Slope-Assisted Brillouin-Based Distributed Fiber-Optic Sensing Techniques

State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Radar Research Lab, School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China Key Laboratory of Electronic and Information Technology in Satellite Navigation (Beijing Institute of Technology), Ministry of Education, Beijing 100081, China Beijing Institute of Technology Chongqing Innovation Center, Chongqing 401120, China


Introduction
Recently, aging degradation and seismic damage of civil infrastructures such as bridges, pipelines, and buildings have posed a serious issue for public security. Diagnosing the health of structures in a fully distributed manner could help prevent the structural collapse of buildings and other civil works. Distributed fiber-optic sensing is a promising technology due to its unique advantages, including a large number of effective sensing points, high sensitivity, long measurement range, high spatial resolution, immunity to electromagnetic interference, small size, and light weight.
Brillouin-based distributed fiber-optic sensing, invented in the late 1980's, is one of the most important fiber-optic sensing techniques since it reveals the temperature and strain information by simply measuring the Brillouin frequency shift (BFS) distribution along with the fiber under test (FUT) [1]. Generally, the Brillouin-based fiber-optic sensors can be classified into two categories: "analysis" based on stimulated Brillouin scattering (SBS) and "reflectometry" based on spontaneous Brillouin scattering (SpBS). For each category, various distributed sensing techniques have been proposed, including Brillouin optical time-domain analysis/reflectometry (BOTDA/R) [1][2][3][4], Brillouin optical frequency-domain analysis/reflectometry (BOFDA/R) [5][6][7][8], and Brillouin optical correlation domain analysis/reflectometry (BOCDA/R) [9][10][11][12][13]. Furthermore, great research efforts have been devoted to further extend the application fields of these techniques through recently achieved enhanced performance in each of its critical dimensions: measurement range has been extended to hundreds of kilometers [14,15]; spatial resolution is of the order of a few millimeters [16][17][18][19]; dynamic events can be captured at sampling rates as high as MHz [20,21]; temperature/strain sensitivity has been enhanced by a factor of six by exploiting the high-order Stokes waves [22,23].
Generally, in a Brillouin-based sensing system, the whole Brillouin gain spectrum (BGS) is supposed to be measured by sweeping the frequency interval between the pump wave and Stoke wave, to extract the BFS and therefore to obtain the temperature/strain information along the FUT. Nevertheless, the frequency sweeping process used to obtain the BGS is relatively time-consuming and therefore limits the sampling rate of the Brillouin-based sensing system. Recently, a novel measurement scheme called slope-assisted technique has been proposed by exploiting the linear slope of the BGS [24]. In this scheme, the frequency interval between the pump wave and probe (or reference) wave is fixed at the middle of the BGS linear slope, to convert the temperature/ strain-induced BFS change to Brillouin signal power variation, where the frequency sweeping process is avoided and the sampling rate is improved significantly.
In this article, the theoretical principles of the slopeassisted Brillouin-based sensing technique are introduced firstly, which is presented in Section 2. Then, in Section 3, the recent research progress on slope-assisted Brillouin timedomain sensing systems is reviewed, including slope-assisted BOTDA (SA-BOTDA), slope-assisted BOTDR (SA-BOTDR), and slope-assisted Brillouin dynamic grating (BDG) sensor. In Section 4, recent advancement on slope-assisted Brillouin correlation domain sensing systems is reviewed, including slopeassisted BOCDA (SA-BOCDA) and slope-assisted BOCDR (SA-BOCDR). At last, the possible future research directions in this area are discussed in Section 5.

Theoretical Principles
Brillouin-based fiber-optic sensing is implemented by using the Brillouin nonlinear process in the optical fiber, where acoustic phonons scatter a forward propagating optical pump wave into a backward propagating Brillouin signal wave. The backscattered lightwave has a characteristic frequency shift from that of the pump wave, called BFS, which changes linearly with the local temperature and the strain applied to the optical fiber. For standard single-mode fibers (SMFs) pumped at wavelengths around 1550 nm, the temperature and strain coefficients are about 1 MHz/°C and 0.05 MHz/με, respectively [25]. Therefore, using appropriate interrogation techniques, the distributed temperature/strain information can be extracted from the BFS distribution along the whole FUT.
In a Brillouin-based sensing system, to obtain the temperature/strain information, the BGS is measured either by using a Brillouin amplification scheme where SBS process is introduced, or by using a Brillouin generation scheme where SpBS is generated [26]. Mathematically, when a pump wave is launched into the optical fiber, the Brillouin gain of the probe (or Stokes) wave can be given by where PðzÞ is the pump power at z, g 0 is the Brillouin gain coefficient, ν is the frequency interval between the pump wave and probe wave (or Stokes), ν B ðzÞ is the BFS at location z, whose typical value is 11 GHz for SMF, Δν B is the full width as half maximum (FWHM) of the BGS, whose typical value is 35 MHz, and K is a coefficient determined by material constants and the relative polarizations of the pump wave and Stoke wave. Figure 1(a) shows the schematic illustration of the slopeassisted measurement scheme. When the ambient temperature is increased or a strain is applied to the optical fiber, the measured BGS curve will shift to a higher frequency, and the Brillouin signal power at a certain pump-probe (or reference) frequency interval will change accordingly. When the frequency interval is set at the linear slope of the BGS, the strain/temperature-induced BFS change is linearly converted to the Brillouin signal power variation. In this case, the timeconsuming frequency sweeping process is avoided, and the measurement speed increases drastically. Figure 1(b) shows that when a dynamic strain is applied to a fiber, the Brillouin signal power at a certain pump-probe (or reference) frequency interval (within the linear-slope range) will change at the same frequency of the dynamic strain. This means that dynamic strains can be measured with a high sampling rate by using the slope-assisted measurement scheme.
3.1. SA-BOTDA. Up to now, various techniques have been proposed to improve the performance of SA-BOTDA in each of its critical dimensions: SA-BOTDA with specially synthesized probe wave has been proposed for distributed dynamic sensing in optical fibers with arbitrary Brillouin profile [24,29]; pump-power-independent measurements can be implemented by double-SA-BOTDA [31]; and a much wider strain dynamic range can be realized by a variety of techniques, such as SA-BOTDA based on Brillouin Phase-Gain Ratio [32], multi-SA-BOTDA [33][34][35], and SA-BOTDA enhanced by BGS engineering [40,41].
3.1.1. SA-BOTDA-Based Sensing in Optical Fibers with Arbitrary Brillouin Profile. The slope-assisted concept is firstly introduced into BOTDA by Peled et al. in 2011 [24], to implement distributed measurement of fast strain variations along the entire fiber used for sensing applications. In this scheme, instead of using a CW probe wave and a swept frequency pump pulse, a pump pulse with a fixed optical frequency and a CW probe wave with variable optical frequency are employed. Since the BFS has a nonuniform spatial distribution along the FUT, the static BGS is firstly measured by using classical BOTDA, and the BFS distribution is extracted accurately. To implement distributed dynamic strain measurement, the frequency of the probe wave is temporally 2 Advanced Devices & Instrumentation tailored in such a way that when the probe wave meets the counter-propagating pump pulse at an arbitrary location along the fiber, the optical frequency difference between these two waves sits as close as possible to the middle of the BGS slope, as shown in Figure 2(a). In this way, the straininduced BFS change is linearly converted to the Brillouin power change, and the time-consuming frequency sweeping process is avoided. Therefore, the measurement speed of the sensing system is greatly improved, and the sampling rate is limited only by the fiber length L and the averaging number N a vg to a value bounded by 1/½2N a vgL/v g , where v g is the fiber group velocity. Figure 2(b) shows the detailed experimental setup, which is similar to the conventional BOTDA system, except for an arbitrary waveform generator (AWG) employed to generate complex probe wave. By using the proposed technique, strain vibrations of a few hundred Hz were measured with a high measurement accuracy of 0.25 MHz (5 με). The measurement range and spatial resolution are 85 m and 1.5 m, respectively, and the strain dynamic range is 30 MHz (600 με), which is determined by the linear slope range of the BGS. Subsequently, the SA-BOTDA is used for monitoring the propagation of the mechanical wave, and the 3D view of the strain distribution is shown in Figure 2(c). The  3 Advanced Devices & Instrumentation propagation velocity of the mechanical wave was measured to be 9 m/s, which matches well with the results measured by the FBG sensors.
3.1.2. Double-SA-BOTDA. A practical problem with SA-BOTDA is the dependence of the conversion factor on variations in the optical power of the pump wave. To solve this problem, a double-SA-BOTDA technique was proposed by Motil et al. in 2014 [31], where the temperature/strain information is extracted from the ratio between readings taken on both slopes of the BGS. In this method, the pump-probe frequency interval ν is set at either the positive slope (ν + ) or the negative slope (ν − ) of the BGS, and the Brillouin gain for these two cases can be given by [31] According to Equations (2) and (3), the Brillouin gain is sensitive to not only the BFS v B ðzÞ but also the pump power PðzÞ, which may lead to a deteriorated measurement accuracy. When double-SA-BOTDA is implemented, the ratio between readings taken on both slopes of the BGS can be expressed as [31] It can be observed that the ratio is a function of the BFS v B ðzÞ but is independent on the pump power PðzÞ. However, since the pump-probe frequency interval is sequentially changed between v + and v − , the ultimate sampling rate is halved compared with the conventional SA-BOTDA.
The experimental setup of the double-SA-BOTDA is similar to SA-BOTDA. Figure 3(a) shows the measured Brillouin gain change using the conventional SA-BOTDA when 55-Hz strain vibrations are applied to the FUT in the presence of >6 dB pump power variation, and Figure 3(b) shows the extracted 55 Hz strain variations using double-SA-BOTDA, where the effect induced by the pump power variation is eliminated, which matches well with the theoretical analysis. By using the proposed method, a sampling rate of 1 kHz and a spatial resolution of 1.5 m over a 13-m-long FUT were realized with good immunity to pump power variation.

SA-BOTDA Based on Brillouin Phase-Gain Ratio.
In the abovementioned SA-BOTDA systems, the strain dynamic range is normally limited to 30 MHz (600 με), which is determined by the linear slope range of the BGS. To extend the strain dynamic range, a novel technique by introducing a new parameter called Brillouin phase-gain ratio (BPGR) has been proposed [32,33], which combines both the Brillouin phase shift and Brillouin gain. Mathematically, the Brillouin phase spectrum (BPS) and BGS can be expressed as [32] BPS Then, the BPGR can be given by [32] BPGR According to Equation (6), the BPGR is linearly proportional to the BFS v B ðzÞ; therefore, a much wider strain dynamic range can be realized. Moreover, the BPGR is independent on the pump power variation, which leads to a high measurement accuracy. Figure 4(a) shows the detailed experimental setup. Different from the conventional SA-BOTDA system, a Mach-Zehnder interferometer with an acousto-optic modulator (AOM) incorporated into its lower branch was employed to extract both the BPS and the BGS. When a periodical strain with a peak-to-peak value of 2000 με was applied to the FUT, the BFS change measured using Brillouin phase shift and BPGR are given in Figures 4(b) and 4(c), which shows that the strain dynamic range is enlarged significantly. By using the proposed system, a strain dynamic range of 100 MHz (2000 με), a sampling rate of 1 kHz, a spatial resolution  [34]. As shown in Figure 5(a), the left part denotes the double-SA-BOTDA, and the right part denotes the multi-SA-BOTDA. In the multi-SA-BOTDA, the probe wave consists of several frequency tones, which is realized using a frequency-agile modulation technique. When the BFS is between Tone 1 and Tone 2, it can be demodulated by the gains of Tone 1 and Tone 2 using the same algorithm as double-SA-BOTDA. When the BFS is between Tone 2 and Tone 3, these two tones can be utilized to extract the BFS. In this way, the BFS can always be determined via a pair of neighboring tones. Since the frequency differences between the probe tones and the pump are known, the BFS can be demodulated accurately. It is worth noting that when a probe wave with N frequency tones is employed, the strain dynamic range can be enlarged by a factor of N − 1, while the sampling rate is reduced by N times compared with the conventional SA-BOTDA. The experimental setup of the multi-SA-BOTDA is similar to the conventional SA-BOTDA system, except for an AWG employed to generate complex probe wave with several frequency tones. In this work, to make the comparison more reliable, two different methods including the multi-SA-BOTDA and the curve-fitting-based fast BOTDA were used to track a nonsine-changed dynamic strain applied to the FUT, and the experimental results are shown in Figure 5(b). The results obtained using these two methods matched well. By using the proposed technique, an ultrawide strain dynamic range of 241 MHz (5000 με), a sampling rate of 1 kHz, a spatial resolution of 1 m, and a measurement range of 32 m were achieved.
Subsequently, to further improve the performance of the sensing system, Zhou et al. proposed a novel technique by combining the BPGR concept and the multislope-assisted measurement scheme [33], and an ultrawide strain dynamic range of 254.3 MHz (5372.9 με) was realized.
In the abovementioned multi-SA-BOTDA systems, the frequency of the probe wave is switched rapidly using a frequency agile modulation technique, where a wide strain dynamic range is achieved at the expense of a reduced sampling rate. Recently, Zheng et al. proposed a novel coherent multi-SA-BOTDA [35], and all the slopes can be interrogated simultaneously; therefore, a large dynamic range can be attained without frequency sweep. Figure 6(a) shows the experimental setup. An AOM at the lower branch was employed to generate the pulsed pump wave. On the upper branch, an electro-optic modulator (EOM) driven by an 11-GHz RF signal along with a fiber Bragg grating (FBG) was employed to generate a downshifted lightwave. Subsequently, another EOM (working frequency: 60 MHz) and AOM (working frequency: 240 MHz) connected after the FBG were used to synthesize the multitone probe wave and the reference wave. The frequency spectrum of the probe wave is shown in the inset of Figure 6(a). In this way, all the Brillouin gain slopes and phase-shift slopes can be extracted simultaneously from the low-frequency beat signals at different frequencies. Figure 6(b) shows the measured dynamic strains when the fiber segment is stretched by an electrical motor with different frequencies. By using this method, a strain dynamic range of 180 MHz, a sampling rate of 1.5 kHz, and a spatial resolution of 2.5 m over a measurement range of 2 km were achieved with good immunity to pump power variation.  [40]. In the proposed method, the pump wave (wP) was firstly modulated by two-tone RF signals (ω RF and 2ω RF ) and then carved to an optical pulse, and the modulated light wave can be expressed as where AðtÞ is the envelope of the pump pulse, A 1 and A 2 are the modulation depths of the two tones, respectively, and φ 1 and φ 2 are the corresponding modulation phases. By properly controlling the modulation frequency and depths, the BGS can be reconfigured to a desired shape with a wide linear slope range, which leads to an enlarged strain dynamic range. The experimental setup is shown in Figure 7(a), where an intensity modulator (IM) and an AOM were used jointly to generate the complex optical pump pulse. BGSs obtained using different pump pulses are shown in Figure 7(b). It can be observed that when two-tone RF signals were utilized, the linear slope range of the BGS was enlarged significantly. Recently, to improve the sensitivity of SA-BOTDA, Feng et al. proposed a novel BGS engineering technique by combining the Brillouin gain and loss [42]. To synthesize the Brillouin spectrum with a desired shape, two probe waves with carefully-designed frequencies were employed, where one generated a Brillouin gain and the other one introduced a Brillouin loss. By using this technique, a much wider drift tolerant frequency range (DTFR) and a measurement accuracy of 8.8 με were achieved, and the sampling rate was as high as 12.5 kHz at the expense of a limited measurement range.
3.2. SA-BOTDR. BOTDA based on SBS provides a high single-to-noise ratio (SNR) and measurement accuracy, but it requires two-end access of optical fibers to make possible the interaction between the two counterpropagating lightwaves. Alternately, BOTDR, as a singleended monitoring system, has a great potential in industrial applications due to its high flexibility and robustness in practical implementation and maintenance, because if the fiber is broken, measurement can still be made up to the breaking point.
To improve the measurement speed of BOTDR, Maraval et al. proposed a novel SA-BOTDR technique for singleended truly distributed dynamic strain measurement in 2018 [42]. In this system, the optical local oscillator frequency is carefully adjusted to measure the backscattered Brillouin signal power at the maximum slope of the BGS   Advanced Devices & Instrumentation along the FUT. In this way, strain-induced BFS change will be detected by amplitude variations. Figure 8(a) shows the experimental setup, and a 10.4-m-long steel pipe was used as the demonstrator, where optical fibers were adhered on its surface. Figure 8(b) shows the measured displacement variations at the central position of the steel pipe when it is oscillated with a frequency of 1.1 Hz, which matches well with the results obtained by the laser sensor. The sampling rate of the SA-BOTDR was set to be 7.6 Hz. Similar to the conventional SA-BOTDA system, the strain dynamic range of SA-BOTDR is limited to 30 MHz (600 με), and the sampling rate is about tens of Hz, which is limited by the low SNR of the BOTDR system.

Slope-Assisted Brillouin Dynamic Grating Sensor.
In SA-BOTDA and SA-BOTDR, the spatial resolution is determined by the duration of the pump pulse, which is practically limited to 10 ns-equivalent to 1 m spatial resolution-since the broadening of the pump spectrum that results from a decreased pulse duration leads to a significant spectral spreading of the measured BGS. To improve the spatial resolution, Bergman et al. proposed a novel dynamic and distributed slope-assisted sensing system based on the BDG in a polarization-maintaining fiber (PMF) [43][44][45]. As shown in Figure 9(a), BDGs are generated in a PMF by two counter-propagating optical pump waves (ω Pump−H and ω Pump−L , where ω Pump−H > ω Pump−L ), which are copolarized along the slow axis of the PMF. The interference between these two optical pump waves generates a moving longitudinal density wave, whose strength depends on the frequency interval between two pumps. Via the elastooptic effect, this induced longitudinal acoustic wave is actually a moving Bragg grating, which can back-reflect an orthogonally polarized probe pulse (ω Probe ), and the reflectivity R Probe depends on the relationship among the three optical frequencies involved: ω Pump−H , ω Pump−L , and ω Probe , attaining a maximum when the phase-matching conditions are met, given by where ν B is the BFS of the PMF, and v BDG is the BDG frequency shift, which is determined by the birefringence of the PMF. According to the theoretical analysis, the reflectivity R Probe is dependent on ν B and v BDG , which are functions of  Advanced Devices & Instrumentation the strain applied to the optical fiber. Therefore, by carefully setting the values of ω Pump−H , ω Pump−L , and ω Probe , the strain information can be extracted from the power variations of the reflected probe wave. It is worth noting that the generated BDG is practically independent on the duration of the probe pulse; therefore, a much higher spatial resolution can be achieved. The detailed experimental setup is shown in Figure 9(a), and two laser diodes were employed to generate the pump and probe waves. Figure 9(b) shows the measured dynamic strains when a sinusoidal vibration with a frequency of 400 Hz was applied to the FUT. By using the proposed technique, an ultrahigh sampling rate of 16 kHz and a high spatial resolution of 4.2 cm over a measurement range of 5 m were realized. Subsequently, a probe coding technique was introduced into the slopeassisted BDG sensing system by the same group [44], to improve the sensitivity and the sampling rate further, and an ultrahigh sampling rate of 1 MHz along with a spatial resolution of 20 cm was achieved.

Slope-Assisted Brillouin Correlation Domain Sensors
Researchers have proposed two kinds of slope-assisted Brillouin correlation domain sensing systems, including SA-BOCDA [11,27,28,[46][47][48] and SA-BOCDR [49][50][51][52][53][54][55][56][57][58].   [11], and dynamic strain measurement was implemented at a fixed sensing point. In 2017, the double-slope-assisted measurement scheme was introduced into the phase-BOCDA system by Morosi et al., and distributed static strain measurement with a spatial resolution of 2 cm and good immunity to pump power variation was realized [46]. In 2019, we proposed a novel double-SA-BOCDA based on synthesis of optical coherence function (SOCF) [27,28]. The experimental setup of the proposed system is shown in Figure 10(a). The laser source was sinusoidally frequency modulated to synthesize periodical correlation peaks, thus to implement distributed measurement. An injectionlocking technique was employed to remove the parasitic intensity noise of the laser source, so as to improve the measurement accuracy and the stability of the system. A PMF was used as the FUT to avoid the polarization-dependent power variations. A lock-in amplifier-(LIA-) based detection technique was also introduced to improve the system SNR.
As a demonstration, the proposed system was used to track the propagation of mechanical wave along the FUT. A 3.0-m-long (5.0 m-8.0 m) fiber section was tightly adhered on the top surface of a thick rubber sheet. A mechanical wave is manually generated and then propagated along the FUT.
The measured temporal variations of strain distribution are shown in Figure 10(b), and the propagation speed was calculated to be 9 m/s, which matches well with the results measured by SA-BOTDA [29]. Moreover, benefiting from the ultrahigh spatial resolution, it is found that the bandwidth of the mechanical wave becomes narrower when it propagates from 5.0 m to 8.0 m. By using the proposed technique, a sampling rate of 625 Hz, a strain dynamic range of 35 MHz (700 με), and a spatial resolution of 7 cm over a measurement range of 10 m were achieved with good immunity to fiber loss and pump power variation.

SA-BOCDA Based on Chaotic Laser.
In the SOCF-based BOCDA system, there is a trade-off between the measurement range and the spatial resolution, and the number of effective sensing points is normally limited to about 1000. Recently, Zhang et al. proposed a novel Brillouin correlation domain sensing system by using a chaotic laser as the optical source of the system, which is called chaotic-BOCDA [19]. Moreover, to improve the measurement speed, the slope-assisted measurement scheme was introduced into this new type of BOCDA sensor [47]. It is worth noting that the linear slope range of the BGS was broadened since the broadband chaos provides a Gaussian-shape pump-probe beat spectrum, and therefore, the strain dynamic range was extended accordingly.

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Advanced Devices & Instrumentation Figure 11(a) shows the experimental setup of the slope-assisted chaotic BOCDA. The output of the chaotic laser was divided into two portions, where one portion was used as the pump, and the other one was used as the probe. A programmable optical delay generator (PODG) was used to localize the sensing position precisely and to implement distributed measurements. The FWHM of measured BGS was around 55 MHz, which matches well with the simulations results. In dynamic measurements, the FUT was stretched periodically via an electric-driven motor. Figure 11(b) shows the measured time traces when sinusoidal dynamic strains with peak-to-peak values of 100 με and 1000 με were applied, and no obvious distortion was observed. By using the slope-assisted chaotic BOCDA, a strain dynamic range of 55 MHz (1200 με) and a spatial resolution of 3.45 cm over a measurement range of 130 m were realized. Dynamic strains with frequencies up to 4.67 Hz was measured, but distributed dynamic measurement was yet to be demonstrated. Recently, the same group has also analyzed the effect of chaotic time delay signature (TDS) on the measured BGS in the slope-assisted chaotic BOCDA [48]. By optimizing the parameters of the chaotic laser and eliminating the TDS, BGS without subpeak was obtained, and dynamic strains with frequency of 1.17 Hz were measured in a fully distributed manner.
4.2. SA-BOCDR. BOCDR is another important Brillouin sensing technique since it provides both high spatial resolution and single-end-access capability. In BOCDR, to spatially resolve the sensing locations, the laser source of the system is sinusoidally frequency-modulated to generate periodical CPs in the FUT, which is similar to BOCDA. The reference wave and the Stokes wave are combined in an optical coupler and, then, detected by a high-sensitivity photodiode (PD). Since the SpBS signal is used for sensing in BOCDR, it provides a unique advantage of single-end-access to FUT and shows good flexibility. In 2016, Mizuno et al. firstly introduced the slope-assisted measurement scheme into the BOCDR system to improve its measurement speed [49]. Similar to SA-BOTDR, in SA-BOCDR. the frequency interval between the pump wave and the reference (local) wave was set at the linear slope of the BGS, and the temperature/strain information was extracted from the Brillouin signal power variations.
The experimental setup of SA-BOCDR is shown in Figure 12(a). The sinusoidally frequency-modulated

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Advanced Devices & Instrumentation lightwave generated by the laser diode was divided into two portions by an optical coupler, one portion was used as the pump wave, and the other one was used as the reference wave. A polarization scrambler was used to suppress the polarization-induced Brillouin power variations. The backscattered Stokes wave was combined with the reference wave by another optical coupler and, then, detected by a highspeed photodetector. The measured BGS is shown in the right part of Figure 12(a), and a linear slope range of 50 MHz was realized. Figure 12(b) shows the measured Brillouin power change distribution along the FUT when strains were locally applied or temperature was changed. It can be observed that the stretched of heated fiber section can be recognized clearly. By using the SA-BOCDR system, a spatial resolution of 8.8 cm and a strain dynamic range of 1000 με were realized with capability of single-end access. However, due to the low system SNR, the measurement accuracy of the system was relatively poor, and dynamic measurement was yet to be demonstrated.
Subsequently, great efforts have been made by the same research group to improve the performance of SA-BOCDR. In 2016, the relationship between the power-change distribution of SA-BOCDR and the actual BFS distribution along the FUT was theoretically and experimentally investigated [50], and a unique "beyond-nominal-resolution" effect was found, which has potential to improve the system spatial resolution further. Subsequently, various special optical fibers, including polymer optical fiber (POF) [51], bending-insensitive fiber [54], and PMF [57], were employed as the FUT in SA-BOCDR to improve its performance in terms of sensitivity, stability, and so on. The trade-off relationship between the strain dynamic range and the spatial resolution in SA-BOCDR was also investigated [56].

Discussion
Slope-assisted Brillouin-based fiber sensing is a powerful tool for structural health monitoring since it can provide continuous temperature and strain information along the whole fiber used for sensing applications in a fully real-time manner. Table 1 gives a comprehensive comparison among different slope-assisted Brillouin-based distributed fiber-optic sensors. It is clear that SBS-based sensors including SA-BOTDA, slope-assisted BDG sensor, and SA-BOCDA provide high performance in terms of sampling rate, measurement range, and measurement accuracy, but they require two-end access to the FUT. On the contrary, SpBS-based sensors including SA-BOTDR and SA-BOCDR has a unique advantage of single-end access to the FUT, but their performance is relatively poor due to the low system SNR.  In future research, to further extend the application fields of slope-assisted Brillouin-based sensors, several potential research directions in this area are discussed: (1) the SA-BOTDA system provides a high sampling rate, a wide dynamic range, and a high measurement accuracy with low-complexity hardware, but its spatial resolution is limited to 1 m due to the limited lifetime of the phonon. Therefore, it is valuable to introduce advanced distributed measurement techniques, such as differential pulse-width pair (DPP) scheme [59,60], Brillouin echoes [61], and dark-pulse measurement scheme [62], into the SA-BOTDA system to improve its spatial resolution; (2) for SBSbased sensors, two-end access to the FUT is required to generate SBS interaction in the optical fiber. To improve the flexibility of the dynamic sensing system, single-end-access measurement techniques are desired to be proposed [63]; (3) for SpBS-based sensors, the measurement accuracy is relatively poor due to the low system SNR, which restricts its applications in real-world environments. Therefore, new techniques and concepts are in demand to improve the SNR of the sensing systems [64,65].

Conclusion
This paper presents a comprehensive and systematic overview of the slope-assisted Brillouin-based distributed fiber-optic sensing techniques. The working principle and the state-ofthe-art of five kinds of slope-assisted Brillouin sensor are introduced, including SA-BOTDA, SA-BOTDR, slope-assisted BDG sensor, SA-BOCDA, and SA-BOCDR. Up to now, various techniques, including double-slope-assisted scheme, multislopeassisted scheme, and BGS engineering technique, have been proposed to improve the performance of the slope-assisted Brillouin sensor in terms of stability, strain dynamic range, sensitivity, and so on. It is anticipated that these distributed dynamic sensing systems will be commercialized and widely put into practice in the near future due to their unique advantages of high sampling rate, high spatial resolution, high measurement accuracy, and fully distributed measurement capability. The applications of the slope-assisted Brillouin-based distributed fiber-optic sensors in civil structural, aerospace, and power industry will finally make this technology beneficial to the society and ensure public security.