Abstract

We demonstrate a cost-effective distributed fiber sensing system for the multi-parameter detection of the vibration, the temperature, and the strain by integrating phase-sensitive optical time domain reflectometry (φ-OTDR) and Brillouin optical time domain reflectometry (B-OTDR). Taking advantage of the fast changing property of the vibration and the static properties of the temperature and the strain, both the width and intensity of the laser pulses are modulated and injected into the single-mode sensing fiber proportionally, so that three concerned parameters can be extracted simultaneously by only one photo-detector and one data acquisition channel. A data processing method based on Gaussian window short time Fourier transform (G-STFT) is capable of achieving high spatial resolution in B-OTDR. The experimental results show that up to 4.8kHz vibration sensing with 3m spatial resolution at 10km standard single-mode fiber can be realized, as well as the distributed temperature and stress profiles along the same fiber with 80cm spatial resolution.

© 2016 Optical Society of America

1. Introduction

During the past several decades, many high efficient and flexible distributed fiber sensing systems have been widely used in numerous fields, such as intrusion monitoring [1], oil-gas depot [2], aerospace and wind-energy industries [3]. Among these techniques, Rayleigh, Brillouin or Raman backscattering based optical time domain reflectometers are very practical owing to their advantages of single-end and simple construction [4,5]. Conventionally, a phase-sensitive optical time-domain reflectometry (φ-OTDR), exploiting Rayleigh backscattering signal of narrow-linewidth laser pulse, is used to measure weak and fast changing perturbations along critical infrastructures [6–9]. Besides, the Brillouin optical time domain reflectometry (B-OTDR), measuring the frequency shift of Brillouin backscattering, has recently attracted extensive attention to determine the distributed temperature and strain over long distances [10–13]. Exploiting avalanche photodetectors (APDs) to detect different Raman anti-Stokes (AS) and Stokes (S) signals induced by temperature, Raman optical time domain reflectometry (R-OTDR) or Raman distributed temperature sensors (RDTS) is widely used to measure distributed temperature with meter-scale spatial resolution [14–17].

At the meantime, multi-parameter measurement is becoming a pressing requirement for fiber optic monitoring system because it provides more valuable information which offers an effective way for a comprehensive identification of fault events. Several novel methods for simultaneous distributed measurement of temperature and strain based on spatially resolving spontaneous Raman and Brillouin backscattered anti-Stokes signals were reported [18–21]. These methods eliminate the Brillouin frequency shift (BFS) cross-sensitivity between the temperature and the static strain. Slope-assisted method, based on the stimulated Brillouin scattering interaction between two counter propagating optical pulses, permits dynamic strain or low frequency vibration to be measured by Brillouin optical time-domain analysis (BOTDA) schemes [22–27]. For the measurement of temperature and strain-induced vibration simultaneously, a BOTDA scheme which combined frequency sweeping with slope-assisted techniques was proposed [27]. Two vibration events and one temperature point are clearly identified. However, slope-assisted method is only suitable for strain-induced low frequency vibration sensing and difficult to measure weak perturbations with nε-level strain. Recently, a hybrid distributed acoustic and temperature sensor was reported based on integration of RDTS and φ-OTDR by utilizing a commercial off-the-shelf distributed feedback laser [28,29]. It controlled and modulated the optical source to ensure inter-pulse incoherence and intra-pulse coherence, assuring that the cyclic simplex coding is effective for both φ-OTDR and RDTS. Although this scheme can realize accurate long-distance measurement of vibrations and temperature with minimal post-processing, it is incapable for static strain measuring.

In this paper, we propose and experimentally demonstrate a hybrid distributed multi-parameter fiber sensing system based on integration of a φ-OTDR and a B-OTDR. Both the width and intensity of the laser pulses are modulated so that the information of the vibration, the temperature and the strain can be extracted simultaneously with only one photo-detector and data acquisition channel. The φ-OTDR sub-system based on direct detection and the B-OTDR sub-system based on the heterodyne detection could alternatively operate by an optic switch. A G-STFT based data processing method is used in the long distance B-OTDR system to improve the spatial resolution.

2. Principles

2.1 Laser pulse modulation

In order to enhance spatial resolution and achieve simultaneous multi-parameter measurement in long sensing range, the pulse width and the intensity of the laser should be modulated accordingly. As shown in Fig. 1(a), each cycle of the modulated pulses is composed of a group of wide pulses I1 with high intensity and a narrow pulse I2 with low intensity. The pulses pattern of single cycle can be defined as

y(t)=a=1NI1(aT-t)+I2((N+1)T-t)
where I1(t) and I2(t), the profiles of pulses, are Gaussian shape in our system to maintain the balance between the pulse power and spatial resolution. Ii(t) can be written as
Ii(t)=Piet2/(τi22ln2)2
where Pi and τi are peak power and full width at half maximum (FWHM) of the pulse, respectively, with P1>P2 and τ12.

 

Fig. 1 Laser pulse modulation and data processing. (a) The modulated laser pulse sequences and signals captured by data acquisition card (DAQ); (b) φ-OTDR data processing at the vibration point; (c) B-OTDR data processing, data after Gaussian window short time Fourier transform (G-STFT), BG: Brillouin Gain.

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Vibration is a rapidly changing parameter which can be detected through intensity variation of Rayleigh backscattering in φ-OTDR. Restricted by the dark current noise and limited responsivity of the photodetector, the pulses I1 with wide duration and high intensity are utilized for vibration detection, due to the fact that intensity based φ-OTDR needs more optical energy to excite enough Rayleigh backscattering signal in the sensing fiber. Furthermore, according to the Nyquist–Shannon sampling theorem [6, 8], high sampling frequency and large number of pulses should be guaranteed for φ-OTDR sensing to broaden the system frequency response range.

The static parameters, such as the temperature and the strain can be detected by frequency shift in B-OTDR. Due to the noises like dark current stably distributed in the frequency domain, the influence of these noises could be decreased when applying the periodic average method. Therefore, the narrow and low intensity pulse I2 is employed for the sensing of the temperature and the strain. It should be noted that a higher peak pulse cannot increase the signal-to-noise ratio (SNR) of B-OTDR, but lead to stimulated Brillouin scattering and other nonlinear optical effects instead.

Due to the fiber attenuation, high power pulse is always required to ensure that the signal from the far end of the long fiber does not submerge in the dark current noise of the photo-detector. A narrow linewidth laser source is a critical element in φ-OTDR which guarantees the coherence of backscattering light in long sensing fiber. However, the narrow linewidth laser with high power often brings significant nonlinear effects [30–32], such as stimulated Brillouin and modulation instability, which leads to the randomization of the scattering light because of the pulse energy transferring from the laser frequency to nearby frequencies. In the proposed system, despite the fact that the high peak power pulse I1 has caused a little stimulated Brillouin scattering, the intensity of Rayleigh scattering is 15dB larger than that of Brillouin scattering which guarantees the far end sensing performance pretty well. The partially stimulated Brillouin is acceptable in the φ-OTDR sensing. However, the pulse peak power cannot be increased when the far end Rayleigh signal decreases because the other nonlinear effects, such as modulation instability, self-modulation, FWM, will be emerged. B-OTDR measures the frequency shift of Brillouin spontaneous backscattering light. The high peak power pulse could excite the stimulated Brillouin light and other nonlinear effects in long sensing range which will deteriorate the sensing performance. These nonlinear effects will deteriorate the SNR of the B-OTDR system or even make the signal unable to be detected. Therefore, the low peak power pulse I2 is used for B-OTDR sensing in order to guarantee that any nonlinear effects will be avoided.

2.2 Principle of operation & data processing

When vibration is loaded to the sensing fiber, the refractive index and the length of the fiber near the local vibrations change, which ultimately changes the local amplitude and the phase of the modulated pulses, as well as the intensity of the backscattered signal [29]. As shown in Fig. 1(a), the red lines of the DAQ signals are Rayleigh signals after light pulses I1 are injected into the sensing fiber. The vibration points, marked by the dotted circle, can be accurately located by comparing different periods of backscattering traces. Figure 1(b) shows the data processing of distributed vibration measurement. By arranging the signals of vibration points along the time line, the time and frequency domain properties of the vibration points can be obtained. The (N + 1)th point is utilized for B-OTDR sensing, and the vibration points are vacant but could be estimated by the linear interpolation of the adjacent signals.

When experiencing temperature or strain changes, linearly red shift happens to the Brillouin scattering frequency shift νB according to the formula [33]

νB=CνBTΔT+CνBεΔε+νB0
Here CνBT(~1MHz/°C) and CνBε (~1MHz/20με) are the temperature and strain coefficients for BFS in single mode silica fibers, ΔT and Δε are the temperature and strain variation at the sensing point, respectively. νB0 is the Brillouin scattering frequency shift (typical in the range of 9~11GHz) of the fiber. A stable single-frequency Brillouin fiber laser (BFL), pumped by the narrow-linewidth laser and shifted about hundreds of MHz from νB, is regarded as local oscillator (LO) for coherent detection in this BOTDR sensing system [33]. The beat signal (hundreds of MHz) of Brillouin scattering and LO are digitized and recorded directly by a high sampling rate data acquisition system, as shown in Fig. 1(a) with blue lines marked by dashed box. The time domain beat signal is proceeded by Gaussian window short time Fourier transform (G-STFT) method to demodulate νB profile, as shown in Fig. 1(c). The operation process will be discussed in more detail below.

To get the frequency spectrum at time t, the beat signal is divide into shorter segments of equal length and multiplied with a Gaussian window whose length is tg, and then Fourier transform is taken, which is illustrated in Fig. 2(a-b). The G-STFT procedure can be explained by formula

PSTFT(t,ω)=|tg/2tg/2ejωτs(τ)g(τt)dτ|2
where g(t) is Gaussian window function
g(t)=et2/(τg22ln2)2
τg is the FWHM of Gaussian window, as shown in Fig. 2(b).

 

Fig. 2 Data processing for B-OTDR. (a) Beat signal of LO and backscattering light is divide into shorter segments of equal length; (b) The processing of Gaussian window short time Fourier transform (G-STFT); (c) Fitting result of weighted Lorentzian nonlinear fitting (WLF)

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According to the Heisenberg-Gabor uncertainty principle [34], the product of the windowed signal duration and the spectrum bandwidth should be not smaller than a constant, i.e. spatial resolution and frequency bandwidth is a trade-off question in our system. Fortunately, the gain spectrum of spontaneous Brillouin is a single peak Lorentz line-shape, whose bandwidth is tens of MHz when the probe pulse is less than 10 ns. The FWHM of laser pulse τp limits the spatial resolution δz in physics according to the formula δzp/2neff, where c represents the speed of light in vacuum and neff is the effective refractive index of the fiber. For the proposed B-OTDR system, δz is finally determined by min(τp, τg) where τg corresponds to the analytical spatial resolution of the post-processing algorithm. However, frequency resolution of time-frequency analysis will reduce when τg is too small which decreases the accuracy of the stain and the temperate sensing. Therefore, FWHM of the window function τg is set to be slightly smaller than the pulse width τp. By increasing the Gaussian window length tg while keeping the FWHM τg unchanged, high spatial resolution and enough frequency resolution could be achieved simultaneously, and the fake signal noises induced by increasing tg can be partially eliminated by averaging hundreds of sampling periods. The window width tg is determined by the DAQ sampling rate and the detected width of spontaneous Brillouin gain spectrum, and is supposed to be tg = 12τg in the proposed system. The moving step ts of Gaussian window is set to τp/5 for a better analytical spatial resolution. Then, the frequency spectrum of STFT at position t can be obtained after hundreds of periods average.

After acquiring the STFT frequency spectrum, weighted Lorentzian nonlinear fitting (WLF) method is adopted to get the accurate BFS center frequency. Considered the spectral asymmetry owing to the impedance mismatch between the DAQ, photodetector and the RF cables, the data at bottom right of spectrum peak are not used for curve fitting. What’s more, normalized under-fit data, severed as the weight value, is multiplied with under-fit data during each fitting iteration, which highlights the weight of data near the peak and reduces iteration times. Fitting result is displayed in Fig. 2(c).

Compared with the conventional B-OTDR, the proposed data post-processing method cuts the system cost and shortens the measurement time because frequency sweeping is not required. For a 10km long fiber, generally, the measurement time is less than one second if only B-OTDR sensing is concerned. Nevertheless, it should be noted that the analysis time is determined by the efficiency of post-processing algorithm and the performance of the computer.

3. Experiment and discussions

3.1 Experimental setup

The experimental setup used to evaluate the performance of the proposed system is shown in Fig. 3(a). A single frequency light source whose linewidth is less than 200Hz (NKT Laser, E15) is injected into the sensing fiber and a Brillouin laser cavity through a coupler. An acoustic-optic modulator (AOM), driven by an arbitrary waveform generator (AWG), is used to generate modulated pulses with different widths and intensities for φ-OTDR and B-OTDR. The pulse widths for φ-OTDR and B-OTDR are 30ns and 8ns, respectively. The light signal is amplified by an Erbium-doped fiber amplifier (EDFA). A narrow band-pass filter (BPF) is used to filter the Amplified Spontaneous Emission (ASE) noise. Through a circulator, Rayleigh and Brillouin backscattering traces of modulated pulses are amplified by another EDFA and the Brillouin backscattering is selectively beaten with Brillouin laser by an SOA (Semiconductor optical amplifier switcher) optical switch (OS, Tianjin Opeak Technology, 0.5ns switch time).

 

Fig. 3 (a) Experimental setup. AOM: Acousto-Optic Modulator, EDFA: Erbium-Doped Fiber Amplifier, BPF: Band-Pass Filter, PZT: Piezoelectric Transducer, AWG: Arbitrary Waveform Generator, BL: Brillouin Laser, PS: Polarization Scrambler, OS: Optical Switch, PD: Photo Detector, DAQ: Data Acquisition card; (b) Scattering spectra of the sensing fiber at different EDFA pump power; (c) Amplified optical pulses for B-OTDR and φ-OTDR

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The backscattering signals are enhanced at the premise that the noises induced by the non-linear effects have no impact on the measurements. We observe the scattering spectra of different pulse power along the 10170m sensing fiber (matched cladding single mode fiber, Yangtze Optical Fiber and Cable Co., Ltd.). The core/cladding diameters are 9.0μm and 124.9μm, respectively. The effective refractive index of the core is 1.467. The CW light is modulated to a 9.7kHz repeating rate light pulse by an AOM. Scattering spectra of the sensing fiber at different EDFA pump power are shown in Fig. 3(b). There are only Rayleigh and Brillouin scattering peaks when the pump current varies from 70mA to 80mA, and the scattering power increases with the pump current. However, when the EDFA pump current is higher than 80mA, new frequency component is generated, while Rayleigh and Brillouin scattering peaks no longer increase. Therefore, 80mA pump current is chosen in the experiment and the peaks power of I1 and I2 are 14W and 3W respectively, as shown in Fig. 3(c).

At the end of 10170m sensing fiber, about 4.6m fiber are placed in a water tank, two short sections (5m and 80cm) of the fiber are glued on two pairs of micro-position stages to apply the strain, and 1m fiber is wounded on a piezoelectric transducer (PZT) tube to simulate external perturbations.

Heterodyned with 1550nm narrow linewidth seed laser, the Brillouin frequency shift (BFS) of the Brillouin laser is 10.324GHz. Fixed in the polyurethane foam, the laser cavity is resistant to the vibrational perturbation. The linewidth of Brillouin laser is ~230Hz, measured by the method in [35].

In order to simultaneously detect vibration, temperature and strain along the sensing fiber, the 30ns pulses and 8ns pulse with repeating rate of 9.7kHz are injected into the fiber. As demonstrated before, the ratio of wide pulse number and narrow pulse number is 100:1, which implies N = 100 in Fig. 1(a). To implement φ-OTDR sensing, the OS is switched off after every high power pulses enter into the sensing fiber. When OS is switched on, the Stokes Brillouin spontaneous peak of backscattering light beats with the Brillouin laser, resulting in a frequency of several hundreds of MHz. All the backscattering signals are detected by a 1.6GHz photodetector (Thorlabs PDB 480C) and recorded by a high speed data acquisition card (DAQ; Gage, 4GSa/s maximum sampling rate) at 2GHz sampling rate.

3.2 Vibration detection results

The PZT tube used as the vibration source is at 10164m of the sensing fiber. The sensing fiber is wounded ~1.07m length on PZT, where the loop diameter and the number of loops are 34mm and 10, respectively.

Figure 4 shows the φ-OTDR traces around PZT section (10155m to 10170m) when the PZT tube is applied by 100Hz and 1kHz sinusoidal signals, respectively. Figures 4(a) and 4(b) are the superposition of ten consecutive Rayleigh backscattering traces recorded by DAQ. Due to the interference fading, the traces are nearly zero at certain places. Figures 4(c) and 4(d) are normalized traces along different sampling periods over 50ms. The interference fading phenomenon is eliminated in these figures while vibration sections are emphasized. The phase change induced by PZT is clearly identified and the spatial resolution is ~3m corresponding to the 30ns pulse, as marked by dotted circles.

 

Fig. 4 φ-OTDR traces at the end section of the sensing fiber when the PZT is driven by 100Hz (a, c) and 1KHz (b, d) sinusoidal signal. (a, b) superposition of ten traces; (c, d) normalized consecutive traces within 50ms

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In order to test the performance of the system at different vibration frequencies, 500Hz, 1KHz, 3kHz and 4.8kHz sinusoidal signals are applied to the PZT tube separately. The FFT transform spectra at the vibration point, as shown in Fig. 5, demonstrate that the system has the capability to detect vibration with up to 4.8kHz frequency response and the SNR is over 10dB.

 

Fig. 5 (a)-(d) FFT transform spectra of the vibration point when 500Hz, 1KHz, 3kHz and 4.8kHz sinusoidal signals are applied to the PZT, respectively.

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3.3 Temperature and strain detection results

The acquired beat electrical signals of B-OTDR are analyzed by G-STFT method as mentioned in section 2.2. After averaging 1000 cycles, the spatial distribution of Brillouin scattering signal along the 10km fiber is shown in Fig. 6(a). BFS peak can be seen around 280MHz and attenuated along the fiber due to fiber losses. But the signal is high enough to be detected at the end of the sensing fiber as shown in Fig. 6(b).

 

Fig. 6 (a) Spatial distribution of Brillouin scattering beat frequency signal along the 10km sensing fiber; (b) BFS of end section of the sensing fiber when applied temperate shift, strain and vibration simultaneously. The color bars represent the measured Brillouin gain values.

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We also performed the distributed measurement of the temperate, the strain and the vibration simultaneously. Figure 6(b) depicts the BFS spectrum distributions along the end section of the sensing fiber with the changes of the temperature, the strain and the vibration which are marked by dotted circles. It clearly demonstrates that the frequency shifts with the temperate and strain regions, however, there is no response with the vibration. This is because the vibration induced disturbance is extremely weak and changes swiftly, which will be eliminated after averaging.

The BFS peaks are extracted through windowed Lorentzian nonlinear fitting method shown in Fig. 7(a), through which we can easily calculate the frequency shift values and identify the temperature and the strain shift locations. Figure 7(b) shows the enlarged BFS peak graph around the 80cm strain section in Fig. 7(a), indicating the spatial resolution is no less then 8cm.

 

Fig. 7 (a) Brillouin frequency shift peaks of Fig. 6(b) extracted by Lorentzian nonlinear fitting; (b) Enlarged frequency shift peak around the 80cm strain section marked by the circle in Fig. 7(a).

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Brillouin temperature measurement is executed from 24.8°C to 72.5°C by changing the water temperature, which is calibrated by a 0.1°C resolution mercurial thermometer. As can be seen from Fig. 8(a), the BFS peaks around the water tank section increases with the water temperature. Figure 8(b) shows the relationship between the average Brillouin frequency of the temperature shift section and the temperature measured by the mercurial thermometer. We can calculate that the average temperature-dependent coefficient of the fiber, is ~0.9876MHz/°C by linear fitting.

 

Fig. 8 (a) BFS peaks around water tank section under different temperature; (b) Relationship between the average Brillouin frequency and temperature

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Shifting the micro-positioner of 5m fiber section by 0.5mm, we performed strain measurement with a range of 2000με. Figure 9(a) gives the BFS peaks around 5m section for different strains, Fig. 9(b) shows the relationship between the average Brillouin frequency and the strain applied to the fiber. It can be seen that the BFS shift within three test rounds is less than ± 1MHz, which indicates that the repeatability of the proposed system complies with the requirements of B-OTDR sensing. The average strain-dependent coefficient of the fiber is ~0.0495MHz/με.

 

Fig. 9 (a) BFS peaks around 5m strain section under different strains; (b) Relationship between the average Brillouin frequency and strain

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3.4 Discussions

The experimental results indicate that the proposed method is capable for multi-parameter sensing, but there are many operating challenges when improving the performance of the system.

  • 1). For distributed vibration sensing, the frequency response range is 0~4.8 kHz for the limits of light pulse round trip time in the sensing fiber. While, in many applications, like sound detection and metro railway monitoring, wide frequency response range is required. Frequency division multiplexing method may be considered to improve the frequency response of vibration detection.

    Due to the arbitrary initial phase property of φ-OTDR, the amplitude of vibration, i.e. the accurate phase, is difficult to be demodulated through the backscattering signals. A complex modulation of light pulse is promising to solve this problem. Inspired by the demodulation of MZI signals, the 3 × 3 coupler, I/Q demodulation and phase generated carrier techniques are also potential solutions.

  • 2). For distributed temperature and strain sensing, our proposed solution has an 80cm spatial resolution corresponding to the 8 ns pulse. A higher spatial resolution can be achieved when combining with the differential pulse-width pair method.

    The sensing fiber used here is cross-sensitive for both temperate and strain. Introducing Raman signal demodulation into the system will eliminate this effect obviously, but it makes the setup complicated and expensive because two additional sampling channels are needed for detecting Raman anti-Stokes (AS) and Stokes (S) signals. While in practical engineering projects, different special fibers can be added in separate locations to detect distinctive parameters, by which the cross-sensitivity of the system can be partially solved. For example, loose tube fiber is barely affected by the strain in the external circumstances and is sensitive to temperature only. Adding a section of loose tube fiber in the sensing fiber to detect the nearby temperature can provide a temperature reference for the surrounding area.

  • 3). The 10 km sensing range value is not the detection limit and can be further expanded by using longer optical pulses or lowering spatial resolution. The best trade-off between the resolution and the sensing range depends on the applications. Besides, more than 100 km sensing range can be realized when amplifying the scattering light through Raman or EDFA amplifiers in the sensing arm.

4. Conclusions

A hybrid distributed multi-parameter fiber sensing system based on modulated pulses φ/B-OTDR has been demonstrated to measure the vibration, the temperature and the strain with one photo detector and one data acquisition channel. The probe sensing pulse is modulated into two kinds of profiles according to the fast changing property of vibration and the static property of the temperature and the strain, and then injected into the sensing fiber sequentially with ratio of 100:1. In order to get a better spatial resolution, the width of pulses is set to 30 ns and 8 ns separately for φ-OTDR and B-OTDR sensing, matching with their different sensing principles. The modulation of the laser pulse width and intensity not only enables multi-parameter sensing, but also minimizes the noises induced by the nonlinear effects, which enhances the signal-to-noise ratio. Furthermore, Gaussian window short time Fourier transform method and weighted Lorentzian nonlinear fitting method are proceeded to demodulate νB in B-OTDR sensing, in which a sub-meter level spatial resolution is achieved in the temperature and the strain detection eventually. The system can clearly identify up to 4.8kHz vibration at 10km distance along a single-mode fiber with 3m spatial resolution. And measurements of the distributed temperature and stress profile along the same fiber by 80 cm spatial resolution have also been realized simultaneously.

Funding

Ministry of Science and Technology (2016YFC0801200); Natural Science Foundation of China (61635004, 61475029, 61377066, 61405020); Science Fund for Distinguished Young Scholars of Chongqing (CSTC2014JCYJJQ40002).

Acknowledgments

We are particularly grateful to Leilei Shi, Lei Gao and Dongmei Huang for their supports on this work.

References and links

1. J. C. Juarez and H. F. Taylor, “Polarization discrimination in a phase-sensitive optical time-domain reflectometer intrusion-sensor system,” Opt. Lett. 30(24), 3284–3286 (2005). [CrossRef]   [PubMed]  

2. F. Peng, H. Wu, X. H. Jia, Y. J. Rao, Z. N. Wang, and Z. P. Peng, “Ultra-long high-sensitivity Φ-OTDR for high spatial resolution intrusion detection of pipelines,” Opt. Express 22(11), 13804–13810 (2014). [CrossRef]   [PubMed]  

3. M. Jones, “Structural-health monitoring: a sensitive issue,” Nat. Photonics 2(3), 153–154 (2008). [CrossRef]  

4. L. Thévenaz, “Review and progress on distributed fibre sensing,” in Optical Fiber Sensors, OSA Technical Digest (CD) (Optical Society of America, 2006), paper ThC1.

5. X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012). [CrossRef]   [PubMed]  

6. Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration sensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

7. A. Masoudi, M. Belal, and T. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013). [CrossRef]  

8. T. Zhu, Q. He, X. Xiao, and X. Bao, “Modulated pulses based distributed vibration sensing with high frequency response and spatial resolution,” Opt. Express 21(3), 2953–2963 (2013). [CrossRef]   [PubMed]  

9. J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express 24(12), 13121–13133 (2016). [CrossRef]   [PubMed]  

10. F. Wang, W. Zhan, X. Zhang, and Y. Lu, “Improvement of spatial resolution for BOTDR by iterative subdivision method,” J. Lightwave Technol. 31(23), 3663–3667 (2013). [CrossRef]  

11. Y. Weng, E. Ip, Z. Pan, and T. Wang, “Single-end simultaneous temperature and strain sensing techniques based on Brillouin optical time domain reflectometry in few-mode fibers,” Opt. Express 23(7), 9024–9039 (2015). [CrossRef]   [PubMed]  

12. Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016). [CrossRef]  

13. S. Matsuura, M. Kumoda, Y. Anzai, and Y. Koyamada, “Distributed strain measurement in GI fiber with sub-meter spatial resolution by DP-BOTDR,” in 2013 18th OptoElectronics and Communications Conference held jointly with 2013 International Conference on Photonics in Switching, (Optical Society of America, 2013), paper MS2_2.

14. M. A. Farahani and T. Gogolla, “Spontaneous Raman scattering in optical fibers with modulated probe light for distributed temperature Raman remote sensing,” J. Lightwave Technol. 17(8), 1379–1391 (1999). [CrossRef]  

15. J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006). [CrossRef]  

16. M. A. Soto, A. Signorini, T. Nannipieri, S. Faralli, G. Bolognini, and F. Di Pasquale, “Impact of loss variations on double-ended distributed temperature sensors based on Raman anti-Stokes signal only,” J. Lightwave Technol. 30(8), 1215–1222 (2012). [CrossRef]  

17. G. Bolognini and A. Hartog, “Raman-based fibre sensors: trends and applications,” Opt. Fiber Technol. 19(6), 678–688 (2013). [CrossRef]  

18. M. N. Alahbabi, Y. T. Cho, and T. P. Newson, “Simultaneous temperature and strain measurement with combined spontaneous Raman and Brillouin scattering,” Opt. Lett. 30(11), 1276–1278 (2005). [CrossRef]   [PubMed]  

19. G. Bolognini and M. A. Soto, “Optical pulse coding in hybrid distributed sensing based on Raman and Brillouin scattering employing Fabry-Perot lasers,” Opt. Express 18(8), 8459–8465 (2010). [CrossRef]   [PubMed]  

20. M. Taki, A. Signorini, C. J. Oton, T. Nannipieri, and F. Di Pasquale, “Hybrid Raman/Brillouin-optical-time-domain-analysis-distributed optical fiber sensors based on cyclic pulse coding,” Opt. Lett. 38(20), 4162–4165 (2013). [CrossRef]   [PubMed]  

21. Y. S. Muanenda, M. Taki, T. Nannipieri, A. Signorini, C. J. Oton, F. Zaidi, I. Toccafondo, and F. Di Pasquale, “Advanced coding techniques for long-range Raman/BOTDA distributed strain and temperature measurements,” J. Lightwave Technol. 34(2), 342–350 (2016). [CrossRef]  

22. R. Bernini, A. Minardo, and L. Zeni, “Dynamic strain measurement in optical fibers by stimulated Brillouin scattering,” Opt. Lett. 34(17), 2613–2615 (2009). [CrossRef]   [PubMed]  

23. Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011). [CrossRef]   [PubMed]  

24. A. Bergman, L. Yaron, T. Langer, and M. Tur, “Dynamic and distributed slope-assisted fiber strain sensing based on optical time-domain analysis of Brillouin dynamic gratings,” J. Lightwave Technol. 33(12), 2611–2616 (2015). [CrossRef]  

25. A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014). [CrossRef]  

26. D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016). [CrossRef]   [PubMed]  

27. J. Hu, L. Xia, L. Yang, W. Quan, and X. Zhang, “Strain-induced vibration and temperature sensing BOTDA system combined frequency sweeping and slope-assisted techniques,” Opt. Express 24(12), 13610–13620 (2016). [CrossRef]   [PubMed]  

28. Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “A distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser,” Proc. SPIE 9634, 96342C (2015). [CrossRef]  

29. Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “Hybrid distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser and direct detection,” Opt. Lett. 41(3), 587–590 (2016). [CrossRef]   [PubMed]  

30. G. P. Agrawal, Nonlinear Fiber Optics (Academic 2007).

31. H. F. Martins, S. Martin-Lopez, P. Corredera, P. Salgado, O. Frazão, and M. González-Herráez, “Modulation instability-induced fading in phase-sensitive optical time-domain reflectometry,” Opt. Lett. 38(6), 872–874 (2013). [CrossRef]   [PubMed]  

32. W. Chen, Z. Meng, H. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012). [CrossRef]  

33. Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012). [CrossRef]  

34. Y. Yao, Y. Lu, X. Zhang, F. Wang, and R. Wang, “Reducing trade-off between spatial resolution and frequency accuracy in BOTDR using Cohen’s class signal processing method,” IEEE Photonics Technol. Lett. 24(15), 1337–1339 (2012). [CrossRef]  

35. S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016). [CrossRef]  

References

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  1. J. C. Juarez and H. F. Taylor, “Polarization discrimination in a phase-sensitive optical time-domain reflectometer intrusion-sensor system,” Opt. Lett. 30(24), 3284–3286 (2005).
    [Crossref] [PubMed]
  2. F. Peng, H. Wu, X. H. Jia, Y. J. Rao, Z. N. Wang, and Z. P. Peng, “Ultra-long high-sensitivity Φ-OTDR for high spatial resolution intrusion detection of pipelines,” Opt. Express 22(11), 13804–13810 (2014).
    [Crossref] [PubMed]
  3. M. Jones, “Structural-health monitoring: a sensitive issue,” Nat. Photonics 2(3), 153–154 (2008).
    [Crossref]
  4. L. Thévenaz, “Review and progress on distributed fibre sensing,” in Optical Fiber Sensors, OSA Technical Digest (CD) (Optical Society of America, 2006), paper ThC1.
  5. X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012).
    [Crossref] [PubMed]
  6. Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration sensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).
  7. A. Masoudi, M. Belal, and T. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
    [Crossref]
  8. T. Zhu, Q. He, X. Xiao, and X. Bao, “Modulated pulses based distributed vibration sensing with high frequency response and spatial resolution,” Opt. Express 21(3), 2953–2963 (2013).
    [Crossref] [PubMed]
  9. J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express 24(12), 13121–13133 (2016).
    [Crossref] [PubMed]
  10. F. Wang, W. Zhan, X. Zhang, and Y. Lu, “Improvement of spatial resolution for BOTDR by iterative subdivision method,” J. Lightwave Technol. 31(23), 3663–3667 (2013).
    [Crossref]
  11. Y. Weng, E. Ip, Z. Pan, and T. Wang, “Single-end simultaneous temperature and strain sensing techniques based on Brillouin optical time domain reflectometry in few-mode fibers,” Opt. Express 23(7), 9024–9039 (2015).
    [Crossref] [PubMed]
  12. Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
    [Crossref]
  13. S. Matsuura, M. Kumoda, Y. Anzai, and Y. Koyamada, “Distributed strain measurement in GI fiber with sub-meter spatial resolution by DP-BOTDR,” in 2013 18th OptoElectronics and Communications Conference held jointly with 2013 International Conference on Photonics in Switching, (Optical Society of America, 2013), paper MS2_2.
  14. M. A. Farahani and T. Gogolla, “Spontaneous Raman scattering in optical fibers with modulated probe light for distributed temperature Raman remote sensing,” J. Lightwave Technol. 17(8), 1379–1391 (1999).
    [Crossref]
  15. J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
    [Crossref]
  16. M. A. Soto, A. Signorini, T. Nannipieri, S. Faralli, G. Bolognini, and F. Di Pasquale, “Impact of loss variations on double-ended distributed temperature sensors based on Raman anti-Stokes signal only,” J. Lightwave Technol. 30(8), 1215–1222 (2012).
    [Crossref]
  17. G. Bolognini and A. Hartog, “Raman-based fibre sensors: trends and applications,” Opt. Fiber Technol. 19(6), 678–688 (2013).
    [Crossref]
  18. M. N. Alahbabi, Y. T. Cho, and T. P. Newson, “Simultaneous temperature and strain measurement with combined spontaneous Raman and Brillouin scattering,” Opt. Lett. 30(11), 1276–1278 (2005).
    [Crossref] [PubMed]
  19. G. Bolognini and M. A. Soto, “Optical pulse coding in hybrid distributed sensing based on Raman and Brillouin scattering employing Fabry-Perot lasers,” Opt. Express 18(8), 8459–8465 (2010).
    [Crossref] [PubMed]
  20. M. Taki, A. Signorini, C. J. Oton, T. Nannipieri, and F. Di Pasquale, “Hybrid Raman/Brillouin-optical-time-domain-analysis-distributed optical fiber sensors based on cyclic pulse coding,” Opt. Lett. 38(20), 4162–4165 (2013).
    [Crossref] [PubMed]
  21. Y. S. Muanenda, M. Taki, T. Nannipieri, A. Signorini, C. J. Oton, F. Zaidi, I. Toccafondo, and F. Di Pasquale, “Advanced coding techniques for long-range Raman/BOTDA distributed strain and temperature measurements,” J. Lightwave Technol. 34(2), 342–350 (2016).
    [Crossref]
  22. R. Bernini, A. Minardo, and L. Zeni, “Dynamic strain measurement in optical fibers by stimulated Brillouin scattering,” Opt. Lett. 34(17), 2613–2615 (2009).
    [Crossref] [PubMed]
  23. Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
    [Crossref] [PubMed]
  24. A. Bergman, L. Yaron, T. Langer, and M. Tur, “Dynamic and distributed slope-assisted fiber strain sensing based on optical time-domain analysis of Brillouin dynamic gratings,” J. Lightwave Technol. 33(12), 2611–2616 (2015).
    [Crossref]
  25. A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
    [Crossref]
  26. D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
    [Crossref] [PubMed]
  27. J. Hu, L. Xia, L. Yang, W. Quan, and X. Zhang, “Strain-induced vibration and temperature sensing BOTDA system combined frequency sweeping and slope-assisted techniques,” Opt. Express 24(12), 13610–13620 (2016).
    [Crossref] [PubMed]
  28. Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “A distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser,” Proc. SPIE 9634, 96342C (2015).
    [Crossref]
  29. Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “Hybrid distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser and direct detection,” Opt. Lett. 41(3), 587–590 (2016).
    [Crossref] [PubMed]
  30. G. P. Agrawal, Nonlinear Fiber Optics (Academic 2007).
  31. H. F. Martins, S. Martin-Lopez, P. Corredera, P. Salgado, O. Frazão, and M. González-Herráez, “Modulation instability-induced fading in phase-sensitive optical time-domain reflectometry,” Opt. Lett. 38(6), 872–874 (2013).
    [Crossref] [PubMed]
  32. W. Chen, Z. Meng, H. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
    [Crossref]
  33. Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
    [Crossref]
  34. Y. Yao, Y. Lu, X. Zhang, F. Wang, and R. Wang, “Reducing trade-off between spatial resolution and frequency accuracy in BOTDR using Cohen’s class signal processing method,” IEEE Photonics Technol. Lett. 24(15), 1337–1339 (2012).
    [Crossref]
  35. S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
    [Crossref]

2016 (7)

J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express 24(12), 13121–13133 (2016).
[Crossref] [PubMed]

Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
[Crossref]

Y. S. Muanenda, M. Taki, T. Nannipieri, A. Signorini, C. J. Oton, F. Zaidi, I. Toccafondo, and F. Di Pasquale, “Advanced coding techniques for long-range Raman/BOTDA distributed strain and temperature measurements,” J. Lightwave Technol. 34(2), 342–350 (2016).
[Crossref]

D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref] [PubMed]

J. Hu, L. Xia, L. Yang, W. Quan, and X. Zhang, “Strain-induced vibration and temperature sensing BOTDA system combined frequency sweeping and slope-assisted techniques,” Opt. Express 24(12), 13610–13620 (2016).
[Crossref] [PubMed]

Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “Hybrid distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser and direct detection,” Opt. Lett. 41(3), 587–590 (2016).
[Crossref] [PubMed]

S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
[Crossref]

2015 (3)

2014 (2)

F. Peng, H. Wu, X. H. Jia, Y. J. Rao, Z. N. Wang, and Z. P. Peng, “Ultra-long high-sensitivity Φ-OTDR for high spatial resolution intrusion detection of pipelines,” Opt. Express 22(11), 13804–13810 (2014).
[Crossref] [PubMed]

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

2013 (6)

2012 (5)

M. A. Soto, A. Signorini, T. Nannipieri, S. Faralli, G. Bolognini, and F. Di Pasquale, “Impact of loss variations on double-ended distributed temperature sensors based on Raman anti-Stokes signal only,” J. Lightwave Technol. 30(8), 1215–1222 (2012).
[Crossref]

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012).
[Crossref] [PubMed]

W. Chen, Z. Meng, H. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Y. Yao, Y. Lu, X. Zhang, F. Wang, and R. Wang, “Reducing trade-off between spatial resolution and frequency accuracy in BOTDR using Cohen’s class signal processing method,” IEEE Photonics Technol. Lett. 24(15), 1337–1339 (2012).
[Crossref]

2011 (1)

2010 (2)

2009 (1)

2008 (1)

M. Jones, “Structural-health monitoring: a sensitive issue,” Nat. Photonics 2(3), 153–154 (2008).
[Crossref]

2006 (1)

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

2005 (2)

1999 (1)

Alahbabi, M. N.

Ba, D.

Bao, X.

Belal, M.

A. Masoudi, M. Belal, and T. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Bergman, A.

Bernini, R.

Bolognini, G.

G. Bolognini and A. Hartog, “Raman-based fibre sensors: trends and applications,” Opt. Fiber Technol. 19(6), 678–688 (2013).
[Crossref]

M. A. Soto, A. Signorini, T. Nannipieri, S. Faralli, G. Bolognini, and F. Di Pasquale, “Impact of loss variations on double-ended distributed temperature sensors based on Raman anti-Stokes signal only,” J. Lightwave Technol. 30(8), 1215–1222 (2012).
[Crossref]

G. Bolognini and M. A. Soto, “Optical pulse coding in hybrid distributed sensing based on Raman and Brillouin scattering employing Fabry-Perot lasers,” Opt. Express 18(8), 8459–8465 (2010).
[Crossref] [PubMed]

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Cai, H.

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Cao, Z.

S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
[Crossref]

Chen, L.

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012).
[Crossref] [PubMed]

Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration sensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

Chen, W.

W. Chen, Z. Meng, H. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Cho, P.

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Cho, Y. T.

Corredera, P.

Danon, O.

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

Deng, M.

S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
[Crossref]

Di Pasquale, F.

Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “Hybrid distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser and direct detection,” Opt. Lett. 41(3), 587–590 (2016).
[Crossref] [PubMed]

Y. S. Muanenda, M. Taki, T. Nannipieri, A. Signorini, C. J. Oton, F. Zaidi, I. Toccafondo, and F. Di Pasquale, “Advanced coding techniques for long-range Raman/BOTDA distributed strain and temperature measurements,” J. Lightwave Technol. 34(2), 342–350 (2016).
[Crossref]

Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “A distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser,” Proc. SPIE 9634, 96342C (2015).
[Crossref]

M. Taki, A. Signorini, C. J. Oton, T. Nannipieri, and F. Di Pasquale, “Hybrid Raman/Brillouin-optical-time-domain-analysis-distributed optical fiber sensors based on cyclic pulse coding,” Opt. Lett. 38(20), 4162–4165 (2013).
[Crossref] [PubMed]

M. A. Soto, A. Signorini, T. Nannipieri, S. Faralli, G. Bolognini, and F. Di Pasquale, “Impact of loss variations on double-ended distributed temperature sensors based on Raman anti-Stokes signal only,” J. Lightwave Technol. 30(8), 1215–1222 (2012).
[Crossref]

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Dong, Y.

Fan, Z.

Farahani, M. A.

Faralli, S.

Frazão, O.

Gan, J.

Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
[Crossref]

Garcia-Ruiz, A.

Gogolla, T.

Gonzalez-Herraez, M.

González-Herráez, M.

Hao, Y.

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Hartog, A.

G. Bolognini and A. Hartog, “Raman-based fibre sensors: trends and applications,” Opt. Fiber Technol. 19(6), 678–688 (2013).
[Crossref]

He, Q.

Hu, J.

Huang, S.

S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
[Crossref]

Ip, E.

Jia, X. H.

Jones, M.

M. Jones, “Structural-health monitoring: a sensitive issue,” Nat. Photonics 2(3), 153–154 (2008).
[Crossref]

Juarez, J. C.

Kim, P.

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Langer, T.

Lee, D.

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Li, H.

Li, J.

Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
[Crossref]

Li, Q.

Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
[Crossref]

Li, X.

S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
[Crossref]

Liu, J.

S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
[Crossref]

Liu, M.

S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
[Crossref]

Lu, Y.

F. Wang, W. Zhan, X. Zhang, and Y. Lu, “Improvement of spatial resolution for BOTDR by iterative subdivision method,” J. Lightwave Technol. 31(23), 3663–3667 (2013).
[Crossref]

Y. Yao, Y. Lu, X. Zhang, F. Wang, and R. Wang, “Reducing trade-off between spatial resolution and frequency accuracy in BOTDR using Cohen’s class signal processing method,” IEEE Photonics Technol. Lett. 24(15), 1337–1339 (2012).
[Crossref]

Y. Lu, T. Zhu, L. Chen, and X. Bao, “Distributed vibration sensor based on coherent detection of phase-OTDR,” J. Lightwave Technol. 28(22), 3243–3249 (2010).

Lu, Z.

Luo, H.

W. Chen, Z. Meng, H. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Martin-Lopez, S.

Martins, H. F.

Masoudi, A.

A. Masoudi, M. Belal, and T. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Meng, Z.

W. Chen, Z. Meng, H. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Minardo, A.

Motil, A.

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
[Crossref] [PubMed]

Muanenda, Y.

Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “Hybrid distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser and direct detection,” Opt. Lett. 41(3), 587–590 (2016).
[Crossref] [PubMed]

Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “A distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser,” Proc. SPIE 9634, 96342C (2015).
[Crossref]

Muanenda, Y. S.

Nannipieri, T.

Newson, T.

A. Masoudi, M. Belal, and T. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Newson, T. P.

Oton, C. J.

Pan, Z.

Y. Weng, E. Ip, Z. Pan, and T. Wang, “Single-end simultaneous temperature and strain sensing techniques based on Brillouin optical time domain reflectometry in few-mode fibers,” Opt. Express 23(7), 9024–9039 (2015).
[Crossref] [PubMed]

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Park, J.

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Park, N.

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

Pastor-Graells, J.

Peled, Y.

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
[Crossref] [PubMed]

Peng, F.

Peng, Z. P.

Qu, R.

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Quan, W.

Rao, Y. J.

Salgado, P.

Signorini, A.

Soto, M. A.

Taki, M.

Taylor, H. F.

Toccafondo, I.

Tur, M.

Wang, B.

Wang, F.

F. Wang, W. Zhan, X. Zhang, and Y. Lu, “Improvement of spatial resolution for BOTDR by iterative subdivision method,” J. Lightwave Technol. 31(23), 3663–3667 (2013).
[Crossref]

Y. Yao, Y. Lu, X. Zhang, F. Wang, and R. Wang, “Reducing trade-off between spatial resolution and frequency accuracy in BOTDR using Cohen’s class signal processing method,” IEEE Photonics Technol. Lett. 24(15), 1337–1339 (2012).
[Crossref]

Wang, R.

Y. Yao, Y. Lu, X. Zhang, F. Wang, and R. Wang, “Reducing trade-off between spatial resolution and frequency accuracy in BOTDR using Cohen’s class signal processing method,” IEEE Photonics Technol. Lett. 24(15), 1337–1339 (2012).
[Crossref]

Wang, T.

Wang, Z. N.

Weng, Y.

Wu, H.

Wu, Y.

Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
[Crossref]

Xia, L.

Xiao, X.

Yang, F.

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Yang, L.

Yang, Z.

Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
[Crossref]

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Yao, Y.

Y. Yao, Y. Lu, X. Zhang, F. Wang, and R. Wang, “Reducing trade-off between spatial resolution and frequency accuracy in BOTDR using Cohen’s class signal processing method,” IEEE Photonics Technol. Lett. 24(15), 1337–1339 (2012).
[Crossref]

Yaron, L.

Ye, Q.

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Yin, M.

Zaidi, F.

Zeni, L.

Zhan, W.

Zhang, Q.

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

Zhang, X.

Zhang, Z.

Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
[Crossref]

Zhou, D.

Zhou, H.

W. Chen, Z. Meng, H. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Zhu, T.

IEEE Photonics J. (1)

Y. Hao, Q. Ye, Z. Pan, F. Yang, H. Cai, R. Qu, Q. Zhang, and Z. Yang, “Design of wide-band frequency shift technology by using compact Brillouin fiber laser for Brillouin optical time domain reflectometry sensing system,” IEEE Photonics J. 4(5), 1686–1692 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (5)

Y. Yao, Y. Lu, X. Zhang, F. Wang, and R. Wang, “Reducing trade-off between spatial resolution and frequency accuracy in BOTDR using Cohen’s class signal processing method,” IEEE Photonics Technol. Lett. 24(15), 1337–1339 (2012).
[Crossref]

S. Huang, T. Zhu, Z. Cao, M. Liu, M. Deng, J. Liu, and X. Li, “Laser linewidth measurement based on amplitude difference comparison of coherent envelope,” IEEE Photonics Technol. Lett. 28(7), 759–762 (2016).
[Crossref]

Q. Li, J. Gan, Y. Wu, Z. Zhang, J. Li, and Z. Yang, “High spatial resolution BOTDR based on differential Brillouin spectrum technique,” IEEE Photonics Technol. Lett. 28(14), 1493–1496 (2016).
[Crossref]

J. Park, G. Bolognini, D. Lee, P. Kim, P. Cho, F. Di Pasquale, and N. Park, “Raman-based distributed temperature sensor with simplex coding and link optimization,” IEEE Photonics Technol. Lett. 18(17), 1879–1881 (2006).
[Crossref]

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photonics Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

J. Lightwave Technol. (6)

Laser Phys. (1)

W. Chen, Z. Meng, H. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Meas. Sci. Technol. (1)

A. Masoudi, M. Belal, and T. Newson, “A distributed optical fibre dynamic strain sensor based on phase-OTDR,” Meas. Sci. Technol. 24(8), 085204 (2013).
[Crossref]

Nat. Photonics (1)

M. Jones, “Structural-health monitoring: a sensitive issue,” Nat. Photonics 2(3), 153–154 (2008).
[Crossref]

Opt. Express (8)

F. Peng, H. Wu, X. H. Jia, Y. J. Rao, Z. N. Wang, and Z. P. Peng, “Ultra-long high-sensitivity Φ-OTDR for high spatial resolution intrusion detection of pipelines,” Opt. Express 22(11), 13804–13810 (2014).
[Crossref] [PubMed]

T. Zhu, Q. He, X. Xiao, and X. Bao, “Modulated pulses based distributed vibration sensing with high frequency response and spatial resolution,” Opt. Express 21(3), 2953–2963 (2013).
[Crossref] [PubMed]

J. Pastor-Graells, H. F. Martins, A. Garcia-Ruiz, S. Martin-Lopez, and M. Gonzalez-Herraez, “Single-shot distributed temperature and strain tracking using direct detection phase-sensitive OTDR with chirped pulses,” Opt. Express 24(12), 13121–13133 (2016).
[Crossref] [PubMed]

Y. Weng, E. Ip, Z. Pan, and T. Wang, “Single-end simultaneous temperature and strain sensing techniques based on Brillouin optical time domain reflectometry in few-mode fibers,” Opt. Express 23(7), 9024–9039 (2015).
[Crossref] [PubMed]

D. Ba, B. Wang, D. Zhou, M. Yin, Y. Dong, H. Li, Z. Lu, and Z. Fan, “Distributed measurement of dynamic strain based on multi-slope assisted fast BOTDA,” Opt. Express 24(9), 9781–9793 (2016).
[Crossref] [PubMed]

J. Hu, L. Xia, L. Yang, W. Quan, and X. Zhang, “Strain-induced vibration and temperature sensing BOTDA system combined frequency sweeping and slope-assisted techniques,” Opt. Express 24(12), 13610–13620 (2016).
[Crossref] [PubMed]

Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
[Crossref] [PubMed]

G. Bolognini and M. A. Soto, “Optical pulse coding in hybrid distributed sensing based on Raman and Brillouin scattering employing Fabry-Perot lasers,” Opt. Express 18(8), 8459–8465 (2010).
[Crossref] [PubMed]

Opt. Fiber Technol. (1)

G. Bolognini and A. Hartog, “Raman-based fibre sensors: trends and applications,” Opt. Fiber Technol. 19(6), 678–688 (2013).
[Crossref]

Opt. Lett. (6)

Proc. SPIE (1)

Y. Muanenda, C. J. Oton, S. Faralli, T. Nannipieri, A. Signorini, and F. Di Pasquale, “A distributed acoustic and temperature sensor using a commercial off-the-shelf DFB laser,” Proc. SPIE 9634, 96342C (2015).
[Crossref]

Sensors (Basel) (1)

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(12), 8601–8639 (2012).
[Crossref] [PubMed]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic 2007).

L. Thévenaz, “Review and progress on distributed fibre sensing,” in Optical Fiber Sensors, OSA Technical Digest (CD) (Optical Society of America, 2006), paper ThC1.

S. Matsuura, M. Kumoda, Y. Anzai, and Y. Koyamada, “Distributed strain measurement in GI fiber with sub-meter spatial resolution by DP-BOTDR,” in 2013 18th OptoElectronics and Communications Conference held jointly with 2013 International Conference on Photonics in Switching, (Optical Society of America, 2013), paper MS2_2.

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Figures (9)

Fig. 1
Fig. 1 Laser pulse modulation and data processing. (a) The modulated laser pulse sequences and signals captured by data acquisition card (DAQ); (b) φ-OTDR data processing at the vibration point; (c) B-OTDR data processing, data after Gaussian window short time Fourier transform (G-STFT), BG: Brillouin Gain.
Fig. 2
Fig. 2 Data processing for B-OTDR. (a) Beat signal of LO and backscattering light is divide into shorter segments of equal length; (b) The processing of Gaussian window short time Fourier transform (G-STFT); (c) Fitting result of weighted Lorentzian nonlinear fitting (WLF)
Fig. 3
Fig. 3 (a) Experimental setup. AOM: Acousto-Optic Modulator, EDFA: Erbium-Doped Fiber Amplifier, BPF: Band-Pass Filter, PZT: Piezoelectric Transducer, AWG: Arbitrary Waveform Generator, BL: Brillouin Laser, PS: Polarization Scrambler, OS: Optical Switch, PD: Photo Detector, DAQ: Data Acquisition card; (b) Scattering spectra of the sensing fiber at different EDFA pump power; (c) Amplified optical pulses for B-OTDR and φ-OTDR
Fig. 4
Fig. 4 φ-OTDR traces at the end section of the sensing fiber when the PZT is driven by 100Hz (a, c) and 1KHz (b, d) sinusoidal signal. (a, b) superposition of ten traces; (c, d) normalized consecutive traces within 50ms
Fig. 5
Fig. 5 (a)-(d) FFT transform spectra of the vibration point when 500Hz, 1KHz, 3kHz and 4.8kHz sinusoidal signals are applied to the PZT, respectively.
Fig. 6
Fig. 6 (a) Spatial distribution of Brillouin scattering beat frequency signal along the 10km sensing fiber; (b) BFS of end section of the sensing fiber when applied temperate shift, strain and vibration simultaneously. The color bars represent the measured Brillouin gain values.
Fig. 7
Fig. 7 (a) Brillouin frequency shift peaks of Fig. 6(b) extracted by Lorentzian nonlinear fitting; (b) Enlarged frequency shift peak around the 80cm strain section marked by the circle in Fig. 7(a).
Fig. 8
Fig. 8 (a) BFS peaks around water tank section under different temperature; (b) Relationship between the average Brillouin frequency and temperature
Fig. 9
Fig. 9 (a) BFS peaks around 5m strain section under different strains; (b) Relationship between the average Brillouin frequency and strain

Equations (5)

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y(t)= a=1 N I 1 (aT-t) + I 2 ((N+1)T-t)
I i (t)= P i e t 2 / ( τ i 2 2ln2 ) 2
ν B = C ν B T ΔT+ C ν B ε Δε+ ν B0
P STFT (t,ω)= | t g /2 t g /2 e jωτ s(τ)g(τt)dτ | 2
g(t)= e t 2 / ( τ g 2 2ln2 ) 2

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