High-Speed Demodulation of weak FBGs Based on Microwave Photonics and Chromatic Dispersion

Transcription

1 Hgh-Speed Demodulaton of weak FBGs Based on Mcrowave Photoncs and Chromatc Dsperson EI ZHOU 1, ZHENGYING I 1,2, *, NA XIANG 1 1 Key aboratory of Fber Optc Sensng Technology and Informaton Processng (Wuhan Unversty of Technology), Mnstry of Educaton, Wuhan , Chna 2 Natonal Engneerng aboratory for Fber Optc Sensng Technology, Wuhan Unversty of Technology, Wuhan , Chna *Correspondng author: zhyl@whut.edu.cn Receved XX Month XXXX; revsed XX Month, XXXX; accepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); publshed XX Month XXXX A hgh speed quas-dstrbuted demodulaton method based on the mcrowave photoncs and the chromatc dsperson effect s desgned and mplemented for weak fber Bragg gratngs (FBGs). Due to the effect of dsperson compensaton fber (), FBG wavelength shft leads to the change of the dfference frequency sgnal at the mxer. Wth the way of crossng mcrowave sweep cycle, all wavelengths of cascade FBGs can be hgh speed obtaned by measurng the frequences change. Moreover, through the ntroducton of Chrp-Z and Hannng wndow algorthm, the analyss of dfference frequency sgnal s acheved very well. By adoptng the sngle-peak flter as a reference, the length dsturbance of caused by temperature can be also elmnated. Therefore, the accuracy of ths novel method s greatly mproved, and hgh speed demodulaton of FBGs can easly realze. The feasblty and performance are expermentally demonstrated usng 105 FBGs wth 0.1% reflectvty, 1 m spatal nterval. Results show that each gratng can be dstngushed well, and the demodulaton rate s as hgh as 40 khz, the accuracy s about 8 pm. OCIS codes: Fber Bragg gratng; mcrowave photoncs; chromatc dsperson; hgh-speed demodulaton. Fber Bragg gratngs (FBGs) can be made nto a varety of sensors, and easy to form a sensng network, whch have been wdely appled n constructon, chemcal, mltary and avaton [1, 2]. But n some specal felds such as aero-engne testng [3], vbraton detecton [4], structural health montorng [5], the detecton of hgh frequency sgnal s lmted by tradtonal demodulaton technques. As a result, hgh speed demodulaton s one of the key technologes to solve the practcal applcaton of FBGs n specal felds. Recently, weak FBG has attracted a close attenton because of ts extremely weak reflectvty, whch wll effectvely reduce the crosstalk between multple gratngs, and greatly ncrease the multplexng capacty and scale of FBG sensng network [6, 7]. Many scholars have carred out actve exploraton n hgh speed demodulaton of weak FBGs. By the method of Fourer doman mode locked (FDM) swept laser [8], eghteen weak gratngs are nterrogated smultaneously wth a rate of 120 khz. However, due to the wavelength sweepng rate of 2.66 nm/μs, the spatal resoluton of FBGs s 20 m. A tme-dvson multplexng (TDM) sensng network wth 12 weak FBGs s verfed [9], n whch spatal resoluton s 0.2 m and accuracy s 10 pm. But lmted to the establshment tme of the tunable laser, t takes 1.5 mn to complete once detecton. For mprovng the demodulaton speed, ths group demonstrated a hgh speed technque for weak FBGs by a pulsed lght source and a chromatc dsperson unt, and demodulated speed of 20 khz s expermentally realzed [10]. But ths method requres extremely hgh samplng rate, such as 40 GHz, whch result n dffcult engneerng applcaton. A demodulaton method of weak FBGs wth 10.2 cm spatal resoluton s also mentoned based on montorng the mcrowave responses [11]. But ts demodulaton speed s lmted by the scannng tme of vector network analyzer (VNA) and the optcal band-pass flter. In addton, the demodulaton technques adoptng frequency-shfted nterferometry [12], optcal low coherent reflecton measurement (OCR) [13], mcrowave asssted technque [14] and unbalanced Mach-Zehnder nterferometer [15] are also reported. However, wavelength scannng or tunable flter stll cannot be avoded generally, whch nduces a slow demodulaton speed of FBGs. And some of these schemes also have problems such as poor stablty and complex structure. In ths etter, we propose a hgh speed quas-dstrbuted demodulaton method based on the mcrowave photoncs and the chromatc dsperson effect. The scheme uses broadband lght source and dsperson compensaton fber (), and wavelength shft of weak FBGs are transformed nto frequency doman. By ntroducng the Chrp-Z and Hannng wndow algorthm, the analyss of dfference frequency sgnal whch demodulaton based s acheved very well. Thus, wth the way of crossng mcrowave sweep cycle, all wavelengths of cascade FBGs can be hgh speed demodulated. Snce the dfference frequency sgnal produced by the mxer s very low, hgh samplng rate s not needed n the demodulaton. Furthermore, we elmnate the length dsturbance of caused by temperature wth adoptng the sngle-peak flter as a reference. In contrast to tradtonal mcrowave demodulaton technologes [16-18], requrng none of wavelength scannng, tunable flter, VNA or hgh samplng rate osclloscope, the demodulaton of weak FBGs at hgh speed s easly realzed wth ths scheme. The prncples of above methods are descrbed n detal, and experments are carred out. The prncple dagram s shown n Fg.1. A broadband lght from amplfed spontaneous emsson (ASE) laser s electro-optcally modulated wth a mcrowave (MW) sgnal. At the output of electrooptc modulator (EOM), the optcal sgnal s splt nto two ways. One s reflected by the FBG sensng network after passng the

2 crculator, and the other s transmtted by the sngle-peak flter (SPF). The SPF has characterstc that ts peak wavelength doesn t change wth temperature, whch s used as a reference. Then, the two ways of optcal sgnal are coupled nto the delay fber and. For the realzaton of crossng sweep cycle accurately, a secton of delay fber s adopted. And s use to provde dsperson for the wavelength to frequency converson. In the system, the optcal band-pass flter and Erbum-doped optcal fber amplfers (EDFA) are used to mprove the sgnal-nose rato (SNR). After the photodode, the sgnals from FBGs and SPF produce dfference frequency wth the orgnal MW sgnal at the mxer and fnally collected by data acquston (DAQ). 0 2n 0 2n eff eff SPF# r FBG# n n n / c NT T (5) / c NT T,( N 0,1,2 ) In Eqs. (4) and (5), SPF#r and FBG#n are the poston of the snglepeak flter and the last gratng, respectvely. N s the number of cycles. When above relatons are satsfed, the sngle-peak flter and all of FBGs produce dfference frequency only wth the N+1 cycle MW sgnal, whch effectvely mproved the demodulaton speed for N tmes. Thus, the frequency alasng wll not occur and hgh speed demodulaton s easly to realze. Fg. 1. Schematc of the proposed system based on mcrowave photoncs and chromatc dsperson. The MW sgnal whose frequency vares lnearly wth tme can be descrbed as: f t f0 Bt / T, 0 t T (1) Where B and T are, respectvely, the frequency bandwdth and the sweep cycle, whle f0 and t are the ntal frequency and the tme varable. In order to acqure the dfference frequency sgnal of the mxer, a mcrowave low-pass flter s used. After flterng the hgh frequency by ths flter, the dfference frequency sgnal V(t) can be expressed as: V t V cos 2Btt / T (2) Therefore, the frequency of V(t) can be descrbed as: f Bt / T B2neff n / Tc (3) Where Δt s the tme dfference between the orgnal and the reflected MW sgnal. V, φ, and are the sgnal ampltude, the ntal phase, the length of sensng fber and the length of, respectvely. neff and n are the effectve ndces of sensng fber and, c s the speed of the lght n vacuum. By Eq. (3), t s known that the dfference frequency sgnal Δf depends on the tme dfference Δt. Wth a long length of provdng the dsperson n system, Δt wll be qute large. In order to avod the frequency alasng, a long sweep cycle T (T > Δt) s generally requred, as shown n Fg. 2(a). In pcture, the orgnal and reflected MW sgnal are shown wth black sold and colorful dash lne, respectvely. However, long sweep cycle T means slow demodulaton rate. For hgh speed demodulaton, we take the way of crossng sweep cycle to form the dfference frequency sgnal, as see n Fg. 2(b) and Fg. 2(c). The sweep cycle T s set smaller than the tme dfference Δt. In ths way, the relatonshp between the sweep cycle T and the length of sensng fber should frstly be satsfed: T n / c (4) Secondly, t should be satsfed: 2 eff Fg. 2. The formng way of dfference frequency sgnal (a) the generally way, (b) the way of crossng sweep cycle, (c) the frequency of dfference frequency sgnal. For the purpose of demodulatng FBG wavelength more and more accurately, t s necessary to consder the length dsturbance of caused by external temperature n long tme demodulaton. We adopt the sngle-peak flter as a reference to elmnate t. ΔfSPF#r and ΔfFBG# are the dfference frequency sgnal produced by the sngle-peak flter SPF#r and the sensng gratng FBG# respectvely, and can be expressed as: fspf#r [2neff SPF#r / c ( ) n / c NT] B/ T (6) ffbg# [2neff ( SPF#r d)/ c ( ) n / c D ( ) NT] B/ T r In Eq. (6), d s the dstance between SPF#r and FBG#, and Δ s the length varaton of nduced by dsturbances. D(λ-λr) s the tme delay caused by the dsperson effect. Wheren, λr and λ are the center wavelengths of SPF#r and FBG#, respectvely, and D s the total dsperson of. Through DAQ to collect sgnals of the photodode, the frequency dfference f between ΔfSPF#r and ΔfFBG# can be obtaned wth the demodulaton algorthm, and can be descrbed as: f 2n d / c D ( )] B/ T (7) [ eff r As shown n Eq. (7), the length varaton s offset by usng the sngle-peak flter as a reference, whch makes the stablty and accuracy further mproved. Meanwhle, due to the sngle-peak wth a constant wavelength λr, when the wavelength λ of FBG# changes, t wll cause the frequency dfference f change. Ths relaton can be expressed as: f T / BD (8) Wheren, Δλ and Δf are the varatons of λ and f, respectvely. Thus, the wavelength demodulaton of weak FBGs can be realzed only by the frequency varaton Δf accordng to Eqs. (8) obvously. Fast Fourer transform (FFT) s used for frequency analyss n our demodulaton algorthm. However, t s known that the frequency resoluton of FFT depends on the samplng tme. If T and B are set as 25 μs and 1 GHz, a wavelength resoluton of 1 pm

3 requres a frequency resoluton of 80 Hz accordng to Eq. (8). To acheve ths resoluton should sample 500 cycles. Obvously, the samplng tme s too long to acheve hgh speed demodulaton. Therefore, we ntroduce Chrp-Z algorthm to zoom the frequency sgnal. One cycle of sgnals wth MHz frequency s smulated and moved 1 khz. We use FFT and Chrp-Z to process t. Fg. 3. The frequency spectrum processed by FFT and Chrp-Z. As shown n Fg. 3, black lnes are the processed results of FFT, whle red lnes for Chrp-Z. The dash lnes are the results when frequency movng. For T of one cycle sgnal s 25 μs, the frequency resoluton of FFT s 40 khz n Fg. 3, whch s hard to locate the peak and dsplay the change. By adoptng Chrp-Z algorthm, the zoomng frequency resoluton s 50 Hz, whch can accurately locate the peak of MHz and dsplay the varaton of 1 khz. However, when dealng wth the dfference frequency sgnals of mult-gratng, there s stll a problem to be solved. The gratng spacng of our FBG network s 1 m, so we smulate the sgnal of two gratngs wth 1 m spacng and process t by Chrp-Z algorthm. As shown n Fg. 4(a) wth black lne, the frequency sdelobes overlap each other and wll nfluence the peak-fndng accurate. By usng Hannng wndow to reduce the spectrum leakage, the result s shown n the red lne of Fg. 4(a). The spectrum leakage s very small and almost no sdelobes overlap. We analyss the peakfndng accurate of Chrp-Z and Chrp-Z + Hannng algorthms by smulaton, and the results are gven n Fg. 4(b) and Fg. 4(c). In the smulaton, the frequency of FBG#1 s constant whle FBG#2 s shfted 2 khz each tme. Fg. 4. The processng results of Chrp-Z and Chrp-Z + Hannng algorthm (a) the frequency spectrum of two algorthm, (b) the peakfndng errors of FBG#1, (c) the peak-fndng errors of FBG#2. In Fg. 4(b), when only usng the Chrp-Z algorthm, the overlap stll has an nfluence on the accuracy. The frequency of FBG#1 should not change, but the max change of FBG#1 s 1200 Hz, whch s about 15 pm of wavelength error due to Eq. (8). And the frequency shft of FBG#2 also cannot match the settng value of horzontal axs. However, almost no nfluence when usng Chrp-Z + Hannng wndow. The frequency of FBG#1 s not changed and the shft of FBG#2 also match the settng. In Fg. 4(c), there s stll an error of FBG#2 when usng Chrp-Z wthout Hannng wndow. Due to the spectrum energy nteracts wth each other, the error of FBG#2 s just the opposte of FBG#1. As we can see n Fg. 4(b) and 4(c), these errors are nearly solved after addng the Hannng wndow. Therefore, by ntroducng the Chrp-Z + Hannng wndow algorthm, the peakfndng accurate of mult-gratng s effectvely mproved even wth only one cycle of tme doman sgnals, whch makes the hgh speed demodulaton easly realzed. For the zoomng resoluton of 50 Hz, the theoretcal wavelength resoluton of the system s about pm accordng to Eq. (8). We fabrcated 105 dentcal weak FBGs wth 1550 nm center wavelength along one optcal fber to verfy the performance of the proposed system. The spacng of FBGs s 1 m, and the peak reflectvty s 0.1 %. The frequency bandwdth B and the sweep cycle T of MW sgnal are set as 1 GHz and 25 μs, and the samplng rate of DAQ s 2 GHz. The length and total dsperson of are about 14.7 km and ns/nm, respectvely. In order to satsfy the constrants of Eqs. (4) and (5), a secton of delay fber (500 m) s attached to the coupler 2. Wth calculaton, the frequency alasng wll not occur and hgh speed demodulaton can be realzed. Fg. 5. The waveforms of 105 weak FBGs (a) tme doman waveform of eght cycles, (b) one cycle of tme doman waveform, (c) frequency spectrum waveform. Fg. 5(a) s the tme doman waveforms acqured by the DAQ. One cycle of tme doman sgnals are ntercepted from Fg. 5(a), as seen n Fg. 5(b), and processed by the Chrp-Z + Hannng wndow algorthm, so the frequency spectrum can be obtaned, as Fg. 5(c) shown. In Fg. 5(c), each gratng can be dstngushed well wth the demodulaton of ths system. The reason why the ampltude of the spectrum for each gratng fluctuates greatly s that all of FBGs are wrtten by hand. In the followng, we tested the demodulaton system by temperature, stran and vbraton experments. In long tme demodulaton, the length dsturbance of wll greatly affect the change of dfference frequency sgnal, resultng n serous error. We elmnate t by adoptng the sngle-peak flter as a reference. Temperature wth s carred out to verfy t. Durng the experment, s put nto the thermotank whose temperature changes from 6 to 51, and FBG#1 of the sensng network s stck on the thermostat wth a constant temperature.

4 The thermotank s used to smulate the external dsturbance, and we collect data every 3. Accordng to Eq. (8), demodulatons are performed n two ways, one s based on the frequency change of FBG#1, and another s the use of reference. The results are shown n Fg. 6(b), dotted lne and sold lne, respectvely. After processng by the Chrp-Z + Hannng wndow algorthm, Fg. 7 s the frequency spectrum. In Fg. 7, the frequency spectrum shft when FBG#1 s subjected to stran. Due to wth a negatve dsperson coeffcent, when the center wavelength of FBG n the OSA shfted to rght for nm, the frequency spectrum shfted to left for 8400Hz. So the wavelength varaton can be calculated for nm by Eq. (8), whch s bascally the same wth the OSA. Thus t s proved the proposed system s feasble, the converson of frequency to wavelength can be acheved well. Fg. 6. The results of temperature experment wth (a) the change of frequency spectrum, (b) the demodulaton results of two ways. In Fg. 6(a), the frequency spectrum shfts as a whole when s heated. The dfference frequency of FBG#1 changes, even f the wavelength of FBG#1 s constant. Thus, f based on the frequency change of FBG#1, the demodulaton error wll very larger. As llustrated n Fg. 6(b), the max change and standard devaton (STD) of demodulaton results are pm and 4211 pm, respectvely. However, by usng the sngle-peak flter as a reference, the demodulaton results almost unchanged. The max change and STD of results are 8 pm and 2.1 pm. Consequently, the usng of snglepeak flter as a reference, can effectvely weaken the nfluence of external dsturbance, whch greatly mproved the stablty and accuracy n long tme demodulaton. Next, the feasblty and accuracy of the system are verfed by the stran experment. In order to compare the demodulaton results wth the Optcal Spectrum Analyzer (OSA), at the port 3 of the crculator, a part of sgnal s transmtted to the OSA by a lght spltter. Snce OSA cannot demodulate dentcal FBGs array, a large bend loss s created between the FBG#1 and FBG#2, so that only the reflected lght from FBG#1 can be returned. Before the stran experment, the frequency dfference of FBG#1 and the sngle-peak flter s calbrated to be MHz. Takng nto account the mechancal strength of FBG, the stran vares n the range of 0 με to 1500 με, and the nterval s 50 με. Durng the stran appled to FBG#1 wth a precson adjust devce, we measured the dfference frequency sgnal by DAQ. Fg. 8. The demodulaton results of the stran experment. The results of the system and the OSA at same stran condton are also shown n Fg.8, where X axs represents the wavelength measured by the OSA and Y for ths system. In Fg. 8, lnear fttng of measurng ponts are made. The R-square of fttng curve s , and the Root mean square error (RMSE) s 8.1 pm. Whch means the demodulaton accuracy of ths system s about 8.1 pm. astly, we carred out a hgh speed vbraton experment to verfy the 40 khz demodulaton speed of the system. Specfcally, the last two weak FBGs of the sensng network are made as vbraton sensors and fxed on the vbraton test bench (Denmark B&K Company). Wth the acton of 2 khz sne vbraton sgnal, the system has demodulated the wavelength of FBG sensors. Fg. 9. The demodulaton results of dynamc sgnal (a) wavelength doman dagram, (b) the frequency spectrum dstrbuton. Fg. 7. The transformaton of gratng spectrum to frequency doman. Fg. 9(a) shows the wavelength vares n the tme doman, n whch black lne represents the demodulaton results of FBG#104 and red lne for FBG#105. In Fg. 9(a), there are 40 samplng ponts n two cycle of 2 khz vbraton sgnal, and the tme nterval of each samplng ponts s 25 μs. Smlarly, another FBG s the same condton, and the dfference n the change of wavelength s due to the senstvty of the two vbraton sensors. Accordng to the sweep cycle T and the samplng ponts of vbraton sgnal, t can be analyzed that the demodulaton rate of the system reaches 40 khz.

5 Fg. 9(b) shows the frequency spectrum dstrbuton acqured by makng FFT of the vbraton wavelengths. As we can see n Fg. 9(b), the vbraton frequences of two sensors demodulated by the system are 2 khz, whch are consstent wth the frequency we have set. In the nset graph, the hgh frequency doublng of 6, 8, 10 and 12 khz can be seen clearly. Accordngly, the vbraton experment demonstrate that the system s deal for the demodulaton of vbraton sgnals, wth complete waveform and hgh response, and the rate s up to 40 khz. In summary, we propose and realze a hgh speed quasdstrbuted demodulaton system for weak FBGs based on the mcrowave photoncs and the chromatc dsperson. Due to the dsperson effect of, wavelength shft of FBGs are transformed nto frequency doman. Wth the way of crossng mcrowave sweep cycle, all wavelengths of cascade FBGs can be hgh speed demodulated by measurng the change of dfference frequency sgnal. Moreover, through adoptng the Chrp-Z and Hannng wndow algorthm, the analyss of dfference frequency sgnal whch demodulaton based s acheved very well. And by usng the sngle-peak flter as a reference, the length dsturbance of caused by temperature s also elmnated, whch makes the accuracy and stablty further mproved. Compared to tradtonal FBG wavelength demodulaton technologes, ths novel method provdes many advantages such as hgher speed and lower samplng rate. Experments show that the system can realze the wavelength demodulaton of weak FBGs wth 0.1% reflectvty, 1 m spatal nterval. It has a good statc and dynamc demodulaton capablty, whle the demodulaton rate s as hgh as 40 khz, the accuracy s about 8 pm, respectvely. 16. J. P. Yao and Q. Wang, IEEE Photon. Technol. ett. 19, 644 (2007). 17. A.. Rcchut, J. Hervás, D. Barrera, S. Sales, and J. Capmany, IEEE Photon. J. 6, 1 (2014). 18. S. Werznger, S. Bergdolt, R. Engelbrecht, T. Thel, and B. Schmauss, J. ghtwave Technol. 34,5270 (2016). Fundng. Natonal Natural Scence Foundaton of Chna ( ). References 1. A. D. Kersey, M. A. Davs, H. J. Patrck, M. eblane, K. P. Koo, C. G. Askns, M. A. Putnam, and E. J. Frebele, J. ghtwave Technol. 15, 1442 (1997). 2. A. ambert, S. Vanlandut, P. B. De, and F. Berghmans, Opt. Express 22, 7099 (2014). 3. H. Sekne, S. E. Fujmoto, T. Okabe, N. Takeda, and T. Y. Jr, Appl. Compos. Mater. 13, 87 (2006). 4. T. C. ang, Y.. n, Opt. Commun. 285, 2363 (2012). 5. Y. Da, Y. u, J. eng, G. Deng, and A. Asund, Opt. aser. Eng. 47, 1028 (2009). 6. R. Cheng,. Xa, C. Sma, Y. Ran, J. Rohollahnejad, J. Zhou, Y. Q. Wen, and C. Yu, Opt. Express 24, 2466 (2016). 7. E. Wkszak, J. Thomas, S. Klngebel, B. Ortac, J. mpert, S. Nolte, and A. Tünnermann, Opt. ett. 32, 2756 (2007). 8. Y. M. Wang, C. C. Hu, Q. u, H. Y. Guo, G.. Yn, and Z. Y., Acta Phys. Sn. 20, (2016). 9. Y. Wang, J. Gong, D. Y. Wang, B. Dong, W. B, and A. Wang, IEEE Photon. Technol. ett. 23, 70 (2011) Ma, C. Ma, Y. Wang, D. Y. Wang, and A. Wang, IEEE Photon. Technol. ett. 28, 1344 (2016) Xa, R. Cheng, W., and D. u, IEEE Photon. Technol. ett. 27, 323 (2015). 12. B. Q, F. Ye,. Qan, and H. K. o, Opt. ett. 38, 1083 (2013). 13. W. u, Z. G. Guan, G. u, G. Yan, and S. He, Sensor Actuat. A Phys. 144, 64 (2008). 14. H. Xao, J. Huang,. Hua, T. We, and X. an, Opt. Express 21, (2013). 15. J. Zhou,. Xa, R. Cheng, Y. Wen, and J. Rohollahnejad, Opt. ett. 41, 313 (2016).