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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 22, NOVEMBER 15, 2010

Operation of Brillouin Optical Correlation-Domain
Reflectometry: Theoretical Analysis andExperimental Validation
Yosuke Mizuno, Weiwen Zou, Member, IEEE, OSA, Zuyuan He, Member, IEEE, OSA, andKazuo Hotate, Fellow, IEEE

Abstract—We theoretically and experimentally analyze theoperation of Brillouin optical correlation-domain reflectometry(BOCDR). First, we experimentally confirm that BOCDR is notbased on stimulated Brillouin scattering but on spontaneous
Brillouin scattering. Then, we theoretically prove that the spatial
resolution of BOCDR is given well by the same expression asthat of Brillouin optical correlation-domain analysis (BOCDA).
Finally, we demonstrate that the modulation amplitude of the laser
frequency, which has been conventionally limited to a half of theBrillouin frequency shift, can be enhanced further by employing
a sensing fiber shorter than a half of the measurement range.
Index Terms—Brillouin scattering, correlation, distributed measurement, modulation, nonlinear optics, reflectometry.

I. INTRODUCTIONB

RILLOUIN scattering-based fiber-optic sensors havebeen widely studied as a promising technology for monitoring conditions in various materials and structures, due totheir capability of a distributed measurement of strain and/or
temperature along a fiber under test (FUT). Above all, thefollowing three techniques have been extensively studied:
Brillouin optical time-domain reflectometry (BOTDR) [1], [3],[4], Brillouin optical time-domain analysis (BOTDA) [5]–[11],and Brillouin optical correlation-domain analysis (BOCDA)[12]–[15]. BOTDR and BOTDA have the measurement range
as long as several tens of kilometers, and BOCDA has anextremely high spatial resolution ( 1.6 mm [14]). However,
Manuscript received July 27, 2010; revised September 13, 2010; accepted
September 20, 2010. Date of publication September 27, 2010; date of current version November 17, 2010. This work was supported in part by the
Grant-in-Aid for Scientific Research (S) and the Global Center of Excellence(G-COE) Program from the Ministry of Education, Culture, Sports, Scienceand Technology (MEXT), Japan. The work of Y. Mizuno was supported by
the Research Fellowships for Young Scientists from the Japan Society for the
Promotion of Science (JSPS).
Y. Mizuno was with the Department of Electrical Engineering and Information Systems, The University of Tokyo, Tokyo 113-8656, Japan. He is now with
Precision and Intelligence Laboratory, Tokyo Institute of Technology, Kanagawa 226-8503, Japan (e-mail: ymizuno@sonic.pi.titech.ac.jp).
W. Zou was with the Department of Electrical Engineering and Information Systems, The University of Tokyo, Tokyo 113-8656, Japan. He is now
with the Department of Electronic Engineering, Shanghai Jiao Tong University,
Shanghai 200240, China (e-mail: wzou@sjtu.edu.cn).
Z. He and K. Hotate are with the Department of Electrical Engineering andInformation Systems, The University of Tokyo, Tokyo 113-8656, Japan (e-mail:ka@sagnac.t.u-tokyo.ac.jp; hotate@sagnac.t.u-tokyo.ac.jp).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2010.2081348

the inherent limitation of the spatial resolution in basic time-domain techniques is about 1 m [16], [17], though several methods
have recently been developed to enhance the resolution [4],[8]–[11]. Meanwhile, in standard BOCDA, two lightwaves
must be injected into both ends of the FUT. Even in the linear
configuration of BOCDA [15], where a mirror is employed at
one end of the FUT, if part of the FUT cracks, the distributed
measurement can no longer be performed.
In order to achieve a high spatial resolution and substantial
one-end accessibility simultaneously, we have proposed Brillouin optical correlation-domain reflectometry (BOCDR) [18],which is based on the correlation control of continuous lightwaves. So far, 13-mm spatial resolution has been obtained fora silica fiber [19]. By using a tellurite glass fiber as the FUT,
6-mm resolution has also been achieved [20].
It has been assumed that BOCDR is based on spontaneous
Brillouin scattering, not on stimulated Brillouin scattering(SBS). However, it was not clarified yet. On the other hand,the expression for the spatial resolution in BOCDR has been
assumed to be the same as that in BOCDA [18], but this was
not theoretically proved yet. Furthermore, the modulation
amplitude and the modulation frequency of the laser frequency
must be increased to achieve a high spatial resolution, but their
theoretical limitations were not clarified yet.
In this paper, first, we experimentally show that BOCDR isnot based on SBS but on spontaneous Brillouin scattering. Next,
we describe that BOCDA and BOCDR are based on quite different operating principles, and that the operation of BOCDR
should be analyzed independently of that of BOCDA. Then, wetheoretically show that the spatial resolution of BOCDR is given
well by the same expression as that of BOCDA, and clarify
the theoretical limitation of the modulation frequency. Finally,
we analyze the Rayleigh scattering-induced noise, and theoretically and experimentally clarify the limitation of the modulation
amplitude.
II. PROOF THAT BOCDR IS BASED ON SPONTANEOUS
BRILLOUIN SCATTERING
If the power of the incident light is extremely high, SBS isobserved even when the light is injected into only one end of
the fiber. This is because the backscattered Stokes light due tospontaneous Brillouin scattering works as a probe lightwave in
SBS. In this section, we experimentally clarified that SBS is not
dominant in BOCDR.

0733-8724/$26.00 © 2010 IEEEMIZUNO et al.: OPERATION OF BRILLOUIN OPTICAL CORRELATION-DOMAIN REFLECTOMETRY

Fig. 1. Conceptual setup of the basic BOCDR system. The OSA is used to directly observe the Stokes light spectrum. 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; OSA, optical spectrum analyzer; PC, personal computer; PD, photodetector.

Fig. 1 depicts the schematic drawing of the BOCDR system[18]. Spontaneous Brillouin scattering caused in the FUT makes
interference with the reference lightwave, which is detected withbalanced photo-detectors (PDs). By modulating the laser frequency with a sinusoidal waveform, a correlation peak is synthesized at one point along the FUT [18]. In the experiment to confirm that the Brillouin scattering caused in the FUT of BOCDR
is spontaneous one, the reference path was removed in Fig. 1,
and an optical spectrum analyzer (OSA) was employed to observe the backscattered Stokes light. The frequency-modulated
light beam from a distributed-feedback laser diode (DFB-LD)
at 1550 nm was amplified up to 28 dBm with an erbium-doped
fiber amplifier (EDFA), and was injected into a 1-km FUT. The
was fixed atmodulation frequency of the laser frequency
68.62 kHz. Since it is difficult to accurately measure the modulabecause of the limited resolution of the OSA,
tion amplitude
the peak-to-peak output voltage of the function generator (FG)providing alternating current (AC) to the DFB-LD was substi, and it was set to 0, 20, 100, and 1000 mV .
tuted for
Fig. 2 shows the measured optical spectra of the Stokes light
was increased. With no modulation applied (whenGHz), the power of the Stokes light is higher than that of theRayleigh-scattered light by more than 20 dB, which indicates
was increased, the power
the presence of SBS. However, asof the Stokes light drastically decreased; when the AC was 1000of about 3 GHz, it was lower thanmV corresponding to
the power of the Rayleigh-scattered light by about 20 dB. Thischange in the power of the Stokes light seems to be caused by thetransition from SBS to spontaneous Brillouin scattering. Since
in BOCDR is generally set to several GHz [18], it was clarified that BOCDR is based not on SBS but on spontaneous Brillouin scattering. Therefore, the Brillouin signal of BOCDR is
expected to be weaker than those of SBS-based techniques such
as BOTDA and BOCDA.
III. COMPARISON BETWEEN BOCDA AND BOCDR
We compare the operating principles between the two correlation-domain techniques: two-end-access BOCDA [12] andone-end-access BOCDR [18]. As shown in Fig. 3, in both systems, the pump light is reflected everywhere in the FUT due to3301

Fig. 2. Measured optical spectra of the reflected light.

Fig. 3. Principles of BOCDA and BOCDR.

spontaneous Brillouin scattering. In order to resolve the position, in BOCDA, SBS is induced selectively at one specific position in the FUT by injecting the frequency-modulated, or correlation-managed, pump and probe light beams into each endof the FUT. Strictly speaking, the effective Brillouin gain spectrum (BGS) obtained in BOCDA is built up of the sum of theBrillouin signals at all the positions along the FUT, and only the
Brillouin signal at the correlation peak is sharp and contributes
to the effective BGS, while the Brillouin signals at other sections
spread out [12]. In contrast, in BOCDR, the Stokes light due
to spontaneous Brillouin scattering from one specific positionin the FUT is selectively observed by the heterodyne detection
with the frequency-modulated, or correlation-managed, reference light (See Fig. 1). Thus, BOCDA and BOCDR are basedon quite different operating principles, so we need to analyze
the operation of BOCDR independently of that of BOCDA.
IV. THEORETICAL ANALYSIS OF BOCDR OPERATION
A. System Formulation
First, we derive the expression of the effective BGS, which isthe final signal observed with the electrical spectrum analyzer(ESA) in BOCDR. We define the position of the correlation peak
, which corresponds to the measuringin the FUT as
position. Suppose the electric field spectra of the reference light,
the pump light (per unit length), and the Stokes light (per unit
length) are, and, respectively.
denotes the operation of Fourier transform. Then, as
Here

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shown in Fig. 4,(See Appendix)

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 22, NOVEMBER 15, 2010

is approximately expressed as

is defined aswhere the beat spectrum

(8)
(1)
where
is the Brillouin frequency shift (BFS),
represents a convolution concerning frequency, andis a complex Lorentzian function
given bycan be expressed as
becauseHere,and
it is a function only of the relative distance between. When sinusoidal modulation is applied to the LD frequency,
is a real function [12], so (7) can be transformed
as

(2)
where
is the Brillouin gain coefficient, andis the Brillouin bandwidth. The Stokes light generated along the whole
length of the FUT is given as(9)

In (9), the real part ofsatisfies(3)
and the total electric field on the detector is expressed as(10)(4)
Then, the interference signal
and the reference light is given as

where we define the intrinsic Brillouin gainas

between the Stokes light(11)
Therefore, (9) can be further transformed as
(5)

where
stands for time-averaging operation, and its AC component around the BFS is(12)
which leads to the following expression of the effective BGS:
(6)
(13)

where c.c. is a complex conjugate term. Then,is expressed as(7),Equation (13) shows that, when the measuring position isthe effective BGS is determined by the square of the 2-dimenand. In contrast,
sional convolution of
in BOCDA, the effective BGS is given by the 2-dimensional
and[12]. Although theconvolution ofderivation and the physical picture are different, (13) is similar
to that of BOCDA.

MIZUNO et al.: OPERATION OF BRILLOUIN OPTICAL CORRELATION-DOMAIN REFLECTOMETRY

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V. LIMITATION OF MODULATION AMPLITUDE
A. Motivation
The measurement rangeof BOCDR, which is the distance
between the neighboring correlation peaks, is given by [18](16)
Fig. 4. Definitions of each symbol in (1).

B. Spatial Resolution
Since the effective BGS in BOCDR is determined by the 2-dimensional convolution of the intrinsic Brillouin gain and thebeat spectrum as well as in BOCDA, the expression for the spatial resolution in BOCDR can be derived in the same way as thatin BOCDA [12].
and slow,
We need to separate in the cases of fast
where
is the modulation frequency of the laser frequency
is higher than the Brillouin bandwidth,[12]. When
we define the spatial resolution
as the distance between thecorrelation peak and the position where the beat spectrum falls
to a half of its peak value. In this case, we estimate only the 0-th
component of the beat spectrum, because the other components
are outside[12]. Then we obtain, as in BOCDA [12],(14)
where is the light velocity in the fiber, andis the modulation amplitude of the laser frequency. Thus, when,
the resolution is in inverse proportion to.
In contrast, when
is lower than
, we must estimate
many components of the beat spectrum within[12]. Weas the distance between the cordefine the spatial resolution
relation peak and the position where the full width of the beat
spectrum broadens twice as wide as[12]. Then we obtain

As shown in (15) and (16), there is a trade-off between the measurement range and the spatial resolution, and the ratio of thetwo values is purely dependent on the modulation amplitude ofthe laser frequency. Therefore,
needs to be increased inorder to obtain substantial improvement in the performance ofhas been limited to a half of the
BOCDR. Conventionally,
BFS because of the Rayleigh scattering-induced noise, which
was also experimentally demonstrated [18], [20].
In this section, however, we theoretically and experimentallyshow that, by using an FUT shorter than a half of the measurebeyond a half
ment range, it becomes possible to enhanceof the BFS.
B. Theory
The electric field of the reference lightreceiver is given asat the heterodyne

(17)
where
is the amplitude, andis the phase noise of thelaser. Then, the electric field of the Rayleigh-scattered light
can be expressed as(18)
is the amplitude, and is the time delay; is thewherephase difference of the sinusoidal modulations between the twolightwaves at the heterodyne receiver. While becomes 0 at thecorrelation peaks, becomes at the middle of the intervals of
two neighboring correlation peaks. Then, thebeating noise between the two lightwaves
can be givenas(15), the resolution is infrom which we know that, when
inverse proportion not only to
but also to . Then, the spatial resolution of BOCDR is given well by the same expression
as that of BOCDA. According to (14) and (15), it is clear thathigher thandoes not contribute to the enhancement of.
When, the resolution given by (14) becomes approximately 1.5 times larger than that given by (15). This is valid
because the definitions of the resolution forandare the least consistent around, wherethere are several, neither one nor many, components of the beat
spectrum within.

(19)
So, ifis negligible, the Rayleigh scatteringinduced noise spreads from 0 Hz to the following frequency:

(20)

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 22, NOVEMBER 15, 2010

Fig. 5. Definitions of L and l in (21).

which must be lower than the BFS. This means that, if there isno point in the FUT wherecan exceed a half of
the BFS. The limitation ofis given, by a function not only
, FUT length , andof BFS but also of measurement range
the distance between the measuring position and the circulator(See Fig. 5), as

1

Fig. 6. (a) Measured electrical spectra when f was increased from 0.1 to
6.9 GHz. Each spectrum is shifted by 20 dB. The values on the ordinate are: GHz. (b) Measured optical spectrum of the reference
valid only for flight after passing the optical filter.

1 =01

(21)
and , the larger length contributes to the limitawhere, of. When a distributed measurement is performed, thetion ofmeasuring position must be scanned along the whole length ofas a sensing system is given by
the FUT. Therefore,(22)
which means that we can enhance
beyond a half of the BFS
by using an FUT shorter than a half of the measurement range.
C. Experimental Verification
The experimental setup to verify (21) is the same as thatreported previously [18], [19]. Using a 100-m FUT (m), the modulation frequency
was set to 286.90 kHz, whichcorresponds tom andm. Fig. 6(a) shows themeasured whole spectra of the electrical output whenwasincreased from 0.1 GHz. As
became larger, the Rayleighscattering-induced noise spread from 0 Hz. When the noise
began to overlap the BGS peak at about 10.85 GHz,wasabout 6.9 GHz as shown in Fig. 6(b), which is the optical
spectrum of the reference light after passing the optical filter.
The spectrum is slightly assymetric due to the dependenceof the LD output on injection current. According to (21), thetheoretical limitation ofis calculated to be 6.98 GHz, whichis in good agreement with the experimental result.
The same experiment was also performed whenkHz,m,m, andm. The experimental results shown in Figs. 7(a) and (b) indicate that thelimitation of
was about 7.95 GHz. This is in good agreement with the theoretical value of 8.01 GHz. The slight discrepancy seems to originate from the assumption that the time dependence of the phase noise, that is, the linewidth of the lightsource, is negligible in deriving (21).
According to (15), eitherormust be increased to enhance the resolution. In [20], by setting
andtoa half of the BFS, 6-mm resolution was obtained using a tellurite glass fiber. So the fact thatcan be higher than a halfof the BFS indicates that the spatial resolution even higher than

1

Fig. 7. (a) Measured electrical spectra when f was increased from 0.1 to
7.95 GHz. Each spectrum is shifted by 20 dB. The values on the ordinate arevalid only for f: GHz. (b) Measured optical spectrum of the reference
light after passing the optical filter.

1 =01

6 mm is feasible in BOCDR. This kind of usage, however, is notbeneficial from the viewpoint of the effective number of sensing
points. In order to enhance the measurement range substantially,
we need to employ either a temporal gating scheme [21] or a
double-modulation scheme [22].
VI. CONCLUSION
We theoretically and experimentally analyzed the operationof BOCDR. First, we clarified that BOCDR is not based on SBS
but on spontaneous Brillouin scattering. Next, we showed thatthe effective BGS in BOCDR is given by the 2-dimensional convolution of the intrinsic Brillouin gain and the beat spectrum.
Although the derivation and the physical picture are different,
this expression is almost the same as that of BOCDA. Then,
we derived the expression for the spatial resolution of BOCDR,
which was the same as that of BOCDA. Finally, we demonstrated that the modulation amplitude of the laser frequency,
which determines the spatial resolution, can be enhanced beyond the conventional limitation of a half of the BFS by employing an FUT shorter than a half of the measurement range.
We believe that the presented results improve our understandingof BOCDR, and provide helpful guidelines for its practical use
in smart materials and structures.

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APPENDIX
We verify (1) and (2) when the linewidth of the pump lightis the frequency of the pump light,
isis 0. When
expressed as(A1)
where the amplitude was normalized. Then,be calculated, using (1) and (2), as

can

(A2)
which is the correct expression for

.

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[12] K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique—Proposal, experiment and simulation,” IEICE Trans. Electron.,
vol. E83-C, pp. 405–412, 2000.
[13] K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing
with 1-cm spatial resolution by correlation-based continuous-wave
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[14] K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurementwith millimeter-order spatial resolution based on Brillouin optical correlation domain analysis,” Opt. Lett., vol. 31, pp. 2526–2528, 2006.
[15] K. Y. Song and K. Hotate, “Brillouin optical correlation domain analysis in linear configuration,” IEEE Photon. Technol. Lett., vol. 20, no.
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[16] A. Fellay, L. Thevenez, M. Facchini, M. Nikles, and P. Robert, “Distributed sensing using stimulated Brillouin scattering: Towards ultimate resolution,” Tech. Dig. Opt. Fiber Sens., vol. 16, pp. 324–327,
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[18] Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR),” Opt. Exp., vol. 16,
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[19] Y. Mizuno, Z. He, and K. Hotate, “One-end-access high-speed distributed strain measurement with 13-mm spatial resolution based on
Brillouin optical correlation-domain reflectometry,” IEEE Photon.
Technol. Lett., vol. 21, no. 7, pp. 474–476, Apr. 2009.
[20] Y. Mizuno, Z. He, and K. Hotate, “Distributed strain measurement
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[22] Y. Mizuno, Z. He, and K. Hotate, “Measurement range enlargementin Brillouin optical correlation-domain reflectometry based on doublemodulation scheme,” Opt. Exp., vol. 18, pp. 5926–5933, 2010.

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Yosuke Mizuno was born in Hyogo, Japan, on October 13, 1982. He received
the B.E., M.E., and Dr. Eng. degrees in electronic engineering from the University of Tokyo, Japan, in 2005, 2007, and 2010, respectively.
In 2004, he worked on optical information processing at the University ofTokyo. From 2005 to 2007, he was engaged in spin- electronics, and studied spin
hot-carrier transistors for his master degree. Since 2007, he had been working
on Brillouin optical correlation-domain reflectometry for his Dr. Eng. at the
University of Tokyo. From 2007 to 2010, he was a Research Fellow, DC1, of
the Japan Society for the Promotion of Science (JSPS). In 2010, he becamea Postdoctoral Research Fellow of Tokyo Institute of Technology, Kanagawa,Japan. He is currently a Research Fellow, PD, of JSPS. His research interests
include fiber-optic sensors, polymer optics, and ultrasonics.
Dr. Mizuno is a member of the Japanese Society of Applied Physics (JSAP),
and the Institute of Electronics, Information, and Communication Engineers(IEICE) of Japan.

Weiwen Zou (S’05-M’08) was born in Jiangxi, China, on January 3, 1981. Hereceived the B.S. degree in physics and the M.S. degree in optics from Shanghai
Jiao Tong University, China, in 2002 and 2005, respectively, and the Dr. Eng.
degree in optoelectronics from the University of Tokyo, Japan, in 2008.
In 2003, he was engaged in research of non-volatile photorefractive-based
holography at University of Electro-Communications, Japan, as an exchange
student. Since 2005, he had been working on Brillouin-scattering-based discriminative sensing of strain and temperature for his doctoral research in electronic engineering, the University of Tokyo, Japan. From 2008 to 2009, he wasa Postdoctoral Research Fellow at the University of Tokyo. In 2009, he became
a Project Assistant Professor of the University of Tokyo. In 2010, he joined
Shanghai Jiao Tong University as an Associate Professor. His current researchinterests include fiber-optic distributed sensors, fiber-optic measurement andoptical information processing.
Dr. Zou is a member of the Optical Society of America (OSA).

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Zuyuan He (M’00) received the B.S. and M.S. degrees in electronic engineeringfrom Shanghai Jiao Tong University, Shanghai, China, in 1984 and 1987, respectively, and the Dr. Eng. degree in optoelectronics from the University of Tokyo,
Tokyo, Japan, in 1999.
He joined Nanjing University of Science and Technology, Nanjing, China as a
Research Associate in 1987, and became a Lecturer in 1990. From 1995 to 1996,
he was a Research Fellow in the Research Center for Advanced Science andTechnology (RCAST), the University of Tokyo. In 1999, he became a Research
Associate of the University of Tokyo, where he worked on measurement andcharacterization of fiber optic components and systems, fiber optic reflectometry, fiber optic sensors, and multi-dimensional optical information processing.
In 2001, he joined CIENA Corporation, Linthicum, Maryland, USA, as a Lead
Engineer responsible for optical testing and optical process development. He
returned to the University of Tokyo as a Lecturer in 2003, and became an Associate Professor in 2005. He is now a Professor at the Center of Excellence (COE)in Electrical and Electronic Engineering, the University of Tokyo. His current
research interests include optical fiber sensors, optical fiber measurement, andoptical information processing.
Prof. He is a member of the Optical Society of America (OSA), and amember of the Institute of Electronics, Information, and Communication
Engineers (IEICE) of Japan.

Kazuo Hotate (M’91–SM’98–F’03) was born in Tokyo, Japan, on June 20,
1951. He received the B.E., M.E., and Dr. Eng. degrees in electronic engineering from the University of Tokyo, Tokyo, Japan, in 1974, 1976, and 1979,
respectively.
In 1979, he joined the University of Tokyo as a Lecturer. He became a
Professor in 1993 at the Research Center for Advanced Science and Technology (RCAST), the University of Tokyo. Currently, he is a Professor in the
Department of Electrical Engineering and Information Systems, School ofEngineering, the University of Tokyo. He served as the Dean of Faculty andGraduate School of Engineering, the University of Tokyo in 2008 and 2009.
He was engaged in projection-type holography, measurement and analysis of
optical fiber characteristics. At present, he is working on photonic sensing.
He has authored and coauthored several books on optical fibers and opticalfiber sensors and more than 370 journal papers and international conference
presentations.
Prof. Hotate is a Fellow of IEEE, a Fellow of Institute of Electronics, Information, and Communication Engineers (IEICE), a Fellow of Society of Instrumentation and Control Engineers (SICE), and a Fellow of Japan Societyof Applied Physics (JSAP). He received academic awards, such as SPIE DSSLife-Time Achievement Award, Ichimura Prize, and Hasunuma Prize (SICE).
He was a BoG member of IEEE Photonic Society. He served as the co-chairs for
SPIE Fiber Optic Gyros: Twentieth Anniversary Conference (1996), the Technical Program Committee Chair for the 13th International Conference on Optical Fiber Sensors (OFS-13) (1999), and the General Chair for OFS-16 (2003).