Cover Page

Title : Distributed strain sensing with long gauge FBG sensors based on opticalfrequency domain reflectometry

Authors: Hideaki Murayama
Hirotaka Igawa, Kazuro Kageyama, Isamu Ohsawa, Kiyoshi Uzawa, Makoto
Kanai, Shunichi Kobayashi, Takehiro ShiraiContact Address : 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
This is the Author’s Information,
Title: Lecturer
Affiliation: School of Engineering, The University of Tokyo
Address: 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656 Japan
E-mail: murayama@giso.t.u-tokyo.ac.jp
Web Page: http://www.gisolab.t.u-tokyo.ac.jp

Distributed Strain Sensing with Long Gauge FBG Sensors
Based on Optical Frequency Domain Reflectometry__________________________________________________________________________________________________________

H. MURAYAMA, H. IGAWA, K. KAGEYAMA, I. OHSAWA, K. UZAWA,
M. KANAI, S. KOBAYASHI AND T. SHIRAIABSTRACT:A quasi-distributed sensing system with fiber Bragg grating (FBG) sensors can be
useful for monitoring comprehensive deformation by measuring strain in a structure.
However, initial damage, such as crack, may generate not an abnormal deformation but
just a local perturbation in a stress distribution. If the area of the perturbation is muchsmaller than the gauge length of the FBG sensor, we will obtain an averaged strain value
from an interrogation system of FBG sensors. Some interrogation system may give us anabnormal one which cannot be quantitatively evaluated or is meaningless. Therefore, astrain sensing system with the higher spatial resolution and accuracy is required to detectdamage reliably and estimate the remaining strength of a structure. In this paper we showthat the distributed strain measurements with the high spatial resolution can be
implemented by the new sensing technique based on optical frequency domainreflectometry (OFDR). We could easily map the strain profile along a FBG from aspectrogram calculated by applying Fourier transform analysis with a sliding window to
the signal obtained from the measurement system. The signal obtained from themeasurement system can be simulated by the transfer matrix method based on coupledmode theory. In the experiments, we used also a long gauge FBG sensor whose gauge
length is 50 or 100 mm as well as an ordinary one whose gauge length is 10 mm. The
strain distribution adjacent to holes of an aluminum tensile specimen was measured by a
10 mm FBG with the polyimide coating and a 50 mm FBG with the acrylate coating. The
agreement between the experimental result of the polyimide coating FBG and thesimulated one was good. This means that the simulation model was reasonable and can beused to design a measurement system with higher performance. However, we could notaccurately measure strain varying sharply near the hole by the acrylate coating FBG.
_____________
H. Murayama, K. Kageyama, I. Ohwasa, K. Uzawa, M. Kanai and S. Kobayashi,
School of Engineering, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo
113-8656, Japan, e-mail: murayama@giso.t.u-tokyo.ac.jp
H. Igawa, Institute of Aerospace Technology, Japan Aerospace Exploration
Agency, 6-13-1 Ohsawa, Mitaka, Tokyo 181-0015, Japan
T. Shirai, Lazoc Inc., 3-40-9 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

INTRODUCTION
Fiber Bragg grating (FBG) sensors are used to measure strain or temperature in
structural sensing applications. Quasi-distributed sensing can be implemented by FBG
sensors which are discretely located along an optical fiber. Various techniques forinterrogating FBG sensors have been developed and they are capable of simultaneously
monitoring a number of FBG elements [1]. In general, such a quasi-distributed sensing
system with FBG sensors can be useful for monitoring deformation and assessing thestiffness of a structural member or the whole structure. However, initial damage, such as
crack or debonding, may generate not an abnormal deformation but just a local
perturbation in a stress distribution. If the area of the perturbation is much smaller than
the gauge length of the FBG sensor that is ordinarily about 10 mm, we will obtain an
strain value averaged within the gauge length from an interrogation system of FBG
sensors. Some interrogation systems may give us an abnormal one which cannot be
quantitatively evaluated or is meaningless. Therefore, a strain sensing system with thehigher spatial resolution and accuracy is required in order to detect damage reliably andestimate the remaining strength of a structure.
While FBG sensors with some interrogation systems are ordinarily employed forquasi-distributed strain or temperature measurements, they can be also applied tofull-distributed sensing. In recent years various techniques for distributed strain
measurements by using FBG have been proposed. If a strain distribution measured ismonotonic, the strain profile along the grating can be determined by analyzing thereflection spectrum [2]. A strain distribution along a chirped grating can be measured by
the phase-based sensing method or the low-coherence reflectometry [3,4]. However,these distributed sensing methods have a drawback, such as elimination of uniform
gratings or short sensing range. By using a tunable laser demodulation, the strain profile
along a uniform grating with a long gauge length can be mapped based on Fouriertransform analysis [5]. Although this sensing system can measure strain distributions
with the high spatial resolution, it seems that signals outputted from several
photodetectors in the sensing system have to be acquired individually and analyzed stepby step. In this paper we show that the distributed strain measurements with the highspatial resolution can be implemented by the new sensing technique based on opticalfrequency domain reflectometry (OFDR) [6].
In quasi-distributed strain measurements OFDR can be used to determine thewavelength of light reflected from hundreds of low reflectivity FBGs distributed alongan optical fiber [7]. The signal at the photodetector in the interferometer consisted of amirror end and FBG array is acquired at the constant wavenumber interval while thewavelength (wavenumber) of the laser light from the tunable laser is swept. The Fouriertransform of the signal sampled at the constant wavenumber interval provides theinformation on the position of each FBG in the array, and a narrow inverse Fouriertransform at specific positions (frequencies) within this Fourier transform can then be
used to recover the wavelength spectrum of a specific FBG.
On the other hand, in the distributed measurement using OFDR, we can easily map
the strain profile along a long gauge FBG or FBG array from a spectrogram given by
applying Fourier transform analysis with a sliding window to the signal at thephotodetecter in the measurement system whose layout is similar to that of Ref. [7]. The

signal in the interferometer with a mirror end and FBG sensors can be simulated by thetransfer matrix method based on coupled mode theory [8, 9]. In the experiments, weused also a long gauge FBG sensor whose gauge length is 50 or 100 mm as well as an
ordinary one whose gauge length is 10 mm. The strain distribution adjacent to holes ofan aluminum tensile specimen was measured by a 10 mm FBG with the polyimide
coating and a 50 mm FBG with the acrylate coating. The agreement between theexperimental result of the polyimide coating FBG and the simulated one was good. Thismeans that the simulation model was reasonable and can be used to design ameasurement system with higher performance. However, we could not accurately
measure strain varying sharply near the hole by the acrylate coating FBG. It is supposedthat the interface between the cladding and the coating was affecting the spatial
resolution in distributed strain sensing.
PRINCIPLE AND SIMULATION MODEL OF DISTRIBUTED STRAINSENSING WITH FBG SENSORS BASED ON OFDR
Optical system and data acquisition
The measurement system with OFDR consists of a wavelength tunable laser (ANDO
AQ4321A), three 3dB couplers (C1, C2, C3), two photodetectors (D1, D2), threebroadband reflectors (R1, R2, R3), FBG sensors and a Pentium PC installed a A/Dconverter (National Instruments PCI 6115) and data acquisition/processing program
written in LabVIEW. The arrangement with a long gauge FBG is shown in Fig. 1.
The laser light from the tunable laser is split by C1 and travels to C2 and C3. C2 isused to form an in-fiber interferometer with the light reflected R1 and R2, detected at
D1. This interferometer has an optical path length difference of 2nLR where n is theeffective refractive index and LR is the path difference of the two paths through theinterferometer. The reflected lights from R1 and R2, RLR1 and RLR2, are given by
RL R1 = exp{i (2nL R1 k + π )}(1)
RLR 2 = exp{i (2nLR 2 k + π )}(2)where LR1 is the distance between D1 and R1 as well as LR2 is that between D1 and R2.
Therefore, the difference between LR2 and LR1 is equal to LR. Additionally, k is thewavenumber of the light and is related to the wavelength λ and given by the following
equation.
2π
k=
(3)

λ

The signal at D1 is given by the following equation.
∗
D1 = (RL R1 + RL R 2 )(RL R1 + RL R 2 )(4)= 2{1 + cos(2nL R k )}As the laser is tuned, Eq. (4) implies light intensity observed by D1 varies in a cycle
depending on a wavenumber change, ∆k, of the following equation.
∆k =

π

(5)
nL R
The positive going zero crossing of the signal at D1 is used to trigger the sampling of
the signal at D2. C3 is used to form an in-fiber interferometer with the light reflected R3
and the long gauge FBG as well as C2 is. Therefore, the signal at D2 is given by

D2 = (RL R 3 + RL FBG )(RL R 3 + RL FBG )(6)
where RLR3 and RLFBG are reflected lights from R3 and the grating, respectively. RLR3 isgiven by
RLR3 = exp{i (2nLR3 + π )}(7)
where LR3 is the distance between D2 and R3. RLFBG can be determined by the transfer
matrix method based on coupled mode theory [10]. First, we divide the grating with thegauge length of L into M uniform sections whose length is ∆z as shown in Fig. 2. The
reflection characteristic of each section is regarded as uniform within the length of ∆z.
The input/output relationship for the interferometer system of Fig. 2 is given by⎡ R0 ⎤⎡ RM ⎤(8)⎢ S ⎥ = T ⎢ S ⎥; T = PG ⋅ F1 ⋅ F2 ⋅ ⋅ ⋅ Fi ⋅ ⋅ ⋅ FM
⎣ M⎦
⎣ 0⎦
where R0 and RM are the amplitudes of the forward propagating mode at the end of thedetector side and the another end, respectively. S0 and SM are the amplitudes of the
backward propagating mode at the end of the detector side and the other side,
respectively. The components of Fi and the phase-shift matrix, PG, are given byσˆκ⎡⎤sinh (γ B ∆z )−i⎢cosh (γ B ∆z ) − i γ sinh (γ B ∆z )
⎥
γB
B
⎥
(9)
Fi = ⎢
κσˆ⎢⎥sinh (γ B ∆z )cosh (γ B ∆z ) + i
sinh (γ B ∆z )
i
⎢⎣
⎥⎦
γB
γB
0
⎡exp{− in(L R 3 + LG )k }⎤(10)
PG = ⎢
0
exp{in(L R 3 + LG )k }⎥⎦⎣∗where σˆ and κ are the general “dc” self-coupling coefficient and the “ac” coupling
coefficient, respectively, and γ B = κ 2 − σˆ 2 [13]. LG is the distance between R3 andthe end of the detector side in the grating. Finally, when the boundary conditions (R0 = 1
and SM = 0) are applied to Eq. (8), we findT
(11)
RLFBG = S 0 = 21
T11
The D2 signal sampled at the constant wavenumber, ∆k, can be calculated by theequations from Eq. (5) to (11).

Figure 1: Schimatic of the measurement system

LR3
Reflector 3
LG

Detector 2L
F1 F2 … FM FBG

PG∆z ∆ z∆z

0z

Figure 2: Interferometer model with FBG
Data analysis
As mentioned above, while the wavelength of the laser light from the tunable laseris swept, the signal at D2 in the interferometer consisted of a mirror end and a longgauge FBG is acquired at the constant wavenumber interval. This signal is represented
by Eq. (6), and we can easily map the strain profile along the long gauge FBG from aspectrogaram given by applying Fourier transform analysis with a sliding window along
the wavenumber axis to the D2 signal. We can predict that there is thewavenumber/length resolution trade-off inherent related to the uncertainty priciple. So awide window gives better length (position) resolution but poor wavenumver(wavelength), while a narrower window gives good wavelength resolution but poor
position resolution.
Simulation result
We simulated the D2 signal obtained from the measuremet system with the FBG
whose gauge length was 100 mm and which was under the stress free condition, and wecompared it with the experiment result. Figure 3 shows the D2 signals and thespectrograms obtained from the experiment and the simulation. In the simulation n, LR,
LG and δn eff the “dc” index change spatially averaged over a grating period are 1.45,
15.47 m, 4.96 m and 3.10×10-6, respectively. The window length is 4000 points and it iscorresponding to the wavenumber width of about 560 /m. The window was slid along
the wavenumber axis as overlapping 3980 points.
The strain distribution can be found by determining the center wavelength of thespectrum at each position along the grating. As shown in the spectrograms of Fig. 3, we
can see that the strain of the actual FBG is varying due to the manufacturing
nonuniformity, while the strain distribution is uniform in the simulation result.
Experiment

1

5.1

0.8
]
u..
a[
er
w
o
P

]
m
[
n
oi
ti
os
P

0.6
0.4
0.2
0
1547.6

1547.81548

1548.2

1548.4

1548.6

Simulation

1

5
4.95
4.9
1547.81548

1548.2

1548.4

1548.6

1548.81548.2
1548.4
Wave Length [nm]1548.6

1548.8Simulation

5.15
5.1
]
m
[
n
oi
t
si
o
P

0.6
0.4
0.2
0
1547.65.05

4.85
1547.6

1548.8

0.8
]
u..
a[
er
w
o
P

Experiment

5.15

1547.81548

1548.2
WaveLength [nm]1548.4

1548.6

1548.8

5.05
5
4.95
4.9
4.85
1547.6

1547.81548

Fig. 3 D2 signals (left) and spectrograms (right) of the experiment and the simulation

DISTRIBUTED STRAIN SENSING IN STRESS CONCENTRATION ZONE

Stress concentration occurs frequently around a discontinuous site in the geometryor the material of a structure. It may cause fracture, and fracture may also cause it.
Therefore, it is important technique to detect or measure stress concentration in
structural health monitoring.
In this study, the strain distribution adjacent to holes of an aluminum tensile
specimen was measured by the distributed strain sensing with OFDR. The aluminumspecimen had a hole with the diameter of 4 mm and two holes with the diameter of 2mm as shown in Fig. 4. An FBG sensor whose gauge length was 10 mm and whose
coating was polyimide was bonded adjacent to the 4 mm hole to measure the strain
distribution which was varying sharply by the stress concentration. Another FBG was
also bonded on the other side along the holes. This FBG had 50 mm gauge length andthe acrylate coating. In the experiments, the specimen was statically subjected to thetensile loads of 1.0, 2.0, 3.0, and 3.5 kN.
Figure 5 shows the strain distributions in the 3.0 kN load. The solid line is the strain
distribution calculated by finite element method (FEM). By using our simulation modeland the FEM result, we could estimate the strain distribution which would be measured
by the sensing system. The estimated distribution is shown as the dashed line in Fig. 5.
This result showed the potential to measure strain accurately. In fact, the agreement
between the results of the FBG sensor with the polyimide coating and FEM is excellent.
However, we cannot see the sharp variation in the strain distribution measured by theacrylate coating FBG. It is supposed that the interface between the cladding and thecoating was affecting the spatial resolution in distributed strain sensing.
CONCLUSIONSIn this paper we showed that the distributed strain measurements with the highspatial resolution can be implemented by the new sensing technique based on OFDR.
Strain profile along a long gauge FBG can be easily determined in a spectrogram
calculated by applying Fourier transform analysis with a sliding window to the signal
obtained from the measurement system. The strain distribution adjacent to holes of analuminum tensile specimen was measured by the FBG with the polyimide coating andthe FBG with the acrylate coating. The agreement between the experimental result of
the polyimide coating FBG and the simulated one was good. This means that thesimulation model was reasonable and can be used to design a measurement system withhigher performance.

Figure 4: Tensile specimen with FBG sensors and holes

1000
800

Strain , µεSimulation

FEM

600
400
50 mm FBG
with acrylate coating

200

10 mm FBG
with polyimide coating

0
0

10

20
30
Position , mm

4050Figure 5: Strain distributions adjacent to the holes

REFERENCES
1.

J. Dakin and B. Culshaw, Optical Fiber Sensors Volume Four: Applications, Analysis, and Future
Trends, Artech House, pp.369-407 (1997)
2. M. LeBlanc, S. Y. Huang, M. Ohn and R. M. Measures, Distributed strain measurement based on afiber Bragg grating and its reflection spectrum analysis, Optics Letters, Vol. 21, No. 17,
pp.1405-1407 (1996)
3. M. Volanthen, H. Geiger and J. P. Dakin, Distributed grating sensors using low-coherence
reflectometry, Journal of Lightwave Technology, Vol. 15, No. 11, pp.2076-2082 (1997)
4. S. Huang, M. M. Ohn and R. M. Measures, Phase-based Bragg intragrating distributed strain sensor,
Applied Optics, Vol. 35, No. 7, pp.1135-1142 (1996)
5. R. M. Measure, M. M. Ohn, S. Y. Huang, J. Bigue and N. Y. Fan, Tunable laser demodulation ofvarious fiber Bragg grating sensing modalities, Smart Materials and Structures, Vol. 7, No. 2,
pp.237-247 (1998)
6. H. Igawa, H. Murayama, T. Kasai, I. Yamaguchi, K. Kageyama and K. Ohta, Measurements ofstrain distributions with a long gauge FBG sensor using optical frequency domain reflectometry,Proc. of SPIE, Vol. 5855, pp.547-550 (2005)
7. B. A. Childers, M. E. Froggatt, S. G. Allison, T. C. Moore, D. A. Hare, C. F. Batten and D. C.
Jegley, Use of 3000 Bragg grating strain sensors distributed on four eight-meter optical fibers during
static load tests of a composite structure, Proc. of SPIE, Vol. 4332, pp.133-142 (2001)
8. M. Froggatt, Distributed measurement of the complex modulation of a photoinduced Bragg grating
in an optical fiber, Applied Optics, Vol. 35, No. 25, pp.5162-5164 (1996)
9. A. M. Abdi, S. Suzuki, A. Schülzgen and A. R. Kost, Fiber Bragg grating array calibration, Proc. of
SPIE, Vol. 5765, pp.552-563 (2005)
10. T. Erdogan, Fiber Grating Spectra, Journal of Lightwave Technology, Vol. 15, No. 8, pp.1277-1294(1997)