Upps al a univ ersit ets l ogot yp
UPTEC F 21053
Examensarbete 30 hp Juni 2021
Simultaneous measurement and discrimination of temperature and strain in distributed fiber optical systems with fiber Bragg gratings
Mastrothanasis Helene Alexandra
Civilingenj örspr ogrammet i t ek nisk fysik
Teknisk-naturvetenskapliga fakulteten Uppsala universitet, Utgivningsort Uppsala
Handledare: Anna Karin Holmér och Michael Fokine Ämnesgranskare: Anders Rydberg
Upps al a univ ersit ets l ogot yp
Simultaneous measurement and discrimination of temperature and strain in distributed fiber optical systems with fiber Bragg gratings
Mastrothanasis Helene Alexandra
Abstract
This master thesis deals with simultaneous measurement and discrimination of temperature and strain using fiber Bragg gratings(FBGs). Saab Avionics is seeking for a further development of the overheat detection system that gives a warning when a heat leakage is detected. A further development is to distinguish between temperature and strain and give a warning when strain occurs that correspond to a temperature increase of 10°C. The present work was
performed for Saab Avionics and the experiments were carried out in Kungliga Tekniska Högskola(KTH) at department of Laser Physics.
The aim of this thesis was to study some methods for simultaneous measurement of temperature and strain with FBGs and try to discriminate them. Two methods were investigated, a sensor design containing a boron-codoped germanosilicate fiber and a germanosilicate fiber and fibers with different cladding diameters. The gratings were heated in an oven and stressed with solder between a translation stage and a stationary stage.
For the boron-codoped germanosilicate fiber the temperature sensitivity was ~ 2 times lower than the germanosilicate fiber, while they had similar strain responses. For the second sensor design with different cladding diameters, for a 80 μm cladding diameter the strain response was
~ 2.5 times higher that the 125 μm cladding diameter, while for a 100 μm cladding diameter the strain response is ~ 1.6 times higher than the 125 μm cladding diameter. For a 125 μm, a 100 μm and a 80 μm cladding diameter the temperature sensitivities were similar.
Tek nisk-nat urvetensk apliga f ak ulteten, Upps ala universit et . Utgiv nings ort U pps al a. H andl edare: Anna Karin H olm ér oc h Mic hael Foki ne, Ämnesgransk are: Anders R ydberg, Ex aminat or: T om as Ny berg
Popul¨ arvetenskaplig sammanfattning
Den senaste ˚ar forskare inom optiska fiber har visat ett stort intresse f¨or att till¨ampa fiber Bragg gitter(FBG) som optiska sensorer. Eftersom optiska fiber har en liten storlek och tillverkas enkelt
¨
ar dem v¨aldigt anv¨andbara. Fiber sensorer kan anv¨andas inom industri och medicin. Saab Avion- ics tillverkar idag sensorsystem med fiber Bragg gitter f¨or bland annat temperaturmonitorering i flygplan.
Fiber Bragg gitter kan simultant m¨ata temperatur och t¨ojning. Beroende p˚a olika dopnings mate- rial och olika cladding diameter av FBG kan responser av temperaturk¨ansligheten och t¨ojningsk¨ans- ligheten urskiljas. Om en bor dopad germaniumsilica fiber svetsas med en germaniumsilica fiber och FBGer skrivs p˚a dessa tv˚a olika fiber, olika temperaturk¨ansligheter uppkommer med ¨okande temperatur medan med ¨okande sp¨anning samma t¨ojningsk¨ansligheter uppst˚ar. Denna sensor de- sign har en liten storlek och en bel¨aggning kan placeras f¨or att skydda den utan att f¨or¨andra sensor designen.
Om fiber med olika cladding diameter anv¨ands f¨or att skriva Bragg gitter, uppst˚ar olika t¨ojn- ingsk¨ansligheter med ¨okande t¨ojning medan temperaturk¨ansligheten med ¨okande temperatur har likande respons. En minsking i cladding diametern ¨okar t¨ojningsk¨ansligheten av sensorn, eftersom fiberns tv¨arnittsarean minskar. Denna sensor design har en liten storlek men en utf¨orlig studie om passande bel¨aggning m˚aste g¨oras f¨or att inte ¨andra sensor design, eftersom tjockleken av bel¨aggnin- gen kan p˚averka t¨ojningsk¨ansligheten.
B˚ada sensor design kan urskilja temperaturk¨ansligheten och t¨ojningsk¨ansligheten och en p˚alitlig system kan produceras. Fiber Bragg gitter har liknade beteende n¨ar t¨ojning och temperatur ap- pliceras och ¨ar sv˚art att urskilja dem, men metoder som fiber med olika dopnings material och fiber med olika cladding diameter kan urskilja dessa. Saab anv¨ander idag system med Fiber Bragg gitter f¨or m¨atning av l¨ackage av varmluft i flygplan. L¨ackage av varmluft kan orsaka ¨overhettning och ¨ar d¨arf¨or viktigt att monitorera. Olika metoder finns f¨or att minimera inverkan av t¨ojning p˚a temperaturm¨otningen. Att kunna m¨ata b˚ade temperatur och t¨ojning g¨or det m¨ojligt att ¨oka noggrannheten och s¨akerheten i m¨atmetoden ytterligare. Samtidift ¨okas systemets kapabilitet och
¨
oppnar upp f¨or anv¨andning ¨aven i andra till¨ampningar.
F¨or temperatur m¨atningar v¨armdes fibern upp och n¨ar den hade stabiliserats vid 400◦C (ca 30-40 min) s¨anktes temperaturen till 100◦C, med en intervall av 50◦C. F¨or t¨ojnings m¨atningar l¨oddes fibern fast p˚a en station¨ar h˚allare och ett translations steg. Fibern t¨ojdes med en l¨angd¨andring av 0.20 mm n¨ar fibern var i rumstemperatur (24◦C). Alla m¨atdata sparades och plottades vilket gav temperatur- och t¨ojningsk¨ansligten.
CONTENTS CONTENTS
Contents
1 Introduction 1
1.1 Background . . . 1
1.2 Assignment . . . 4
1.3 Literature study . . . 4
1.4 Chosen methods . . . 6
1.5 Outline of the thesis . . . 6
2 Theoretical background 7 2.1 Optical fibers . . . 7
2.2 Fiber Bragg gratings . . . 8
2.3 Strain and temperature sensitivity of fiber Bragg grating . . . 8
2.4 Simultaneous measurements of strain and temperature . . . 9
3 Method 11 3.1 Fabrication of FBGs . . . 11
3.2 Basic setup . . . 11
3.3 Temperature measurements . . . 12
3.4 Strain measurements . . . 13
3.5 Old setup . . . 14
4 Results 17 4.1 Boron-Codoped Germanosilicate and Germanosilicate Fiber . . . 17
4.1.1 GF4A and UHNA1 . . . 17
4.1.2 GF3 and UHNA1 . . . 18
4.2 Fiber Diameters . . . 19
4.3 Error analysis . . . 20
5 Discussion 25 5.1 Suggestions . . . 26
6 Conclusions 28
7 Further study 29
8 Acknowledgment 30
A Appendix 33
LIST OF FIGURES LIST OF FIGURES
List of Figures
1 Image of a typical strain gauge [3]. . . 1 2 The structure of a strain gauge. A strain gauge consists of a resistive foil that is
mounted on a backing and current passes through two electrical wires(leads). . . . 2 3 Circuit diagram of the Wheatstone bridge [7]. . . 2 4 The circuit diagram of the quarter bridge strain gauge. The quarter bridge strain
gauge is a Wheatstone bridge where the resistor R4is replaced with an active strain gauge [9]. . . 3 5 The circuit diagram of half bridge strain gauge. It is a Wheatstone bridge where two
resistors are replaced with two strain gauges. This configuration is used to eliminate the temperature effects [12]. . . 3 6 The structure of an optical fiber, where the core has a refractive index n1 and the
cladding has n2. The cladding is surrounded by a protective coating. . . 7 7 When an incident ray hits the interface the ray is refracted and/or reflected. Partial
reflection occurs when θr> θI(and n1> n2). When the incident angle increases the refracted angle also increases and the largest value of the refracted angle is θr= 90◦. It is called critical angle when θr= 90◦. Total internal reflection occurs when θI > θc. 7 8 The dimensions of the multi-mode and the single-mode fiber. Both have a cladding
diameter of 125 µm, but the core diameter for the multi-mode fiber is 50 µm and for a single-mode fiber is 9 µm [22]. . . 8 9 Schematic representation of a Bragg grating inscribed in the core of a fiber. An
incident spectrum is reflected when the Bragg condition is satisfied and the rest is transmitted through the core of an optical fiber. . . 8 10 The system used to write Bragg gratings. A UV light sends light through a phase
mask and with the help of an cylinder lens parallel with an optical fiber, fiber Bragg gratings are inscribed in the core of it (picture provided by my supervisor M.Fokine). 11 11 The setup where fiber Bragg gratings are connected for temperature and strain
measurements. The white light source(WL) is connected with a circulator, where light sends through and is reflected back in the circulator by the fiber Bragg grating.
The reflected Bragg wavelengths are recorded in the optical spectrum analyzer(OSA). 12 12 The Carbolite cwf 11/5 chamber furnace [27]. . . 13 13 How the FBG was placed beside the thermocouple in the oven. . . 13 14 Graphically setup for strain measurements. A fiber with a written Bragg grating
and length L, mounted with solder on the top of a stationary and a translation stage. 13 15 The setup for strain measurements. Fiber Bragg grating fastened with solder be-
tween a stationary holder(nr 2) and a translation stage(nr 3). The outer section of the fiber were fastened on the stationary holders(nr 1 and nr 4). . . 14 16 The setup of the oven, where two ceramic plates(no 1 and no 2) and a polyimide
heater mat were used. . . 14 17 The oven setup where two ceramic tubes were fastened on a metallic sheet and
heated by a polyimide heater mat. . . 15 18 The experimental setup. The Bragg grating was placed on the oven(in the mid-
dle) and fastened with nail polish on the stationary holder(to the left) and on the translation stage(to the right). . . 15 19 In the first test setup the fiber was fastened with nail polish on the top of the
translation stage. Due to the fact that the fiber was slipping when it was stressed, the method was improved and the the nail polish was replaced with solder. . . 16 20 Temperature response when temperature is applied on boron-codoped germanosili-
cate fiber(GF4A) and on germanosilicate fiber(UHNA1). . . 17 21 Strain response when the boron-codoped germanosilicate fiber(GF4A) and germanosil-
icate fiber(UHNA1) is stressed. . . 17 22 Temperature response when temperature is applied on boron-codoped germanosili-
cate fiber(GF3) and on germanosilicate fiber(UHNA1). . . 18 23 Strain response when the boron-codoped germanosilicate fiber(GF3) and germanosil-
icate fiber(UHNA1) is stressed. . . 18 24 Temperature response when temperature is applied on germanosilicate fibers with
100 µm and 125 µm cladding diameter. . . 19
LIST OF FIGURES LIST OF FIGURES
25 Strain response when germanosilicate fibers with cladding diameters of 100 µm and 125 µm is stressed. . . 19 26 Strain response of 80 µm and 125 µm cladding diameters of germanosilicate fiber
when they are stresses. . . 20 27 Wavelength shifts of boron-codoped germanosilicate fiber(GF4A) and germanosili-
cate fiber(UHNA1) as a function of the simulated temperatures. . . 21 28 Wavelength shifts of boron-codoped germanosilicate fiber(GF4A) and germanosili-
cate fiber(UHNA1) as a function of the simulated strains. . . 21 29 Wavelength shifts of boron-codoped germanosilicate fiber(GF3) and germanosilicate
fiber(UHNA1) as a function of the simulated temperatures. . . 22 30 Wavelength shifts of boron-codoped germanosilicate fiber(GF3) and germanosilicate
fiber(UHNA1) as a function of the simulated strains. . . 22 31 Wavelength shifts of 100µm cladding diameter and 125µm cladding diameter as a
function of the simulated temperatures. . . 23 32 Wavelength shifts of 100µm cladding diameter and 125µm cladding diameter as a
function of the simulated strains. . . 23 33 The applied temperature as a function of simulated temperature for the sensor design
with different dopings(GF4A and UHNA1, GF3 and UHNA1) and with different cladding diameters(100µm and 125µm). . . 26 34 The applied strain as a function of simulated strain for the sensor design with
different dopings(GF4A and UHNA1, GF3 and UHNA1) and with different cladding diameters(100µm and 125µm). . . 26
LIST OF TABLES LIST OF TABLES
List of Tables
1 The temperature and strain sensitivities of each studied method [15][16][17][18][19][20].
The sensitivities for sampled FBG and phase shifted Bragg grating(DFB) are not know and they are not tabulated. . . 6 2 Characteristics of different types of fibers. . . 11 3 The Bragg wavelength, the fastened length and the cladding diameter of the boron-
codoped germanosilicate fiber(GF4A) and germanosilicate fiber(UHNA1). . . 17 4 Temperature and strain sensitivities of boron doped germanosilicate fiber(GF4A)
and germanosilicate fiber(UHNA1). . . 18 5 The Bragg wavelength, the fastened length and the cladding diameter of the boron-
codoped germanosilicate fiber(GF3) and germanosilicate fiber(UHNA1). . . 18 6 The temperature and strain coefficients of boron doped germanosilicate fiber(GF3)
and germanosilicate fiber(UHNA1). . . 19 7 The Bragg wavelength, the fastened length and the cladding diameter of the ger-
manosilicate fibers with 100 µm and 125 µm cladding diameters. . . 19 8 Temperature and strain sensitivities of germanosilicate fibers with 100 µm and 125
µm cladding diameters. . . 19 9 The Bragg wavelength, the fastened length and the cladding diameter of the ger-
manosilicate fibers with 80 µm and 125 µm cladding diameters. . . 20 10 Strain sensitivities of 80 µm and 125 µm cladding diameter. . . 20 11 From the simulated temperature the applied temperature, applied strain and the
error is calculated for the boron doped germanosilicate fiber(GF4A) and the ger- manosilicate fiber(UHNA1). . . 21 12 From the simulated strain the applied temperature, applied strain and the error is
calculated for the boron doped germanosilicate fiber(GF4A) and the germanosilicate fiber(UHNA1).. . . 22 13 From the simulated temperature the applied temperature, applied strain and the
error is calculated for the boron doped germanosilicate fiber(GF3) and the ger- manosilicate fiber(UHNA1). . . 22 14 From the simulated strain the applied temperature, applied strain and the error is
calculated for the boron doped germanosilicate fiber(GF3) and the germanosilicate fiber(UHNA1). . . 23 15 From the simulated temperature the applied temperature, applied strain and the
error is calculated for the 100µm cladding diameter and 125µm cladding diameter. 23 16 From the simulated strain the applied temperature, applied strain and the error is
calculated for the 100µm cladding diameter and 125µm cladding diameter. . . 24 17 Summary of the results. . . 25 18 Strain that correspond a temperature increase of 10◦C for every studied method. . 26 19 The software that was used and it characteristics. . . 33
1 INTRODUCTION
1 Introduction
Saab Avionics Systems has been developing cutting edge aircraft and avionics for more than 80 years. Today, Saab Avionics Systems works with the development of innovative projects into civil and military aircraft. In 2013 Saab Avionic began system development for monitoring high tem- perature bleed air leakage and the system is called the Overheat Detection System(OHDS) [1].
This system uses Fiber Bragg gratings(FBGs) sensors, for measuring temperature along a fiber optical cable. It allows a large number of sensing points that can be located a few centimeters apart, each of them working as an individual temperature sensor. Essentially, in OHDS the Bragg gratings are utilized to monitor the heat along the air ducts and it provides a warning when a hot air leakage is detected in the aircraft [1]. A further development is to investigate the possibility of usage optical grating sensors to simultaneous measure and discriminate strain and temperature in the already existing system. This would further increase the accuracy and capability of the current system and open up a possibility for new types of applications.
1.1 Background
Before the invention of optical sensors, scientists were using electronic strain gauges [2]. A resistor is used in strain gauges to measure the strain on an object. Strain gauges are available in different sizes and one is depicted in figure1.
Figure 1: Image of a typical strain gauge [3].
Strain and stress describe the strain gauge. Strain is the elongation or compression of a system caused by force applied on it, while stress is the force applied on a system divided by the material cross-sectional area [4]. Hence, the effect of stress on a material is named as strain. Figure 2 shows the structure of a resistance strain gauge. A strain gauge consists of a resistive foil that is a long thin piece of metal which folds back on itself and it is mounted on a backing material [5].
Current pass through the two electrical wires(leads) and while the material expands or contracts the resistance of the metal changes [5].
1.1 Background 1 INTRODUCTION
Figure 2: The structure of a strain gauge. A strain gauge consists of a resistive foil that is mounted on a backing and current passes through two electrical wires(leads).
When the structure of the strain gauge is changed due to applied stress the resistance also changes.
The change in resistance can be measured with the so called Wheatstone bridge, illustrated in fig- ure3. The Wheatstone bridge consists of four resistors(R1, R2, R3, R4) and an input voltage(U1) is applied across the nodes(A-C). The output voltage Uo is measured between the nodes B and D(see figure 3) and has a zero value, then the bridge is in balance. If any of the four resistors are replaced with an active strain gauge the bridge will no longer be in balance and produce a nonzero output voltage. The number of active resistors in Wheatstone bridge determine the kind of bridge configuration [6]. There are three types of bridge configurations, the quarter bridge, the half bridge and the full bridge [6].
Figure 3: Circuit diagram of the Wheatstone bridge [7].
Figure4 shows the quarter bridge strain gauge and is used when only one strain gauge is active.
In figure4 the resistor R4 is replaced with an active strain gauge and R2 is set to a value equal to the active strain resistance with no force applied on it [8]. The resistors R1 and R3 is set to equal values. With this process the system is now in balance and the output voltage is zero when no force is applied to the strain gauge [8] .
1.1 Background 1 INTRODUCTION
Figure 4: The circuit diagram of the quarter bridge strain gauge. The quarter bridge strain gauge is a Wheatstone bridge where the resistor R4 is replaced with an active strain gauge [9].
A main disadvantage of resistance strain gauges is that they are sensitive to temperature changes [5]. Temperature variations affect the resistance of the strain gauge and this end up that the strain gauge measure the change in temperature not in strain [10]. To eliminate the temperature fluctuations on a strain gauge the full and half bridge configurations are used [11]. Figure5shows, the half bridge strain gauge where two gauges are mounted where the one is located in the strain area and the other is placed in the are where no strain is applied on the system. Both are placed close to each other so that they can expect the same temperature change [10]. Then a temperature change will cause both gauges to change resistance by the same amount [10].
Figure 5: The circuit diagram of half bridge strain gauge. It is a Wheatstone bridge where two resistors are replaced with two strain gauges. This configuration is used to eliminate the temperature effects [12].
Due to the fact that the resistance strain gauge consists of two electrical leads, the strain gauges are affected by corrosion, are much larger than an optical fiber and recalibrations are required quite often [2]. Strain gauges are used for many applications, to measure the torque applied by a motor, engine, turbine, propellers and it can be found in power plants, ships, aerospace, cable bridges and rail monitoring.
In the last decades the optical fibers have revolutionized the world around us. By a network of cables under the ground and the oceans, huge amount of information such as emails, pictures and games are transmitted within a very short time span [13]. Optical cables can be made of thousands cable strands, where a single fiber strand is as thick as human hair. An optical fiber contain a core, a cladding and a protective coating where information are transmitted through the fiber in the form of light. Since the invention of Fiber Bragg gratings(FBGs) in 1978 by Hill, scientists have showed a high interest how to utilize them [2]. Bragg gratings are refractive index struc-
1.2 Assignment 1 INTRODUCTION
tures manufactured by exposing its core to an intense periodic UV light [13]. This ability to alter the refractive index of the core is called photosensitivity [13]. FBGs can be used for wavelength multiplexing [2]. However, researcher in the fiber sensor field have utilized FBGs as sensors to measure temperature and strain [2]. Relative to electrical sensors, Bragg gratings have high levels of immunity to electromagnetic interference, have small size, are lightweight, can operate in high temperatures and have a high degree of corrosion resistance [2]. However, fiber Bragg gratings compared to electrical sensors are compatible with multiplexing and distributed sensing capabil- ities [2]. All this characteristics of Bragg gratings are applicable into aerospace, civil structure, environmental, naval and land vehicle systems [2]. The fiber grating sensor acts as a strain gauge and has the ability for simultaneous measurement of strain and temperature and multiaxis strain [2]. Fiber sensors can easily be embedded into a material with minimal effects on its properties and, relative to electrical sensors, optical sensors can be applied to many applications where the application of electrical sensors are problematic [2].
Researchers in the fiber sensor field have studied and proposed a substantial amount of techniques for strain and temperature discrimination. The first sensing head presented in 1994 by Xu et al.
and it was based on two superimposed FBGs operating at two different wavelengths [14]. Sub- sequently, the multi-parameter discrimination of temperature and strain has been the subject of intense research.
1.2 Assignment
Before the invention of grating sensors a tube packed with thermally sensitive eutectic salt sensors and a nickel wire center conductor was used for heat detection in aircraft. If a high temperature was detected the resistance of the eutectic salt dropped, enabling flow of electrical current to pro- vide the warning. Today that system is replaced with optical fibers where it reduces the weight and increasing the accuracy and capability of the aircraft.
Hence, the overheat detection system measure the variation of temperature while the strain is not measured. Due to the fact that the Bragg gratings have similar behavior with applied temperature and strain, appropriate calibrations were made to eliminated strain measurements in the system.
A disadvantage with the current system is that if the optical fiber is stressed at a point, the optical fiber experiences a strain and a false indication is given because this change is read as a tempera- ture change.
In OHDS more than 5000 FBGs are spaced over several optical fibers and all of them together amount to a 150 m long optical fiber. Through switching between the fiber threads, each thread is divided into several divisions and they are directed by Time Division Multiplexing (TDM). Each division have inscribed 20-25 Bragg gratings and each of them work as a single point sensor.
The assignment of this master thesis project is to investigate several methods for temperature and strain discrimination with optical gratings, and chose the most suitable for the current system.
Then the chosen methods will be experimental tested and finally suggest the most appropriate method where the OHDS will give a warning when strain exceeds a temperature increase of 10◦C.
1.3 Literature study
Several sensor configurations were studied in the beginning of this thesis for simultaneous mea- surement of temperature and strain with FBGs. The studied sensor designs were the
1. Boron co-doped germanosilicate fiber and germanosilicate fiber [15]
P.M. Cavaleiro et al. [15] proposed a sensor that utilizes the effect of boron codoping on the temperature dependence of the refractive index in germanosilicate fibers. They found that writing gratings, at similar wavelengths, in undoped and boron doped germanosilicate fibers, caused different temperature sensitivities while the strain sensitivities were not affected. Due to the fact that the fibers were spliced close to each other, the sensor head had a total length of L < 15mm and because of their identical geometry and numerical aperture a standard
1.3 Literature study 1 INTRODUCTION
low loss splice could be achieved.
2. Fibers with different cladding diameters [16]
S.W. James et al. [16] demonstrated a sensor design in which the discrimination of tem- perature and strain arises from the sensing head geometry. Two Bragg gratings with close wavelengths and different cladding diameters were spliced close to each other, this sensor design showed different strain sensitivities to applied strain but similar temperature sensitiv- ities to increased temperature.
3. First-and second order diffraction wavelength [17],
J. Echevarr´ıa et al. [17] presented a new device for simultaneous measurement of strain and temperature where a first- and a second order diffraction wavelength were used. Bragg gratings were designed to measure the reflected and the transmitted wavelengths and the temperature and strain sensitivities were differentiated with this method.
4. FBGs and multimode fibers [18],
Da-Peng Zhou et al. [18] proposed the combination of a fiber Bragg grating and a section of multimode fiber(MMF) that acts as a Mach-Zender interferometer and had different sen- sitivity responses from those with FBG. This configuration was used as a sensor head for temperature and strain discrimination. The temperature and strain sensitivities of multi- mode fibers varied with the core sizes and the materials and a high resolution was achieved by selecting a suitable combination of FBG and MMF.
5. Superstructure FBG [19]
Bai-Ou Guan et al. [19] proposed a sensor design based on a superstructure fiber Bragg grating (SFBG) for simultaneous strain and temperature measurement. This method com- bined FBGs and long period gratings and introduced very broad-band loss peaks in the transmission spectrum. The transmission spectrum of the sensor had several narrow-band loss peaks situated on the slope of a broad-band loss peak. Any of this loss peaks could be chosen and by measuring the transmitted intensity, strain and temperature were measured si- multaneously. The sensor head had a total length of 1 cm and was relative simple to fabricate.
6. Single Bragg grating and an erbium-doped fiber amplifier [20]
Jaehoon Jung et al. [20] presented a sensor suitable for simultaneous measurement of strain and temperature with a single FBG and an erbium-doped fiber amplifier (EDFA). The tem- perature sensitivity was determined by a linear variation in the amplified spontaneous emis- sion power of the EDFA with temperature, but if the transmission dip shift of the FBG was measured and the temperature effect was subtracted from it, strain was determined.
7. Sampled FBG [21],
8. Phase shifted Bragg grating(DFB) [21],
For the phase shifted Bragg grating(DFB) and the sampled FBG the strain and temperature sensitivity have not yet been investigated and articles are not published, but it should be interest- ing if any of this methods can be studied and if a simultaneous measurement of temperature and strain is possible.
1.4 Chosen methods 1 INTRODUCTION
Table 1: The temperature and strain sensitivities of each studied method [15][16][17][18][19][20].
The sensitivities for sampled FBG and phase shifted Bragg grating(DFB) are not know and they are not tabulated.
Sensitivities (Wavelength) KT[pm/◦C] K[pm/µ]
Method 1 Boron codoped 7.37 0.949
Germanium doped 8.43 0.969
Method 2 125 µm cladding diameter 5.73 0.00064
80 µm cladding diameter 6.99 0.00068
Method 3 First order diffraction wavelength 9.70 1.092 Second order diffraction wavelength 4.89 0.472
Method 4 FBG 12.6 1.14
MMF 5.68 -0.84
Method 5 Broad band peak 80 -2.8
Narrow band peak 10 1.06
Sensitivities (Intensity) KT[dBm/◦C] K[dBm/µ]
Method 6 Boron doped -0.04248 0.949
Method 7 Sampled FBG ? ?
Method 8 Phase shifted Bragg grating(DFB) ? ?
The first method with the boron co-doped and the undoped germanosilicate fibers proposed by P.M Cavaleiro et al. [15] and the second method with different cladding diameters by S.W. James et al. [16] were chosen. Both methods are simple in fabrication, with low complexity, cost effective and with low losses to measure temperature and strain sensitivity. In the case of time limitation several methods can not be studied, also other methods such as the sensor design with first and second order diffraction wavelengths was excluded because the wavelength measurement range was limited. The superstructure FBG and the combination of FBGs with multimode fibers have high losses compared to the chosen sensor designs and for this reason they are excluded. The sensors design with a single Bragg grating combined with an erbium-doped fiber amplifier can not be used in complex designs where several amplifiers have to be used for simultaneous measurement of temperature and strain. Due to time limitation the sampled FBG and phase shifted Bragg grating(DFB) will not be investigated.
1.4 Chosen methods
The selected sensor designs for temperature and strain discrimination are the sensor configurations with
• a boron co-doped germanosilicate fiber and a germanosilicate fiber
• two fibers with different diameters.
This methods were chosen because of their simplicity in fabrication and their low complexity. To investigate these two sensor designs the FBGs will be heated in an oven and stressed between a stationary and a translation stage, to obtain the temperature sensitivity(KT) and the strain sensitivity(K) of the Bragg gratings. Then the applied strain(∆) and temperature(∆T ) will be calculated and an error analysis of each method will be reported. The goal of this thesis is to further examine each method in order to contribute to the advancement of the OHDS.
1.5 Outline of the thesis
This thesis will give to the reader an understanding of the two sensor designs for temperature and strain discrimination. Section 2 gives the relevant theoretical background of fiber Bragg gratings and their property as temperature and strain sensor. Section 3 introduces the system where the FBGs was fabricated and the method to measure the temperature and strain sensitivity. Section 4 presents the results of each chosen method and in Section 5 the results are discussed. Section 6 gives the conclusions of this thesis and finally in Section 7 some recommendations of further study is presented.
2 THEORETICAL BACKGROUND
2 Theoretical background
This section is an introduction to fiber Bragg gratings and will give to the reader an understanding of the most important definitions and equations of the area, leading to the definition of temperature and strain sensitivity of FBGs. The section starts with the definition of total internal reflection, it continues with the definition of fiber Bragg gratings, the temperature and strain sensitivity of FBG and it ends with the matrix form of temperature and strain sensitivity of fiber Bragg gratings.
2.1 Optical fibers
Basically optical fibers are used as waveguides for light transmission [22]. Figure 6 depicts the structure of an optical fiber which contains a core, a cladding and a protective coating. The core has a high refractive index (n1 > n2) where light travels through it and it is enclosed by the cladding which keeps the light inside the core. The cladding is surrounded by a coating to protect the fiber.
Figure 6: The structure of an optical fiber, where the core has a refractive index n1 and the cladding has n2. The cladding is surrounded by a protective coating.
Since the core has a higher refractive index than the cladding and the angle of the incident light inside the core is higher than the critical angle (see figure7), then total internal reflection occurs at the interface between the core and the cladding [23]. The total internal reflection is the basic guiding principle of optical fibers and can be seen in figure7.
(a) Partial reflection. (b) Critical angle. (c) Total internal reflection.
Figure 7: When an incident ray hits the interface the ray is refracted and/or reflected. Partial reflection occurs when θr > θI(and n1 > n2). When the incident angle increases the refracted angle also increases and the largest value of the refracted angle is θr = 90◦. It is called critical angle when θr= 90◦. Total internal reflection occurs when θI > θc.
The core is usually doped with germanium and the cladding is made of pure silica [24]. Usually for optical-communication fibers the cladding diameter is 125 µm while the core diameter is 9-50 µm [24]. The are two types of optical fibers based on the mode numbers, the multi-mode fiber and the single-mode fiber and they are depicted in figure8[22].
2.2 Fiber Bragg gratings 2 THEORETICAL BACKGROUND
Figure 8: The dimensions of the multi-mode and the single-mode fiber. Both have a cladding diameter of 125 µm, but the core diameter for the multi-mode fiber is 50 µm and for a single-mode fiber is 9 µm [22].
Multi-mode fibers permit more than one mode to propagate at a time and they have a core size of 50-62.5 µm [25]. Multi-mode fibers are ideally for high bandwidth(a few GHz) and they are utilized to short distance communications such as in high speed local area networks [22] [25]. In difference to multi-mode fibers, single-mode fibers permit only one mode to propagate, and they have a small core diameter of 5-10 µm [22]. Single-mode fibers are utilized for long communication distances and are capable of wide bandwidths (e.g. > 40 GHz) [22] [25].
2.2 Fiber Bragg gratings
Fiber Bragg gratings are constructed in selected locations in the core of the optical fiber and the consist of a periodic variation of the refractive index. The ability to alter the refractive index of the core by exposure to light, is called photosensitivity and is the main mechanism that allows the fabrication of Bragg gratings [21]. When the core is illuminated from the side with an UV light a broadband light is coupled into the core and a periodic refractive index structure, Bragg grating occurs, as shown in the figure9. When light travels through the fiber a small amount of light is reflected at the FBG location while the rest of the spectrum is transmitted through the fiber [21].
Figure 9: Schematic representation of a Bragg grating inscribed in the core of a fiber. An incident spectrum is reflected when the Bragg condition is satisfied and the rest is transmitted through the core of an optical fiber.
The reflected wavelength which is called the Bragg wavelength must satisfy the Bragg condition
λB= 2nef fΛ, (1)
where n is the effective refractive index of the core and Λ is the periodicity of the grating(see figure 9). Equation1 implies that the reflected wavelength can be affected by physical and mechanical properties. If strain or temperature is applied on the FBG, the effective refractive index of the core and the periodicity of the grating is affected [21]. This property implies the sensitivity of Bragg grating due to applied temperature and/or strain. Photosensitivity occurs in the core of an FBG due to the fact that germanium oxide dopants are present in the core [21]. Different codopants such as boron enhance the photosensitivity of germanosilica fibers [21].
2.3 Strain and temperature sensitivity of fiber Bragg grating
A property of Bragg gratings is that they can be used as strain and temperature sensors, because the Bragg wavelength shifts due to applied strain and temperature [21]. Changes in strain and temperature affect the effective index of refraction and the periodic spacing between the grating
2.4 Simultaneous measurements of strain and temperature2 THEORETICAL BACKGROUND
planes [21]. Calculating the partial derivative of equation 1 with respect to temperature, the temperature sensitivity is described by the formula
∆λB
λB = 1 Λ
∂Λ
∂T + 1 nef f
∂nef f
∂T
∆T, (2)
where the first term is the thermal expansion coefficient of the fiber (α) and the second term is the thermo-optic coefficient (η). The index change is the dominant effect for temperature dependence [21]. Substituting α and η in equation2, the equation of thermal sensitivity of the Bragg grating is
∆λB
λB
= (α + η)∆T. (3)
In order to calculate the strain sensitivity of the Bragg grating, the partial derivative of equation 1is calculated with respect to displacement
∆λB
λB = 1 Λ
∂Λ
∂L+ 1 nef f
∂nef f
∂L
∆L. (4)
The first term is the strain of the grating period due to the extension of the fiber and the second term is the photo-elastic coefficient for axial strain (pe) [21]. Consider a fiber of length L containing an FBG that is stressed with ∆L, the strain is then calculated from the ratio ∆L/L.
Similarly if the FBG has a length LF BG and it is stressed with ∆LF BG then the strain applied on it is ∆LF BG/LF BG. Since ∆LLf bg
f bg = ∆LL , the first term is equal the unit and substituting it in equation4the strain sensitivity of the Bragg grating is
∆λB
λB = (1 − pe)z, (5)
where z is the axial strain of the grating. Combining the equation5 and3, the sensitivity of the FBG due to strain and temperature is described by the formula
∆λB λB
= (1 − pe)z+ (α + η)∆T. (6)
Some common values for silica is α = 0.55·10−6, for germanium doped silica core is η = 8.6·10−6 and for silica fibers is pe = 0.22 [21]. Substituting the constants in equation 4 and 2 when the Bragg wavelength is 1550 nm, the sensitivity of the grating due to temperature and strain is approximately
∆λB
∆T = 13.7pm/◦C (7)
and ∆λB
∆ = 1.2pm/µ. (8)
If a boron-codoped germanosilicate fiber is used the refractive index decreases and the tempera- ture sensitivity is affected [21,15]. The refractive index change because the thermo-optic coefficient decreases and has a value η = 7.5 · 10−6 [26]. A common value for boron-codoped germanosilicate fibers is
∆λB
∆T = 7.38pm/◦C. (9)
However, the strain sensitivity can vary if fibers with different cladding diameters are used. This happens due to the fact that the cross-section area of the smaller cladding diameter is more sensitive to applied strain.
2.4 Simultaneous measurements of strain and temperature
For simultaneous measurement of temperature and strain, two Bragg gratings with different Bragg wavelengths are inscribed in the same fiber. Temperature and strain variations cause variations in their Bragg wavelengths
∆λBi= KT i∆T + Ki∆, (10)
2.4 Simultaneous measurements of strain and temperature2 THEORETICAL BACKGROUND
where i = 1,2 represent the two gratings written on the fiber. The first term KT i represent the thermal sensitivity of the fiber and is KT i= (α + η)λB, while the second term Ki represent the strain sensitivity on the fiber and is Ki = (1 − pe)λB. For simplicity, equation10can be written in matrix form
∆λB1
∆λB2
=K1 KT 1
K2 KT 2
∆
∆T
(11) The applied temperature and strain can be obtained simultaneously from the inverse matrix of equation11
∆T
∆
= 1 D
K2 −K1
−KT 2 KT 1
∆λB1
∆λB2
, (12)
where D = KT 1K2− K1KT 2 is the determinant of the matrix and D 6= 0 must hold [14]. The errors are given by
δT δ
= 1 D
| K2|| δλB1 | + | K1|| δλB2 |
| KT 2|| δλB1 | + | KT 1|| δλB2 |
, (13)
where δλBi (i=1,2) are the errors in the determination of ∆λBi (i=1,2) [14].
3 METHOD
3 Method
This section, starts with a short description of the process of fabrication of FBGs and the used fibers are tabulated. Then the setup is demonstrated, where the measurements of the reflected Bragg wavelengths were carried out. The section ends, with a brief description, of how the temperature sensitivity ∆λB/∆T and the strain sensitivity ∆λB/∆ were measured. Appendix A gives the characteristics of the used software and instruments.
3.1 Fabrication of FBGs
Table2presents the different types of fibers used for temperature and strain measurements.
Table 2: Characteristics of different types of fibers.
Item Operating wavelength [nm] Core composition Company
GF3 1500-1600 Germanium and boron doped ThorLabs
GF4A 1500-1600 Germanium and boron doped ThorLabs
UHNA1 1100-1600 Germanium doped ThorLabs
Figure 10 presents how the gratings were fabricated on the different types of fibers that is tabulated on table2. A phase mask was used to write gratings, where ±1 order diffracted beams occurred. Then with the usage of two stationary mirrors, two motorized mirrors and a cylinder lens, the UV laser beam was focused on the optical fiber and a Bragg grating was inscribed on the optical fiber. With this process FBGs were fabricated with a specific Bragg wavelength λB.
Figure 10: The system used to write Bragg gratings. A UV light sends light through a phase mask and with the help of an cylinder lens parallel with an optical fiber, fiber Bragg gratings are inscribed in the core of it (picture provided by my supervisor M.Fokine).
3.2 Basic setup
Figure11shows graphically the setup where the temperature and strain measurements were carried out. The white light source (WL) where sending light through a fiber into the circulator via the
3.3 Temperature measurements 3 METHOD
port 1 to the FBG via port 2, where the Bragg grating sends back the reflected wavelength in the circulator. Then the reflected wavelength which is the Bragg wavelength is measured with the optical spectrum analyzer (OSA) and displayed with the BaySpec Sense 20/20 software. The data analysis was carried out in Python, where a linear regression was made to get the temperature sensitivity KT and strain sensitivity K of the Bragg gratings.
Figure 11: The setup where fiber Bragg gratings are connected for temperature and strain mea- surements. The white light source(WL) is connected with a circulator, where light sends through and is reflected back in the circulator by the fiber Bragg grating. The reflected Bragg wavelengths are recorded in the optical spectrum analyzer(OSA).
3.3 Temperature measurements
To carry out the temperature measurements a carbolite cwf 11/5 chamber furnace was used (see figure12). The FBG was placed inside a glass tube and the edge outside the furnace was taped with a heat resistant kaptone tape. Beside the glass tube with the FBG, a thermocouple was placed(see figure 13) to measure the temperature in the furnace. Then, the glass tube and the thermocouple were placed inside a ceramic tube in the furnace. The glass tube with the FBG was attached into port 2 of circulator, as described in section 3.2. The thermocouple was connected into a thermocouple data logger(TC-08 Thermocouple Data Logger) and during the measurements the temperature was recorded with the PicoLog software.
3.4 Strain measurements 3 METHOD
Figure 12: The Carbolite cwf 11/5 chamber furnace [27].
Figure 13: How the FBG was placed beside the thermocouple in the oven.
To measure the thermal response of the Bragg gratings, the furnace was first heated up to 400◦C and after ∼ 30-40 minutes, while temperature was stabilized, the reflected wavelengths and the temperature were recorded from the BaySpec Sense 20/20 and PicoLog softwares. This proce- dure was repeated until the furnace reached 400◦C with a temperature interval of 50◦C and also the measurement at room temperature. Eight data points were plotted in Python for every mea- surement. It is important to notice that the gratings were held unstrained during the temperature measurements.
*The procedure was developed in a previous project: ” Study on the wavelength stability of Chemical Composition Gratings at high temperatures ” (1FA492 project in applied physics), where the behavior of nickel-coated CCG(a type of FBG) was investigated at high temperature.
3.4 Strain measurements
To carry out the strain measurements a stationary stage and a manual translation stage were used (see figure14). An optical fiber with a grating in the middle, was fastened with solder on the top of the stationary and the translation stage. The FBG was connected with the circulator via port 2 (see description in section 3.2). The used translation stage has an accuracy of 0.01 mm. The outer section of the fiber was attached on two mounted stages, as it can be seen in figure15 in order to ensure that the fiber will not slide. Before the measurements, the length of the fastened fiber L was measured between the solders.
Figure 14: Graphically setup for strain measurements. A fiber with a written Bragg grating and length L, mounted with solder on the top of a stationary and a translation stage.
3.5 Old setup 3 METHOD
Figure 15: The setup for strain measurements. Fiber Bragg grating fastened with solder between a stationary holder(nr 2) and a translation stage(nr 3). The outer section of the fiber were fastened on the stationary holders(nr 1 and nr 4).
To carry out the strain sensitivity of the FBG the fiber was stressed up to 0.20 mm in steps of 0.01 mm. Twenty-one data points were plotted in Python and the strain sensitivity was calculated with the method of linear regression. When the strain sensitivity was measured the FBG was kept in 24◦C to avoid errors due to temperature variations.
*From the literature study (section 1.3) several methods were demonstrated for strain measure- ments. Most of them used a translation stage and glue to fasten the fiber. B. Guan [19] proposed to fix both ends with epoxy and stretch the fiber with a translation stage [19]. J.Jung [20] used two translation stages and adhesive to fix the ends of the fiber [20].
3.5 Old setup
In the beginning of this master thesis it was decided to build an oven. Due to the fact that the temperature in the oven was not stable, the cwf carbolite 11/5 oven was instead used to carry out the temperature measurements.
Figure 16, depicts the oven. It was build with two ceramic plates(no 1 and no 2) and between them a polyimide heater mat was placed on a metal sheet. A thermocouple was placed on the bottom ceramic plate(no 1) and on the top of the metal sheet the optical grating was placed. Then the ceramic plates were fastened with a metallic base(no 3) and the system was mounted on a mounting platform. The heater mat was connected to a power supply and the fiber was attached into port 2 of the circulator(see section section 3.2).
Figure 16: The setup of the oven, where two ceramic plates(no 1 and no 2) and a polyimide heater mat were used.
Lot of thermal losses occurred with this configuration. The metallic plate, the mounting platform
3.5 Old setup 3 METHOD
and holder (no 4) were also heated during the heating process. Due to the fact that the ceramic surfaces were big, it took time to heat up the system up to ∼ 100◦C. So the oven was reconstructed with smaller surfaces to minimize the heat losses. As before the heat mat was placed on a metallic sheet but the ceramic plates were replaced with two ceramic tubes. This configuration is depicted in figure17.
Figure 17: The oven setup where two ceramic tubes were fastened on a metallic sheet and heated by a polyimide heater mat.
Figure 17 depicts, the oven where two ceramic tubes were fastened with kaptone tape on a metallic sheet. In the one ceramic tube the FBG was placed and in the second one a thermocouple was placed and the temperature was recorded with PicoLog software. On the other side of the metallic sheet(where the heat mat was placed) another thermocouple was placed that measured the temperature on the heater mat. The oven was surrounded by plexiglass and the heater mat was connected with a power supply. Figure18shows the oven with the stationary holder and the translation stage.
Figure 18: The experimental setup. The Bragg grating was placed on the oven(in the middle) and fastened with nail polish on the stationary holder(to the left) and on the translation stage(to the right).
Some test measurements were carried out and it was observed that the thermal losses was mini- mized with the usage of smaller surfaces but it was still hard to stabilize temperature in the oven.
With an input voltage of ∼ 17V the oven was rapidly heated up to ∼ 120◦C, but the grating did not experience the same temperature change, so a more reliable oven was instead used. Generally
3.5 Old setup 3 METHOD
it is tricky to build a stable oven and further studies is needed to construct a reliable and stable oven for this application.
Regarding the strain test-setup, on the top of the translation stage the optical fiber was fastened with nail polish. Due to the fact that the fiber was slipping when it was stressed the nail polish was replaced with solder. In figure19 it can be seen the fiber fastened with nail polish on the translation stage.
Figure 19: In the first test setup the fiber was fastened with nail polish on the top of the translation stage. Due to the fact that the fiber was slipping when it was stressed, the method was improved and the the nail polish was replaced with solder.
4 RESULTS
4 Results
In this section the results of each studied method are separately presented. First, the temperature and strain sensitivities in the undoped and boron codoped germanosilicate fibers are presented.
This method is separated into two subsections because two different types of boron-codoped fibers were investigated and compared to a germanium doped fiber(UHNA1). Then the responses of strain and temperature of different cladding diameters are presented.
4.1 Boron-Codoped Germanosilicate and Germanosilicate Fiber
The sensitivity of the Bragg gratings on applied temperature and strain, were examined with a boron-codoped germanosilicate fiber and a undoped germanosilicate fiber. Due to the fact that the doping concentration of boron was not published by ThorLabs, two boron-codoped germanosilicate fibers were investigated, the GF4A fiber and the GF3 fiber.
4.1.1 GF4A and UHNA1
The first Bragg grating was written in an boron-codoped germanosilicate fiber(GF4A) and the second in an undoped germanosilicate fiber(UHNA1). In table3, the written Bragg wavelength, the fastened length between the stages and the cladding diameters of the used fibers are summarized.
Table 3: The Bragg wavelength, the fastened length and the cladding diameter of the boron- codoped germanosilicate fiber(GF4A) and germanosilicate fiber(UHNA1).
Item λB [nm] L[mm] Cladding diameter [µm]
GF4A 1551 125.75 129.4
UHNA1 1546 125.46 124.8
Figures 20 and 21 depicts the temperature and strain measurements of boron codoped ger- manosilicate fiber and germanosilicate fiber and in table4, the coefficients of the applied temper- ature (KT) and applied strain (K) are tabulated.
Figure 20: Temperature response when tem- perature is applied on boron-codoped ger- manosilicate fiber(GF4A) and on germanosili- cate fiber(UHNA1).
Figure 21: Strain response when the boron- codoped germanosilicate fiber(GF4A) and ger- manosilicate fiber(UHNA1) is stressed.
Figure20shows that the thermal response of boron-codoped germanosilicate fiber(GF4A) was smaller than the thermal response of the germanosilicate fiber(UHNA1), but with applied strain the fibers had similar responses as it can be seen in figure21. In table4the numerical value of the responses are shown. The thermal response of GF4A was ∼ 2 times lower than UHNA1.
4.1 Boron-Codoped Germanosilicate and Germanosilicate Fiber 4 RESULTS
Table 4: Temperature and strain sensitivities of boron doped germanosilicate fiber(GF4A) and germanosilicate fiber(UHNA1).
Item KT [pm/◦C] K [pm/µ]
GF4A 6.1124 ± 0.2279 1.1081 ± 0.0070 UHNA1 12.5372 ± 0.3439 1.1235 ± 0.0047 The substitution of the coefficients from table4in matrix12yields
∆T
∆
= 1
7.08
1.12 −1.10
−12.17 6.11
∆λB1
∆λB2
. (14)
4.1.2 GF3 and UHNA1
The temperature and strain sensitivities of Bragg gratings were carried out with the boron-codoped germanosilicate fiber (GF3) and the germanosilicate fiber (UHNA1). The Bragg wavelengths, the length where the fibers were fastened between the stages and the cladding diameters are tabulated in table5.
Table 5: The Bragg wavelength, the fastened length and the cladding diameter of the boron- codoped germanosilicate fiber(GF3) and germanosilicate fiber(UHNA1).
Item λB [nm] L [mm] Cladding diameter [µm]
GF3 1544 125.99 125.2
UHNA1 1546 125.54 124.8
Figure22and23depicts the temperature and strain sensitivities when temperature and strain were applied on the boron-codoped germanosilicate fiber(GF3) and the undoped germanosilicate fiber(UHNA1).
Figure 22: Temperature response when tem- perature is applied on boron-codoped ger- manosilicate fiber(GF3) and on germanosilicate fiber(UHNA1).
Figure 23: Strain response when the boron- codoped germanosilicate fiber(GF3) and ger- manosilicate fiber(UHNA1) is stressed.
In figure 22, it can be seen that with applied increasing temperature the boron-doped ger- manosilicate fiber(GF3) had a similar slope with the undoped germanosilicate fiber(UHNA1) and with applied strain they had similar responses, as can be seen in figure23. The coefficients of the applied temperature (KT) and applied strain (K) are tabulated in table6. It can be seen that the boron-doped germanosilicate fiber(GF3) had a lower temperature response, but it is quite close to the temperature response of the germanosilicate fiber(UHNA1).
4.2 Fiber Diameters 4 RESULTS
Table 6: The temperature and strain coefficients of boron doped germanosilicate fiber(GF3) and germanosilicate fiber(UHNA1).
Item KT [pm/◦C] K [pm/µ]
GF3 11.53 ± 0.3229 1.1142 ± 0.0074 UHNA1 12.82 ± 0.3025 1.1235 ± 0.0047
The applied temperature and strain was calculated from matrix12and was
∆T
∆
= 1
1.32
1.12 −1.11
−12.82 11.53
∆λB1
∆λB2
. (15)
4.2 Fiber Diameters
Temperature and strain measurements were carried out on two germanosilicate fibers, where the cladding diameters were 125 µm and 100 µm. In table7, the Bragg wavelength, the fastened length between the stages and the cladding diameters of the 125µm and 100 µm fibers are tabulated.
Table 7: The Bragg wavelength, the fastened length and the cladding diameter of the germanosil- icate fibers with 100 µm and 125 µm cladding diameters.
Item λB [nm] L [mm] Cladding diameter [µm]
UHNA1 1549 153.69 100
UHNA1 1554 153.69 125
Figure 24 and 25 depicts two Bragg gratings with different cladding diameters. The orange dots represent the 125 µm cladding diameter while the blue dots represent the 100 µm cladding diameter.
Figure 24: Temperature response when temper- ature is applied on germanosilicate fibers with 100 µm and 125 µm cladding diameter.
Figure 25: Strain response when germanosilicate fibers with cladding diameters of 100 µm and 125 µm is stressed.
In figure25, it can be seen that with increased strain the germanosilicate fiber with the decreased cladding diameter had a higher response, while with increasing temperature they had similar responses, as can be seen in figure24. From table8 the strain sensitivity of the 100 µm cladding diameter is ∼ 1.6 higher than the 125 µm cladding diameter.
Table 8: Temperature and strain sensitivities of germanosilicate fibers with 100 µm and 125 µm cladding diameters.
Cladding diameter [µm] KT[pm/◦C] K[pm/µ]
100 12.2950 ±0.2609 1.6652 ±0.0053 125 12.8171 ±0.3025 1.0629 ±0.0045
4.3 Error analysis 4 RESULTS
Substitution of the obtained temperature and strain coefficients from table8in matrix12yields that the applied temperature and strain were
∆T
∆
= 1
8.25
1.06 −1.66
−12.82 12.29
∆λB1
∆λB2
. (16)
Then a measurement of strain sensitivity was carried out with cladding diameters of 80 µm and 125 µm. The temperature response of the 80 µm and a 125 µm cladding diameter were not calculated in case that the Bragg grating was destroyed. In table9, the Bragg wavelength, the fastened length and the cladding diameter of the 80 µm and the 125 µm germanosilicate fibers are tabulated.
Table 9: The Bragg wavelength, the fastened length and the cladding diameter of the germanosil- icate fibers with 80 µm and 125 µm cladding diameters.
Item λB [nm] L [mm] Cladding diameter [µm]
UHNA1 1547 184 80
UHNA1 1554 184 125
Figure 26 depicts the strain sensitivity of the Bragg wavelengths with 80 µm and 125 µm cladding diameters.
Figure 26: Strain response of 80 µm and 125 µm cladding diameters of germanosilicate fiber when they are stresses.
From table 10, the strain response of the 80 µm cladding diameter was ∼ 2.5 times higher than the 125 µm cladding diameter.
Table 10: Strain sensitivities of 80 µm and 125 µm cladding diameter.
Cladding diameter [µm] K [pm/µ]
80 2.5073 ±0.0111
125 1.0287 ±0.0114
4.3 Error analysis
To evaluate the accuracy of each method and estimate the errors from the calibrated data, simulated values for temperature and strain were chosen and the applied temperature(∆T ) and strain(∆) were calculated. Theoretically when the applied temperature is calculated the applied strain has a
4.3 Error analysis 4 RESULTS
zero value. When the applied temperature for the simulated temperature is calculated the applied strain will have a non zero value. The same holds when the applied strain is calculated.
Three simulated temperatures where chosen from the temperature response respective strain re- sponse and the applied temperature and strain were calculated. Each simulated temperature has a wavelength shift(∆λi, i=1,2). Figure27shows the wavelength shifts as a function of the simulated temperatures. The wavelength shifts were then applied in the matrix equation14and the applied temperatures and strains were calculated. Figure28 depicts the wavelength shifts as a function of simulated strains, where the applied temperatures and strains were also calculated with matrix equation14.
Figure 27: Wavelength shifts of boron-codoped germanosilicate fiber(GF4A) and germanosili- cate fiber(UHNA1) as a function of the simu- lated temperatures.
Figure 28: Wavelength shifts of boron-codoped germanosilicate fiber(GF4A) and germanosili- cate fiber(UHNA1) as a function of the simu- lated strains.
In table11, the applied temperature and strain is tabulated for each simulated temperature and, the errors from the calibrated data were computed from the difference of the applied and simulated temperature.
Table 11: From the simulated temperature the applied temperature, applied strain and the error is calculated for the boron doped germanosilicate fiber(GF4A) and the germanosilicate fiber(UHNA1).
GF4A and UHNA1 Simulated
Temp [◦C]
∆T [◦C] ∆ [µ] Error [◦C]
181.29 181.86 1.66 ± 0.57
229.11 230.06 5.76 ± 0.95
277.8 278.23 0.83 ± 0.43
In table12, the applied temperature and strain is tabulated for each simulated strain and, the er- rors from the calibrated data were computed from the difference of the applied and simulated strain.
4.3 Error analysis 4 RESULTS
Table 12: From the simulated strain the applied temperature, applied strain and the error is cal- culated for the boron doped germanosilicate fiber(GF4A) and the germanosilicate fiber(UHNA1)..
GF4A and UHNA1 Simulated
strain [µ]
∆T [◦C] ∆ [µ] Error [µ]
398.28 0.94 390.97 ± 7.31
795.23 0.32 790.60 ± 4.63
1194.84 1.27 1181.55 ± 13.29
Figure29depicts the wavelength shifts as a function of simulated temperatures for the boron doped germanosilicate fiber(GF3) and germanosilicate fiber(UHNA1). The wavelength shifts were then applied in the matrix equation15and the applied temperatures and strains were calculated. Figure 30depicts the wavelength shifts as a function of simulated strains, where the applied temperatures and strains were also calculated with matrix equation15.
Figure 29: Wavelength shifts of boron-codoped germanosilicate fiber(GF3) and germanosilicate fiber(UHNA1) as a function of the simulated temperatures.
Figure 30: Wavelength shifts of boron-codoped germanosilicate fiber(GF3) and germanosilicate fiber(UHNA1) as a function of the simulated strains.
In table13, the applied temperature and strain is tabulated for each simulated temperature and, the errors from the calibrated data were computed from the difference of the applied and simulated temperature.
Table 13: From the simulated temperature the applied temperature, applied strain and the error is calculated for the boron doped germanosilicate fiber(GF3) and the germanosilicate fiber(UHNA1).
GF3 and UHNA1 Simulated
Temp [◦C]
∆T [◦C] ∆ [µ] Error [◦C]
177.09 177.95 15.38 ± 0.86
226.75 181.59 512.95 ± 45.16
277.32 236.14 458.56 ± 41.18
In table14, the applied temperature and strain is tabulated for each simulated strain and, the er- rors from the calibrated data were computed from the difference of the applied and simulated strain.
4.3 Error analysis 4 RESULTS
Table 14: From the simulated strain the applied temperature, applied strain and the error is calculated for the boron doped germanosilicate fiber(GF3) and the germanosilicate fiber(UHNA1).
GF3 and UHNA1 Simulated
strain [µ]
∆T [◦C] ∆ [µ] Error [µ]
396.86 5.07 342.65 ± 54.21
793.71 1.74 772.65 ± 21.06
1194.84 1.67 1212.42 ± 17.58
Figure31depicts the wavelength shifts as a function of simulated temperatures for the 100µm and 125µm cladding diameters. The wavelength shifts were then applied in the matrix equation16and the applied temperatures and strains were calculated. Figure32depicts the wavelength shifts as a function of simulated strains, where the applied temperatures and strains were also calculated with matrix equation16.
Figure 31: Wavelength shifts of 100µm cladding diameter and 125µm cladding diameter as a function of the simulated temperatures.
Figure 32: Wavelength shifts of 100µm cladding diameter and 125µm cladding diameter as a function of the simulated strains.
In table15, the applied temperature and strain is tabulated for each simulated temperature and, the errors from the calibrated data were computed from the difference of the applied and simulated temperature.
Table 15: From the simulated temperature the applied temperature, applied strain and the error is calculated for the 100µm cladding diameter and 125µm cladding diameter.
100µm cladding diameter and 125µm cladding diameter Simulated
Temp [◦C]
∆T [◦C] ∆ [µ] Error [◦C]
177.09 176.65 5.97 ± 0.44
226.75 227.05 0.47 ± 0.3
277.32 276.17 10.51 ± 1.15
In table16, the applied temperature and strain is tabulated for each simulated strain and, the er- rors from the calibrated data were computed from the difference of the applied and simulated strain.
4.3 Error analysis 4 RESULTS
Table 16: From the simulated strain the applied temperature, applied strain and the error is calculated for the 100µm cladding diameter and 125µm cladding diameter.
100µm cladding diameter and 125µm cladding diameter Simulated
strain [µ]
∆T [◦C] ∆ [µ] Error [µ]
390.40 1.02 399.28 ± 8.88
780.79 0.02 783.67 ± 2.88
1171.19 1.04 1182.96 ± 11.77
5 DISCUSSION
5 Discussion
Table17summarizes the results.
Table 17: Summary of the results.
Item Cladding diameter [µm]
Core composition ∆λ/∆T [pm/◦C] ∆λ/∆[pm/µ]
UHNA1 125 Germanium doped 12.1748 1.1235
GF4A 125 Boron-codoped 6.1124 1.1081
GF3 125 Boron-codoped 10.5528 1.1142
UHNA1 100 Germanium doped 12.2950 1.6652
UHNA1 80 Germanium doped - 2.5073
From table 17, it can be observed that the strain sensitivities exhibited similar responses when the fibers were boron-codoped, this happened due to the fact that the boron codoping had no effect on the mechanical properties of the fiber. With increasing temperature the boron codoped germanosilicate fiber and the germanosilicate fiber had different temperature responses. A com- mon value for the ∆λ/∆T ratio is 7.37 pm/◦C when a germanosilicate fiber is boron codoped [15].
It is therefore showed that the temperature response of GF4A was much better than GF3 and correspond to theory . An assumption why the ∆λ/∆T ratio of GF3 was close to the temperature response of UHNA1, is that GF3 probably contained a lower concentration of boron than GF4A (the exact concentrations were not provided by ThorLabs).
Compared from the boron doped fibers, when germanosilicate fibers with different cladding diam- eters are utilized as sensor heads, they exhibit different strain sensitivities caused by their reduced cross-sectional area while their temperature responses remains similar [16]. This happens because the smaller cross-sectional area of the fiber is more sensitive to applied strain and it is the reason why it exhibit a bigger strain response [16]. From table17, when the cladding diameter is 125 µm the strain sensitivity is ∼ 2.5 times lower than the 80 µm cladding diameter. In addition, when the cladding diameter is 100 µm the ∆λ/∆ ratio is ∼ 1.5 higher than the 125 µm cladding diameter.
A common value for the ∆λ/∆ ratio when the cladding diameter is 125 µm is 1.2 pm/µ [21]. It is therefore evident from the theory, that the strain sensitivity for the smaller cladding diameters were increased due to their small cross-sectional areas.
The results of both investigated methods build on existing evidence. Both methods were sim- ple in fabrication, had a small size and were cost effective. The sensor heads had a small length(L < 184mm) for the reason that the gratings can be written with close proximity. Also the complexity of the sensor designs was reduced compared to other sensor designs(SFBG, discussed in section 1.3), because the gratings could be spliced in the same fiber and in that way create a sensor head that can simultaneous measure strain and temperature. This characteristics of the sensor heads makes the systems attractive for wavelength multiplexed sensing system.
Some limitations of this sensor designs also occurred. The measurement range was between 1510- 1590 nm and the resolution of the optical spectrum analyzer was 1 pm. Hence, Bragg wavelengths out of this measurement region were excluded. Also the different cladding diameter sensor design had the limitation because it reduced the sensor mechanical strength. However, the photosensitiv- ity was reduced with ∼ 50% when Bragg gratings were written in the core of the 100 µm cladding diameter while for the 80 µm cladding core the photosensitivity was ∼ 5% when gratings were written in its core. Another limitation of the different cladding diameter sensor design was that the fiber became fragile when the cladding diameter decreased, while this effect was not seen in the boron doped sensor design. Finally an appropriate thick coating material have to be chosen for the different cladding diameters that does not affect the mechanical properties of the fiber, this does not have any impact on the sensor design with different dopings.
