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Abstract
We developed a large multiplexing capacity dense ultra-short (DUS)-FBG array for high spatial resolution distributed sensing applications. With identical central wavelength and low peak reflectivity (−40 dB), all the ultra-short FBGs share the short length (1 mm) and extremely small spacing (500 μm). The large multiplexing capacity and lower crosstalk of the DUS-FBG is investigated through both simulation and experiment. Use of DUS-FBG array interrogated by optical frequency domain reflectometry (OFDR) for distributed temperature and non-uniform strain sensing was conducted. We demonstrated high spatial resolution over 6680 FBGs along a 10 m-long fiber, and temperature and strain precision of 1.00 °Cand 20.02 με. Distributed temperature and non-uniform strain sensing experiment results are consistent with the theoretical analysis, and verify the high spatial resolution and large multiplexing capacity.
© 2017 Optical Society of America
1. Introduction
In general, optical fiber sensing (OFS) based on optical reflectometry technology mainly includes intrinsic scattering of fibers (Raman, Brillouin and Rayleigh) [1–4] or Fiber Bragg Grating (FBG)-based sensors [5,6]. Rayleigh backscattering in optical fiber is caused by the imperfections of the optic fiber such as inhomogeneous doping and diameter variations, and benefits from distributed data and long sensing length. Using optical frequency domain reflectometry (OFDR) technology, Rayleigh-based sensing system can achieve high spatial resolution [7]. In [8], OFDR technology based on 30 m single mode fiber-28 (SMF-28) is utilized for distributed temperature sensing with the temperature sensitivity of 1 °C on a spatial resolution of 2 mm. In [9], single-mode optical fiber with length of 300 meters is utilized for distributed temperature and strain sensing detection, and the sensing spatial resolution is 7 cm, but the sensing resolution deteriorates at a far distance. A UV exposed SMF-28 using frequency domain Rayleigh scatter based technology has been demonstrated [10], it presents a technique to lower noise level and improve back-scattered signal to obtain a higher detection sensitivity.
Compared to Rayleigh-based technology, FBGs-based technology can achieve higher Signal-Noise ratio (SNR) since it possesses much higher back-scattering light coupling efficiency, but its total length is limited by the multiplexing capacity [11,12]. Childers et al. proposed 800 FBG sensors in an 8-meters single array using OFDR. For the FBGs-based OFDR technology, it is the current maximum multiplexing number and maximum detection distance experimentally [13], and the distributed strain measurement with about 4mm spatial resolution was achieved. In [14], 5 m long fiber containing 500 9-mm long FBGs using microwave photonic filters technology can achieve spatial resolution under 1mm is demonstrated. For the high spatial resolution, except for the FBG array based, 10 cm long-length FBG based technology was also proposed. Measuring non-uniform strain along a 10 cm-long FBG with millimeter spatial resolution using OFDR is proposed and experimentally demonstrated [15], and a simulation result for a 200 cm-long FBG is presented. 10 cm-long FBG based with 2 millimeters spatial resolution using optical time-domain reflectometry (OTDR) [16] was also proposed, however, this method requires ultrafast light modulation and detection, which is very expensive. In [17], the Bragg wavelength distribution in a 10 cm-long FBG was measured with synthesis of optical coherence function (SOCF) scheme. It successfully achieved a few mm spatial resolution and 5pm spectral resolution, but the demodulation setup is very complicated. However, fabricating a long, continuous, and homogenous FBG with no phase hopping requires an extremely long phase mask (≥100mm) or a very precision optical mechanical platform [18,19].
In this paper, we developed a dense ultra-short (DUS) FBG array for high-spatial resolution distributed sensing applications. With identical central wavelength, short length (1 mm) and low peak reflectivity (−40 dB), all the ultra-short FBGs are equally separated by an extremely small spacing of 0.5 mm. In order to improve the detection distance, it is necessary to increase the system multiplexing capacity. We intentionally vary the central wavelength and the interval of the FBGs array to overcome the spectral shadowing and the multi-reflection crosstalk, and the feasibility of the method to improve the multiplexing capacity is verified by simulation and experiment. Distributed sensing of temperature and strain based on the OFDR interrogator were conducted. We demonstrated 1.5 mm spatial resolution over 6680 FBGs along a 10 m-long fiber, with temperature and strain precision of 1.00 °Cand 20.02 με.
2. Distributed sensing system using dense Ultra - short FBG
2.1 High spatial resolution system
The structure of the FBG-based OFDR demodulation system is shown in Fig. 1, the basic principle of the system is based on the classical OFDR system [11,20,21]. Light from a tunable laser is divided into three channels. The measuring channel consists of the sensor array and a reference arm to form a Mach-Zehnder interferometer, and polarization-split detectors. The reference channel is a Mach-Zehender interferometer with large optical path difference (OPD), and its interference fringe is used to realize the nonlinear correction of the laser. In the calibration channel, a Fabry-Pérot (FP) etalon filter is used to calibrate the swept wavelength of laser. In addition, in measuring channel, a delay fiber is insert at the front end of the sensing fiber to change the frequency of the sensing beat signal, in order to avoid the overlap between the crosstalk beat signal and sensing beat signal in the frequency domain, and not affect the position information demodulation of the DUS-FBG array. The beat signal from OFDR is resampled by using frequency multiplying algorithm. Typical time/ frequency pair in FFT are corresponding to wavenumber and position, a sliding window function is used to extract a signal in a wavenumber range for applying fast Fourier transform (FFT) to calculate the amplitude distribution along the frequency (position) direction. Then, the window slides with the prescribed distance for the same process, until the whole wavenumber range is covered. In this way, the reflected spectrum at an arbitrary position on the FBG can be obtained, and the sensing distribution can be calculated.
The nonlinear frequency sweep of the laser will broaden the interference spectrum and reduce the spatial resolution. In this paper, the measuring channel and reference channel signal are acquired at the same time and a frequency multiplying algorithm is used to resample the measured channel signal. The algorithm resamples beat signals by the interpolation algorithms, in order to suppress a TLS nonlinearity after the date acquisition also has many other methods, such as linear and cubic spline interpolations [22–24]. A major advantage of these interpolation resampling algorithms is that an OFDR’s maximum measurement range is independent on auxiliary interferometer’s path length difference. The basic principle of the frequency multiplying algorithm is to find the zero-crossing point of the beat signal in reference channel, N-1 zero points are inserted evenly between two adjacent zero crossing points as a new zero-crossing point, an N-fold multiplier signal is obtained. Figure 2(a) illustrates a method for improve sampling frequency by means of zero crossing point interpolation with M-1 groups of N-1 zero points are inserted among M zero crossing points. To guarantee the uniform insertion of zero points is valid, the laser tuning rate must remain constant during a single period of the reference beat signal. In order to eliminate the effect of DC offset and high frequency noise, the pretreatment of the band-pass filter is carried out to ensure the accuracy of zero crossing point localization. Due to the time inhomogeneity between zero crossing points, the time sequence is with unequal intervals. The nonlinear correction of laser tuning can be realized by sampling the measurement channel at the points of the time sequence obtained from the reference channel and rearranging it with equal interval. In this way, we can eliminate the nonlinear sweep, and obtained a higher sampling frequency without recurring in long delay lines in the reference channel sampling frequency and thus relaxing the demand of the laser coherence length.
Fig. 2 The process and test of the system nonlinear calibration: (a) Process of nonlinear compensation algorithm; (b) OFDR-like traces before (black line) and after (red line) using amendment; (c) The enlarged drawing of the red line in (b).
The spatial resolution of the demodulation system depends on the frequency resolution of the FFT. It can be expressed as:
where ΔT is the duration of the acquired signal (0.1 s), so the spatial resolution ΔL in theory is approximate 81.8 μm. As shown in Figs. 2(b) and 2(c), the broadening is very wide before the nonlinear amendment, and the black curve shows that the spatial resolution in this situation is about 5 m. After nonlinear compensation, the system's spatial resolution is reduced to be less than 0.5 mm. The algorithm can eliminate the nonlinear frequency and improve the spatial resolution of the system effectively.To validate the limit of the measurement channel detection length under the premise of high spatial resolution, we change the reference frequency beat fiber length with the OPD of Mach-Zehnder interferometer kept at 50 m at the reference channel. When the reference frequency beat length is within 50 m, adjacent FBGs are clearly separated e.g. at the length of 12.7 m (Fig. 3(a)) and 27.7 m (Fig. 3(b)). At 47.4 m in Fig. 3(c), although its signal-to-noise ratio has been reduced, the system can still distinguish the locations of each FBGs at the condition of high spatial resolution demodulation. Continue to increase the reference frequency beat length in Fig. 3(d), the system suffers a lower signal-to-noise ratio which makes it difficult to demodulate in this high spatial resolution. The traditional method of auxiliary interferometer playing as data acquisition trigger, the maximum measurement length is only a quarter of the OPD between the two arms of the auxiliary interferometer according to the Nyquist sampling criteria [23]. The system SNR decreases with the increase of detection distance due to the laser coherent length, the detection distance of the system has been increased to the length of OPD through the experiment. Frequency multiplying algorithm enables a higher sampling frequency, which shortens the required length of delay fiber in the reference channel as well as the coherence length of laser, and improves the maximum detection range.
Fig. 3 Demodulation comparison of different reference frequency beat length: (a) 12.7 m; (b) 27.7 m; (c) 47.4 m; (d) 57.2 m; (e), (f), (g), (h) shows the enlarged drawing of the position of (14.6-14.62m), (29.6-29.62 m), (49.32-49.34 m), (59-59.02 m).
2.2 Simulation and discussion of the system multiplexing capacity
The multiplexing capacity is limited by spectral shadowing and multiple-reflection crosstalk [25]. Spectral shadowing effect describes the spectral distortion of the downstream FBGs caused by the insertion loss of the upstream FBGs. Multiple-reflection crosstalk refers to the spectral distortion induced by the false signal, which undergoes multiple reflections between the upstream FBGs and arrives at the detector at the same time with the real signal of the downstream FBGs. The spectral shadowing is usually suppressed by reducing the FBG reflectivity, but if the reflectivity is too weak, the FBG cannot be reliably made [26]. Therefore, we proposed a new method of random center-wavelength to weaken the spectral shadowing effect. The center wavelengths of ultra-short FBGs are randomized within the appropriate range such as ± 0.2 nm. Assume that 5000 FBGs were fabricated on a single mode fiber, and the simulation results of the reflected spectrum of the last FBG are plotted in Fig. 4(a). The black curve is the reflected spectrum of the FBG#5000 at random wavelengths condition, while the red curve is the reflected spectrum at identical wavelengths condition. Obviously, the intensity of the black curve has been promoted that of the red one. Theoretically, the multiplexing capacity is significantly improved. Figure 4(b) shows the influence of reflectivity and multiple crosstalk on multiplexing capacity. Considering the effects of multipath reflection, when the reflectivity of a single grating is −40 dB, the system multiplexing capacity is about 4800 as red curve shown in Fig. 4(b). In order to further reduce crosstalk and increase the multiplexing capacity, the random space between adjacent FBG is proposed. If the grating spacing is randomly distributed in the range of 0.5 mm ± 5 μm, the multiplexing capacity can rise by one order of magnitude as black curve shown in Fig. 4(b).
Fig. 4 Simulation of system multiplexing capacity: (a) Spectral shadowing effect suppression: last single FBG reflection; (b) Multiple-reflection crosstalk effect suppression.
The way to increase the multiplexing capacity is mainly by overcome the crosstalk. In addition to reducing the reflectivity of a single grating, there are two other methods, one is by randomizing center wavelength in a certain range to overcome the spectral shadowing, another is through a certain range of random spacing to overcome the multi-reflection crosstalk. The ultra-weak DUS-FBG array was fabricated with phase mask and improved on-line identical FBG writing technique. The key parameters include the grating interval, central wavelength and reflectivity of single FBG. In the processing of the DUS-FBG array fabrication previously reported [27, 28], there is always small fluctuation (speed and tension) to control the fiber diameter in the qualified range, the uniform of the center wavelength and grating spacing will affected. We improved this on-line fabrication system to realize the real-time adjustment of the repetition rate of the ArF excimer laser and drawing speed obtained, and the grating spacing can be precisely controlled. In addition, we rapidly adjustment the fiber temperature through the temperature controller before the FBG is written, it can control the FBG center wavelength randomly within a certain range.
As shown in Fig. 5, four arrays with the same DUS-FBGs number of 4000 but different consistency of center-wavelength and spacing were tested: DUS-FBG1 is composed of 4000 identical ultra-weak (reflectivity is about −40 dB) FBGs whose Bragg wavelengths are 1549.85 nm at room temperature, these FBGs are 1 mm long and separated by 500 μm. In the latter three types DUS-FBG array, the FBG arrays with random center wavelength and random spacing in the certain range were produced by the fabrication system introduced above, which called as DUS-FBG2 is with randomized center wavelength and equal spacing, DUS-FBG3 is with identical center wavelength and randomized spacing, and DUS-FBG4 is with randomized center wavelength and spacing. It is worth noting that the wavelength consistency of DUS-FBG1 is based on the disregard of the wavelength and spacing fluctuations induced by random error in the system. It can be seen that the uniformity of the center-wavelength and spacing of the DUS-FBG1 is significantly higher than that of the latter three groups. According to the test data, the intrinsic system error on FBG center wavelength is ± 0.1 nm, while the random range of wavelength can be controlled within ± 0.2 nm by the temperature controller and tiny adjustment of tension. As for the grating spacing, the system error fluctuates within ± 0.1 mm, and the control system can make it within ± 0.2 mm.
Fig. 5 The parameters of DUS-FBG array with the same 4000 US-FBGs: Spacing: (a) DUS-FBG1; (b) DUS-FBG2; (c) DUS-FBG3; (d) DUS-FBG4; Center wavelength: (e) DUS-FBG1; (f) DUS-FBG2; (g) DUS-FBG3; (h) DUS-FBG4.
Through the simulation, we expect the multiplexing capacity of DUS-FBG2, 3and 4 are larger than that of the reference all-in-phase sample DUS-FBG1, because reducing the consistence of the wavelength and spacing could suppress the multiple reflection effect and spectral shadowing effect. The results are shown in Fig. 6, The SNR of DUS-FBG1 in the frequency domain is not high, the positions of FBG cannot be identified basically, and the subsequent demodulation is difficult to conduct, but the latter three groups especially DUS-FBG4 have high enough SNR to provide the location information. As shown in Fig. 7, we gradually reduce the multiplexing capacity of DUS-FBG1, the SNR is still not high when the number is 3000. Until the number down to 2500, the SNR is improved obviously like the larger view of Fig. 7(d). The maximum multiplexing capacity is about 2500, while the other two groups have more than 4000. Meanwhile, we increase the FBG number to 6680 with the total length of 10 m. The demodulation result is shown in Fig. 7, the SNR is high enough to distinguish the position of each grating. In other words, the experimental results show that the proposed method can effectively suppress crosstalk and improve the multiplexing capacity of the system.
Fig. 6 Four types DUS-FBG array of the amplitude distribution at various positions: (a) DUS-FBG1, (b) DUS-FBG2, (c) DUS-FBG3, (d) DUS-FBG4; Zoom in:(e) DUS-FBG1(14.6-14.62 m), (f) DUS-FBG2 (29.6-29.62 m),(g) DUS-FBG3 (49.32-49.34 m),(h) DUS-FBG4 (59-59.02 m).
Fig. 7 DUS-FBG multiplexing capacity discussion, the amplitude distribution at various positions: (a) DUS-FBG1 (3000 FBGs), (b) DUS-FBG1 (2500 FBGs), (c) DUS-FBG4 (6680 FBGs); Zoom in: (d) DUS-FBG1 (3000 FBGs) (8.0 m-8.02 m), (e) DUS-FBG1 (2500 FBGs) (7.3 m-7.32 m), (f) DUS-FBG4 (6680 FBGs) (13.0 m-13.02 m).
3. Experimental setup for distributed temperature and non-uniform strain sensing
3.1 System strain/temperature calibration
In the system temperature performance test, we use the standard thermotank (range from 20 to 80 °C with step of 5 °C) to calibrate the temperature sensitivity of the sensor. Each ultra-short FBG is demodulated by the demodulation system with a scanning range of 1550 nm-1560 nm. Figure 8(a) illustrates the peak wavelength of each FBGs at different temperatures. Figure 8(b) shows the sensitivities of each FBG which is estimated with linear curve fitting and ranges from 9.4 to 10 pm/°C, the average temperature sensitivity is 9.765 pm/°C. The small variation is mainly due to the measurement errors determined by the SNR of the resolved spectra of the FBGs. Figure 8(c) shows the distribution linearity of each FBG, and the decoded temperatures are very linear to the set temperatures, which have R-square of linear fit higher than 0.99. The standard deviation of each FBG ranged from 3.51 pm to 19.45 pm with a mean value of 9.77 pm, which is equivalent to a temperature accuracy of 1.00 °C.The difference in the measurement errors is mainly caused by the different FBG reflectivities and hence different SNRs of the weak FBGs. The reason of temperature drift may be due to the uneven temperature distribution in the thermotank, and the average error can indicate that the system has a high accuracy at temperature sensing.
Fig. 8 The temperature test of system performance: (a) temperature coefficient calibration; (b) Ratio coefficient; (c) The linearity of DUS- FBG array.
Strain was precisely induced in the DUS-FBG array by mounting a stainless steel linear bearing translation stage with 0.5 μm resolution, clamping the FBG array on the stage and on a distant point on the rail. In this manner tensile strains over the range of 0 to 2000 με with a length of 200 mm were generated. Figure 9 shows the experimental results of the strain induced wavelength shift. In Fig. 9(a), the wavelength shift under different strain, which was increased from 64.52 με to 1935.48 με with an increment of 64.52 με, is shown along the DUS-FBG array at position of 0.6 m and 9.5 m with a length of 0.2 m. Figures 9(b)-9(e) presents the average wavelength shift with respect to varying strain at 0.6 m and 9.5 m where linear regressing is applied and the strain sensitivity coefficients are calculated to be 1.05 pm/με and 1.06 pm/με, respectively. The average wave-length shift measurement errors at two positions are 23.12 pm and 23.35 pm, corresponding to strain precision of 22.02 με and 22.03 με. However, the accuracy of the strain sensing is affected by the experimental environment (especially temperature), and there exists a further improvement in this performance. The results of the FBG array's strain/temperature coefficient calibration show that the sensitivity and measurement error are almost the same from the first FBG to the last one in the whole array (10 m). For the strain and temperature measurement, the accuracy of DUS-FBG array is no less than the OFDR system using a 10 cm long length FBG [15, 29] when the array length increases to 10 m.
Fig. 9 The strain test of system performance: (a) strain coefficient calibration; (b) Ratio coefficient (0.60.8 m); (c) Ratio coefficient (9.5-9.7 m); (d) linearity of strain (0.6-0.8 m); (e) linearity of strain (9.5-9.7 m).
3.2 Distributed temperature sensing
The proposed method is capable of detecting multi-spot events. In order to make the visual effect of distributed temperature sensing be more obvious, we adopts three soldering irons as a hot-spots group to heat the FBG array, hot spots group placed at the front, the middle and the end of the sensor array respectively for three distributed temperature tests. As shown in Fig. 10, three test were placed at the points where L was 0.95 m, 5.25 m, 8.6 m distance from the staring points. The coverage radius of the hot spots is about 2 mm. Moreover, the sensing information of the heated zones is calculated by evaluating the center-wavelength changes between the normal temperatures and the heating temperatures relating to the hot spots. Figures 10 shows the experimental results. As expected, the detected positions of maximum wavelength changed were at the center of each hot spots.
Fig. 10 Temperature distributions sensing test: (a) Test 1; (b) Test 2; (3) Test 3; Inset graph shows the enlarged drawing of the position of (0.85-1.15 m), (5.2-5.6 m), (8.6-9 m).
3.3 Distributed non-uniform strain sensing test
The aluminum tensile specimen used in the experiment is shown in Fig. 11(a), three identical via holes with 15 mm radius and 60 mm interval were designed on the tensile specimen. Strain distribution along the areas adjacent to the hole became non-uniform when tension is applied to the test specimen. Simulated strain distribution along the test specimen is given in Fig. 11(a), which show that relatively larger strain gradient occurs around the hole and the direction is tangential to the loading direction, and the strain decreases gradually as the interval distance increase. A 1-mm segment of DUS-FBG was stuck on the via hole boundary. Non-uniform strain distribution along the specimen is measured by the DUS-FBG using OFDR. The 10m long DUS-FBG array is arranged at a distance of d1 = 1 mm and d2 = 2 mm parallel to the circular hole, corresponding to the position of the DUS-FBG sensor (2 m, 2.15 m) and (9.15 m,9.3 m). The load cases in the test are shown in Figs. 11(c) and 11(d). The vertical axis indicates the FBG position, and the horizontal axis indicates the strain. The maximum strain is found around the center of the three circles (the position where the FBG is tangential to the hole), and the strain decreases as the interval distance increases.
Fig. 11 Non-uniform Strain distributed sensing test: (a) Tensile tests on simply beams with through holes; (b) Strain simulation; (c) d1 = 2 mm, non-uniform distributed strain demodulation result; (d) d2 = 1 mm, non-uniform distributed strain demodulation result.
Tensile loading was changed from 0 to 4 kN in step of 1 kN, remaining at each step for 5 s, and then slowly decreased to 0 kN. This process was repeated three times. Figures 12(a) and 12(c) shows the strain distributions which are measured by FBGs and calculated by ANSYS at the loads of 1 kN-4 kN in the load cases of specimens. Figures 12(b) and 12(d) shows the measured strain distributions under four load cases. The actual measurement results and the theoretical simulation results have the same strain distribution trend. The error in simulation and actual detection due to the slight error of the arrangement of the sensor. The simulation is expected to be utilized for various purposes such as determination of effective sensor positions, optimization of signal processing, troubleshooting the unexpected noise.
Fig. 12 Non-uniform distributed sensing test: (a) Simulation (2-2.15 m); (b) Experiment (2-2.15 m); (c) Simulation (9-9.15 m); (d) Experiment (9-9.15 m).
4. Conclusion
We developed a DUS-FBG array for high-spatial-resolution distributed sensing applications. With identical central wavelength and low peak reflectivity (−40 dB), all the ultra-short FBGs share the short length (1 mm) and extremely small spacing (500 μm). In order to improve the detection distance, it is necessary to increase the system multiplexing capacity. We intentionally vary the central wavelength and the interval of the FBGs array to overcome the spectral shadowing and the multi-reflection crosstalk, and the feasibility of the method to improve the multiplexing capacity is verified by simulation and experiment. Distributed sensing of temperature and non-uniform strain based on the OFDR interrogator were conducted. The problem of nonlinear frequency sweep has been solved in the system, indicating that the use of reference optical path and compensation frequency multiplication algorithm introduce significant improvements on spatial-resolution. Basic experiments on non-uniform strain and distributed temperature detection were carried out to verify the system, experimental results are consistent with the theoretical values, and the system has sufficient theoretical spatial resolution to interrogate the 1 mm length of each FBG and the 500 μm gap. In addition, we demonstrated 1.5 mm spatial resolution over 6680 FBGs along a 10m-long fiber, and temperature and strain precision of 1.00 °Cand 20.02 με.
Funding
National Natural Science Foundation of China (NSFC) (Grant Nos. 61735013,61575149); Major Project of Hubei Technological Innovation Special Fund (2016AAA008).
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