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Distributed strain and temperature fast measurement in Brillouin optical time-domain reflectometry based on double-sideband modulation

Jianqin Peng, Yuangang Lu, Yuyang Zhang, and Zelin Zhang

Open Access Open Access

Abstract

A novel distributed strain and temperature fast measurement method in Brillouin optical time-domain reflectometry (BOTDR) system based on double-sideband (DSB) modulation is proposed. The single-wavelength probe light is modulated into dual-wavelength probe light with a fixed phase difference by using carrier suppressed DSB modulation. The interaction between the Brillouin scattering signals corresponding to dual-wavelength probe light forms a Brillouin beat spectrum (BBS). The distributed temperature and strain are obtained by only measuring the peak power trace of the BBS and one of the slope power trace of the two Brillouin gain spectrum (BGS) corresponding to dual-wavelength probe light. The proposed method does not require scanning the Brillouin spectrum and does not require using optical fibers with multiple Brillouin scattering peaks as sensing fibers, and thus features fast measurement speed and wide variety of sensing fiber types. In a proof-of-concept experiment, the temperature uncertainty of 1.3 °C and the strain uncertainty of 36.3 με are respectively achieved over a 4.5-km G.657 fiber with 3 m spatial resolution and 30 s measurement time. The experimental measurement uncertainties of temperature and strain of the proposed method are almost equivalent to that of the method by using BGS scanning and special fibers.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

To monitor the nondestructive structural health, distributed optical fiber sensors based on Brillouin scattering have been used for temperature and strain sensing [1–3]. Various methods have been reported thus far, including time-domain [4–7], frequency-domain [8,9] and correlation-domain [10–12]. Among them, the Brillouin optical time domain (BOTD) technologies are the most common technologies. They are categorized into two types: Brillouin optical time-domain reflectometry (BOTDR) and Brillouin optical time domain analyzer (BOTDA). The BOTDR sensor is a one-end-access system, in which only one laser is injected into one end of the sensing fiber. The BOTDA sensor is a more complicated two-end-access system, in which two contra- propagating lasers need to be injected into both ends of a sensing fiber. Although the BOTDA sensor can achieve larger measurement range, they cannot determine the location of the breakpoint when the fiber is broken. Therefore, the one-end-access BOTDR system is more convenient in practical applications.

Generally, the BOTDR methods need to sweep the entire Brillouin gain spectrum (BGS) to obtain the Brillouin frequency shift (BFS) along the fiber. Since the BFS is sensitive to temperature and strain, only measuring one BFS cannot be used to demodulate the temperature and strain. Excellent researches have been carried out to solve the cross-sensitivity problem of temperature and strain. Different combinations of parameters such as double Brillouin frequency shifts (BFS) [13,14], BFS and birefringence [15], BFS and linewidth [16] were measured. However, those measurement methods usually take a lot of time to perform a complete distributed measurement due to they need to sweep the entire BGS.

Recently, many techniques have been proposed for rapid measurement in BOTDR. In 2014, a short-time Fourier transform (STFT) based on BOTDR was proposed. The vibration frequency of 16.7 Hz over 12 m fiber has been measured [17]. In 2017, a slope assisted (SA)-BOTDR method was used to measure a 7.6 Hz vibration of 10 m pipeline [18]. In 2020, a fast BOTDR based on the Frequency-Agile (FA) achieved a 6.82 Hz sampling rate in 172 m single-mode fiber [19]. In addition, a Mach-Zhender interferometer (MZI) based on BOTDR was proposed, which can detect dynamic vibration over 2 km of sensing fiber in every 0.5 s [20]. Most of the fast methods could only be used for the measurement of a single parameter. It is a challenge to achieve fast dual-parameter measurement. Although our proposed method [21,22] based on the intensity of Brillouin beat spectrum (BBS) peak and BGS slope can be used to quickly realize the distributed measurement of temperature and strain, it needs to use the fibers with multiple Brillouin scattering peaks as sensing fiber. In addition, the BGSs excited by these fibers usually only have a strong main peak, thus the intensity of the Brillouin beat peak formed by the interaction of the main peak with other peaks is relatively small. Therefore, the application field of the previously proposed methods is limited.

In this paper, we propose a novel fast dual-parameter sensing method to realize distributed temperature and strain sensing, which is based on double-sideband BOTDR (DSB-BOTDR). The single-wavelength light emitted by the laser is modulated into dual-wavelength light with a fixed phase difference through carrier suppressed DSB modulation. The interaction between the Brillouin scattering peaks excited by double-wavelength light forms a strong BBS peak. One of the advantages of our proposed method is that it can achieve fast measurement without frequency scanning. The temperature and strain variation along the sensing fiber can be obtained by only measuring two power traces corresponding to the BGS slope and the BBS peak. Another advantage is that our proposed method does not require using optical fibers with multiple Brillouin scattering peaks as sensing fibers, thus different types of optical fibers can be used, which greatly expands the application field of the method. In a proof-of-concept experiment, we obtained the temperature measurement uncertainty of 1.3 °C and the strain measurement uncertainty of 36.3 με in a 4.5-km G.657 fiber with 3 m spatial resolution and 30 s measurement time. The experimental measurement uncertainties of temperature and strain of the proposed method are almost equivalent to that of the method by using BGS scanning and special fibers [13,14].

2. Principles

A schematic diagram of the proposed scheme is shown in Fig. 1. A single-wavelength light with frequency v0 is carrier suppressed modulated into dual-wavelength light by a phase modulator (for example an electro-optic modulator (EOM)). Therefore, the dual-wavelength probe light can be obtained by double-sideband (DSB) modulation. The modulator is driven by a RF (radio frequency) signal with frequency ve, whose value is about several hundred MHz for the convenience of detecting the BBS signal at the intermediate frequency. When dual-wavelength probe light is injected into the sensing fiber, the corresponding backward scattering signal will be excited. Then the interaction of Brillouin scattering light form a BBS. The Brillouin scattered light beats with the local reference light to form the BGS whose frequencies are about 11 GHz. After square-law detection in the photodetector (PD), the BGS and the BBS are extracted by the data acquisition system. Finally, the power traces of the BGS slope and the BBS peak (corresponding to the two measured frequency points in Fig. 1) along the sensing fiber are used to realize distributed temperature and strain sensing. We name such a BOTDR system based on DSB modulation as DSB-BOTDR.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the DSB-BOTDR

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In the DSB-BOTDR system, the light source is a single-wavelength laser with frequency v0. The single-wavelength light can be expressed as

$${E_{\textrm{single}}}(t) = {E_0}\exp (i2\pi {\nu _0}t + i{\varphi _0})$$
where E0 and φ0 are respectively the initial amplitude and initial phase of the laser. The carrier suppressed modulation signal generated by the EOM can be written as
$${E_{EOM}}(t) = \frac{\textrm{1}}{\textrm{2}}{E_0}\exp (i2\pi {\nu _0}t)exp\{ iC\cos (2\pi {\nu _e}t) + i{\varphi _\textrm{1}}\}$$
where C=πV/Vπ is the phase modulation index, V is the magnitude of the RF signal, and Vπ is the half-wave voltage of the EOM. In Eq. (2), the φ1=πV/2Vπ is the additional phase. Based on the Bessel function expansion, the ±1st-order sideband signals in Eq. (2) can be expressed as
$${E_{\pm 1}}(t) = A\{\exp(i2\pi({\nu _0} - {\nu _e})t) + {\exp} (i2\pi({\nu _0} - {\nu _e})t)\}$$
where A = E0J1(C)sinφ0/2 is a constant, and J1 is the first-order Bessel functions of the first kind. When the dual-wavelength probe light is injected into the sensing fiber with n Brillouin scattering peaks, the corresponding backward scattering signal will be excited. Then, the Brillouin scattering light in the DSB-BOTDR system can be expressed as
$${E_{ - \textrm{1},bk}}(t) = {\alpha _{bk}}A\exp \{ i2\pi ({\nu _0} - {\nu _e} - {\nu _{ - bk}})t + i{\varphi _{ - bk}}\}$$
and
$${E_{ + \textrm{1,}bk}}(t) = {\alpha _{bk}}A\exp \{ i2\pi ({\nu _0} + {\nu _e} - {\nu _{ + bk}})t + i{\varphi _{ + bk}}\}$$
where αbkis the Brillouin scattering coefficient of the k-th BGS peak (1 ≤ k ≤ n). The v-bk and φ-bk respectively represent the BFS and phase of the k-th BGS peak corresponding to the -1st-order sideband light. The v+bk and φ+bk respectively represent the BFS and phase of the k-th BGS peak corresponding to the +1st-order sideband light. Usually, the frequency difference between the ±1st-order sideband lights is usually less than 2 GHz, which can be ignored compared with 193.5THz (corresponding to the light frequency v0 of about 1550 nm wavelength). Therefore, the BFSs of the ±1st-order sideband lights are almost the same (∼11 GHz in silica optical fibers), i.e., v-bk ≈ v+bk. The local reference light Elocal(t) is expressed as Eq. (1). Then these backward Brillouin scattering signals combined with the local signal, and they can be expressed as $\sum\limits_{i = \textrm{1}}^n {{E_{ - \textrm{1},bi}}(t)} + \sum\limits_{j = \textrm{1}}^n {{E_{\textrm{ + 1},bj}}(t)} + {E_{local}}(t).$ We denote their complex conjugate ${[\sum\limits_{i = \textrm{1}}^n {{E_{ - \textrm{1},bi}}(t)} + \sum\limits_{j = \textrm{1}}^n {{E_{\textrm{ + 1},bj}}(t)} + {E_{local}}(t)]^\ast }$ as the form of $\sum\limits_{i^{\prime} = \textrm{1}}^n {{E^\ast }_{ - \textrm{1},bi^{\prime}}(t)} + \sum\limits_{j^{\prime} = \textrm{1}}^n {{E^\ast }_{\textrm{ + 1},bj^{\prime}}(t)} + {E^\ast }_{local}(t)$. The symbol * represents complex conjugation. After square-law detection in the PD, the electrical signals can be expressed as [23]
$$\begin{aligned} {I_{PD}}(t) &= \eta [\sum\limits_{i = \textrm{1}}^n {{E_{ - \textrm{1},bi}}(t)} + \sum\limits_{j = \textrm{1}}^n {{E_{\textrm{ + 1},bj}}(t)} + {E_{local}}(t)] \cdot [\sum\limits_{i^{\prime} = \textrm{1}}^n {{E^\ast }_{ - \textrm{1},bi^{\prime}}(t)} + \sum\limits_{j^{\prime} = \textrm{1}}^n {{E^\ast }_{\textrm{ + 1},bj^{\prime}}(t)} + {E^\ast }_{local}(t)]\\ &= \sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {\textrm{2}\eta {\alpha _{bi}}{\alpha _{bj}}{A^2}\cos (2\pi (2{\nu _e} - {\nu _{ + bj}} + {\nu _{ - bi}})t + {\varphi _{ + bj}} - {\varphi _{ - bi}})} } \\ &+ \sum\limits_{i = 1}^n {\sum\limits_{i^{\prime} = 1}^n {\eta {\alpha _{bi}}{\alpha _{bi^{\prime}}}{A^2}\cos (2\pi ({\nu _{ - bi}} - {\nu _{ - bi^{\prime}}})t + {\varphi _{ - bi}} - {\varphi _{ - bi^{\prime}}})} } \\ &+ \sum\limits_{j = 1}^n {\sum\limits_{j^{\prime} = 1}^n {\eta {\alpha _{bj}}{\alpha _{bj^{\prime}}}{A^2}\cos (2\pi ({\nu _{ + bj}} - {\nu _{ + bj^{\prime}}})t + {\varphi _{ + bj}} - {\varphi _{ + bj^{\prime}}})} } \\ &+ \sum\limits_{i = 1}^n {\textrm{2}\eta {\alpha _{bi}}E_0^{}A\cos (2\pi ({\nu _{ - bi}} + {\nu _e})t + {\varphi _0} - {\varphi _{ - bi}})} \\ &+ \sum\limits_{j = 1}^n {\textrm{2}\eta {\alpha _{bj}}E_0^{}A\cos (2\pi ({\nu _{ + bj}} - {\nu _e})t + {\varphi _0} - {\varphi _{ + bj}})} + \frac{\textrm{1}}{4}\eta E_0^2 \end{aligned}$$
where η is the responsivity of the PD. In Eq. (6), the first term is the BBS formed by the beating between the n BGS peaks of -1st-order sideband light and the n BGS peaks of +1st-order sideband light. This BBS contains many peaks with different center frequencies such as 2ve+v-b1-v+b1, 2ve+v-b2-v+b1 and 2ve+v-b2-v+b2. However, for the sensing fiber that has multiple BGS peaks, there usually exists only one primary peak with a greater intensity. For example, the primary BGS peak is about 7 dB higher than the other peaks in Ref. [21]. Therefore, in the first term, there is only a dominant beat peak appearing at the frequency of 2ve+v-b1-v+b1, which is originated from the beat of two primary BGS peaks. Since v-b1 ≈ v+b1, the dominant beat peak appears at the frequency of 2ve. The second term is the BBS components formed by the beating among the n BGS peaks corresponding to the -1st-order sideband light. The third term is the BBS components formed by the beating among the n BGS peaks corresponding to the +1st-order sideband light. Compared with the intensity of the dominant beat peak appears at the frequency of 2ve, the intensities of beat peaks in the second and third terms are very small. The fourth term is the BGS with the frequency shifted up by ve, which corresponds to -1st-order sideband light. The fifth term is the BGS with the frequency shifted down by ve, which corresponds to +1st-order sideband light. The intensities of the two primary BGS peaks in the fourth and fifth terms are relatively big. Since ve is about several hundred MHz, the BGSs are still distributed around the frequency of 11GHz. The sixth term is the DC signal generated by the local light. As we can see from Eq. (6), one BBS peak with center frequency of 2ve and two BGS peaks with center frequencies of v-b1+ve and v+b1-ve have greater intensity. Thus, the photocurrent signal of the three dominant peaks in the DSB-BOTDR system can be expressed as
$$\begin{aligned} {I_{\textrm{do}mi}}(t) &= \sum\limits_{i = j}^n {\sum\limits_{j = 1}^n {\textrm{2}\eta {\alpha _{bi}}{\alpha _{bj}}{A^2}\cos (2\pi (2{\nu _e})t + {\varphi _{ + bj}} - {\varphi _{ - bi}})} } \\ &+ 2\eta {\alpha _{b1}}E_0^{}A\cos (2\pi ({\nu _{ - b1}} + {\nu _e})t + {\varphi _0} - {\varphi _{ - b1}})\\ &+ 2\eta {\alpha _{b1}}E_0^{}A\cos (2\pi ({\nu _{ + b1}} - {\nu _e})t + {\varphi _0} - {\varphi _{ + b1}}) \end{aligned}$$

To avoid frequency sweeping, we can realize distributed temperature and strain sensing by measuring the power traces of two frequency points on the BGS and BBS. The measurement principles of the power on the BBS peak and the power on the BGS slope are shown Fig. 2. The first peak is the BBS peak, which corresponds to the first term in Eq. (7). The second and third peaks are the BGS peaks, which respectively correspond to the second and third terms in Eq. (7). For the BGS peak, the ΔfR is the linear region of the low frequency slope of the BGS peak (corresponding to the +1st-order sideband light), which is usually defined as the region where the change in the BGS slope is suppressed within 20% compared to its maximum [24]. The BFS, linewidth and peak power of BGS peak will change as the temperature T1and strain ε1 change to T 2 and ε2, resulting in a change in the BGS slope power at the measurement frequency point vS (i.e., the BGS slope power Pslope(T1, ε1) changes to Pslope(T2, ε2)). As for the BBS peak, the frequency of the beat peak is not sensitive to temperature and strain. The BBS peak power at the measurement frequency point vF is affected by the linewidth and peak power of the BGS peaks. When temperature T1 and strain ε1 change to T 2 and ε2, the BBS peak power Pbeat(T1, ε1) changes to Pbeat(T2, ε2).

 figure: Fig. 2.

Fig. 2. Principle of the power measurement on the BGS slope and the BBS peak.

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The change powers on the BGS slope and the BBS peak, ΔPslope and ΔPbeat, are related to the temperature variation ΔT and strain change Δε by the following equations

$$\Delta {P_{slope}} = {C_{slope - T}}\Delta T + {C_{slope\textrm{ - }\varepsilon }}\Delta \varepsilon$$
and
$$\Delta {P_{beat}}/{P_{beat0}} = {C_{beat\textrm{ - }T}}\Delta T + {C_{beat\textrm{ - }\varepsilon }}\Delta \varepsilon$$
where Cslope-T and Cslope-ε are respectively the temperature coefficient and strain coefficient of the power on the BGS slope. Cbeat-T and Cbeat-ε are the temperature coefficient and strain coefficient of the power on the BBS peak, respectively. Pbeat0 is the reference power of the BBS peak when the fiber is in a loose condition and at the initial temperature. It is worth noting that the power change on the BGS slope, ΔPslope, is expressed in logarithmic form and the power change on the BBS peak, ΔPbeat/Pbeat0, is expressed in the form of relative percentage value. Then the measurement uncertainties of the temperature and strain are respectively [25,26]
$$\delta T\textrm{ = }\frac{{\sqrt {{{({C_{beat\textrm{ - }\varepsilon }}\delta {P_{slope}})}^2} + {{({C_{slope\textrm{ - }\varepsilon }}\delta {P_{beat}})}^2}} }}{{\textrm{|}{C_{slope - T}}{C_{beat\textrm{ - }\varepsilon }} - {C_{beat\textrm{ - }T}}{C_{slope\textrm{ - }\varepsilon }}\textrm{|}}}$$
and
$$\delta \varepsilon = \frac{{\sqrt {{{({C_{beat\textrm{ - }T}}\delta {P_{slope}})}^2} + {{({C_{slope - T}}\delta {P_{beat}})}^2}} }}{{\textrm{|}{C_{slope - T}}{C_{beat\textrm{ - }\varepsilon }} - {C_{beat\textrm{ - }T}}{C_{slope\textrm{ - }\varepsilon }}\textrm{|}}}$$
where δPslope and δPbeat are the power uncertainty on the BGS slope and the power uncertainty on the BBS peak, respectively. Thus, distributed temperature and strain measurement can be realized in DSB-BOTDR by measuring the power trace of the BGS slope and the power trace of BBS peak.

In addition, the spontaneous scattered Brillouin signal is a broadband spectrum in the BOTDR system, the measurement process is different from that of BOTDA system. Take the power measurement on the BGS slope as an example. The power trace of a frequency vS in a BOTDR system is generally obtained by filtering the BGS, and can be expressed as

$${P_{meas}}({v_S},t) = \int_{{v_S} - \Delta v}^{{v_S} + \Delta v} {f(v){P_{si }}} (v,t)dv$$
where Pmeas represents the measured power trace, Psi represents the power trace of a single frequency, f(v) is the filter function, and Δv is the filter bandwidth. It is worth noting that the time response of the filter is closely related to its bandwidth. The shorter the time response of the filter, the larger the corresponding bandwidth. In order to avoid signal distortion, a broadband filter is required in the BOTDR system [4,18]. However, the BOTDR reconstructed from the power trace is affected by different filter bandwidths, which affects the measurement frequency point and sensitivity of the slope power. In the BOTDR experiment, the filter bandwidth is usually around 100 MHz [4,18]. Therefore, the filter bandwidth is set as 100 MHz in our experiment.

3. Experimental results

In a proof-of-concept experiment, the experimental setup of the DSB-BOTDR is shown in Fig. 3. The light source is a 1549.96 nm distributed feedback laser with linewidth 5kHz, which was divided into two branches by a 10/90 coupler. In the branch with 90% power component, the probe light was DSB modulated by an EOM. The frequency of the probe light was down-shifted and up-shifted 400 MHz from that of the original light, respectively. Then the dual-wavelength probe light modulated by Acousto-optic modulator (AOM) to generate a square pulse. The probe pulse was amplified by an erbium-doped fiber amplifier (EDFA), EDFA1, and then amplified spontaneous emission (ASE) is filtered out by a 12.5-GHz-bandwidth optical band pass filter (OBPF). The polarization scrambler (PS) was used to eliminate the fiber birefringence induced power trace fluctuation [27]. The back scattered light was amplified by EDFA2 and EDFA3. An OBPF (OBPF2) with 12.5 GHz-bandwidth and an OBPF (OBPF3) with 3.5 GHz-bandwidth were used to filter the Rayleigh and ASE noise. The Brillouin scattering signal was coupled with the local signal by a coupler and then was detected by a 12.5 GHz-bandwidth PD. Finally, an electrical spectrum analyzer (ESA) was used to acquire the two power traces corresponding to the BGS slope and the BBS peak.

 figure: Fig. 3.

Fig. 3. Experimental setup of the DSB-BOTDR

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In our experiment, the pulse width was 30 ns and the peak power was 100 mW. The measured BGS and BBS are shown in Fig. 4. We choose the low-frequency slope of the first Brillouin scattering peak as the slope measurement area, and the linear range of low-frequency slope of the first Brillouin scattering peak is about 50 MHz. In the distributed measurement experiment, only one power trace of the BBS peak and one power trace of the BGS slope were measured by using the in-phase/quadrature (I/Q) analysis mode in the ESA (R&S FSW). The BBS peak signal centered at 800 MHz and the BGS slope signal centered at 10.03 GHz were measured, respectively. The sampling rate was set as 200 MHz, which corresponds to a spatial resolution of 0.5 m.

 figure: Fig. 4.

Fig. 4. The experimentally measured result of the G.657 fiber. (a) Brillouin scattering spectrum. (b) Brillouin beat spectrum.

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In order to investigate the temperature and strain characteristics of the BGS slope and the BBS peak of the G.657 fiber under test, a 50 m fiber section and a 20 m section were respectively heated and stressed at the end of the G.657 fiber. The rest of the fiber was kept in loose state and at room temperature (∼22 °C) as shown in Fig. 3. To eliminate the fluctuation along the power traces, the measurement results were averaged 20000 times, and the total measurement time was 30 s. In the temperature experiment, six different temperatures between 22 °C and 62 °C were measured with temperature step of 8 °C. As shown in Fig. 5(a), the calibration temperature-power coefficients of BGS slope and BBS peak are -0.094 ± 0.03 dB/°C and (3.4 ± 0.2)×10−3 /°C, respectively. The power traces of the BGS slope and the BBS peak at six different temperature stages are shown in Fig. 5(b) and Fig. 5(c), respectively. As for the strain experiment, the device of stretching the fiber is shown in the Fig. 3. The length of the stretched fiber is 20.4 m. When the displacement driver moves 2 mm, the strain of the optical fiber is 196 με. Thus the 20.4-m-long section of the fiber was stretched to generate five different strain states of 196, 392, 588, 784 and 980 με. As shown in the Fig. 6(a), the strain-power coefficients within the stressed fiber section on BGS slope and BBS peak are (-4.5 ± 0.2) ×10−3 dB/με and (−9.5 ± 0.7)×10−6 /με, respectively. The power traces of the BGS slope and the BBS peak at six different strain stages are shown in Fig. 6(b) and Fig. 6(c), respectively. The spatial resolutions corresponding to BGS signal and BBS signal are both 3 m.

 figure: Fig. 5.

Fig. 5. Temperature measurement results. (a) Temperature coefficients calibration. (b) Power traces of the BGS slope. (c) Power traces of the BBS peak.

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 figure: Fig. 6.

Fig. 6. Strain measurement results. (a) Strain coefficients calibration. (b) Power traces of the BGS slope. (c) Power traces of the BBS peak.

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When the heating section was heated to 54 °C and the stretching section was stressed to 588 με, the power traces of BGS slope and BBS peak are shown in Fig. 7(a). Then the temperature and strain distributions can be obtained by using the Eq. (8) and Eq. (9), and the results are shown in Fig. 7(b). The experimental measurement uncertainty of temperature (δTe) in the heating section (from 4299 m to 4343 m) and that of strain (δεe) in the stretching section (from 4369 m to 4385 m) are respectively 1.3 °C and 36.3 με. In our experiment, the power uncertainties, δPslope and δPbeat, are respectively 0.07 dB and 0.4%, which can be obtained by calculating the standard deviations of 20 data points. By solving the Eq. (10) and Eq. (11), the theoretical measurement uncertainties of temperature (δTt) and strain (δεt) are respectively 1.1 °C and 27.5 με. The differences between the theoretical measurement uncertainties and the experimental measurement uncertainties may originate from the estimation errors of linear coefficients (Cslope-T, Cslope-ε, Cbeat-T and Cbeat-ε) and temperature fluctuation of the temperature control system. The experimental measurement uncertainties of temperature and strain of the proposed method are almost equivalent to that of the methods by using BGS scanning and special fiber (1.7 °C and 39 με in Ref. [13], 1 °C and 33 με in Ref. [14]). Compared with our previous research [21,22], the sensing fiber used in this method is no longer limited to the fiber with multiple peaks. The appropriate optical fiber can be selected according to actual needs for improving the sensing performance. In our experiment, we choose the G.657 fiber as the sensing fiber to obtain stronger BGS peak and BBS peak. And the G.657 fiber is a bending-insensitive fiber, which can reduce the influence of bending loss on measurement. However, the linear range of the BGS slope is usually about 50 MHz [18], which corresponds to approximately 50 °C or 1000 με. Although the 50 °C or 1000 με measurement range is narrow to some extent, it can still meet the measurement requirements of many applications.

 figure: Fig. 7.

Fig. 7. When the heating section was heated to 54 °C and the stretching section was stressed to 588 με, (a) the power traces of BGS slope and BBS peak, (b) the temperature and strain distributions.

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4. Conclusion

In conclusion, we have proposed and experimentally demonstrated a distributed temperature and strain sensing in BOTDR based on DSB modulation. This system only needs to measure the power trace of the two frequency points corresponding to BGS slope and BBS peak. The optical fibers with a strong Brillouin scattering peak are suitable for this method. In a proof-of-concept experiment, a 4.5-km G.657 fiber with only a Brillouin scattering peak was used for temperature and strain sensing, and the total measurement time was 30 s. A temperature measurement uncertainty of 1.3 °C and a strain measurement uncertainty of 36.3 με are obtained, respectively. The experimental measurement uncertainties of temperature and strain of the proposed method are almost equivalent to that of the method by using BGS scanning and special fiber. By choosing different optical fibers, this approach will have more industrial applications with better sensing performance (such as higher measurement accuracy and longer measurement range).

Funding

National Natural Science Foundation of China (61377086, 61875086, 62175105).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (7)
Fig. 1.
Fig. 1. Schematic diagram of the DSB-BOTDR

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Fig. 2.
Fig. 2. Principle of the power measurement on the BGS slope and the BBS peak.

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Fig. 3.
Fig. 3. Experimental setup of the DSB-BOTDR

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Fig. 4.
Fig. 4. The experimentally measured result of the G.657 fiber. (a) Brillouin scattering spectrum. (b) Brillouin beat spectrum.

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Fig. 5.
Fig. 5. Temperature measurement results. (a) Temperature coefficients calibration. (b) Power traces of the BGS slope. (c) Power traces of the BBS peak.

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Fig. 6.
Fig. 6. Strain measurement results. (a) Strain coefficients calibration. (b) Power traces of the BGS slope. (c) Power traces of the BBS peak.

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Fig. 7.
Fig. 7. When the heating section was heated to 54 °C and the stretching section was stressed to 588 με, (a) the power traces of BGS slope and BBS peak, (b) the temperature and strain distributions.

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Equations (12)

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E single ( t ) = E 0 exp ⁡ ( i 2 π ν 0 t + i φ 0 )
E E O M ( t ) = 1 2 E 0 exp ⁡ ( i 2 π ν 0 t ) e x p { i C cos ⁡ ( 2 π ν e t ) + i φ 1 }
E ± 1 ( t ) = A { exp ⁡ ( i 2 π ( ν 0 − ν e ) t ) + exp ( i 2 π ( ν 0 − ν e ) t ) }
E − 1 , b k ( t ) = α b k A exp ⁡ { i 2 π ( ν 0 − ν e − ν − b k ) t + i φ − b k }
E + 1, b k ( t ) = α b k A exp ⁡ { i 2 π ( ν 0 + ν e − ν + b k ) t + i φ + b k }
I P D ( t ) = η [ ∑ i = 1 n E − 1 , b i ( t ) + ∑ j = 1 n E  + 1 , b j ( t ) + E l o c a l ( t ) ] ⋅ [ ∑ i ′ = 1 n E ∗ − 1 , b i ′ ( t ) + ∑ j ′ = 1 n E ∗  + 1 , b j ′ ( t ) + E ∗ l o c a l ( t ) ] = ∑ i = 1 n ∑ j = 1 n 2 η α b i α b j A 2 cos ⁡ ( 2 π ( 2 ν e − ν + b j + ν − b i ) t + φ + b j − φ − b i ) + ∑ i = 1 n ∑ i ′ = 1 n η α b i α b i ′ A 2 cos ⁡ ( 2 π ( ν − b i − ν − b i ′ ) t + φ − b i − φ − b i ′ ) + ∑ j = 1 n ∑ j ′ = 1 n η α b j α b j ′ A 2 cos ⁡ ( 2 π ( ν + b j − ν + b j ′ ) t + φ + b j − φ + b j ′ ) + ∑ i = 1 n 2 η α b i E 0 A cos ⁡ ( 2 π ( ν − b i + ν e ) t + φ 0 − φ − b i ) + ∑ j = 1 n 2 η α b j E 0 A cos ⁡ ( 2 π ( ν + b j − ν e ) t + φ 0 − φ + b j ) + 1 4 η E 0 2
I do m i ( t ) = ∑ i = j n ∑ j = 1 n 2 η α b i α b j A 2 cos ⁡ ( 2 π ( 2 ν e ) t + φ + b j − φ − b i ) + 2 η α b 1 E 0 A cos ⁡ ( 2 π ( ν − b 1 + ν e ) t + φ 0 − φ − b 1 ) + 2 η α b 1 E 0 A cos ⁡ ( 2 π ( ν + b 1 − ν e ) t + φ 0 − φ + b 1 )
Δ P s l o p e = C s l o p e − T Δ T + C s l o p e  -  ε Δ ε
Δ P b e a t / P b e a t 0 = C b e a t  -  T Δ T + C b e a t  -  ε Δ ε
δ T  =  ( C b e a t  -  ε δ P s l o p e ) 2 + ( C s l o p e  -  ε δ P b e a t ) 2 | C s l o p e − T C b e a t  -  ε − C b e a t  -  T C s l o p e  -  ε |
δ ε = ( C b e a t  -  T δ P s l o p e ) 2 + ( C s l o p e − T δ P b e a t ) 2 | C s l o p e − T C b e a t  -  ε − C b e a t  -  T C s l o p e  -  ε |
P m e a s ( v S , t ) = ∫ v S − Δ v v S + Δ v f ( v ) P s i ( v , t ) d v
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