Measurement Science and Technology
Meas. Sci. Technol. 30 (2019) 075204 (6pp)

https://doi.org/10.1088/1361-6501/ab22ec

Trade-off relation between strain dynamic
range and spatial resolution inslope-assisted Brillouin opticalcorrelation-domain reflectometry
Heeyoung Lee , Kohei Noda , Yosuke Mizuno

and Kentaro Nakamura

Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan
E-mail: hylee@sonic.pi.titech.ac.jp
Received 20 February 2019, revised 1 May 2019
Accepted for publication 20 May 2019
Published 4 June 2019
Abstract

Slope-assisted Brillouin optical correlation-domain reflectometry (SA-BOCDR) is one of thehigh-speed distributed strain sensing techniques, but its strain dynamic range has been limited
to approximately 0.15%, which is far from being sufficient for some practical applications.
In this paper, we clarify that, unlike widely used time-domain techniques, SA-BOCDR has a
trade-off relation between the strain dynamic range and the spatial resolution. This trade-off
originates from the unique bell-shaped noise floor inherently involved in the Brillouin gain
spectrum observed with correlation-domain techniques. We experimentally show that, at thecost of three times lowered spatial resolution, the strain dynamic range of >0.6% can beachieved.
Keywords: Brillouin scattering, distributed optical fiber sensor, strain dynamic range(Some figures may appear in colour only in the online journal)of BOCDR have been implemented to achieve better sensing
performance including spatial resolution [16–18], and measurement range [21, 22]. BOCDR suffered from its relatively
long measurement time, but recently this issue has been mitigated by two frequency-sweeping-free configurations, calledphase-detected (PD-) BOCDR [25] and slope-assisted (SA-)
BOCDR [26]. Although PD-BOCDR has a high sampling rateof hundreds of kilohertz, its strain dynamic range is limited
to approximately 0.2%. Though some attempts to extend thestrain dynamic range have been made [27], it is still one of the
major drawbacks of PD-BOCDR. Here, we concentrate attention on SA-BOCDR.
SA-BOCDR enables high-speed operation by exploiting
the slope of the Brillouin gain spectrum (BGS). After demonstrating its basic operation [26], we have clarified its uniquefeatures such as beyond-nominal-resolution detectability [28]and adjustable sensitivity [29]. We have also shown its practical usefulness by providing a case example of distributed
strain monitoring along an FUT embedded in a composite
structure [30]. Remarkable progress has thus been made since

1. Introduction
Brillouin-scattering-based sensing [1] has been one of themost extensively studied topics in fiber-optic sensing community. It enables us to diagnose damaged civil infrastructures
exploiting its capability of distributed strain/temperature measurement along fiber under tests (FUTs). Distributed Brillouinsensors are generally classified into two types: ‘analysis’ and‘reflectometry’. In the former, two lightwaves need to be
injected into both ends of an FUT, while in the latter, light
injection to one end of an FUT is sufficient for proper operation. For each type, different schemes for acquiring position
information, namely, time-[2–9], frequency-[10–13], and correlation-[5, 14–24] domain schemes, have been developed.
Although different configurations have different merits anddemerits, the target of this paper is Brillouin optical correlation-domain reflectometry (BOCDR), which is the only
scheme with advantages such as single-end accessibility,
random accessibility to sensing positions, and relatively
high spatial resolution. To date, a number of configurations
1361-6501/19/075204+6$33.00

1© 2019 IOP Publishing Ltd Printed in the UKH Lee et al

Meas. Sci. Technol. 30 (2019) 075204

Figure 1. Experimental setup of SA-BOCDR. AC, alternating current; CW, continuous wave; DC, direct current; EDFA, erbium-doped
fiber amplifier.

its first proposal, but one of the important problems unsolved
yet is its strain (or temperature) dynamic range limited by
the narrow linear range of the BGS slope. The linear range is
generally reported to be several tens of megahertz [1], whichcorresponds to a relatively small strain of ~0.15% (or temperature change of ~64 K). This value is even lower than that of
PD-BOCDR and is far from being sufficient for some practical applications [31–33].
The simplest idea to improve the strain dynamic range
is to exploit not only the linear range but also the nonlinear
range of the BGS. However, this approach may not operate soeffectively as expected, because the BGS observed in BOCDR
involves a unique bell-shaped background noise floor [34, 35],
which is not sensitive to the strain applied to the sensing position. Thus, it is crucial to extend the upper limit of the measurable strain by another method.
In this work, to start with, we experimentally confirm thatthe aforementioned idea, i.e. additonal use of the nonlinear
range of the BGS, is not effective. The maximal measurable
strain obtained by this approach is found to be merely ~0.25%.
Then, we clarify that SA-BOCDR has a trade-off relation
between the strain dynamic range and the spatial resolution
and that the former can be extended at the sacrifice of thelatter. In the experiment, we achieve a strain dynamic range
of >0.6% when the spatial resolution is three times lower.

Figure 2. Structure of FUT.

dm =

c
,
2nfm

(1)

where c is the velocity of light in vacuum and n is the refractive
index of the fiber core. The spatial resolution Δz is reported
to be given by [36]
Δz =

cΔνB
,
2πnfm Δf(2)

where ΔνB is the Brillouin bandwidth and Δf is the modulation amplitude of the optical frequency.
Brillouin-based sensing generally exploits the strain (ortemperature) dependence of the Brillouin frequency shift(BFS) [1]. In standard BOCDR, the BFS is derived after
acquiring the whole BGS, which is relatively time-consuming
because optical frequency needs to be swept. In contrast,
SA-BOCDR enables frequency-sweeping-free higher-speed
operation by using, instead of the BFS itself, a spectral power
PB0 at a certain frequency νB0 on the BGS slope. If we desire
to measure tensile strain (or heat) applied to the FUT, νB0 is
set to lower frequency than the BFS.
When SA-BOCDR was first developed, we determined thestrain dynamic range by the linear range of the BGS slope [26].
It may be feasible to extend the dynamic range if the nonlinear
range (foot of the BGS) is additonally used to measure strain at
the cost of the deteriorated sensitivity. However, the effect of
this method is probably limited because the BGS observed in
BOCDR inherently involves a bell-shaped background noise

2. Principle
BOCDR operates based on correlation control of continuous
lightwaves, which enables high spatial resolution and signalto-noise ratio (SNR). By modulating the driving current of alight source, the optical frequency of its output is sinusoidally
modulated to generate a ‘correlation peak’ in the FUT, whichenables position-selective detection of Brillouin signal. By
sweeping the modulation frequency f m, the correlation peakcan be scanned along the FUT for distributed measurement.
Since multiple correlation peaks are generated periodicallyalong the FUT, in a standard BOCDR configuration, the measurement range dm is given by their interval as [36]2H Lee et al

Meas. Sci. Technol. 30 (2019) 075204

Figure 3. (a) Measured distribution of the normalized power change when the applied strain was 0.25%. (b) Normalized power changeplotted as a function of applied strain. The dotted curve is an exponential fit. (c) BGSs measured at strains of 0, 0.1, 0.2, 0.25, 0.3% when
the strained length Lε was the same as the nominal spatial resolution Δz (=~0.37 m).

of 1.55 μm was divided into two light beams: pump and reference. After amplified to ~26 dBm using an erbium-doped fiber
amplifier (EDFA), the pump light was injected into the FUT.
The Brillouin-scattered Stokes light was then amplified to~2 dBm using another EDFA and coupled with the reference
light for heterodyne detection. The reference light was amplified to ~1 dBm after passing through a ~1 km-long delay fiber.
After converted into an electrical signal using a photodiode,the heterodyned signal was guided to an electrical spectrum
analyzer (ESA; video bandwidth: 10 kHz, resolution bandwidth: 10 MHz). Using the narrowband-pass filtering functionof the ESA, the change in the spectral power at 10.80 GHz
was transmitted to an oscilloscope (OSC). The repetition rate
was 100 Hz, and averaging was performed 512 times on the
OSC to achieve a higher SNR.
As shown in figure 2, we used a 7.5 m-long silica singlemode fiber (SMF) with a BFS of 10.82 GHz at room temperature (20 °C). A bending loss was applied near the open end to
suppress the Fresnel reflection.
We performed two experiments: one was to measure thestrain dynamic range of standard SA-BOCDR and to confirm the origin of its limitation, and the other was to investigate the trade-off relation between the strain dynamic range
and the spatial resolution. In the first experiment, we set thefloor. This noise is caused by accumulation of the Brillouinsignals from non-correlation (or non-sensing) sections along
the FUT [34, 35]. As the nonlinear range of the BGS is mostly
located on this noise floor, drastic improvement of the strain
dynamic range cannot be expected by this method.
Here, we draw attention to the fact that the bell-shaped
noise floor consists predominantly of the Brillouin signals
from the non-sensing sections close to the sensing section (inother words, the closer the non-correlation sections are to thecorrelation peak, the greater their contributions to the noise
floor become) [34, 35]. Therefore, if we intentionally lower
the spatial resolution and include initially non-sensing sections into newly defined sensing section, the noise floor will
be drastically diminished; as a result, the strain dynamic range
will be greatly enhanced. Thus, SA-BOCDR has a trade-off
relation between the strain dynamic range and the spatial resolution. We give experimental analysis on this nature in thispaper.
3. Experimental setup
The experimental setup of SA-BOCDR is depicted in figure 1,
which is essentially the same as that previously reported [26].
A continuous lightwave from a laser with a center wavelength3

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Meas. Sci. Technol. 30 (2019) 075204

Figure 4. (a) BGSs measured at strains of 0–0.6% (step: 0.1%) when the strained length Lε was 3Δz, where Δz is ~0.37 m. (b) Normalized
power changes plotted as functions of applied strain when the Lε values were Δz, 1.5Δz, 2Δz, and 3Δz. The dotted curves are exponential
fits. (c) Maximal measurable strain plotted as a function of Lε. The dotted line is a linear fit.

modulation frequency f m and modulation amplitude Δf to
9.80–9.97 MHz and 0.27 GHz, respectively, which correspondto the meausrement range dm of ~10.3 m and the theoreticalspatial resolution Δz of ~0.37 m according to equations (1)and (2). Distributed strain measurements were performed
when strains of 0%–0.7% were applied to a ~0.37 m-long section (same as Δz). We simultaneously measured the BGSs in
the strain range of 0%–0.3% when the correlation peak was
located ~4.0 m away from the end of the second-port SMF
of an optical circulator (see figure 2; f m was 9.89 MHz). In
the second experiment, similar measurements of strain distributions and single-point BGSs were performed, but withelongated strained lengths Lε from Δz to 3Δz, which can be
regarded as intentionally lowered spatial resolutions.

indicates the correct operation of SA-BOCDR when thestrained length equals the sptatial resolution [28]. Similar
measurements were performed at various strains in the range
of 0%–0.7%. Figure 3(b) shows the measured dependence ofthe normalized power change (at the midpoint of the strained
section) on applied strain. With increasing strain, the powerchange also increased, but the slope became gradually small(moderately fitted by an exponential curve). When strain
was smaller than ~0.15%, the dependence was almost linear,which agrees well with previous reports [26, 28]. However,in the strain range of approximately 0.15%–0.25%, the slope
became smaller, which can still be used to measure strain
because the power change and strain are in one-to-one correspondence. In contrast, once the strain exceeded ~0.25%,
the power change showed no significant growth and becamealmost constant. These results indicate that the use of thenonlinear range of the BGS slope is not an effective method
for improving the strain dynamic range, which was slightly
extended from 0.15% to 0.25% in this experiment. We alsomeasured the BGSs while applying strains of 0%–0.3% to the~0.37 m-long section in the FUT. As shown in figure 3(c), withincreasing strain, the spectral power at 10.80 GHz decreased
when the applied strain was smaller than ~0.25%, which corresponds to the trend in figure 3(b). However, it is clear that,when strain was larger, the spectral power stopped decreasing

4. Experimental results
First, we present the results of SA-BOCDR-based distributed strain measurements when relatively large strains wereapplied. Figure 3(a) shows an example of the measured distribution of the spectral power change along the whole FUT
when a 0.25% strain was applied to a ~0.37 m-long section. The vertical axis was normalized so that the maximal
power change became 1. The power change at the strained
section was detected; a triangular shape (not rectangular)
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Meas. Sci. Technol. 30 (2019) 075204

because of the aforementioned bell-shaped background noise
floor. This observation confirms that the strain dynamic rangeof SA-BOCDR is, even when the nonlinear range of the spectral slope is exploited, significantly restricted by this uniquenoise structure.
Subsequently, we show the results when the spatial resolution was lowered. Figure 4(a) shows the BGSs measured
when the strains of 0–0.6% were applied to a 1.1 m-long section (corresponding to 3Δz) in the FUT. Unlike in the casewhere the strained length Lε was Δz, the spectral power at 10.80
GHz decreased even when the applied strain was larger than
0.25%. This is because part of the noise floor shifted to higher
frequency owing to the lowered resolution. This trend wasbasically the same when Lε was 1.5Δz and 2Δz. Figure 4(b)shows the strain dependence of the normalized power change(at the midpoint of the strained section). Regardless of Lε, thepower change increased with increasing applied strain. The
slope became gradually small, and the power change finallybecame almost constant, in the same manner as in figure 3(b).
However, is is notable that, with increasing Lε, the strain
at which the power change became constant increased. In
figure 4(c), as a function of Lε, we finally plotted the maximal
measurable strain, which we defined as the strain at which
the power change reaches ~86.5% of its saturated value. As
Lε increased, the maximal measurable strain increased almost
linearly with a coefficient of ~0.2% in this experiment. Whenthe spatial resolution was three times lowered, the strain
dynamic range was >0.6%. Thus, we proved that the strain
dynamic range can be improved at the cost of the spatial resolution in SA-BOCDR.

Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers
17H04930 and 17J07226 and by a research grants from the
Fujikura Foundation.

ORCID iDs
Heeyoung Lee https://orcid.org/0000-0003-3179-0386
Kohei Noda https://orcid.org/0000-0003-4976-9657
Yosuke Mizuno https://orcid.org/0000-0002-3362-4720
Kentaro Nakamura https://orcid.org/0000-0003-2899-4484
References[1] Agrawal G P 1995 Nonlinear Fiber Optics (Cambridge, MA:
Academic)[2] Horiguchi T and Tateda M 1989 BOTDA-nondestructive
measurement of single-mode optical fiber attenuation
characteristics using Brillouin interaction: theory J.
Lightwave Technol. 7 1170
[3] Kurashima T, Horiguchi T, Izumita H, Furukawa S andKoyamada Y 1993 Brillouin optical-fiber time domainreflectometry IEICE Trans. Commun. E76-B 382[4] Dong Y, Ba D, Jiang T, Zhou D, Zhang H, Zhu C, Lu Z,
Li H, Chen L and Bao X 2013 High-spatial-resolution
fast BOTDA for dynamic strain measurement based on
differential double-pulse and second-order sideband of
modulation IEEE Photonics J. 5 2600407[5] Elooz D, Antman Y, Levanon N and Zadok A 2014 Highresolution long-reach distributed Brillouin sensing basedon combined time-domain and correlation-domain analysis
Opt. Express 22 6453
[6] Yang G, Fan X, Wang B and He Z 2018 Enhancing strain
dynamic range of slope-assisted BOTDA by manipulating
Brillouin gain spectrum shape Opt. Express 26 32599[7] Dong Y, Wang B, Pang C, Zhou D, Ba D, Zhang H and Bao X
2018 150 km fast BOTDA based on the optical chirp chain
probe wave and Brillouin loss scheme Opt. Lett. 43 4679
[8] Lalam N, Ng W P, Dai X, Wu Q and Fu Y Q 2018
Performance improvement of Brillouin ring laser based
BOTDR system employing a wavelength diversity
technique J. Lightwave Technol. 36 1084
[9] Mao Y, Guo N, Yu K L, Tam H Y and Lu C 2012 1-cm-spatialresolution Brillouin optical time-domain analysis based onbright pulse Brillouin gain and complementary code IEEE
Photonics J. 4 2243
[10] Garus D, Krebber K, Schliep F and Gogolla T 1996
Distributed sensing technique based on Brillouin opticalfiber frequency-domain analysis Opt. Lett. 21 1402
[11] Minardo A, Bernini R, Ruiz-Lombera R, Mirapeix J, LopezHiguera J M and Zeni L 2016 Proposal of Brillouin opticalfrequency-domain reflectometry (BOFDR) Opt. Express
24 29994[12] Bernini R, Minardo A and Zeni L 2012 Distributed sensing
at centimeter-scale spatial resolution by BOFDA:
Measurements and signal processing IEEE Photonics J.
4 48[13] Minardo A, Bernini R and Zeni L 2014 Distributed
temperature sensing in polymer optical fiber by BOFDA
IEEE Photonics Technol. Lett. 26 387

5. Conclusion
We clarified that SA-BOCDR has a trade-off relation between
the strain dynamic range and the spatial resolution. To start
with, we measured the BGSs when applied strains were larger
than the previously reported upper limit (~0.15%), and provedthat the limited strain dynamic range is caused by the bellshaped noise floor peculiar to the correlation-domain techniques. Then, by making use of the nature of this noise floor,
we showed that the strain dynamic range can be improved at
the cost of the spatial resolution. In the experiment, a strain
dynamic range of >0.6% was achieved with a spatial resolution lowered by three times. Considering that the spatial
resolution of BOCDR is relatively high even in its standard
configuration, such a lowered spatial resolution should still
be useful in some applications. We have some other ideas toimprove the strain dynamic range; for instance, by low-passfiltering the BGS, the dynamic range will be improved, but
at the sacrifice of the measurement sensitivity. Using multiple spectral powers will be another approach, but the signal
processing will be more complicated. Thus, we believe that
our simple approach to widening the strain dynamic range of
SA-BOCDR will be of significant use for practical applications in structural health monitoring in the future.

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H Lee et al

Meas. Sci. Technol. 30 (2019) 075204[26] Lee H, Hayashi N, Mizuno Y and Nakamura K 2016 Slopeassisted Brillouin optical correlation-domain reflectometry:
Proof of concept IEEE Photonics J. 8 6802807[27] Mizuno Y, Hayashi N, Fukuda H and Nakamura K 2017
Single-end-access distributed strain sensing with wide
dynamic range using higher-speed Brillouin opticalcorrelation-domain reflectometry Japan. J. Appl. Phys.
56 072501[28] Lee H, Hayashi N, Mizuno Y and Nakamura K 2016
Operation of slope-assisted Brillouin optical correlationdomain reflectometry: comparison of system output withactual frequency shift distribution Opt. Express 24 29190[29] Lee H, Mizuno Y and Nakamura K 2017 Measurement
sensitivity dependencies on incident power and spatial
resolution in slope-assisted Brillouin optical correlationdomain reflectometry Sens. Actuators A 268 68[30] Lee H, Ochi Y, Matsui T, Matsumoto Y, Tanaka Y,
Nakamura H, Mizuno Y and Nakamura K 2018 Distributed
strain measurement and possible breakage detection of
optical-fiber-embedded composite structure using slopeassisted Brillouin optical correlation-domain reflectometry
Appl. Phys. Express 11 072501[31] Zou L, Bao X, Ravet F and Chen L 2006 Distributed
Brillouin fiber sensor for detecting pipeline bucklingin an energy pipe under internal pressure Appl. Opt.
45 3372[32] Villalba S and Casas J R 2013 Application of optical fiber
distributed sensing to health monitoring of concrete
structures Mech. Syst. Signal Process. 39 441[33] Zhao X, Gong P, Qiao G, Lu J, Lv X and Qu J 2011 Brillouincorrosion expansion sensors for steel reinforced concrete
structures using a fiber optic coil winding method Sensors
11 10798[34] Song K Y, He Z and Hotate K 2006 Optimization of
Brillouin optical correlation domain analysis system
based on intensity modulation scheme Opt. Express
14 4256[35] Song K Y, He Z and Hotate K 2007 Effects of intensity
modulation of light source on Brillouin optical correlation
domain analysis J. Lightwave Technol. 25 1238
[36] Mizuno Y, Zou W, He Z and Hotate K 2010 Operationof Brillouin optical correlation-domain reflectometry:
Theoretical analysis and experimental validation J.
Lightwave Technol. 28 3300

[14] Hotate K and Hasegawa T 2000 Measurement of Brillouingain spectrum distribution along an optical fiber using acorrelation-based technique -proposal, experiment andsimulation IEICE Trans. Electron. E83-C 405[15] Mizuno Y, Zou W, He Z and Hotate K 2008 Proposalof Brillouin optical correlation-domain reflectometry(BOCDR) Opt. Express 16 12148[16] Mizuno Y, He Z and Hotate K 2009 One-end-access highspeed distributed strain measurement with 13-mm spatial
resolution based on Brillouin optical correlation-domainreflectometry IEEE Photonics Technol. Lett. 21 474[17] Manotham S, Kishi M, He Z and Hotate K 2012 1-cm
spatial resolution with large dynamic range in strain
distributed sensing by Brillouin optical correlation domainreflectometry based on intensity modulation Proc. SPIE
8351 835136[18] Mizuno Y, He Z and Hotate K 2009 Dependence of theBrillouin frequency shift on temperature in a tellurite glass
fiber and a bismuth-oxide highly-nonlinear fiber Appl. Phys.
Express 2 112402[19] López-Gil A, Martin-Lopez S and Gonzalez-Herraez M 2017
Phase-measuring time-gated BOCDA Opt. Lett. 42 3924
[20] Song K Y and Choi J H 2018 Measurement error induced by
the power-frequency delay of the light source in opticalcorrelation-domain distributed Brillouin sensors Opt. Lett.
43 5078[21] Mizuno Y, He Z and Hotate K 2009 Measurement range
enlargement in Brillouin optical correlation-domainreflectometry based on temporal gating scheme Opt.
Express 17 9040
[22] Mizuno Y, He Z and Hotate K 2010 Measurement range
enlargement in Brillouin optical correlation-domainreflectometry based on double-modulation scheme Opt.
Express 18 5926
[23] Jeong J H, Lee K, Song K Y, Jeong J and Lee S B 2012
Differential measurement scheme for Brillouin Optical
Correlation Domain Analysis Opt. Express 20 27094[24] Zhang C, Kishi M and Hotate K 2015 5,000 points/s highspeed random accessibility for dynamic strain measurement
at arbitrary multiple points along a fiber by Brillouin opticalcorrelation domain analysis Appl. Phys. Express 8 042501[25] Mizuno Y, Hayashi N, Fukuda H, Song K Y and Nakamura K
2016 Ultrahigh-speed distributed Brillouin reflectometry
Light: Sci. Appl. 5 e16184

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