Dissertation
学位請求論文PROPOSAL AND PERFORMANCE IMPROVEMENT OF
BRILLOUIN OPTICAL CORRELATION-DOMAIN
REFLECTOMETRY
ブリルアン光相関領域リフレクトメトリの提案と性能向上Supervisor:

Professor Kazuo HOTATE

指導教員:

保立 和夫

教授

Submitted on December 15, 20092009 年 12 月 15 日提出

Department of Electronic Engineering
Graduate School of Engineering, The University of Tokyo東京大学大学院工学系研究科電子工学専攻
37-077083

Yosuke MIZUNO
水野 洋輔

Abstract

Abstract

Recently, increasing efforts have been made to diagnose earthquake-induced damage
and time deterioration of large structures, such as buildings, dams, bridges, tunnels,
pipelines, airplanes, ships, etc. by embedding optical fibers in them. The
fiber-embedded structures that can “feel pain” just as human beings do are called“fiber-optic nerve systems.” Among various kinds of optical fiber sensors proposed todevelop the fiber-optic nerve systems, Brillouin scattering-based sensors have attracted
a great deal of attention due to their capability to measure strain and temperature. Above
all, the following three techniques have been vigorously studied: Brillouin optical
time-domain analysis (BOTDA), Brillouin optical time-domain reflectometry (BOTDR),
and Brillouin optical correlation-domain analysis (BOCDA). However, though BOTDA
and BOTDR have a measurement range as long as several tens of kilometers, theirinherent limitation of the spatial resolution is about 1 m, and their measurement time is
as long as several minutes. Meanwhile, though BOCDA has an extremely high spatial
resolution (cm- or mm-order) and a high sampling rate (~ 1 kHz), we must inject twolightwaves into both ends of the fiber under test (FUT), and thus, if part of the FUT
cracks, the measurement can no longer be performed.
To resolve these problems of conventional techniques, in this thesis, we propose anovel sensing technology named Brillouin optical correlation-domain reflectometry(BOCDR), which can measure the distribution of strain and/or temperature along an
FUT by light injection only from one end of the fiber. BOCDR operates based on the
combination of spontaneous Brillouin scattering and the correlation control ofDissertation 2009, The University of TokyoiAbstractcontinuous lightwaves. A spatial resolution of 13 mm is experimentally demonstrated
with a sampling rate of 50 Hz. We also improve its performance from a variety of
aspects, such as enlargement of the measurement range, enhancement of the sampling
rate, application to polarization beat length distribution measurement, improvement of
the stability and the signal-to-noise (S/N) ratio, and achievement of 6-mm spatial
resolution using a specialty fiber.
In Chapter 1: “Introduction,” the concept of fiber-optic nerve systems for smart
materials and structures is reviewed as the background of this work. Then, the principleof Brillouin scattering and conventional time-domain techniques such as BOTDR and
BOTDA are explained. Furthermore, the principle of the correlation-domain techniquecalled BOCDA based on the synthesis of the optical coherence function (SOCF) is also
described with some recent progress.
In Chapter 2: “Proposal of BOCDR,” first, we explain that BOCDR operates basedon the combination of spontaneous Brillouin scattering and the SOCF technique. The
comparison of the operating principle between BOCDR and BOCDA is discussed as well.
Then, in the preliminary experiment, 40-cm spatial resolution and 50-Hz sampling rate
are simultaneously obtained. A spatial resolution of 13 mm is also achieved, which is thebest value ever reported in other Brillouin scattering-based reflectometers as well as
two-end-access BOTDA systems. The real-time detection of vibrated strains is alsopresented. Finally, it is experimentally shown that BOCDR is based not on stimulated
Brillouin scattering (SBS) but on spontaneous Brillouin scattering.
In Chapter 3: “Theoretical analysis of BOCDR analysis,” first, we theoretically showthat the effective Brillouin gain spectrum (BGS) of BOCDR is determined by the
2-dimensional convolution of the intrinsic Brillouin gain and the beat power spectrum,
which is the same expression as that of BOCDA. Then, a simulation on the typicalshapes of the detected BGS is performed. By estimating the shape of the beat power
spectrum, the expression of the spatial resolution is also derived. Finally, the Rayleigh

Dissertation 2009, The University of Tokyoii

Abstract

scattering- induced noise is analyzed, and the limitation of the spatial resolution is
discussed.
In Chapter 4: “Enlargement of measurement range based on temporal gating
scheme,” we develop a temporal gating scheme to enlarge the measurement range of
BOCDR while maintaining the spatial resolution. In the experiment, 66-cm spatial
resolution and 1-km measurement range are simultaneously obtained with 50-Hz
sampling rate. This means that the ratio between the measurement range and the spatial
resolution is enhanced from the conventional value 570 to 1515.
In Chapter 5: “Enlargement of measurement range based on double-modulation
scheme,” we propose a double-modulation scheme as another method to mitigate thetrade-off between the measurement range and the spatial resolution. First, wetheoretically analyze the operating principle, and perform a simulation to verify theeffectiveness of this scheme. Then, in the experiment, 53-cm resolution and 1.5-km
measurement range are simultaneously obtained. Furthermore, 27-cm resolution and1.5-km measurement range are also simultaneously achieved when a noise-floor
compensation technique is employed. This means that the ratio between the measurement
range and the spatial resolution is enhanced to 2845 or 5690.
In Chapter 6: “Enhancement of sampling rate utilizing optical heterodyne detection,”
we implement BOCDR using a single-sideband modulator (SSBM) with fast Fouriertransform (FFT), and examine the possibilities of improvement on the S/N ratio and thesampling rate as well as cost reduction. In the experiment, the S/N ratio is not goodcompared to the conventional BOCDR, but the sampling rate is enhanced to 400 Hz. In
addition, noise inherent to this scheme is observed and discussed.
In Chapter 7: “Application to polarization beat length distribution measurement,” wepresent that BOCDR can be used to perform a distributed measurement of polarization
beat length in single-mode optical fibers (SMFs). The beat lengths of SMFs wound on
mandrels with radii 10.0 cm, 7.4 cm and 3.1 cm are measured to be 25.4 m, 12. 1 m andDissertation 2009, The University of Tokyoiii

Abstract

2.56 m, respectively, which agree well with the theoretical calculations. A distributed
measurement is also successfully performed using an SMF comprising two sections withdifferent mandrel radii.
In Chapter 8: “Stable entire-length measurement based on polarization scramblingand noise-floor compensation,” we demonstrate a stable entire-length measurement ofstrain distribution by suppressing the BGS fluctuations with polarization scrambling. In
the experiment, we perform a distributed strain measurement along the entire length of a
100-m FUT with 40-cm spatial resolution and 19-Hz sampling rate. Furthermore, wedevelop a new method of compensating the noise-floor of the electrical spectrum
analyzer (ESA) to improve the S/N ratio of the system.
In Chapter 9: “Distributed strain measurement using tellurite glass fiber,” we employ
a tellurite glass fiber as the FUT in BOCDR to perform a short-range but
high-spatial-resolution distributed strain measurement. The investigation on thedependences of the Brillouin frequency shift (BFS) on temperature and strain shows thatthe BFS in the tellurite fiber shifts toward lower frequency with increasing temperatureand strain, and their coefficients are –1.14 MHz/K and –0.023 MHz/με, respectively. The
BFS dependence on temperature in a bismuth-oxide fiber is also investigated, and –0.88
MHz/K is obtained as its coefficient. These negative dependences seem to be caused by
the negative dependences of the Young’s modulus of these fibers on temperature andstrain. Then, a distributed strain measurement with BOCDR is demonstrated using thetellurite fiber. With the high Brillouin gain of the tellurite fiber and thus the enhanced
S/N ratio in the BGS measurement, a 1-cm strain-applied section is successfully detectedwith 6-mm nominal spatial resolution, which is the inherent limitation of the fiber.
In Chapter 10: “Conclusions,” we summarize the achievements of this work and givesome open problems and future prospects.

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Contents

Contents
1

Introduction
1.1

1Background ··············································································11.1.1

Birth of optical fibers······························································1

1.1.2 Optical fiber sensors·······························································22

1.2

Brillouin scattering ·····································································4

1.3

Time-domain techniques ·······························································81.3.1

Brillouin optical time-domain analysis (BOTDA) ····························8

1.3.2

Brillouin optical time-domain reflectometry (BOTDR) ···················· 10

1.4

Brillouin optical frequency-domain analysis (BOFDA) ························· 11

1.5

Brillouin optical correlation-domain analysis (BOCDA)························ 12

1.6

Purpose and constitution of this thesis ············································· 15

Proposal of Brillouin optical correlationdomain reflectometry (BOCDR)

17

2.1

Introduction············································································ 17

2.2

Principle················································································ 18

2.3

Experimental setup ··································································· 22

2.4

Preliminary experiments ····························································· 23

2.5

Spatial resolution of 13 mm ························································· 25

2.6 Real-time measurement ······························································ 27
2.7

Spontaneous or stimulated ··························································· 29

2.8Conclusions············································································ 31

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3

Theoretical analysis of BOCDR operation
3.1

32

Introduction············································································ 32

3.2 System formulation ··································································· 33
3.3

Simulation on detected BGS ························································ 35

3.4 Spatial resolution······································································ 38
3.5Discussion on noise (1) ······························································ 41

3.6

Discussion on noise (2) ······························································ 45

3.7Discussion on noise (3) ······························································ 49

3.8

Conclusions············································································ 50

Appendix A··················································································· 50
Appendix B··················································································· 51

4Enlargement of measurement range based on
temporal gating scheme

5

53

4.1

Introduction············································································ 53

4.2

Temporal gating scheme ····························································· 54

4.3

Verification experiments ····························································· 49

4.4

Distributed strain measurement ····················································· 60

4.5Conclusions············································································ 62

Enlargement of measurement range based on
double-modulation scheme
5.1

63

Introduction············································································ 63

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6

5.2

Double-modulation scheme ························································· 65

5.3

Theoretical analysis and simulation ················································ 66

5.4

Verification experiments ····························································· 68

5.5

Distributed strain measurement ····················································· 70

5.6Conclusions············································································ 75

Enhancement of sampling rate utilizing
optical heterodyne detection

7

76

6.1

Introduction············································································ 76

6.2

Optical heterodyne detection ························································ 77

6.3

Experiments ··········································································· 78

6.4

Discussion on noise··································································· 82

6.5Conclusions············································································ 84

Application to polarization beat length
distribution measurement

86

7.1

Introduction············································································ 86

7.2

Principle················································································ 87

7.3

Verification experiments ····························································· 88

7.4

Distributed measurement ···························································· 95

7.5

Conclusions············································································ 97

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Contents

8

Stable entire-length measurement based on polarization
scrambling and noise-floor compensation

98

8.1

Introduction············································································ 98

8.2

Polarization scrambling in BOCDR ················································ 99

8.2.1

Principle··········································································· 99

8.2.2 Experiments ·····································································102
8.3

Noise-floor compensation ··························································104

8.3.1

Principle··········································································104

8.3.2 Experiments ·····································································1058.4

9Conclusions···········································································109

Distributed strain measurement using tellurite glass fiber

110

9.1

Introduction···········································································110

9.2

Tellurite glass fibers ·································································111

9.3

Inherent limitation of spatial resolution···········································112

9.4

Temperature-dependence of BFS ··················································113

9.4.1

Experiments with tellurite glass fiber ········································116

9.4.2

Experiments with bismuth-oxide fiber·······································116

9.4.3

Discussion ·······································································119

9.5

Strain-dependence of BFS ··························································120

9.5.1 Experiments ·····································································120
9.5.2

Discussion ·······································································121

9.6

Spatial resolution of 6 mm··························································123

9.7

Conclusions···········································································125

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Contents

10 Conclusions

127

Acknowledgements

131

Abbreviations

133

References

136

Publications related to this thesis

147

Dissertation 2009, The University of Tokyoix

List of figures and tables

List of figures and tables

1.1

Schematics of the spectra of the reflected light due toRayleigh, Brillouin, and Raman scattering in silica fibers.

1.2

5

Schematics of (a) spontaneous Brillouin scattering,and (b) stimulated Brillouin scattering.

6

1.3

Schematic of basic BOTDA system.

9

1.4

Schematic of basic BOTDR system.

11

1.5

Schematic of basic BOCDA system.

12

1.6

Schematic of the correlation peak in BOCDA.

13

2.1

Conceptual schematic of BOCDR.

18

2.2

Operating principle of basic BOCDR.

19

2.3

Comparison of the operating principle between BOCDA and BOCDR.

20

2.4

Experimental setup of basic BOCDR.

21

2.5

Structure of the FUT.

23

2.6

Measured distribution of BGS.

24

2.7

Measured distribution of BFS.

24

2.8

Structure of the FUT.

25

2.9

Photo of the FUT around the strain-applied section.

25

2.10

Measured distribution of BGS.

26

2.11

Measured distribution of BFS.

27

2.12

Results of dynamic strain measurement with sinusoidal driving

Dissertation 2009, The University of TokyoxList of figures and tables

voltages applied to the PZT at (a) 1 Hz, (b) 2 Hz, and (c) 4 Hz,
respectively. Note that the sampling rate is 19 Hz.

28

2.13

Experimental setup. OSA, optical spectrum analyzer.

29

2.14

Measured optical spectra of the reflected light.

30

3.1

Definitions of each symbol in Equation (3.1).

33

3.2

Simulated beat power spectrum with strain applied to a 25-cm section.

36

3.3

Simulated intrinsic BGS with strain applied to a 25-cm section.

36

3.4

Convoluted BGS with strain applied to a 25-cm section.

37

3.5

Detected BGS and intrinsic BGS with strain applied to a 25-cm section.

37

3.6

Simulated beat power spectrum with strain applied to a 50-cm section.

38

3.7

Simulated intrinsic BGS with strain applied to a 50-cm section.

38

3.8

Convoluted BGS with strain applied to a 50-cm section.

39

3.9

Detected BGS and intrinsic BGS with strain applied to a 50-cm section.

39

3.10

Schematics of (a) optical spectra of the reference light and thereflected light when the frequency of the light source is modulatedwith the amplitude Δf, (b) electrical spectra with sufficiently
small Δf, and (c) electrical spectra with large Δf.

42

3.11

Measured BGS when Δf is 5.4 GHz, 5.5 GHz, and 5.6 GHz.

43

3.12

Measured electrical spectra when the modulation amplitude

Δf was increased from 0.1 to 4.0 GHz. A tellurite glass fiber
was used as the FUT. Each spectrum is shifted by 35 dB.
The values on the ordinate are valid only for Δf = 0.1 GHz.
3.13

44

Measured electrical spectra when Δf was increased from 0.1 to
6.9 GHz. Each spectrum is shifted by 20 dB. The values on theordinate are valid only for Δf = 0.1 GHz.

3.14

47

Measured optical spectrum of the reference light

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List of figures and tables

after passing the optical filter.
3.15

47

Measured electrical spectra when Δf was increased from 0.1
to 7.95 GHz. Each spectrum is shifted by 20 dB.
The values on the ordinate are valid only for Δf = 0.1 GHz.

3.16

Measured optical spectrum of the reference lightafter passing the optical filter.

3.17

48

48

Schematic noise floor inherent to the ESA, which limits
the spatial resolution and the largest detectable strain magnitude.

49

4.1

Experimental setup of BOCDR with the temporal gating scheme.

54

4.2

Pulse shapes of the pump light and the reference light.

55

4.3

Structure of the FUT.

56

4.4

Measured distribution of BGS.

56

4.5

Measured distribution of BFS.

57

4.6

Measured BGS without the temporal gating scheme applied,
when there are multiple correlation peaks within the FUT.
The length of the FUT is 1 km. dm represents the interval
between the correlation peaks, and N the number of undesired
peaks within the FUT.

4.7

58

Measured BGS when (a) the first, (b) the second, and (c) the third
correlation peaks were selected, with (blue) and without (orange)
strain applied to the section corresponding to the third correlation peak.

49

4.8

Structure of the FUT.

60

4.9

Measured distribution of BGS.

61

4.10

Measured distribution of BFS.

62

5.1

Experimental setup of BOCDR with the double-modulation scheme.

64

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List of figures and tables

5.2

Operating principle of double-modulation scheme.

65

5.3

Synthesized coherence functions with the modulation at f0 only.

66

5.4

Synthesized coherence functions with the modulation at 4 f0 only.

67

5.5

Synthesized coherence functions with the modulation at f0 and 4 f0.

68

5.6

Measured strain-dependence of BGS without double-modulation scheme.

69

5.7

Measured strain-dependence of BGS with double-modulation scheme.

70

5.8

Measured distribution of BGS when the double-modulation
scheme was not employed.

5.9

Measured distribution of BFS when the double-modulation
scheme was not employed.

5.10

73

Measured distribution of BGS with the double-modulation scheme
when the noise-floor compensation technique was employed (NR = 5690).

5.13

73

Measured distribution of BFS when the double-modulation
scheme was employed (NR = 2845).

5.12

72

Measured distribution of BGS when the double-modulation
scheme was employed (NR = 2845).

5.11

72

74

Measured distribution of BFS with the double-modulation scheme
when the noise-floor compensation technique was employed (NR = 5690).

74

6.1

Experimental setup of BOCDR using optical heterodyne detection.

77

6.2

Measured optical spectra of the reference light.

78

6.3

Measured BGS at each microwave frequency.

79

6.4

Measured BGS with and without strain applied to the FUT.

79

6.5

BGS measured with the digitizer and FFT.

80

6.6

Spectral change near BGS with increasing modulation amplitude Δf.

81

6.7

Schematics of (a) optical spectra of the reference light and thereflected light, and (b) electrical spectra of their heterodyned beat signal.

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List of figures and tables

6.8

Measured optical spectra of the reference light before
and after the filter adjustment.

83

6.9

Measured electrical spectra near BGS before and after the filter adjustment.

84

7.1

Measured BGS at the relative positions 39 m and 45 m (R = 10.0 cm).

88

7.2

Measured distribution of the BGS peak power
when the mandrel radius R was 10.0 cm.

7.3

90

Calculated PSD of the BGS peak power distribution in log scale
when the mandrel radius R was 10.0 cm.
The inset shows the same graph in linear scale.

7.4

Measured distribution of the BGS peak power
when the mandrel radius R was 7.4 cm.

7.5

92

Measured distribution of the BGS peak powerwith no bending applied (R = ∞).

7.9

92

Calculated PSD of the BGS peak power distribution in log scale
when the mandrel radius R was 3.1 cm.

7.8

91

Measured distribution of the BGS peak power
when the mandrel radius R was 3.1 cm.

7.7

91

Calculated PSD of the BGS peak power distribution in log scale
when the mandrel radius R was 7.4 cm.

7.6

90

93

Polarization beat length as a function of the mandrel radius.
The curve shows the theoretical values.

94

7.10

Structure of the FUT.

95

7.11

Measured distribution of the BGS peak power.
The mandrel radii were 7.4 cm and 10.5 cm corresponding
to the ranges of 0 – 40 m and 40 – 100 m, respectively.

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List of figures and tables

8.1

Experimental setup of BOCDR with a polarization scrambler.

8.2

Schematic setup of BOCDR for the theoretical analysis

99of the polarization scrambling scheme.

100

8.3

Structure of the FUT.

102

8.4

Measured distribution of BFS along the entire length of
the 100-m FUT with (blue) and without (red) a polarization scrambling.

8.5

Magnified view of Figure 8.4 around the range of 30 – 40 mwith (blue) and without (red) a polarization scrambling.

8.6

104

Magnified view of Figure 8.4 around the range of 70 – 80 mwith (blue) and without (red) a polarization scrambling.

8.7

103

105

Measured BGS without noise-floor compensation.
Strains of 0, 0.08, 0.16, 0.24, and 0.32% were applied.

106

8.8

Measured BGS with noise-floor compensation.

106

8.9

Measured distributions of BGS.

107

8.10

Measured distributions of BFS.
The insets show the magnified views around strain-applied positions.

9.1[Table] n, BFS, and Δzmin of silica, bismuth-oxide,
As2Se3 chalcogenide, and tellurite fibers.

9.1

108

111

Experimental setup based on BOCDR for characterizing
the temperature dependences of specialty fibers.

112

9.2

Structures of the FUT comprising the tellurite fiber.

113

9.3

Structures of the FUT comprising the Bi-NLF.

113

9.4

Measured BGS from the 5-m tellurite fiber with Pin of 28 dBm.

115

9.5

Measured BGS from the 1-m Bi-NLF with Pin of 26 dBm.

115

9.6

Temperature-dependences of the BGS in the tellurite fiber.

117

9.7

Temperature-dependences of the BFS in the tellurite fiber.

117

Dissertation 2009, The University of Tokyoxv

List of figures and tables

9.8

Temperature-dependences of the BGS in the Bi-NLF.

118

9.9

Temperature-dependences of the BFS in the Bi-NLF.

118

9.10

Strain-dependences of the BGS in the tellurite fiber.

121

9.11

Strain-dependences of the BFS in the tellurite fiber.

122

9.12

Structure of the FUT.

123

9.13

Photo of the FUT around the strain-applied section.

123

9.14

Measured distribution of the BGS.

124

9.15

Measured distribution of the BFS.

125

Dissertation 2009, The University of Tokyoxvi

1. Introduction

1

Introduction

This Chapter describes the overall background and the purpose of this thesis. We startby reviewing the history of optical fibers and their sensing applications called“fiber-optic nerve systems.” A basic principle of fiber-optic sensors based on Brillouinscattering is also described. Then, conventional sensing technologies such as Brillouin
optical time-domain analysis/reflectometry (BOTDA/R) and Brillouin opticalfrequency-domain analysis (BOFDA) are surveyed. Finally, the principle and the recent
progress of Brillouin optical correlation-domain analysis (BOCDA) are overviewed.

1. 1

Background1. 1. 1Birth of optical fibers

This year, in 2009, the Nobel Prize in Physics was awarded for two scientificachievements that have helped to shape the foundations of today’s networked societies.
They have created many practical innovations for everyday life and provided new tools
for scientific exploration. In 1966, Charles K. Kao [1] made a discovery that led to abreakthrough in fiber optics. He carefully calculated how to transmit light over long
distances via optical glass fibers. With a fiber of purest glass it would be possible totransmit light signals over 100 km, compared to only 20 m for the fibers available in the
1960’s [2-4]. Kao's enthusiasm inspired other researchers to share his vision of the
future potential of fiber optics. The first ultrapure fiber with a loss below 20 dB/km wasDissertation 2009, The University of Tokyo1

1. Introduction

successfully fabricated just four years later, in 1970 [5]. Further progress in fabrication
technology [6] resulted in a loss of only 0.2 dB/km in the 1.55-μm wavelength region[7], a loss level limited mainly by the fundamental process of Rayleigh scattering. The
availability of low-loss silica fibers led not only to a revolution in the field of opticalfiber communications [8-11] but also to the advent of the new field of optical fiber
sensors [12-17].

1. 1. 2

Optical fiber sensors

Monitoring of structures, such as buildings, bridges, highways, tunnels, dams,
pipelines, containers, airplanes, ships etc., is useful from the economic and security
points of view; and so is monitoring of materials, such as planar lightwave circuits(PLCs). With a proper sensing system, it is possible to achieve information about thehealth of the materials and structures which can be used for designing repair schedules
and for giving early warnings of degradation that might lead to a catastrophic failure in
the long term. When this purpose is achieved by embedding optical fiber sensors inthem, we call these systems “fiber-optic nerve systems for smart materials andstructures” because these materials and structures can “feel pain” just as human beings
do [18-22].
Health monitoring is traditionally based on visual inspection [23]. This method is,
however, limited in time and scope, since it is only possible to see degradations that are
visible and apparent at the time of the inspection. Moreover, one can only see
degradations relative to the original state or the state at the previous inspection, but
structural deficiencies that might have been hidden in the structure from the start cannot
be detected. Fitting the structure with a comprehensive sensor network capable ofcontinuously gathering information on all relevant structural parameters offers a betterway of assessing its real behavior. Various types of sensors have been developed during

Dissertation 2009, The University of Tokyo2

1. Introduction

the last 50 years or so for measuring structural parameters, such as strain, temperature,pressure, rotation, oscillation, humidity, and acceleration.
Conventional strain sensors such as electrical strain gauges are widely used due totheir high accuracy, fast measurement speed, high reliability and low cost [24]. The
problem with strain gauges and other conventional sensors is that there is no means ofreading several successive sensors with a common interrogation unit, i.e. it is notpossible to multiplex the sensors. Since each strain gauge needs two wires for power,
two wires for the signal path and an amplifier unit, the sensor system becomes quite
complex, especially in the case of large buildings. For example, when the sensors areembedded inside the wall material, the wire harness of a strain gauge network may
disturb its operation or even be harmful to the integrity of the structure by causing
delaminations. Other problems with strain gauges apart from their poor multiplexing
capability are susceptibility to electromagnetic interference (EMI), long-term
degradation and sometimes a restricted temperature range.
The demonstration of the first fiber-optic strain sensor in 1978 [25] was an essential
milestone in this field, as was the invention of a fiber Bragg grating (FBG) sensor [26]and Fabry-Perot interferometer (FPI) sensor [27] about ten years later. The firstcommercial products were acoustic hydrophone arrays and gyroscopes [28-31] formilitary and other special applications, but as general-purpose strain and temperature
sensors emerged onto the market in the mid-1990’s, engineers started to use fiber-optic
technology in ordinary measurement applications as well. This was due to the many
advantages that fiber-optic sensors can offer over their conventional counterparts,
among which their extreme multiplexing capability is obviously the most prominent.
With a proper multiplexing technique, such as time-division multiplexing (TDM) or
wavelength-division multiplexing (WDM), it is possible to read responses from tens oreven hundreds of sensors along a single fiber path [32]. A completely-distributed
measurement is also feasible, which enables the building of comprehensive sensor

Dissertation 2009, The University of Tokyo3

1. Introduction

networks in a relatively simple manner. The growing interest in fiber-optic sensors is
also due to properties such as their light weight, small size, immunity to EMI,high-temperature performance, broad bandwidth, environmental robustness with respect
to vibration and shock, high sensitivity [28, 33]. And now, the implementation of thefiber-optic nerve systems is one of the most challenging targets for researchers in
optical engineering.
For the realization of fiber-optic nerve systems, optical fiber sensors based on
Brillouin scattering have been widely studied so far. In Section 1.2, the principle of
Brillouin scattering is explained. Then, in Sections 1.3 and 1.4, conventional
time-domain and frequency-domain distributed sensing techniques based on Brillouinscattering are reviewed. In Section 1.5, the principle and some recent progress ofcorrelation-domain distributed sensing techniques are explained. In Section 1.6, thepurpose and the constitution of this thesis are described.

1. 2Brillouin scattering

Light scattering in optical fibers is omnipresent irrespective of the amount of opticalpower present in the fibers. It can be categorized into two regimes: spontaneous andstimulated scatterings [34]. Spontaneous light scattering refers to the process underconditions such that the optical material properties are unaffected by the presence of theincident electric field. For input optical fields of sufficient intensities, spontaneous lightscattering becomes quite intense; thus in the stimulated regime the nature of thescattering process grossly modifies the optical properties of the material system andvice versa. Spontaneous and stimulated scattering in optical fibers can result from
Raman, and Brillouin scattering phenomena. Each scattering process is always present
in optical fibers, because no fiber is free from microscopic defects or thermal
fluctuations which originate the three processes. For a monochromatic incident
Dissertation 2009, The University of Tokyo4

1. Introduction

lightwave at frequency f0, the three processes are well described in Figure 1.1.
These scattering phenomena physically correspond to two main cases: elastic
scattering and inelastic scattering. In elastic scattering, that is, Rayleigh scattering, thescattered photons maintain their energy and thus have the same frequency of theincident light. On the other hand, in inelastic scattering, that is, Brillouin scattering(interaction with acoustic phonons) and Raman scattering (interaction with opticalphonons), the scattered photons lose or gain energy and thus undergo a frequency shift.
In “Stokes-type” scattering, the photons lose energy and their frequency is
down-shifted; in “anti-Stokes-type” scattering, the photons gain energy with theirfrequency up-shifted. Here we should note that there is large difference in frequency
shift between these scatterings for either Stokes-type or anti-Stokes-type scattering,
though we made a combined depiction of them in Figure 1.1.
Among the three scatterings, Brillouin scattering is especially suitable for making

Figure 1.1 Schematics of the spectra of the reflected light due to Rayleigh,Brillouin, and Raman scattering in silica fibers.

Dissertation 2009, The University of Tokyo5

1. Introduction

Figure 1.2 Schematics of (a) spontaneous Brillouin scattering,and (b) stimulated Brillouin scattering.

distributed sensors, because its frequency shift is linearly dependent on both strain [35]and temperature [36], as described later. So, in this thesis, we will focus on Brillouinscattering. Brillouin scattering is a photon-phonon interaction, in other words, it isbased on the annihilation of a pump photon that creates a Stokes photon and a phonon
simultaneously. The phonon is the vibrated modes of atoms, which is also called a
propagation density wave or an acoustic phonon. The Brillouin frequency shift (BFS) is
about 11 GHz in silica fibers, and the Brillouin-scattered light is dominantly
down-shifted in frequency due to the Doppler effect associated with theforward-moving acoustic waves.
The spectrum of the Brillouin-scattered Stokes light is called Brillouin gain
spectrum (BGS), which includes three important parameters: the Brillouin gain peakcoefficient gB0, the BFS, and the Brillouin bandwidth ΔνB. The gain peak coefficient gB0
lies in the range of 1.5-3 ×10 −11 m/W [37, 38]. The BFS fB is given by [34]
fB =

2

λ

n ⋅ va ,(1.1)

where n is the effective refractive index of the fiber, and va is the effective longitudinal
acoustic velocity. Both n and va are determined by the waveguide structures of the
optical modes and the longitudinal modes, which are related to the silica dopant

Dissertation 2009, The University of Tokyo6

1. Introduction

materials and their distributions along the cross section of the fiber [39]. The Brillouinbandwidth ΔνB is originally decided by the damping lifetime τ dp (= 1 Γ ) of acoustic
phonons asΔν B =

Γ
,
2π

(1.2)

where Γ denoted the decay rate of the acoustic phonons in the fiber. The typical value ofΔνB is about 30 MHz.
As is already mentioned, Brillouin scattering is classified into two configurations:spontaneous Brillouin scattering and stimulated Brillouin scattering (SBS). The
configuration for spontaneous Brillouin scattering is shown in Figure 1.2(a), where only
one pump light beam is injected into one end of the fiber. Its reflectivity is –90 dB/m,
which is even lower than Rayleigh scattering. In contrast, the reflectivity of stimulated
Brillouin scattering is about –50 dB/m. However, in order to induce stimulation, a probe
light beam has to be injected to the other end of the fiber in addition to the pump light,
as shown in Figure 1.2(b).
Around 1990, it was clarified that the BFS has a good linear dependences on strain[35] and/or temperature [36], which can be expressed by
ΔBFS = f B − f B 0 = C ε ⋅ Δε + CT ⋅ ΔT ,(1.3)

where Cε and CT are the strain and temperature coefficients of the BFS in the fiber; fB0
is the BFS at room temperature and in loose state as a reference point. Although thestrain and temperature coefficients even in single-mode fibers (SMFs) are slightly
different among each fiber, their typical values are Cε ~ 0.04-0.05 MHz/με and CT ~1.0-1.2 MHz/K at 1.55-μm wavelength. These linear dependences of the BFS on strain
and temperature are the basic principles to measure the magnitude of strain andtemperature change in Brillouin scattering-based optical fiber sensors.

Dissertation 2009, The University of Tokyo7

1. Introduction

1. 3

Time-domain techniques

Fiber-optic distributed strain/temperature sensors must involve two basic functions. One
is to measure the magnitude of the strain or temperature change, and the other is toresolve the position where strain or temperature change is applied. The former function
was already explained in Section 1.2. There are some methods to resolve the position,such as time-domain techniques and correlation-domain techniques. In this Section,
conventional time-domain techniques are reviewed.

1. 3. 1

Brillouin optical time-domain analysis (BOTDA)

While the efficiency of spontaneous Brillouin scattering is extremely low, SBS allows
much stronger signals to be produced. The first concept of Brillouin scattering-based
distributed sensing was demonstrated by Horiguchi et al. and was named Brillouin
optical time-domain analysis (BOTDA) [40-42]. In their configuration, as shown
schematically in Figure 1.3, a short pump pulse is sent into one end of the FUT, while acontinuous wave probe beam with a frequency offset corresponding to the nominal BFS
is launched into the other end of the FUT. The continuous wave (CW) probe light
experiences Brillouin gain at the locations in the FUT where the frequency offset ismatched to the peak Brillouin gain. Thus, the time dependence of the detected CW lightprovides the gain profile experienced by the probe light as the pump pulse passes along
the FUT. Measurements carried out with a wide range of frequency offsets allow a full
picture of the Brillouin frequency for each location in the FUT to be achieved. As aconsequence, the distribution of strain and temperature can be derived within the spatial
resolution determined by the width of the pump pulse τw, as
Δz =

cτ w
,
2n

(1.4)

where c is the light velocity in a vacuum.
Dissertation 2009, The University of Tokyo8

1. Introduction

Figure 1.3

Schematic of basic BOTDA system.

Horiguchi et al. [43, 44] demonstrated 1-m spatial resolution with an 11-km SMF
using 10-ns optical pulses generated by modulating 1.55-μm distributed-feedback laser
diode (DFB-LD) with a combination of a fast electro-optic modulator (EOM) and an
acousto-optic modulator (AOM). In their experiment, the linewidth of the measured
BGS was about 80 MHz, which is about twice of that of spontaneous Brillouinscattering in the SMF. This is because the 10-ns optical pulse is comparable inbandwidth to the intrinsic BGS, and the frequency-convolved spectrum between thewide pulse and the BGS suffers broadening. As a consequence, it becomes difficult toaccurately diagnose the BFS, and the reported accuracy was ~ 5 MHz corresponding to~ 100 με. Hence, the ultimate spatial resolution of BOTDA is in principle limited to ~ 1
m [45, 46].
Up to now, many researchers have been reporting some improvement of BOTDA[47-56]. Nikles et al. [50] proposed a method to stabilize the distribution of BGS and
BFS by using an EOM to modulate a DFB-LD at 1.55 μm and thus generate the pumpand the probe light beams from the same DFB-LD source. They achieved 80-cm spatial
resolution and 1-km measurement range simultaneously, with a frequency resolution of
1 MHz corresponding to 20 με. Bao et al. [51] developed a Brillouin-loss-based
BOTDA by reversing the functions of the coherent pulse laser and CW light. In thisconfiguration, the strong CW light acts as a Brillouin pump wave, and the optical pulse
with a scanned down-shifted frequency from that of the CW light works as a probe
Dissertation 2009, The University of Tokyo9

1. Introduction

wave. By monitoring the Brillouin loss profile due to Brillouin interaction between the
two light beams as a function of time or position along the FUT, they reported 25-cm
spatial resolution [52] with a strain resolution of ~ 40 με. Recently, a “pulse pre-pump
BOTDA (PPP-BOTDA)” system was proposed [53, 54], where ~ 10-ns pulse followedby 1-ns pulse was used to pre-excite the phonon field and obtain a resolution of ~10 cm.
A “dark-pulse BOTDA” system was also developed [55, 56], and 2-cm spatial
resolution was achieved, which is the highest value ever reported in BOTDA systems.

1. 3. 2

Brillouin optical time-domain reflectometry (BOTDR)

Spontaneous Brillouin scattering-based fiber-optic distributed sensors called Brillouin
optical time-domain reflectometry (BOTDR) was also explored [57, 58]. One of thebiggest advantages of BOTDR is that it works by light injection only from one end of
the fiber. The techniques for BOTDR can be classified into two: the direct detection[57] and the coherent (heterodyne) detection [58]. In direct detection [57], the Brillouinsignal must be optically separated from the large Rayleigh component before its
detection, using FPIs, Mach-Zehnder interferometers (MZIs), FBG-based optical filters,
etc. Since the BFS is small, these optical filters must be highly stabilized.
In coherent detection [58], a strong narrow-linewidth reference oscillator such aspart of the pump lightwave is employed, which allows excellent electrical selection of
the Brillouin component as well as a greater dynamic range. The coherent detection had
been achieved by the methods that employ frequency shift between the reference
oscillator and the sensing pulses that is approximately equal to the BFS, bringing thesignal-reference beat frequency within the bandwidth of a conventional photo-detector(PD). This frequency shift of the reference oscillator was attained by an AOM [58] or an
EOM [59]. However, thanks to the development of electronics, recently PDs withextremely wide bandwidths (20 GHz or higher) have become commercially available.
Dissertation 2009, The University of Tokyo10

1. Introduction

Figure 1.4

Schematic of basic BOTDR system.

So, nowadays we do not necessarily employ the frequency shifter in the reference path.
As was explained in the case of BOTDA [45, 46], the spatial resolution of basic
BOTDR is also limited to 1 m, because the BGS broadens rapidly as the optical pulse
width decreases below 10 ns. However, a “double-pulse BOTDR (DP-BOTDR)” system
was recently proposed by Koyamada et al. [60-62] to enhance the spatial resolution
further, where double optical pulses are transmitted into the FUT instead of aconventional single optical pulse. So far, they have experimentally obtained 20-cm
resolution. To enlarge the measurement range, Raman amplification was employed to
BOTDR with the coherent detection, resulting in 150-km range [63]. A new BOTDR
system based on optical-pulse coding has also been proposed and studied [64, 65].

1. 4

Brillouin optical frequency-domain analysis (BOFDA)

An alternative technique to build Brillouin scattering-based distributed sensors wasdemonstrated based on frequency-domain method, and was named Brillouin opticalfrequency-domain analysis (BOFDA) [66-69]. It employs a CW probe beam and apump beam with sinusoidally-modulated intensity. When SBS occurs, the probe signal
acquires an intensity modulation at the same frequency of the pump, and the induced
modulation is measured by a vector network analyzer for a range of modulation
frequencies. The baseband transfer function provides information similar to the pulse
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1. Introduction

response measured in BOTDA or BOTDR. This frequency-domain approach seems topermit improvement of the signal-to-noise (S/N) ratio due to a synchronous detection,
but the data analysis is still performed in the time domain after an inverse Fouriertransform of the measured huge-size data.

1. 5

Brillouin optical correlation-domain analysis (BOCDA)

In order to mitigate the limitation of the spatial resolution and the measurement time inother techniques, a novel correlation-domain technology named Brillouin opticalcorrelation-domain analysis (BOCDA) was proposed by Hotate et al. [70-92]. BOCDA
is based on the technique called the synthesis of the optical coherence function (SOCF)[93-106], where the correlation between frequency-modulated lightwaves is controlled.
The SOCF technique has so far been employed to develop FBG-multiplexed sensing

Figure 1.5 Schematic of basic BOCDA system. AC, alternating current; DAQ, dataacquisition; DC, direct current; DFB-LD, distributed-feedback laser diode; EDFA,
erbium-doped fiber amplifier; EOM, electro-optic modulator; FUT, fiber under test;
GPIB, general-purpose interface bus; PC, personal computer; PD, photo-detector.

Dissertation 2009, The University of Tokyo12

1. Introduction[95-97], optical coherence tomography (OCT) [98, 99], dynamic grating in
erbium-doped fiber (EDF) [100-102], lateral-force sensing based on polarization-mode
coupling [103, 104], and Rayleigh scattering-based reflectometry [105, 106] as well.
The basic experimental setup of BOCDA is depicted in Figure 1.5. In BOCDA, thefrequencies of counter-propagating pump and probe lightwaves are sinusoidally
modulated. They are synchronous in phase because the two lightwaves are obtained by
dividing the same light source except for a frequency difference, which can be
expressed as
f pump = f 0 + Δf sin (2πf mt ) ,(1.4)

f probe = f 0 − f B + Δf sin (2πf mt ) ,(1.5)

where f0 is the optical frequency of the laser source without frequency modulation, fm
the sinusoidal-modulation frequency, Δf the sinusoidal-modulation amplitude, and fB thefrequency difference between pump and probe lightwaves, which is around the BFS of
the FUT.

Figure 1.6

Schematic of the correlation peak in BOCDA.

Dissertation 2009, The University of Tokyo

13

1. Introduction

The synchronously-modulated pump and probe lightwaves generate beat power
spectra and then intensify the acoustic phonons due to electrostriction effect that interact
with the probe amplification from the pump light. The beat spectra have adelta-function-shaped distribution along the fiber due to the SOCF effect [93, 94] asshown in Figure 1.6. According to Hasegawa et al.’s detailed calculations [70, 71], theobserved BGS is expressed, by a 2-dimensional convolution of the beat spectra and the
local BGS concerning frequency f and position z, as
G (z , f ) = B(z , f ) ⊗ g (z , f ) ,(1.6)

where B(z, f) is the synthesized beat spectra given by
B( z , f ) = F ⎡ E pump ( z , t )E probe ( z , t ) ⎤ .
⎢⎣
⎥⎦
*

2

(1.7)

Here F[ . ] denotes the operation of Fourier transform, and g(z, f) is a local intrinsic
BGS given by
g (z, f ) =

g B0
2 .
1 + 4[{ f − f B ( z )} Δν B ](1.8)

The spatial resolution Δz is determined by the relation between the broadened beat
spectra and the intrinsic BGS. Meanwhile, the measurement range dm is determined by
the interval between two correlation peaks, because only one correlation peak should
exist within the range of the FUT to correctly resolve the strain-applied positions.
According to detailed calculations [70, 71], the spatial resolution Δz and themeasurement range dm are given byΔz =vg ⋅ Δν B

2π f m Δfv
dm = g ,
2 fm

,

(1.9)
(1.10)

where vg (= c/n) is the light velocity in the FUT. By sweeping fm, the position of the
non-0th correlation peaks can be scanned along the FUT, and thus a distributed
measurement becomes feasible.
Up to now, the performance of BOCDA has been improved from a great variety of
Dissertation 2009, The University of Tokyo14

1. Introduction

aspects [75-88]. First, the polarization diversity scheme was employed to suppress thepolarization-dependent BGS fluctuations and thus to enhance the stability of themeasurement [75]. Next, apodization based on intensity modulation was implemented
to enhance the dynamic range [76, 77]. Then, a low-coherence BOCDA (LC-BOCDA)
system was proposed to resolve the trade-off between the spatial resolution and themeasurement range [78, 79]. The temporal gating scheme was also developed tomitigate this trade-off [80, 81]. Furthermore, extremely high nominal resolutions up to
1.6 mm were achieved using a single-sideband modulator (SSBM) instead of an EOM
based on the double-lock-in scheme [82] and the beat-lock-in scheme [83]. To reducethe cost, a simplified BOCDA (S-BOCDA) system, in which an SSBM is not used, wasimplemented [84]. As for the sampling rate, it was enhanced to 1 kHz by employing an
unbalanced Mach-Zehnder (UMZ) delay line to the S-BOCDA [85]. A discriminative
measurement of strain and temperature has also been performed by Zou et al. withBOCDA using a novel acoustic grating [86, 87]. Finally, a quasi-one-end-access
BOCDA system called “in-line BOCDA” was developed, with a mirror located at one
end of the FUT [88]. Recently, many experiments from practical application standpoints
have also been performed with fruitful results, such as health monitoring of aircraft andtunnels [89-92].

1. 6

Purpose and constitution of this thesis

The purpose of this thesis is the proposal and the performance improvement of a newsensing technology named Brillouin optical correlation-domain reflectometry (BOCDR)
to resolve the problems of the conventional techniques including BOTDA, BOTDR,BOFDA, and BOCDA.
This thesis consists of 10 chapters. Following the Introduction, in Chapter 2, we
propose BOCDR and show the preliminary experimental results. In Chapter 3, theDissertation 2009, The University of Tokyo

15

1. Introduction

operation of BOCDR is theoretically analyzed and the relation between the spatial
resolution and the inherent noise is discussed. In Chapter 4 and Chapter 5, we proposeand demonstrate two independent methods to enlarge the measurement range while
maintaining the spatial resolution. In Chapter 6, the sampling rate is enhanced by
optical heterodyne detection. In Chapter 7 and Chapter 8, polarization-related
phenomena in BOCDR are discussed. After showing that BOCDR can be used tomeasure the distribution of polarization beat length, polarization scrambling andnoise-floor compensation technique are newly implemented to enhance the stability andthe S/N ratio. In Chapter 9, a tellurite fiber is employed to achieve the inherent
limitation of the spatial resolution. Finally, in Chapter 10, we present our concluding
remarks of this thesis and describe remaining problems and outlook for the future.

Dissertation 2009, The University of Tokyo16

2. Proposal of BOCDR

2

Proposal of Brillouin optical correlationdomain reflectometry (BOCDR)

In this Chapter, we propose Brillouin optical correlation-domain reflectometry(BOCDR), which can measure the distribution of strain and/or temperature along a fiber
under test (FUT) from a single end of the fiber, by detecting spontaneous Brillouinscattering based on the interference control of continuous lightwaves. Compared toconventional Brillouin optical time-domain reflectometry (BOTDR) based on opticalpulses, the continuous- wave-based BOCDR does not suffer from the inherent limitationof 1-m resolution, and has real-time measurability and random accessibility tomeasuring positions. In the preliminary experiment, a spatial resolution of 40 cm isachieved with sampling rate of 50 Hz. Then, real-time measurement is demonstrated.
Furthermore, a spatial resolution as high as 13 mm is obtained, which is the best result
ever reported in any Brillouin scattering-based reflectometry and even superior to thatobtained in Brillouin optical time-domain analysis (BOTDA). Finally, we
experimentally show that BOCDR is based not on stimulated Brillouin scattering but on
spontaneous Brillouin scattering.

2. 1

Introduction

As was mentioned in Chapter 1, optical fiber sensors based on Brillouin scattering havebeen intensively studied as a promising technology for monitoring conditions in various
materials and structures, due to the possibility of distributed measurement of strain
and/or temperature along an optical fiber. To obtain the location information of
Dissertation 2009, The University of Tokyo17

2. Proposal of BOCDR

strain/temperature along the fiber, conventionally, pulse-based time-domain systems[40-65] have been used, which have the advantage of long measurement range over
several tens of kilometers. Their long measurement time (~ several minutes) andinherent limitation in spatial resolution (~ 1 m) [45, 46], however, are not satisfactoryfor practical applications.
In this Chapter, we propose BOCDR to measure the strain/temperature distribution
along an FUT by light injection only from one end of the fiber, based on spontaneous
Brillouin scattering and the interference control of continuous lightwaves. The
advantages of BOCDR, such as high spatial resolution and high sampling rate, areexperimentally demonstrated.

2. 2

Principle

The conceptual schematic of the proposed BOCDR system is shown in Figure 2.1. A

Figure 2.1 Conceptual schematic of BOCDR. AC, alternating current; DAQ, dataacquisition; DC, direct current; ESA, electrical spectrum analyzer; FUT, fiber under
test; PD, photo diode.

Dissertation 2009, The University of Tokyo

18

2. Proposal of BOCDR

light beam from a laser is divided into pump and reference light beams. The pump lightis injected into the FUT, and the Stokes light is directed into a heterodyne receivercomposed of two balanced photodiodes (PDs). The reference light is used as an optical
local oscillator (LO). The electrical beat signal of the two light beams is monitored byan electrical spectrum analyzer (ESA). Since there is a frequency difference of about 11
GHz between the Stokes light and the reference light, this configuration is called aself-heterodyne scheme.
In order to resolve the position in the FUT, the optical frequency of the laser output
is modulated in a sinusoidal waveform by directly modulating the injection current to
the laser. From the viewpoint of time averaging, the correlation (or coherence) function
is synthesized into a series of periodical peaks [93, 94], whose period is inversely
proportional to the frequency of the sinusoidal modulation fm. We control fm to leave
only one correlation peak within the range of the FUT, so that only the Brillouinscattering generated at the position correspondent to the peak has high correlation withthe reference light, and then gives high heterodyne output. The peak frequency observed

Figure 2.2

Operating principle of basic BOCDR.

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2. Proposal of BOCDR

with the ESA gives the Brillouin frequency shift (BFS) caused at the position. By
sweeping fm, the position of the correlation peak is scanned along the FUT, and thus the
distribution of the Brillouin gain spectrum (BGS) or the BFS is obtained.
Here we give another explanation of the operating principle of BOCDR using
Figure 2.2. When the laser frequency is sinusoidally modulated, the frequencies of thereference light and the Stokes light at the heterodyne receiver are expressed by theequations shown in Figure 2.2, where φ and ψ are phase factors. While φ is a 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 + 2π n (n: integer), thefrequency difference of the reference light and the Stokes light is always the same
regardless of time, and so the beat signal can be detected. In contrast, when the pumplight is reflected at Position B and φ ≠ ψ + 2π n, the frequency difference of the twolight beams changes according to time, and so the beat signal cannot be observed. Fromthe 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

Figure 2.3

Comparison of the operating principle between BOCDA and BOCDR.

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2. Proposal of BOCDR

correlation peak should be left within the range 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 fm.
The spatial resolution Δz and the measurement range dm (distance between theneighboring correlation peaks) of BOCDR are given by the same equations as those for
BOCDA [70, 71]:
vg ΔνBΔz = 2πf Δf ,

(2.1)

vg
dm = 2 f ,

(2.2)

m

m

where vg is the group velocity of light, ΔνB the Brillouin gain bandwidth (~ 30 MHz) in
optical fibers, and Δf the modulation amplitude of the light source. Equation (2.1) was
originally derived for BOCDA (See Equation (1.9)), so it is not evident that the spatial
resolution of BOCDR is also given by this expression. The derivation of Equation (2.1)
in BOCDR is described in Chapter 3.
Next, we compare the operating principle between BOCDA and BOCDR using

Figure 2.4 Experimental setup of basic BOCDR. DFB-LD, distributed-feedback
laser diode; EDFA, erbium-doped fiber amplifier; GPIB, general-purpose interface
bus; PC, polarization controller
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2. Proposal of BOCDR

Figure 2.3. In both systems, the pump light is reflected everywhere in the FUT due tospontaneous Brillouin scattering. 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 scatteringfrom 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.
Finally, we discuss the measurement accuracy, that is, the strain resolution. The
most dominant factor in determining the measurement accuracy is the bandwidth of theobserved BGS in principle. As was discussed in Section 1.3, in time-domain techniques,
the BGS bandwidth is inversely proportional to the spatial resolution. When the
resolution is high (~ several tens of centimeters), the bandwidth broadens for about 1
GHz [45, 46], which drastically deteriorates the measurement accuracy. On the other
hand, in BOCDR, the BGS bandwidth is not in inverse proportion to the spatial
resolution. It was much narrower than 1 GHz, even when the resolution was several
centimeters, as will be shown in Section 2.5. This means that BOCDR potentially has ahigher measurement accuracy than time-domain techniques.

2. 3

Experimental setup

The actual experimental setup of BOCDR is depicted in Figure 2.4. Before heterodyne
detection, the reference light at frequency f0 passed through a several-km delay fiber,
which is used to select the order of periodical correlation peaks, an erbium-doped fiber
amplifier (EDFA) to enhance the beat signal, and an optical filter to suppress theDissertation 2009, The University of Tokyo22

2. Proposal of BOCDR

Figure 2.5

Structure of the FUT.

amplified spontaneous emission (ASE) noise. The pump light at frequency f0 was
injected into the FUT after being amplified with a high-power EDFA (~28 dBm). The
weak Stokes light at frequency f0 – fB backscattered from the FUT was amplified again
with an EDFA. An optical filter was inserted after the EDFA in order to suppress theRayleigh scattering and the Fresnel reflection from the FUT at frequency f0. Before
processing with an ESA, the heterodyned signal was amplified with an electricalpre-amplifier.

2. 4

Preliminary experiments

The modulation frequency fm was set to 457.4 – 458.4 kHz, which corresponds to themeasurement range of 228 m according to Equation (2.2). The amplitude of thefrequency modulation Δf was 5.4 GHz, and the spatial resolution Δz was calculated to
be about 40 cm from Equation (2.1). Figure 2.5 shows the structure of the FUT
comprising a 100-m standard single-mode fiber (SMF), in which a 0.2-% strain isapplied to a 50-cm section fixed on a translation stage using epoxy glue. One end of the
FUT was spliced to a circulator, and the other end was kept open. The overall sampling
rate of the BGS measurement for a single position was 50 Hz, which is much higher
than that of the time-domain techniques with a typical measurement time of several
minutes.
Figure 2.6 shows the measurement result of the distribution of the BGS along theDissertation 2009, The University of Tokyo23

2. Proposal of BOCDR

FUT. The BGS at the strain-applied section was clearly recognized. Figure 2.7 shows
the distribution of the BFS. A spatial resolution higher than 50 cm was achieved. Thechange of the BFS was about 100 MHz, which is in good agreement with the applied
strain of 0.2 %.

Figure 2.6

Measured distribution of BGS.

Figure 2.7

Measured distribution of BFS.

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2. Proposal of BOCDR

2. 5

Spatial resolution of 13 mm

The modulation frequency fm was 13.4624 – 13.4672 MHz, which corresponds to ameasurement range dm of 7.6 m according to Equation (2.1). The amplitude of thefrequency modulation Δf was 5.4 GHz, and the nominal spatial resolution Δz was
calculated to be about 13 mm from Equation (2.2). Figures 2.8 and 2.9 show thestructure of the FUT comprising a 5-m SMF, in which a 0.1-% strain was applied to a
3-cm section fixed on a translation stage with epoxy glue. One end of the FUT was
spliced to a circulator, and the other end was bent to suppress the Fresnel reflection. The
overall sampling rate of the measurement for a single position was 50 Hz, which is quite

Figure 2.8

Figure 2.9

Structure of the FUT.

Photo of the FUT around the strain-applied section.

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2. Proposal of BOCDR

high compared with the time-domain techniques.
Figure 2.10 shows the measured distribution of the BGS along the FUT. The BGS at
the strain-applied section was recognized. Figure 2.11 shows the distribution of the BFS.
A spatial resolution higher than 3 cm was achieved, and a resolution of one-half (15mm) of the marked width is obviously available. It is in good agreement with thecalculated value of 13 mm. The change of the BFS was about 50 MHz, which agrees
well with the applied strain of 0.1 %. The accuracy of the measurement at a single
position was about +/– 5 MHz, which corresponds to the strain of +/– 0.01 % (+/– 100με) in this experiment. However, the signal-to-noise (S/N) ratio for this case wasdeteriorated, so that the peak of the BGS was mostly buried by the electrical noise floorof the ESA if the resolution was set even higher.
The spatial resolution of 13 mm is the best result ever reported in spontaneous
Brillouin scattering-based one-end-access reflectometers, and is even superior to thatobtained in stimulated Brillouin scattering-based two-end-access BOTDA systems (The

Figure 2.10

Measured distribution of BGS.

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2. Proposal of BOCDR

Figure 2.11

Measured distribution of BFS.

best nominal resolution of BOTDA was 20 mm, achieved using dark optical pulses [55,56]). The inherent limitation of the spatial resolution in BOCDR is discussed in Chapter
9.

2. 6

Real-time measurement

We confirmed the real-time measurement capability of BOCDR by a dynamic strain
sensing experiment. When data processing to find the peak in the BGS was employed,
the maximum sampling rate was 19 Hz. In order to obtain higher S/N ratio, themodulation frequency fm and the modulation amplitude Δf were set to 828.26 kHz and
5.4 GHz, respectively, which correspond to 22-cm spatial resolution and 124.9-m
measurement range. A 5-m SMF was used as the FUT, in which dynamic strains wereapplied to a 28-cm section (420 – 448 cm) by a piezoelectric transducer (PZT) with themost achievable strain of about +/– 450 με (+/– 22.5 MHz in BFS).
Sinusoidally-modulated voltages were applied to the PZT at the frequencies of 1 Hz, 2

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2. Proposal of BOCDR

Hz, and 4 Hz. The measurement results are shown in Figure 2.12, where the strain
oscillations were clearly observed. The amplitude discrepancy seems to originate fromthe mitigation effect of the fiber jacket. The accuracy of the measurement is limited by
the electrical noise of the ESA as well as the instability of polarization state.

(a)

(b)

(c)

Figure 2.12

Results of dynamic strain measurement with sinusoidal

driving voltages applied to the PZT at (a) 1 Hz, (b) 2 Hz, and (c) 4 Hz,
respectively. Note that the sampling rate is 19 Hz.

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2. Proposal of BOCDR

2. 7

Spontaneous or stimulated

In this Chapter, BOCDR has been assumed to be based on spontaneous Brillouinscattering. However, if the power of the incident light is extremely high, stimulated
Brillouin scattering (SBS) is observed even when the light is injected into only one endof the fiber. This is because the reflected light due to spontaneous Brillouin scattering
works as a probe lightwave in SBS. So, we experimentally clarified that SBS is not
dominant in BOCDR.
The experimental setup is depicted in Figure 2.13. The frequency-modulated lightbeam was amplified up to 28 dBm with an EDFA, and was injected into a 1-km FUT.
Then, the backscattered Stokes light was observed with an optical spectrum analyzer(OSA). Since there is no reference path in the setup, correlation peaks are not produced.
The modulation frequency fm was fixed at 68.62 kHz (this is the same fm as those ofsome experiments described in Chapter 4). Since it is difficult to accurately measure themodulation amplitude Δf because of the limited resolution of the OSA, the peak-to-peak
output voltage of the function generator (FG) providing alternating current (AC) was
substituted for Δf, and it was set to 0, 20, 100, and 1000 mVpp.

Figure 2.13

Experimental setup. OSA, optical spectrum analyzer.

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2. Proposal of BOCDR

Figure 2.14

Measured optical spectra of the reflected light.

Figure 2.14 shows the measured optical spectra of the Stokes light when Δf wasincreased. With no modulation applied (Δf = 0 mVpp), the power of the Stokes light ishigher than that of the Rayleigh-scattered light by more than 20 dB, which indicates thepresence of SBS. Meanwhile, as Δf was increased, the power of the Stokes lightdrastically decreased; when the AC was 1000 mVpp corresponding to Δf of about 3 GHz,it was lower than the power of the Rayleigh-scattered light by about 20 dB. This change
in the power of the Stokes light seems to be caused by the transition from SBS tospontaneous Brillouin scattering. Since Δf in BOCDR is generally set to several GHz(e.g., 5.4 GHz for silica fibers), it was clarified that BOCDR is based not on SBS but on
spontaneous Brillouin scattering.

2. 8

Conclusions

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2. Proposal of BOCDR

We proposed a BOCDR system, a new sensing technology based on spontaneous
Brillouin scattering and the correlation control of continuous lightwaves, anddemonstrated a one-end-access distributed strain measurement with 40-cm spatial
resolution and 50-Hz sampling rate in the preliminary experiment. We also measured
the BFS along a 3-cm strain-applied section with 13-mm nominal spatial resolution,
though the S/N ratio was deteriorated. Such a high resolution and a high sampling rate
have not yet been achieved by other Brillouin scattering-based reflectometers as well as
two-end-access BOTDA systems. The real-time detection of vibrated strains at
frequencies of up to 4 Hz was also presented. Furthermore, it was experimentally shownthat BOCDR is based not on SBS but on spontaneous Brillouin scattering.

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3. Theoretical analysis of BOCDR operation

3

Theoretical analysis of BOCDR operation

In this Chapter, the operation of Brillouin optical correlation-domain reflectometry(BOCDR) is theoretically analyzed. First, we show that the effective Brillouin gain
spectrum (BGS) is determined by the 2-dimensional convolution of the intrinsic
Brillouin gain and the beat power spectrum, and that the spatial resolution of BOCDR isgiven by the same expression as that of Brillouin optical correlation-domain analysis(BOCDA). We also simulate the typical shapes of the detected BGS. Then, we
demonstrate that the modulation amplitude of the laser frequency, which is in inverse
proportion to the spatial resolution, is limited to a half of the Brillouin frequency shift(BFS) under normal measurement conditions. We also show that this limitation of themodulation amplitude can be mitigated by employing a fiber under test (FUT) shorter
than a half of the measurement range.

3. 1

Introduction

In Chapter 2, the expression of the spatial resolution in BOCDR was assumed to be thesame as that in BOCDA, which was not evident. Besides, in order to achieve highspatial resolution, the modulation amplitude and the modulation frequency of the laser
frequency must be increased, but their theoretical limitations were not clarified yet.
In this Chapter, we theoretically show that the spatial resolution of BOCDR is givenby the same expression as that of BOCDA, and clarify the limitation of the modulation
frequency. We also discuss the Rayleigh scattering-induced noise, and clarify theDissertation 2009, The University of Tokyo

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3. Theoretical analysis of BOCDR operation

limitation of the modulation amplitude.

3. 2

System formulation

First, we derive the expression of the effective BGS, which is the final signal observedwith the electrical spectrum analyzer (ESA). We define the position of the correlation
peak in the FUT as z = zm, which corresponds to the measuring position. Suppose the~electric fields of the reference light, the pump light, and the Stokes light are Er(f) (=~~F[Er(t)]), Ep(z–zm,f) (= F[Ep(z–zm,t)]), and ES(z–zm,f) (= F[ES(z–zm,t)]), respectively.
Here F[ . ] denotes the operation of Fourier transform. Then, as shown in Figure 3.1,~ES(z–zm,f) is approximately expressed as (See Appendix A at the end of this Chapter)~~~
ES (z − zm , f ) = E p (z − z m , f + f B (z )) ⊗ f D(z, f )~~≡ E S′ ( z − z m , f ) ⊗ f D ( z , f ) ,(3.1)

where fB(z) is the BFS, ⊗ f represents a convolution concerning frequency, and~D(z,f) (= F[D(z,t)]) is a complex Lorentzian function given by

Figure 3.1

Definitions of each symbol in Equation (3.1).

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3. Theoretical analysis of BOCDR operation~
D (z , f ) =

12

g B0
,
1 − j 2 f Δν B

(3.2)

where gB0 is the Brillouin gain coefficient. The interference signal I(z–zm,t) between thereference light and the Stokes light is given by

I ( z − z m , t ) = Er (t ) + ES ( z − z m , t )

2

,

(3.3)

where < . > stands for time-averaging operation, and its alternating-current (AC)component is

I AC ( z − z m , t ) ∝ Er (t ) ⋅ ES ( z − z m , t )∗= Er (t ) ⋅ ES′ ( z − z m , t ) ⋅ D(z, t ) .
∗

(3.4)

~
Here, the complex conjugate term was omitted. Then I AC(z–zm,f) (= F[IAC(z–zm,t)]) is
expressed as

{

}

~
∗
I AC ( z − z m , f ) ∝ F {D( z, t )} ⊗ f F Er (t ) ⋅ E S′ ( z − z m , t )~~≡ D(z, f ) ⊗ f B (z − z m , f ) .
~where the beat B(z–zm,f) is defined as

{

}

~
∗
B (z − z m , f ) = F Er (t ) ⋅ ES′ (z − z m , t ) .

(3.5)

(3.6)

~
~
Here, the beat B ( z − z m , f ) can be expressed as B ( z m − z, f ) because it is a function
only of the distance between zm and z. Since the interaction length between the
Brillouin-scattered lightwaves generated at different positions is short (~ 100 μm)
compared to the spatial resolution (>> 1 mm), the effective BGS is given, by integrating~
the square of the amplitude of I AC(z–zm,f) along the whole length of the FUT (SeeAppendix B), as
2~~
BGS ( z m , f ) ∝ ∫ dz ⋅ D( z , f ) ⊗ f B ( z m − z , f )
FUT

2
2
~
~
= ∫ dz ⋅ D(z , f ) ⊗ f B (z m − z, f ) .

(3.7)

FUT

Here, if we define the intrinsic Brillouin gain gB(z,f) and the beat power spectrum Sb(z,f)
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3. Theoretical analysis of BOCDR operation

2~g B ( z , f ) = D( z , f ) =gB0
2
1 + 4 f 2 Δν B ,2~
Sb (z , f ) = B (z , f ) ,

(3.8)
(3.9)

the effective BGS can be expressed as
BGS ( z m , f ) ∝ ∫ dz ⋅ g B ( z, f ) ⊗ f S b ( z m − z, f )FUT∞= ∫ dz ∫ df ′ ⋅ g B ( z , f ′) ⋅ S b ( z m − z , f − f ′)
FUT

−∞
∞

= ∫ dz ∫ df ′ ⋅ g B (z , f − f ′) ⋅ S b ( z m − z, f ′) ,FUT

(3.10)−∞

where gB(z,f) is the intrinsic Brillouin gain, and Sb(z,f) is the beat power spectrum.
Equation (3.10) shows that, when the measuring position is zm, the effective BGS isdetermined by the 2-dimensional convolution of gB(z,f) and Sb(z,f). Although thederivation and the physical picture are different, this expression is the same as that of
BOCDA [70, 71].

3. 3

Simulation on detected BGS

Based on Equation (3.10), we simulate the shape of the detected BGS when thecorrelation peak is present at the middle of the strain-applied section. The spatial
resolution was set to 25 cm, and the magnitude of strain was set to about 0.4%, whichcorresponds to a frequency shift of 200 MHz. The simulation was performed on twocases where strain was applied to sections with different lengths.
First, we show the simulation results when the strain-applied section was set to 25
cm, which is the same as the spatial resolution. The beat power spectrum, the intrinsic
BGS, and the convoluted BGS are shown in Figures 3.2, 3.3, and 3.4, respectively.
Figure 3.5 shows the comparison between the detected BGS and the intrinsic BGS, fromwhich we know that only the real signal is shifted from the original position in response

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3. Theoretical analysis of BOCDR operation

Figure 3.2

Simulated beat power spectrum with strain applied to a 25-cm section.

Figure 3.3

Simulated intrinsic BGS with strain applied to a 25-cm section.

to the applied strain, while the background noise is unchanged. Since the noise
spectrum is pyramid-shaped structure centered on the initial BFS of the fiber, thepeak-to-peak ratio between the signal and the noise is decreased with larger strain.
Beyond certain strain limit, the signal is decreased below the noise level, resulting in
the failure of the strain measurement.
Then, we also performed a similar simulation when the strain-applied section was
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3. Theoretical analysis of BOCDR operation

Figure 3.4

Figure 3.5

Convoluted BGS with strain applied to a 25-cm section.

Detected BGS and intrinsic BGS with strain applied to a 25-cm section.

set to 50 cm. The beat power spectrum, the intrinsic BGS, and the convoluted BGS are
shown in Figures 3.6, 3.7, and 3.8, respectively. The comparison between the detected
BGS and the intrinsic BGS is shown in Figure 3.9, where the background noise is lower
than that in Figure 3.5. Thus, the noise decreases when the strain-applied section is longcompared to the spatial resolution. In Section 3.7: “Discussion on noise (3)”, we show it
is not this background noise that is critical to the actual BOCDR measurement.
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3. Theoretical analysis of BOCDR operation

Figure 3.6

Simulated beat power spectrum with strain applied to a 50-cm section.

Figure 3.7

3. 4

Simulated intrinsic BGS with strain applied to a 50-cm section.

Spatial resolution

In order to derive the expression of the spatial resolution in BOCDR, we evaluate theshape of the beat power spectrum Sb(z,f) near the correlation peak (z ~ zm). For
simplicity, we redefine z as the relative position from zm. So, E’S(z–zm,t) and~~B ( z m − z, f ) become E’S(z,t) and B(z,f), respectively.

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3. Theoretical analysis of BOCDR operation

Figure 3.8

Figure 3.9

Convoluted BGS with strain applied to a 50-cm section.

Detected BGS and intrinsic BGS with strain applied to a 50-cm section.

When the laser frequency is sinusoidally modulated, Er(t) and E’S(z,t) can be
expressed as

Er (t ) = ar exp( jΦ(t )) ,E S′ (z , t ) = a S exp( jΦ (t − 2 z v g )) ,(3.11)(3.12)

where ar and aS are the amplitudes, and Φ (t) is given as

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3. Theoretical analysis of BOCDR operation

Φ (t ) =Δfsin (2πf mt ) .
fm(3.13)

Then, the Er*(t)･E’S(z,t) is calculated as

E r (t ) ⋅ E S′ ( z , t ) = a r a S exp (− jΦ (t ))exp ( jΦ (t − 2 z v g ))∗dΦ(t ) ⎞⎛= ar aS exp⎜ − j 2( z vg )
⎟
dt ⎠
⎝

= ar aS exp( j 2( z vg )2πΔf sin (2πf mt − π 2 ))∞= ar aS ∑ J k (2( z vg )2πΔf )exp( jk (2πf mt − π 2)) .
k = −∞(3.14)~
So the beat B(z,f) is

{

}

~
∗
B ( z, f ) = F Er (t ) ⋅ ES′ ( z, t )∞= ar a S ∑ J k (2( z v g )2πΔf )δ [2π ( f − kf m )] .
k = −∞(3.15)~
Thus, the beat power spectrum Sb(z,f) (=|B(z,f)|2) is composed of discrete spectra withintervals of fm.
To evaluate Equation (3.10) and formulate the spatial resolution, we must separate
in the cases of fast fm and slow fm. When fm is higher than the Brillouin bandwidth ΔνB,
only the 0-th component of Sb(z,f) is within the linewidth of the Brillouin gain gB(z,f).
Here, we estimate the spatial resolution by the distance between the correlation peak~
and the position where the beat B(z,f) falls to a half of its peak value, which is the samedefinition as in BOCDA [70, 71]. Then we obtain

J 0 (2(Δz 2vg )2πΔf ) = 1 / 2 .

(3.16)

Since J0(1.52) = 0.501, the resolution is given asΔz =1.52vg2πΔf,(3.17)

which means that, when fm > ΔνB, the resolution is in inverse proportion to Δf.
Then, when fm is lower than ΔνB, several components of Sb(z,f) is within the
linewidth of gB(z,f). Here we estimate the spatial resolution by the distance between the~correlation peak and the position where the full width of the beat B(z,f) broadens twice

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3. Theoretical analysis of BOCDR operation

as wide as ΔνB, which is also the same as in BOCDA [70, 71]. If we assume that theJn(4πΔf z/vg) of the n-th spectral component takes a significant value when n < 4πΔf z/vg,~
the full width of the beat B(z,f) is calculated to be 2fm･4πΔf z/vg. So, we obtain4( Δ z 2v g ) 2πΔ f ⋅ f m = 2 Δ ν B ,(3.18)

leading to the expression for the resolution:Δz =vg Δν B

2π f m Δf ,(3.19)

from which we know that, when fm < ΔνB, the resolution is in inverse proportion not
only to Δf but also to fm. Thus, it was theoretically shown that the expression of thespatial resolution of BOCDR is the same as that of BOCDA.

3. 5

Discussion on noise (1)As shown in Equations (2.1) (or 3.19) and (2.2), there is a trade-off between themeasurement range and the spatial resolution in BOCDR, and the ratio of the twovalues is purely dependent on the amplitude of the frequency modulation Δf. Therefore,Δf needs to be increased in order to obtain substantial improvement in the performanceof BOCDR. However, Δf cannot be increased beyond the limit discussed below.
Figure 3.10(a) shows the schematic optical spectra of the reference light and thereflected light just before the heterodyne detection when the laser frequency issinusoidally modulated with the modulation amplitude Δf. The Rayleigh scattered lightis too strong to be suppressed completely with an optical filter, so it remains in thereflected light. The schematic electrical spectra after the heterodyne detection with
sufficiently small Δf are shown in Figure 3.10(b). The spectrum of the Brillouinscattered light broadens in both directions for 2Δf with a center frequency fB. On theother hand, the spectrum of the Rayleigh scattered light broadens from 0 Hz to 2Δf,considering that negative frequency is folded back to positive one. Figure 3.10(c) shows
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3. Theoretical analysis of BOCDR operation

(a)

(b)

(c)

Figure 3.10 Schematics of (a) optical spectra of the reference light andthe reflected light when the frequency of the light source is modulated withthe amplitude Δf, (b) electrical spectra with sufficiently small Δf, and (c)electrical spectra with large Δf.

the schematic electrical spectra when 2Δf is increased to the value slightly lower than fB.
Though the Rayleigh spectrum is approaching the detection area, so long as it is outside
the area, the measurement is free from its influence. However, if 2Δf is further increased
beyond fB, the Rayleigh spectrum starts to overlap with the detection area, resulting in aconsiderable amount of noise. Thus, it is undesirable for Δf to be higher than a half of fB.

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3. Theoretical analysis of BOCDR operation

Figure 3.11 Measured BGS when Δf is 5.4 GHz, 5.5 GHz, and 5.6 GHz.

In the experiment, Δf was set to 5.4 GHz, which is slightly lower than a half of the
11-GHz BFS in a silica single-mode fiber (SMF). If Δf larger than 5.4 GHz was applied
to the system, the signal-to-noise (S/N) ratio decreased drastically, as shown in Figure
3.11.
We investigated the behavior of this noise using a tellurite glass fiber with highBrillouin gain, the details of which are discussed in Chapter 9. Figure 3.12 shows thewhole spectra of the electrical output of the BOCDR system when Δf was increased
from 0.1 to 4.0 GHz. Due to the high Brillouin gain coefficient of the tellurite fiber, theevolution of the spectra was observed much more clearly than that in our previous
experiment with a silica SMF. As Δf became larger, the spectrum of theBrillouin-scattered light broadened in both directions for 2Δf around the BGS peak at
about 8 GHz. In Figure 3.12, a large amount of noise spreading from 0 Hz to 2Δf is also

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3. Theoretical analysis of BOCDR operation

Figure 3.12 Measured electrical spectra when the modulation amplitude
Δf was increased from 0.1 to 4.0 GHz. A tellurite glass fiber was used as the
FUT. Each spectrum is shifted by 35 dB. The values on the ordinate arevalid only for Δf = 0.1 GHz.

clearly shown, which is induced by the Rayleigh scattering. When Δf was 4.0 GHz, thenoise began to overlap the BGS peak. This result confirms experimentally that thelimitation of Δf is a half of the BFS of the fiber.

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3. Theoretical analysis of BOCDR operation

3. 6

Discussion on noise (2)As has been discussed, the modulation amplitude Δf must be lower than a half of the
BFS of the FUT under normal measurement conditions. In this Section, however, weshow that the beating noise spreads up to 2Δf due to the Rayleigh scattering from the
middle point between two correlation peaks. So, by using an FUT shorter than a half ofthe measurement range, it becomes possible to enhance Δf beyond a half of the BFS.
The electric field of the reference light Er(t) at the heterodyne receiver was given by
Equation (3.11). If we employ the phase noise of the laser φ(t) it is expressed as⎧ Δf⎫
E r (t ) = a r exp j ⎨ sin (2πf m t ) + φ (t )⎬ .
⎩ fm⎭

(3.20)

Then, the electric field of the Rayleigh-scattered light ER(t) can be expressed as⎧ Δf⎫
E R (t ) = a R exp j ⎨ sin (2πf m t + ϕ ) + φ (t + τ )⎬ ,⎩ fm⎭

(3.21)

where aR is the amplitude, and τ is the time delay; ϕ is the phase difference of thesinusoidal modulations between the two lightwaves at the heterodyne receiver. While ϕbecomes 0 at the correlation peaks, ϕ becomes π at the middle of the intervals of twoneighboring correlation peaks (0 ≤ ϕ ≤ π). Then, the beating noise between the twolightwaves Ibeat(t) can be calculated as
I beat (t ) = E r (t ) + E R (t )

2

⎧
2Δf
ϕ ⎞ ⎛ ϕ ⎞⎫⎛cos ⎜ 2π f mt + ⎟ sin ⎜ ⎟ ⎬= ar 2 + aR 2 + 2ar aR cos ⎨{φ ( t ) − φ ( t + τ )} −fm
2 ⎠ ⎝ 2 ⎠⎭⎝⎩. (3.22)

So, if φ(t) – φ(t+τ) is negligible, the Rayleigh scattering-induced noise spreads from 0
Hz to the following frequency:⎡ 1 ∂ ⎧ 2Δf⎧ ⎛ ϕ ⎞⎫ϕ ⎞ ⎛ ϕ ⎞ ⎫⎤⎛max ⎢ ⋅ ⎨−cos ⎜ 2π f mt + ⎟ sin ⎜ ⎟ ⎬⎥ = 2Δf ⋅ max ⎨sin ⎜ ⎟ ⎬ , (3.23)
2 ⎠ ⎝ 2 ⎠ ⎭⎦⎥⎝⎩ ⎝ 2 ⎠⎭⎣⎢ 2π ∂t ⎩ f mwhich must be lower than the BFS. This means that, if there is no point in the FUT
where ϕ = π (if the length of the FUT is shorter than a half of the measurement range),
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3. Theoretical analysis of BOCDR operation

Δf can exceed a half of the BFS. The limitation of Δf is given, by a function not only of
BFS but also of FUT length L, measurement range dm, and the distance l between themeasuring position and the circulator, asΔfmax =

π max(L – l, l)
BFS
cosec
.
2
dm

(3.24)The experimental setup to verify Equation (3.24) is the same as that in Chapter 2.
Using a 100-m FUT (L = 100 m), the modulation frequency fm was set to 286.90 kHz,
which corresponds to dm = 349.2 m and l = 1 m. Figure 3.13 shows the measured whole
spectra of the electrical output when Δf was increased from 0.1 GHz. As Δf became
larger, the Rayleigh scattering-induced noise spread from 0 Hz. When the noise began
to overlap the BGS peak at about 10.85 GHz, Δf was about 6.9 GHz as shown in Figure
3.14, which is the optical spectrum of the reference light after passing the optical filter.
According to Equation (3.24), the theoretical limitation of Δf is calculated to be 6.98
GHz, which is in good agreement with the experimental result. The same experiment
was also performed when fm = 296.17 kHz, dm = 338.3 m, L = 100 m, and l = 80 m. The
experimental results shown in Figures 3.15 and 3.16 indicate that the limitation of Δf
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 phase noise, thatis, the linewidth of the light source, is negligible in deriving Equation (3.24).
According to Equation (3.19), either fm or Δf must be increased to enhance theresolution. In Chapter 9, by setting fm to its limitation ΔνB and Δf to a half of the BFS,
6-mm resolution is obtained using a tellurite glass fiber. So the fact that Δf can be higher
than a half of the BFS indicates that the spatial resolution even higher than 6 mm is
feasible in BOCDR.

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3. Theoretical analysis of BOCDR operation

Figure 3.13 Measured electrical spectra when Δf was increased from 0.1
to 6.9 GHz. Each spectrum is shifted by 20 dB. The values on the ordinate
are valid only for Δf = 0.1 GHz.

Figure 3.14 Measured optical spectrum of the reference light after passing
the optical filter.
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3. Theoretical analysis of BOCDR operation

Figure 3.15 Measured electrical spectra when Δf was increased from 0.1
to 7.95 GHz. Each spectrum is shifted by 20 dB. The values on the ordinate
are valid only for Δf = 0.1 GHz.

Figure 3.16 Measured optical spectrum of the reference light after passing
the optical filter.

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3. Theoretical analysis of BOCDR operation

3. 7

Discussion on noise (3)In this Section, we discuss the noise unrelated to the Rayleigh scattering. When theRayleigh scattering-induced noise described in preceding Sections is outside thedetection area, the BGS suffers from other noise, which can be classified into two
components: (i) random noise due to shot noise or thermal noise, and (ii) fixed noise
floor inherent to the ESA.
The effect of the random noise is observed, for example, in Figures 2.6 or 2.10,
where the signal power randomly fluctuates. These power fluctuations can besuppressed by averaging or optimizing the integrating time, as shown, for example, in
Figures 8.7, 9.10 or 9.14. The random noise has an influence on the measurement
accuracy or the strain resolution.

Figure 3.17 Schematic noise floor inherent to the ESA, which limits thespatial resolution and the largest detectable strain magnitude.

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3. Theoretical analysis of BOCDR operation

On the other hand, the background noise floor has a fixed shape, as shown in
Figures 2.6 or 8.7. This is not due to the noise discussed in Section 3.3 (See Figures 3.5
and 3.9) but due to the noise floor inherent to the ESA, as the shape was quite different
when another ESA was used. It was also experimentally clarified that the noise floor is
not dependent on the optical input to the ESA. This noise floor has more influence on
the BOCDR-based measurement than the random noise, limiting the spatial resolution
and the largest detectable strain magnitude, as schematically shown in Figure 3.17. A
method to mitigate the effect of the noise floor is developed and experimentally verified
in Chapter 8.

3. 8

Conclusions

We theoretically analyzed the operation of BOCDR. First, we showed that the effective
BGS is given by the 2-dimensional convolution of the intrinsic Brillouin gain and thebeat power spectrum. Then, we performed a simulation on the typical shapes of thedetected BGS. We also derived the expression of the spatial resolution in BOCDR,
which was the same as that of BOCDA. Furthermore, we demonstrated that themodulation amplitude of the laser frequency, which determines the spatial resolution, islimited to a half of the BFS under normal measurement conditions, using a silica fiberand a tellurite glass fiber. Finally, we also showed that this limitation of the modulation
amplitude can be mitigated by employing an FUT shorter than a half of themeasurement range.

Appendix A~
We verify Equations (3.1) and (3.2) when the linewidth of the pump light is 0. Ep(z,f)

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3. Theoretical analysis of BOCDR operation

is expressed as[~
E p (z, f ) = δ f − f p],(3.25)~
where fp is the frequency of the pump light. Then, ES(z–zm,f') can be calculated, using
Equations (3.1) and (3.2), as

[

]

~
~
E S ( z − z m , f ′) = δ f + f B ( z ) − f p ⊗ D( z , f )∞~= ∫ df ⋅ δ [ f + f B (z ) − f p ]⋅ D(z, f ′ − f )−∞~= D (z , f ′ − f p + f B ( z ))
12

=

g B0
1 − j 2( f ′ − f p + f B ( z )) Δν B
12

g B0
=
1 − j 2( f ′ − ( f p − f B ( z ))) Δν B ,(3.26)~
which is the correct expression for ES(z–zm,f').

Appendix B
We derive the following equation used in Equation (3.7):
2

2

A⊗ B = A ⊗ B

2,(3.27)

where A and B are arbitrary complex functions.
In general, the convolution satisfies the following algebraic properties:

A⊗ B = B ⊗ A ,(3.28)A ⊗ (B ⊗ C ) = ( A ⊗ B ) ⊗ C ,(3.29)a( A ⊗ B ) = (aA) ⊗ B = A ⊗ (aB ) ,(3.30)

where C is an arbitrary complex function, and a is an arbitrary complex constant.
Here, the left side in Equation (3.27) can be expanded as2

A ⊗ B = ( A ⊗ B )( A ⊗ B ) * = ( A ⊗ B )( A* ⊗ B * ) ,(3.31)

which can be further transformed, by using Equations (3.28)-(3.30), as

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3. Theoretical analysis of BOCDR operation{}( A ⊗ B)( A* ⊗ B * ) = ( B ⊗ A) A* ⊗ B *

{ (

)}

2

(

)

= B ⊗ A ⋅ A* ⊗ B * = A ⊗ B ⊗ B * .

(3.32)

Equation (3.31) can also be transformed as

{

} (

)

( A ⊗ B )( A* ⊗ B * ) = A* ⊗ ( A ⊗ B ) B * = A ⊗ A* ⊗ B

2.

(3.33)

By comparing Equations (3.32) and (3.33), we can derive Equation (3.27).

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4. Enlargement of measurement range based on temporal gating scheme

4

Enlargement of measurement range
based on temporal gating scheme

In this Chapter, we newly develop a temporal gating scheme to enlarge themeasurement range of Brillouin optical correlation-domain reflectometry (BOCDR)
while maintaining the spatial resolution. In this scheme, the trade-off problem between
the measurement range and the spatial resolution can be dissolved. A spatial resolutionof 66 cm and a measurement range of 1 km were simultaneously obtained with 50-Hz
sampling rate.

4. 1

Introduction

BOCDR suffers from a trade-off between the measurement range and the spatial
resolution. As discussed in Chapter 3, their ratio NR was fixed at approximately 570 due
to the limitation of Rayleigh scattering. This means that, for example, when the spatial
resolution was 40 cm or 13 mm, the measurement range was 224 m or 7.6 m,
respectively. Thus, in order to achieve kilometer-order measurement range, the spatial
resolution must be about 2 m or larger, which is even worse than that of Brillouin
optical time-domain reflectometry (BOTDR) [45, 46].
In this Chapter, we newly implement a temporal gating scheme to obtain higher NR,
namely, to enlarge the measurement range of BOCDR while maintaining the spatial
resolution. In this scheme, any correlation peak within the fiber under test (FUT) can bearbitrarily selected, so that multiple correlation peaks can be utilized. A spatial
resolution of 66 cm and a measurement range of 1 km (NR = 1515) were simultaneously

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4. Enlargement of measurement range based on temporal gating scheme

achieved with 50-Hz sampling rate.

4. 2

Temporal gating scheme

The number of effective sensing points NR, which can be regarded as the evaluation
parameter, is given, by the ratio between dm and Δz, asdm
πΔf
NR = Δz = Δν .
B

(4.1)

So, Δf needs to be increased to substantially enhance the measurement range. However,
it is difficult to increase Δf higher than a half of the Brillouin frequency shift (BFS) of
the fiber, which is about 5.4 GHz for standard silica single-mode fibers (SMFs).
Another way to enhance the measurement range is to utilize multiple intervals of thecorrelation peaks. In this case, we select only one correlation peak for a distributed
measurement, but suppress other peaks to avoid cross-talk. Therefore, the measurement
range is multiplied. The temporal gating scheme is an effective method for this purpose,and has been applied to Brillouin optical correlation-domain analysis (BOCDA) [80,Figure 4.1

Experimental setup of BOCDR with the temporal gating scheme.

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4. Enlargement of measurement range based on temporal gating scheme

Figure 4.2

Pulse shapes of the pump light and the reference light.

81].
The concept of the temporal gating scheme in BOCDR is explained, referring to an
experimental setup depicted in Figure 4.1. Compared to the basic configuration shownin Figure 2.2, two LiNbO3 intensity modulators (IMs) are newly employed in the pump
path and the reference path. First, the pump light is converted into optical pulses asshown in Figure 4.2. By setting the pulse width tW to be the same as the interval ofcorrelation peaks as
1
tW = 2 f

m

,

(4.2)

the Stokes light from each correlation peak can be temporally resolved. The interval of
optical pulses is set to double the length of the FUT to avoid the overlap of reflectedsignals. Then, by adjusting the relative phase, at the right time when the Stokes lightfrom a particular correlation peak returns, it is heterodyned with the reference light,
which is also converted into optical pulses with the same width tW. Thus, it becomes
possible to arbitrarily select any particular correlation peak within the FUT.

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4. Enlargement of measurement range based on temporal gating scheme

4. 3

Verification experiments

The structure of the FUT used for the verification experiments is shown in Figure 4.3. It
was composed of a 1-km standard SMF, in which about 0.1-% strain was applied to a
3-m section (990 - 993 m) fixed on a translation stage using epoxy glue (It is difficult toapply accurately 0.1-% strain to a section as long as 3 m due to the FUT’s own weight).
One end of the FUT was spliced to a circulator, and the other end was kept open. The

Figure 4.3

Figure 4.4

Structure of the FUT.

Measured distribution of BGS.

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4. Enlargement of measurement range based on temporal gating scheme

overall sampling rate of the measurement for a single position was 50 Hz.
In order to experimentally confirm that, without the temporal gating scheme, themeasurement cannot be performed correctly if there are multiple correlation peaks
within the FUT, first, we consider the case where there is no undesired correlation peak
(N = 0). The modulation frequency fm was 68.40 – 68.84 kHz, which corresponds to ameasurement range dm of 1.5 km according to Equation (2.2). The amplitude of thefrequency modulation Δf was 5.4 GHz, and the nominal spatial resolution Δz was
calculated to be about 2.6 m from Equation (2.1). Figure 4.4 shows the measured
distribution of the Brillouin gain spectrum (BGS) along the FUT. The BGS at thestrain-applied section was recognized. Figure 4.5 shows the distribution of the BFS. The
applied strain of 3 m was successfully detected. The change of the BFS was about 60
MHz, which agrees with the applied strain of about 0.1 %. The accuracy of themeasurement at a single position was about +/– 5 MHz, which corresponds to the strainof +/– 0.01 % (+/– 100 με) in this experiment.

Figure 4.5

Measured distribution of BFS.

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4. Enlargement of measurement range based on temporal gating scheme

Next, we consider the effect of multiple correlation peaks within the FUT. By
adjusting fm and Δf, the spatial resolution was constantly kept to 2.6 m, with one of thecorrelation peaks within the strain-applied section. The interval between the correlation
peaks was set to 1.5 km, 753 m, 377 m, 188 m, and 94 m, which correspond to the cases
where there are 0, 1, 2, 4, and 9 undesired correlation peaks in the 1-km FUT,
respectively.
As shown in Figure 4.6, when there is no undesired correlation peak (N = 0), the
BGS has its peak at about 10.9 GHz corresponding to the applied strain. However, when
there is one undesired correlation peak (N = 1), the peak at 10.9 GHz is overlapped withthat at 10.85 GHz corresponding to zero strain, which makes distributed strain
measurement impossible. The further the number of the undesired peaks is increased,
the larger the peak at 10.85 GHz becomes, and so the peak at 10.9 GHz becomes

Figure 4.6 Measured BGS without the temporal gating scheme applied, when there
are multiple correlation peaks within the FUT. The length of the FUT is 1 km. dm
represents the interval between the correlation peaks, and N the number of undesired
peaks within the FUT.

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4. Enlargement of measurement range based on temporal gating scheme

unobservable. Thus, it was confirmed that the basic BOCDR measurement without thetemporal gating scheme cannot be performed correctly if there are multiple correlation
peaks within the FUT.
Then, we verified the operation of the temporal gating scheme, using the two
LiNbO3 IMs inserted before the EDFAs in the pump path and the reference path in
Figure 4.1. The same 1-km SMF was used as the FUT, in which strain was applied tothe same 3-m section (990 - 993 m). The modulation frequency fm was 276.1 kHz,
which corresponds to a 377-m interval of correlation peaks according to Equation (2.2).
This means that there are three correlation peaks (two undesired peaks) within the FUT.

Figure 4.7 Measured BGS when (a) the first, (b) the second, and (c) the third
correlation peaks were selected, with (blue) and without (orange) strain applied tothe section corresponding to the third correlation peak.

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4. Enlargement of measurement range based on temporal gating scheme

The modulation amplitude Δf was set to 1.4 GHz, and the spatial resolution Δz was
calculated to be 2.6 m from Equation (2.1). These conditions are almost the same as
those for the experiment already described above (See Figure 4.6, N = 2). According toEquation (4.2), the width and the period of the optical pulses were set to 1.81 μs and11.50 μs, respectively (duty cycle = 15.7 %). The overall sampling rate of the BGS
measurement for a single position was 50 Hz.
The changes of the BGS with and without strain applied when each peak was
selected are shown in Figure 4.7. The relative phase differences of optical pulses were226, 113, and 0 degrees for Figures 4.7(a), (b), and (c), respectively, where a positive
phase difference means that the phase of the reference pulses is faster than that of thepump pulses. In Figures 4.7(a) and (b), the BGS shows hardly any change because theselected correlation peaks are outside the strain-applied section. In contrast, in Figure
4.7(c), the peak of the BGS shifts because the selected correlation peak is within thestrain-applied section. Thus, the effectiveness of the temporal gating scheme wasexperimentally verified.

4. 4

Distributed strain measurement

Finally, a distributed strain measurement based on the temporal gating scheme was
performed. Figure 4.8 shows the structure of the FUT. Strain of 0.3% was applied to a

Figure 4.8

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Structure of the FUT.

60

4. Enlargement of measurement range based on temporal gating scheme

Figure 4.9

Measured distribution of BGS.

90-cm section (990 – 990.9 m). The modulation frequency fm was 275.65 – 276.25 kHz,and the modulation amplitude Δf was set to 5.4 GHz, and so the spatial resolution Δz
was calculated to be 66 cm. Figures 4.9 and 4.10 show the measurement results of the
distribution of the BGS and the BFS, respectively. The strain-applied 90-cm section was
clearly detected. The change of the BFS was about 150 MHz, which is in good
agreement with the applied strain of 0.3 %. The accuracy of the measurement at a single
position was about +/– 20 MHz, which corresponds to a strain resolution of +/– 0.04 %(+/– 400 με) in this experiment.
Thus, we succeeded in achieving 1-km measurement range and 66-cm spatial
resolution simultaneously. Their ratio NR is calculated to be 1515, which is about threetimes as large as that of the basic BOCDR system (about 570). In order to enhance NR
further by this method, the S/N ratio of the system must be improved (See Chapter 8 forthe improvement on the S/N ratio).

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4. Enlargement of measurement range based on temporal gating scheme

Figure 4.10

4. 5

Measured distribution of BFS.

Conclusions

In this Chapter, a temporal gating scheme was newly developed to enlarge themeasurement range of the BOCDR system while maintaining the high spatial resolution.
In the experiment, 66-cm spatial resolution and 1-km measurement range were
simultaneously achieved with 50-Hz sampling rate. This means that the ratio between
the measurement range and the spatial resolution was enhanced from the conventional
value 570 to 1515.

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5. Enlargement of measurement range based on double-modulation scheme

5

Enlargement of measurement range
based on double-modulation scheme

In this Chapter, we demonstrate a double-modulation scheme to enlarge themeasurement range of Brillouin optical correlation-domain reflectometry (BOCDR)
while maintaining the spatial resolution. In this scheme, the frequency 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-kmmeasurement

range

were

also

simultaneously achieved when a noise-floor compensation technique was employed.

5. 1

Introduction

As was mentioned in Chapter 3, BOCDR suffers from a trade-off between themeasurement range and the spatial resolution. Their ratio NR was fixed at approximately
570. To obtain higher NR, a temporal gating scheme was implemented in Chapter 4,
where any correlation peak within the fiber under test (FUT) can be arbitrarily selectedbased on a time-domain technique. In the experiment, 66-cm resolution and 1-km
measurement range were simultaneously achieved. The ratio NR was 1515, which isabout 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, amultiple-modulation scheme is known to be an alternative method to obtain higher NR[73], where the frequency of the laser output is simultaneously modulated with multiple
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5. Enlargement of measurement range based on double-modulation scheme

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 threetimes.
In this Chapter, we demonstrate a double-modulation scheme to enlarge themeasurement 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 their amplitudes. Then, the operation principle of the scheme is theoreticallyanalyzed and simulated. 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.

Figure 5.1

Experimental setup of BOCDR with the double-modulation scheme.

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5. Enlargement of measurement range based on double-modulation scheme

5. 2

Double-modulation scheme

One 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 ismultiplied while the spatial resolution is maintained. Along with the temporal gating
scheme developed in Chapter 4, the double-modulation scheme is an effective method
for this purpose, and was applied to BOCDA [73].
The experimental setup of BOCDR based on the double-modulation scheme isdepicted in Figure 5.1. The pump light and the reference light are sinusoidally
frequency-modulated with two different frequencies, f0 (+ fε) and m f0, where f0 is afundamental frequency, m is an integer, and fε (~ 0.5 kHz) is needed to avoid beating
between the two frequencies, which causes large fluctuations of the Brillouin gain
spectrum (BGS). The amplitudes of the modulation at f0, Δf1, and at m f0, Δfm, are set to
be several hundreds of MHz (difficult to measure accurately due to the frequency
characteristics of the laser circuit) and about 5.4 GHz (a little lower than a half of the

Figure 5.2

Operating principle of double-modulation scheme.

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5. Enlargement of measurement range based on double-modulation scheme

Brillouin frequency shift (BFS) in silica fibers), respectively. Then, as shown in Figure
5.2, the spatial resolution is determined by m f0, while the correlation peaks of which theorders are not multiples of m are suppressed by f0. Since the modulation at f0 does not
influence on the resolution due to the low Δf1, it becomes possible to achieve the spatial
resolution determined by m f0 and the measurement range determined by f0
simultaneously, leading to a larger NR by m times.

5. 3

Theoretical analysis and simulation

The operation principle of the double-modulation scheme was theoretically analyzed.
The frequency modulation of the laser output is represented asf (t ) = f c + Δf m sin(2πmf 0 t ) + Δf1 sin(2πf 0t ) ,(5.1)

where fc is the center frequency. Then, the electric field of the laser output E(t) is
A

E

A

A

E

A

expressed as

E (t ) = exp(− jΦ(t )) ,

(5.2)

where

Figure 5.3

Synthesized coherence functions with the modulation at f0 only.

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5. Enlargement of measurement range based on double-modulation scheme

Figure 5.4

Synthesized coherence functions with the modulation at 4 f0 only.

Φ(t ) = ∫ 2πf (t ′)dt ′t

0= 2πf c t −Δf m(cos(2πmf 0t ) − 1) − Δf1 (cos(2πf 0t ) − 1) .
mf 0
f0

(5.3)

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 thelight source, or in other words, the autocorrelation function of the electric field of thelight source [93, 94]. Therefore, the absolute value of the optical coherence function is
calculated asγ (τ d ) = lim

T

1 2
T exp(− jΦ (t ) ) exp( jΦ (t − τ d ) )dt
T →∞ T ∫−
2

T
⎡ ⎧
⎛
⎛
Δf m
Δf
1 2
⎛ τ ⎞⎞⎛ τ ⎞ ⎞ ⎫⎤sin (πmf 0τ d )sin ⎜⎜ 2πmf 0 ⎜ t − d ⎟ ⎟⎟ + 2 1 sin (πf 0τ d )sin ⎜⎜ 2πf 0 ⎜ t − d ⎟ ⎟⎟⎬⎥ dt
T exp ⎢ j ⎨− 2πf cτ d + 2∫
T →∞ T −
mf 0
f0
2 ⎠⎠
2 ⎠ ⎠⎭⎦⎥
⎝
⎝
⎝
⎝
2
⎣⎢ ⎩

= lim

T
⎛ Δf m
⎞
⎞
⎧
⎧
1 2 ∞
⎛ τ d ⎞⎫ ∞ ⎛ Δf1⎛ τ ⎞⎫
⎜
⎟
π
τ
π
2
sin
exp
2
sin (πf 0τ d )⎟⎟ exp⎨ j 2πqf 0 ⎜ t − d ⎟⎬dt
J
(
mf
)
j
pmf
⎜ t − ⎟⎬ ⋅ ∑ J q ⎜⎜ 2
⎨
∑
T
p
d
0
0
⎜ mf
⎟
T → ∞ T ∫−2 ⎠⎭ q = −∞ ⎝ f 0
2 ⎠⎭
⎝
⎝
⎩
⎩
0
⎝
⎠
⎠
2 p = −∞= lim

T
⎛ Δf m⎞⎛ Δf⎞⎧
1 2 ∞ ∞⎛ τ ⎞⎫⎜sin (πmf 0τ d )⎟⎟ ⋅ J q ⎜⎜ 2 1 sin (πf 0τ d )⎟⎟ ⋅ exp ⎨ j 2π ( pm + q ) f 0 ⎜ t − d ⎟⎬dt
T ∑ ∑ J p⎜2
T →∞ T ∫−2 ⎠⎭⎝⎩⎝ mf 0⎠⎝ f0⎠
2 p = −∞ q = −∞

= lim

∞
⎛ Δf
⎞
⎛ Δf
⎞
= ∑ J p ⎜⎜ 2 m sin (πmf 0τ d )⎟⎟ ⋅ J − pm ⎜⎜ 2 1 sin (πf 0τ d )⎟⎟ ,p = −∞⎝ mf 0⎠⎝ f0⎠

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67

5. Enlargement of measurement range based on double-modulation scheme

Figure 5.5

Synthesized coherence functions with the modulation at f0 and 4 f0.

where τd is the time delay and Jp(x) is the p-th Bessel function of the first kind. When m>> 1, Equation (5.4) is approximately equal to⎛ Δf m⎞⎛ Δf⎞sin (πmf 0τ d )⎟⎟ ⋅ J 0 ⎜⎜ 2 1 sin (πf 0τ d )⎟⎟⎝ mf 0⎠⎝ f0⎠ ,γ (τ d ) ≈ J 0 ⎜⎜ 2

(5.5)

which shows that the synthesized coherence function in the double-modulation scheme
is roughly given by the product of the coherence functions synthesized into a series of
periodical delta-function-like peaks by each modulation frequency.
Based on Equation (5.4), we simulated the synthesized coherence function when m= 4, as shown in Figures 5.3, 5.4, and 5.5. The ratio of the modulation amplitudes (Δf4 /Δf1) was set to 10. In Figure 5.5, the 1st, 2nd, 3rd, 5th, 6th, 7th, and 9th correlation
peaks were suppressed, which shows that the measurement range was multiplied by 4times while maintaining the spatial resolution.

5. 4

Verification experiments

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Figure 5.6

Measured strain-dependence of BGS without double-modulation scheme.

The effectiveness of the double-modulation scheme was experimentally verified. As thetwo modulation frequencies, f0 and 5f0 were used (Δf5 = 5.4 GHz), where f0 was set to
68.481 kHz. According to Equations (2.1) and (2.2), the spatial resolution and themeasurement range determined by the conventional single modulation at 5f0 were 53.1
cm and 302.1 m, respectively. A single-mode fiber (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 (PCs) so that the peak intensity of BGS
without strain applied becomes maximal. Averaging was conducted 10 times to measure
one BGS.
Figure 5.6 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,
the change of BGS was not observed as a clear shift of the peak. Here, a kink observed

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5. Enlargement of measurement range based on double-modulation scheme

Figure 5.7

Measured strain-dependence of BGS with double-modulation scheme.

at 10.9 GHz was caused by range switching of the electrical spectrum analyzer (ESA).
In contrast, Figure 5.7 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 seems to originate
from the other correlation peaks that were not completely suppressed.

5. 5

Distributed strain measurement

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). Withf0 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 Section. The measured distributionsof BGS and BFS with the single modulation at 5f0 are shown in Figures 5.8 and 5.9,
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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
double-modulation scheme with f0 and 5f0 are shown in Figures 5.10 and 5.11. The
strain-applied 90-cm section was correctly detected. The measurement accuracy in thisexperiment was about +/– 7 MHz, corresponding to about +/– 120 με. The ratio NR was
2845 (= 1.51 km / 53.1 cm), which is much higher than 1515 obtained in Chapter 4 in
the temporal gating scheme.
Finally, the double-modulation scheme was implemented with f0 and 10f0 (Δf10 = 5.4
GHz) using a noise-floor compensation technique, which is proposed in Chapter 8. A
strain of 0.15% was applied to a 40-cm section (990.0 – 990.4 m). With f0 swept from68.362 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 areshown in Figure 5.12 and 5.13. Although the S/N ratio was deteriorated compared tothat in Figure 5.10, the strain-applied 40-cm section was successfully detected. The
measurement accuracy was about +/– 15 MHz, corresponding to about +/– 260 με.

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5. Enlargement of measurement range based on double-modulation scheme

Figure 5.8
Measured distribution of BGS when the doublemodulation scheme was not employed.

Figure 5.9
Measured distribution of BFS when the doublemodulation scheme was not employed.

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5. Enlargement of measurement range based on double-modulation scheme

Figure 5.10 Measured distribution of BGS when the doublemodulation scheme was employed (NR = 2845).

Figure 5.11 Measured distribution of BFS when the doublemodulation scheme was employed (NR = 2845).

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5. Enlargement of measurement range based on double-modulation scheme

Figure 5.12 Measured distribution of BGS with the double-modulation scheme
when the noise-floor compensation technique was employed (NR = 5690).

Figure 5.13 Measured distribution of BFS with the double-modulation scheme
when the noise-floor compensation technique was employed (NR = 5690).

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5. Enlargement of measurement range based on double-modulation scheme

5. 6

Conclusions

In this Chapter, we developed a double-modulation scheme to mitigate the trade-off
between the measurement 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

and1.5-kmmeasurement

range

were

also

simultaneously achieved when a noise-floor compensation technique was employed.
These results mean that the ratio between the measurement range and the spatial
resolution was enhanced from the conventional value 570 (or 1515 obtained in Chapter4) to 2845 or 5690.

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6. Enhancement of sampling rate utilizing optical heterodyne detection

6

Enhancement of sampling rate utilizing
optical heterodyne detection

In this Chapter, we examine the possibilities of improvement on the signal-to-noise(S/N) ratio and the sampling rate as well as cost reduction with a new configuration of
Brillouin optical correlation-domain reflectometry (BOCDR) based on optical
heterodyne detection. The system uses a single-sideband modulator (SSBM) with fast
Fourier transform (FFT) and contains no electrical spectrum analyzer (ESA). In theexperiment, the S/N ratio was not as good as that of the conventional BOCDR, but the
sampling rate was enhanced to 400 Hz. Furthermore, noise inherent to this scheme wasobserved and discussed.

6. 1

Introduction

In Chapter 2, we obtained 13-mm spatial resolution and 50-Hz sampling rate. However,this resolution, which is closely related to the S/N ratio, was limited by the electricalnoise of the ESA. The sampling rate was also limited by the sweep rate of the ESA.
Therefore, if BOCDR can be implemented without using the ESA, the S/N ratio and thesampling rate are expected to be improved, and besides, the system cost can be reduced.
In this Chapter, we implement a new scheme of BOCDR using a SSBM with FFT,
which contains no ESA. In this scheme, the sampling rate was 400 Hz, but the S/N ratio
was not improved. In addition, noise inherent to this scheme was observed anddiscussed.

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6. Enhancement of sampling rate utilizing optical heterodyne detection

6. 2

Optical heterodyne detection

The implementation of BOCDR without using an ESA is one of the methods to improve
the S/N ratio and the sampling rate and to reduce the cost. The function of the ESA isrealized by a digitizer (analog-to-digital converter) and FFT on the computer. Since thedigitizer has an upper limit of its detectable frequency (500 MHz), the Brillouin gain
spectrum (BGS) at frequency fB = 10.86 GHz needs to be down-shifted to less than 500
MHz. Therefore, an SSBM was employed to down-shift the frequency of the reference
light, leading to the down-shifted frequency of the heterodyned beat signal.
The experimental setup is depicted in Figure 6.1. The configuration of the pump
path is the same as that described in Chapter 2. In the reference path, we employed a
5-km delay fiber to control the order of the correlation peak, an SSBM to down-shift thefrequency of the heterodyned beat signal, an erbium-doped fiber amplifier (EDFA) toenhance the beat signal, and an optical filter to improve the suppression ratio by the
SSBM and to suppress the amplified spontaneous emission (ASE) noise of the EDFA. A

Figure 6.1

Experimental setup of BOCDR using optical heterodyne detection.

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6. Enhancement of sampling rate utilizing optical heterodyne detection

microwave generator was used to adjust the amount of the frequency shift by the SSBM.
The optical beat signal of the reference light and the Stokes light was detected withbalanced photo-detectors (PDs) and converted to an electrical signal. After being
amplified with an electrical pre-amplifier, the signal was directed to a digitizer. After
FFT, the heterodyned beat spectrum was observed.

6. 3

Experiments

First, we verified the operation of the SSBM. Figure 6.2 shows the measured optical
spectra of the reference light before the SSBM, after the SSBM, and after the SSBM,
the EDFA and the optical filter. Here, the microwave frequency fMW was set to 10.51
GHz. With the SSBM, the components at undesired frequencies were suppressed bymore than 25 dB. By additionally using the EDFA and the optical filter, the suppression
ratio was enhanced to about 45 dB.

Figure 6.2

Measured optical spectra of the reference light.

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6. Enhancement of sampling rate utilizing optical heterodyne detection

Figure 6.3

Figure 6.4

Measured BGS at each microwave frequency.

Measured BGS with and without strain applied to the FUT.

Next, we confirmed the down-shift of the BGS. No modulation was applied to thelaser frequency, and a standard 5-m single-mode fiber (SMF) was used as an FUT.

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Figure 6.3 shows the measured electrical spectra in the range lower than 500 MHz
observed with an ESA when the microwave frequency fMW was set to 10.41, 10.51,
10.61, 10.71, and 10.81 GHz. The BGS in each case was observed at the frequency fB –fMW, where fB is about 10.86 GHz. When fMW was 10.51 GHz, if strain was applied to
the whole length of the FUT, the BGS shifted towards the upper frequency, as shown in
Figure 6.4. These results indicate that the BGS was correctly down-shifted to the lower
frequency region. The large component around 0 Hz is considered to be the 1/f noise of
the ESA.
Then, we realized the function of the ESA by using a digitizer (NI-5152) and FFTwith a flat-top window, which can acquire the signal of lower than 500 MHz. The
electrical spectrum observed in this scheme is shown in Figure 6.5, of which theordinate is not normalized. Averaging was applied 4 times and a 5-m SMF was used as
the FUT. The microwave frequency fMW was 10.51 GHz, so the BGS was observed atabout 350 MHz. The S/N ratio of this scheme was, however, lower than that of the

Figure 6.5

BGS measured with the digitizer and FFT.

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6. Enhancement of sampling rate utilizing optical heterodyne detection

conventional BOCDR using the ESA, probably due to the frequency characteristics ofthe digitizer and the pre-amplifier. On the other hand, when no averaging was applied,
the sampling rate was enhanced to 400 Hz, which is 8 times higher than that of theconventional BOCDR.
Finally, we investigated the BGS when sinusoidal modulation was applied to thelaser frequency for a distributed measurement. Figure 6.6 shows the measured electrical
spectra observed with the ESA, when the modulation amplitude Δf was increased from0 to 200 MHz. The modulation frequency fm was set to 13.223 MHz, resulting in themeasurement range dm = 7.8 m according to Equation (2.2). As Δf increases, the spatial
resolution decreases according to Equation (2.1), which leads to the reduction of thereflected signal from the corresponding section of the FUT. Therefore, it is valid that the
BGS gradually became small. However, at the same time, noise began to spread from 0
Hz toward higher frequency region. When Δf was 200 MHz, which corresponds to thetheoretical spatial resolution Δz = 37 cm, the noise began to overlap the BGS and it
became difficult to detect the peak.

Figure 6.6Spectral change near BGS with increasing modulation amplitude Δf.

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6. 4

Discussion on noise

There are two noise factors inherent to the new scheme of BOCDR. The first one is thebeat between the Rayleigh-scattered light and the undesired component of the reference
light at frequency f0, which cannot be suppressed sufficiently with the SSBM. Since
these two have the same center frequencies, when the laser frequency is sinusoidally
modulated with the amplitude Δf, their beat spreads from 0 to 2Δf. Therefore, thecondition under which this noise does not overlap the BGS is given by
fL

Δf < 2 ,(6.1)

where fL (= fB – fMW) is the peak frequency of the down-shifted BGS, and is, forexample, 350 MHz.
The second one is the “folded-back noise” of the beat between the Brillouinscattered light and the down-shifted reference light. The optical spectra of the reference

(a)

(b)

Figure 6.7 Schematics of (a) optical spectra of the reference light and thereflected light, and (b) electrical spectra of their heterodyned beat signal.

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6. Enhancement of sampling rate utilizing optical heterodyne detection

light and the reflected light are schematically shown in Figure 6.7(a). The down-shifted
center frequency of the reference light is f0 – fB + fL. When these two light beams areheterodyned, their electrical beat spectrum becomes as shown in Figure 6.7(b). Since
the negative frequency component is folded back to the positive one, this noise also
overlaps the BGS at frequency fL. The condition under which this noise does notoverlap the BGS is given by

Δf < fL .

(6.2)

Considering that, in Figure 6.6, the noise was present even when Δf was as small as,
for example, 80 MHz, the noise observed in the experiment is considered to be the firstone, the beat between the Rayleigh-scattered light and the undesired component of thereference light. Equation (6.1) agrees well with the experimental result that, when Δf
was 200 MHz, the noise began to overlap the BGS at 350 MHz.
Finally, we performed the experiment to verify the origin of the noise. By adjusting

Figure 6.8 Measured optical spectra of the reference light before
and after the filter adjustment.

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6. Enhancement of sampling rate utilizing optical heterodyne detection

Figure 6.9 Measured electrical spectra near BGS before and after
the filter adjustment.

the optical filter installed after the SSBM, the suppression ratio of the initial frequency
component was decreased, while other frequency components did not largely change.
Figure 6.8 shows the measured optical spectra of the reference light before and after the
adjustment of the optical filter. The suppression ratio was decreased from 45 to 33 dB.
The electrical spectra in the two cases observed with the ESA are shown in Figure 6.9.

Δf was set to 200 MHz, at which the noise begins to overlap the BGS. It is found thatthe amount of the noise is dependent on the suppression ratio of the SSBM. Thus, theorigin of the noise was verified.

6. 5

Conclusions

In this Chapter, we implemented a new scheme of BOCDR using an SSBM with FFT,and examined the possibilities of improvement on the S/N ratio and the sampling rate as

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6. Enhancement of sampling rate utilizing optical heterodyne detection

well as cost reduction. In the experiment, the S/N ratio was not good compared to theconventional BOCDR, but the sampling rate was enhanced to 400 Hz. Besides, noise
inherent to this scheme was observed, and its origin was theoretically andexperimentally clarified.

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7. Application to polarization beat length distribution measurement

7

Application to polarization beat length
distribution measurement

In this Chapter, we demonstrate that the polarization beat length distribution along asingle-mode fiber (SMF) can be measured with Brillouin optical correlation-domainreflectometry (BOCDR). The measurement was successfully performed with uniquefeatures such as one-end access, 25-cm spatial resolution, and 20-Hz sampling rate.

7. 1

Introduction

For high-speed fiber-optic communication systems, such as those with transmission rateof 40 Gbps and above, polarization-mode dispersion (PMD), that is, the differential
group delay (DGD) between the two polarization-mode propagations in the SMF, is oneof the most serious effects that reduce the transmission capacity of the fibers. Therefore,
the knowledge of DGD is of high interest. Various methods have been used for the PMD
measurement [107, 108], but these methods give us no distributed information about
DGD along the fiber but only the overall DGD of the link. A simple method based onRayleigh reflectometry using polarized light, which is called polarization-sensitive
optical time-domain reflectometry (POTDR), has been proposed [109, 110], and its
potential to measure local birefringence (the beat length) over a long distance wasdemonstrated, but with a low spatial resolution and a long integration time [111]. Thebeat length measurements with a very high resolution have been achieved bypolarization-sensitive optical frequency-domain reflectometry (POFDR) [112], but overa short distance. Recently, as an alternative approach, the polarization dependence ofDissertation 2009, The University of Tokyo86

7. Application to polarization beat length distribution measurement

stimulated Brillouin scattering (SBS) has been used to measure the beat length
distribution along the fiber [113, 114]. One of the methods is based on Brillouin opticalcorrelation-domain analysis (BOCDA), and has obtained a spatial resolution as high as
2.7 cm [113]. However, in these methods, we need to access both ends of the fiber under
test (FUT), which is often not feasible in long-range application, and cannot work
completely when the FUT has even one breakage point. In most long-range practicalapplications, one-end access reflectometers are more favorable.
In this Chapter, we propose a new method to measure the beat length distribution
based on BOCDR, which was originally proposed in Chapter 2 to measure the
distribution of strain and/or temperature along an FUT. This method shows uniquefeatures such as one-end access, random access to measuring positions, high spatial
resolution, and high-speed measurement.

7. 2

Principle

In BOCDR, the peak power P of the BGS observed at the electrical spectrum analyzer(ESA) is given as
P = κ < E ref ･ E *Stokes > ,(7.1)

where E ref and E Stokes are the electrical fields of the reference light and the Stokes light,
respectively, at the heterodyne receiver, κ is a proportionality coefficient, and < ･ >stands for time-averaging operation. When the modulation frequency fm is changed toperform a distributed measurement, E ref is kept constant but E Stokes changes according
to the birefringence distribution along the FUT. As a consequence, P varies reflecting
the distribution of the birefringence. Thus, by measuring the distribution of the peak
power P of the BGS by the use of BOCDR, we can obtain distributed information ofbirefringence and estimate the distribution of polarization beat length. Here, due to theroundtrip of the backscattered Stokes light, the beat length LB is obtained as twice as theDissertation 2009, The University of Tokyo87

7. Application to polarization beat length distribution measurement

observed spatial period of P variation [115].
In theory, the beat length LB (m) can be calculated as [116]R| n 4p λ(1+ν)
r |,2

LB (m) =

3

2

(7.2)

where λ (μm) is the wavelength of the light, R (cm) the radius of the mandrel, n therefractive index, p the strain-optical coefficient, ν the Poisson’s ratio, and r (μm) theradius of the fiber cladding.

7. 3

Verification experiments

The experimental setup was the same as that in Chapter 2. A 1-km SMF was used as an
FUT, which was wound on a mandrel with radius R = 10.0 cm to induce birefringenceintentionally. One end of the FUT was spliced to a circulator, and the other end was kept
open. The sampling rate was set to about 20 Hz, which is higher than that of POTDR

Figure 7.1

Measured BGS at the relative positions 39 m and 45 m (R = 10.0 cm).

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7. Application to polarization beat length distribution measurement[109, 110]. The 400-m position from the circulator was defined as the relative position 0
m. First, the oscillation of the peak power of the BGS according to the measuring
positions was observed. The BGSs at the relative positions 39 m and 45 m are shown in
Figure 7.1. Since, the peak of the BGS was observed at 10.896 GHz when no
modulation was applied to the laser frequency, the BGS peak power is defined as the
BGS power at this frequency. The BGS peak power decreased from –66.1 dBm to –67.1
dBm, as the measuring positions changed. Then, a distributed measurement of the BGS
peak power was performed at every 1 m from the relative position 0 m to 100 m. The
modulation frequency fm was changed from 98.19 kHz to 103.09 kHz, and themodulation amplitude Δf was set to 5.4 GHz, which corresponds to the spatial
resolution Δz of about 1.8 m and the measurement range dm of about 1 km by Equations(2.1) and (2.2). The measured distribution of the Stokes light is shown in Figure 7.2,
where a periodical oscillation was observed. In order to estimate its spatial period, thepower spectral density (PSD) was calculated using fast Fourier transform (FFT), and isshown in Figure 7.3. The peak of the PSD appeared at 0.079 /m, which corresponds tothe spatial period of 12.7 m. Therefore, LB is calculated to be 25.4 m.
Next, in order to verify the reproducibility, a 100-m SMF was used as an FUT,
which was wound on a mandrel with radius R = 7.4 cm. One end of the FUT was kept
open. The 40-m position from the circulator was defined as the relative position 0 m,
and the measurement was performed at every 30 cm from the relative position 0 m to 30
m. With fm changed from 666.07 kHz to 674.20 kHz and Δf set to 2.7 GHz, Δz and dm
were calculated to be about 55 cm and about 155 m, respectively. The distribution of the
BGS peak power and its PSD are shown in Figures 7.4 and 7.5, respectively. The peakof the PSD appeared at 0.165 /m, which corresponds to the spatial period of 6.06 m andthe beat length LB of 12.1 m.

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7. Application to polarization beat length distribution measurement

Figure 7.2 Measured distribution of the BGS peak power when the mandrel
radius R was 10.0 cm.

Figure 7.3 Calculated PSD of the BGS peak power distribution in log scale
when the mandrel radius R was 10.0 cm. The inset shows the same graph inlinear scale.

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7. Application to polarization beat length distribution measurement

Figure 7.4 Measured distribution of the BGS peak power when the mandrel
radius R was 7.4 cm.

Figure 7.5 Calculated PSD of the BGS peak power distribution in log scale
when the mandrel radius R was 7.4 cm.

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7. Application to polarization beat length distribution measurement

Figure 7.6 Measured distribution of the BGS peak power when the mandrel
radius R was 3.1 cm.

Figure 7.7 Calculated PSD of the BGS peak power distribution in log scale
when the mandrel radius R was 3.1 cm.

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7. Application to polarization beat length distribution measurement

Figure 7.8 Measured distribution of the BGS peak power with no bending
applied (R = ∞).

Then, a 5-m SMF wound on a mandrel with radius R = 3.1 cm was used as an FUT,
which is short enough to be straightened. One end of the FUT was spliced to a circulator,
and the other end was bent to suppress the Fresnel reflection. The position of thecirculator was defined as the relative position 0 m, and the measurement was performed
at every 10 cm along the entire length of the FUT. Since fm was changed from 1311.03
kHz to 1313.63 kHz and Δf was set to 3.0 GHz, Δz was about 25 cm and dm was about
78.8 m. The distribution of the measured BGS peak power is shown in Figure 7.6. The
power decreases drastically at the relative positions 0 m and 5 m, because, at the fiberends, the correlation peak is not completely present within the range of the FUT. Its
PSD is shown in Figure 7.7, where the peak appeared at 0.78 /m, corresponding to thespatial period of 1.28 m and the beat length LB of 2.56 m. Next, when whole the FUT
was straightened, a distributed measurement of the BGS peak power was performed atevery 20 cm along the entire length of the FUT. Experimental result is shown in Figure
7.8. The drastic power decrease is explicable in the same way as in Figure 7.6. No

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7. Application to polarization beat length distribution measurement

Figure 7.9 Polarization beat length as a function of the mandrel radius. The
curve shows the theoretical values.

periodical fluctuations were observed, which verifies that, when no bending is applied
to an SMF, the induction of birefringence is extremely small.
Figure 7.9 depicts the measured and theoretical beat length against the mandrel
radius. The theoretical values were calculated by substituting into Equation (7.2)
parameters: λ = 1.55 μm, n = 1.46, p = –0.15, ν = 0.17 [117], and r = 63 μm. The
experimental results seem to agree well with the theory. The slight discrepancy seems tooriginate from the following three factors: (i) The number of sampling points of the
PSD is not sufficient. (ii) When a long optical fiber is wound on a mandrel, small strain
will remain. As a consequence, the BGS shifts toward the upper frequency, and so thedetected power changes even if the polarization state does not change. (iii) Someparameters such as p and ν, which are difficult to measure, may slightly vary amongfibers, and their accurate values are unknown.

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7. Application to polarization beat length distribution measurement

7. 4

Distributed measurement

Finally, a distributed beat length measurement was performed using an FUT comprising
two SMFs with different mandrel radii. The schematic structure of the FUT is shown in
Figure 7.10. A 200-m SMF wound on a mandrel with radius R = 10.5 cm was spliced toa 100-m SMF wound on a mandrel with radius R = 7.4 cm. The 60-m position from thecirculator was defined as the relative position 0 m, and consequently, the mandrel radiuschanges at the relative position 40 m. The measurement of the BGS peak power was
performed at every 50 cm from the relative position 0 m to 100 m. The modulation
frequency fm was changed from 125.64 kHz to 130.95 kHz, and the modulation
amplitude Δf was set to 5.4 GHz, which corresponds to the spatial resolution Δz of
about 1.4 m and the measurement range dm of about 800 m. The experimental result isshown in Figure 7.11. The spatial period of the fluctuations certainly changed at therelative position 40 m. The calculated PSDs within the range of 0 – 40 m and 40 – 100m became maximal at frequency 0.17 /m and 0.067 /m, which correspond to the beatlengths LB of 11.76 m and 29.8 m, respectively. Their theoretical values are 15.6 m and31.5 m, respectively. Considering the error causes discussed in the preceding Section,

Figure 7.10

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Structure of the FUT.

95

7. Application to polarization beat length distribution measurement

Figure 7.11 Measured distribution of the BGS peak power. The mandrel radii
were 7.4 cm and 10.5 cm corresponding to the ranges of 0 – 40 m and 40 – 100m, respectively.

these experimental values are valid.
While a distributed beat length measurement based on BOCDR has been proposedin this paper, a polarization-sensitive optical correlation-domain reflectometry(POCDR) may also be possible, where Rayleigh-scattered light is spatially resolved bya correlation-domain method. At present, POCDR has not been reported yet. Since
Rayleigh scattering is stronger than spontaneous Brillouin scattering, the S/N ratio of
POCDR is expected to be higher than that of the BOCDR-based method. However,compared to self-heterodyne BOCDR, POCDR needs a frequency shifter in thereference path. Moreover, POCDR is less convenient than BOCDR because POCDR
itself cannot measure strain and/or temperature distribution, while BOCDR can measure
it without altering the experimental setup. Therefore, the BOCDR-based method and
POCDR have their own drawbacks and advantages.

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7. 5

Conclusions

In this Chapter, we presented that BOCDR can be used to perform a distributed
measurement of polarization beat length in SMFs. The measurement was successfully
performed with unique features such as one-end access, 25-cm spatial resolution, and
20-Hz sampling rate. The beat lengths of SMFs wound on mandrels with radii 10.0 cm,
7.4 cm and 3.1 cm were measured to be 25.4 m, 12. 1 m and 2.56 m, respectively, which
agreed well with the theoretical calculations. A distributed measurement was also
successfully performed using an SMF comprising two sections with different mandrel
radii.

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8. Stable entire-length measurement based on polarization scrambling

8

Stable entire-length measurement
based on polarization scramblingand noise-floor compensation

In this Chapter, we perform a stable high-speed entire-length measurement of strain
distribution based on Brillouin optical correlation-domain reflectometry (BOCDR) by
suppressing the signal fluctuations automatically using polarization scrambling. The
strain distribution along the entire length of a 100-m fiber under test (FUT) was
successfully measured with 40-cm spatial resolution and 19-Hz sampling rate. We also
improved a signal-to-noise (S/N) ratio by compensating the noise-floor of the electrical
spectrum analyzer (ESA).

8. 1

Introduction

In Chapter 7, it was demonstrated that BOCDR can be used to perform a distributed
measurement of polarization beat length. This measurement is based on the fact that theBrillouin-scattered signal obtained in BOCDR is sensitive to the state of polarization(SOP). However, due to this polarization dependence, frequent SOP optimization bymanually adjusting polarization controllers (PCs) was needed for a distributed
strain/temperature measurement along a long FUT, and consequently, the measurement
time became long in practice. In order to accomplish a stable high-speed distributed
measurement along a long FUT, the polarization effect needs to be suppressed
automatically. Several techniques have thus far been proposed to mitigate thepolarization dependence, including adaptive polarization controllers [118], polarization
diversity [75, 119], Faraday rotation [120], and polarization scrambling [121, 122].
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8. Stable entire-length measurement based on polarization scrambling

Among them, polarization scrambling is advantageous over the others on the point thatit can avoid the need of continuous actuation and the use of extra devices, and does notdeteriorate the sampling rate. Polarization scrambling has already been used to solve
polarization-originated problems, such as polarization mismatch in coherent detection[121] or polarization-dependent gain in optically-amplified fiber communication
systems [122].
In this Chapter, we perform a stable high-speed entire-length measurement of strain
distribution by suppressing the signal fluctuations with polarization scrambling. We
experimentally demonstrate a stable distributed strain measurement along the entire
length of a 100-m FUT with 40-cm spatial resolution and 19-Hz sampling rate. Besides,
we develop a new method to improve the S/N ratio of the system by compensating thenoise-floor of the ESA.

8. 2

Polarization scrambling in BOCDR

8. 2. 1

Principle

Figure 8.1

Experimental setup of BOCDR with a polarization scrambler.

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8. Stable entire-length measurement based on polarization scrambling

In BOCDR, the polarization scrambler (PSCR) changes the SOP of the light much fasterthan the sampling rate, and therefore the Brillouin gain spectrum (BGS) becomes
independent of the instantaneous SOP mismatch between the reference light and the
Stokes light. The experimental setup of BOCDR with polarization scrambling is
depicted in Figure 8.1. A PSCR which can modulate the SOP at 1 MHz [121, 122] wasemployed in the reference path. The other configurations are the same as those in
Chapter 2.
Here we analyze the effect of polarization scrambling, using the schematic
experimental setup depicted in Figure 8.2. The optical frequency of the laser output issinusoidally modulated, as given by
f r = f 0 + Δf sin 2π f mt .

(8.1)

Then the optical fields of the reference light and the Stokes light can be expressed ast
Er = E0 α rκ sκ c exp j ⎛⎜ 2π ∫ f r dt + φ ' (t ) ⎞⎟
0
⎝
⎠

⎛
⎞
Δf
Δf
= E0 α rκ sκ c exp j ⎜⎜ 2π f 0t −+ φ ' (t ) ⎟⎟,cos 2π f mt +
fm
fm
⎝
⎠

(8.2)

Figure 8.2 Schematic setup of BOCDR for the theoretical analysis of
the polarization scrambling scheme.

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8. Stable entire-length measurement based on polarization scrambling

ES = E0 α S (1 − κ s )(1 − κ c )

{

t1

t −τ

0

t1

}

exp j 2π ∫ f r dt + 2π ∫ ( f r − f B ) dt + φ ' (t − τ )⎧= E0 α S (1 − κ s )(1 − κ c ) exp j ⎨2π f 0 (t − τ )⎩− 2π f B (t − τ − t1 ) −⎫Δf
Δf
cos 2π f m (t − τ ) ++ φ ' (t − τ )⎬,
fm
fm
⎭

(8.3)

where E0 is the optical field amplitude of the laser output, αr and αS are factors which
account for optical loss or gain associated with the reference and the Stokes paths, κsand κc are the power coupling coefficients of the two fiber couplers, φ’(t) is the random
phase noise of the laser output, τ is the differential optical propagation time delay
between the reference light and the Stokes light, and t1 is the time when the pump lightis reflected at the correlation peak in the FUT. Er can be resolved into two orthogonal
polarization components of amplitude, as Er|| = Er cos η and Er⊥ = Er sin η, one of whichmatches the SOP of ES. Then the output intensity of the BGS can be expressed as

I = (ES + Er|| ) 2 + Er ⊥
= ES

2

+ Er

2

2

+ 2 Er|| ES ,
*

(8.4)

where < ･ > stands for time-averaging operation. Using Equations (8.2), (8.3) and(8.4), the output intensity is given as{

I = I 0 α r κ sκ c + α S (1 − κ s )(1 − κ c )+ 2 α r α S κ s (1 − κ s )κ c (1 − κ c ) ⋅ γ (τ ) ⋅ cosη

},

(8.5)

where I0 (= E02) is the input intensity, and γ(τ) isγ (τ ) = C 2π f 0τ + 2π f B (t − τ − t1 )−Δfcos 2π f mτ + φ ' (t ) − φ ' (t − τ ) ,
fm

(8.6)

where C is a constant.
Here, 2η is the angle subtended by the circle arc at the center of the Poincare spherejoining the SOPs at the heterodyne receiver [123]. Therefore, when polarization isDissertation 2009, The University of Tokyo101

8. Stable entire-length measurement based on polarization scrambling

scrambled,cos η = cos

π
4

=

1
2

(8.7)

is obtained, and thus, the output intensity is expressed as:{

I = I 0 α r κ sκ c + α S (1 − κ s )(1 − κ c )}.

+ 2α r α S κ s (1 − κ s )κ c (1 − κ c ) ⋅ γ (τ )(8.8)

Comparing Equation (8.8) with Equation (8.5), it is clear that the polarization-related
fluctuations of the BGS power in BOCDR can be suppressed with the polarization
scrambling.

8. 2. 2

Experiments

The structure of the FUT is shown in Figure 8.3. It was composed of a standard
single-mode fiber (SMF) with a length of about 100 m, in which 0.3-% strains wereapplied to a 1-m section (33.8 – 34.8 m) and a 50-cm section (76.8 – 77.3 m) fixed ontranslation stages using epoxy glue. One end of the FUT was spliced to a circulator, andthe other end was kept open. The modulation amplitude Δf was set to 3.3 GHz and themodulation frequency fm was changed from 735.86 to 766.28 kHz, which corresponds toFigure 8.3

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8. Stable entire-length measurement based on polarization scrambling

Figure 8.4 Measured distribution of BFS along the entire length of the
100-m FUT with (blue) and without (red) a polarization scrambling.

the measurement range dm of about 140 m and the spatial resolution Δz of about 40 cm
according to Equations (2.1) and (2.2). The span of the ESA was set to 10.763 – 11.063
GHz. The overall sampling rate of the BGS measurement for a single position was 19
Hz (including data processing time), and 1001 data were acquired for one BGS.
Therefore, the sampling rate of one datum is 19 kHz, which is over 50 times lower thanthe polarization modulation frequency of 1 MHz. The total measurement time was 40 s,
which can be set even shorter if the number of sensing points is reduced (currently, 760
points).
Figure 8.4 shows the measurement results of the distribution of the Brillouinfrequency shift (BFS) along the entire length of the FUT, with and without thepolarization scrambling. When polarization was not scrambled, at some positions where
the SOP was not optimized, the signal level largely fluctuated within the range of the
span of the ESA as the measuring position shifted, and consequently, the frequency at

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8. Stable entire-length measurement based on polarization scrambling

Figure 8.5 Magnified view of Figure 8.4 around the range of 30 – 40 mwith (blue) and without (red) a polarization scrambling.

which the power became maximal was unstable. Meanwhile, when polarization was
scrambled, the fluctuations were suppressed, and the large changes of the BFS werestably detected only at the strain-applied positions. The magnified views around thestrain-applied sections are shown in Figures 8.5 and 8.6. Thus, 1-m and 50-cm strains
were successfully detected with 40-second measurement time. The accuracy of themeasurement at a single position was about +/– 10 MHz, which corresponds to thestrain of +/– 0.02% (+/– 200 με) in this experiment.

8. 3

Noise-floor compensation

8. 3. 1

Principle

Next, we developed a new method to improve the S/N ratio of the system byDissertation 2009, The University of Tokyo104

8. Stable entire-length measurement based on polarization scrambling

Figure 8.6 Magnified view of Figure 8.4 around the range of 70 – 80 mwith (blue) and without (red) a polarization scrambling.

compensating the noise-floor of the ESA. Since BOCDR is based on weak spontaneous
Brillouin scattering, its S/N ratio is low especially when the spatial resolution is high.
The noise-floor compensation is performed by the following procedures: (1) suppress
the fluctuations of the BGS by polarization scrambling, (2) acquire the BGS with
sufficiently large strain applied, as noise-floor, and (3) after a conventional distributed
strain measurement, use the difference calculated by subtracting the noise-floor fromthe observed BGS, as “net BGS.”

8. 3. 2

Experiments

First, the effect of the compensation was experimentally verified when the measuring
position was fixed. Figures 8.7 and 8.8 show the measured BGS without and with thenoise-floor compensation, respectively, when the correlation peak was located at theDissertation 2009, The University of Tokyo105

8. Stable entire-length measurement based on polarization scrambling

Figure 8.7 Measured BGS without noise-floor compensation.
Strains of 0, 0.08, 0.16, 0.24, and 0.32% were applied.

Figure 8.8

Measured BGS with noise-floor compensation.

center of a 1-m strain-applied section. The resolution was set to 80 cm, and themagnitudes of the applied strains were 0, 0.08, 0.16, 0.24, and 0.32%. Averaging wasDissertation 2009, The University of Tokyo106

8. Stable entire-length measurement based on polarization scrambling

Figure 8.9

Measured distributions of BGS.

carried out 10 times for one BGS, and the sampling ratio was about 2 Hz. The large
strain used for acquiring the noise-floor was 0.5%. When the noise-floor was notcompensated, as shown in Figure 8.7, the width of the BGS changed according to the
BFS, that is, the magnitude of the applied strain. It became larger near the frequencies atwhich the noise-floor had relatively high power (e.g., when 0.24-% strain was applied),
which leads to the deterioration of the measurement accuracy. Meanwhile, when thenoise-floor was compensated, as shown in Figure 8.8, the width of the BGS was stable,
resulting in a higher measurement accuracy. The BGS power fluctuations in Figure 8.7
were larger than that in Figure 8.8, not only because the noise-floor shape was involvedin the power fluctuations but because the SOP was optimized. In Figure 8.8, the signal
power decreased around 11.04 GHz, which can be removed by employing a strain of
more than 0.5% as the large strain used to acquire the noise-floor. Thus, thiscompensation was confirmed to improve the S/N ratio of the system when themeasuring position was fixed.

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8. Stable entire-length measurement based on polarization scrambling

Figure 8.10 Measured distributions of BFS. The insets show the magnified
views around strain-applied positions.

Then, a distributed strain measurement was performed using this compensation. The
FUT was composed of a standard SMF with a length of about 100 m, in which 0.2- and0.14-% strains were applied to a 1-m section (33.8 – 34.8 m) and a 50-cm section (76.8– 77.3 m), respectively. One end of the FUT was spliced to a circulator, and the otherend was kept open. The modulation amplitude Δf was set to 5.4 GHz and themodulation frequency fm was about 750 kHz, which corresponds to the measurement
range dm of about 140 m and the spatial resolution Δz of about 24 cm. Averaging was
carried out 5 times for one BGS, and the sampling rate was about 4 Hz. The measured
distributions of BGS and BFS are shown in Figures 8.9 and 8.10, respectively. The S/Nratio was drastically improved compared to that in Chapter 2, and the measurement
accuracy at a single position was enhanced to about +/– 5 MHz, which corresponds tothe strain of +/– 0.01% (+/– 100 με). This result indicates that the influence of thereflected light from the correlation peak sidelobes is much smaller than the noise-floorof the ESA in BOCDR.

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8. Stable entire-length measurement based on polarization scrambling

8. 4Conclusions

We performed a stable entire-length measurement of strain distribution by suppressing
the BGS fluctuations with polarization scrambling. In the experiment, we demonstrated
a distributed strain measurement along the entire length of a 100-m FUT with 40-cm
spatial resolution and 19-Hz sampling rate. Furthermore, we developed a new methodof compensating the noise-floor of the ESA to improve the S/N ratio.

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9. Distributed strain measurement using tellurite glass fiber

9 Distributed strain measurement using
tellurite glass fiber

In this Chapter, a tellurite glass fiber with a high Brillouin gain was employed for a
distributed strain measurement with Brillouin optical correlation-domain reflectometry(BOCDR). The dependences of the Brillouin frequency shift (BFS) on temperature andstrain in the tellurite glass fiber were investigated, showing negative dependences withcoefficients of –1.14 MHz/K and –0.023 MHz/με. These negative dependences seem tooriginate from the negative dependences of the Young’s modulus of the tellurite fiber ontemperature and strain. Then, using this tellurite fiber, the distribution of the BFS
around a 1-cm strain-applied section was successfully measured with a nominal spatial
resolution of 6 mm.

9. 1

Introduction

In Chapter 2, we achieved a spatial resolution of 13 mm. Though this resolution is thebest ever reported in spontaneous Brillouin scattering-based reflectometers, it waslimited by the signal-to-noise (S/N) ratio of the system. So, the spatial resolution is
expected to be improved by using a specialty fiber with a large Brillouin gain
coefficient as a fiber under test (FUT) to enhance the S/N ratio.
In this Chapter, a tellurite glass fiber is employed in BOCDR to realize high-spatialresolution distributed strain sensing. Although the background loss (~0.02 dB/m at 1550nm) of the tellurite fibers is much higher than that of silica fibers (~0.0005 dB/m), bymaking use of their high Brillouin gain, we believe tellurite fibers can be used toDissertation 2009, The University of Tokyo

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9. Distributed strain measurement using tellurite glass fiber

develop short-range but high-spatial-resolution Brillouin sensors. First, the spatial
resolution of BOCDR using the tellurite fiber is theoretically evaluated. Next, thetemperature- and strain-dependences of the BFS in a tellurite fiber are investigated. It isfound that, with increasing temperature and strain, the BFS in the tellurite fiber shifts
toward lower frequency with coefficients of –1.14 MHz/K and –0.023 MHz/με. These
negative dependences seem to be caused by the negative temperature- andstrain-dependences of the Young’s modulus of the tellurite fiber. Finally, a distributed
strain measurement is performed by using this tellurite fiber as the FUT in BOCDR
with a nominal spatial resolution of 6 mm, which is the inherent limitation as describedlater.

9. 2

Tellurite glass fibers

Among various specialty fibers, tellurite glass fibers [124, 125] have been vigorously
studied due to their high refractive index (n = 2.03), high nonlinearity, and broad Ramangain bandwidth, and thus far been applied to develop some optical devices, such as

Table 9.1 n, BFS, and Δzmin of silica, bismuth-oxide,
As2Se3 chalcogenide, and tellurite fibers.

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9. Distributed strain measurement using tellurite glass fiber

ultra-wide-band Raman fiber amplifiers (RFAs) [126], efficient Tm3+-doped tellurite
fiber lasers [127], and carrier-envelope offset (CEO)-locked frequency combs [128]. In
addition to these applications, they can also be used as the gain medium for Brillouinscattering. Abedin [125] investigated the properties of stimulated Brillouin scattering(SBS) and the performance of slow light generation in an Er3+-doped tellurite fiber, andshowed that a tellurite fiber has a large Brillouin gain coefficient (gB ~ 1.7×10–10 m/W)
and is suitable for slow light generation.

9. 3

Inherent limitation of spatial resolution

The spatial resolution and the measurement range of BOCDR are given by Equations(2.1) and (2.2), where Equation (2.1) is valid when the modulation frequency fm is lower
than the Brillouin gain bandwidth ΔνB, as discussed in Chapter 3. In addition, Δf must

Figure 9.1 Experimental setup based on BOCDR for characterizing thetemperature dependences of specialty fibers.

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9. Distributed strain measurement using tellurite glass fiber

Figure 9.2

Structures of the FUT comprising the tellurite fiber.

Figure 9.3

Structures of the FUT comprising the Bi-NLF.

be lower than a half of the BFS of the FUT because of the behavior of Rayleighscattering-related noise as described also in Chapter 3. Therefore, under the condition of
fm = ΔνB, the limitation of the spatial resolution Δzmin is given, by the BFS, asΔzmin =cπ ⋅ n ⋅ BFS .

(9.1)

In Table 9.1, n, BFS, and Δzmin of silica, bismuth-oxide [129], As2Se3 chalcogenide[130], and tellurite fibers are summarized. About 6-mm spatial resolution is expected byusing a tellurite fiber.

9. 4

Temperature-dependence of BFS

We investigated the temperature-dependences of the BFS in not only a tellurite fiber but
also a bismuth-oxide highly-nonlinear fiber (Bi-NLF). The experimental setup is shownin Figure 9.1, which is basically the same as that in Chapter 8, where a polarization

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9. Distributed strain measurement using tellurite glass fiber

scrambler is installed in the reference path to suppress the Brillouin gain spectrum(BGS) fluctuations. The structures of the FUTs comprising a tellurite fiber and a
Bi-NLF are shown in Figures 9.2 and 9.3, respectively. Since it is difficult to directly
splice a tellurite fiber (5 m) and a Bi-NLF (1 m) to single-mode fibers (SMFs), a
dispersion-compensation fiber (DCF) (30 cm) [131] and a high-numerical-aperture fiber(HNAF) (30 cm) were employed between them, respectively. Each end of the tellurite
fiber and the Bi-NLF was bent to suppress the Fresnel reflection. Since the tellurite
fiber and the Bi-NLF were short, the measurement was conducted using BOCDR toplace the measurement window (the correlation peak) within the tellurite fiber and the
Bi-NLF; then the effects of the other fibers were removed. In the measurement of thetellurite fiber, Δf and fm were set to 1 GHz and 7.8028 MHz, respectively, whichcorrespond to the measurement range dm of 9.47 m and the spatial resolution Δz of
about 3 cm from Equations (2.1) and (2.2); in the measurement of the Bi-NLF, Δf and fm
were set to 2 GHz and 1.0654 MHz, respectively, corresponding to dm of 63.4 m and Δzof 79.9 cm. In general, the Brillouin gain bandwidth ΔνB depends on the power Pin of
the light beam injected into the fiber [132], and, in our experiment, it was 10 MHz in
the tellurite fiber (Pin = 28 dBm) and 79.2 MHz in the Bi-NLF (Pin = 26 dBm) as shownin Figures 9.4 and 9.5. Different temperature changes were applied to a 40-cm sectionof the tellurite fiber and the whole length of the Bi-NLF placed on a hot plate. In bothmeasurements, the position of the correlation peak was fixed at the middle of thesection where temperature changes were applied, and the sampling rate of the BGS
acquisition was about 2 Hz including 10-times averaging.

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9. Distributed strain measurement using tellurite glass fiber

Figure 9.4

Figure 9.5

Measured BGS from the 5-m tellurite fiber with Pin of 28 dBm.

Measured BGS from the 1-m Bi-NLF with Pin of 26 dBm.

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9. Distributed strain measurement using tellurite glass fiber

9. 4. 1

Experiments with tellurite glass fiber

The temperature-dependence of the BGS in the tellurite fiber is shown in Figure 9.6, in
which the BGS shifted toward lower frequency with increasing temperature. We canplot the temperature-dependence of the BFS as shown in Figure 9.7. The error bars are+/–2.5 MHz, corresponding to the BFS fluctuations when temperature was fixed. The
slope of the straight-line approximation was calculated to be –1.14 MHz/K. It is notablethat the sign of the temperature-dependence is opposite to that of a standard silica SMF(+1.18 MHz/K [36]).

9. 4. 2

Experiments with bismuth-oxide fiber

The temperature-dependence of the BGS in the Bi-NLF is shown in Figure 9.8. Also inthis case, the BGS shifted toward lower frequency with increasing temperature. The
BGS peak power was so weak that it changed due to the noise floor of the electrical
spectrum analyzer (ESA), which can be suppressed by a noise-floor compensation
technique proposed in Chapter 8. The temperature-dependence of the BFS in the
Bi-NLF is shown in Figure 9.9. The error bars are +/–2.5 MHz, which is the same as thepreceding Section. The coefficient was calculated to be –0.88 MHz/K. The sign was
also negative.

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9. Distributed strain measurement using tellurite glass fiber

Figure 9.6

Temperature-dependences of the BGS in the tellurite fiber.

Figure 9.7

Temperature-dependences of the BFS in the tellurite fiber.

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9. Distributed strain measurement using tellurite glass fiber

Figure 9.8

Temperature-dependences of the BGS in the Bi-NLF.

Figure 9.9

Temperature-dependences of the BFS in the Bi-NLF.

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9. Distributed strain measurement using tellurite glass fiber

9. 4. 3

Discussion

In general, the temperature coefficient of the normalized BFS is given by1 ∂ν B 1 ∂n 1 ⎛ 1 ∂C 1 ∂ρ ⎞ 1 ∂n 1 ⎛ 1 ∂C
⎞
⎟⎟ =
=
+ ⎜⎜
−
+ ⎜
+β⎟ ,
n ∂T 2 ⎝ C ∂T ρ ∂T ⎠ n ∂T 2 ⎝ C ∂T
ν B ∂T⎠(9.2)

where C is the effective elastic constant (in optical fibers, C is almost the same as theYoung’s modulus), ρ the density, and β the volume expansion coefficient of a material.
For a tellurite crystal, Sonehara et al. [133] have reported that the term (1/C)(∂C/∂T)
becomes dominant and is negative, though the values are slightly different depending on
the crystal orientation. From their experimental result, we can estimate the temperature
coefficient in the tellurite crystal at around room temperature to be approximately –1.06
MHz/K (= –0.04 × 7950 MHz / 300 K), which roughly agrees with the experimental
value (–1.14 MHz/K) in the case of the tellurite fiber. The negative dependence of anelastic constant on temperature may also be the origin of the negative
temperature-dependence of the BFS in the Bi-NLF, but further research is needed toclarify this point.
Next, we discuss the potential performances of the distributed temperature sensing
based on BOCDR using the tellurite fiber or the Bi-NLF from the aspects of the numberof effective sensing points or the ratio between the measurement range and the spatial
resolution, and the measurement accuracy. First, the number of effective sensing points
NR, which can be regarded as the evaluation parameter of the sensing system, is givenby the ratio between dm, Equation (2.2), and Δz, Equation (2.1), as
dm πΔf π BFS
NR = Δz = Δν < 2Δν .
A

A

E

A

B

A

E

A

B

A

(9.3)

E

Here, the inequality holds true because Δf must be lower than a half of the BFS of the
FUT due to the Rayleigh scattering-induced noise, as discussed in Chapter 3. While NR
is about 570 in a silica fiber, it can be enhanced to 1250 by using the tellurite fiber (ΔνB

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9. Distributed strain measurement using tellurite glass fiber= 10 MHz), but is reduced to 175 by using the Bi-NLF (ΔνB = 79.2 MHz). Second, themeasurement accuracy of BOCDR using the Bi-NLF is worse than that using thetellurite fiber or a silica fiber, because the absolute value of the temperature coefficientof BFS in the Bi-NLF (0.88 MHz/K) is lower than that in the tellurite fiber (1.14
MHz/K) or a silica fiber (1.18 MHz/K). For example, the BFS fluctuations of +/–2.5
MHz in the Bi-NLF, the tellurite fiber, and a silica fiber, correspond to the measurement
accuracy of +/–2.84, +/–2.19, and +/–2.12 K, respectively. Thus, from the viewpoint not
only of the Brillouin gain and the optical loss, but also of the number of effective
sensing points and the measurement accuracy, the tellurite fiber is more favorable thanthe Bi-NLF as a specialty fiber employed to enhance the performance of the BOCDR
system.

9. 5
9. 5. 1

Strain-dependence of BFS
Experiments

The strain-dependence of the BFS in the tellurite fiber was also investigated using
BOCDR with the same FUT depicted in Figure 9.2. Δf and fm were set to 1 GHz and7.8028 MHz, respectively, which correspond to the measurement range dm of 9.47 m
and the spatial resolution Δz of about 3 cm. Pin was set to 28 dBm, resulting in ΔνB of 10
MHz as already shown in Figure 9.4. In the tellurite fiber, different strains were applied
to a 40-cm section (5.7 – 6.1 m from the circulator) fixed on a translation stage using
epoxy glue. The position of the correlation peak was fixed at the middle of thestrain-applied section, and the sampling rate of the BGS measurement was about 2 Hz
including 10-times averaging.

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9. Distributed strain measurement using tellurite glass fiber

Figure 9.10

Strain-dependences of the BGS in the tellurite fiber.

The strain-dependence of the BGS in the tellurite fiber is shown in Figure 9.10. As
the applied strain increased, the BGS shifted toward lower frequency. From these
spectra, we can plot the strain-dependence of the BFS as shown in Figure 9.11. The
error bars are +/–2.5 MHz, corresponding to the BFS fluctuations when strain was fixed.
The slope of the straight-line approximation was calculated to be –0.023 MHz/με. The
sign of the strain-dependence is also found to be opposite to that of a silica SMF(+0.058 MHz/με [35]).

9. 5. 2

Discussion

In general, the strain coefficient of the normalized BFS in optical fibers is given by

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9. Distributed strain measurement using tellurite glass fiber

Figure 9.11

Strain-dependences of the BFS in the tellurite fiber.

1 ∂ν B 1 ∂n 1 ∂E 1 ∂ρ=+−,
ν B ∂εn ∂ε 2 E ∂ε 2 ρ ∂ε

(9.4)

where E is the Young’s modulus, and ρ the density. The values of each term have been
determined as –0.23, 2.88, and 0.36 by Horiguchi et al. [35] for silica fibers with n =1.46. Since the BFS is about 10.86 GHz in silica SMFs, the strain coefficient iscalculated to be +0.033 MHz/με, which roughly matches the measured value (+0.058
MHz/με). In order to estimate the case of tellurite fibers with n = 2.03, we make two
assumptions as follows: (i) the first term is –0.445 (= –0.23×2.032/1.462) because it is
proportional to the square of n [35], and (ii) the third term is 0.16 (= 0.36×2.2/5.1)
because ρ of silica crystals is 2.2 g/cm3, while that of tellurite crystals is 5.1 g/cm3 [134].
Using the measured strain coefficient (–0.023 MHz/με), the second term can becalculated back to be –2.61. This negative dependence of the Young’s modulus on strain

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9. Distributed strain measurement using tellurite glass fiberhas been observed also in soda glass fibers (silica + Na2O + CaO) by Mallinder et al.
[135], with a second term of –2.555. Thus, we presume that the negative
strain-dependence of the BFS is due to the negative dependence of the Young’s modulus
on strain in the tellurite fiber.

9. 6

Spatial resolution of 6 mm

Finally, this tellurite fiber was employed as the FUT in a distributed strain measurementwith BOCDR to improve the S/N ratio and thus to achieve the inherent limitation of thespatial resolution given by Equation (9.1). The modulation frequency fm was set to9.972599 – 9.975924 MHz (fm ≤ ΔνB of the tellurite fiber), which corresponds to ameasurement range dm of 7.4 m according to Equation (2.2). The amplitude of the

Figure 9.12

Figure 9.13

Structure of the FUT.

Photo of the FUT around the strain-applied section.

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9. Distributed strain measurement using tellurite glass fiber

Figure 9.14

Measured distribution of the BGS.

frequency modulation Δf was 3.94 GHz (Δf ≤ BFS/2), and the nominal spatial resolution
Δz was calculated to be about 6 mm from Equation (2.1) or (9.1). The structure of the
FUT is shown in Figures 9.12 and 9.13. The length of the tellurite fiber was 3.7 m, and0.15-% strain was applied to a 1-cm section. Other conditions concerning the FUT were
the same as those for the preceding Section. Polarization scrambling was employed, andthe sampling rate of the measurement for a single position was 10 Hz including 5-times
averaging. The measurement was performed at 50 points sequentially for 5 seconds.
Figure 9.14 shows the measured distribution of the BGS along the FUT. The BGS at
the strain-applied section was recognized with much higher S/N ratio than that in ourprevious experiment described in Chapter 2 with an SMF as the FUT. Figure 9.15
shows the distribution of the BFS. The 1-cm strain-applied section was detected with anominal spatial resolution of 6 mm, which is the inherent limitation given by Equation(9.1). The gradual variation of the BFS seems to originate from the strain distribution

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9. Distributed strain measurement using tellurite glass fiber

Figure 9.15

Measured distribution of the BFS.

inside the epoxy glue. The change of the BFS was about –34 MHz, which corresponds
to 0.148-% strain. This value is in good agreement with the applied strain of 0.15 %.
The accuracy of the measurement at a single position was about +/– 2.5 MHz, whichcorresponds to a strain accuracy of +/– 0.01 % (+/– 100 με) in this experiment.

9. 7

Conclusions

We employed a tellurite glass fiber as the FUT in BOCDR to perform a short-range but
high-spatial-resolution distributed strain measurement. The investigation on thedependences of the BFS on temperature and strain showed that the BFS in the tellurite
fiber shifts toward lower frequency with increasing temperature and strain, and theircoefficients were –1.14 MHz/K and –0.023 MHz/με, respectively. The BFS dependence
on temperature in a Bi-NLF was also investigated, and –0.88 MHz/K was obtained as

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9. Distributed strain measurement using tellurite glass fiber

its coefficient. These negative dependences seem to be caused by the negative
dependences of the Young’s modulus of these fibers on temperature and strain. Then, a
distributed strain measurement with BOCDR was demonstrated using the tellurite fiber.
With the high Brillouin gain of the tellurite fiber and thus the enhanced S/N ratio in the
BGS measurement, a 1-cm strain-applied section was successfully detected with 6-mm
nominal spatial resolution, which is the inherent limitation of the fiber.

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10. Conclusions

10

Conclusions

In this thesis, we proposed a novel sensing technology named Brillouin opticalcorrelation-domain reflectometry (BOCDR), which can measure the distribution of strain
and/or temperature along a fiber under test (FUT) by light injection only from one end of
the fiber. BOCDR operates based on the combination of spontaneous Brillouin scatteringand the correlation control of continuous lightwaves. A spatial resolution of 13 mm was
experimentally demonstrated with a sampling rate of 50 Hz. We also improved its
performance from various aspects, such as enlargement of the measurement range,enhancement of the sampling rate, application to polarization beat length distribution
measurement, improvement of the stability and the signal-to-noise (S/N) ratio, andachievement of 6-mm spatial resolution using a specialty fiber.
In Chapter 1: “Introduction,” fiber-optic nerve systems for smart materials/structures
were reviewed as the background of this work. Then, the principle of Brillouin scatteringand conventional time-domain techniques such as Brillouin optical time-domainreflectometry (BOTDR) and Brillouin optical time-domain analysis (BOTDA) wereexplained.

The

principle

and

some

recentprogressofBrillouin

opticalcorrelation-domain analysis (BOCDA) based on the synthesis of the optical coherencefunction (SOCF) were also described.
In Chapter 2: “Proposal of BOCDR,” first, we explained that the operating principleof BOCDR is the combination of spontaneous Brillouin scattering and the SOCF
technique, and that it is quite different from that of BOCDA. Then, in the preliminary
experiment, 40-cm spatial resolution and 50-Hz sampling rate were simultaneously

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10. Conclusions

obtained. We also achieved 13-mm spatial resolution, which is the best value everreported in other Brillouin scattering-based reflectometers as well as two-end-access
BOTDA systems. The real-time detection of vibrated strains was also presented.
Furthermore, it was experimentally shown that BOCDR is based not on stimulated
Brillouin scattering (SBS) but on spontaneous Brillouin scattering.
In Chapter 3: “Theoretical analysis of BOCDR analysis,” first, we theoreticallyshowed that the effective Brillouin gain spectrum (BGS) is determined by the
2-dimensional convolution of the intrinsic Brillouin gain and the beat power spectrum,
which is the same expression as that in BOCDA. Then, we performed a simulation on the
typical shapes of the detected BGS. By estimating the shape of the beat power spectrum,
the expression of the spatial resolution was also derived. Finally, the Rayleigh scatteringinduced noise was analyzed, and the limitation of the spatial resolution was discussed.
In Chapter 4: “Enlargement of measurement range based on temporal gating
scheme,” we developed a temporal gating scheme to enlarge the measurement range of
BOCDR while maintaining the spatial resolution. In the experiment, 66-cm spatial
resolution and 1-km measurement range were simultaneously obtained with 50-Hz
sampling rate. This means that the ratio between the measurement range and the spatial
resolution was enhanced from the conventional value 570 to 1515.
In Chapter 5: “Enlargement of measurement range based on double-modulation
scheme,” we proposed a double-modulation scheme as another method to mitigate thetrade-off between the measurement range and the spatial resolution. First, wetheoretically analyzed the operating principle, and performed a simulation to verify theeffectiveness of this scheme. Then, 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 a noise-floor
compensation technique was employed. This means that the ratio between themeasurement range and the spatial resolution was enhanced to 2845 or 5690.

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10. Conclusions

In Chapter 6: “Enhancement of sampling rate utilizing optical heterodyne detection,”
we implemented BOCDR using a single-sideband modulator (SSBM) with fast Fouriertransform (FFT), and examined the possibilities of improvement on the S/N ratio and thesampling rate as well as cost reduction. In the experiment, the S/N ratio was not goodcompared to the conventional BOCDR, but the sampling rate was enhanced to 400 Hz.
Besides, noise inherent to this scheme was observed and discussed.
In Chapter 7: “Application to polarization beat length distribution measurement,” wepresented that BOCDR can be used to perform a distributed measurement of polarization
beat length in single-mode fibers (SMFs). The beat lengths of SMFs wound on mandrels
with radii 10.0 cm, 7.4 cm and 3.1 cm were measured to be 25.4 m, 12. 1 m and 2.56 m,
respectively, which agreed well with the theoretical calculations. A distributed
measurement was also successfully performed using an SMF comprising two sections
with different mandrel radii.
In Chapter 8: “Stable entire-length measurement based on polarization scramblingand noise-floor compensation,” we performed a stable entire-length measurement ofstrain distribution by suppressing the BGS fluctuations with polarization scrambling. In
the experiment, we demonstrated a distributed strain measurement along the entire lengthof a 100-m FUT with 40-cm spatial resolution and 19-Hz sampling rate. Furthermore, wedeveloped a new method of compensating the noise-floor of the electrical spectrum
analyzer (ESA) to improve the S/N ratio of the system.
In Chapter 9: “Distributed strain measurement using tellurite glass fiber,” weemployed a tellurite glass fiber as the FUT in BOCDR to perform a short-range but
high-spatial-resolution distributed strain measurement. The investigation on thedependences of the Brillouin frequency shift (BFS) on temperature and strain showedthat the BFS in the tellurite fiber shifts toward lower frequency with increasing
temperature and strain, and their coefficients were –1.14 MHz/K and –0.023 MHz/με,
respectively. The BFS dependence on temperature in a bismuth-oxide fiber was also

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10. Conclusions

investigated, and –0.88 MHz/K was obtained as its coefficient. These negative
dependences seem to be caused by the negative dependences of the Young’s modulus ofthese fibers on temperature and strain. Then, a distributed strain measurement with
BOCDR was demonstrated using the tellurite fiber. With the high Brillouin gain of thetellurite fiber and thus the enhanced S/N ratio in the BGS measurement, a 1-cm
strain-applied section was successfully detected with 6-mm nominal spatial resolution,
which is the inherent limitation of the fiber.
Thus, BOCDR has been evolving rapidly, improved in performance from a variety of
aspects. It is, however, a new-born technology, and still leaves many problems, such as
the limitation of the modulation amplitude, resulting in a limited spatial resolution. It
also requires the enhancement of the measurement accuracy, the improvement of the S/Nratio, and cost reduction. A discriminative measurement of strain and temperature isanother topic to be considered. If these problems are resolved in future, I am sure that
BOCDR will be accepted as one of the main tools to realize fiber-optic nerve systems
and contribute to a safer society.

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Acknowledgements

Acknowledgements

I would like to express my deepest gratitude to my supervisor, Professor Kazuo Hotate, forproviding me this precious opportunity to study as a Ph.D student in his laboratory. Without his
minute guidance, considerate encouragement, and invaluable discussion, writing this thesis
would not be possible.
I would like to express my sincere appreciation to Professor Zuyuan He for his continuous
guidance, encouragement, and help throughout the course of this work.
I am extremely grateful to Professor Shinji Yamashita and Professor Masato Kishi for theirinsightful comments and suggestions. Prof. Yamashita also provided me a bismuth-oxide fiber
sample, which contributed to Chapter 9.4 of this thesis.
I also gratefully acknowledge the other members of my thesis committee, Professor
Motoichi Ohtsu, Professor Kazuro Kikuchi, and Professor Yoshiaki Nakano.
My heartfelt appreciation also goes to Prof. K. Y. Song and Dr. W. Zou, who pioneered theimprovement of Brillouin scattering-based correlation-domain sensing techniques. They
provided me a high-level starting point for this work.
Of course, I am grateful to Prof. H. Ma, Dr. K. K. Chow, Dr. X. Fan, Dr. K. Kashiwagi, Mr.
K. Kajiwara, Ms. X. Wang, Mr. H. Kuno, Mr. Y. Nakazaki, Mr. H. Takahashi, Mr. W. M. Goh,
Mr. K. Chigusa, Mr. K. R. Yamashita, Mr. M. Numasawa, Mr. T. Ashida, and all the othermembers and alumni of the Hotate-Yamashita-He Laboratory for their warm camaraderie.
Furthermore, I am greatly indebted to the secretaries of the laboratory, Ms. M. Masuhara, Ms. K.
Machida, Ms. N. Mizuno, and Ms. Y. Sayama, for their kind help and personal advice in various
aspects.
Special thanks is also due to Dr. A. Mori at NTT Photonics Laboratories for providing atellurite glass fiber sample, which contributed fruitfully to Chapter 9 of this thesis.

Dissertation 2009, The University of Tokyo131

Acknowledgements

This work was financially supported by the Japan Society for the Promotion of Science(JSPS) Research Fellowships for Young Scientists, the Grant-in-Aid for Creative Scientific
Research, 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.
Finally, I would like to express my indebtedness to my family for their understanding,patience, and support during the entire period of my study, without which this thesis could not
be completed.

Dissertation 2009, The University of Tokyo132

Abbreviations

Abbreviations

AC

alternating current

AOM

acousto-optic modulator

ASE

amplified spontaneous emission

BFS

Brillouin frequency shift

BGS

Brillouin gain spectrum

Bi-HNFbismuth-oxide highly-nonlinear fiber

BOCDA

Brillouin optical correlation-domain analysis

BOCDR

Brillouin optical correlation-domain reflectometry

BOFDA

Brillouin optical frequency-domain analysis

BOTDA

Brillouin optical time-domain analysis

BOTDR

Brillouin optical time-domain reflectometry

CEOcarrier-envelope offset

CW

continuous wave

DAQ

data acquisitionDC

direct current

DCF

dispersion-compensation fiber

DFB-LD

distributed-feedback laser diode

DGD

differential group delay

DP-BOTDR

double-pulse BOTDR

EDF

erbium-doped fiber

EDFA

erbium-doped fiber amplifier

Dissertation 2009, The University of Tokyo133

Abbreviations

EMIelectro-magnetic interference

EOMelectro-optic modulator

ESAelectrical spectrum analyzer

FBG

fiber Bragg grating

FFT

fast Fourier transformFG

function generator

FPI

Fabry-Perot interferometer

FUT

fiber under test

GPIB

general-purpose interface bus

HNAF

high-numerical-aperture fiberIM

intensity modulator

LC-BOCDA

low-coherence BOCDA

LO

local oscillator

MZI

Mach-Zehnder interferometer

OCT

optical coherence tomography

OSA

optical spectrum analyzer

PC

polarization controllerPDphoto-detector

PLC

planar lightwave circuit

PMD

polarization-mode dispersion

POCDR

polarization-sensitive optical correlation-domain reflectometry

POFDR

polarization-sensitive optical frequency-domain reflectometry

POTDR

polarization-sensitive optical time-domain reflectometry

PPP-BOTDA

pulse pre-pump BOTDA

PSCR

polarization scrambler

PSD

power spectral density

PZT

piezo-electric transducer

Dissertation 2009, The University of Tokyo134

Abbreviations

RFA

Raman fiber amplifier

S-BOCDA

simplified BOCDA

SBS

stimulated Brillouin scattering

SMF

single-mode fiber

S/N ratio

signal-to-noise ratio

SOCF

synthesis of optical coherence function

SOP

state of polarization

SSBM

single-sideband modulator

TDM

time-division multiplexing

UMZ

unbalanced Mach-Zehnder

WDM

wavelength-division multiplexing

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135

References

References[1]

K. C. Kao and G. A. Hockham, “Dielectric-fibre surface waveguides for opticalfrequencies”, IEE Proc. 113, 1151 (1966).

[2]

H. Lamm, “Biegsame optische gerate”, Z. Instrumenten. 50, 579 (1930).

[3]

A. C. S. van Heel, “A new method of transporting optical images without
aberrations”, Nature 173, 39 (1954).

[4]

H. H. Hopkins and N. S. Kapany, “Transparent fibres for the transmission of
optical images”, Opt. Acta 1, 164 (1955).

[5]

F. P. Kapron, D. B. Keck, and R. D. Maurer, “Radiation losses in glass opticalfibers”, Appl. Phys. Lett. 17, 423 (1970).

[6]

W. G. French, J. B. MacChesney, P. B. O’Connor, and G. W. Tasker, “Opticalwaveguides with very low loss”, Bell Syst. Tech. J. 53, 951 (1974).

[7]

T. Miya, Y. Terunuma, T, Hosaka, and T, Miyashita, “Ultimate low-loss
single-mode fiber at 1.55 pm”, Electron. Lett. 15, 106 (1979).

[8]

R. Ramaswani and K. Sivarajan, Optical Networks: A Practical Perspective, 2nded. (Morgan Kaufmann Publishers, San Francisco, 2002).

[9]

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, New York,
2002).

[10]

I. P. Kaminow and T. Li, Eds., Optical Fiber Telecommunications, Vols. 4A and
4B (Academic Press, Boston, 2002).

[11]

G. P. Agrawal, Lightwave Technology: Telecommunication System (Wiley,
Hoboken, NJ, 2005).

[12]

D. Davies and S. A. Kingsley, “The use of optical fibers as instrumentationtransducers”, Proc. CLEO’76, 24, 1976.

[13]

V. Vali and R. W. Shorthill, “Fiber ring interferometer”, Appl. Opt. 15, 1099
(1976).

Dissertation 2009, The University of Tokyo

136

References[14]

E. Udd, Fiber Sensors (Wiley, New York, 1991).

[15]

C. Menadier, C. Kissinger, and H. Adkins, “The fotonic sensor”, Instrum. &Control Syst. 40, 114 (1967).

[16]

B. Culshaw, Optical Fiber Sensing and Signal Processing (Peter Pereginus,
London, 1984).

[17]

T. G. Giallorezi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C.
Rashleigh, and R. C. Priest, “Optical fiber sensor technology”, IEEE J. Quantum
Electron. 18, 624 (1982).

[18]

K. Hotate, “Application of synthesized coherence function to distributed opticalsensing”, Meas. Sci. Technol. 13, 1746 (2002).

[19]

T. Horiguchi, A. Rogers, W. C. Michie, G. Stewart, and B. Culshaw, in OpticalFiber Sensors, ed. J. Dakin and B. Culshaw (Artech House, Boston, 1997), Vol.
IV, Chap. 14, 309.

[20]

A. D. Kersey, in Optical Fiber Sensors, ed. J. Dakin and B. Culshaw (Artech
House, Boston, 1997), Vol. IV, Chap. 15, 369.

[21]

L. Thevenaz, in Trends in Optical Non-Destructive Testing and Inspection, ed. P.
Rastogi and D. Inaudi (Elsevier, Amsterdam, 2000), Chap. 29, 447.

[22]

K. Hotate, “Fiber sensor technology today”, Jpn. J. Appl. Phys. 45, 6616 (2006).

[23]

D. Inaudi, A. Ruefenacht, B. von Arx, H. P. Noher, S. Vurpillot, and B. Glisic,“Monitoring of a concrete arch bridge during construction”, Proc. SPIE 4696,
146 (2002).

[24]

S. Katz, “Factors affecting strain gauge selection for smart structure application”,
Proc. SPIE 3330, 20 (1998).

[25]

C. Butter and G. Hocker, “Fiber optics strain gauge”, Appl. Opt. 17, 2867 (1978).

[26]

W. Morey, G. Meltz, and W. Glenn, “Fiber optic Bragg grating sensors”, Proc.
SPIE 1169, 98 (1989).

[27]

C. Lee and H. Taylor, “Interferometric optical fibre sensors using internal
mirrors”, Electron. Lett. 24, 193 (1988).

[28]

E. Udd, “The emergence of fiber optic sensor technology”, in Fiber Optic
Sensors – An Introduction for Engineers and Scientists (John Wiley & Sons,
USA, 1991).

[29]

H. Lefevre, The Fiber-Optic Gyroscope (Artech House, Boston, 1993).

[30]

K. Hotate, in Optical Fiber Sensors, ed. J. Dakin and B. Culshaw (Artech House,
Boston, 1997), Vol. IV, Chap. 11, 167.

Dissertation 2009, The University of Tokyo

137

References[31]

K. Hotate, in Trends in Optical Non-Destructive Testing and Inspection, ed. P.
Rastogi and D. Inaudi (Elsevier, Amsterdam, 2000), Chap. 32, 487.

[32]

A. Kersey, “Fiber optic sensor multiplexing techniques”, in Fiber Optic Smart
Structures (John Wiley & Sons, USA, 1991).

[33]

B. Culshaw, “Basic concepts of optical fiber sensors”, in Optical Fiber Sensors:
Principles and Components (Artech House, USA, 1988)[34]

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic Press, New York,
1995).

[35]

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence ofBrillouin frequency shift in silica optical fibers”, IEEE Photon. Technol. Lett. 1,
107 (1989).

[36]

T. Kurashima, T. Horiguchi, and M. Tateda, “Thermal effects of Brillouin gain
spectra in single-mode fibers”, IEEE Photon. Technol. Lett. 2, 718 (1990).

[37]

M. Nikles. L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum
characterization in single-mode optical fibers”, OSA/IEEE J. Lightwave Technol.
15, 1842 (1997).

[38]

D. Cotter, “Stimulated Brillouin scattering in optical fibers”, J. Opt. Commun. 4,
10 (1982).

[39]

N. Shibata, K. Okamoto, and Y. Azuma, “Longitudinal acoustic modes andBrillouin-gain spectra for GeO2-doped-core single-mode fibers”, J. Opt. Soc.
Amer. B 6, 1167 (1989).

[40]

T. Horiguchi and M. Tateda, “BOTDA – nondestructive measurement of
single-mode optical fiber attenuation characteristics using Brillouin interaction:
theory”, OSA/IEEE J. Lightwave Technol. 7, 1170 (1989).

[41]

T. Horiguchi, T. Kurashima, and M. Tateda, “A technique to measure distributed
strain in optical fiber”, IEEE Photon. Technol. Lett. 2, 352 (1990).

[42]

T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-temperature sensing
using stimulated Brillouin scattering in optical silica fibers”, Opt. Lett. 15, 1038
(1990).

[43]

T. Horiguchi, T. Kurashima, and Y. Koyamada, “1 m spatial resolution
measurement of distributed Brillouin frequency shift by single-mode fibers”,
Tech. Dig. Opt. Fiber Meas. 2, 73 (1994).

[44]

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada,“Development of a distributed sensing technique using Brillouin scattering”,

Dissertation 2009, The University of Tokyo

138

References

OSA/IEEE J. Lightwave Technol. 13, 1296 (1995).
[45]

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. 16, 324 (1997).

[46]

H. Naruse and M. Tateda, “Trade-off between the spatial and the frequency
resolutions in measuring the power spectrum of the Brillouin backscattered lightin an optical fiber”, Appl. Opt. 38, 6516 (1999).

[47]

X. Bao, D. J. Webb, and D. A. Jackson, “32-km distributed temperature sensor
using Brillouin loss in optical fiber”, Opt. Lett. 18, 1561 (1993).

[48]

A. Vedadi, D. Alasia, E. Lantz, H. Maillotte, L. Thevenaz, M. Gonzalez-Herraez,
and T. Sylvestre, “Brillouin optical time-domain analysis of fiber-optic
parametric amplifiers”, IEEE Photon. Technol. Lett. 19, 179 (2007).

[49]

W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA forhigh spatial resolution sensing”, Opt. Express 16, 21616 (2008).

[50]

M. Nikles, L. Thevenaz, and P. A. Robert, “Simple distributed fiber sensor basedon Brillouin gain spectrum analysis”, Opt. Lett. 21, 758 (1996).

[51]

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental
and theoretical studies on a distributed temperature sensor based on Brillouinscattering”, OSA/IEEE J. Lightwave Technol. 13, 1340 (1995).

[52]

A. W. Brown, M. DeMerchant, X. Bao, and T. W. Bremmer, “Spatial resolution
enhancement of a Brillouin-distributed sensor using a novel signal processing
method”, OSA/IEEE J. Lightwave Technol. 17, 1179 (1999).

[53]

K. Kishida, C. H. Li, S. Lin, and K. Nishiguchi, “Pulsed pre-pump method toachieve cm-order spatial resolution in Brillouin distributed measuring technique”,
IEIC Tech. Rep. 104, 15 (2004).

[54]

K. Kishida, C. H. Li, and K. Nishiguchi, “Pulse pre-pump method for cm-order
spatial resolution of BOTDA”, Proc. SPIE 5855, 559 (2005).

[55]

A. W. Brown, B. G. Colpitts, and K. Brown, “Distributed sensor based on
dark-pulse Brillouin scattering”, IEEE Photon. Technol. Lett. 17, 1501 (2005).

[56]

A. W. Brown, B. G. Colpitts, and K. Brown, “Dark-pulse Brillouin optical
time-domain sensor with 20-mm spatial resolution”, OSA/IEEE J. Lightwave
Technol. 25, 381 (2007).

[57]

T. Kurashima, T. Horiguchi, H. Izumita, S. Furukawa, and Y. Koyamada,“Brillouin optical-fiber time domain reflectometry”, IEICE Trans. Commun.

Dissertation 2009, The University of Tokyo

139

References

E76-B, 382 (1993).
[58]

K. Shimizu, T. Horiguchi, Y. Koyamada, and T. Kurashima, “Coherent
self-heterodyne Brillouin OTDR for measurement of Brillouin frequency shift
distribution in optical fibers”, OSA/IEEE J. Lightwave Technol. 12, 730 (1994).

[59]

H. Izumita, T. Sato, M. Tateda, and Y. Koyamada, “Brillouin OTDR employing
optical frequency shifter using side-band generation technique with high-speed
LN phase-modulator”, IEEE Photon. Technol. Lett. 12, 1674 (1996).

[60]

Y. Koyamada, “Proposal and simulation of double-pulse Brillouin optical
time-domain reflectometry” IEIC Tech. Rep. 106, 35 (2007).

[61]

Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, “Novel technique toimprove spatial resolution in Brillouin optical time-domain reflectometry”, IEEE
Photon. Technol. Lett. 23, 1910 (2007).

[62]

Y. Sakairi, S. Matsuura, S. Adachi, and Y. Koyamada, “Prototype double-pulse
BOTDR for measuring distributed strain with 20-cm spatial resolution”, SICE
Annual Conf. 2008, 1106 (2008).

[63]

M. N. Alahbabi, Y. T. Cho, and T. P. Newson, “150-km-range distributed
temperature sensor based on coherent detection of spontaneous Brillouinbackscatter and in-line Raman amplification”, J. Opt. Soc. Amer. B 22, 1321
(2005).

[64]

M. A. Soto, P. K. Sahu, G. Bolognini, and F. D. Pasquale, “Brillouin-based
distributed temperature sensor employing pulse coding”, IEEE Sens. J. 8, 225(2008).

[65]

M. A. Soto, G. Bolognini, and F. D. Pasquale, “Analysis of optical pulse codingin spontaneous Brillouin-based distributed temperature sensors”, Opt. Express 16,
19097 (2008).

[66]

D. Garus, K. Krebber, F. Schliep, and T. Gogolla, “Distributed sensing techniquebased on Brillouin optical-fiber frequency-domain analysis”, Opt. Lett. 21, 1402
(1996).

[67]

D. Garus, K. Krebber, F. Schliep, and T. Gogolla, “Brillouin optical-fiber
frequency-domain analysis for distributed temperature and strain measurements”,
OSA/IEEE J. Lightwave Technol. 15, 654 (1997).

[68]

R. Bernini, L. Crocco, A. Minardo, F. Soldovieri, and L. Zeni,“Frequency-domain approach to distributed fiber-optic Brillouin sensing”, Meas.
Sci. Technol. 27, 288 (2002).

Dissertation 2009, The University of Tokyo

140

References[69]

R. Bernini, A. Minardo, and L. Zeni, “Stimulated Brillouin scattering
frequency-domain analysis in a single-mode optical fiber for distributed sensing”,
Opt. Lett. 29, 1977 (2004).

[70]

T. Hasegawa, Dissertation for master degree, The University of Tokyo, 1999.

[71]

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. E83-C, 405 (2000).

[72]

K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm
spatial resolution by correlation-based continuous-wave technique”, IEEE
Photon. Technol. Lett. 14, 197 (2002).

[73]

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. E84-C, 1823 (2001).

[74]

K. Hotate and S. S. L. Ong, “Distributed dynamic strain measurement using acorrelation-based Brillouin sensing system”, IEEE Photon. Technol. Lett. 15, 272(2003).

[75]

K. Hotate, K. Abe, and K. Y. Song, “Suppression of signal fluctuation in
Brillouin optical correlation domain analysis system using polarization diversity
scheme”, IEEE Photon. Technol. Lett. 18, 2653 (2006).

[76]

K. Y. Song, Z. He, and K. Hotate, “Optimization of Brillouin optical correlation
domain analysis system based on intensity modulation scheme”, Opt. Express 14,4256 (2006).

[77]

K. Y. Song, Z. He, and K. Hotate, “Effects of intensity modulation of light sourceon Brillouin optical correlation domain analysis”, OSA/IEEE J. Lightwave
Technol. 25, 1238 (2007).

[78]

K. Hotate, W. M. Goh, Y. Mizuno, and Z. He, “Brillouin optical correlationdomain analysis based on simultaneous utilization of sinusoidal and noise
modulation”, Proc. IEICE General Conf. 2008, 469 (2008).

[79]

K. Hotate, K. Chigusa, Y. Mizuno, M. Kishi, and Z. He, “Improvement on S/Nratio of low-coherence BOCDA”, Proc. IEICE General Conf. 2009, 242 (2009).

[80]

M. Kannou, S. Adachi, and K. Hotate, “Temporal gating scheme for enlargementof measurement range of Brillouin optical correlation domain analysis for opticalfiber distributed strain measurement”, Proc. OFS-16, 454, 2003.

Dissertation 2009, The University of Tokyo

141

References[81]

K. Hotate, H. Arai, and K. Y. Song, “Range-enlargement of simplified Brillouin
optical correlation domain analysis based on a temporal gating scheme”, SICE J.
Cont. Meas. Syst. Int. 1, 271 (2008).

[82]

K. Y. Song and K. Hotate, “Enlargement of measurement range in a Brillouin
optical correlation domain analysis system using double lock-in amplifiers and asingle-sideband modulator”, IEEE Photon. Technol. Lett. 18, 499 (2006).

[83]

K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurement withmillimeter-order spatial resolution based on Brillouin optical correlation domain
analysis”, Opt. Lett. 31, 2526 (2006).

[84]

K. Hotate and T. Yamauchi, “Fiber-optic distributed strain sensing system by
Brillouin optical correlation domain analysis with a simple and accurate
time-division pump-probe generation scheme”, Jpn. J. Appl. Phys. 44, L1030(2005).

[85]

K. Y. Song and K. Hotate, “Distributed fiber strain sensor with 1-kHz sampling
rate based on Brillouin optical correlation domain analysis”, IEEE Photon.
Technol. Lett. 19, 1928 (2007).

[86]

W. Zou, Dissertation for doctoral degree, The University of Tokyo, 2007.

[87]

W. Zou, Z. He, and K. Hotate, “Complete discrimination of strain andtemperature using Brillouin frequency shift and birefringence in apolarization-maintaining fiber”, Opt. Express 17, 1248 (2009).

[88]

K. Y. Song and K. Hotate, “Brillouin optical correlation domain analysis in linear
configuration”, IEEE Photon. Technol. Lett. 20, 2150 (2008).

[89]

T. Yari, K. Nagai, M. Ishioka, K. Hotate, and Y. Koshioka, “Aircraft structural
health monitoring using on-board BOCDA system”, Proc. SPIE 6933, 69330S(2008).

[90]

Y. Kumagai, S. Matsuura, S. Adachi, and K. Hotate, “Enhancement of BOCDA
system for aircraft health monitoring”, SICE Annual Conf. 2008, 2184 (2008).

[91]

M. Imai, S. Miura, and K. Hotate, “Health monitoring of a full scale tunnel
model using BOCDA-based fiber-optic distributed sensor”, Int. Conf. on Struc.
Health Mon. & Int. Infra. 2005, 385 (2005).

[92]

S. S. Ong, H. Kumagai, H. Iwaki, and K. Hotate, “Crack detection in concrete
using a Brillouin optical correlation domain analysis based fiber optic sensor”,
IEIC Tech. Rep. 102, 49 (2003).

[93]

Z. He, Dissertation for doctoral degree, The University of Tokyo, 1999.

Dissertation 2009, The University of Tokyo

142

References[94]

K. Hotate and Z. He, “Synthesis of optical coherence function and its
applications in distributed and multiplexed optical sensing”, OSA/IEEE J.
Lightwave Technol. 24, 2541 (2006).

[95]

K. Hotate, M. Enyama, S. Yamashita, and Y. Nasu, “A multiplexing technique offiber Bragg grating sensors with the same reflection wavelength by the synthesisof optical coherence function”, Meas. Sci. Technol. 15, 148 (2004).

[96]

M. Enyama, Z. He, and K. Hotate, “Expansion of spatial measurement range byuse of vernier effect in multiplexed fibre Bragg grating strain sensor withsynthesis of optical coherence function”, Meas. Sci. Technol. 16, 977 (2005).

[97]

K. Hotate and K. Kajiwara, “Proposal and experimental verification of Bragg
wavelength distribution measurement within a long-length FBG by synthesis of
optical coherence function”, Opt. Express 16, 7881 (2008).

[98]

Z. He and K. Hotate, “Synthesized optical coherence tomography for imaging of
scattering objects by use of a stepwise frequency-modulated tunable laser diode”,
Opt. Lett. 24, 1502 (1999).

[99]

K. Hotate, Z. He, and T. Kitazume, “Surface shape measurement for
multi-layered object by synthesis of optical coherence function”, IEEE J. Sel.
Topics Quantum Electron. 6, 723 (2000).

[100] B. Zhu, T. Saida and K. Hotate, “Variable optical filter using dynamic grating in
Er-doped fiber controlled by synthesis of optical coherence function: proposal
and experimental verification”, IEICE Trans. Electron. E86-C, 97 (2003).
[101] X. Fan, Z. He, Y. Mizuno, and K. Hotate, “Bandwidth-adjustable dynamic
grating in erbium-doped fiber by synthesis of optical coherence function”, Opt.
Express 13, 5756 (2005).
[102] X. Fan, Z. He, and K. Hotate, “Novel strain- and temperature-sensing mechanism
based on dynamic grating in polarization-maintaining erbium-doped fiber”, Opt.
Express 14, 556 (2005).
[103] T. Saida and K. Hotate, “Distributed fiber-optic stress sensor by synthesis of the
optical coherence function”, IEEE Photon. Technol. Lett. 9, 484 (1997).
[104] Z. He and K. Hotate, “Distributed fiber-optic stress-location measurement byarbitrary shaping of optical coherence function”, OSA/IEEE J. Lightwave
Technol. 20, 1715 (2002).
[105] M. Kashiwagi and K. Hotate, “Elongation of measurement range by successively
shifting measurement window in a high spatial resolution reflectometry for

Dissertation 2009, The University of Tokyo

143

References

optical subscriber networks by synthesis of optical coherence function”, Meas.
Sci. Technol. 15, 1512 (2004).
[106] Z. He, T. Tomizawa, and K. Hotate, “High-speed high-reflectance-resolution
reflectometry by synthesis of optical coherence function”, IEICE Electron.
Express 3, 122 (2006).
[107] C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurement basedon transmission spectra through a polarizer”, OSA/IEEE J. Lightwave Technol.
12, 917 (1994).
[108] B. L. Heffner, “Automated measurement of polarization mode dispersion using
Jones matrix eigenanalysis”, IEEE Photon. Technol. Lett. 4, 1066 (1992).
[109] A. J. Rogers, “Polarization-optical time domain reflectometry: a technique forthe measurement of field distributions”, Appl. Opt. 20, 1060 (1981).
[110] A. Galtarossa and L. Palmieri, “Spatially resolved PMD measurements”,
OSA/IEEE J. Lightwave Technol. 22, 1103 (2004).
[111] M. Wuilpart, G. Ravet, P. Megret, and M. Blondel, “Polarization mode dispersion
mapping in optical fibers with a polarization-OTDR”, IEEE Photon. Technol.
Lett. 14, 1716 (2002).
[112] M. Wegmuller, M. Legre, and N. Gisin, “Distributed beatlength measurement insingle-mode fibers with optical frequency-domain reflectometry”, OSA/IEEE J.
Lightwave Technol. 20, 828 (2002).
[113] Y. Yamamoto and E. Sasaoka, “Distributed birefringence measurement in opticalfibers with ultra-high spatial resolution by Brillouin gain analysis”, Proc.
ECOC’07, paper Th.10.1.3, 2007.
[114] L. Thevenaz, S. F. Mafang, M. Nikles, “Fast measurement of local PMD withhigh spatial resolution using stimulated Brillouin scattering”, Proc. ECOC’07,
paper Th.10.1.2, 2007.
[115] M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida, “Measurement andanalysis on polarization properties of backward Rayleigh scattering forsingle-mode optical fibers”, IEEE J. Quantum Electron. QE-17, 2326 (1981).
[116] R. Ulrich, S. C. Rashleigh, and W. Eickhoff, “Bending-induced birefringence insingle-mode fibers”, Opt. Lett. 5, 273 (1980).
[117] D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill,
New York, 1972).
[118] A. D. Kersey, M. J. Marrone, A. Dandridge, and A. B. Tveten, “Optimization and

Dissertation 2009, The University of Tokyo

144

References

stabilization of visibility in interferometric fiber-optic sensors using inputpolarization control”, OSA/IEEE J. Lightwave Technol. 6, 1599 (1988).
[119] K. Utchiyama, S. Kawanishi, H. Takara, T. Morioka, and M. Saruwatari, “100Gbit/s to 6.3 Gbit/s demultiplexing experiment using polarisation-independent
nonlinear optical loop mirror”, Electron. Lett. 30, 873 (1994).
[120] R. Calvani, F. Cisternino, R. Girardi, and E. Riccardi, “Polarisation independent
all-optical demultiplexing using four wave mixing in dispersion shifted fibre”,
Electron. Lett. 35, 72 (1999).
[121] R. Noe, H. Rodler, A. Ebberq, G. Gaukel, B. Noll, J. Wittmann, and F. Auracher,“Comparison of polarization handling methods in coherent optical systems”,
OSA/IEEE J. Lightwave Technol. 9, 1353 (1991).
[122] F. Bruyere, O. Audouin, V. Letellier, G. Bassier, and P. Marmier, “Demonstrationof an optimal polarization scrambler for long-haul optical amplifier systems”,
IEEE Photon. Technol. Lett. 6, 1153 (1994).
[123] M. Born and E. Wolf, Principles of Optics, fourth ed. (Pergamon, London,1970).
[124] J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate forfiber devices”, Opt. Mater. 3, 187 (1994).
[125] K. S. Abedin, “Stimulated Brillouin scattering in single-mode tellurite glass
fiber”, Opt. Express 14, 11766 (2006).
[126] A. Mori, H. Masuda, K. Shikano, and M. Shimizu, “Ultra-wide-band
tellurite-based fiber Raman amplifier”, OSA/IEEE J. Lightwave Technol. 21,
1300 (2003).
[127] B. Richards, Y. Tsang, D. Binks, J. Lousteau, and A. Jha, “Efficient ~2 μm Tm3+
-doped tellurite fiber laser”, Opt. Lett. 33, 402 (2008).
[128] A. Ishizawa, T. Nishikawa, S. Aozasa, A. Mori, O. Tadanaga, M. Asobe, and H.
Nakano, “Demonstration of carrier envelope offset locking with low pulse
energy”, Opt. Express 16, 4706 (2008).
[129] J. H. Lee, T. Tanemura, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N.
Sugimoto, “Experimental comparison of a Kerr nonlinearity figure of meritincluding the stimulated Brillouin scattering threshold for state-of-the-art
nonlinear optical fibers”, Opt. Lett. 30, 1698 (2005).
[130] K. Y. Song, K. S. Abedin, K. Hotate, M. G. Herraez, and L. Thevenaz, “Highly
efficient Brillouin slow and fast light using As2Se3 chalcogenide fiber”, Opt.

Dissertation 2009, The University of Tokyo

145

References

Express 14, 5860 (2006).
[131] M. Yamada, A. Mori, K. Kobayashi, H. Ono, T. Oikawa, Y. Nishida, and Y.
Ohishi, “Gain-flattened tellurite-based EDFA with a flat amplification bandwidthof 76 nm”, IEEE Photon. Technol. Lett. 10, 1244 (1998).
[132] A. Yeniay, J. M. Delavaux, and J. Toulouse, “Spontaneous and stimulated
Brillouin scattering”, OSA/IEEE J. Lightwave Technol. 20, 1425 (2002).
[133] T. Sonehara, E. Tatsu, and S. Saikan, “Temperature dependence of the Brillouinfrequency shift in crystals”, J. Appl. Phys. 101, 103507 (2007).
[134] A. El-Adawy and R. El-Mallawany, “Elastic modulus of tellurite glasses”, J. Mat.
Sci. Lett. 15, 2065 (1996).
[135] F. P. Mallinder and B. A. Proctor, “Elastic constants of fused silica as a functionof large tensile strain”, Phys. Chem. Glass 5, 91 (1964).

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146

Publications related to this thesis

Publications related to this thesis

A.

Journal papers[1]

Yosuke Mizuno, Weiwen Zou, Zuyuan He, and Kazuo Hotate, “Proposal of
Brillouin optical correlation-domain reflectometry (BOCDR),” Optics Express,
vol. 16, no. 16, pp. 12148-12153 (2008).

[2]

Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “One-end-access high-speed
distributed strain measurement with 13-mm spatial resolution based on Brillouin
optical correlation-domain reflectometry,” IEEE Photonics Technology Letters,
vol. 21, no. 7, pp. 474-476 (2009).

[3]

Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Polarization beat length
distribution measurement in single-mode optical fibers with Brillouin opticalcorrelation-domain reflectometry,” Applied Physics Express, vol. 2, no. 4, 046502(2009).

[4]

Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Stable entire-length
measurement of fiber strain distribution by Brillouin optical correlation-domainreflectometry with polarization scrambling and noise-floor compensation,”
Applied Physics Express, vol. 2, no. 6, 062403 (2009).

[5]

Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Measurement range enlargementin Brillouin optical correlation-domain reflectometry based on temporal gating
scheme,” Optics Express, vol. 17, no. 11, pp. 9040-9046 (2009).

[6]

Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Dependence of the Brillouinfrequency shift on temperature in a tellurite glass fiber and a bismuth-oxide
highly-nonlinear fiber,” Applied Physics Express, vol. 2, no. 11, 112402 (2009).

[7]

Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Measurement range enlargement

Dissertation 2009, The University of Tokyo

147

Publications related to this thesis

in Brillouin optical correlation-domain reflectometry based on double-modulation
scheme,” Optics Express, vol. 18, no. 6, pp. 5926-5933 (2010).
[8]

Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Distributed strain measurement
using a tellurite glass fiber with Brillouin optical correlation-domainreflectometry,” Optics Communications, in press.

[9]

Yosuke Mizuno, Weiwen Zou, Zuyuan He, and Kazuo Hotate, “Operation of
Brillouin optical correlation-domain reflectometry: theoretical analysis andexperimental validation,” Journal of Lightwave Technology, submitted.

B.

International conference papers[10] Yosuke Mizuno, Weiwen Zou, Zuyuan He, and Kazuo Hotate, “Proposal andexperiment of BOCDR - Brillouin optical correlation-domain reflectometry -”,19th International Conference on Optical Fibre Sensors (OFS-19), paper 7004-122,
Perth, Western Australia, April 14-18, 2008.
[11] Yosuke

Mizuno,Zuyuan

He,

and

Kazuo

Hotate,“Brillouin

opticalcorrelation-domain reflectometry with 13-mm spatial resolution and 50-Hz
sampling rate”, International Conference on Lasers and Electro-Optics / Quantum
Electronics and Laser Science Conference (CLEO/QELS 2008), paper CMZ2,
San Jose, CA, USA, May 4-9, 2008.
[12] Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Enlargement of measurement
range of Brillouin optical correlation-domain reflectometry based on temporalgating scheme”, the 34th European Conference and Exhibition on OpticalCommunication 2008 (ECOC 2008), paper We.3.B.7, Brussels, Belgium,
September 21-25, 2008.
[13] Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Polarization beat length
distribution measurement in single-mode optical fibers with Brillouin opticalcorrelation-domain reflectometry”, The Optical Fiber Communication Conference
and Exposition and the National Fiber Optic Engineers Conference 2009 (OFC/NFOEC 2009), paper OMP5, San Diego, CA, USA, March 22-26, 2009.
[14] Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Stable entire-length

Dissertation 2009, The University of Tokyo

148

Publications related to this thesis

measurement of fiber strain distribution by Brillouin optical correlation-domainreflectometry

based

on

polarization

scrambling

scheme”,

International

Conference on Lasers and Electro-Optics / Quantum Electronics and Laser
Science Conference (CLEO/QELS 2009), paper CMNN6, Baltimore, USA, May
31 - June 5, 2009.
[15] Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Distributed strain measurement
withmillimeter-order

spatialresolution

based

on

Brillouin

opticalcorrelation-domain reflectometry using tellurite glass fiber”, 20th International
Conference on Optical Fibre Sensors (OFS-20), paper OF101-10, Edinburgh, UK,
October 5-9, 2009.
[16] Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Measurement range enlargementin Brillouin optical correlation-domain reflectometry based on double-modulation
scheme”, 20th International Conference on Optical Fibre Sensors (OFS-20),
post-deadline paper PDP-03, Edinburgh, UK, October 5-9, 2009.
[17] Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Dependence of the Brillouinfrequency shift on temperature in a bismuth-oxide highly-nonlinear fiber”, 15th
International Microoptics Conference (MOC’09), paper C-3, Tokyo, Japan,
October 25-28, 2009.
[18] Yosuke Mizuno, Weiwen Zou, Zuyuan He, and Kazuo Hotate, “Spatial resolution
limitationbyRayleighscattering-induced

noise

in

Brillouin

opticalcorrelation-domain reflectometry”, International Conference on Lasers andElectro-Optics/

Quantum

Electronics

and

Laser

Science

Conference(CLEO/QELS 2010), submitted.

C.

Domestic conference papers[19] 水野洋輔、鄒衛文、何祖源、保立和夫, "ブリルアン光相関領域リフレクト
メトリ(BOCDR)の提案と実験的検証", 応用物理学会第 40 回光波センシン
グ技術研究会(LST-40)講演論文集, pp. 141-146, 東京大学本郷キャンパス、
2007 年 12 月 11 日-12 日.
[20] 水野洋輔、何祖源、保立和夫, "時間ゲート法を用いた BOCDR の測定レン
ジの拡大", 応用物理学会第 41 回光波センシング技術研究会(LST-41)講演

Dissertation 2009, The University of Tokyo

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Publications related to this thesis

論文集, pp. 161-166, 東京理科大学神楽坂キャンパス、2008 年 6 月 10 日-11
日.
[21] 水野洋輔、鄒衛文、何祖源、保立和夫, "光ヘテロダイン検波を用いたブリルアン光相関領域リフレクトメトリ", 電子情報通信学会 2008 年度第 4 回
光ファイバ応用技術研究会(OFT)講演論文集, pp. 33-38, 日本文理大学湯布院研修所、2008 年 11 月 20 日-21 日.
[22] 水野洋輔、何祖源、保立和夫, "ブリルアン光相関領域リフレクトメトリによるシングルモード光ファイバ中のビート長の分布測定", 応用物理学会
第 42 回光波センシング技術研究会(LST-42)講演論文集, pp. 149-156, 埼玉大学東京ステーションカレッジ、2008 年 12 月 9 日-10 日.
[23] 水野洋輔，何 祖源, 保立和夫, "偏波スクランブリングを用いたブリルアン
光相関領域リフレクトメトリによる歪分布全長測定の安定化," 電子情報通信学会 2008 年度第 10 回光エレクトロニクス研究会(OPE)講演論文集, pp.
31-38, 機会振興会館、2009 年 3 月 6 日. [光エレクトロニクス研究会 学生
優秀研究賞受賞].
[24] 水野洋輔、何祖源、保立和夫, "テルライトファイバにおけるブリルアン周
波数シフトの歪および温度依存性とその BOCDR への応用", 応用物理学会
第 43 回光波センシング技術研究会(LST-43)講演論文集, pp. 161-166, 埼玉大学東京ステーションカレッジ、2009 年 6 月 9 日-10 日.
[25] 保立和夫、千種健二、水野洋輔、岸眞人、何祖源, "低コヒーレンスブリル
アン光相関領域解析法の S/N 比の向上", 応用物理学会第 43 回光波センシ
ング技術研究会(LST-43)講演論文集, pp. 143-148, 埼玉大学東京ステーションカレッジ、2009 年 6 月 9 日-10 日.
[26] 水野洋輔、何祖源、保立和夫, "二重周波数変調を用いた BOCDR の測定レ
ンジの拡大", 応用物理学会第 44 回光波センシング技術研究会(LST-44)講演論文集, pp. 57-62, 東京理科大学神楽坂キャンパス、2009 年 12 月 8 日-9日.
[27] 水野洋輔、鄒衛文、何祖源、保立和夫, "ブリルアン光相関領域リフレクト
メトリにおけるレイリー散乱誘起雑音と空間分解能に関する考察", 電子
情報通信学会 2009 年度第 5 回光ファイバ応用技術研究会(OFT)講演論文集,

Dissertation 2009, The University of Tokyo

150

Publications related to this thesis

pp. 21-26, 大濱信泉記念館、石垣島、2010 年 1 月 21 日-22 日.

D.

Domestic annual meeting presentations[28] 水野洋輔、何祖源、保立和夫, "ブリルアン光相関領域リフレクトメトリの提案と実験的検証", 電子情報通信学会 2007 年ソサイエティ大会, B-13-9,
鳥取大学鳥取キャンパス、2007 年 9 月 10 日-14 日.
[29] 水野洋輔、何祖源、保立和夫, "ブリルアン光相関領域リフレクトメトリによる歪分布測定 ～13 mm の空間分解能と 50 Hz のサンプリングレートの両立～", 電子情報通信学会 2008 年総合大会, B-13-25, 北九州学術研究都
市 三大学、2008 年 3 月 18 日-21 日.
[30] 保立和夫、ゴウィミン、水野洋輔、何祖源, "Brillouin optical correlationdomain analysis based on simultaneous utilization of sinusoidal and noise
modulation", 電子情報通信学会 2008 年総合大会, B-13-23, 北九州学術研究
都市 三大学、2008 年 3 月 18 日-21 日.
[31] 水野洋輔、何祖源、保立和夫, "ブリルアン光相関領域リフレクトメトリによる歪分布測定 ～km オーダの測定レンジと 50 Hz のサンプリングレートの両立～", 2008 年（平成 20 年）春季第 55 回応用物理学関連連合講演会,
27a-ZQ-5, 日本大学船橋キャンパス、2008 年 3 月 27 日-30 日.
[32] 水野洋輔、何祖源、保立和夫, "ブリルアン光相関領域リフレクトメトリによるリアルタイム歪分布測定の実証", 2008 年（平成 20 年）秋季第 69 回応用物理学会学術講演会, 4p-ZM-8, 中部大学春日井キャンパス、2008 年 9 月
2 日-5 日.
[33] 水野洋輔、何祖源、保立和夫, "時間ゲート法を用いた BOCDR の測定レン
ジの拡大", 電子情報通信学会 2008 年ソサイエティ大会, C-3-69, 明治大学
生田キャンパス、2008 年 9 月 16 日-19 日.
[34] 水野洋輔、鄒衛文、何祖源、保立和夫, "光ヘテロダイン検波を用いたブリルアン光相関領域リフレクトメトリ", 電子情報通信学会 2008 年ソサイエ
ティ大会, C-3-70, 明治大学生田キャンパス、2008 年 9 月 16 日-19 日.
[35] 水野洋輔、何祖源、保立和夫, "偏波スクランブリングを用いたブリルアン
光相関領域リフレクトメトリによる歪分布全長測定の安定化", 電子情報通信学会 2009 年総合大会, C-3-88, 愛媛大学、2009 年 3 月 17 日-20 日.

Dissertation 2009, The University of Tokyo

151

Publications related to this thesis[36] 水野洋輔、何祖源、保立和夫, "ブリルアン光相関領域リフレクトメトリによるシングルモード光ファイバ中の偏波ビート長の分布測定", 電子情報通信学会 2009 年総合大会, C-3-89, 愛媛大学、2009 年 3 月 17 日-20 日.
[37] 保立和夫、千種健二、水野洋輔、岸眞人、何祖源, "低コヒーレンスブリル
アン光相関領域解析法の S/N 比の向上", 電子情報通信学会 2009 年総合大会, C-3-91, 愛媛大学、2009 年 3 月 17 日-20 日.
[38] 水野洋輔、何祖源、保立和夫, "ノイズフロア補正による偏波スクランブリ
ングを用いた BOCDR の S/N 比の向上", 2009 年（平成 21 年）春季第 56 回
応用物理学関連連合講演会, 2a-P15-12, 筑波大学、2009 年 3 月 30 日- 4 月 2日.
[39] 水野洋輔、何祖源、保立和夫, "酸化ビスマスファイバにおけるブリルアン
周波数シフトの温度依存性", 電子情報通信学会 2009 年ソサイエティ大会,
B-13-41, 新潟大学、2009 年 9 月 15 日-18 日.
[40] 保立和夫、芦田哲郎、水野洋輔、岸眞人、何祖源, "低コヒーレンスブリル
アン光相関領域解析法の空間分解能向上", 電子情報通信学会 2010 年総合大会, 発表予定.

E.

Patents[41] 保立和夫、何祖源、水野洋輔、「光ファイバ特性測定装置及び光ファイバ特性測定方法」特願 2007－316440.

E.

Awards[42] 水野洋輔、第 22 回 独創性を拓く先端技術大賞 フジテレビジョン賞。「ブリルアン光相関領域リフレクトメトリの提案～光ファイバ神経網の実現に向けて～」に対して (2008 年 7 月 17 日).
[43] 水野洋輔、平成 20 年度 グローバル COE 博士課程成果報告会 優秀発表賞。
「ブリルアン光相関領域リフレクトメトリ(BOCDR)の性能向上」に対して(2009 年 3 月 9 日).
[44] 水野洋輔、何祖源、保立和夫, 平成 20 年度 光エレクトロニクス研究会 学
生優秀研究賞。
「偏波スクランブリングを用いたブリルアン光相関領域リフ
レクトメトリによる歪分布全長測定の安定化」に対して (2009 年 5 月 15

Dissertation 2009, The University of Tokyo

152

Publications related to this thesis

日).

F.

Others[45] Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Proposal and demonstration of
Brillouin optical correlation-domain reflectometry”, Symposium of Secure-Life
Photonics in Todai Week at Tsinghua, Tsinghua University, Beijing, China, May
19-21, 2008.
[46] 水野洋輔、"ブリルアン光相関領域リフレクトメトリの提案～光ファイバ神
経網の実現に向けて～", 全日本科学機器展 in 東京 2008, 東京ビッグサ
イト、2008 年 11 月 26 日-28 日. <invited>[47] Yosuke Mizuno, Zuyuan He, and Kazuo Hotate, “Distributed strain measurement
based on Brillouin optical correlation-domain reflectometry”, Asian Doctoral
Innovation Conference 2009 (ADIC2009), Zhejiang University, Hangzhou, China,
Nov. 22-25, 2009. <invited>

Dissertation 2009, The University of Tokyo

153