Measurement of creep of optical fiber by a low coherent white light double
interferometer system
Zhihong Xua and Farhad Ansarib
Science School, Nanjing University of Science&Technology, Nanjing , China, 210014,
b
Dept. of Civil&Material Engineering,University of Illinois at Chicago, Chicago,IL, USA ,60607
a
ABSTRACT
In this paper the optical fiber are simplified as viscoelastic model and the creep properties are studied. A low coherent
white light double interferometer system is designed and calibrated. The creep deformations of optical fibers under static
and cyclic loadings are measured with the interferometer system. The theoretic and experiment results show that
polymer coated optical fibers creeps at the beginning when they are under static or cyclic load. But as the number of the
cyclic loading or the static loading time increase the creep tend to stop. Thus to ensure the optical fiber keeps pre-stress
for long time, it is recommended that the fiber should be tensioned cyclically before fixed into the sensor device.
Introduction
Pressure is a fundamental reservoir-engineering parameter in down-hole in oil well and its permanent monitoring is
utilized to guarantee the production process go on safely. The use of fiber optic technology, particularly for down-hole
applications, is driven by the inherent advantages of fiber optics over conventional sensor technology such as immunity
to electromagnetic interference, lightweight, small size, stability and durability in harsh environment [1-3] .Optical fiber
with Bragg grating is often used in mechanical transducer as sensing element and the sensing direction is the longitude
of the fiber. The optical fiber is very thin and it can only take tensile stress axially so in pressure sensor device the optic
fiber is intrinsically under a permanent tension. For the permanent down-hole monitoring system, the fiber optic sensors
have no chance to re-calibrate once they are put to use, so to keep the pre-tensioned stress in the fiber for long time is
the key problem for the reliability of the sensing system. Optical fiber is a kind of composite material, typically consisting
of a silica-based core and cladding surrounded by one or two layers of polymeric material. Silica is a brittle material and
the polymer coating can be considered as a visco-elastic one. When they are combined, the appeared properties of this
composite material will be visco-elasitc[4]. For the pre-stressed optical fiber, the creep property is the most important to
be considered to avoid the stress relaxation [5-8]. In this paper, the polymeric coating is considered as the Maxwell
viscoelastic material. The whole mechanic properties of the polymeric coated optical fiber simplified as three element
visco-elastic model .The creep properties of the optical fiber is studied experimentally. In experiment study, the optical
fiber are under cyclic loading and static loading respectively and the creeps are measured with a low coherence double
reflected interferometer. The theoretical analysis, experiment methodologies, instruments and experiment results are
outlined in the following sections.
Principle of the experiment setup
A schematic representation of the white light low coherence interferometer measure system is show in Fig.1. White light
from a wide-band LED in 1300 nm waveband with an FWHM (full width at half maximum) of 100 nm is launched into a
single mode fiber and then directed toward the specimen by means of a 2 × 1 coupler. At the two end surfaces of the
specimen the lights are reflected back to the 2 × 1 coupler where the beams are recombined with a relatively delay due
to the optical path length difference Ls and half of the reflected beam is fed into the second interferometer by a
2 × 2 coupler. The second one is of Michelson type consists of two reference arms, one of them has adjustable length
Lm ended by a mobile mirror mounted on a micrometric displacement table with a resolution of 1um and an operating
range of 50mm , the other one has a fixed geometric length L f .
Specimen
Lead line
2 × 1 coupler
LED
Reference arm
PD
2 × 2 coupler
Scan mirror
Data processor
Amplifier
Figure.1. Schematic of Low Coherent white light double interferometer system
The intensity at the output of the interferometer is measured with a photodiode and may be expressed as
I (λ ) = A{1 + b cos(ϕ (λ ) + φ )}
and
ϕ (λ ) =
(1)
2πnδL
(2)
λ
Where λ is wavelength, A is a constant depending on the light source and coupling losses, b the fringe visibility, φ
the phase difference between the interferometer arms, ϕ the introduced phase shift , n the refractive index of the
interferometer medium and
δL is the optical path-difference (OPD) between the coherent light.
Considering the common optical paths, the interference fingers appear and the intensity output
value
I max (λ )
I (λ )
get its maximum
when.
l f − lm − l s ≤ lc
(3)
l f , lm and ls are optic lengths correspond Ls , Lm and L f , lc is the coherence length of the light source.
In this system, the light source have 1300 nm wavelength and 100 nm , the coherence length is about 30 nm .
The relationship between the optical length difference ∆l and the geometric length deformation ∆L is given below [9]
1
(4)
∆l = {n − n 3 [( P12 + P11 )ν + P11 ]}∆L
2
Where
Where p11 and p12 are Pokels constants and υ the Possion’s ratio
Defining the effective refractive index of the fiber glass as
1
neff = n − n 3 [( p12 + p11 )ν + p11 ]
2
(5)
Equation (2) becomes
∆l = neff ∆L
(6)
For silica material at wave length
p11 = 0.121 , p12 = 0.27
λ = 1300 nm ,
and Possion’s ratio
the parameters are n = 1.46 , and photoelastic constants
v = 0.25 , the effective index can be calculated as neff ≈ 1.19 .
Calibration of the measuring system
To calibrate the interferometer, a device is designed to stretch fiber specimens. As shown in Fig.2. one end of the optical
fiber specimen is mounted on the stage and the other end is fixed. A micrometer controls the displacement of the moving
stage manually.
Figure.2. Setup of the stretch test
Figure.3 The end of the specimen
The specimens are made of commercial available telecommunication optical fibers, which are usually used to make
sensors. The gauge length is 1 meter. The ends of the specimens are stripped and soldered into ferrules with special
epoxy. The end surfaces of the fiber are polished carefully in order to reflect light. A plastic tube is used to protect the
fiber from damage during the test. Fig.3 shows the end of the specimen.
The specimen is tensioned slightly at first step. By adjusting the mirror position to satisfy equation (3), the first
interference position A, as shown in Fig 4, can be found and is used as reference. Then the specimen is stretched step
by step by moving the stage. For every step the geometric deformation of the specimen can be read out directly from
micrometer, considering (6), the corresponding interference position can be found by offset the mirror. In this way the
relationship of the geometric deformation of the specimen and the difference of interference positions can be established.
The positions of the mirror and the output signal of the interferometer are recorded by a computer based data acquisition
system as shown in Fig.4 and the pulses are the corresponding interference position. The calibration results are shown
in Fig.5.
output voltage(mv)
3
B
A
2.5
2
1.5
1
0.5
0
0
100
200
300
400
500
600
700
800
900 1000
Position of the mirror(um)
Deformation of the optical
fiber(um)
Figure.4 The interference position measured by interferometer
900
800
700
600
500
400
Measured by
micometr
Measured by
interfrometer
300
200
100
0
0
2
4
Number of the step
6
8
Figure.5 Deformation of the fiber specimen measured by the micrometer and interferometer system
Experiment program and discussion
In static load creep test, the specimens are hanged vertically and divided into two groups. The two groups are loaded
with weights of 3N and 5N respectively. The gauge length of the specimens is 0.5m. A specimen free of load is
measured at same time to provide the reference to compensate the influence of the temperature. The creep deformation
of the fibers is measured for every 24 hours (one day). The elongations of the fiber via the time are shown in Fig. 6.
Creep deformation(um)
300
250
200
150
100
weight=3N
weight=5N
50
0
0
2
4
6
8 10 12 14 16 18 20 22 24
Time(day)
Figure.6. Creep of the optical fiber under static load
In this test a high-speed step motor is employed to drive the moving of the stage, as shown in Fig.2. The specimens are
stretched cyclically as the stage goes back and forward. The position resolution of the stage is 1µm and the loading
frequency is 2Hz. The mean strain level was 0.5% in group 1 and 0.75 % in group 2, and the strain oscillation amplitude
was 0.25%. For each 10000 cycles the specimen is removed from the stage and the length difference is measured by
interferometer at stress free condition. The tests are done in room temperature and humidity. Fig. 7 shows the elongation
of two groups of optical fibers after they are released from cyclic load. It can be seen that the limitation of the elongation
of the optical fiber was about 250mm/m (250 µε ). The elongation of the fiber length is relatively larger at the beginning.
As the increase of the cycle number the length of the fiber tends to stable. This phenomenal is similar to that with static
load.
Creep deformation(um)
300
250
200
150
100
0.75 mean strain
50
0.5 mean strain
0
0
100000
200000
300000
counts of the cyclic loading
Figer.7. The creep of optical fibers under cyclic loading
Because of the inconsistent deformability of the coating and the silica core (including the core and cladding) in
production process, there are residual stresses in the optical fiber. The residual deformation of the core and cladding was
released as the fiber undergoes cyclic loading or loaded for a period time, the coating creeps and the residual stress is
released. With the cycle number or loading time increase, the coating creeps, residual stress gets smaller and smaller.
The effect of the coating gets weaker and weaker and the silica core determines the material properties of the optical
fiber, the silica core is a typical brittle material and no creep deformation in it.
Conclusions
The creep properties of the optical fiber used to make fiber optic sensor have been studied. Creeps under static and
cyclic load are measured with a permanent loading free elongation of the long gauge fiber optic sensors under cyclic
loading are measured with a low coherent white light double interferometer system. The experiment results show that
polymer coated optical fibers creeps at the beginning when they are under static or cyclic load. But as the number of the
cyclic loading or the static loading time increase the creep tend to stop. Thus to ensure the optical fiber keeps pre-stress
for long time, it is recommended that the fiber should be tensioned cyclically before fixed into the sensor device.
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