appliedsciences
Review

Recent Advances in Brillouin Optical
Correlation-Domain Reflectometry
Yosuke Mizuno * , Heeyoung Lee and Kentaro Nakamura
Institute of Innovative Research, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku,
Yokohama 226-8503, Japan; hylee@sonic.pi.titech.ac.jp (H.L.); knakamur@sonic.pi.titech.ac.jp (K.N.)* Correspondence: ymizuno@sonic.pi.titech.ac.jp; Tel.: +81-45-924-5052
Received: 13 September 2018; Accepted: 5 October 2018; Published: 8 October 2018


Featured Application: Structural health monitoring.
Abstract: Distributed fiber-optic sensing based on Brillouin scattering has been extensively studied
and many configurations have been developed so far. In this paper, we review the recent advances inBrillouin optical correlation-domain reflectometry (BOCDR), which is known as a unique techniquewith intrinsic single-end accessibility, high spatial resolution, and cost efficiency. We briefly discuss theadvantages and disadvantages of BOCDR over other Brillouin-based distributed sensing techniques,and present the fundamental principle and properties of BOCDR with some special schemes forenhancing the performance. We also describe the recent development of a high-speed configuration of
BOCDR (slope-assisted BOCDR), which offers a beyond-nominal-resolution detectability. The paper
is summarized with some future prospects.
Keywords: Brillouin scattering; optical fiber sensing; optical correlation-domain reflectometry; distributed
sensing; strain sensing; temperature sensing; nonlinear optics; structural health monitoring

1. Introduction
Since the Brillouin frequency shift (BFS) in optical fibers was found to be dependent on applied
strain and ambient temperature [1–4], extensive research has been conducted to exploit Brillouinscattering to develop distributed fiber-optic sensors. The first demonstrations were performed bytime-of-flight techniques; they are called Brillouin optical time-domain analysis (BOTDA) [5] andBrillouin optical time-domain reflectometry (BOTDR) [6]. In both techniques, optical pulses are
injected into fibers under test (FUTs), and by measuring the time until the reflected signals are returned,
the locations in the FUTs can be derived. In BOTDR, optical pulses are injected into only one end of
the FUT, and they are partially returned via spontaneous Brillouin scattering. In contrast, in BOTDA,
a continuous wave (probe) is injected into the other end of the FUTs in addition to the optical pulses(pump). The frequency of the probe light is downshifted by the BFS in advance, and then the pumpand probe lights interact with each other, inducing stimulated Brillouin scattering (SBS). As SBS ismuch stronger than spontaneous Brillouin scattering, the signal-to-noise ratio (SNR) of BOTDA ismuch higher than that of BOTDR, leading to a shorter measurement time because of the reduced
averaging count. However, unlike BOTDR with single-end accessibility, the two-end-access natureof BOTDA is not beneficial to users, because the degree of freedom in deploying the fiber is lowered
and the measurement can no longer be continued if the fiber has one breakage point. Thus, BOTDRand BOTDA are in a trade-off relationship. The spatial resolution of these time-domain techniques isdetermined by the pulse width of the pump light. The basic limitation of the pulse width is known
to be approximately 10 ns (corresponding to the spatial resolution of ~1 m) because of the spectral
broadening of the Brillouin gain spectrum (BGS) and reduced accuracy of BFS detection [7]. It is
Appl. Sci. 2018, 8, 1845; doi:10.3390/app8101845

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noteworthy that the performance including the spatial resolution has been drastically enhanced withvarious schemes both in BOTDR [8–11] and in BOTDA [12–20]; refer to each reference for the details.
Researchers have also developed Brillouin optical frequency-domain analysis (BOFDA) [21–23] andBrillouin optical frequency-domain reflectometry (BOFDR) [24], which seem to suffer from theirrelatively slow operation speed because of the large amount of calculation; their details are also out of
the scope of this paper.
The other configurations of Brillouin-based distributed fiber-optic sensors are Brillouin opticalcorrelation-domain analysis (BOCDA) [25–35] and Brillouin optical correlation-domain reflectometry(BOCDR) [36,37]. These techniques utilize not optical pulses but frequency-modulated continuous
waves to achieve distributed measurements and thus possess so-called random accessibility tosensing points and high spatial resolution without specially configured implementations. BOCDA
is a two-end-access system, which operates based on stimulated Brillouin scattering and thus has
a relatively high SNR. The details of BOCDA will be fully described in other papers of this Special Issue.
Although the SNR of BOCDR is lower than that of BOCDA, its single-end accessibility is beneficial
to users as the degree of freedom in embedding the fiber is higher and distributed sensing can becontinued even when the fiber is broken at a certain point during the measurement.
In this paper, we review the fundamentals and recent advances in BOCDR, with an emphasis
on its high-speed configuration. In Section 2, we describe the basic principle of BOCDR and clarify
its difference from that of BOCDA. In Section 3, we present some configurations for improving its
performance. In Section 4, we focus on slope-assisted BOCDR and present its principle along with someunique features including the beyond-nominal-resolution effect. In Section 5, we provide a summaryand discuss the future prospects of BOCDR technology.
2. Basic Principle of BOCDR
When a light beam is injected into an FUT, it interacts with acoustic phonons, generatingbackscattered light called Stokes light. This phenomenon is called spontaneous Brillouin scattering.
Caused by the exponential decay of the acoustic phonons, the backscattered Brillouin light spectrum,
known as BGS, takes the shape of a Lorentzian function with the bandwidth of several tens ofmegahertz. If the power of the pump light is higher than the Brillouin threshold power Pth , the Stokes
light caused by spontaneous Brillouin scattering acts as a seed of stimulated scattering, and there
occurs a transition from spontaneous Brillouin scattering to SBS; as a result, the Stokes light poweris drastically enhanced. This transition can be promoted using a so-called pump-probe technique,in which a probe light beam (frequency-downshifted by the BFS) is additionally injected into the otherend of the FUT. This is the reason why SBS-based distributed sensor configurations, such as BOTDA,BOFDA, and BOCDA, require light injection into both ends of the FUT.
In Brillouin scattering, whether it is spontaneous or stimulated, the frequency at which the peak
power is obtained in the BGS is downshifted by several gigahertz from the incident light frequency,
and the amount of this frequency shift is called BFS. In optical fibers, the BFS νB is given by [1]:
νB =

2nνA
,
λp

(1)

where n is the refractive index, νA is the acoustic velocity in the fiber, and λp is the wavelengthof the incident pump light. If tensile strain is applied or temperature is changed in a standard
silica single-mode fiber (SMF), the BFS shifts to higher frequency in proportion to the applied strain(+480 MHz/%) [3] and the temperature change (+1.18 MHz/K) [4] at 1.55 µm. In some specialty fibers,
such as tellurite glass fibers and polymer optical fibers (POFs), it is known that the BFS moves to lower
frequency with increasing applied strain (−230 MHz/% [38] and −122 MHz/% [39,40], respectively)
and temperature (−1.14 MHz/K [41] and −4.09 MHz/K [39,40], respectively). In both cases, we canderive the strain amplitude and temperature change by measuring the BFS in the fiber.

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One of the most essential features of Brillouin-based sensors is their distributed sensing capability.
In BOCDR, distributed sensing is achieved using a technique called the synthesis of an opticalcoherence function (SOCF). The conceptual setup of BOCDR is schematically shown in Figure 1.
The optical output from a laser diode is divided into pump and reference light beams. The pump lightis injected into the FUT, and the Stokes light is directed into a photodiode (PD). The reference lightis used as an optical local oscillator. The electrical beat signal of the two light beams is monitored
using an electrical spectrum analyzer (ESA). Since there is a frequency difference of approximately 11
GHz between the Stokes light and the reference light, this configuration is called a self-heterodyne
scheme. In order to resolve the position in the FUT, the optical frequency of the laser output ismodulated in a sinusoidal waveform by directly modulating the injection current of the laser. Fromthe viewpoint of temporal averaging, the coherence function is synthesized into a series of periodical
peaks [25], of which the period is inversely proportional to the frequency of the sinusoidal modulationf m . We control f m to generate only one correlation peak within the range of the FUT, so that only the
Brillouin scattering generated at the position correspondent to the peak has high correlation with thereference light, and then gives high heterodyne output. The peak frequency observed using the ESA
gives the BFS caused at the position. By sweeping f m , the position of the correlation peak is scannedalong the FUT, and thus the distribution of the BGS or the BFS is obtained. Note that a delay line isoften inserted in the reference path so that the order of the correlation peak in the FUT may not be
zero; the 0th-order correlation peak cannot be scanned along the FUT by controlling f m .

Figure 1. Conceptual schematic of BOCDR. AC, alternating current; DC, direct current; ESA, electrical
spectrum analyzer; FUT, fiber under test; PD, photodiode.

Here, we give another explanation of the operating principle of BOCDR using Figure 2. When thelaser frequency is sinusoidally modulated, the frequencies of the reference light and the Stokes light at
the PD are expressed by the equations shown in Figure 2, where ϕ and ψ are phase factors. While ϕ isa constant, ψ changes according to where, in the FUT, the pump light is reflected. For example, when
the pump light is reflected at Position A and ϕ = ψ + 2 π n (n: integer), the frequency difference of thereference light and the Stokes light is always the same regardless of time, and so the beat signal can bedetected. In contrast, when the pump light is reflected at Position B and ϕ 6= ψ + 2 π n, the frequency
difference of the two light beams changes according to time, and so the beat signal cannot be observed.
From the viewpoint of time averaging, we interpret that a correlation peak is standing at Position
A. Now the modulation of the laser frequency is a periodical sinusoidal waveform, these correlation
peaks appear periodically along the FUT, so only one correlation peak should be located within therange of the FUT to resolve the position properly, resulting in the limited measurement range. The
position of the correlation peak can be scanned along the fiber by adjusting the modulation frequency
f m.

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Figure 2. Operating principle of basic BOCDR.

The spatial resolution ∆z and the measurement range dm (distance between the neighboringcorrelation peaks) of BOCDR are given by the same equations as those for BOCDA [25,37]:∆z =vg ∆νB,
2π f m ∆ f

(2)

vg
,
2 fm

(3)

dm =

where vg is the group velocity of light, ∆νB is the Brillouin gain bandwidth (~30 MHz) in opticalfibers, and ∆f is the modulation amplitude of the light source. Equation (2) was originally derived
for BOCDA, so it is not evident that the spatial resolution of BOCDR is also given by this expression;refer to Reference [37] for the derivation of Equation (2) in BOCDR. According to Equations (2) and(3), it is evident that ∆z and dm are in a trade-off relationship, and thus their ratio (=dm /∆z) is often
used to evaluate the performance of BOCDR. Considering that ∆f is limited to a half of the BFS,
the resolution-to-range ratio of silica-fiber-based BOCDR is limited to 570, which can be extended bysome special configurations (refer to the next section). Note that the SNR of BOCDR cannot be simply
given as a function of system parameters, such as ∆f, f m , and fiber length.
Finally, we compare the operating principle between BOCDA and BOCDR as shown in Figure 3.
In both systems, the pump light is reflected everywhere in the FUT due to spontaneous Brillouinscattering. In order to resolve the position, in BOCDA, stimulated Brillouin scattering is strongly
induced at one specific position in the FUT by injecting the frequency-modulated pump and probe
light beams into each end of the FUT. In contrast, in BOCDR, the Stokes light due to spontaneous
Brillouin scattering from one specific position in the FUT is selectively observed by the heterodyne
detection with the frequency-modulated reference light. As a consequence, the Stokes light from the
FUT in one-end-access BOCDR becomes much smaller than that in two-end-access BOCDA. Hence,
another point of BOCDR is to utilize the heterodyne detection not only to resolve the position but also
to enhance the beat signal.

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Figure 3. Comparison of the operating principles of BOCDA and BOCDR.

3. Various Configurations of BOCDR
Since the proposal of BOCDR, numerous special configurations have been developed to enhance
its performance. For instance, in order to mitigate the trade-off relationship between the spatial
resolution and the measurement range, a temporal gating scheme [42] and a double modulation
scheme [43] were developed. In the temporal gating scheme (Figure 4a), the measurement range
was extended while maintaining the spatial resolution by exploiting relatively long optical pulses
generated using intensity modulators (IMs). Then, we can arbitrarily select a single correlation
peak from multiple correlation peaks located in the FUT. In contrast, in the double modulation
scheme (Figure 4b), by modulating the optical frequency at two different frequencies simultaneously,
the spatial resolution is given by the higher frequency while the measurement range is given by thelower frequency. These techniques can be simultaneously employed.

Figure 4. Special BOCDR configurations with extended measurement ranges. (a) Temporal gating
scheme and (b) double modulation scheme. AC, alternating current; DAQ, data acquisition; DC,
direct current; DFB-LD, distributed-feedback laser diode; EDFA, erbium-doped fiber amplifier;
ESA, electrical spectrum analyzer; FUT, fiber under test; GPIB, general-purpose interface bus; IM,intensity modulator; PC, polarization controller; PD, photodiode; PSCR, polarization scrambler. [42,43].
Copyright (2009,2010) OSA.

Regarding the polarization, BOCDR was found to have an ability to measure the beat length
distribution [44], while the polarization-dependent fluctuations of the Brillouin signals were
suppressed by polarization scrambling [45,46]. Some specialty fibers, such as tellurite fibers [38,40],
bismuth-oxide fibers [47], and polymer fibers [48], were used in BOCDR to make the most of their
special features (high Brillouin gain coefficients, high flexibility, etc.). The influence of a ghost
correlation peak was investigated and its suppression was shown to be extremely important [49].
Some simple configurations of BOCDR were developed to further reduce the system cost [50–52].
An apodization scheme based on synchronous intensity modulation [53] and a lock-in detection
scheme [54] were also performed to suppress the noise floor and to enhance the strain dynamic
range, etc. Finally, to achieve high-speed operation (the sampling rate was limited to <20 Hz inAppl. Sci. 2018, 8, 1845

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the standard configuration [55]), phase-detected BOCDR [56–58] and slope-assisted BOCDR weredeveloped. In both schemes, the idea for high-speed operation is the same; namely, the omission of thefrequency-scanning process for acquiring the BGS. In phase-detected BOCDR, the BGS is converted
from a frequency domain into a time domain and approximated by a one-period sinusoidal waveform,
the phase of which is detected at a high speed. The slope-assisted BOCDR is the main focus of thispaper and will be detailed in the following section.
4. Development of Slope-Assisted BOCDR
In this section, we describe the fundamentals, unique features, and recent advances of thehigh-speed configuration of BOCDR, named slope-assisted BOCDR [59–61], with an emphasis on theso-called beyond-nominal-resolution effect.
4.1. Principle and Fundamental Operation
In the standard configuration of BOCDR, the BFS at a single sensing point is derived after
acquiring the whole BGS. In contrast, the slope-assisted BOCDR provides the BFS information using
the BGS slope. This idea has been already proposed for BOTDA [62–64]. As depicted in Figure 5a,
the BFS is in one-to-one correspondence with the spectral power PB0 at a certain frequency νB0 , which is
set at the high-frequency point in the linear region (lower-frequency side) of the BGS slope. Then, whenthe BFS slightly shifts to higher frequency by strain, etc., PB0 decreases linearly; when the slight loss
occurs in the FUT, the spectral power of the BGS entirely decreases, also leading to the reduction of PB0 .
Even if the BFS change is so large that νB0 gets out of the linear region, so long as PB0 is in one-to-one
correspondence with the BFS, this system operates properly (with a reduced sensitivity) by simple
nonlinear compensation. One may point out that the noise floor of correlation-domain techniques isinfluenced by the sidelobes of the correlation peak and that the slope-assisted configuration does notwork properly in principle, but this issue can be mitigated if we accept the deterioration of the spatial
resolution to some extent just in the same manner as in the phase-detected BOCDR [56].

Figure 5. Schematic illustrations of the operating principle of slope-assisted BOCDR. (a) One-to-one
correspondence between the BFS and the spectral power PB0 at frequency νB0 . The dotted curve isthe initial BGS, and the solid curve is the BGS shifted to higher frequency because of strain and/or
heat. (b) PB0 distributions along the FUT with (solid curve) and without (dotted line) partial strain
and heat. (c) PB0 distributions along the FUT with (solid curve) and without (dotted line) a point loss.
Reproduced with permission from [59]. Copyright (2016) IEEE.

Figure 5b,c schematically show the changes in the PB0 distributions when strain (or heat) andloss are locally applied, respectively. The strain and temperature effects cannot be separated in thismethod, but the loss effect can be discriminated from the locally applied strain (or temperature change)
in most cases, because the decreased PB0 value does not return to the initial value. The PB0 change
distributions (calculated by substituting the resultant PB0 distributions (solid curves) from their initial
distributions (dotted lines)) are used as final measurement data.
To evaluate the optimal νB0 value and the bandwidth of the linear region, we analyzed a raw BGS
with a BFS of 10.89 GHz (see Figure 6a), which was experimentally obtained when the FUT length
L and experimental conditions (such as the modulation frequency f m and amplitude ∆f ) were set toAppl. Sci. 2018, 8, 1845

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the same values as those for the initial experiment (L = 5.0 m, f m = 8.0 MHz, ∆f = 1.4 GHz) [59]. Here,
we defined the linear region as the region where the change in the BGS slope was suppressed within
20% compared to its maximum. Based on the slope (i.e., differential coefficient) dependence on thefrequency (Figure 6b) obtained by differentiating the BGS with respect to frequency, the optimal νB0value to widen the linear region was found to be 10.85 GHz. The bandwidth of the linear region wasapproximately 50 MHz, which corresponds to the strain of up to ~1035 µε and the temperature changeof ~45 K. In this linear region, the theoretical strain and temperature dependence coefficients were
calculated to be 2.1 × 10−4 dB/µε and 4.3 × 10−3 dB/K, respectively.

Figure 6. (a) Measured BGS and (b) its differential coefficient at each frequency. The linear region of
the lower-frequency side is indicated. Reproduced with permission from [59]. Copyright (2016) IEEE.

The FUT employed in the initial experiment was a 5.0-m-long silica SMF with a BFS of 10.89 GHz
at 1.55 µm at room temperature. The experimental setup of slope-assisted BOCDR is schematicallyshown in Figure 7, which is basically the same as Figure 1; the only essential difference lies in the final
signal processing. The output light from a distributed-feedback laser diode at 1.55 µm was divided
into two light beams, pump and reference. The pump light was amplified to ~24 dBm using an EDFA
and injected into the FUT. After passing through a ~1-km-long delay line and another EDFA (amplified
to ~5 dBm), the reference light was used for heterodyne detection with the Stokes light, which was
amplified to ~2 dBm. The polarization-dependent fluctuations were suppressed using a polarization
scrambler (PSCR). The heterodyned optical signal was converted into an electrical signal using a PD
and was guided to an ESA. Using the narrowband-pass filtering function of the ESA, the PB0 change ata fixed frequency νB0 (=10.85 GHz) was sequentially output to an oscilloscope (OSC).

Figure 7. Experimental setup of slope-assisted BOCDR. AMP, amplifier; EDFA, erbium-doped fiber
amplifier; ESA, electrical spectrum analyzer; FUT, fiber under test; LD, laser diode; OSC, oscilloscope;PD, photodiode; PSCR, polarization scrambler. Reproduced with permission from [59]. Copyright(2016) IEEE.

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In the initial experiment, a 0.1-m-long section around the distal open end of the FUT was bent
to suppress the Fresnel reflection. The modulation frequency f m and amplitude ∆f were set to7.975–8.055 MHz and 1.4 GHz, respectively, corresponding to the measurement range of 12.9 m and thetheoretical spatial resolution of 88 mm. The repetition rate was 100 Hz, and averaging was performed
16 times on the OSC. The room temperature was 26 ◦ C. The measured results of the fundamental
characterization, i.e., the PB0 change dependencies on strain, temperature, and loss, are presented in
Reference [59] (the data are not presented here because of the low SNR). The strain-, temperature-,
and loss-dependence coefficients of the output signal were 1.95 × 10−4 dB/µε, 4.42 × 10−3 dB/K, and
0.191, respectively. A proof-of-concept demonstration of slope-assisted BOCDR was then performedby simultaneous measurement of strain, temperature, and loss. The structure of the 5.0-m-long FUT
is shown in Figure 8a; the ambient temperature was changed to 55 ◦ C along the 1.9–2.1-m section,
a 0.64-dB loss was applied at the midpoint, and a 550 µε strain was applied to the 3.5–3.7-m section.
Figure 8b shows the measured PB0 change distribution along the FUT. The PB0 changes corresponding
to the temperature change, loss, and strain were observed at the expected sections. The amountsof the PB0 changes for the temperature change, loss, and strain were approximately 0.16, 0.14, and0.12 (=0.26–0.14) dB (corresponding to the temperature change, loss, and strain of ~62 ◦ C, ~0.73 dB,
and ~615 µε, respectively). The measurement errors probably originate from the signal fluctuations
and the resultant low SNR.

Figure 8. (a) Structure of the FUT. (b) Measured PB0 change distribution. Reproduced with permission
from [59]. Copyright (2016) IEEE.

4.2. Beyond-Nominal-Resolution Effect
One fundamental issue that must be solved to characterize the slope-assisted BOCDR operationis the correspondence between the final system output (i.e., power-change distribution) and theactual BFS distribution. In standard BOCDR based on frequency information, these two distributions
have been proven to be identical in principle; however, in slope-assisted BOCDR based on power
information, no report has been made. Here, we theoretically and experimentally show that the final
system output of slope-assisted BOCDR is generally different from the actual BFS distribution. We also
show that, even when the strained section is shorter than the nominal resolution, some shift in the
power change can be observed. This feature is unique to the slope-assisted BOCDR and useful forpractical applications.
To start with, we simulated the system output of slope-assisted BOCDR. We assumed that one
section of the FUT was uniformly strained. The magnitude of the strain was assumed to constantly
lie below the upper limit of the linear region (~2000 µε). The lengths of the strained section were set
to 0.25R, 0.5R, 0.75R, R, 2R, 5R, and 10R, where R indicates the nominal spatial resolution calculatedusing Equation (2). First, the simulation results for the strain distributions acquired using the standard

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BOCDR (deduced from the BFS distributions using the linear BFS-to-strain relationship) are shownin Figure 9a, which completely reproduce the actual BFS distributions. Next, the simulation results
for the strain distributions obtained from the slope-assisted BOCDR (also deduced from the final
power-change distributions simply based on the linear power-to-strain relationship) are shown in
Figure 9b (strained: 0.5R, R, 2R, 5R, and 10R) and Figure 9c (strained: 0.25R, 0.5R, 0.75R, and R). Here,for simplicity, we neglected both the complicated longitudinal shape of the correlation peak and theinfluence of its sidelobes [65]; that is, the longitudinal shape of the correlation peak was approximatedby a rectangular profile with a length of R. At the ends of the strained section (i.e., the boundaries
between the strained and non-strained sections), the power change varied linearly with the lengthof R; consequently, each whole power-change distribution showed a trapezoidal shape (including
triangular). Thus, we see that when the strained section is sufficiently longer than R, the power-change
distribution almost reproduces the actual BFS distribution. In contrast, when the length of the strained
section is approximately R or only a few times longer than R, the correct BFS distribution cannot bedirectly obtained (under the assumption that the strain is uniformly applied; however, the correct
information can be easily derived). What is notable here is that, even when the strained section isshorter than R, we can observe a trapezoidal-shaped shift in the power change and thereby obtain theinformation that some irregularity has occurred at that point. For instance, when the length of thestrained section is 0.5R, a trapezoidal shape with a maximal power-change shift (corresponding to half
the amount obtained with a strained section longer than R) is observed.

Figure 9. Deduced strain distributions directly obtained from the final power outputs of (a) standard
BOCDR and (b,c) slope-assisted BOCDR. Note that the traces in (a) give the correct strain distributions.
Reproduced with permission from [60]. Copyright (2016) OSA.

Subsequently, the aforementioned simulation results including this “beyond-nominal-resolution”
effect are experimentally verified (note that with this effect, we cannot distinguish two hot spots ofwhich the distance is smaller than the nominal resolution, as the two hot spots are broadened; we
can just detect an extremely short hot spot, and in this meaning, the spatial resolution of the system
is not enhanced with this effect). The setup was basically the same as that in Figure 7; the change
in the spectral power at 10.81 GHz was sequentially output to the OSC (owing to the difference inthe video bandwidth of the ESA). The FUT was a 13.0-m-long silica SMF with a BFS of 10.86 GHz
at 1.55 µm at room temperature (25 ◦ C). Measurements were performed using two configurations:
one for a relatively high spatial resolution and the other for a relatively low resolution (required toAppl. Sci. 2018, 8, 1845

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investigate the beyond-nominal-resolution effect). In the first configuration with a high resolution,strains of 750 µε and 1500 µε were applied to 5-cm-, 10-cm-, 20-cm-, 50-cm-, and 100-cm-long sectionsof the FUT, as depicted in Figure 10a. The modulation frequency f m and amplitude ∆f were set to
7.11–7.31 MHz and 1.3 GHz, respectively, corresponding to the measurement range of 14.5 m and thetheoretical spatial resolution of 9.5 cm according to Equations (2) and (3). In the second configuration
with a low resolution, a strain of 1500 µε was applied to 5-cm-, 10-cm-, 15-cm-, and 20-cm-long sectionsof the FUT (see Figure 10b). The modulation frequency f m was swept in the same range (7.11–7.31
MHz), thus giving the same measurement range (14.5 m). The modulation amplitude ∆f was reduced
to 0.7 GHz, corresponding to a theoretical spatial resolution of 19.6 cm. In both configurations, therepetition rate was set to 100 Hz, and averaging was performed 64 times on the OSC to improve
the SNR.

Figure 10. (a) Structure of an FUT with a relatively high spatial resolution (9.5 cm); and (b) structureof an FUT with a relatively low spatial resolution (19.6 cm). Reproduced with permission from [60].
Copyright (2016) OSA.

First, we present the experimental results with a relatively high spatial resolution (9.5 cm).
An example of the measured power change distribution (converted into strain) along the whole lengthof the FUT (with a 1500 µε strain applied to a 20-cm-long section) is shown in Figure 11a. At this scale,it appears that the correct amount of strain was detected at the correct location. The strain distributions
measured when strains of 750 µε and 1500 µε were applied (magnified views around the strained
sections), simply deduced from the power-change distributions based on the linear power-to-strain
relationship, are shown in Figure 11b,c, respectively. Each distribution is shifted by 3000 µε, and thesimulated data are indicated by dotted lines. The trends in the measured distributions agree wellwith the simulation results, including the case where the strained section is half the nominal spatial
resolution. This indicates that our relatively rough simulation is almost sufficient to predict theexperimental results, which is beneficial from the viewpoint of simulation cost.
We then performed similar experiments with a relatively low spatial resolution (19.6 cm) toevaluate the beyond-nominal-resolution effect. The magnified views of the strain distributions (simply
deduced from the power-change distributions), measured when a strain of 1500 µε was applied, areshown in Figure 12. As the strained section becomes shorter, the maximal power-change shift becomes
smaller. The trend in the measured distributions is basically in good agreement with the simulation
results. As the strained section is shortened further, the signal is buried by the noise. The standard
deviation of the noise floor (power fluctuations corresponding to the strain of the non-strained sections)
was calculated to be approximately 130 µε in this measurement. This amount is theoretically obtained
as the maximal strain when the strained section is 1.7 cm, which could be regarded as the shortest
detectable length. Note that this value is influenced by various experimental parameters such as theamount of the actual strain, the number of averaging, the incident power, etc., the details of which aredescribed in the following subsection.

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Figure 11. Deduced strain distributions with a spatial resolution of 9.5 cm: (a) example measurement
along the whole length of the FUT when a 1500 µε strain was applied to a 20-cm-long section,and magnified views when strains of (b) 750 µε and (c) 1500 µε were applied to 5-cm- to 100-cm-longsections. In (b,c), each distribution was shifted by 3000 µε, and the dotted lines indicate the simulated
data. Reproduced with permission from [60]. Copyright (2016) OSA.

Figure 12. Magnified views of the deduced strain distributions with a spatial resolution of 19.6 cm;
a 1500 µε strain was applied to 5-cm- to 20-cm-long sections. Each distribution was shifted by 3000 µε,
and the dotted lines indicate the simulated data. Reproduced with permission from [60]. Copyright(2016) OSA.

4.3. Detection of Extremely Short Hot Spots
Here, we performed more detailed characterization of the beyond-nominal-resolution effect ofslope-assisted BOCDR. First, using a silica SMF, we found that a strained section which is over 50 times

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shorter than the nominal spatial resolution can be detected. Then, we showed the usefulness of thebeyond-nominal-resolution effect by detecting a 2-mm-long strained section along a silica SMF anda 5-mm-long heated section along a POF. These values are smaller than the world records previously
reported, which are 3 mm [66] and 100 mm [67] for a silica SMF and a POF, respectively.
First, to characterize the beyond-nominal-resolution effect, we employed a 14.0-m-long silica
SMF as an FUT. The output light from a laser was amplified to ~25 dBm using an EDFA and injected
into the FUT. The BFS of the FUT was 10.89 GHz at 1.55 µm at 26 ◦ C (room temperature). The open
end of the FUT was bent to suppress the Fresnel reflection. The spectral power-change at 10.87 GHz(determined by differentiating the BGS) was monitored using an OSC. The modulation amplitude∆f and the modulation frequency f m were set to 0.19 GHz and 5.10–5.26 MHz, respectively, leading
to the nominal spatial resolution of 1.01 m and the measurement range of 20.1 m. A strain of 0.1%
was applied to 0.01-, 0.02-, 0.05-, 0.10-, 0.20-, 0.50-, and 1.00-m-long sections of the FUT, as shown in
Figure 13a. When the length of the strained section was changed, the position of its proximal end was
fixed. Averaging was performed 512 times on the OSC.
Subsequently, exploiting the beyond-nominal-resolution effect, we attempted to detect the
shortest-ever strained and heated sections along a silica SMF and a POF. In this experiment, we injected~28 dBm light to the FUTs to enhance the measurement sensitivity, and averaging was performed 1024
times. To begin with, we employed a 2.0-m-long silica SMF as an FUT, the BFS of which was 10.85
GHz at room temperature. We applied strains of 0.10, 0.15, and 0.20% to a 2-mm-long section (~55
times shorter than the nominal spatial resolution; see below), as depicted in Figure 13b. The nominal
spatial resolution and the measurement range were 0.11 m and 7.64 m (∆f : 0.67 GHz; f m : 13.45–13.54
MHz), respectively. The change in the spectral power at 10.84 GHz was observed using the OSC. Then,a 2.0-m-long perfluorinated graded-index POF [39,68,69] (core diameter: 50 µm; propagation loss at
1.55 µm: 0.25 dB/m; BFS at room temperature: 2.75 GHz) was used as an FUT. A 5-mm-long section
was heated to 35, 45, and 55 ◦ C (see Figure 13c). The modulation amplitude ∆f and the modulation
frequency f m were set to 0.69 GHz and 24.70–24.84 MHz, respectively, resulting in the nominal spatial
resolution of 0.21 m and the measurement range of 4.5 m. Note that the length of the heated section
was over 40 times shorter than the nominal spatial resolution. The change in the spectral power at 2.78
GHz was monitored.

Figure 13. (a) Structure of a silica SMF under test. The length of the strained section Lε was set to0.01, 0.02, 0.05, 0.10, 0.20, 0.50, and 1.00 m. (b) Structure of a silica SMF under test, which was locallystrained for 0, 0.10, 0.15, and 0.20%. (c) Structure of a POF under test, which was locally heated to 26,
35, 45, and 55 ◦ C. Reproduced with permission from [61]. Copyright (2016) JSAP.

The power-change distributions measured when the length of the strained section Lε was reduced
from 1.00 m to 0.01 m are shown in Figure 14a. Note that the nominal spatial resolution was 1.01 m

Appl. Sci. 2018, 8, 1845

13 of 19throughout the measurement. The vertical axis was normalized so that the maximal power-change
became 1 when Lε was 1.00 m. Each distribution was displayed with a vertical interval of 0.5. When Lεwas 1.00 m, the power-change distribution showed a triangular shape. As Lε decreased, the maximal
power-change also decreased. When Lε was 0.02 m, the power-change was still clearly detected, but it
became almost comparable to the signal fluctuations when Lε was 0.01 m. Thus, in this experimental
condition, a strained section, which was over 50 times shorter than the nominal spatial resolution,
was shown to be detectable. Figure 14b shows the normalized maximal power-change plotted asa function of Lε . The error bars were standard deviations of the signal fluctuations at non-strained
sections. The maximal power-change decreased almost linearly with decreasing Lε , which agrees wellwith the theory. The observed length of non-zero-power-change section was almost equal to the sumof the strained length Lε and the nominal spatial resolution, which also agrees with the theory.

Figure 14. (a) Normalized power-change distributions measured when the length of the strained
section Lε was reduced from 1.00 m to 0.01 m; each distribution was shifted by 0.5. Dotted lines indicate
the theoretical trends. (b) Maximal power-changes plotted as a function of Lε . The error bars were
calculated as standard deviations of the signal fluctuations at non-strained sections. The dotted line isa linear fit. The inset shows the magnified view at Lε shorter than 0.1 m. Reproduced with permission
from [61]. Copyright (2016) JSAP.

Finally, exploiting the beyond-nominal-resolution effect verified above, we attempted to detect
the shortest-ever strained and heated sections along a silica SMF and a POF. Figure 15a shows thenormalized power-change distributions measured when the strain of 0.10, 0.15, and 0.20% were applied
to a 2-mm-long section of the silica SMF. The local power-changes corresponding to the strain wereobserved at the correct position. The lengths of the power-changed sections appeared to be much
longer than 2 mm; in theory, they should be almost the same as the nominal resolution (0.11 m),
which moderately agrees with the measured results. The maximal normalized power-change of each
distribution in Figure 15a was plotted as a function of applied strain in Figure 15b. With increasingstrain, the power-change also increased almost linearly, which indicated the magnitude of the strain
can be correctly measured in this strain range. Then, we performed a similar experiment using the
POF. The normalized power-change distributions measured when the 5-mm-long section was heatedto 26 (room temperature), 35, 45, and 55 ◦ C are shown in Figure 16a. The abrupt power-changes wereobserved at the correct position along the POF. The lengths of the power-changed sections moderately

Appl. Sci. 2018, 8, 1845

14 of 19agreed with the nominal resolution (0.21 m). The magnitude of the maximal power-change was inproportion to the temperature change, as shown in Figure 16b, indicating the potential feasibility of
distributed temperature sensing.

Figure 15. (a) Normalized power-change distributions along a silica SMF measured at four strains.
(b) Maximal power-changes plotted as a function of strain. The dotted line is a linear fit. Reproducedwith permission from [61]. Copyright (2016) JSAP.

Figure 16. (a) Normalized power-change distributions along a POF measured at four temperatures.
(b) Maximal power-changes plotted as a function of temperature. The dotted line is a linear fit.
Reproduced with permission from [61]. Copyright (2016) JSAP.

4.4. Other Achievements
In addition to the detection of the extremely short hot spots using the beyond-nominal-resolution
effect, a number of remarkable advances have been made in the slope-assisted BOCDR. First,
by analyzing the BGS shape, the measurement sensitivity dependencies on the incident power
and the spatial resolution were investigated [70]. The sensitivity was shown to be enhanced withhigher incident power and/or lower spatial resolution; this result was verified through distributed
temperature measurements. Then, we implemented slope-assisted BOCDR using a high-loss POF [71].
Owing to the gradual reduction in the transmitted power along the POF, the measurement sensitivities
were found to depend on the sensing position. This unique effect was investigated experimentally,
and a correct POF-based distributed measurement was performed by compensating this effect. We also
demonstrated loss-insensitive operation by employing a special silica fiber with low bending loss [72].
We measured the coefficients of the power-change dependencies on strain and temperature, and bycomparing the distributed strain and temperature measurement results using a standard silica fiber andthe special fiber, showed that this configuration offers highly stable loss-insensitive operation. Anotheradvance was made from a more practical viewpoint; we presented an example of diagnosis using
a composite structure with carbon fiber-reinforced plastics [73]. A silica SMF was embedded in thiscomposite structure during a vacuum-assisted resin transfer molding process. When the composite
structure was bent, the system output agreed well with the actual compressive and tensile strain

Appl. Sci. 2018, 8, 1845

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distributions. We were also able to detect the breakage of the embedded fiber, which indicated that theslope-assisted system is potentially beneficial for structural health monitoring. In addition, very recent
advances include the enhancement of the stability and strain sensitivity using polarization-maintaining
fibers [74] and the demonstration of the beyond-nominal-resolution effect with a long measurement
range of over 10 km.
5. Conclusions
We reviewed the BOCDR technology from the basic principle to the recent advances. In Section 1,
a variety of Brillouin-based distributed sensing techniques including BOCDR and BOTDA wereintroduced. In Section 2, the basic operating principle of BOCDR was presented. In Section 3,
some configurations for improving the performance of BOCDR were described. In Section 4,
the slope-assisted BOCDR was detailed; the operating principle and some unique features including
the beyond-nominal-resolution effect were presented. Thus, significant technical advances have beenachieved to enhance the performance of BOCDR. However, there still remain some important issues
to be tackled. One unclarified point of this system is the measurement accuracy, which should be ina trade-off relationship with some parameters such as an average count (or measurement time), spatial
resolution, incident optical power, etc. Full investigation of the measurement accuracy is extremely
important in order for users to judge whether BOCDR can be employed or not for their purposes.
Another point is the clarification of the maximal sampling rate, which is currently limited by theelectronic devices used in the setup (in any configuration of BOCDR). The measurement instability
caused by the power fluctuations is also a problem in the slope-assisted configuration, which could
be mitigated using the ratio between the spectral powers at two frequencies; this push-pull scheme
will provide another configuration for loss-insensitive operation. In addition, the dynamic range ofslope-assisted BOCDR currently limited by the BGS shape could be extended by low-pass filtering thespectrum (at the cost of the sensitivity). Brillouin-based distributed sensing is, in general, constantly
confronted with a problem of discriminative sensing of strain and temperature, and BOCDR is no
exception. Combined use of some other sensing mechanisms [75–84] will be necessary. Finally,
the current setup is not suitable for field tests outside the laboratory. The system portability should be
improved by implementing the functions of the relatively large devices, such as the ESA, the EDFAs,
the PSCR, and the frequency-modulated laser, using local electronic circuits and/or module-typedevices. These replacements will also lead to reduction in the system cost. We hope that BOCDR will,in the near future, serve as one of the most promising Brillouin-based distributed sensing techniques
for practical applications because of its single-end accessibility and many other advantages.
Author Contributions: Y.M. and H.L. performed the experiments, and Y.M., H.L. and K.N. analyzed the data.
Y.M. wrote the review paper.
Funding: This work was supported in part by JSPS KAKENHI (17H04930, 17J07226) and the research grants
from the Japan Gas Association, the ESPEC Foundation for Global Environment Research and Technology,
the Association for Disaster Prevention Research, the Fujikura Foundation, and the Japan Association for
Chemical Innovation.
Acknowledgments: The authors are indebted to Kazuo Hotate, the Toyota Technological Institute (formerly,
the University of Tokyo), Japan, for his insightful comments and suggestions regarding the future prospectsof BOCDR.
Conflicts of Interest: The authors declare no conflicts of interest.

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