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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