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Royal Institute of Technology
Bachelor Thesis
Fiber Bragg Gratingsin Temperature and Strain Sensors
Author:
Ilian Haggmark
Supervisor:
Michael Fokine
Laser Physics Group
Department of Applied Physics
May 2014
ROYAL INSTITUE OF TECHNOLOGY
Abstract
Laser Physics Group
Department of Applied Physics
SA104X Degree Project in Engineering Physics, First Cycle
Fiber Bragg Gratings
in Temperature and Strain Sensors
by Ilian Haggmark
Supervisor: Michael Fokine
A Fiber Bragg Grating (FBG) is a periodic variation of the refractive index in an optic
fiber. It works as a wavelength selective filter and is used in several different applications
such as telecommunication and sensor technology. Fiber sensors are based on a simple
principle; the fiber is affected by strain, temperature etc. due to which the selection
of wavelengths in the FBG change. With an optical spectrum analyzer the changes in
wavelength reflection can be observed and converted to the physical quantity measured.
In this thesis the properties of FBGs used in temperature and strain sensors are tested.
Experiments to improve the precision of the sensors by embedding FBGs in metal are
also carried out.
KUNGLIGA TEKNISKA HOGSKOLAN
Sammanfattning
Laserfysikgruppen
Institutionen for Tillampad Fysik
SA104X Examensarbete inom Teknisk Fysik, Grundniva
Fiberbraggitter
i Temperatur- och Spanningssensorer
av Ilian Haggmark
Handledare: Michael Fokine
Ett fiberbraggitter (FBG) ar en periodisk variation av brytningsindex i en optisk fiber.
FBG fungerar som ett vaglangdsselektivt filter och har flera olika tillampningar inom
bland annat telekomunikation och sensorerteknik. Fibersensorer bygger pa en enkel
princip; fibern paverkas av temperatur, spanning m.m. och da forandras filtreringen
av vaglangder i FBG. Med en optisk spektrumanalysator kan forandringar i vaglangd
registreras och konverteras till den storhet som mats. In detta examensarbete testas de
egenskaper hos FBG som utnyttjas i temperatur- och spanningssensorer. Experiment for
att forbattra precisionen hos sensorerna genom att gjuta in FBG i metall utfors ocksa.
Acknowledgements
I would like to thank Michel Fokine, my supervisor, for helping me with everything, from
explanations of theoretical concepts, to construction of equipment and components down
in the workshop. Thanks also to PhD student Patrik Holmberg for help with practical
issues such as fusion splicing and acquiring and processing of data.
iii
Contents
Abstract i
Abstract in Swedish ii
Acknowledgements iii
Contents iv
List of Figures vi
List of Tables vii
Abbreviations viii
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Fiber Bragg Gratings and Sensors 2
2.1 Fiber Bragg Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1.1 Optical fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1.2 Main properties of FBG . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1.3 1st vs. 2nd order . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Manufacturing process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Experimental Setup 7
3.1 Measurement of development of reflection peaksduring writing process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Measurement of strain dependence . . . . . . . . . . . . . . . . . . . . . . 8
3.3 Measurement of temperature dependence . . . . . . . . . . . . . . . . . . 10
3.4 Measurement of FBG embedded in metal . . . . . . . . . . . . . . . . . . 11
3.4.1 Process to embed the FBG in metal . . . . . . . . . . . . . . . . . 11
3.4.2 Temperature dependence for embedded fiber . . . . . . . . . . . . 11
iv
Contents v
4 Results 13
4.1 Measurement of development of reflection peaksduring writing procsess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Measurement of strain dependence . . . . . . . . . . . . . . . . . . . . . . 14
4.3 Measurement of temperature dependence . . . . . . . . . . . . . . . . . . 15
4.4 Measurement of FBG embedded in metal . . . . . . . . . . . . . . . . . . 17
4.4.1 Measurements during casting process . . . . . . . . . . . . . . . . . 17
4.4.2 Temperature dependence for embedded fiber . . . . . . . . . . . . 19
5 Discussion 20
5.1 Temperature and strain dependence . . . . . . . . . . . . . . . . . . . . . 20
5.2 FBGs embedded in metal . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
6 Conclusions 21
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6.2 Suggestions for further study . . . . . . . . . . . . . . . . . . . . . . . . . 22
A Appendix A - Software and Hardware used 23
B Appendix B - Fibers 24
Bibliography 25
List of Figures
2.1 Peaks from first and second order . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Interference pattern created with laser . . . . . . . . . . . . . . . . . . . . 5
2.3 Peak movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 Setup for FBG writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Basic setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Strain setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.4 Mould 1 from side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.5 Mould 1 from top . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.1 Position of peak at 775 nm and 776 nm . . . . . . . . . . . . . . . . . . . 13
4.2 Height of peak at 775 nm and 776 nm . . . . . . . . . . . . . . . . . . . . 14
4.3 Strain dependence (1541 nm) . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4 Temperature dependence (1541 nm) . . . . . . . . . . . . . . . . . . . . . 16
4.5 Temperature dependence (778/779 nm) . . . . . . . . . . . . . . . . . . . 16
4.6 Embedded fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.7 Wavelength during casting process . . . . . . . . . . . . . . . . . . . . . . 18
4.8 Temperature dependence for embedded fiber . . . . . . . . . . . . . . . . 19
6.1 Comparison between embedded and unembedded fiber . . . . . . . . . . . 22
vi
List of Tables
3.1 Strain measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Temperature measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.1 Results from strain measurements . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Results from temperature measurements . . . . . . . . . . . . . . . . . . . 17
6.1 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
A.1 Properties of optical spectrum analyzers used . . . . . . . . . . . . . . . . 23
B.1 Properties of fibers used . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
vii
Abbreviations
FBG Fiber Bragg Grating
OSA Optic Spectrum Analyzer
FWHM Full Width Half Maximum
SMF Single Mode Fiber
viii
Introduction
1.1 Background
The massive increase in electronic communication during the last decades has spurred the
development of ways to transport and process large quantities of data. One important
contribution to this development has been the invention and development of optical
fibers. Though the possibilities opened up by this technology are great, there were
(and still are) many challenges involved. The transport medium has been given new
advantageous properties, but other equipment used, for example optical components
such as reflectors and wavelength selectors also need to develop to answer to the ever
increasing demand of fast, low cost and environmentally friendly equipment [1]. In 1978
Hill et al. made a major contribute to this with the creation of the first Fiber Bragg
Gratings (FBGs) [2]. A FBG is a periodic change of the refractive index in an optic
fiber. This grating can therefore be used as a wavelength specific selector. The selective
property has made FBGs an important tool in telecommunication, sensors and other
applications using optics.
1.2 Objective
The goal of this Bachelor thesis project is to make a short overview of FBGs application
in temperature and strain sensors and to discuss some improvements that can be done.
This thesis will consist of a brief description of FBG, experiments to study the properties
that enable fibers to be used as sensors and experiments to test the effects of embedding
FBGs in metal.
1
Fiber Bragg Gratings and Sensors
2.1 Fiber Bragg Gratings
2.1.1 Optical fibers
An optical fiber is a waveguide, i.e. a device that light (electromagnetic radiation) can
travel through over long distances with little dispersion. The basic idea behind optical
fibers is that the core of the fiber, through which the light travels, is surrounded by a
layer of material (cladding) that has lower refractive index than the core. Snell’s law,
ncore sin θi = ncladding sin θt (2.1)
where ncore is the refractive index of the core, ncladding is the refractive index of the
cladding, θi is the angle of a light beam heading for a core-cladding boundary and θt
the angle of the light beam that leaves the boundary, show why the light is not leaving
the fiber. If ncore > ncladding and the angle θi is large enough, Snell’s law will have no
solution which means that the transmission of light is zero, i.e. total internal reflection
occurs.
2.1.2 Main properties of FBG
A Fiber Bragg Grating (FBG) is a periodic modulation of the refractive index in the
core of an optic fiber. Waves travelling in a fiber with FBG will be reflected or refracted
trough the planes of the grating. Interference will therefore cause different wavelengths
to be either reflected or transmitted. To be reflected the wavelengths must satisfy the
2
Section 2. Fiber Bragg Gratings and Sensors 3
Bragg condition,
λB = 2nΛ (2.2)
where λB is the Bragg wavelength, n the effective refractive index and Λ the period of
the grating [2]. The Bragg wavelength can thus be altered by changing the parameters
n, Λ. The Bragg wavelength is also affected by additional factors such as the grating
length. Figure 2.1 shows an example of how a reflection peak from a FBG can look.
FBGs can be used in various applications where wavelength selection is advantageous
such as telecommunications for sorting of large quantities of data. Another growing area
for FBGs is sensors technology. The benefit of using FBGs as optical components and
sensors is that they are small, passive, robust, and have high sensitivity (precision) [3].
774 775 776 777 1530 1535 1540 1545 1550 15550.0
0.2
0.4
0.6
0.8
1.0
Powe
r (a.u
.)
Wavelength (nm)
Figure 2.1: Example of 1st and 2nd order reflection peaks from a FBG.
2.1.3 1st vs. 2nd order
In the interference pattern that creates the gratings several orders of maxima exists.
However the higher order maxima are usually so small that they can be neglected (see
figure 2.1) or lie outside the spectrum of interest. In common FBGs the Bragg wave-
length for the first maxima is around 1.54µm (micrometer, i.e. 10−6 m) while the second
order is around 0.78µm. The first order maxima is thus in the dominant telecom wave-
length band (1.530µm -1.565µm), which often is wanted since the telecom industry use
Section 2. Fiber Bragg Gratings and Sensors 4
FBGs in many applications. One negative aspect of using higher order peaks for dif-
ferent measurements is that the change in wavelength, ∆λ, is much smaller for higher
order peaks (see equation 2.3), which mean that the resolution will be inferior. The
down step in resolution will therefore be by a factor two for the second order peak. The
second order may however still be a desirable choice in practical applications since OSA
that operate in that range is cheaper.
2.2 Manufacturing process
The idea behind the process of creating FBGs (often referred to as writing) is to change
the refractive index of the core of the fiber with a powerful light source. There are a
few different methods used, each with advantages and disadvantages. There are also
different pretreatment methods to change the final product directly or to prepare the
fiber for the writing part of the process.
There are three commonly used methods for writing FBGs; Interferometric, phase mask,
and point by point. In the interferometric method a laser beam is spilt in two and then
directed with mirrors in such a way that the two beams intersect at the fiber. When
the two beams intersect they will create an interference pattern on the fiber (see figure
2.2) that will increase the refractive index at parts exposed light (i.e. the maxima’s
of the interference pattern). By changing the position and angle of mirrors and other
components the properties of the pattern inscribed can be changed. The use of many
mechanical components will however also give rise to increased sensitivity to vibrations.
The phase mask method is a method that has less sensitivity to vibrations. Its main
component is a phase mask, i.e. a transparent plate with a slit pattern inscribed. The
light directed at the phase mask will be split up in zeroth order and higher order. The
higher order beams may be focused on a fiber to create the FBG. The phase mask does
not suffer from the mechanical problems that the interferometric method does and is
therefore one of the most effective methods. The split of zeroth order and higher order
also makes it easy to suppress the zero order which improves the result. That is because
the zeroth order will increase the refractive index continuous over the fiber.
Section 2. Fiber Bragg Gratings and Sensors 5
����������������@
@@@@@@@@@@@@@@@�
���������������@
@@@@@@@@@@@@@@@
i i6
fiber
6
Interference pattern
@@R
��
UV beams
Figure 2.2: Interference pattern created on a fiber by two intersecting laser beams ofUV light.
Point by point is a method where only one point of the fiber is illuminated by the
powerful light source. By translation this point can be moved along the fiber while the
intensity of the light is changed to create the difference in refractive index. This method
gives great possibilities in changing the period, strength and other characteristics of the
FBG, but it depends heavily on the precision of the translator. [2]. The precision is also
limited by the spot size of the laser due to diffraction limits.
2.3 Sensors
Extrinsic and Intrinsic sensors are the two main groups of sensors. Extrinsic sensors use
fiber optics as part of the sensor and in intrinsic sensors the fiber is the sensor. In this
thesis focus will lie solely on intrinsic sensors.
The basics idea behind fiber sensors is that the properties of the FBG change due to
environmental variations. The amplitude of the index modulation, the period, the optic
strain, etc. are changes which alter the Bragg condition. As a result the spectrum of
the reflected (and transmitted) waves is changed (see figure 2.3). With the appropriate
equipment the changes in the spectrum may be measured and analyzed to determine
the value of temperature, strain, and other parameters of interest.
Section 2. Fiber Bragg Gratings and Sensors 6
The change in Bragg wavelength is described by the formula
∆λB = [(1 − pe)ε+ (αΛ + αn)∆T ]λB (2.3)
where pe is the strain optic coefficient, αΛ is the thermal expansion coefficient and αn is
the thermo-optic coefficient. As can be seen in equation 2.3 the change in wavelength is
not only dependent of effects that change refractive index and period but also the Bragg
wavelength. This means that the change in wavelength caused by an applied strain or
temperature rise will be greater if the Bragg wavelength is longer. To measure change
of wavelength in the telecom band will therefore give a precision that is more than twice
as high as for measurements in the visible spectra.
1530 1535 1540 1545 1550
0.0
0.2
0.4
0.6
0.8
1.0
Powe
r (a.u
.)
Wavelength (nm)
Figure 2.3: Three spectrums with varying degree of external influence (temperature,strain, etc.) from one FBG. The black spectrum is for room temperature and withoutexternal strain. The other two spectrums have been affected by heat and strain which
have push the spectrums to higher wavelengths.
FBGs have established an important role in telecommunication and sensor technology
during the last decade. In the future we will most likely see more and more applications
and wide spread use of FBGs as manufacturing of FBGs become more routine than it
is today. Today are sensors often expensive and vulnerable components of machines.
Fiber sensors might however change this fact in the future.
Experimental Setup
Three different experiments were carried out. First a measurement of the development of
reflection peaks during the writing process (i.e. creation of FBG). The objective was to
get a qualitatively comprehension of the peak development, especially for the second or-
der peaks. The second experiment was a test of wavelength change due to strain (∆L/L,
that is change in length per initial length) and temperature changes. The objective was
to confirm theoretical values. Temperature and strain were measured separately in dif-
ferent test so the combination of temperature and strain were not taken into account for
the sake of simplicity, even though it is a reality that must be considered when creating
real temperature and strain sensors. In the third test a FBG was embedded into metal.
There are several reasons why one would want to embed a FBG in a material such as
metal. It serves as a certain protection and more importantly, in the case of tempera-
ture sensors, increases the resolution of the measurement if a material of high thermal
expansion coefficient is used. The response to a temperature change, i.e. the change in
wavelength, will be greater if the thermal expansion coefficient of the metal is higher
than the fiber. That is because the metal expands more than the fiber normally would
and the metal thus stretch the fiber. This will add extra change in wavelength due to
the strain. A greater change in wavelength will be easier to measure and the precision
will therefore increase. The objective of the experiment was hence to see how much this
increase in precision would be.
3.1 Measurement of development of reflection peaks
during writing process
To be able to study the development of FBG (qualitatively) during the writing process
a grating was created by making multiple fast sweeps with a UV laser. This made it
7
Section 3. Experimental Setup 8
possible to gather data on the reflection spectrum between each sweep. The setup of the
FBG writing equipment is shown in figure 3.1. The spectrum at the first order peak,
at ca. 1541 nm (nanometer, i.e. 10−9 m), and the second order peaks, at ca. 776 nm,
was acquired with a Advantest OSA (see Appendix A). The OSA 50 average (i.e. the
final spectrum is the average of 50 acquired spectrums) was used to reduce the impact
of noise. Fiber FBG2 (see Appendix B) was used.
Figure 3.1: The setup for writing of FBGs (courtesy of M. Fokine).
3.2 Measurement of strain dependence
To confirm the theoretical values of change in wavelength due to strain (∆λ/ε ratio) in
the fiber each end of the fiber was fastened in small tracks with nail polish. One end was
attached to a stationary track and the other to a small translator that could be moved
with high precision. The Basic setup can be seen in figure 3.2. Light from the light
source travelled through the fiber to the circulator and was passed on in the downward
Section 3. Experimental Setup 9
Light source &%'$
OSA?
-
fiber
FBG
Circulator
Figure 3.2: Basic setup for measurements
direction (in the figure). The light that was reflected by the FBG (depicted as a rect-
angle though it is part of the fiber) returned to the circulator and was directed to the
OSA. The reflected light for different strains was measured with the Bay spec OSA (see
Appendix B) and then automatically analyzed in the Bay spec software to determine
the wavelength of the reflection peak. The data acquiring for the second order peak(s)
was done with the Mightex OSA. The analyzing of the data was done with a B-spline
in the origin software for Mightex OSA. After an increase in strain four to six measure-
ments were taken with a 30 seconds interval to see if the fiber was slipping. Finally the
wavelength was plotted as a function of microstrain (µε, i.e. strain in parts per million)
and the slope was calculated with the origin software. Changes in wavelength for the
“same” strain were consequently represented as vertical displacement of the data points.
An alternative stacking mechanism was also used (see figure 3.3). The ends of the fiber
were infused inside small tin spheres (instead of using nail polish). Two different fibers
were used. Fiber N3, that had one second order peak and FBG1 that had two second
order peaks. Each measurement with corresponding parameter/method is tabulated in
table 3.1.
Section 3. Experimental Setup 10
Fiber with FBGSolder Solder
Translation stageStationary stage
Figure 3.3: Setup for measurements of ∆λ/ε ratio.
nr. stacking method fiber average (Bay spec) average (Mightex)
1 nail polish N3 10 (0.1 s/acquisition) -2 nail polish N3 1000 (0.1 s/acquisition) no avg3 tin spheres N3 2000 (0.1 s/acquisition) no avg4 tin spheres FBG1 200 (0.1 s/acquisition) 1000
Table 3.1: Parameters and method for measurements of ∆λ/ε ratio.
3.3 Measurement of temperature dependence
To confirm the theoretical values of change in wavelength due to temperature (∆λ/∆T
ratio) in the fiber it was placed on a hot plate between sheets of aluminum foil. Per-
pendicular to the fiber a thermocouple was placed so that the tip of the thermocouple
was in close proximity of the FBG. A ceramic plate was placed on top as insulation.
The temperature was recorded with the software PicoLog and the wavelength with the
Bay spec and Mightex OSA. The setup of the FBG, the OSA and the light source was
the same as for the measurements of ∆λ/ε (see figure 3.2) The hot plate was turned on
for about 30 min and reach a temperature of about 70 ◦C. An alternative method for
measurement of wavelength dependence on temperature was also used. The tempera-
ture of the hot plate was increased and then allowed to reach a near equilibrium point
(in respect to added effect to the hot plate and lost effect through cooling). Six data
points were taken at 25, 50, 75, 100, 125, and 150 ◦C. The data acquiring was made
with the Bay spec for first order peak and the Mightex for the second order peaks. Each
measurement with corresponding parameter/method is tabulated in table 3.2.
Section 3. Experimental Setup 11
nr. method fiber average (Bay spec) average ( Mightex)
1 continuous increase N3 2000 (0.1 s/acquisition) -2 continuous increase N3 2000 (0.1 s/acquisition) -3 continuous increase N3 - 1000 (10 ms/exposure)4 equilibrium FBG1 200 (0.1 s/acquisition) 100 (10 ms/exposure)
Table 3.2: Parameters and method for measurements of ∆λ/∆T ratio
3.4 Measurement of FBG embedded in metal
3.4.1 Process to embed the FBG in metal
An alloy between tin (Sn) and lead (Pb) (i.e. solder) with proportions 63/37 was used.
The alloy was melted in a small crucible and then poured into a mould. The time before
the alloy would solidify was quite short (a few seconds) so the fiber had to be properly
stretched in the mould before the alloy was poured into the mould. Two different moulds
were used. A proper mould (see figure 3.4 and 3.5) and a solid metal cylinder in brass
with one quarter removed. The second one was quite crude, but the fiber could easily
be stretched along the removed quarter of the cylinder. The high surface tension of the
tin-lead alloy allowed the melt to stay in the mould without draining. During the casting
process, i.e. when the melt was poured into the mould and until the metal clearly had
solidified, a measurement of wavelength was made. To be able to get enough resolution
a high frequency peak sampling (500 Hz) was used.
3.4.2 Temperature dependence for embedded fiber
The fiber (FBG1) embedded in the tin-lead alloy was heated in an oven. The temperature
was allowed to stabilize at different points and measurements of wavelength with the
Bay spec (1000 avg, 0.1 s/acquisition) and Mightex (Dark subtracted, 1000 avg,
10 ms/exposure) OSA were taken.
Section 3. Experimental Setup 12
Figure 3.4: The first mould. The black dashed line shows where the fiber lies.
Figure 3.5: The first mould. The black dashed line shows where the fiber lies.
Results
4.1 Measurement of development of reflection peaks
during writing procsess
Three peaks were identified, one at 1540 nm and two at 776 nm. For each peak the
position of the peak maximum, the peak height and FWHM was plotted. All peaks
showed a clear linear trend to move to a longer wavelength for each scan (see figure 4.1).
The change in peak position was about half a nanometer for 9 scans (a little less for the
second order peaks).
0 1 2 3 4 5 6 7 8 9775.0
775.2
775.4
775.6
775.8
776.0
776.2
776.4
Wav
eleng
th (n
m)
Scan Nr.
775 nm 776 nm
Figure 4.1: Position of the reflection peaks at 775 nm and 776 nm.
The height of the first order peak rose quickly (it reached full height after the second
scan) and remained fairly constant under the following scans. The second order peaks
13
Section 4. Results 14
however rose and then began to descend (see figure 4.2). The FWHM didn’t show such
a clear result. The first order peak rose slowly (in comparison to the change in height)
and seemed to approach a constant value of ca 0.95 nm. The second order peak at 775
nm seemed to grow and then shrink, which would be consistent with the behavior of the
height but too few data point were taken to make any certain conclusions. The FWHM
of the second order peak at 776 nm was fairly constant.
0 1 2 3 4 5 6 7 8 9
0
50
100
150
200
250
300
350
400
Powe
r (pW
)
Scan Nr.
775 nm 776 nm
Figure 4.2: Height of the reflection peaks at 775 nm and 776 nm.
4.2 Measurement of strain dependence
test nr. 1st order [pm/µε] 2nd order [pm/µε]
1 0.479 ± 0.0035 -2 0.673 ± 0.0264 0.450 ± 0.04383 1.18 ± 0.0155 0.562 ± 0.07644 1.21 ± 0.0156 0.610 ± 0.0063&0.613 ± 0.0054
Table 4.1: Results from measurements of ∆λ/ε.
The results from the strain measurements are summarized in table 4.2. The common
value for this kind of fiber is 1.2 pm/µε for the first order and half that for the second [2].
The two first measurements were consequently quite bad. It also became evident that
the method was insufficient since the data points (from test nr. 1) for the same strain
in figure 4.3 show a clear vertical displacement i.e. the wavelength changed even though
Section 4. Results 15
the strain was supposed to be constant. The room temperature was monitored during
measurement to make sure that it had no impact on the result. It was 21.3 ± 0.1 ◦C
which was not enough to causes any major disturbance. One of the main contributors
to the error was observed to be the stacking mechanism. When the translator returned
to zero after completing the measurement the fiber was clearly bent i.e. the stacking
mechanism proved to be insufficient since the fiber was slipping. This conclusion was
also confirmed by the fact that after an increase in strain, which induced an increase
in wavelength by a hundred pm or so, the wavelength decreased a few tenths of a pm
(discernible as vertical displacement in figure 4.3). With the tin sphere stacking method
a much better result was achieved. The slope for the first order peak was 1.18 pm/µε
for the N3 fiber and 1.21 pm/µε for the FBG1 fiber.
0 500 1000 1500 2000
0.0
0.2
0.4
0.6
0.8
1.0
Delta
Wav
eleng
th (n
m)
Microstrain
Measured Linear fit
Figure 4.3: Change of wavelength as a function of microstrain at 1541 nm for test nr.1.
4.3 Measurement of temperature dependence
In table 4.2 are the results from measurements presented. A common value for the
∆λ/∆T ratio for the kind of fiber used is 10 pm/◦C for the first order. It is therefore
evident from the table that the method used in test number 4 was better. The data
from the fourth measurement is plotted in figure 4.4 (Bay spec) and 4.5 (Mightex).
Section 4. Results 16
20 40 60 80 100 120 140 1601541.0
1541.2
1541.4
1541.6
1541.8
1542.0
1542.2
1542.4
Wav
eleng
th (n
m)
Temperature (°C)
Measured Linear fit
Figure 4.4: Change of wavelength as a function oftemperature at 1541 nm for testnr. 4.
20 40 60 80 100 120 140 160778.4
778.6
778.8
779.0
779.2
779.4
779.6
779.8
780.0
Wav
eleng
th (n
m)
Temperature (°C)
Measured (779 nm) Measured (778 nm) Linear fit
Figure 4.5: Change of wavelength as a function oftemperature at 778 nm and 779 nmfor test nr. 4.
Section 4. Results 17
test nr. 1st order [pm/◦C] (Bay spec) 2nd order [pm/◦C] (Mightex)
1 8.91 ± 0.295 -2 8.61 ± 0.321 -3 - 4.19 ± 0.2544 10.0 ± 0.051 5.08 ± 0.037 & 4.81 ± 0.154
Table 4.2: Results from measurements of ∆λ/∆T ratio.
4.4 Measurement of FBG embedded in metal
4.4.1 Measurements during casting process
The first mould used gave a fine metal piece, but since the fiber was quite brittle (there
was no coating around the FBG) it proved difficult to remove the fiber embedded in
metal from the mould without breaking the fiber in the process. The second mould was
more sufficient (see figure 4.6).
Figure 4.6: The fiber embedded in alloy and a sketch of the cross section of the fiberand alloy below. The FBG is denoted by the little rectangle in the middle of the alloy.
The plot of wavelength as a function of time (see figure 4.7) shows both clearly the
different stages in the casting process and the concept enabling fibers to work as sensors.
The wavelength was first constant, and then when the melt was poured into the mould
the wavelength rose fast due to the quick change in temperature. The oven was about
300 ◦C, but the amount of melt was quite small so the temperature should have decreased
Section 4. Results 18
while the melt was taken from the oven until it was poured into the mould. In previous
measurements the ratio ∆λ/∆T have been determined to be about 10 pm/◦C. The
change in wavelength at 5 seconds is about 2500 pm so the increase in temperature
should be 250 ◦C. With a room temperature of 21 ◦C the peak temperature was about
271 ◦C, which seems reasonable given the temperature of the oven. At about 6 seconds
a small change in the decrease can be seen. Still using the 10 pm/◦C the temperature
should be about 200 ◦C. The melting point of the alloy is 183 ◦C so the change at 6
seconds is probably the melt beginning to solidify. The change at 10 seconds could
therefore be the point where the now solid alloy exert enough pressure to affect the
strain of the fiber. Beyond the point at 10 seconds a new ∆λ/∆T ratio applies. Since
this ratio is higher, due to larger thermal expansion coefficient, the wavelength at room
temeprature will be less than before. For wavelengths below 1541 nm, i.e. the wavelength
for a fiber (not embedded) in room temperature, is the fiber affected by compression.
-5 0 5 10 15 20 25 30 35
1538
1539
1540
1541
1542
1543
1544
Wav
eleng
th (n
m)
Time (s)
Figure 4.7: Change of wavelength as the melt was poured on to the fiber.
Section 4. Results 19
4.4.2 Temperature dependence for embedded fiber
The measurement with the Mightex OSA showed a clear result; 25.2±0.48 pm/◦C. The
peaks from the Bay spec OSA had little problem with splitting of the peaks, but with
a few data points omitted the result 50.9 ± 1.46 pm/◦C was achieved. The result from
the first order alone had quite a large uncertainty. However when comparing the results
from the first and second order peaks it became clear that the result probably was quite
good since the ratio ∆λ/∆T for the first order was almost exactly twice that of the
second order (see figure 4.8) in accordance with the theory (see section 2).
20 40 60 80 100 120 140
0
1
2
3
4
5
6
Delta
Wav
eleng
th (n
m)
Temperature (°C)
1st order 2nd order Linear fit
Figure 4.8: The temperature dependence for the first and second order peak for theembedded fiber.
Discussion
5.1 Temperature and strain dependence
Fiber N3 had two second order peaks that were overlapping. Fiber FBG1 had on the
other hand two clearly separated second order peaks. This was probably a contributor
to the better result that FBG1 yielded. Three important factors that determined the
precision of the temperature or strain measurement became evident during the test.
First of all, and quite obvious, the resolution of the OSA is important, secondly the
shape of the peak. For example a broad peak could be difficult to read because it is
dubious where the top is or where you should measure. In a program with an automatic
peak finder this could be observed as a constant fluctuation in peak wavelength even
though the temperature/strain was constant. The third factor is the ratio ∆λ/∆T and
∆λ/ε. Higher ratio means that a change in temperature or strain will result in a greater
change in wavelength that will be easier to resolve with the OSA. As mentioned in
section 2 the ratio is smaller for higher peaks so one would normally use the first order
peak to achieve the greatest ratio and consequently resolution. As we have seen are
there however ways of changing the ratio.
5.2 FBGs embedded in metal
The advantages of embedding a FBG in an alloy are quite obvious from the result.
The resolution can be increased by a factor five and even if the second order is used
for a sensor application the resolution will be two and a half times greater than for the
normal first order. By embedding a fiber in an alloy of high thermal expansion coefficient
a higher resolution can be achieved even when higher order peaks are used.
20
Conclusions
6.1 Conclusions
From the measurements in section 4 and 5 it is evident that FBGs are good candidates
for creating small efficient sensors. The results of the measurements a summarized in
table 6.1.
Bare fiber Metal coated fiber
λ [nm] ∆λ/∆T ∆λ/ε ∆λ/∆T ∆λ/ε
1540 10.0 pm/◦C 1.21 pm/µε 50.9 pm/◦C -780 5.08 pm/◦C 0.61 pm/µε 25.2 pm/◦C -
Table 6.1: Summary of results.
Three important parameters that determine the precision are the FBG, the resolution
of the OSA and the ratio ∆λ/∆T (or ∆λ/ε). With the Mightex OSA the resolution was
not high enough to resolve the peaks properly so the data had to be analyzed with a
B-spline to determine an approximate peak maximum. The Bay spec OSA had higher
resolution although this was achieved with a built in spline method. The OSAs used
in the experiments were however OSAs for general lab use and therefore had quite a
broad spectral range (see Appendix B). Only about a hundredth of the range was used
in the measurement (little less for the Bay spec). For a more thorough study or for
commercially produced sensors an OSA with much more narrow range could be used.
This would also mean that the resolution could be increased about two orders of magni-
tude since there always is a compromise between range and resolution for cheap OSAs.
Broad range reduces the resolution and narrow range makes it possible to achieve a high
resolution.
21
Section 6. Conclusions 22
20 40 60 80 100 120 140 160
0
1
2
3
4
5
6
Delta
Wav
eleng
th (n
m)
Temperature (°C)
1st order (embedded) 2nd order (embedded) 1st order (not embedded)
Figure 6.1: The temperature dependence for the first and second order peak for theembedded fiber and 1st order for a normal fiber.
The idea of embedding a FBG in a material of high expansion coefficient proved quite
successful. The ratio ∆λ/∆T was increased with a factor five (see figure 6.1) which
improved the possibilities of creating FBG sensors with high accuracy. The higher ratio
reduces the disadvantages of using higher order peaks so sensors working in the visible
range with good accuracy can be created.
6.2 Suggestions for further study
In this project the main focus has been on the ratio ∆λ/∆T so subjects for further
study could therefore be variations of alloy composition, optimal FBG characteristics or
different kinds of OSA (preferably cheaper and with small range that could be used for
actual applications).
Appendix A - Software and Hardware used
Hardware:
Table A.1 lists the OSA used. The (white) light source was a Koheras Super K, 450 nm
– 2.2 µm. For temperature measurements a type K thermocouple was used.
Name Spectral range [nm] Maximal resolution [nm]
Mightex 200-1050 0.2-0.9Bay spec 1510-1590 0.001 (with software analysis)Advantest 600-1750 0.1
Table A.1: Different optical spectrum analyzers used
Software:
Origin Lab Pro 6.1 and 9 (General plotting and data processing software) and PicoLog
for measurements of temperature.
23
Appendix B - Fibers
Name Type H2 loaded time in room temperaturebefore FBG writing
Fiber N3 SMF-28 Yes 1 hFBG1 SMF-28 Yes 24 hFBG2 SMF-28 Yes 24 h
Table B.1: Different fibers used. H2 loading done at 120 bars for 12 days and thenstored in -60◦C until use.
24
Bibliography
[1] Raman Kashyp. Fiber Bragg Gratings. Elsevier, 2nd edition, 2010.
[2] Andreas Othonos. Fiber bragg gratings. Review of Scientific Instruments, 68(12),
1997.
[3] Spillman E. Udd. Fiber Optic Sensors. Springer, 2nd edition, 2010.
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