [email protected]; Tel.: +86-138-3515-5702

 Received: 9 December 2018; Accepted: 21 December 2018; Published: 25 December 2018 

Featured Application: Brillouin-based distributed optical fiber sensing technology, such as BOTDR, BOTDA, BOCDR, BOCDA.

Abstract: This paper analyzes the influence of laser linewidth on the measurement accuracy of a frequency-scanning Brillouin optical time domain reflectometer (FS-BOTDR), allowing for both the width of Brillouin spectrum and the signal-to-noise ratio (SNR) of the BOTDR system. The measurement accuracy of the Brillouin frequency shift (BFS) is theoretically investigated versus the duration of the probe pulse and the linewidth of the laser source, by numerically simulating how a FS-BOTDR works and evaluating the Brillouin gain spectrum (BGS) width and the system SNR. The simulation results show that the BFS accuracy is improved as the laser linewidth becomes narrower when the probe pulse width is fixed. We utilize five types of with respective linewidths of 1.05 MHz, 101 kHz, 10.2 kHz, 3.1 kHz, and 98 Hz to compare the BFS measurement accuracy over a ~10 km optical sensing fiber. The experimental results demonstrate that the root-mean-square error (RMSE) of BFS decreases with the laser linewidth narrowing from 1.05 MHz to 3.1 kHz, which is in good agreement with the numerical simulation. However, the RMSE of BFS increases when the laser linewidth is less than 3.1 kHz, which may arise from the coherent Rayleigh noise due to a too narrow laser linewidth. The results can provide a theoretical basis and experimental guidance for choosing the appropriate laser linewidth in BOTDR.

Keywords: Distributed optical fiber sensing; BOTDR; measurement accuracy; laser linewidth; signal-to-noise ratio

1. Introduction Brillouin optical time domain reflectometer (BOTDR) was firstly proposed as continuously- distributed optical fiber sensing technology in 1993 [1]. In recent decades, it has attracted much attention due to its advantages of long-distance measurement, corrosion resistance, anti-electromagnetic interference, and one-end access especially [2–4]. Meanwhile, with the development of its capacity of simultaneous measurement of strain and [5,6], BOTDR has been more and more widely utilized in many industrial applications, such as monitoring operation status and structural health conditions of transmission lines, soil slopes, large-scale bridges, gas/oil pipelines, transportation tunnels,

Appl. Sci. 2019, 9, 58; doi:10.3390/app9010058 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 58 2 of 18 and underground mines [7–10]. Consequently, the measurement accuracy of Brillouin frequency shift (BFS), which determines the temperature and strain accuracy, has inevitably been a focused issue for performance enhancement of BOTDR. The measurement accuracy of BFS can be affected by numerous factors, such as the fitting algorithm for Brillouin gain spectrum (BGS), the features of probe pulses, and even the characteristics of the laser source. Hence, a large number of papers have focused on above factors to discuss and improve the accuracy of BOTDR. Originally, a simple Levenberg-Marquart algorithm was used for BGS fitting [11]. Then, a series of time-frequency analysis methods called Cohen’s class were proposed for the signal processing of BOTDR, reducing the BFS fluctuation by three times [12]. For improving both the measurement accuracy and data processing speed, a similarity matching method was proposed, making the standard derivation of BFS results three times better [13]. An iterative quadratic fitting method can also be utilized to extract BFS from noisy signals for improvement of the BFS accuracy [14]. Besides, the features of probe light pulses also have a significant influence on the accuracy of BFS, including the pulse shape and pulse extinction ratio. Hao et al. analyzed the effects of different modulated pulse on the backscattered Brillouin power spectra of BOTDR, including the pulse shapes of Lorentzian, Gaussian, hyperbolic-secant, super Gaussian, triangular, and rectangular pulses [15,16]. The pulse sequences were complementarily coded in a BOTDR scheme to achieve a high measurement accuracy and fast measurement speed [17]. The simplex pulse codes were also testified to be beneficial for improving the signal-to-noise ratio ratio (SNR) of the BOTDR signal and the measurement accuracy of BFS [18]. The higher extinction ratio of the probe pulses was capable of enhancing the SNR as well as reducing the measurement uncertainty of BFS [19,20]. Moreover, it is noted that the and linewidth of the laser source likewise impact BFS accuracy. Lalam et al. used a wavelength diversity technique with a Brillouin ring laser in a conventional BOTDR system to improve SNR [21]. A multi-wavelength heterodyne-detection technique was utilized to provide 4.2 dB SNR enhancement, enabling the measurement accuracy to be increased by two times [22]. As an important parameter of the laser, the wide linewidth imposes a broadening effect on BGS, which affects the BFS accuracy partly, but the broadening effect is indistinctive when the laser linewidth is less than 1 MHz [23]. Meanwhile, it has been proven that the BFS accuracy is determined not only by the width of BGS, but also by the SNR of the BOTDR system [24]. The system SNR of BOTDR is inherently related with the laser linewidth closely, because the coherent heterodyne detection, which is sensitive to the laser linewidth, is commonly used in BOTDR [25]. Hence, the influence of the laser linewidth on the BFS accuracy of BOTDR needs to be further discussed in detail, considering both the BGS width and the system SNR. In this paper, how the BFS accuracy is determined by the linewidth of the laser source is theoretically analyzed and experimentally verified in a frequency-scanning BOTDR (FS-BOTDR). The broadening effect of BGS was analyzed, allowing for both the pulse width of the probe light and the frequency-scanning process in an FS-BOTDR. Then, the SNR of BOTDR with coherent heterodyne detection was calculated, treating the phase fluctuation as the primary noise source. The BFS accuracy was finally simulated numerically taking into account both the BGS and the SNR synthetically. We used five lasers with respective linewidths of 1.05 MHz, 101 kHz, 10.2 kHz, 3.1 kHz, and 98 Hz to perform temperature measurement in the BOTDR sensing system and verify the numerical simulation. The results of this research will be helpful to choose the laser linewidth for the BOTDR.

2. Numerical Simulation Figure1 gives a classical schematic diagram of BOTDR with coherent heterodyne detection [ 26]. One branch of the seed laser is modulated by an optical modulator to generate probe pulse light, which is injected into the tested fiber through an optical circulator. The other one branch passing a polarization controller is injected into a photodetector to beat with the Brillouin backscattering. The output electronic signal is orderly down-converted by mixing with a frequency scanner, filtered by a band-pass filter (BPF), and acquired by a data acquisition (DAQ) digitalizer. Appl. Sci. 2019, 9, 58 3 of 18 Appl. Sci. 2018, 12, x FOR PEER REVIEW 3 of 18

Figure 1. Schematic diagram of frequency-scanning B BOTDROTDR (FS-BOTDR) with coherent heterodyne detection: AWGAWG == Arbitrary Arbitrary Waveform Waveform Generator; Generator; BPF =BPF Band-pass = Band-pass Filter; DAQ Filter; = Data DAQ Acquisition. = Data Acquisition. The measurement error of BFS in FS-BOTDR is related with both the width of BGS denoted as W and the system SNR, which is given by Equation (1) [1]: BGSThe measurement error of BFS in FS-BOTDR is related with both the width of BGS denoted as WBGS and the system SNR, which is given by EquationW (1) [1]: ∆α = √ BGS (1) 2(WSNR)1/4 Δα BGS = (1) 2(SNR )1/4 hence, the values of WBGS and SNR need to be both analyzed for figuring out the BFS accuracy of ∆α, as specified below. hence, the values of WBGS and SNR need to be both analyzed for figuring out the BFS accuracy of Δα, When the continuous lightwave is injected into the tested fiber, the obtained BGS presents a as specified below. Lorentzian shape, given by [27]: When the continuous lightwave is injected into the tested fiber, the obtained BGS presents a (w/2)2 Lorentzian shape, given by [27]: ( ) = GB f g0 2 2 (2) ( f − fB) + (w/2) (/2)w 2 Gf()= g B0−+22 (2) where w is the full-width at half maximum (FWHM)()(/2)ff ofB BGS, wf B is the Brillouin frequency shift, and g0 is the Brillouin gain coefficient, which is the BGS peak value when f = f B. w f 0 whereWhen is the the full-width continuous at lightwavehalf maximum is modulated (FWHM)into of BGS, the pulseB is the light Brillouin with a frequency peak power shift, of Pand0 and g ispulse the Brillouin width of τgain, the coefficient, power spectrum which ofis the BGS pulse peak probe value light when can be f = expressed fB. as:

When the continuous lightwave is modulated into the pulse2 light with a peak power of P0 and sin π( f − f0)τ pulse width of τ, the power spectrumPp( fof, fthe.0) =pulseP0[ probe light can] be, expressed as: (3) π( f − f0) sinπτ (ff− ) = 0 2 where f 0 is the optical frequency ofPff thep.00(, probe ) light.P [ Hence, the ] Brillouin, backscattered-light power(3) π ()ff− spectrum for pulse light can be calculated by [24]: 0 where f0 is the optical frequency of the probe light.n Hence,2 − τthewπ Brillouin2 backscattered-lighto power ( ) = R +∞ ( ) ( ) = g0P0τ + η −1−e [(η −1) cos τwηπ+2σ sin ητwπ] QB f −∞ Pp f , f0 GB f 2+ 1 ( 2+ ) (4) spectrum for pulse light can be calculated byη [24]:1 τw η 1 π where: f − f −τπ +∞ gPτ η =η 22−−1eB w [(ητηπσητπ − 1)cosww + 2sin ] (5) Qf()=+ PffGf (, ) () = 00 1 w/2 Bp0B−∞ 22(4) ητηπ++1(1)w In the FS-BOTDR, the power spectrum, QB(f ), is always measured by the frequency-scanning method. When the frequency scanner is tuned at a certain frequency point, the integrated power of where:every frequency segment passing the BPF is acquired by DAQ. Hence, as the frequency scanner is tuned step by step, the final measured spectrum after frequency-scanning process, denoted as H (f, N), f − f B can be given by: η = B (5) w /2 n 1 2 N o HB( f , N) = QB( f ), QB( f ),..., QB ( f ) (6) In the FS-BOTDR, the power spectrum, QB(f), is always measured by the frequency-scanning method. When the frequency scanner is tuned at a certain frequency point, the integrated power of every frequency segment passing the BPF is acquired by DAQ. Hence, as the frequency scanner is Appl. Sci. 2018, 12, x FOR PEER REVIEW 4 of 18 tuned step by step, the final measured spectrum after frequency-scanning process, denoted as HB(f, N), can be given by:

= 12 N H BBBB(fN , ) { Q ( f ), Q ( f ), ... , Q ( f ) } (6) Appl. Sci. 2019, 9, 58 4 of 18

fif+−(1) + B /2 Qfi ( )==s step Qfdfi ( ) , 1, 2, ..., N . BB fif+−(1) − B /2 (7) s step Z fs+(i−1) f +B/2 i step QB( f ) = QB( f )d f , i = 1, 2, . . . , N. (7) fs+(i−1) fstep−B/2 where fs and fstep are, respectively, the start frequency and frequency step during the frequency- scanningwhere f sprocess,and f stepN is theare, number respectively, of frequency the startpoints, frequency and B is the and bandwidth frequency of the step BPF. during Based theon frequency-scanning process, N is the number of frequency points, and B is the bandwidth of the Equation (4)~ Equation (7), the broadening effect of BGS in FS-BOTDR is numerically simulated. The BPF. Based on Equation (4)~ Equation (7), the broadening effect of BGS in FS-BOTDR is numerically modelsimulated. parameters The model utilized parameters for simulations utilized are for list simulationsed in Table are A1 listed of Appendix in Table A1A. ofThe Appendix simulationA. resultsThe simulation are shown results in Figure are shown 2. It can in Figurebeen clearly2. It can seen been that clearly the finally seen that measured the finally BGS measured width in BGS FS- BOTDR,width in denoted FS-BOTDR, as W denotedBGS, is larger as W thanBGS, isboth larger the thanoriginal both BGS the width original for BGS continuous width for light continuous and the BGS light widthand the for BGS pulse width light. for Hence, pulse light.the broadening Hence, the effect broadening of BGS effectin FS-BOTDR of BGS in must FS-BOTDR be taken must into beaccount taken into account when the BFS accuracy is evaluated according to Equation (2). when the BFS accuracy is evaluated according to Equation (2).

FigureFigure 2. NumericalNumerical simulationsimulation of of the the broadening broadening effect effect of Brillouin of Brillouin gain spectrumgain spectrum (BGS) in(BGS) FS-BOTDR: in FS-

BOTDR:GB(f ) is theGB( originalf) is the original BGS for theBGS continuous for the continuous light; QB light;(f ) is theQB( BGSf) is the for theBGS pulse for the light pulse with light a width with ofa width22 ns; ofHB 22(f, ns;N) isHB the(f, N final) is the measured final measured BGS through BGS through the frequency-scanning the frequency-scanning process whenprocess the when width the of widththe probe of the pulse probe is 22pulse ns. is 22 ns.

FigureFigure 33aa givesgives profilesprofiles ofof HHB(f, N)) under under different probe pulse widths. The The peak peak power power is is normalizednormalized by by that that of of the spectr spectrumum profile obtained when the pulsepulse width is 12 ns. The The spectrum spectrum width and and relative relative power versus the probe pulse width are plotted in Figure 33b.b. From Figure3 3a,a, itit isis obviousobvious thatthat thethe BGS BGS spectrum spectrum becomes becomes narrower narrower and higherand higher as the as pulse the width pulse increases. width increases. The spectrum The spectrumwidth of H widthB(f, N ),of denoted HB(f, N), as denotedWBGS, decreases as WBGS, fromdecreases 107.9 from MHz 107.9 to 87.15 MHz MHz. to 87.15 The relativeMHz. The peak relative power peakof HB power(f, N), denotedof HB(f, N as), Pdenotedrp, increases as Prp as, increases the pulse as width the pulse is increased width is from increased 12 ns tofrom 52 ns. 12 ns to 52 ns. Appl.Appl. Sci. Sci.2019 2018, 9,, 5812, x FOR PEER REVIEW 5 of5 18 of 18 Appl. Sci. 2018, 12, x FOR PEER REVIEW 5 of 18

(a) (b) (a) (b) Figure 3. Numerical simulation results: (a) Profiles of HB(f, N) under different probe pulse widths; (b) FigurespectrumFigure 3. 3.Numerical Numericalwidth and simulation simulationrelative po wer results: versus (a (a) )Profilesprobe Profiles pulse of of H Bwidth.H(fB, N(f), underN ) under different different probe probe pulse pulsewidths; widths; (b) (b)spectrum spectrum width width and and relative relative po powerwer versus versus probe probe pulse pulse width. width. Following simulation analysis of the BGS broadening, the relationship between the system SNR andFollowing theFollowing laser simulationlinewidth simulation should analysis analysis be of emphaticallyof thethe BGSBGS broadening,broade discussed.ning, the theThe relationship relationship photocurrent between between in coherent the the system systemdetection SNR SNR andcanand the bethe laser expressed laser linewidth linewidth as Equation should should be(8) be emphaticallynegl emphaticallyecting the discussed. polarization discussed. The Themismatch photocurrent photocurrent [28]: in in coherent coherent detection detection can can be expressed as Equation (8) neglecting the polarization mismatch [28]: be expressed as Equation (8) neglectingΔ=ϕ the polarization ⋅ ⋅ mismatchπ +Δϕ [28]: it(, ) GRPSpB P Rf cos(2 ft B ) (8) Δ=ϕ ⋅ ⋅π +Δϕ it(, ) GRPq SpB P Rf cos(2 ft B ) (8) ( ) = · · ( + ) where G and R are, respectively,i t, ∆ϕ the GRgain andPSpB responsivityPRf cos 2 πoff Bthet detector,∆ϕ PSpB(t) and PRf are the(8) where G and R are, respectively, the gain and responsivity of the detector, PSpB(t) and PRf are the power of the spontaneous Brillouin backscattering and the reference light, respectively, fB is the BFS, where G and R are, respectively, the gain and responsivity of the detector, PSpB(t) and PRf are the power andpower Δφ of is thethe spontaneousphase difference. Brillouin backscattering and the reference light, respectively, fB is the BFS, of the spontaneous Brillouin backscattering and the reference light, respectively, f is the BFS, and ∆ϕ and Δφ is the phase difference. B is the phaseBecause difference. the coherent detection is highly phase sensitive, the phase fluctuation caused by Δφ will Because the coherent detection is highly phase sensitive, the phase fluctuation caused by Δφ will greatlyBecause decrease the coherent the SNR detectionand even islead highly to the phase centra sensitive,l frequency the jitter phase [25]. fluctuation It has been caused proven by that∆ ϕthewill greatlyphasegreatly decrease fluctuation decrease the the in SNR SNRthe and coherentand even even leaddetection lead toto thethe can centralcentra be viewedl frequency as a jitter jitternonstationary [25]. [25]. It It has has randombeen been proven proven process that that and the the phasefollowsphase fluctuation fluctuation normal indistribution thein the coherent coherent with detection thedetection mean can value becan viewed be of viewed µ and as a the nonstationaryas avariance nonstationary of randomσ2, given random process by Equationprocess and follows and (9) σ2 2 normal[29]:follows distribution normal distribution with the mean with valuethe mean of µ valueand the of varianceµ and the of variance, given of byσ , Equationgiven by (9)Equation [29]: (9) [29]: ∆ϕΔ==Δ⋅Δ∼ϕμσμσπN (NnfLcµ(,, σ2)22, ),µ = 0, 0, σ2 = 22πn∆ f · ∆ /L/ c (9) (9) Δ==Δ⋅Δϕμσμσπ NnfLc(,22 ), 0, 2 / (9) wherewheren is n theis the refractive index of of optical optical fiber, fiber,c c isis thethe light speed speed in in , vacuum, Δ∆f isf isthe the laser laser linewidth, linewidth, andandwhere∆L ΔisL n theis is the the optical optical refractive path path index difference difference of optical between between fiber, the thec is probe probthe lighte beam beam speed andand in thethe vacuum, referencereference Δf is beam. the laser Figure Figure linewidth, 4 gives a histogramaand histogram ΔL is of the∆ ofϕ optical Δutilizedφ utilized path in difference thein the simulation simulation between when when the∆ prob fΔ=f =1.05 1.05e beam MHz, and Δ∆ theL=20= reference 20 km. km. beam. Figure 4 gives a histogram of Δφ utilized in the simulation when Δf =1.05 MHz, ΔL=20 km.

Figure 4. Histogram of ∆ϕ utilized in the simulation when ∆f =1.05 MHz and ∆L = 20 km. Appl. Sci. 2018, 12, x FOR PEER REVIEW 6 of 18

Figure 4. Histogram of Δφ utilized in the simulation when Δf =1.05 MHz and ΔL=20 km.

To analyze the relationship between SNR and Δφ succinctly, we treated phase fluctuation as a

Appl.major Sci. noise2019, 9contribution,, 58 regardless of the thermal noise and shot noise. The power of useful signal6 of 18 can be expressed as:

1 τ To analyze the relationship between<>=Δit22 SNR() and ∆ itϕ (,succinctly,ϕ ) dt we treated phase fluctuation(10) as a S τ 0 major noise contribution, regardless of the thermal noise and shot noise. The power of useful signal can beThe expressed power of as: noise can be expressed as: Z τ 2 1 2 < iS(t) >= i (t, ∆ϕ)dt (10) Nt τ 0 [(ikΔΔ t ,ϕ ) − ik ( Δ t ,0)]2 The power of noise can be expressed2 as:k =1 (11) <>=it() N − Nt 1 N t 2 ∑ [i(k∆t, ∆ϕ) − i(k∆t, 0)] where Δt is the sampling interval of i(t,Δφ), andk=1 Nt=τ/Δt is the number of samples. Hence, the SNR can < i2 (t) >= (11) N − be given by Equation (12): Nt 1 where ∆t is the sampling interval of i(t,∆ϕ), and Nt=τ/∆t is the number of samples. Hence, the SNR τ 1 2 can be given by Equation (12): 2 Pitdt()τϕ (,Δ ) <>it() rp 0 =⋅τ S = τ SNR Prp () <>it2 ()2 Nt 1 R τ 2 PrpΔΔ(τ)ϕ −i ( Δt, ∆ϕ)2dt (12) SNR = P (τ) · S =[(ik t ,τ )0 ik ( t ,0)] (12) rp 2 = N < i (t) >k 1 t 2 N ∑ [i(k∆t−,∆ϕ)−i(k∆t,0)] k=1 (1)Nt (Nt−1) where Prp((ττ) )is is the the relative relative peak peak power power of of the the measured measured BGS BGS closely closely related related with with the the width of the probe pulse. The relative SNR versus laser linewidthlinewidth under different pulse widths was numerically simulated and is plotted in Figure5a according to Equation (12). Further, the BFS measurement error simulated and is plotted in Figure 5a according to Equation (12). Further, the BFS measurement error was calculated based on Equation (1) and normalized as shown in Figure5b. was calculated based on Equation (1) and normalized as shown in Figure 5b.

(a) Relative SNR (b) BFS error

Figure 5.5. NumericalNumerical simulation simulation results results versus versus laser laser linewidth linewidth under under different different pulse widths: pulse widths: (a). Relative (a). Relativesignal-to-noise signal-to-noise ratio (SNR); ratio (b). (SNR); BFS accuracy. (b). BFS Model accuracy. parameters Model parameters utilized for simulationsutilized for simulations are listed in Tableare listed A1. in Table A1.

From Figure5 5,, itit isis obviousobvious thatthat thethe SNRSNR isis improvedimproved asas thethe pulsepulse widthwidth increasesincreases andand thethe laserlaser linewidth narrows. Under Under the the same same pulse pulse width, width, the the BFS BFS error, error, ∆Δαα,, increases increases sharply sharply as as the laser linewidth broadens broadens from from 0.1 0.1 kHz kHz to to 10 10 kHz, kHz, and and grows grows slowly slowly when when the the laser laser linewidth linewidth exceeds exceeds 10 10kHz. kHz. Based Based on onthe the above above numerical numerical simulations, simulations, it itisis theoretically theoretically proven proven that that the the BFS BFS accuracy accuracy of BOTDR is improved as the laser width narrows andand thethe pulsepulse widthwidth increases.increases. Appl. Sci.Appl. 2018 Sci.,Appl. 122019, x Sci.FOR, 9, 2018 58 PEER, 12 REVIEW, x FOR PEER REVIEW 7 of 18 7 of 187 of 18 Appl. Sci. 2018,Appl. 12, x Sci.FOR 2018 PEER, 12 REVIEW, x FOR PEER REVIEW 7 of 18 7 of 18 Appl. Sci. 2018, 12, x FOR PEER REVIEW 7 of 18 Appl. Sci.Appl. 2018 Sci., 12 2018, x FOR, 12, xPEER FOR REVIEW PEER REVIEW 7 of 187 of 18 Appl.3. Experiment Sci. 2018, 3.Appl.12 ,Experiment xSetup Sci.FOR 2018 PEER , 12 REVIEW, Setupx FOR PEER REVIEW 7 of 18 7 of 18 3.Appl. Experiment Sci. 2018,Appl. 12, Setupx Sci.FOR 2018 PEER , 12 REVIEW, x FOR PEER REVIEW 7 of 18 7 of 18 3. Experiment3. Experiment3. Experiment Setup Setup Setup 3. Experiment3. Experiment3. Experiment Setup Setup Setup 3.1.3. Experiment Experiment3.1.3. Experiment Setup SetupExperiment for Measuring SetupSetup for Laser Measuring Linewidth Laser Linewidth 3.1. Experiment3.1. Experiment3.1.3. Experiment SetupExperiment Setupfor Measuring Setup forSetup Measuring for Laser Measuring Linewidth Laser LinewidthLaser Linewidth 3.1. ExperimentTo3.1. measure Experiment3.1. SetupExperiment the forSetuplinewidth Measuring Setupfor Measuring of for theLaser Measuring utilized Linewidth Laser LaserLinewidthlase rs, Linewidth a linewidth measurement setup based on the 3.1. ExperimentTo measure3.1. SetupExperimentTo the measure forlinewidth Measuring Setup the of forlinewidth Laserthe Measuring utilized Linewidth of the Laserlase utilizedrs, Linewidth a linewidth lase rs, a measurement linewidth measurement setup based setup on the based on the delayed3.1. Experiment self-heterodyneTo3.1. measure SetupExperimentTo measure for the Measuring interferometer linewidthSetup the forlinewidth Laser Measuring of (DSHI) theLinewidth of utilized theLaser was utilized Linewidthconfigured lasers, lase a linewidthrs, as a shown linewidth measurement in Figure measurement 6. setup setup based based on the on the To measureTodelayed measureTo the measureself-heterodyne linewidth the linewidth the of linewidth the interferometer ofutilized the of utilized thelase utilized rs,(DSHI) lase a linewidthrs, lasewas a linewidthrs, configured ameasurement linewidth measurement as shownmeasurement setup in setup basedFigure setup basedon 6. the based on the on the delayedTodelayed measureself-heterodynedelayed self-heterodyneTo the measureself-heterodyne linewidth interferometer the interferometer of linewidth the interferometer utilized (DSHI) of (DSHI) thelase was utilizedrs, (DSHI)configuredwas a linewidth configured lasewasrs, asconfigured a shownmeasurement linewidth as shown in as Figure shownmeasurement in setup Figure 6. in based Figure6. setup on 6. the based on the delayedTodelayed measureself-heterodynedelayed self-heterodyneTo the measureself-heterodyne linewidth interferometer the interferometer of linewidth the interferometer utilized (DSHI) of (DSHI)the lasewas utilized rs, (DSHI)configured wasa linewidth configured lasewasrs, asconfigured ashownmeasurement linewidth as shown in as Figure shownmeasurement in setup Figure 6. in basedFigure 6. setup on 6. the based on the delayed self-heterodynedelayed self-heterodyne interferometer interferometer (DSHI) was (DSHI)configured was asconfigured shown in as Figure shown 6. in Figure 6. delayed self-heterodynedelayed self-heterodyne interferometer interferometer (DSHI) was (DSHI) configured was asconfigured shown in as Figure shown 6. in Figure 6.

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Finally,lower after Finally,signalPDbeam the was two afterpasses theacquired beams PDtwo through was beatbeams and acquired in recordedan abeat photodetectoracoustic inand bya recordedphotodetector anoptical electrical through modulator by an spectrum athrough electrical 3-dB (AOM) coupler. analyzera spectrum3-dB to The becoupler. (ESA). electronicfrequency analyzer FiveThe signal (ESA). Five shiftedelectronicshifted by signal200shiftedmismatch. by MHz. after200 by MHz.Finally, PD200The was MHz. lowerFinally, theacquired Finally,twobeam the beams andpassestwo the recorded beamstwobeat through beamsin beat aby photodetector an aninbeat acousticelectricala photodetectorin a photodetector optical spectrum through modulatorthrough analyzera 3-dB through a coupler.(AOM)3-dB (ESA). a 3-dBcoupler. FivetoThe becoupler. frequencyThe The lasers with shiftedelectronicdifferent by signallinewidths200 MHz. after Finally,PDwere was utilized theacquired two in beams andthe recordedexperiments. beat in bya photodetector an Table electrical 1 gives spectrum through their analyzeranominal 3-dB coupler. (ESA). FiveThe electronicshiftedafterelectronic by signal PD200laserselectronicshifted was MHz. signalafter with acquiredby signal Finally,PD 200 afterdifferent was MHz. and PDafter theacquired recordedwas Finally,PDlinewidthstwo acquired was beams and by theacquired anrecorded weretwoandbeat electrical recorded beams inandutilized bya recordedphotodetector spectruman beat electricalbyin inanthe by a analyzerelectrical photodetector experiments.an spectrum through electrical (ESA). spectrum analyzera spectrum Five3-dBTablethrough analyzer lasers coupler. (ESA).1 givesanalyzera with 3-dB (ESA). Five The differenttheir coupler. (ESA). Five nominal FiveThe electroniclasers with signal electroniclasersdifferent after with signalPDlinewidths different was after acquired PDlinewidthswere was andutilized acquired recorded were in andutilizedthe by recorded experiments.an electricalin the by experiments.an spectrum Table electrical 1 analyzergives spectrumTable their (ESA).1 analyzergivesnominal Five their (ESA). nominal Five lasersspecifications.electronic linewidthswith signal specifications.different wereafter PD utilizedlinewidths was inacquired thewere experiments. andutilized recorded in Table the by 1 experiments. angives electrical their nominal spectrumTable specifications.1 givesanalyzer their (ESA). nominal Five lasersspecifications. laserswith laserselectronic differentwith withdifferent signallinewidths different afterlinewidths PDwerelinewidths was utilizedwere acquired wereutilized in andutilizedthe inrecordedexperiments. the in experiments. the by experiments.an Table electrical Table1 gives spectrumTable 1 givestheir 1 givesanalyzernominaltheir theirnominal (ESA). nominal Five specifications.lasers withlasers specifications.different with linewidths different linewidthswere utilized were in utilizedthe experiments. in the experiments. Table 1 gives Table their 1 givesnominal their nominal specifications.specifications.specifications.lasers with different linewidths were utilized in the experiments. Table 1 gives their nominal specifications.specifications. Table 1.Table Nominal Table 1. Nominal specifications1. Nominal specifications specifications of the offive the lasers five of the lasersused five in used lasers thein experiments. used the experiments. in the experiments. specifications.Table 1. Nominal Table specifications1. Nominal specifications of the five lasers of the used five in lasers the experiments. used in the experiments. Table 1. Nominal specifications of the five lasers used in the experiments. Table 1.Table Nominal Table1. Nominal specifications1.Model Nominal specifications specifications of theDFB-LSM-1550-20-PM five of the lasers offive the used lasers five in lasersused the experiments. in used theManufacturer inexperiments. the experiments. Table 1.Model NominalModel specificationsModelDFB-LSM-1550-20-PM of DFB-LSM-1550-20-PM theDFB-LSM-1550-20-PM five lasers usedManufacturer in the experiments. Manufacturer Manufacturer Table 1. NominalTable specifications1. Nominal specificationsModel of the five lasers of the DFB-LSM-1550-20-PMused five in lasers the experiments. used in the experiments. Manufacturer WavelengthModelWavelengthModel Wavelength Model DFB-LSM-1550-20-PM 1550.12nmDFB-LSM-1550-20-PMDFB-LSM-1550-20-PM 1550.12 1550.12nm nm Manufacturer Manufacturer Manufacturer WavelengthModel Wavelength ModelDFB-LSM-1550-20-PM 1550.12nmDFB-LSM-1550-20-PM 1550.12nm Manufacturer Manufacturer NominalWavelengthModel linewidthNominal linewidthDFB-LSM-1550-20-PM1550.12nm 1.1 MHz 1.1 MHz Manufacturer NominalWavelengthNominal linewidthWavelength linewidthWavelengthModel 1550.12nm 1.1 MHzDFB-LSM-1550-20-PM1550.12nm 1.1 1550.12nm MHz Manufacturer NominalWavelength linewidth 1550.12nm 1.1 MHz NominalWavelengthMaxNominal powerlinewidthNominal Wavelength Maxlinewidth power linewidth 1550.12nm 1.1 20 MHzmw 1.1 MHz 1550.12nm 1.1 20 MHzmw NominalMax powerlinewidthMaxNominal power Max powerlinewidth 1.1 20 MHzmw 20 mw 1.1 20 MHzmw NominalMaxModel power linewidth KG-DFB-15-M-10-S-FP 1.1 20 MHzmw Manufacturer ModelMaxNominal powerMaxModel power linewidth KG-DFB-15-M-10-S-FP KG-DFB-15-M-10-S-FP 20 mw 1.1 20 MHzmw Manufacturer Manufacturer Max powerModel MaxModel power 20 KG-DFB-15-M-10-S-FP mwKG-DFB-15-M-10-S-FP 20 mw Manufacturer Manufacturer WavelengthMaxModel powerModel Wavelength Max Model powerKG-DFB-15-M-10-S-FP 1550.12KG-DFB-15-M-10-S-FP 20 mwKG-DFB-15-M-10-S-FP nm 1550.12 20 mw nmManufacturer Manufacturer Manufacturer WavelengthModel Wavelength ModelKG-DFB-15-M-10-S-FP 1550.12KG-DFB-15-M-10-S-FP nm 1550.12 Manufacturernm Manufacturer NominalWavelengthModel linewidthWavelengthNominal linewidthKG-DFB-15-M-10-S-FP1550.12 100 kHz nm 1550.12 100 nm kHz Manufacturer NominalWavelength linewidthWavelengthWavelength Model 1550.12 100 kHzKG-DFB-15-M-10-S-FP1550.12 nm 1550.12 nm nm Manufacturer Nominal NominalWavelength linewidth linewidth 1001550.12 kHz 100 kHz nm NominalWavelengthMaxNominal powerlinewidthNominal Wavelength Maxlinewidth power linewidth 1550.12 100 20 mwkHz 100nm kHz1550.12 100 20 mwkHz nm NominalMax powerlinewidthNominal Max powerlinewidth 100 20 mwkHz 100 20 mwkHz Nominal MaxModel power linewidthMax power Model COSF-SC-1550-M 100 20 mwkHzCOSF-SC-1550-M 20 mw Manufacturer Manufacturer MaxModel powerMaxNominal power Max power linewidth COSF-SC-1550-M 20 mw 20 mw 100 20 mwkHzManufacturer MaxModel power COSF-SC-1550-M 20 mw Manufacturer WavelengthMaxModel powerModel Wavelength Max Model powerCOSF-SC-1550-M 1550.12 20COSF-SC-1550-M COSF-SC-1550-Mmw nmCOSF-SC-1550-M 1550.12 20 mw nmManufacturer Manufacturer Manufacturer Manufacturer WavelengthModel Wavelength ModelCOSF-SC-1550-M 1550.12 nmCOSF-SC-1550-M 1550.12 Manufacturernm Manufacturer NominalWavelengthModel linewidthNominal linewidthCOSF-SC-1550-M1550.12 10 kHz nm 10 kHzManufacturer NominalWavelength linewidthWavelengthWavelength Model 1550.12 10 kHz1550.12 nm 1550.12COSF-SC-1550-M 1550.12 nm nm nm Manufacturer WavelengthMax powerNominalWavelength linewidth 1550.12 10 mw nm 1550.12 10 kHz nm NominalNominal linewidthNominal WavelengthMaxlinewidth power linewidth 10 kHz 10 kHz1550.12 10 kHzmw nm NominalMaxNominal powerlinewidthNominal linewidthMax powerlinewidth 10 10 kHzmw 10 kHz 10 10 kHzmw Nominal MaxModel power linewidth Model SDAS-NLW-PL 10 kHzmw SDAS-NLW-PL Manufacturer Manufacturer MaxModel powerMaxNominal power Max power linewidth SDAS-NLW-PL 10 mw 10 mw 10 kHzmwManufacturer Max powerMaxModel power SDAS-NLW-PL 10 mw 10 mw Manufacturer WavelengthMaxModel powerModel Wavelength Max Model power SDAS-NLW-PL 1550.12 10SDAS-NLW-PL mw nm SDAS-NLW-PL 1550.12 10 mw nm Manufacturer ManufacturerManufacturer WavelengthModelModel Wavelength Model SDAS-NLW-PL 1550.12 SDAS-NLW-PL nmSDAS-NLW-PL 1550.12 Manufacturernm Manufacturer Manufacturer NominalWavelengthModel linewidthNominal linewidthSDAS-NLW-PL1550.12 3 kHz nm 3 kHzManufacturer NominalWavelength linewidthWavelengthWavelength Model 1550.12 3 kHz1550.12 nm SDAS-NLW-PL 1550.12 nm nm Manufacturer WavelengthMax powerWavelengthNominalWavelength linewidth 1550.12 17 mw 1550.12nm 1550.12 3 nm kHz nm NominalNominal linewidthNominal WavelengthMaxlinewidth power linewidth 3 kHz 3 kHz1550.12 17 3 kHz mw nm NominalMax power linewidthNominal Max powerlinewidth 173 kHz mw 17 3 kHz mw NominalMaxModelNominal power linewidth linewidthModel Koheras 17 3 kHz mwBasiK Koheras 3 E15 kHz BasiK Manufacturer E15 Manufacturer MaxModel power MaxNominal power Max power linewidth Koheras 17 mwBasiK 17 mwE15 17 3 kHz mw Manufacturer MaxModel power Koheras 17 mwBasiK E15 Manufacturer WavelengthMaxModel power MaxModel powerWavelength Max Model power Koheras 1550.12 17Koheras BasiKmw Koherasnm 17 BasiK E151550.12 mw 17 BasiKmw E15 nm Manufacturer E15 Manufacturer Manufacturer WavelengthModel Wavelength Model Koheras 1550.12 BasiK Koherasnm E15 1550.12 BasiK Manufacturernm E15 Manufacturer NominalWavelengthModel linewidthNominal linewidth Koheras1550.12 <100 BasiK Hz nm E15 <100 Hz Manufacturer NominalWavelength linewidthWavelengthModelWavelength Model 1550.12 <100 Koheras 1550.12Hz nm Koheras 1550.12 BasiK nm BasiK E15 nm E15 Manufacturer Manufacturer WavelengthMax power NominalWavelength linewidth 1550.12 40 mw nm 1550.12 <100 Hz nm NominalNominal linewidthWavelengthNominal WavelengthMaxlinewidth power linewidth <100 Hz <1001550.12 1550.12 Hz <100 40 nm mw Hz nm NominalMax power linewidth Max power <100 40 mw Hz 40 mw Nominal Max power linewidthNominal linewidth <100 40 mw Hz <100 Hz MaxNominal power MaxNominal power linewidthMax power linewidth 40 mw 40 <100 mw <100 40Hz mw Hz 3.2. FS-BOTDR Setup for Measuring BFS Max power 40 mw 3.2. FS-BOTDR3.2. FS-BOTDRSetup for Measuring SetupMax for BFS Measuring power Max BFS power 40 mw 40 mw 3.2. FS-BOTDR3.2. SetupFS-BOTDR for Measuring Setup for BFS MeasuringMax power BFS 40 mw A3.2. FS-BOTDR FS-BOTDR3.2. FS-BOTDR for Setup measuring Setupfor Measuring for BFSMeasuring change BFS BFS arising from temperature was built to verify the 3.2. FS-BOTDRA FS-BOTDR3.2. SetupFS-BOTDRA FS-BOTDRfor for measuring Measuring Setup for for BFSmeasuring BFSMeasuring change BFSBFS arising change from arising temperature from temperature was built towas verify built the to verify the influence3.2. FS-BOTDR of3.2. the FS-BOTDRSetuplaserA FS-BOTDR linewidthfor Measuring Setup foron for BFSBFSmeasuring Measuring meas urement BFSBFS change accuracy, arising as shown from intemperature Figure 7. was built to verify the A FS-BOTDRAinfluence FS-BOTDRA FS-BOTDRfor of measuringthe for laser measuring for linewidth measuringBFS change BFS on BFSchangeBFS arising meas change arising urementfrom arising temperaturefrom accuracy, fromtemperature temperature as was shown built was in tobuiltFigurewas verify builtto 7. verifythe to verify the the influenceA FS-BOTDR ofinfluence the laserA FS-BOTDRfor linewidthof measuringthe laser foron linewidth BFSmeasuringBFS meas change onurement BFSBFS arising meas change accuracy, urementfrom arising temperature as accuracy, shown from intemperature as Figurewas shown built 7. in to Figurewas verify built 7. the to verify the influenceAinfluence FS-BOTDR ofinfluence the oflaserA the FS-BOTDRfor linewidthof laser measuringthe linewidthlaser foron linewidth BFSmeasuringBFS on meas changeBFS onurement meas BFSBFS arising urementmeas change accuracy, urementfrom accuracy,arising temperature as accuracy, shown from as shown intemperature as Figurewas shown in built Figure 7. in toFigurewas 7.verify built 7. the to verify the influence ofinfluence the laser linewidthof the laser on linewidth BFS meas onurement BFS meas accuracy,urement as accuracy, shown in as Figure shown 7. in Figure 7. influence ofinfluence the laser linewidthof the laser on linewidth BFS meas onurement BFS meas accuracy,urement as accuracy, shown in as Figure shown 7. in Figure 7. Appl. Sci. 2019, 9, 58 8 of 18

3.2. FS-BOTDR Setup for Measuring BFS A FS-BOTDR for measuring BFS change arising from temperature was built to verify the influence ofAppl. the Sci. laser 2018, linewidth 12, x FOR PEER on BFS REVIEW measurement accuracy, as shown in Figure7. 8 of 18

Figure 7. FS-BOTDR setup for temperature sensing. Figure 7. FS-BOTDR setup for temperature sensing. The continuous light from the laser was divided into two beams through a 90:10 coupler. The 10% The continuous light from the laser was divided into two beams through a 90:10 coupler. The beam as reference light beats with the Brillouin backscattering for coherent heterodyne detection. 10% beam as reference light beats with the Brillouin backscattering for coherent heterodyne detection. The polarization scrambler (PS) was for eliminating the polarization noise. The 90% beam was The polarization scrambler (PS) was for eliminating the polarization noise. The 90% beam was attenuated to the proper power via a variable optical attenuator (VOA) and injected into a pulse attenuated to the proper power via a variable optical attenuator (VOA) and injected into a pulse modulator for generating probe pulses. The peak power of the probe pulse was amplified by a pulse modulator for generating probe pulses. The peak power of the probe pulse was amplified by a pulse erbium-doped fiber amplifier (Pulse EDFA) and filtered by a dense wavelength division multiplexer erbium-doped fiber amplifier (Pulse EDFA) and filtered by a dense wavelength division multiplexer (DWDM1) to remove the amplified (ASE) noise. Then, the probe pulse was (DWDM1) to remove the amplified spontaneous emission (ASE) noise. Then, the probe pulse was launched into the sensing fiber through an optical circulator (OC). The Brillouin backscattering was launched into the sensing fiber through an optical circulator (OC). The Brillouin backscattering was amplified by the low-noise EDFA (LN-EDFA), filtered by the DWDM2, and then beats with the reference amplified by the low-noise EDFA (LN-EDFA), filtered by the DWDM2, and then beats with the light in a 13.5-GHz photodetector (PD) through a 50:50 coupler. The beating signal was amplified by reference light in a 13.5-GHz photodetector (PD) through a 50:50 coupler. The beating signal was an electronic low-noise amplifier (LNA) and connected to a microwave heterodyne system. amplified by an electronic low-noise amplifier (LNA) and connected to a microwave heterodyne In the microwave heterodyne system, the beating signal was mixed with a tunable microwave system. source to perform frequency scanning, the output frequency of which increased from 11.2 GHz to In the microwave heterodyne system, the beating signal was mixed with a tunable microwave 11.4 GHz with a fixed frequency internal. The mixed signal was filtered by a BPF with the center source to perform frequency scanning, the output frequency of which increased from 11.2 GHz to frequency of 600 MHz and bandwidth of 87 MHz. The time-domain power trace along the sensing fiber 11.4 GHz with a fixed frequency internal. The mixed signal was filtered by a BPF with the center at every scanned frequency obtained by a logarithmic detector and acquired by the data acquisition frequency of 600MHz and bandwidth of 87 MHz. The time-domain power trace along the sensing (DAQ) digitalizer. Every power trace was averaged 213 times. Eventually, the power points obtained at fiber at every scanned frequency obtained by a logarithmic detector and acquired by the data all scanned frequencies were fitted to the Lorentzian profile in an industrial personal computer (IPC), acquisition (DAQ) digitalizer. Every power trace was averaged 213 times. Eventually, the power for calculating the BFS distribution along the fiber. points obtained at all scanned frequencies were fitted to the Lorentzian profile in an industrial 4.personal Experiment computer Results (IPC), and for Discussions calculating the BFS distribution along the fiber.

4.1.4. Experiment Measurement Results of Laser and Linewidth Discussions The length of the delay fiber can be settled to 25km for measuring the nominal linewidth from 4.1. Measurement of Laser Linewidth 3 kHz to 1.0 MHz [30], and can be settled to 2950 m for less than 100 Hz [31]. The beating spectrums and fittingThe length results of arethe showndelay fiber in Figure can be8. Insettled Figure to8 25kma–d, the for FWHMmeasuring of the the fitted nominal spectrum linewidth was twicefrom 3 kHz to 1.0 MHz [30], and can be settled to 2950 m for less than 100 Hz [31]. The beating spectrums and fitting results are shown in Figure 8. In Figure 8a–d, the FWHM of the fitted spectrum was twice the laser linewidth, hence the measured linewidths of five lasers were, respectively, 1.05 MHz, 101 kHz, 10.2 kHz, and 3.1k Hz, which were close to the nominal specifications. For the linewidth less than 100 Hz, the accurate measured linewidth was calculated by utilizing the value of ΔS by the amplitude difference comparison of coherent envelope (ADCCE) method (See Appendix B) [31], because the length of the 2950 m delay fiber was much shorter than the length of the Appl. Sci. 2019, 9, 58 9 of 18 the laser linewidth, hence the measured linewidths of five lasers were, respectively, 1.05 MHz, 101 kHz, 10.2 kHz, and 3.1k Hz, which were close to the nominal specifications. For the linewidth less than 100 Hz, the accurate measured linewidth was calculated by utilizing the value of ∆S by the amplitude differenceAppl. Sci. 2018 comparison, 12, x FOR PEER of coherentREVIEW envelope (ADCCE) method (See AppendixB)[ 31], because9 of 18 the length of the 2950 m delay fiber was much shorter than the of the measured laser. measured laser. The accurate linewidth was 98 Hz, as shown in Figure 8e, according to the ADCCE The accurate linewidth was 98 Hz, as shown in Figure8e, according to the ADCCE method. method.

(a) Nominal linewidth = 1.1 MHz (b) Nominal linewidth = 100 kHz

(c) Nominal linewidth = 10 kHz (d) Nominal linewidth = 3 kHz

(e) Nominal linewidth < 100 Hz

FigureFigure 8. Linewidth 8. Linewidth measurement measurement results results of five of lasers, five lasers, of which of wh theich nominal the nominal linewidth linewidth are respectively: are (a). 1.1 MHz; (brespectively:). 100 kHz; (ca). 1.1 10 kHz;MHz; ( d(b).). 3100 kHz; kHz; (e ).(c <100). 10 kHz; Hz. (d). 3 kHz; (e). <100 Hz.

4.2. BFS Distribution Measurement To verify whether the built FS-BOTDR is capable of measuring the BFS change normally, the temperature measurements were firstly performed utilizing the five lasers mentioned above as the Appl. Sci. 2019, 9, 58 10 of 18

4.2. BFS Distribution Measurement

Appl.Appl. Sci.ToSci. 20182018 verify,, 1212,, xx whether FORFOR PEERPEER the REVIEWREVIEW built FS-BOTDR is capable of measuring the BFS change normally,1010 ofof 1818 the temperature measurements were firstly performed utilizing the five lasers mentioned above seedasseed the source,source, seed source, respectively.respectively. respectively. FigureFigure Figure 99 givesgives9 gives thethe the configurationconfiguration configuration ofof of thethe the testedtested tested fiber fiberfiber forfor temperaturetemperaturetemperature measurement.measurement. TheThe fiberfiber fiber 1 1 with with the the length length of of 9865 9865 m m and and the the fiber fiberfiber 3 3 with with the the length length of of 305 305 m m werewere placedplaced atat roomroom temperaturetemperature ofof ~25~25~25 °◦°C.C. TheThe fiberfiber fiber 22 withwith the the length length of of 30m 30m was was placed placed in in a a thermostat, thermostat, thethe temperaturetemperature of of which which was was adjusted adjusted to toto change change the thethe BFS BFS of of fiber fiberfiber 2. 2. AsAs a a contrast, contrast, the the BFS BFS of of fiber fiberfiber 1 1 andand fiberfiberfiber 33 werewere keptkept nearlynearly constantconstant inin thethe roomroomroom temperature.temperature.temperature.

FigureFigure 9.9. ConfigurationConfigurationConfiguration of of the the testedtested fiberfiberfiber forfor temperaturetemperature measurement.measurement. During the experiments, the width of the probe pulse light was set to 42 ns and the peak power was DuringDuring thethe experiments,experiments, thethe widthwidth ofof thethe probeprobe pulsepulse lightlight waswas setset toto 4242 nsns andand thethe peakpeak powerpower set to 23.09 dBm. The thermostat temperature was sequentially adjusted to 30 ◦C, 40 ◦C, 50 ◦C, 60 ◦C, waswas setset toto 23.0923.09 dBm.dBm. TheThe thermostatthermostat temperaturetemperature waswas sequentiallysequentially adjustedadjusted toto 3030 °°C,C, 4040 °°C,C, 5050 °°C,C, 6060 and 70 ◦C, respectively. Then, the BFS distribution measured by five lasers at different °°C,C, andand 7070 °°C,C, respectively.respectively. Then,Then, thethe BFSBFS distributidistributionon measuredmeasured byby fivefive laserslasers atat differentdifferent are shown in Figure 10a–e. temperaturestemperatures areare shownshown inin FigureFigure 10a–e.10a–e.

((aa)) LaserLaser linewidthlinewidth == 1.051.05 MHzMHz ((bb)) LaserLaser linewidthlinewidth == 101101 kHzkHz

((cc)) LaserLaser linewidthlinewidth == 10.210.2 kHzkHz ((dd)) LaserLaser linewidthlinewidth == 3.13.1 kHzkHz

Figure 10. Cont. Appl. Sci. 2019, 9, 58 11 of 18 Appl. Sci. 2018, 12, x FOR PEER REVIEW 11 of 18

(e) Laser linewidth = 98 Hz (f) Measured results of BFS versus temperature

FigureFigure 10. 10. BFSBFS distributions distributions at atdifferent different temperat temperaturesures when when the the laser laser linewidth linewidth is: ( is:a) 1.05 (a) 1.05MHz; MHz; (b) 101(b) 101kHz; kHz; (c) 10.2 (c) 10.2 kHz; kHz; (d) 3.1 (d) kHz; 3.1 kHz; and and (e) 98 (e) Hz. 98 Hz.(f) Measured (f) Measured results results of BFS of BFS versus versus temperature. temperature.

FromFrom Figure 10a–e,10a–e, it it can be clearly seen that all obtained BFS BFS for for fiber fiber 2, which was placed in in ◦ ◦ thethe thermostat, thermostat, increased linearlylinearly asas thethe temperaturetemperature increasedincreased from from 30 30°C to 70 °C.C. As As a a contrast, contrast, the the ◦ BFSBFS for fiber fiber 1 and fiber fiber 3, which stayed in the room temperature ofof 2525°C,C, remained remained almost almost constant. constant. Besides,Besides, the the measured measured spatial spatial resolution resolution was was 4.2 4.2 m, m, which which conformed conformed to to the the pulse pulse width width of of 42 42 ns. ns. FigureFigure 10f10f plots the the measured results of BFS versus temperature temperature in in detail, detail, and and the the linear linear fitting fitting was was performed based on on the measured data. It It shows shows that that the the slope slope coefficient coefficient between the the temperature ◦ andand the BFS was 1.14 MHz/°C,C, neatly neatly coincided coincided with with that that we we reported reported previously previously [32]. [32]. The The adjusted adjusted R-squareR-square was 0.99978, which indicates a strong linear relationship. FromFrom the above experimental experimental results, results, it it is is prov provenen that the built FS-BOTDR setup setup was was capable capable of of measuringmeasuring the BFSBFS changechange normally, normally, although although utilizing utilizing five five linewidth-different linewidth-different lasers lasers as the as seedthe seed light lightsource, source, respectively. respectively. In the In following the following section, section, further further experiments experiments were taken were based taken on based this setupon this to setupevaluate to evaluate the influence the influence of the laser of linewidththe laser linewid on theth BGS on spectrum the BGS spectrum and the BFS and accuracy the BFSin accuracy detail. in detail. 4.3. BGS Width Evaluation

4.3. BGSTo verifyWidth theEvaluation influence of the laser linewidth on the BGS width, multiple BFS measurements were taken by utilizing the five lasers mentioned above as the seed source, respectively, when the To verify the influence of the laser linewidth on the BGS width, multiple BFS measurements temperature of the thermostat was fixed at 50 ◦C. The room temperature was kept at a roughly constant were taken by utilizing the five lasers mentioned above as the seed source, respectively, when the temperature of 25 ◦C. The width of the probe pulse was orderly adjusted to 12 ns, 22 ns, 32 ns, and 42 ns, temperature of the thermostat was fixed at 50 °C. The room temperature was kept at a roughly with the same peak power of 23.09 dBm. For further analysis, we extracted the measured BGSs at constant temperature of 25°C. The width of the probe pulse was orderly adjusted to 12 ns, 22 ns, 32 9880 m of tested fiber, the middle of the heated fiber, and fitted them to the Lorentzian profile based ns, and 42 ns, with the same peak power of 23.09 dBm. For further analysis, we extracted the on the Levenberg-Marquart algorithm. These BGSs were finally normalized by peak power and are measured BGSs at 9880 m of tested fiber, the middle of the heated fiber, and fitted them to the presented in Figure 11a–e, where the relative frequency of the horizontal axis was obtained by f − f . Lorentzian profile based on the Levenberg-Marquart algorithm. These BGSs were finally normalizedB The BGS widths versus the laser linewidth is summarily plotted in Figure 11f, when the width of the by peak power and are presented in Figure 11a–11e, where the relative frequency of the horizontal probe pulse was increased from 12 ns to 42 ns. axis was obtained by f - fB. The BGS widths versus the laser linewidth is summarily plotted in Figure From Figure 11f, the BGS width narrowed from ~108 MHz to ~88 MHz as the probe pulse width 11f, when the width of the probe pulse was increased from 12 ns to 42 ns. was increased from 12 ns to 42 ns, which roughly agrees with the theoretical simulations (see Figure3b, From Figure 11f, the BGS width narrowed from ~108 MHz to ~88 MHz as the probe pulse width blue line). However, the BGS width showed no distinct tendency as the laser width was broadened was increased from 12 ns to 42 ns, which roughly agrees with the theoretical simulations (see Figure from 98 Hz to 1.05 MHz. Hence, it proves that the measured BGS width depended largely on the 3b, blue line). However, the BGS width showed no distinct tendency as the laser width was probe pulse width when the laser linewidth was less than 1MHz, which conformed to the conclusion broadened from 98 Hz to 1.05 MHz. Hence, it proves that the measured BGS width depended largely reported previously [23]. on the probe pulse width when the laser linewidth was less than 1MHz, which conformed to the conclusion reported previously [23]. Appl. Sci. 2019, 9, 58 12 of 18

Appl. Sci. 2018, 12, x FOR PEER REVIEW 12 of 18

(a) Linewidth = 1.05 MHz (b) Linewidth = 101 kHz

(c) Linewidth = 10.2 kHz (d) Linewidth = 3.1 kHz

(e) Linewidth = 98 Hz (f) BGS widths versus laser linewidth and pulse width

FigureFigure 11. 11. NormalizedNormalized BGS BGS extracted extracted at atthe the middle middle of ofthe the heated heated fiber fiber when when the thelaser laser linewidth linewidth is: (a is:) 1.05(a) 1.05 MHz, MHz, (b) (101b) 101 kHz,( kHz,c) 10.2 (c) 10.2 kHz, kHz, (d) ( d3.1) 3.1 kHz, kHz, and and (e) ( e98) 98 Hz; Hz; (f ()f BGS) BGS widths widths versus versus laser laser linewidth linewidth andand pulse pulse width. width.

4.4. BFS Accuracy Evaluation For further evaluating the influence of the laser linewidth on the BFS accuracy, the measured BFS over the heated fiber were specially extracted and are shown in the inset of Figure 12a–e, Appl. Sci. 2019, 9, 58 13 of 18

4.4. BFS Accuracy Evaluation Appl.For Sci. further2018, 12, x evaluating FOR PEER REVIEW the influence of the laser linewidth on the BFS accuracy, the measured13 of 18 BFS over the heated fiber were specially extracted and are shown in the inset of Figure 12a–e, eliminating the eliminating the rise and fall edge of BFS change. The root-mean-square errors (RMSEs) of the riseextracted and fall BFS edge distribution of BFS change. were Thecalculated root-mean-square and plotted versus errors (RMSEs)the laser linewidth of the extracted and pulse BFS width, distribution as wereshown calculated in Figure and 12f. plotted versus the laser linewidth and pulse width, as shown in Figure 12f.

(a) Linewidth = 1.05 MHz (b) Linewidth = 101 kHz

(c) Linewidth = 10.2 kHz (d) Linewidth = 3.1 kHz

(e) Linewidth = 98 Hz (f) BFS RMSEs versus laser linewidth and pulse width

FigureFigure 12. 12.Measured Measured BFSBFS distributiondistribution when when the the linewidth linewidth is: is: (a ()a 1.05) 1.05 MHz, MHz, (b) ( b101) 101 kHz, kHz, (c) 10.2 (c) 10.2 kHz, kHz, (d()d 3.1) 3.1 kHz, kHz, and and ( e(e)) 9898 Hz;Hz; ((ff) BFS root-mean-square root-mean-square errors errors (RMSEs (RMSEs)) versus versus laser laser linewidth linewidth and and probe probe pulsepulse width. width.

From Figure 12f, it can be seen that the RMSE of BFS was related with both the laser linewidth and the probe pulse width. It decreased obviously when the pulse width was extended from 12 ns to Appl. Sci. 2019, 9, 58 14 of 18

From Figure 12f, it can be seen that the RMSE of BFS was related with both the laser linewidth and the probe pulse width. It decreased obviously when the pulse width was extended from 12 ns to 42 ns. When the pulse width was fixed, the RMSE of BFS decreased with the laser linewidth narrowing from 1.05 MHz to 3.1 kHz, which was in good agreement with the numerical simulations. However, it unexpectedly increased as the laser linewidth narrowed from 3.1 kHz to 98 Hz, which was inconsistent with the simulation results. We contribute this exception to the coherent Rayleigh noise (CRN). The CRN increases sharply as the laser linewidth becomes narrower [33]. Additionally, it has been proven that the CRN cannot be reduced by signal averaging [34]. Hence, the accuracy of BOTDR will decrease once the linewidth of the seed laser becomes narrow to a certain value, such as 98 Hz in this paper, because the extremely-narrow laser linewidth enhances the CRN largely and further results in sharp SNR deterioration of the BOTDR. Based on the above analysis, it was demonstrated that the BFS accuracy improves when the laser linewidth narrows. However, the BFS accuracy will deteriorate when the laser linewidth is so narrow that the CRN is enhanced sharply. The measured results of BFS RMSE and BGS width (WBGS) by respectively utilizing five different-linewidth lasers as the seed source are summarily listed in Table2, where the probe pulse width was 12 ns, 22 ns, 32 ns, and 42 ns with the same peak power of 23.09 dBm.

Table 2. Summary list of measured results in experiments.

Laser Peak 12 ns 22 ns 32 ns 42ns Linewidth Power RMSE WBGS RMSE WBGS RMSE WBGS RMSE WBGS —— dBm MHz MHz MHz MHz MHz MHz MHz MHz 1.05 MHz 23.09 1.090 108.6 0.524 93.6 0.399 92.2 0.360 89.5 101 kHz 23.09 1.084 106.9 0.521 91.6 0.397 90.2 0.358 89.2 10.2 kHz 23.09 1.021 105.8 0.460 90.9 0.335 90.5 0.272 89.2 3.1 kHz 23.09 0.805 108.6 0.424 93.3 0.261 90.9 0.212 89.5 98 Hz 23.09 1.051 107.9 0.531 92.2 0.409 88.8 0.306 89.8

5. Conclusions In this paper, the influence of the laser linewidth on BFS accuracy in the FS-BOTDR was analyzed. The BGS broadening effect and the SNR of the FS-BOTDR was numerically simulated by taking phase fluctuation as the major noise contribution. The simulation results presented that the RMSE of BFS decreases when the laser linewidth narrows. In the experiments, we utilized five different lasers as the seed source, respectively, to measure the BFS change. The linewidth of the five lasers were, correspondingly, 1.05 MHz, 101 kHz, 10.2 kHz, 3.1 kHz, and 98 Hz. As the pulse width increased from 12 ns to 42 ns, the BGS width and BFS accuracy were further evaluated and discussed in detail. The experimental results indicate that the BFS accuracy improves with the laser linewidth narrowing. However, the BFS accuracy will deteriorate when the laser linewidth decreases to a certain value, such as 98 Hz in this paper. The exception may arise from the increasing CRN related closely with the narrowing linewidth. Therefore, how the CRN affects the BFS accuracy needs to be further theoretically explained and experimentally verified in future, if an extremely-narrow-linewidth laser is utilized in a FS-BOTDR. The results in this paper will be helpful to choose an appropriate laser for BOTDR, and provide potential techniques for improving the measurement accuracy of temperature or strain based BOTDR.

Author Contributions: B.J. proposed the idea; Q.B. performed the theoretical analysis and wrote the paper; M.Y. performed the temperature experiments; B.X. tested the laser linewidths; D.W. and Y.W. analyzed the data; H.Z., Y.G. and M.Z. revised the manuscript. Funding: This research was funded in part by the National Natural Science Foundation of China (61805167), in part by the Coal-Bed Methane Joint Research Fund of Shanxi Province, China (2015012005 and 2016012011), and in part by the Social Development Project of Shanxi Province Key Research Plan (201703D321034). Appl. Sci. 2019, 9, 58 15 of 18

Acknowledgments: The 1.05-MHz-linewidth laser and the 3.1-kHz-linewidth laser used in the experiments were freely provided by the Tianjin Opeak Technology Co. Ltd and Laser Institute of Shandong Academy of Science (LISD) in China, respectively. They are very helpful to the experiments in this paper. The authors thank the two companies very much. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A

Table A1. The model parameters for numerical simulations.

Parameter Symbol Value Unit BGS width for continuous light w 28 MHz Brillouin frequency shift f B 10.7 GHz Startting frequecy for scanning f 10.4 GHz frequency s Frequency step f step 1 MHz Number of frequency-scanning points N 671 —— Bandwidth of the BPF B 87 MHz in vacuum c 3×108 m/s Refractive index n 1.5 —— Pulse width τ 12, 22, 32, 42, 52 ns Laser linewidth ∆f 100, 3000, 10,000, 100,000, 1,050,000 Hz Optical path difference ∆L 20 km

Appendix B AppendixB mainly describes how the laser linewidth was measured with the delay fiber, the length of which was much shorter than the coherence length of the measured laser. It is well known that self-heterodyne interferometer (DSHI) is a frequently-used technology to measure laser linewidth. The output power spectrum of the DSHI can be expressed by S(f, ∆f )[31]:

S( f , ∆ f ) = S1S2 (B1)

2 2 P0 ∆ f S1 = (B2) 2 2 4π ∆ f + ( f − f1)

sin[2π( f − f1)τd] S2 = 1 − exp(−2π∆ f τd)[cos[2π( f − f1)τd] + ∆ f ] (B3) f − f1 where f is the optical frequency, and f 1 = 200 MHz is the frequency shift of AOM. τd = nL/c is the delay time caused by the delay fiber, L = 2950 m is the length of delay fiber, c = 3 × 108 m/s is the speed of light in vacuum, n = 1.5 is the refractive index, and ∆f = 98 Hz is the laser linewidth. The normalized power spectra of S(f, ∆f ), S1, and S2 obtained by numerical simulation are plotted in Figure A1a. It has been experimentally and theoretically proven that the value of the contrast difference between the second peaks and second troughs (CDSPST, denoted as ∆S), as shown in Figure A1a, is related closely to the product of the measured laser linewidth and the length of delay fiber. The relationship curve is plotted in Figure A1b. Appl. Sci. 2019, 9, 58 16 of 18 Appl. Sci. 2018, 12, x FOR PEER REVIEW 16 of 18

(a) (b)

FigureFigure A1. A1.( a(a)) Normalized Normalized powerpower spectraspectra ofof S;(; (b)) relationshiprelationship curve between Δ∆SS andand Δ∆f⋅fL.·L.

Hence,Hence, the the value value of of∆ ΔSScan can be be used used for for calculating calculating the the measured measured laser laser linewidth linewidth once once the the length length of theof delaythe delay fiber isfiber fixed. is Fromfixed. FigureFrom8 e,Figure the obtained 8e, the valueobtained of ∆ valueS was 25.95of ΔS dB, was and 25.95 the correspondingdB, and the valuecorresponding of ∆f ·L was value 288921 of Δ Hzf⋅L ·wasm,as 288921 shown Hz in∙m, Figure as shown A1b. in Figure A1b. Thus,Thus, thethe laserlaser linewidthlinewidth cancan bebe calculatedcalculated according to the below expression: 288921 Δ=f 288921 ≈98 Hz ∆ f = ≈ 98 Hz 2950

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