Measurement range enlargement in Brillouin
optical correlation-domain reflectometry basedon double-modulation scheme
Yosuke Mizuno, Zuyuan He, and Kazuo Hotate*
Department of Electrical Engineering and Information Systems, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,
Tokyo 113-8656, Japan*hotate@sagnac.t.u-tokyo.ac.jp

Abstract: We have demonstrated a double-modulation scheme to enlarge
the measurement range of Brillouin optical correlation-domainreflectometry for fiber-optic distributed strain sensing. In this scheme, thefrequency of the laser output is simultaneously modulated with two different
frequencies. In the experiment, 53-cm resolution and 1.5-km measurement
range were simultaneously obtained. Furthermore, 27-cm resolution and1.5-km measurement range were also simultaneously achieved when anoise-floor compensation technique was employed.
©2010 Optical Society of America
OCIS codes: (060.2370) Fiber optics sensors; (280.4788) Optical sensing and sensors;(290.5830) Scattering, Brillouin.

References and links
1.

Y. Mizuno, W. Zou, Z. He, and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry(BOCDR),” Opt. Express 16(16), 12148–12153 (2008).
2. 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.
21(7), 474–476 (2009).
3. A. Fellay, L. Thevenaz, M. Facchini, M. Nikles, and P. Robert, “Distributed sensing using stimulated Brillouinscattering: towards ultimate resolution,” Proc. 12th Intern. Conf. Optical Fiber Sensors, 324–327 (1997).
4. T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada, “Brillouin optical-fiber time domainreflectometry,” IEICE Trans. Commun,” E 76-B, 382–390 (1993).
5. T. Horiguchi and M. Tateda, “BOTDA-nondestructive measurement of single-mode optical fiber attenuation
characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
6. Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel technique to improve spatial resolution in
Brillouin optical time-domain reflectometry,” IEEE Photon. Technol. Lett. 19(23), 1910–1912 (2007).
7. W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,”
Opt. Express 16(26), 21616–21625 (2008).
8. Y. Mizuno, Z. He, and K. Hotate, “Measurement range enlargement in Brillouin optical correlation-domainreflectometry based on temporal gating scheme,” Opt. Express 17(11), 9040–9046 (2009).
9. K. Hotate, and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using acorrelation-based technique – proposal, experiment and simulation,” IEICE Trans. Electron E 83-C, 405–412(2000).
10. K. Hotate, and M. Tanaka, “Correlation-based continuous-wave technique for optical fiber distributed strain
measurement using Brillouin scattering with cm-order spatial resolution – applications to smart materials,”
IEICE Trans. Electron E 84-C, 1823–1828 (2001).
11. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, California, 1995).
12. T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica
optical fibers,” IEEE Photon. Technol. Lett. 1(5), 107–108 (1989).
13. T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects on the Brillouin frequency shift in jacketed opticalsilica fibers,” Appl. Opt. 29(15), 2219–2222 (1990).
14. K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurement with millimeter-order spatial resolution basedon Brillouin optical correlation domain analysis,” Opt. Lett. 31(17), 2526–2528 (2006).
15. Y. Mizuno, Z. He, and K. Hotate, “Stable entire-length measurement of fiber strain distribution by Brillouin
optical correlation-domain reflectometry with polarization scrambling and noise-floor compensation,” Appl.
Phys. Express 2, 062403 (2009).
16. Y. Ohtsuka, “Optical coherence effects on a fiber-sensing Fabry-Perot interferometer,” Appl. Opt. 21(23), 4316–
4320 (1982).
17. A. W. Brown, M. D. DeMerchant, X. Bao, and T. W. Bremner, “Spatial resolution enhancement of a Brillouindistributed sensor using a novel signal processing method,” J. Lightwave Technol. 17(7), 1179–1183 (1999).
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Received 8 Dec 2009; revised 1 Mar 2010; accepted 3 Mar 2010; published 10 Mar 2010

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18. M. P. Song, and B. Zhao, “Accuracy enhancement in Brillouin scattering distributed temperature sensor based on
Hilbert transform,” Opt. Commun. 250(4-6), 252–257 (2005).

1. Introduction
Among various kinds of fiber-optic sensors, Brillouin optical correlation-domainreflectometry (BOCDR) [1] has the capacity to measure the distribution of strain and/or
temperature along a fiber under test (FUT) from a single end. So far, 13-mm spatial resolution
has been obtained in a silica fiber [2], which is the best result ever reported in spontaneous
Brillouin scattering-based reflectometers. However, BOCDR suffers from a trade-off between
the measurement range and the spatial resolution. Their ratio NR is fixed at approximately 570
due to the limitation caused by Rayleigh scattering-induced noise [1]. For example, when thespatial resolution is set to 40 cm or 13 mm, the measurement range becomes 224 m [1] or 7.6
m [2], respectively. Thus, in order to achieve kilometer-order measurement range, theresolution must be 2 m or larger, which is even worse than that of basic time-domain
techniques (~1 m [3]), such as Brillouin optical time-domain reflectometry (BOTDR) [4] andBrillouin optical time-domain analysis (BOTDA) [5]. In the time-domain systems, some
progress has also been made to enhance the resolution [6]-[7].
To obtain higher NR, a temporal gating scheme was implemented [8], where any
correlation peak within the FUT can be arbitrarily selected by a time-domain technique. In theexperiment, 66-cm resolution and 1-km measurement range were simultaneously achieved.
The ratio NR was 1515, which is about three times as high as that of the basic BOCDR.
However, the signal-to-noise (S/N) ratio was so low that NR could not be enhanced further.
In the case of Brillouin optical correlation-domain analysis (BOCDA) systems [9], amultiple-modulation scheme is known to be an alternative method to obtain higher NR [10],where the frequency of the laser output is simultaneously modulated with multiple different
frequencies. In the previous experiment, by modulating the laser output at 2f0 and 3f0
simultaneously (where f0 is a fundamental frequency), NR was enhanced by three times.
In this paper, we demonstrate a double-modulation scheme to enlarge the measurement
range of BOCDR while maintaining the spatial resolution. The optimized modulation
parameters are described, such as the combination of the frequencies to be used, and theiramplitudes. Then, the operating principle of the scheme is theoretically analyzed andsimulated. In the experiment, a strain-applied 90-cm section is successfully detected with
53.1-cm resolution and 1.51-km measurement range (NR = 2845). Moreover, a strain-applied
40-cm section is also detected with 26.5-cm resolution and 1.51-km measurement range(NR = 5690) by the use of a noise-floor compensation technique.
2. Principle
Spontaneous Brillouin scattering occurs when light is Bragg-reflected by the refractive index
modulations produced by acoustic phonons. Since the phonons decay exponentially, thebackscattered Brillouin light (Stokes light) spectrum, also known as Brillouin gain spectrum(BGS), takes the shape of a Lorentzian function [11]. The Stokes light suffers a Doppler shiftcalled Brillouin frequency shift (BFS), which depends on tensile strain and temperaturechange applied to the optical fiber. For example, in a standard silica single-mode fiber (SMF),
BFS of about 11 GHz slightly varies to higher frequency in proportion to the applied strain
and the temperature change with coefficients of 0.058 MHz/µε [12] and 1.18 MHz/K [13],respectively. Hence, BFS can provide the information on the magnitude of strain andtemperature change in the fiber.
BOCDR [1] is a technology to measure the distribution of strain and/or temperature along
an FUT from a single end, based on the correlation control of continuous lightwaves. The
Stokes light due to the spontaneous Brillouin scattering of the pump light in the FUT isheterodyned with the reference light (self heterodyne). In order to resolve the strain-applied
position, the pump light and the reference light are sinusoidally frequency-modulated,
producing periodical correlation peaks along the FUT. The measurement range dm, that is, theinterval of the correlation peaks, and the spatial resolution ∆ z are given by:#121173 - $15.00 USD(C) 2010 OSA

Received 8 Dec 2009; revised 1 Mar 2010; accepted 3 Mar 2010; published 10 Mar 2010

15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5927

dm =

∆z =

c

,

(1)

2 n f modc ∆ν B

2π n f mod ∆f,(2)respectively, where c is the velocity of light, n the refractive index, fmod the modulation
frequency of the light source, ∆ν Β the Brillouin gain bandwidth in optical fibers, and ∆ f themodulation amplitude of the light source. The number of effective sensing points NR, which
can be regarded as the evaluation parameter of the system, is given by the ratio between dm
and ∆ z, as:
NR =

dm
∆z

=

π ∆f
∆ν B

.

(3)

According to Eq. (3), ∆f needs to be increased to obtain higher NR. Although ∆f is not limitedin BOCDA [14], ∆f must be lower than a half of BFS in the fiber in BOCDR [1], which
results in NR lower than about 570 for standard silica fibers.
Another way to achieve higher NR is to utilize multiple intervals of the correlation peaks.
In this case, we select only one correlation peak for a distributed measurement, but suppress
other peaks to avoid the crosstalk. Therefore, the measurement range is multiplied while thespatial resolution is maintained. Along with the temporal gating scheme [8], the doublemodulation scheme is an effective method for this purpose, and was applied to BOCDA [10].

Fig. 1. Experimental setup of BOCDR based on double-modulation scheme: DAQ, dataacquisition; DC, direct current; EDFA, erbium-doped fiber amplifier; ESA, electrical spectrum
analyzer; FUT, fiber under test; GPIB, general-purpose interface bus; PC, polarization
controller; PD, photo-detector; PSCR, polarization scrambler.

The experimental setup of BOCDR based on the double-modulation scheme is depicted inFig. 1. The roles of each device including the polarization scrambler (PSCR) and the opticalfilters are the same as described in [15]. The pump light and the reference light aresinusoidally frequency-modulated with two different frequencies, f0 ( + fε) and m f0, where f0 isa fundamental frequency, m is an integer, and fε (~0.5 kHz) is needed to avoid beating
between the two frequencies, which causes large fluctuations of BGS. The amplitude of thefrequency modulation at f0, denoted as ∆f1, is set to be several hundreds of MHz (difficult tomeasure accurately due to the frequency characteristics of the laser circuit). The amplitude at
m f0, denoted as ∆fm, is about 5.4 GHz (a little lower than a half of BFS in silica fibers). Then,as shown in Fig. 2, the spatial resolution is determined by m f0, while the correlation peaks ofwhich the orders are not multiples of m are suppressed by f0. Since the modulation at f0 does
not influence on the resolution due to the low ∆f1, it becomes possible to achieve the spatial#121173 - $15.00 USD(C) 2010 OSA

Received 8 Dec 2009; revised 1 Mar 2010; accepted 3 Mar 2010; published 10 Mar 2010

15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5928

resolution determined by m f0 and the measurement range determined by f0 simultaneously,
leading to a larger NR by m times.

Fig. 2. Operating principle of double-modulation scheme.

3. Theoretical analysis and simulation

The operating principle of the double-modulation scheme was theoretically analyzed. The
frequency modulation of the laser output is represented as Eq. (4):f ( t ) = f c + ∆f m sin ( 2π mf0 t ) + ∆f1 sin ( 2π f 0 t ) ,(4)

where is the center frequency. Then, the electric field of the laser output is expressed as Eq.
(5):
E ( t ) = exp {− j Φ ( t )} ,(5)

Φ (t ) =(6)

where Φ(t) is defined by Eq. (6):∫ 2π f ( t ′ ) dt ′.
t0

It is known that the optical coherence function, which is the shape of the correlation peaks
along the FUT, is given by the Fourier transform of the spectral density of the light source, orin other words, the autocorrelation function of the electric field of the light source [16].
Therefore, the absolute value of the optical coherence function is calculated as
1γ (τ d ) = lim

T →∞ T

1

T
2
T exp
−
2

∫

 

T

{− jΦ ( t )} exp { jΦ ( t − τ )} dt
d



∆f m

τd 



∫ 2T exp  j −2π f τ + 2 mf sin ( π mf τ ) sin  2π mf  t − 2  
T →∞ T −

= lim

2

 

+2

∆f1
f0

= lim

1

T →∞ T

c

0

d

0

0







sin ( π f 0τ d ) sin  2π f0  t −

T
∞
2
Jp
T
− p =−∞2∫ ∑dτ d       dt

2   

{

}

 ∆f

 τ 
sin ( π mf τ )  exp j 2π pmf  t − 
2
 2
 mf

m

0

0

{

d

d

0

}

∞
τ
 ∆f

⋅ ∑ J  2 sin ( π f τ )  exp j 2π qf  t −  dt
 2
q =−∞
 f

1

0

q

0

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d

d

0

Received 8 Dec 2009; revised 1 Mar 2010; accepted 3 Mar 2010; published 10 Mar 2010

15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5929

1

= lim

T
∞
∞
2
Jp
T
− p =−∞ q =−∞
2

∫ ∑ ∑

T →∞ T{ ∆f  ∆f
 2 mf sin ( π mf τ )  ⋅ J  2 f sin ( π f τ ) 

 

m

1

0

0

d

0

q

d

0

}

τ
⋅ exp j 2π ( pm + q ) f  t −  dt
 2
d

0

 ∆f

∞

=



∑ J  2 mf sin ( π mf τ )  ⋅ J

p =−∞

p

m

0



0

d



 ∆f

 2 f sin ( π f τ )  ,


1

− pm

0

d

(7)

0

where τd is the time delay and Jp(x) is the p-th Bessel function of the first kind. When m >> 1,
Eq. (7) is approximately equal to Eq. (8): ∆f mγ (τ d ) ≈ J 0  2

 mf0



 ∆f1





sin ( π mf0τ d )  ⋅ J 0  2

f0

sin ( π f0τ d )  ,(8)which shows that the synthesized coherence function in the double-modulation scheme isroughly given by the product of the coherence functions synthesized into a series of periodicaldelta-function-like peaks by each modulation frequency.
Based on Eq. (7), we simulated the synthesized coherence function when m = 4, as shownin Figs. 3(a)-3(c). The ratio of the modulation amplitudes (∆f4 / ∆f1) was set to 10. In Fig. 3(c),the 1st, 2nd, 3rd, 5th, 6th, 7th, and 9th correlation peaks were suppressed, which shows thatthe measurement range was multiplied by 4 times while maintaining the spatial resolution.

Fig. 3. Synthesized coherence functions with the modulation at (a) f0 only, (b) 4f0 only, and (c)f0 and 4f0 .

4. Experiments

First, the effectiveness of the double-modulation scheme was experimentally shown. As thetwo modulation frequencies, f0 and 5f0 were used (∆f5 = 5.4 GHz), where f0 was set to 68.481
kHz. According to Eqs. (1) and (2), the spatial resolution and the measurement range
determined by the conventional single modulation at 5f0 were 53.1 cm and 302.1 m,
respectively. An SMF of 1 km was used as the FUT, and about 0.15-% strain was applied to a
3-m section (990 – 993 m). The correlation peak was placed at the middle of the strain-applied
section. The polarization state was optimized by adjusting polarization controllers so that thepeak intensity of BGS without strain applied becomes maximal. Averaging was conducted 10
times to measure one BGS.
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Received 8 Dec 2009; revised 1 Mar 2010; accepted 3 Mar 2010; published 10 Mar 2010

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Fig. 4. Measured strain-dependences of BGS (a) without and (b) with double-modulation
scheme.

Figure 4(a) shows the measured BGS with and without strain applied when the single
modulation at 5f0 was applied. Since there were three correlation peaks within the FUT, thechange of BGS was not observed as a clear shift of the peak. Here, a kink observed at 10.9
GHz was caused by range switching of the electrical spectrum analyzer (ESA). In contrast,
Fig. 4(b) shows the measured BGS when the double-modulation scheme was employed. The
applied strain was observed as a clear shift of the BGS peak. The remaining peak at about
10.86 GHz in the curve with strain applied, which can be regarded as noise, originates fromthe correlation sidelobes that were not completely suppressed. As long as this remaining peakis lower in power than the BGS peak, the measurement is performed correctly. In practicalcases with two or more strains applied along the FUT, the power of the remaining peak
becomes even smaller.
Then, the double modulation and the single modulation were compared in a distributed
strain measurement. A strain of 0.15% was applied to a 90-cm section (990.0 – 990.9 m).
With f0 swept from 68.362 kHz to 68.497 kHz, BGS was measured every 5 cm. The otherconditions were the same as those in the preceding experiment. The measured distributions of
BGS and BFS with the single modulation at 5f0 (m = 5) are shown in Figs. 5(a) and 5(b),respectively. Although BGS slightly changed at the strain-applied section, a correct
distribution of BFS was not acquired. On the other hand, the measured results in the doublemodulation scheme with f0 and 5f0 are shown in Figs. 6(a) and 6(b). The strain-applied 90-cm
section was correctly detected. The measurement accuracy in this experiment was about +/– 7MHz, corresponding to about +/– 120 µε. The ratio NR was 2845 ( = 1.51 km / 53.1 cm),
which is much higher than 1515 obtained previously in the temporal gating scheme.

Fig. 5. Measured distributions of (a) BGS, and (b) BFS when the double-modulation scheme
was not employed.

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Fig. 6. Measured distributions of (a) BGS, and (b) BFS when the double-modulation scheme
was employed (NR = 2845).

The upper limit of m is determined by noise floor of the ESA, polarization state, FUT
length, nonlinear dependence of LD frequency, etc. As m is increased, the S/N ratio is
deteriorated due to the following two reasons: (i) the remaining peak (noise) in Fig. 4(b)becomes larger; (ii) the spatial resolution becomes higher, which accompanies the reductionof the BGS signal power. The second reason also deteriorates the measurement accuracy.
Finally, the double-modulation scheme was implemented with f0 and 10f0 (∆f10 = 5.4 GHz)
using a noise-floor compensation technique [15]. A strain of 0.15% was applied to a 40-cm
section (990.0 – 990.4 m). With f0 swept from 68.362 kHz to 68.474 kHz, the spatial
resolution and the measurement range were 26.5 cm and 1.51 km, respectively, corresponding
to NR of 5690. The measured results are shown in Figs. 7(a) and 7(b). Although the S/N ratio
was deteriorated compared to that in Fig. 6, the strain-applied 40-cm section was successfully
detected. The measurement accuracy was about +/– 15 MHz, corresponding to about +/– 260µε. We think further research is needed to enhance the measurement accuracy by employing
some methods such as those described in Refs [17]-[18].

Fig. 7. Measured distributions of (a) BGS, and (b) BFS with the double-modulation scheme
when the noise-floor compensation technique was employed (NR = 5690).

5. Conclusion

In this paper, we developed a double-modulation scheme to mitigate the trade-off between themeasurement range and the spatial resolution in BOCDR. In the experiment, 53-cm resolution
and 1.5-km measurement range were simultaneously obtained. Furthermore, 27-cm resolution
and 1.5-km measurement range were also simultaneously achieved when a noise-floor
compensation technique was employed. We expect the double-modulation scheme will
provide BOCDR with more feasibility as a fiber-optic nerve system in smart materials andstructures.
#121173 - $15.00 USD(C) 2010 OSA

Received 8 Dec 2009; revised 1 Mar 2010; accepted 3 Mar 2010; published 10 Mar 2010

15 March 2010 / Vol. 18, No. 6 / OPTICS EXPRESS 5932

Acknowledgments

The authors thank Mr. Koji Kajiwara at the University of Tokyo, Japan, for helpful
discussions and comments. Yosuke Mizuno is grateful to the Japan Society for the Promotionof Science (JSPS) Research Fellowships for Young Scientists. This work was supported 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, Science and Technology (MEXT),
Japan.

#121173 - $15.00 USD(C) 2010 OSA

Received 8 Dec 2009; revised 1 Mar 2010; accepted 3 Mar 2010; published 10 Mar 2010

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