Vol. 24, No. 25 | 12 Dec 2016 | OPTICS EXPRESS 29190

Operation of slope-assisted Brillouin opticalcorrelation-domain reflectometry: comparisonof system output with actual frequency shift
distribution
HEEYOUNG LEE,1,* NEISEI HAYASHI,2 YOSUKE MIZUNO,1 AND KENTARO
NAKAMURA1
1

Institute of Innovative Research, Tokyo Institute of Technology, 4259, Nagatsuta-cho, Midori-ku,
Yokohama 226-8503, Japan
2
Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1, Komaba,
Meguro-ku, Tokyo 153-8904, Japan*hylee@sonic.pi.titech.ac.jp

Abstract: Although the proof of concept for slope-assisted (SA-) Brillouin opticalcorrelation-domain reflectometry (BOCDR) has been demonstrated, no reports on its detailed
operation have been provided to date. We theoretically and experimentally investigate therelationship between the system output (power-change distribution) of SA-BOCDR and theactual Brillouin frequency shift (BFS) distribution along the sensing fiber and show that these
two are not identical. When the strained fiber section is much longer than the nominal spatial
resolution, the actual distribution of the BFS (i.e., strain) is well reproduced by the powerchange distribution. However, when the length of the strained section is equal to or only a few
times the nominal resolution, the correct BFS distribution cannot be directly obtained. Even
when the strained section is shorter than the nominal resolution, a shift in the power change
can still be observed, which is not the case for standard BOCDR systems. This unique“beyond-nominal-resolution” effect will be of great use in practical applications.
© 2016 Optical Society of America
OCIS codes: (060.2370) Fiber optics sensors; (120.0280) Remote sensing and sensors; (280.4788) Optical sensing
and sensors.

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http://dx.doi.org/10.1364/OE.24.029190
Received 23 Aug 2016; revised 21 Oct 2016; accepted 21 Oct 2016; published 8 Dec 2016

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1. Introduction
Due to increasing demand for structural health monitoring of civil infrastructure, a variety offiber-optic sensors have been extensively studied [1–3]. In particular, distributed optical fiber
sensors based on Brillouin scattering [4] have been receiving considerable attention due totheir measurement capabilities for strain and temperature change. Hence, many types ofBrillouin-based measurement schemes have been developed, including Brillouin optical time, frequency-, and correlation-domain analysis (BOTDA [5–9], BOFDA [10–12], and BOCDA[13–17]), and Brillouin optical time- and correlation-domain reflectometry (BOTDR [18–22]
and BOCDR [23–30]). Each scheme is being extensively studied and has its own advantages

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and disadvantages; here, we focus on BOCDR, which has a high spatial resolution andoperates by single-end light injection.
Since the basic BOCDR system was first proposed in 2008 [23], numerous configurations
have been implemented in order to improve its performance [24–34]. For example, themeasurement range was elongated using temporal gating [24] and double modulation [25];millimeter-order spatial resolution was achieved by use of a tellurite glass fiber [26] and by
apodization [27]; and the strain dynamic range was extended using polymer optical fibers [28,29]. In addition, one of the latest breakthroughs is phase-detection-based BOCDR [30], whichenables a high sampling rate of >100 kHz per point. We have recently developed anotherhigh-speed configuration, motivated by previous implementations in the time domain [31–33], called slope-assisted (SA-) BOCDR [34], in which the spectral power of the Brillouingain spectrum (BGS) is exploited to deduce the Brillouin frequency shift (BFS). Thisconfiguration can potentially allow for higher-speed operation than the phase-detection-based
method, and for detection of not only changes in strain and temperature, but also opticallosses, if necessary. Although the proof of concept for SA-BOCDR has been demonstrated[34], there is still much room for performance improvement. One fundamental issue that must
be solved in order to characterize SA-BOCDR operation is the correspondence between the
final system output (i.e., power-change distribution) and the actual BFS distribution. In
standard BOCDR systems based on frequency information, these two distributions have been
proven to be identical, in principle; however, in an SA-BOCDR system based on power
information, no report has been made so far.
In this paper, we theoretically and experimentally show that the final system output of
SA-BOCDR is generally different from the actual BFS distribution. When the strained section
is sufficiently longer than the nominal spatial resolution, the power-change distribution
almost reproduces the actual BFS (or strain) distribution. However, when the strained sectionis almost equal to or only a few times longer than the nominal resolution, the actual BFS
distribution is not directly obtained (further data processing is necessary). We also show thateven when the strained section is shorter than the nominal resolution some shift in the powerchange can be observed. This feature is unique to SA-BOCDR and potentially useful forpractical applications.
2. Principle
In general, fiber-optic distributed Brillouin sensors operate based on the dependence of the
BFS on strain and temperature [4]. As mentioned above, BOCDR is the only technique withintrinsic single-end accessibility and a relatively high spatial resolution. It resolves thesensing locations using a so-called correlation peak [23], which can be generated in the fiber
under test (FUT) via sinusoidal frequency modulation of the laser output. The location of thecorrelation peak can be scanned for along the FUT by sweeping the modulation frequency fm;
thus, distributed BFS measurement becomes feasible. Sinusoidal frequency modulation
results in the periodic generation of multiple correlation peaks along the FUT, and theirfrequency determines the measurement range dm by [35]
dm =

c
,
2 n fm(1)

where c is the velocity of light in vacuum and n is the core refractive index. When fm is lower
than the Brillouin bandwidth ∆νB, the spatial resolution ∆z is given by [35]Δz =c Δν B,2 π n f m Δfwhere ∆f is the modulation amplitude of the optical frequency.

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In conventional BOCDR, the BFS at one sensing position is determined from a peakfrequency after the acquisition of the whole BGS [23, 35], while in SA-BOCDR, it isobtained using the spectral power change at a fixed frequency, by exploiting its one-to-one
correspondence with the BFS [34]. Consequently, the BFS distribution along the FUT is
obtained as a power-change distribution in SA-BOCDR. The measurement range and thespatial resolution are given by the same equations as are used for standard BOCDR (Eqs. (1)and (2)). Note that with this scheme, loss points can also be detected in a distributed mannerand the sampling rate can potentially be drastically enhanced (refer to Ref. 18 for the detailed
operating principle of SA-BOCDR).
3. Simulation
We simulated the system output of SA-BOCDR. We assumed that one section of the FUT
was uniformly strained. The magnitude of the strain was assumed to constantly lie below theupper limit of the linear region (~2000 µε) [34]. The length of the strained section was set to
0.25R, 0.5R, 0.75R, R, 2R, 5R, and 10R, where R indicates the nominal spatial resolution
calculated using Eq. (2). First, the simulation results for the strain distributions acquired using
standard BOCDR (deduced from the BFS distributions using the linear BFS-to-strain
relationship) are shown in Fig. 1(a), which completely reproduce the actual BFS distributions.
Next, the simulation results for the strain distributions obtained from SA-BOCDR (alsodeduced from the final power-change distributions simply based on the linear power-to-strain
relationship) are shown in Fig. 1(b) (strained: 0.5R, R, 2R, 5R, and 10R) and Fig. 1(c)(strained: 0.25R, 0.5R, 0.75R, and R). Here, for simplicity, we neglected both the complicatedlongitudinal shape of the correlation peak and the influence of its sidelobes [36]; that is, thelongitudinal shape of the correlation peak was approximated by a rectangular profile with alength of R. At the ends of the strained section (i.e., the boundaries between the strained andnon-strained sections), the power change varied linearly with the length of 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 thestrained section is approximately R or only a few times longer than R, the correct BFS
distribution cannot be directly obtained (under the assumption that the strain is uniformly
applied; however, the correct information can be easily derived). What is notable here is thateven when the strained section is shorter than R, we can observe a trapezoidal-shaped shift in
the power change and thereby obtain the information that some irregularity has occurred atthat point. For instance, when the length of the strained section is 0.5R, a trapezoidal shapewith a maximal power-change shift corresponding to half the amount seen with a strained
section longer than R is observed. This “beyond-nominal-resolution” information, which
neither standard BOCDR systems nor SA-BOTDR/BOTDA systems can provide (note thatstandard BOCDR systems determine the BFS as the frequency at which the highest spectral
peak is observed; even when the local Brillouin spectrum includes a low spectral peakcorresponding to strain, as long as this peak is lower than the initial spectral peakcorresponding to the non-strained sections, it does not contribute to the derived BFS), will beof great use in practical applications. One important benefit is that using this effect, we caneffectively elongate the measurement range of BOCDR, which generally suffers from thetrade-off relation between the spatial resolution and the measurement range.

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Fig. 1. Deduced strain distributions directly obtained from the final power outputs of (a)standard BOCDR and (b, c) SA-BOCDR. Note that the traces in (a) give the correct strain
distributions.

4. Experimental setup
The experimental setup for SA-BOCDR used to evaluate the aforementioned simulation
results is shown schematically in Fig. 2(a), following the same basic setup as previously
reported [34]. The light output from a 1.55 µm laser was divided into pump and reference
beams. The pump beam was guided through a polarization scrambler (PSCR) to suppress thepolarization-dependent signal fluctuations, then amplified to ~27 dBm using an erbium-doped
fiber amplifier (EDFA) and injected into the FUT. The backscattered Stokes light was
amplified to ~2 dBm using another EDFA. The reference beam was guided through a ~1-kmlong delay line and amplified to ~1 dBm. The Stokes and the reference beams were thenmixed (heterodyned), converted into an electrical signal using a photo diode (PD), and guided
to an electrical spectrum analyzer (ESA). Using the narrow band-pass filtering function of the
ESA (with the video bandwidth and resolution bandwidth set to 10 kHz and 10 MHz,
respectively), the change in the spectral power at 10.81 GHz was sequentially output to an
oscilloscope (OSC). An electrical amplifier was not used in this measurement.
The FUT was a 13.0-m-long single-mode silica fiber with a BFS of 10.86 GHz at 1.55 µm
at room temperature. Measurements were performed using two configurations: one for a
relatively high spatial resolution and the other for a relatively low resolution (required toinvestigate the beyond-nominal-resolution effect). In the first, high-resolution configuration,strains of 750 µε and 1500 µε were applied to 5-cm-, 10-cm-, 20-cm-, 50-cm-, and 100-cmlong sections of the FUT, as depicted in Fig. 2(b). The modulation frequency fm andamplitude ∆f were set to 7.11–7.31 MHz and 1.3 GHz, respectively, corresponding to themeasurement range of 14.5 m and the theoretical spatial resolution of 9.5 cm according toEqs. (1) and (2). In the second, low-resolution configuration, a strain of 1500 µε was applied
to 5-cm-, 10-cm-, 15-cm-, and 20-cm-long sections of the FUT (see Fig. 2(c)). The
modulation frequency fm was swept in the same range (7.11–7.31 MHz), thus giving the samemeasurement 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 64 times averaging was performed on the OSC to
improve the signal-to-noise ratio (SNR). The room temperature was 25 °C.

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Fig. 2. (a) Experimental setup for SA-BOCDR, which is basically the same as Fig. 3 of Ref.
34. EDFA: erbium-doped fiber amplifier, ESA: electrical spectrum analyzer, FUT: fiber under
test, OSC: oscilloscope, PD: photo diode, PSCR: polarization scrambler. The blue curvesindicate silica fibers, and the green lines indicate electrical cables. (b) Structure of an FUTwith a relatively high spatial resolution (9.5 cm). (c) Structure of an FUT with a relatively low
spatial resolution (19.6 cm).

5. Experimental results
First, we present the experimental results with relatively high spatial resolution (9.5 cm). An
example of the measured power change distribution (converted into strain) along the whole
length of the FUT (with a 1500 µε strain applied to a 20-cm-long section) is shown in Fig.
3(a). 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 Fig. 3(b) and 3(c),respectively. Each distribution is shifted by 3000 µε, and the simulated data is indicated bydotted lines. The trends in the measured distributions agree well with 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 the experimental
results, which is beneficial from the viewpoint of simulation cost. The discrepancy from thesimulation results probably originates from signal fluctuations due to an insufficient SNR andthe fact that the influence of the correlation peak sidelobes was not considered in thesimulation process.
Subsequently, we performed similar experiments with a relatively low spatial resolution(19.6 cm) to evaluate the beyond-nominal-resolution effect. The magnified views of the strain
distributions (simply deduced from the power-change distributions), measured when a strainof 1500 µε was applied, are shown in Fig. 4. As the strained section becomes shorter, themaximal power-change shift becomes smaller. The trend in the measured distributions isbasically 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 (powerfluctuations corresponding to the strain of the non-strained sections) was calculated to beapproximately 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 suchas the amount of the actual strain, the number of averaging, the incident power, etc.

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Fig. 3. 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 20cm-long section, and magnified views when strains of (b) 750 µε and (c) 1500 µε were applied
to 5-cm- to 100-cm-long sections. In (b) and (c), each distribution was shifted by 3000 µε, andthe dotted lines indicate the simulated data.

Fig. 4. 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 by3000 µε, and the dotted lines indicate the simulated data.

6. Conclusions
The final system output (i.e., the power-change distribution) of the SA-BOCDR system has
been shown, both theoretically and experimentally, not to reproduce the actual BFS (or strain)
distribution. When the strained section was sufficiently longer than the nominal spatial
resolution, the system output almost corresponded to the actual BFS distribution. In contrast,
when the length of the strained section was equal to or only a few times the nominal
resolution, the BFS distribution was not reproduced correctly. These findings will be of great
importance in improving the performance of SA-BOCDR systems in the future. In addition,
we have also demonstrated that a strained section that is even shorter than the nominal
resolution can still be detected as a shift in the power change. Beyond-nominal-resolution
sensing of temperature change will be also feasible in the same way (cf. the influence of

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thermal expansion [37] is smaller than the noise floor fluctuations in this measurement). As
for loss sensing, as it is point detection, the same effect cannot be observed (not available); in
theory, the measured power gradually changes along the length equal to the nominal
resolution. We anticipate that this feature, unique to SA-BOCDR, will be an attractive
advantage in every application where even slight strain or heat cannot be permitted (regarded
as irregular) because of the required high-level constancy, such as nuclear plant monitoring.
Funding
JSPS KAKENHI (25709032, 26630180, 25007652); Iwatani Naoji Foundation; SCAT
Foundation; Konica Minolta Science and Technology Foundation.