High-Spatial-Resolution Dynamic Strain Measurement Based on Brillouin Optical Correlation-Domain Sensors

Abstract

Brillouin-scattering-based sensors have been widely applied in distributed temperature or strain measurement in recent 20 years. Brillouin optical correlation-domain technology has extensive development and application prospects because of its millimeter-level spatial resolution, distribution measurement, and high accuracy. Traditional Brillouin-scattering-based sensors, requiring a time-consuming frequency-sweep process, struggle to achieve dynamic strain measurement. In this article, Brillouin optical correlation-domain analysis and reflectometry based on fast-sweep frequency and slope-assisted methods will be reviewed. The main merits, drawbacks, and performances of these schemes are compared, and the avenues for future research and development of these two technologies are also explored.

1. Introduction

Recently, health monitoring in the fields of the mechanized automation industry and sizeable building structures has been significantly urgent for social safety and progress, especially the reliable measurement of dynamic covariates [1]. Consequently, the real-time monitoring of dynamic strain has become the major trend in the development of distributed optical fiber sensors (DOFSs).

DOFSs based on Brillouin scattering can provide continuous measurement of temperature or strain at arbitrary sections along the fiber, which has been a research hotspot in recent decades and has promising applications. According to the probe signal and sensing mechanism, the Brillouin-based DOFS technology can be classified into several categories: Brillouin optical time-domain reflectometry (BOTDR) [2,3,4,5,6] and Brillouin optical time-domain analysis (BOTDA) [7,8,9,10,11], based on pulsed light stimulation and detection of the Brillouin gain signal (BGS), and Brillouin optical correlation-domain reflectometry (BOCDR) [12,13,14,15,16] and Brillouin optical correlation-domain analysis (BOCDA) [17,18,19,20,21,22,23], based on the Brillouin gain excited by narrow-band correlation peaks (CPs) generated by low-coherence light sources. Among them, the correlation-domain-based technology can break through the pulse-width limitation of the traditional time-domain-based system, so the spatial resolution (SR) is in the order of millimeters or even sub-millimeters [24].

Generally, in Brillouin-based sensing systems, the temperature or strain information along the fiber is obtained by scanning the probe frequency to obtain the BGS, which is time-consuming, limiting the technique to static measurements [25]. To achieve fast monitoring of dynamic signals in real time, novel Brillouin-scattering-based DOFSs, such as fast-sweep, sweep-free, and slope-assisted sensors, have been proposed [26,27,28,29,30,31].

This paper reviews several Brillouin optical correlation-domain analysis or reflectometry (BOCDA/R) sensors for achieving high-spatial-resolution dynamic strain measurements, including fast-sweep (FS) BOCDA, slope-assisted (SA) BOCDA, FS-BOCDR, and SA-BOCDR. The major advantages and main drawbacks are summarized, and the prospects for the development of Brillouin optical correlation-domain dynamic strain sensing technology are presented.

2. Basic Principle

2.1. Brillouin Gain Spectrum and Brillouin Frequency Shift

Brillouin scattering is essentially caused by the interaction between incident light and acoustic phonons. The atoms, molecules, or ions in the medium form the continuous elastic mechanical vibration due to the self-heating motion, resulting in a spontaneous acoustic field inside the fiber. Phonons propagate in the direction of the fiber, periodically modulating the fiber density and refractive index, resulting in spontaneous Brillouin scattering (SpBS) [32]. The scattered light has a Brillouin frequency shift (BFS) with respect to the pump. When the incident light intensity is greater than the threshold, the pump light interferes with the Stokes light and transfers energy to the Stokes light, which, in turn, interacts with the pump light. The amplified Stokes light interacts with the pump light to excite a stronger acoustic field. The pump light, Stokes light, and acoustic wave fields continue to interact with one another, finally reaching a stable level of stimulated Brillouin scattering (SBS). When the frequency difference between the pump light and Stokes light is equal to the BFS, the SBS effect and Stokes light amplification are strongest. Therefore, the SBS process is a nonlinear interaction of pump light and Stokes light propagating opposite one another through an acoustic field, as shown in Figure 1 [33].

In Brillouin scattering, the Brillouin gain can be expressed as follows [34]:

$$g=g_0\frac{{({\Gamma }_B/2)}^2}{{({\Omega }_B-\Omega )}^2+{({\Gamma }_B/2)}^2},$$

(1)

where g₀ is the peak gain at the Brillouin center frequency [35], Г_B is the Brillouin linewidth, Ω is the acoustic field frequency (i.e., the frequency difference between the pump and Stokes waves), and Ω_B is the central frequency of Brillouin scattering in the optical fibers. Equation (1) shows that the BGS has a Lorentz distribution with a certain linewidth, while the frequency of the Lorentz curve peak is equal to the BFS, as shown in Figure 2.

The BFS in the fiber is the frequency offset between Stokes light and incident light, as follows:

$${\nu }_B=\frac{2\mathrm{n}{V}_a}{{\lambda }_P},$$

(2)

where n and V_a are the effective refractive index and sound velocity in the fiber, respectively, λ_P is the wavelength of incident light in a vacuum, and ν_B is linear with the variations in temperature or strain within limits [36,37], as follows:

$$v_B(\epsilon )=v_B(0)(1+C_{\epsilon }\epsilon ),$$

(3)

$$v_B(T)=v_B(T_r)[1+C_T(T-T_r)],$$

(4)

where ε is the strain on the fiber under test (FUT), C_ε is the strain coefficient, T is the temperature, T_r is the reference temperature, and C_T is the temperature coefficient. When the wavelength of incident light is 1550 nm, the typical values of C_ε and C_T are 0.05 MHz/με and 1 MHz/°C for some single-mode fibers (SMFs), respectively.

In the experimental measurement, the frequency-sweep process is employed with a microwave generator (MWG) and an electro-optical modulator (EOM) to reconstruct the BGS. The BFS of the fiber can be calculated to achieve the strain or temperature measurement. Reducing the frequency step and expanding the frequency range can improve the detection accuracy and SR. However, it will increase the measurement time, making it difficult to achieve a dynamic measurement.

Limitations on the measuring time of Brillouin sensing systems include the following [38]:

• The average number of signals, N_ave. Multiple averages can improve the signal-to-noise ratio (SNR) of sensing data.
• The limited frequency switching time, T_switch. When the BGS is reconstructed from the sweeping frequency, the switching time of the optical frequency is usually determined by the frequency-switching time of the microwave signal, which would delay the acquisition time to milliseconds or even slower.
• The number of sweeps, N_f. Large strain or temperature ranges require extended sweep frequency ranges (f_span), and higher accuracy requires a smaller sweep interval (Δf_step). The number of sweeps is

$$N_f={\mathrm{f}}_{\mathrm{span}}^{}/\Delta {\mathrm{f}}_{step},$$

(5)

For 1, the average number can be reduced by increasing the pump and probe power to increase the SNR. For 2, the switching time of the optical frequency is mainly limited by the performance of the MWG or arbitrary waveform generator (AWG). For 3, there is a trade-off problem between the high accuracy or wide range and fast measurement. In order to achieve high-speed and real-time measurement, especially of dynamic strain caused by vibration, fast Brillouin DOFSs based on fast-sweep [39,40,41,42,43,44,45,46,47,48,49,50,51,52], sweep-free [53,54,55], and slope-assisted [56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] methods have been proposed.

2.2. Dynamic Strain Sensing Method

The basic principles of the above methods are shown in Figure 3. The fast-sweep scheme adopts a high-performance AWG to perform IQ modulation on the vector MWG to sweep the probe light. The AWG, with a nanosecond-order switching time, is much faster than the MWG (in millisecond order). The sensing speed is determined by the average number, the number of sweeps, and the length of the sensing fiber. Peled Y et al. achieved dynamic strain sensing with a sampling rate of 10 kHz and a strain accuracy of 5 µε on a 100 m fiber in 2012 [39]. Then, cyclic coding [40], polarization-independent [41], and a co-propagating dual-wave interferometer-assisted method that measured the vibration of a 2 km fiber with a sampling rate of 10 kHz and an SR of 2 m [42], were proposed and demonstrated successively.

The sweep-free method avoids the time-consuming sweep process and demodulates the BGS by introducing a frequency comb into the pump or probe light. The sensing speed is limited by the average number and the length of the sensing fiber. Chaube et al. achieved strain sensing with a dynamic response of 3.9 kHz and an SR of 12 m in 2008 [53]. In 2018, Dong et al. proposed a single-shot BOTDA technology based on an optical chirp chain (OCC), which achieved a sampling rate of 6.25 MHz on a 10 m polarization-maintaining (PM) fiber [54].

The slope-assisted method demodulates strain variation by using the power–strain conversion coefficient. The probe frequency is fixed at the midpoint of the BGS’s ascending or descending linear region. The longitudinal tensile strain causes the frequency shift, which results in the power of the probe light changing at a fixed frequency. In 2009, Bernini et al. first achieved dynamic strain measurement with a frequency of 12.3 Hz and a 3 m SR on a 30 m fiber [56]. In 2017, Zhou et al. achieved a large-range dynamic strain measurement of 5372.9 με using a multi-slope assisted BOTDA system with the vector SBS and frequency agility technology [57].

SR is an important index in DOFS systems. However, in Brillouin optical time-domain systems, the SR is limited by the phonon lifetime (10 ns) in the order of meters. Differential pulses [72,73], dark pulses [74], and other methods have been proposed to improve the spatial resolution, but the complex hardware system and data processing increase the measurement time. It is also difficult to achieve a dynamic strain measurement. The Brillouin optical correlation-domain sensors can overcome this shortcoming and have immense potential to achieve dynamic strain sensing with a higher SR.

3. Dynamic Strain Sensing Based on BOCDA

The typical experimental setup of a BOCDA system is shown in Figure 4. A high-correlated laser, such as sinusoidal frequency modulation (sine-FM) [75,76], a phase-modulated (PM) laser [77,78], or a chaotic laser [64,79], serves as a light source. The SR based on the sine-FM system is related to the modulation frequency and the depth of the light source, which can break the phonon lifetime to reach the millimeter scale. However, it has a bottleneck in that the sensing distance and spatial resolution cannot be balanced. The coupling of sensing range and SR based on PM systems performs well, but the SR in the periodic correlated peak system deteriorates with the variation in the CP width and the increase in the sensing range, as well as restricting the expansion of the sensing range. The system based on chaotic lasers overcomes the limitation of periodic CPs, but it requires a variable delay line for localization. The comparison of the three light source systems is shown in

Table 1. Summary of the advantages and disadvantages of typical BOCDA structures.

Categories	Merits	Disadvantages
Sine-FM BOCDA [75,76]	Best MR or SR	MR and SR contradictory SR deterioration
PM BOCDA [77,78]	Best coupling of MR and SR
Chaos-based BOCDA [64,79]	High-incoherence source	Use of variable delay line

. The output is split into two branches by a coupler, one of which is shifted by a sideband modulator as the probe light, while the other is used as the pump light. A series of CPs will be generated at the correlation positions in the fiber, where the pump–probe frequency difference is equal to the BFS, and the SBS interaction will occur continuously. In addition, the Brillouin interactions between the two beams at the non-correlation position are negligible in short-range sensing. Distributed sensing across the fiber is achieved by shifting the interest position of the CPs by varying the sine-wave or coding frequency, or the optical path of the chaos delay.

3.1. FS-BOCDA

In 2015, Zhang et al. performed dynamic strain measurements based on a fast-sweep method with a sampling rate of 5000 points/s at multiple arbitrary points along the fiber [43]. A voltage-controlled oscillator (VCO) replaced the MWG for fast probe-wave scanning, while a faster lock-in amplifier (LIA) was used to improve data acquisition. Figure 5a represents the relationship between the VCO’s tuning voltage and the oscillation frequency, which can be swept faster (above 10 MHz) by inputting a high-frequency ramp voltage waveform. The experimental setup is shown in Figure 5b, and the BGS is simultaneously measured at five points in a sine-FM BOCDA, as shown in Figure 5c. Finally, a dynamic strain range of 500 µε was achieved on a 6 m fiber, with a measurement error of 83 µε.

However, the measurement speed is limited by the performance of the LIA. Furthermore, Wang et al. proposed a LIA-free scheme to obtain the BGS in a sine-FM system [44]. As shown in Figure 6a, the probe traces with or without SBS interaction are sampled by a high-speed analog-to-digital converter (ADC) and differential to obtain the BGS, which solves the sampling rate limitation of the LIA. In addition, the injection-locking scheme is used to improve the SNR. The results of the dynamic strain at different frequencies on the 30 m fiber are shown in Figure 6b; the measured data are generally consistent with the theoretical values. Finally, an SR of 8 cm and a measurement accuracy of 84 µε were achieved at a 200 kS/s sampling rate.

To address the lack of flexibility due to the double-end access to the fiber in the conventional BOCDA system, a single-end sine-FM BOCDA system was proposed in 2019, which can provide an ultrahigh sampling rate, single-end access, a large dynamic range, and high SR simultaneously [45]. The principle shown in Figure 7, the polarization-orthogonal pump and probe waves are launched to the same end of the PM fiber with a polarization beam splitter/combiner (PBS/C). The PBS/C at the other end is used to reflect the probe wave and change its polarization state, and the backward pump light is blocked by the PM isolator, where the balanced photodetector (BPD) is used to remove the DC noise, improving the measurement accuracy and the SNR. Eventually achieving a sampling rate of 200 kS/s and a dynamic strain frequency of 10 kHz. Meanwhile, Wang et al. proposed a BGS reconstruction algorithm to further improve the SR to 8 cm over a 700 m fiber and extend the strain range to 800 MHz [46].

Furthermore, Preter et al. proposed a sweep-free BOCDA scheme in 2016, which demodulated the BFS by the temporal step response of the output signal, determined by the detuning frequency between the BFS and the SBS acoustic field [55]. Although the distributed BFS of the 42 m fiber was reconstructed, dynamic strain measurements were not achieved, due to the complex data processing and broadband detectors.

3.2. SA-BOCDA

Fast-sweep techniques using VCOs are costly and have a lower SR. Furthermore, in 2003, Hotate et al. observed Brillouin intensity variations at a fixed probe frequency and successfully identified a 50 Hz sinusoidal oscillation on a 5 cm FUT, deriving the slope-assisted concept [58]. In 2019, Wang et al. introduced the dual-slope-assisted (DSA) technique to the sine-FM BOCDA system [59]. The ratio of the gain at the center frequency of the negative (ν⁻) and positive (ν⁺) slopes was used for dynamic strain measurements, as defined in Equation (6), where R_B is insensitive to the pump power and fiber loss. Figure 8 represents the principle of the double-slope-assisted BOCDA experiment. Finally, a fully distributed measurement with a 7 cm SR and 100 Hz dynamic strain was achieved at a 625 Hz repeat frequency, but the measurement range was only 700 µε.

$${\mathrm{R}}_{\mathrm{B}}({\mathrm{\nu }}^{-},{\mathrm{\nu }}^{+})=\frac{{\mathrm{G}}_{\mathrm{S}\mathrm{B}\mathrm{S}-}}{{\mathrm{G}}_{\mathrm{S}\mathrm{B}\mathrm{S}+}}=\frac{\mathrm{S}(({\mathrm{\nu }}^{-}-{\mathrm{\nu }}_{\mathrm{B}}(\mathrm{z}))/\Delta {\mathrm{\nu }}_{\mathrm{B}})}{\mathrm{S}(({\mathrm{\nu }}^{+}-{\mathrm{\nu }}_{\mathrm{B}}(\mathrm{z}))/\Delta {\mathrm{\nu }}_{\mathrm{B}})},$$

(6)

In the slope-assisted technique, the dynamic range is determined by the linear region (i.e., spectral width) of the BGS. A wider linear BGS range corresponds to a wider range of strain measurements. A chaotic laser [80], featuring low coherence and a wideband optical spectrum, was adopted by the author’s group to enlarge the dynamic strain range. The normal chaos spectrum S_ƒ can be expressed as shown in Equation (7), where f₀ is the spectral center frequency, A is the spectral area integral, and Δƒ is the −3 dB chaos linewidth. Based on the chaos-based BOCDA system, where the pump and probe spectra are both Gaussian continuous broadband distributions, the SBS gain of the probe light can be expressed as shown in Equation (8), where the beat spectrum S_b is shown in Figure 9a, and G_SBS is the inherent Brillouin gain of a 30 MHz linewidth [60]. For chaotic SBS interactions [81], the linewidth of S_b increases proportionally to the source linewidth Δƒ, and the full width at half-maximum (FWHM) of the BGS also widens (up to 70 MHz), as shown in Figure 9b. As a result, the inherently broadband BGS of the chaos-based BOCDA system provides an extended linear region without any external modulation.

$$S(f)=\frac{A}{\Delta f\sqrt{\pi /2}}\exp \left[-2{(\frac{f-f_0}{\Delta f})}^2\right],$$

(7)

$$BGS=S_b\otimes G_{SBS}$$

(8)

In addition, the inherent time-delay signature (TDS) and non-zero autocorrelation structure of the chaotic laser lead to multiple weak coherent interactions, which accumulate as significant noise along the FUT. Therefore, in 2020, we investigated the effects of chaotic TDSs on the BGS profile and the dynamic strain measurement range using the main–sub–peak ratio (MSPR) [61]. It was found that the MSPR decreased with the increase in TDS, and the influence of the MSPR on the dynamic strain measurement range was as follows: the range was <400 με for MSPR < 0 dB, while it was <600 με for MSPR > 0 dB, as shown in Figure 10. Therefore, a 100 m SMF was added to the single feedback structure of the chaotic laser to increase the external feedback delay time, which caused the position of the TDS to be outside the FUT, eliminating the limitation of the TDS on the dynamic strain range. In order to further improve the SNR of the system, in 2023, a long-range chaotic BOCDA system based on optimized time-domain gating and differential denoising techniques was proposed [62]. Finally, distributed strain sensing with an SR of 2.69 cm was achieved along the 27.54 km measurement range, and the number of resolving points was more than 1,020,000, providing a method for high-performance DOFSs.

Additionally, dynamic strain can be measured using a single-slope-assisted chaotic BOCDA system [60]. A broadband chaotic source of 5.6 GHz linewidth, as shown in Figure 11a, was used to generate a BGS with an FWHM of 55 MHz, as shown in Figure 11b, corresponding to a dynamic strain range of at least 1000 µε. As shown in Figure 11c, a dynamic strain of 4.67 Hz with a dynamic range of 1200 µε and an SR of 3.45 cm was finally measured on the 130 m FUT.

In some applications, large strain measurement and high measurement accuracy are required. To fulfill these requirements, a double-slope-assisted (DSA) technique was proposed in 2021 [63], combined with time-domain gating [64] and the gain-switching (GS) modulation method [65] to obtain a higher measurement accuracy. The results are shown in Figure 12, with (b) indicating that the measured frequency of the dynamic strain is 1.03 Hz. Finally, 800 µε dynamic measurements were achieved on a 25 m fiber with a strain resolution of 15 µε, a standard deviation of 6.2 µε, and a 3.8 cm SR.

Recently, a cross-aligned multiple-slope-assisted (MSA) chaos-based BOCDA system was proposed to further extend the dynamic strain measurement range and the slope utilization rate (SUR) [66]. The cross-arranged MSA model diagram is shown in Figure 13a, where the black solid lines are the BGSs obtained by applying different pre-strain, the blue solid lines are the linear regions corresponding to the rising and falling edges of each BGS, and the solid red points are the central frequency of the linear region. Dynamic strain in different regions can be measured by periodically switching the fixed frequencies. The results are shown in Figure 13b,c, ultimately achieving a 4780 µε dynamic range—about four times that of the single-slope-assisted technique, with an SR of 4.2 cm and a standard deviation of 23.3 µε. However, several drawbacks, such as lower frequency and inferior accuracy, are expected to be solved by introducing a VCO or a wider-phase chaos laser.

4. Dynamic Strain Sensing Based on BOCDR

The basic protocol of the BOCDR system is shown in Figure 14. The laser is modulated by the sinusoidal wave [82,83] or the noise signal [16], and the output light is split into two beams through the coupler. One beam is injected into the delay fiber as the reference light, and the other beam is injected through the optical circulator into the sensing fiber as the pump light. The pump wave generates SpBS in the sensing fiber, and the generated light returns to be detected through the circulator. A series of CPs appear in the relevant pump and probe light positions in the fiber, where the frequency difference between the Brillouin scattering light and the reference light is exactly equal to the BFS of the fiber, and the frequency difference at other positions changes randomly. Distributed measurement can be achieved by changing the modulation frequency or the delay fiber length.

4.1. FS-BOCDR

Yosuke et al. took advantage of BOCDR’s single-end injection and introduced a VCO to obtain the BGS at high speed to verify the strain sampling rate of 100 kHz by detecting local dynamic strain of 1 kHz in 2016 [47]. Figure 15a shows the ultrahigh-speed BOCDR experimental setup. Dynamic strains at 30 Hz, 100 Hz, 300 Hz, and 1 kHz were applied to a 0.4 m section of a 12.8 m silica SMF using a vibration generator. The temporal variations in the output voltage are shown in Figure 15b, where dynamic strain up to 1 kHz was accurately detected. The temporal variation in the strain distribution is shown in Figure 15c, indicating that the propagation speed of the mechanical wave was ~10 ms⁻¹. However, the lower measurement accuracy, the SR (degraded by a factor of three), and the limited dynamic range (0~2000 µε) are major drawbacks of this system. Employing a noise-floor compensation method, a strain range up to 20,000 µε was realized. However, the use of a microwave frequency sweeper (MFS) limits the sampling rate to 50 Hz [48].

For improving the sampling rate, a VCO driven by a function generator can replace the MFS. An experimental setup is shown in Figure 16a, where the electrical spectrum analyzer (ESA) was used to observe the mixed signal, converting the original frequency-domain BGS into a time-domain signal. The speed of frequency sweeping in the ESA is substituted with the repetition rate of voltage sweeping applied to the VCO, which allows for higher-speed operation. By widening the sweeping range of the VCO output, the measurement range can be arbitrarily extended. Zhu et al. replaced the MFS with a VCO to increase the sampling rate from 50 Hz to 20 kHz in 2022 [49]. Vibration signals of 40 Hz at different sampling rates were observed in the 0.64 m strain zone of a 4 m fiber.

To overcome the contradiction between measurement speed and SNR, machine learning methods of principal component analysis (PCA) and support-vector machine (SVM) were used in the signal processing for the BGSs by Yao et al. in 2022 [50]. Figure 17 shows the BFSs when an 8 kHz BGS sampling rate and a dynamic strain of ±2500 µε sinusoidal vibration were applied to a 0.64 m fiber. The proposed methods are 27.3 times faster than the conventional method without PCA and can achieve a dynamic frequency of 40 Hz.

For achieving continuous detection, a phagocytic neural network (NN) was introduced to achieve real-time dynamic strain sensing with a repetition rate of 20 kHz and a strain range of 4000 µε in 2023 [51]. The root-mean-square error (RMSE) was estimated to be 582.4, 379.9, and 296.1 µε by different NN layers when the repetition frequency is 20 kHz. The number of NN layers restricts the system error, which is difficult to increase further. The experimental setup of BOCDR with a NN is shown in Figure 18, demonstrating a high repetition rate and real-time signal processing function through the structure design of the NN.

Furthermore, another BOCDR system based on compressed sensing (CS) was proposed by the same group, and the effective repetition rate of the sensing signals was enhanced 10-fold [52]. The experimental setup of the CS-assisted BOCDR is shown in Figure 19a, where the frequency modulation applied to the laser source was designed to generate the random undersampling function. Then, the temporal variations and BFS distribution were reconstructed according to the CS based on discrete cosine transform (DCT). The BFS distribution at different undersampling rates (USRs) at frequencies of 20 Hz and 40 Hz is shown in Figure 19b. A lower USR performs better in depicting applied sinusoidal stress by providing more sampling points at the same time.

4.2. SA-BOCDR

The slope-assisted BOCDR technique was first demonstrated as a proof-of-concept by Lee et al. in 2016 [67]. The BFS corresponds to the P_B0 power at a given frequency in the linear region of the BGS, while the P_B0 power is a function of the fiber strain, temperature, and loss. In 2017, the authors investigated the relationship between the output power change distribution and the BFS distribution of the sensing fiber in SA-BOCDR to further explore the agreement between the output power change distribution and the actual BFS [68]. When the strain section is much larger than the SR, the power change distribution replicates the BFS distribution well. When the strain section is equal to or only a few times the SR, the correct BFS distribution cannot be obtained directly. When the strain section is smaller than the SR, the power variation can still be observed, as shown in Figure 20 and further confirmed in [69].

SA-BOCDR is a high-speed measurement method with a dynamic range limited to about 1500 µε [70]. To further improve the dynamic strain range, in 2019 the trade-off relationship between dynamic strain range and SR was verified, achieving a dynamic strain range of >6000 µε with the SR reduced by a factor of three [71]. Different strains were applied to the 7.5 m fiber, and the results of the 0.37 m (Δz) and 1.1 m (3·Δz) ranges are shown in Figure 21a,b, respectively, where the dynamic range is increased from 1500 µε to 6000 µε while the SR is reduced by a factor of three.

5. Discussion

In this paper, a brief overview of the developments of dynamic strain sensing with high spatial resolution is summarized for Brillouin optical correlation-domain technology, as shown in

Table 2. Summary of the recent progress and the main merits and disadvantages of Brillouin optical correlation-domain technology.

Categories	Enhanced Techniques	Performances 1	Merits	Disadvantages
FS-BOCDA	VCO [43]	6 m; 3 cm; 5 Hz; 500 µε	Ultrahigh speed	Dynamic strain range limitation	Short sensing range
	LIA-free [44]	30 m; 8 cm; 20,000 Hz; 1200 µε		SR deterioration
	Single-ended access [45]	45 m; 5.6 cm; 10,000 Hz; 1200 µε	Flexible structure	PMF sensing
	convexity extraction algorithm [46]	700 m; 8 cm; 200 Hz; 400 µε	High SNR, large dynamic range
FS-BOCDR	VCO [47,49]	4 m; 64 cm; 1000 Hz; 2000 µε		Single-point measurement
		20.4 m; 39 cm; 40 Hz; 4500 µε	Ultrahigh speed	Dynamic strain range limitation
	PCA, SVM algorithm [50]	0.64 m; 50 cm; 40 Hz; 4000 µε
	NN algorithm [51]	0.64 m; 50 cm; 40 Hz; 4000 µε	Large dynamic range	Measurement accuracy deterioration
	CS algorithm [52]	80 m; 25 cm; 40 Hz; 1200µε	High effective repetition rate	Dynamic strain range limitation
SA-BOCDA	Dual-slope-assisted [59]	20 m; 7 cm; 100 Hz; 700 µε	Insensitive to pump and fiber loss	Repetition rate limitation
	Chaos-based [60,63,66]	130 m; 3.45 cm; 4.67 Hz; 1200µε	High SR, large dynamic range	Measurement accuracy deterioration
		25 m; 4.2 cm; 0.2232 Hz; 4780µε
		25 m; 3.8 cm; 1.03 Hz; 800 µε	Measurement accuracy	Dynamic strain range limitation
SA-BOCDR	Single-slope-assisted [68,71]	14.5 m; 9.5 cm	Proof-of-concept	Static strain

¹ The performance of BOCDA is referred to as distance; SR; frequency; range.

. The data of Table 2 were sourced from references [43,44,45,46,47,48,49,50,51,52,59,60,61,62,63,64,65,66,67,68,69,70,71].

• In FS-BOCDA and FS-BOCDR systems, the VCO is introduced to obtain the BGS at high speed, and the sampling rate is increased to tens of kHz, where BEF is introduced to suppress the system noise and improve the dynamic strain range. Furthermore, the LIA-free scheme based on data difference eliminates the limitation of the LIA on measurement speed and achieves a 200 kHz sampling rate. Therefore, convexity extraction algorithms, PCA and SVM algorithms, NNs, and CS algorithms are also proposed to improve the SNR, sensing speed, dynamic strain range, and effective repetition rate without additional hardware complexity.
• In SA-BOCDA and SA-BOCDR systems, the strain is demodulated by the Brillouin signal power at a fixed frequency, which avoids the time-consuming sweep process in principle. The SA sine-FM BOCDA system has been proven. Then, the chaotic laser was introduced by our group to expand the linear range of the BGS, combined with single-SA, dual-SA, and multi-SA technologies to achieve high spatial resolution, high precision, and a large dynamic range. The proof-of-concept of SA-BOCDR has been proposed to achieve distributed strain measurement, but not dynamic strain demodulation.

The main challenges and improvements are as follows:

• The contradiction between the sensing range and spatial resolution. In the Brillouin correlation-domain system, the SR and sensing range of the sine-FM system can be expressed as shown in Equations (9) and (10), which in the PM system can be expressed as Equations (11) and (12), respectively. Here, V_g is the group velocity of light in the fiber, Δν_B is the FWHM of the gain spectrum, ƒ_m is the modulation frequency, Δƒ is the modulation amplitude, and T_b and M are the code width and code length of the phase-coded sequence, respectively. It is clear that in sine-FM and PM systems, the SR will deteriorate with the increase in the sensing range, limiting its further expansion. At the same time, the width of the periodic correlation peak will change slightly during the localization process, which leads to the SR worsening in principle. It is noticeable that the SR and sensing range of the chaos-based system are expressed as Equations (13) and (14), respectively, where Δτ and τ_d are the FWHM and delay period of the light source correlation peak, respectively. The SR is only dependent on the chaos bandwidth, which can overcome the trade-off problem between long sensing range and high SR. The low-noise phase-chaos laser can improve the SNR to extend the sensing range.

  $$\Delta z=\frac{V_g\Delta {\upsilon }_B}{2\pi f_m\Delta f},$$

  (9)

  $$d_m=\frac{V_g}{2f_m},$$

  (10)

  $$\Delta z=\frac{1}{2}{V}_g{T}_b,$$

  (11)

  $$d_m=\frac{1}{2}M{V}_g{T}_b=M\Delta z,$$

  (12)

  $$\Delta z=\frac{1}{2}{V}_g\Delta \tau ,$$

  (13)

  $$d_m={\frac{1}{2}}_{}{V}_g{\tau }_d$$

  (14)
• The contradiction between the dynamic strain range and frequency. In Brillouin correlation-domain systems, the signal acquisition speed is limited by the use of the low-speed MFS and LIA, and the dynamic strain’s change speed is limited by the low-speed stepper motor. In FS-BOCDA and FS-BOCDR systems, the dynamic strain range depends on the sweep frequency range, and the large sweep frequency range and detectable dynamic strain frequency are mutually restricted. In SA-BOCDA and SA-BOCDR systems, the dynamic range is determined by the linear region of the BGS, and the dynamic strain frequency is limited by the signal acquisition speed and the dynamic strain’s change speed. In future research, a VCO could be introduced into an SA system to provide high-frequency dynamic strain and a high-speed digital oscilloscope for real-time sampling to achieve vibration measurement at the kHz scale, with a large range of dynamic strain. The BGS’s ascending and descending linear regions are complementary to the Brillouin phase spectrum (BPS) of the SA system; combining the BGS with the BPS can expand the dynamic range and improve the measurement accuracy [84].
• Distributed measurement. SBS occurs at the relevant position of the two lights in the fiber, while the Brillouin interactions at the non-correlation position are weak. As a result, the correlation-domain system is essentially a single- or multi-point measurement. To achieve fully distributed measurement, ultra-long delay lines or programmable optical delay lines are used, which is time-consuming. The chaotic correlation demodulation method and synchronous demodulation method, which combine the time domain and the correlation domain, could be adopted to achieve rapidly distributed measurement of vibrations along optical fibers.
• Difficult practical engineering. Dynamic strain measurements in Brillouin optical correlation-domain systems with high SR have not been applied in engineering. The stability, simplicity, and cost should also be considered, as they are important in practical applications.

6. Conclusions

In this review, the principle of strain demodulation and the limitations on measurement time were introduced. Then, two dynamic strain sensing methods in correlation-domain systems (FS-BOCDA/R and SA-BOCDA/R) were overviewed. Finally, the recent progress and the main merits and disadvantages of the proposed protocols were summarized, and the development prospects were also explored. In conclusion, the Brillouin correlation-domain system with dynamic strain measurement can achieve mm-level SR, which may offer broad prospects in practical applications, including aerospace structural vibrations, bridge tunnel safety detection, and so on.