a dissertation preliminary report on - ajay kumar...
TRANSCRIPT
![Page 1: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/1.jpg)
A Dissertation Preliminary Report
On
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
Submitted in partial fulfillment of the requirements
For the degree of
MASTER OF TECHNOLOGY
IN
COMMUNICATION SYSTEMS
BY
AJAY KUMAR GAUTAM
(Roll No. P08EC901)
Under the guidance of
Prof. B. R. TAUNK & Prof. V. N. MISHRA
2008-2009
Electronics Engineering Department
Sardar Vallabhbhai National Institute of Technology Surat-395007, Gujarat, India.
![Page 2: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/2.jpg)
Sardar Vallabhbhai National Institute of Technology Surat-395007, Gujarat, India.
Electronics Engineering Department
CERTIFICATE
This is to certify that AJAY KUMAR GAUTAM, Roll no. P08EC901 of M.Tech.-II (Communication System) has satisfactory completed a Project
Preliminary on “A DESIGN OF HIGH TEMPERATURE HIGH
BANDWIDTH FIBER OPTIC PRESSURE SENSORS” during the
year 2009-2010.
Signature of Guide Signature of HOD
Prof. B. R. Taunk Prof. B.R. Taunk
Head, ECED
Prof. V.N. Mishra
Signature of Internal Examiners:
(1)
(2) SEAL OF DEPARTMENT
![Page 3: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/3.jpg)
Contents
List of figures i
Abstract ii
1. Introduction
1.1 Motivation
1
1
2. Fundamentals of pressure sensing 2-3
2.1 Pressure measurement sensors
2.2 Pressure measurement methods
2.3 Conventional electronic pressure sensors
2
2
2
3. Fundamentals of Optical Fiber
3.1 Basic structure of an optical fiber
4-13
5
3.2 Applications of Optical Fiber
3.3 Principle Of Operation
3.4 Mechanisms of attenuation
5
7
11
4. Fiber optic pressure sensors
4.1 Classification of FOPS
4.2 Fabry -Perot interferometer sensors
4.3 Fiber optic engine pressure sensors
4.4 Operating Principle of FOPS
4.5 Advantages of FOPS
4.6 Applications of FOPS
14-23
14
16
18
20
21
22
5. Analytical Treatment of Three Layer Optical Fiber
5.1 Fiber without coating
24-27
24
6. Result 28-31
7. Summary and Future Work
7.1 Summary
7.2 Future Work
32
32
32
Reference 33-34
![Page 4: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/4.jpg)
List of Figures
Figure 1 Optical fiber types
4
Figure 2. Structure of Optical Fiber
5
Figure 3. The propagation of light through a multi-mode optical fiber
9
Figure 4. The structure of a typical single-mode fiber
10
Figure 5. Specular reflection
12
Figure 6. Illustration of an EFPI fiber optic sensor 18
Figure 7. Basic elements of an optical fiber sensing system
21
Figure 8. Classification of optical fiber sensors
21
Figure 9. Bessel function of first kind (integer value 0, 1)
28
Figure 10. Bessel function of first kind (non- integer value 0.5, 1.5)
29
Figure 11. Bessel function of second kind (integer value 0, 1) 30
Figure 12 Bessel function of second kind (non-integer value 0.5, 1.5) 31
i
![Page 5: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/5.jpg)
Abstract
Pressure measurements are required in various industrial applications, including extremely harsh environments such as turbine engines, power plants and material- processing
systems. Conventional sensors are often difficult to apply due to the high temperatures, highly corrosive agents or electromagnetic interference (EMI) noise that may be present in
those environments. Fiber optic pressure sensors have been developed for years and proved themselves successfully in such harsh environments. Especially, diaphragm based fiber optic pressure sensors have been shown to possess advantages of high sensitivity, wide bandwidth,
high operation temperature, immunity to EMI, lightweight and long life.
Static and dynamic pressure measurements at various locations of a gas turbine engine are highly desirable to improve its operation and reliability. However, the operating environment, in which temperatures may exceed 600 °C and pressures may reach 100 psi (690
kPa) with about 1 psi (6.9kPa) variation, is a great challenge to currently available sensors. To meet these requirements, a novel type of fiber optic engine pressure sensor has been
developed. This pressure sensor functions as a diaphragm based extrinsic Fabry-Pérot interferometric sensor. One of the unique features of this sensor is the all silica structure, allowing a much higher operating temperature to be achieved with an extremely low
temperature dependence. In addition, the flexible nature of the sensor design such as wide sensitivity selection, and passive or adaptive temperature compensation, makes the sensor
suitable for a variety of applications.
ii
![Page 6: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/6.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 1
Chapter 1
Introduction
1.1 Motivation
Pressure measurement is an essential technology in many industry applications, for
example, pressure monitoring in oil storage tanks and vacuum level control in chambers.
Some applications such as gas turbine engines and oil wells involve harsh environments.
Acquiring accurate pressure measurements in these harsh environments has always challenged
the available measurement technology. The motivation of this research is to meet the
recent increasing needs for optical fiber pressure sensors capable of operating accurately
and reliably in these harsh environments, especially in turbine engines.
Gas turbine engines employed in civilian and military aircraft consume large amounts of jet
fuel daily, and the energy consumption attributed to this industry is increasing. Under
increasing demand by engine users, manufacturers are extending operating envelopes of
gas turbine engines to their limits to achieve higher thrust, better efficiency, lower
emissions, improved reliability and longer engine life. The industry consensus is that these
goals can be realized by strategic measurements at various locations in an engine for
design optimization and real-time diagnosis during service . However, the operating
environment within the engine, characterized strong EMI and high temperature, pressure, and
turbulence, shortens the lifetimes of currently available sensors.
The widely used semiconductor pressure sensors have several major drawbacks. These include a
limited maximum operating temperature of 482ºC, poor reliability at high temperatures,
severe sensitivity to temperature changes, and susceptibility to electromagnetic interference.
Compared with conventional electronic sensors, fiber optic sensors have many advantages
including small size, light weight, high sensitivity, large bandwidth, high reliability, immunity
to electromagnetic interference and anti-corrosion and absence of a spark source hazard for
flammable environments. Fiber optic sensors can also survive at much higher temperatures than
conventional pressure sensors.
The basic operating principle of an extrinsic Fabry-Perot interferometric (EFPI) enables the
development of sensors that can operate in the harsh conditions associated with turbine engines
and other aerospace propulsion applications, where the flow environment is dominated by
high-frequency pressure caused by combustion instabilities, blade passing effects, and other
unsteady aerodynamic phenomena. Both static and dynamic pressures exist in turbine engines,
which must be measured by one sensor. Diaphragm-based Fabry-Perot Interferometric (DFPI)
fiber optic pressure sensors are capable of measuring static and dynamic pressure
simultaneously.
![Page 7: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/7.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 2
Chapter 2
Fundamentals of pressure sensing
Pressure is defined as the force per unit area, which is a derived quantity and as such has no
primary standard. Development of pressure standards is therefore based on the primary quantities
of mass and length.
1 psi = 51.714 mmHg = 6.8946 kPa
1 bar = 14.504 psi
1 atm = 14.696 psi
2.1 Pressure measurement sensors
Basically, there are two types of pressure measurement sensors, absolute and differential
pressure sensors, which are distinguished as follows:
2.1.1 Absolute pressure sensor
As the rear side of the sensing element is not accessible, pressure can only be applied on the
front side of the sensor. To achieve an absolute pressure signal, the reference pressure is set
to vacuum.
2.1.2 Differential pressure sensor
The rear side of the sensing element is accessible. Pressure can be applied to both sides
of the sensing element, and the difference in these pressures is measured. If atmospheric
pressure is taken as the reference pressure, the sensor works as a pressure gauge.
2.2 Pressure measurement methods
In general, there are two basic approaches to measuring pressure, either directly, by
determining the force applied to a known area, or indirectly, by determining some effect
of an applied pressure. The simplest direct method is balancing an unknown pressure
against the pressure produced by a column of liquid of known density (manometric
techniques). The second method uses an elastic member of known area as the sensing element
on which pressure acts and the resultant stress or strain is then measured to calculate the actual
pressure value.
2.3 Conventional electronic pressure sensors
In order to improve the sensitivity and resolution as well as to provide means for
compensating for nonlinear effects and the ability to transmit data over considerable distance,
![Page 8: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/8.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 3
electrical/electronic devices were later added for converting mechanical displacements into
an electrical signal thereby creating a whole family of electronic pressure transducers. Many
years of research and development of pressure measurement techniques have resulted in
various pressure transducers including:
Capacitive
Differential transformer
Inductive
Force balance
Piezoelectric
Piezoresistive
Potentiometric
Vibrating wire or tube
Strain gauges
In almost all these pressure transducers, the pressure signal is converted to the deflection
or movement of the pressure-sensing element, and thereafter measured by different electronic
sensing techniques. the transducers vary widely in performance and cost.
![Page 9: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/9.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 4
Chapter 3
Fundamentals of Optical Fiber
An optical fiber (or fibre) is a glass or plastic fiber that carries light along its length. Fiber
optics is the overlap of applied science and engineering concerned with the design and
application of optical fibers. Optical fibers are widely used in fiber-optic communications, which
permits transmission over longer distances and at higher bandwidths (data rates) than other forms
of communications. Fibers are used instead of metal wires because signals travel along them
with lessloss, and they are also immune to electromagnetic interference. Fibers are also used for
illumination, and are wrapped in bundles so they can be used to carry images, thus allowing
viewing in tight spaces. Specially designed fibers are used for a variety o f other applications,
including sensors and fiber lasers.
Light is kept in the core of the optical fiber by total internal reflection. This causes the fiber to
act as a waveguide. Fibers which support many propagation paths or transverse modes are
called multi-mode fibers (MMF), while those which can only support a single mode are
called single-mode fibers (SMF). Multi-mode fibers generally have a larger core diameter, and
are used for short-distance communication links and for applications where high power must be
transmitted. Single-mode fibers are used for most communication links longer than 550 metres
(1,800 ft).
Fig. 1 Optical fiber types.
Joining lengths of optical fiber is more complex than joining electrical wire or cable. The ends of
the fibers must be carefully cleaved, and then spliced together either mechanically or
![Page 10: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/10.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 5
by fusing them together with an electric arc. Special connectors are used to make removable
connections.
3.1 Basic structure of an Optical Fiber
The basic structure of an optical fiber consists of three parts; the core, the cladding, and the
coating or buffer. The basic structure of an optical fiber is shown in figure 2. The core is a
cylindrical rod of dielectric material. Dielectric material conducts no electricity. Light propagates
mainly along the core of the fiber. The core is generally made of glass. The core is described as
having a radius of (a) and an index of refraction n1. The core is surrounded by a layer of material
called the cladding. Even though light will propagate along the fiber core without the layer of
cladding material, the cladding does perform some necessary functions.
Fig. 2 Structure of Optical Fiber
3.2 Applications of Optical Fiber
3.2.1 Optical fiber communication
Optical fiber can be used as a medium for telecommunication and networking because it is
flexible and can be bundled as cables. It is especially advantageous for long-distance
communications, because light propagates through the fiber with little attenuation compared to
electrical cables. This allows long distances to be spanned with few repeaters. Additionally, the
per-channel light signals propagating in the fiber can be modulated at rates as high as
111 gigabits per second, although 10 or 40 Gb/s is typical in deployed systems. Each fiber can
carry many independent channels, each using a different wavelength of light (wavelength-
division multiplexing (WDM)). The net data rate (data rate without overhead bytes) per fiber is
the per-channel data rate reduced by the FEC overhead, multiplied by the number of channels
(usually up to eighty in commercial dense WDM systems as of 2008). The current laboratory
fiber optic data rate record, held by Bell Labs in Villarceaux, France, is multiplexing 155
channels, each carrying 100 Gbps over a 7000 km fiber.
For short distance applications, such as creating a network within an office building, fiber-optic
cabling can be used to save space in cable ducts. This is because a single fiber can often carry
![Page 11: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/11.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 6
much more data than many electrical cables, such as Cat-5 Ethernet cabling.[vague] Fiber is also
immune to electrical interference; there is no cross-talk between signals in different cables and
no pickup of environmental noise. Non-armored fiber cables do not conduct electricity, which
makes fiber a good solution for protecting communications equipment located inhigh
voltage environments such as power generation facilities, or metal communication structures
prone to lightning strikes. They can also be used in environments where explosive fumes are
present, without danger of ignition. Wiretapping is more difficult compared to electrical
connections, and there are concentric dual core fibers that are said to be tap-proof.
Although fibers can be made out of transparent plastic, glass, or a combination of the two, the
fibers used in long-distance telecommunications applications are always glass, because of the
lower optical attenuation. Both multi-mode and single-mode fibers are used in communications,
with multi-mode fiber used mostly for short distances, up to 550 m (600 yards), and single-mode
fiber used for longer distance links. Because of the tighter tolerances required to couple light into
and between single-mode fibers (core diameter about 10 micrometers), single-mode transmitters,
receivers, amplifiers and other components are generally more expensive than multi-mode
components.
3.2.2 Fiber optic sensors
Fibers have many uses in remote sensing. In some applications, the sensor is itself an optical
fiber. In other cases, fiber is used to connect a non-fiberoptic sensor to a measurement system.
Depending on the application, fiber may be used because of its small size, or the fact that
no electrical power is needed at the remote location, or because many sensors can
bemultiplexed along the length of a fiber by using different wavelengths of light for each sensor,
or by sensing the time delay as light passes along the fiber through each sensor. Time delay can
be determined using a device such as an optical time-domain reflectometer.
Optical fibers can be used as sensors to measure strain, temperature, pressure and other quantities
by modifying a fiber so that the quantity to be measured modulates
the intensity,phase, polarization, wavelength or transit time of light in the fiber. Sensors that vary
the intensity of light are the simplest, since only a simple source and detector are required. A
particularly useful feature of such fiber optic sensors is that they can, if required, provide
distributed sensing over distances of up to one meter.
Extrinsic fiber optic sensors use an optical fiber cable, normally a multi-mode one, to
transmit modulated light from either a non-fiber optical sensor, or an electronic sensor connected
to an optical transmitter. A major benefit of extrinsic sensors is their ability to reach places
which are otherwise inaccessible. An example is the measurement of temperature
inside aircraft jet engines by using a fiber to transmit radiation into a radiation pyrometer located
outside the engine. Extrinsic sensors can also be used in the same way to measure the internal
temperature of electrical transformers, where the extreme electromagnetic fields present make
![Page 12: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/12.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 7
other measurement techniques impossible. Extrinsic sensors are used to measure vibration,
rotation, displacement, velocity, acceleration, torque, and twisting.
3.2.3 Other uses of optical fibers
Fibers are widely used in illumination applications. They are used as light guides in medical and
other applications where bright light needs to be shone on a target without a clear line-of-sight
path. In some buildings, optical fibers are used to route sunlight from the roo f to other parts of
the building (see non- imaging optics). Optical fiber illumination is also used for decorative
applications, including signs, art, and artificial Christmas trees.Swarovski boutiques use optical
fibers to illuminate their crystal showcases from many different angles while only employing one
light source. Optical fiber is an intrinsic part of the light-transmitting concrete building
product, LiTraCon.
Optical fiber is also used in imaging optics. A coherent bundle of fibers is used, sometimes along
with lenses, for a long, thin imaging device called an endoscope, which is used to view objects
through a small hole. Medical endoscopes are used for minimally invasive exploratory or
surgical procedures (endoscopy). Industrial endoscopes (see fiberscope or borescope) are used
for inspecting anything hard to reach, such as jet engine interiors.
In spectroscopy, optical fiber bundles are used to transmit light from a spectrometer to a
substance which cannot be placed inside the spectrometer itself, in order to analyze its
composition. A spectrometer analyzes substances by bouncing light off of and through them. By
using fibers, a spectrometer can be used to study objects that are too large to fit inside, or gasses,
or reactions which occur in pressure vessels.
An optical fiber doped with certain rare earth elements such as erbium can be used as the gain
medium of a laser or optical amplifier. Rare-earth doped optical fibers can be used to provide
signal amplification by splicing a short section of doped fiber into a regular (undoped) optical
fiber line. The doped fiber is optically pumped with a second laser wavelength that is coupled
into the line in addition to the signal wave. Both wavelengths of light are transmitted through the
doped fiber, which transfers energy from the second pump wavelength to the signal wave. The
process that causes the amplification is stimulated emission.
Optical fibers doped with a wavelength shifter are used to collect scintillation light
in physics experiments.
Optical fiber can be used to supply a low level of power (around one watt) to electronics situated
in a difficult electrical environment. Examples of this are electronics in high-powered antenna
elements and measurement devices used in high voltage transmission equipment.
3.3 Principle Of Operation
An optical fiber is a cylindrical dielectric waveguide (nonconducting waveguide) that transmits
light along its axis, by the process of total internal reflection. The fiber consists of a core
surrounded by a cladding layer, both of which are made of dielectric materials. To confine the
![Page 13: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/13.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 8
optical signal in the core, the refractive index of the core must be greater than that of the
cladding. The boundary between the core and cladding may either be abrupt, in step-index fiber,
or gradual, in graded-index fiber
3.3.1 Index of refraction
The index of refraction is a way of measuring the speed of light in a material. Light travels
fastest in a vacuum, such as outer space. The actual speed of light in a vacuum is about 300
million meters (186 thousand miles) per second. Index of refraction is calculated by dividing the
speed of light in a vacuum by the speed of light in some other medium. The index of refraction
of a vacuum is therefore 1, by definition. The typical value for the cladding of an optical fiber is
1.46. The core value is typically 1.48. The larger the index of refraction, the slower light travels
in that medium. From this information, a good rule of thumb is that signal using optical fiber for
communication will travel at around 200 million meters per second. Or to put it another way, to
travel 1000 kilometres in fiber, the signal will take 5 milliseconds to propagate. Thus a phone
call carried by fiber between Sydney and New York, a 12000 kilometre distance, means that
there is an absolute minimum delay of 60 milliseconds (or around 1/16th of a second) between
when one caller speaks to when the other hears. (Of course the fiber in this case will probably
travel a longer route, and there will be additional delays due to communication equipment
switching and the process of encoding and decoding the voice onto the fiber).
3.3.2 Total internal reflection
When light traveling in a dense medium hits a boundary at a steep angle (larger than the "critical
angle" for the boundary), the light will be completely reflected. This effect is used in optical
fibers to confine light in the core. Light travels along the fiber bouncing back and forth off of the
boundary. Because the light must strike the boundary with an angle greater than the critical
angle, only light that enters the fiber within a certain range of angles can travel down the fiber
without leaking out. This range of angles is called the acceptance cone of the fiber. The size of
this acceptance cone is a function of the refractive index difference between the fiber's core and
cladding.
In simpler terms, there is a maximum angle from the fiber axis at which light may enter the fiber
so that it will propagate, or travel, in the core of the fiber. The sine of this maximum angle is
the numerical aperture (NA) of the fiber. Fiber with a larger NA requires less precision to splice
and work with than fiber with a smaller NA. Single-mode fiber has a small NA.
3.3.3 Multi-mode fiber
Fiber with large core diameter (greater than 10 micrometers) may be analyzed by geometrical
optics. Such fiber is called multi-mode fiber, from the electromagnetic analysis (see below). In a
step- index multi-mode fiber, rays of light are guided along the fiber core by total internal
![Page 14: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/14.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 9
reflection. Rays that meet the core-cladding boundary at a high angle (measured relative to a
line normal to the boundary), greater than the critical angle for this boundary, are completely
reflected. The critical angle (minimum angle for total internal reflection) is determined by the
difference in index of refraction between the core and cladding materials. Rays that meet the
boundary at a low angle are refracted from the core into the cladding, and do not convey light
and hence information along the fiber. The critical angle determines the acceptance angle of the
fiber, often reported as a numerical aperture. A high numerical aperture allows light to propagate
down the fiber in rays both close to the axis and at various angles, allowing efficient coupling of
light into the fiber. However, this high numerical aperture increases the amount of dispersion as
rays at different angles have different path lengths and therefore take different times to traverse
the fiber.
Fig. 3 The propagation of light through a multi-mode optical fiber
In graded- index fiber, the index of refraction in the core decreases continuously between the a xis
and the cladding. This causes light rays to bend smoothly as they approach the cladding, rather
than reflecting abruptly from the core-cladding boundary. The resulting curved paths reduce
multi-path dispersion because high angle rays pass more through the lower- index periphery of
the core, rather than the high- index center. The index profile is chosen to minimize the difference
in axial propagation speeds of the various rays in the fiber. This ideal index profile is very close
to a parabolic relationship between the index and the distance from the axis.
3.3.4 Single-mode fiber
Fiber with a core diameter less than about ten times the wavelength of the propagating light
cannot be modeled using geometric optics. Instead, it must be analyzed as
an electromagnetic structure, by solution of Maxwell's equations as reduced to
the electromagnetic wave equation. The electromagnetic analysis may also be required to
understand behaviors such as speckle that occur when coherent light propagates in multi-mode
![Page 15: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/15.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 10
fiber. As an optical waveguide, the fiber supports one or more confined transverse modes by
which light can propagate along the fiber. Fiber supporting only one mode is called single-
mode or mono-mode fiber. The behavior of larger-core multi-mode fiber can also be modeled
using the wave equation, which shows that such fiber supports more than one mode of
propagation (hence the name). The results of such modeling of multi-mode fiber approximately
agree with the predictions of geometric optics, if the fiber core is large enough to support more
than a few modes.
Fig. 4 The structure of a typical single-mode fiber.
1. Core: 8 µm diameter
2. Cladding: 125 µm dia.
3. Buffer: 250 µm dia.
4. Jacket: 400 µm dia.
The waveguide analysis shows that the light energy in the fiber is not complete ly confined in the
core. Instead, especially in single-mode fibers, a significant fraction of the energy in the bound
mode travels in the cladding as an evanescent wave.
![Page 16: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/16.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 11
The most common type of single-mode fiber has a core diameter of 8–10 micrometers and is
designed for use in the near infrared. The mode structure depends on the wavelength of the light
used, so that this fiber actually supports a small number of additional modes at visible
wavelengths. Multi-mode fiber, by comparison, is manufactured with core diameters as small as
50 micrometers and as large as hundreds of micrometers. The normalized frequency V for this
fiber should be less than the first zero of the Bessel function J0 (approximately 2.405).
3.3.5 Special-purpose fiber
Some special-purpose optical fiber is constructed with a non-cylindrical core and/or cladding
layer, usually with an elliptical or rectangular cross-section. These include polarization-
maintaining fiber and fiber designed to suppress whispering gallery mode propagation.
Photonic-crystal fiber is made with a regular pattern of index variation (often in the form of
cylindrical holes that run along the length of the fiber). Such fiber uses diffraction effects instead
of or in addition to total internal reflection, to confine light to the fiber's core. The properties of
the fiber can be tailored to a wide variety of applications.
3.4 Mechanisms of attenuation
Attenuation in fiber optics, also known as transmission loss, is the reduction in intensity of the
light beam (or signal) with respect to distance travelled through a transmission medium.
Attenuation coefficients in fiber optics usually use units of dB/km through the medium due to the
relatively high quality of transparency of modern optical transmission media. The medium is
typically usually a fiber of silica glass that confines the incident light beam to the inside.
Attenuation is an important factor limiting the transmission of a digital signal across large
distances. Thus, much research has gone into both limiting the attenuation and maximizing the
amplification of the optical signal. Empirical research has shown that attenuation in optical fiber
is caused primarily by both scattering and absorption.
3.4.1 Light scattering
The propagation of light through the core of an optical fiber is based on total internal reflection
of the lightwave. Rough and irregular surfaces, even at the molecular level, can cause light rays
to be reflected in random directions. This is called diffuse reflection or scattering, and it is
typically characterized by wide variety of reflection angles.
Light scattering depends on the wavelength of the light being scattered. Thus, limits to spatial
scales of visibility arise, depending on the frequency of the incident light-wave and the physical
dimension (or spatial scale) of the scattering center, which is typically in the form of some
specific micro-structural feature. Since visible light has a wavelength of the order of
one micron (one millionth of a meter) scattering centers will have dimensions on a similar spatial
scale.
Thus, attenuation results from the incoherent scattering of light at
internal surfaces and interfaces. In (poly) crystalline materials such as metals and ceramics, in
![Page 17: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/17.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 12
addition to pores, most of the internal surfaces or interfaces are in the form of grain
boundaries that separate tiny regions of crystalline order. It has recently been shown that when
the size of the scattering center (or grain boundary) is reduced below the size of the wavelength
of the light being scattered, the scattering no longer occurs to any significant extent. This
phenomenon has given rise to the production of transparent ceramic materials.
Fig.5 Specular reflection
Similarly, the scattering of light in optical quality glass fiber is caused by molecular level
irregularities (compositional fluctuations) in the glass structure. Indeed, one emerging school of
thought is that a glass is simply the limiting case of a polycrystalline solid. Within this
framework, "domains" exhibiting various degrees of short-range order become the building
blocks of both metals and alloys, as well as glasses and ceramics. Distributed both between and
within these domains are micro-structural defects which will provide the most ideal locations for
the occurrence of light scattering. This same phenomenon is seen as one of the limiting factors in
the transparency of IR missile domes. At high optical powers, scattering can also be caused by
nonlinear optical processes in the fiber.
![Page 18: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/18.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 13
3.4.2 UV-Vis-IR absorption
In addition to light scattering, attenuation or signal loss can also occur due to selective absorption
of specific wavelengths, in a manner similar to that responsible for the appearance of color.
Primary material considerations include both electrons and molecules as follows:
1) At the electronic level, it depends on whether the electron orbitals are spaced (or
"quantized") such that they can absorb a quantum of light (or photon) of a specific
wavelength or frequency in the ultraviolet (UV) or visible ranges. This is what gives rise
to color.
2) At the atomic or molecular level, it depends on the frequencies of atomic or molecular
vibrations or chemical bonds, how close-packed its atoms or molecules are, and whether
or not the atoms or molecules exhibit long-range order. These factors will determine the
capacity of the material transmitting longer wavelengths in the infrared (IR), far IR, radio
and microwave ranges.
The design of any optically transparent device requires the selection of materials based upon
knowledge of its properties and limitations. The lattice absorptioncharacteristics observed at the
lower frequency regions (mid IR to far- infrared wavelength range) define the long-wavelength
transparency limit of the material. They are the result of the interactive coupling between the
motions of thermally induced vibrations of the constituent atoms and molecules of the solid
lattice and the incident light wave radiation. Hence, all materials are bounded by limiting regions
of absorption caused by atomic and molecular vibrations (bond-stretching)in the far- infrared
(>10 µm).
Thus, multi-phonon absorption occurs when two or more phonons simultaneously interact to
produce electric dipole moments with which the incident radiation may couple. These dipoles
can absorb energy from the incident radiation, reaching a maximum coupling with the radiation
when the frequency is equal to the fundamental vibrational mode of the molecular dipole (e.g.
Si-O bond) in the far- infrared, or one of its harmonics.
The selective absorption of infrared (IR) light by a particular material occurs because the
selected frequency of the light wave matches the frequency (or an integral multiple of the
frequency) at which the particles of that material vibrate. Since different atoms and molecules
have different natural frequencies of vibration, they will selectively absorb different frequencies
(or portions of the spectrum) of infrared (IR) light.
Reflection and transmission of light waves occur because the frequencies of the light waves do
not match the natural resonant frequencies of vibration of the objects. When IR light of these
frequencies strike an object, the energy is either reflected or transmitted.
![Page 19: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/19.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 14
Chapter 4
Fiber optic pressure sensors
Fiber optic sensors can be used to measure pressure and possess a number of inherent
advantages including
(i) immunity to electromagnetic interference,
(ii) wide range of potential measurands,
(iii) high resolution,
(iv) remote sensing capability,
(v) high reliability and
A variety of fiber optic pressure sensors (FOPS) have been developed and proven themselves in
many applications.
The light transmitted through an optical fiber can be characterized by such parameters as
intensity, wavelength, phase, and polarization. By detecting the change of these parameters
resulting from the interaction between the optical fiber and the measurand, fiber optic sensors
can be designed to measure a wide variety of physical and chemical parameters.
4.1. Classification of FOPS
Accordingly, fiber optic sensors can be categorized into four major groups including: intensity
based fiber optic sensors, color modulated fiber optic sensors, phase modulated (or
interferometric) fiber optic sensors, and polarization modulated fiber optic sensors. More than
three decades of extensive research in fiber optic sensor technologies has greatly enhanced the
technical background of all the sensor categories, and the applications of each group of
the sensors are expanding very rapidly.
4.1.1 Polarization-modulated pressure sensor
The mainstream of developed polarization-modulated fiber optic sensors are based on two
different physical effects: the Faraday effect and the photoelastic effect. Sensors based on the
Faraday effect are mainly used to measure electrical or magnetic field with the typical
application of the measurement of the electrical current. On the other hand, photoelastic fiber
sensors are naturally suitable for developing into pressure sensors because the photoelastic
effect directly transfers the applied pressure into the change of the polarization property in
the optical medium. Although silica glass fiber itself exhibits a very weak photoelastic effect,
external optical crystals are often used as the sensing element for better control and more
accurate measurement.
![Page 20: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/20.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 15
The first fiber optic pressure sensor based on the photoelastic effect was introduced in 1982 by
Spillman. Since then, many photoelastic fiber sensors have been reported by different
authors with their emphases on the development of clever methods to compensate for the
optical power variation of the system. With a very good self- compensation mechanism, an
external photoelastic pressure sensor could achieve an accuracy of 0.2%. However, the self-
compensation had to be constructed at the same location as the external sensing element, which
made the sensor head very bulky and difficult to be protected in harsh environments.
4.1.2 Wavelength-modulated pressure sensor
The most popular wavelength-modulated fiber optic sensor has been the Fiber grating-based
sensor ever since the first fiber grating was manufactured in 1989 through transverse UV
exposure. Fiber sensors based on both Bragg gratings and long period gratings have been
developed for the measurement of temperature, stra in and pressure. By coating the grating
region with specially designed elastic material or encapsulating the grating into a glass bubble,
fiber grating sensors have been used to measure hydrostatic pressure with a typical resolution of
0.5% . Fiber grating sensors have the advantages of immunity to the optical power loss
variation of the optical network and the capability of multiplexing many sensors to share
the same signal processing unit. However, the long-term reliability of the fiber grating
sensors has been a concern due to the degradation of optical properties and mechanical
strength when the grating is exposed to high temperature and high pressure environments.
Moreover, when used for pressure measurements, fiber grating sensors exhibit relatively
large temperature dependence, which limits their scale of applications for harsh
environmental sensing.
In summary, although optical fiber-based pressure sensors have the potential opportunity to
replace the majority of conventional electronic pressure transducers in existence in today’s
sensor market because of their unique set of advantages that can’t be offered by other
technologies, technical difficulties still exist and delay this becoming a reality. The most
common concerns about the practical applications of fiber optic pressure sensors include the
stability issue and the cross-sensitivity among multiple environmental parameters. The
fluctuation of source power and the change in fiber loss can easily introduce errors to the
measurement results, which make most optical fiber-based sensors unstable. The fact that most
fiber sensors are cross sensitive to temperature changes also makes it difficult to use fiber
optic sensors to measure parameters other than temperature in many practical applications. In
order to be able to apply fiber optic sensors to real applications, research must be performed to
overcome these technical difficulties.
4.1.3 Intensity-based FOPS
In general, intensity-based FOPS are inherently simple and require only a modest signal
processing complexity through a direct detection of the change in optical power either in
![Page 21: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/21.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 16
transmission or reflection. A well-developed and successfully commercialized intensity-
based sensor is the multimode optical fiber microbend sensor, which bases its principle on
the physical phenomenon that mechanical periodic microbends can cause the energy of the
guided modes to be coupled to the radiation modes and consequently results in attenuation
of the transmitted light. Pressure sensors can thus be constructed by designing the mechanical
microbending device to transfer the applied pressure to the optical intensity change.
Although microbend pressure sensors have been reported with very high resolution
(typically better than 0.1%), the large hysteresis and the power fluctuation associated with the
optical source and fiber loss limit their accuracy within a few percent of the full scale. The large
size of the mechanical microbending mechanism also makes the microbend fiber optic pressure
sensor impractical in many sensing applications where the size of the sensor is restricted to a
very small dimension.
4.1.4 Interferometry based FOPS
To date, four types of interferometric FOPSs have been investigated for the
measurements of displacement, temperature, strain, pressure and acoustic signals. These
are the Mach-Zehnder, Michelson, Fabry-Perot, and Sagnac interferometers. Among them,
the first three interferometric sensors have been developed into pressure sensors while the
Sagnac interferometer has been primarily used for gyroscopes.
Mach-Zehnder and Michelson interferometers are the two intrinsic fiber sensors that were
investigated extensively for acoustic pressure detection in the early stage of fiber sensor
development. For example, underwater hydrophones based on these two interferometers
were reported to have very high resolution of 0.01% . However, due to the very low level of
photoelastic or stress-optic coefficients of the silica glass fibers, a very long length of sensing
fiber is necessary to obtain the desirable sensitivity, which unavoidably makes the sensor
thermally unstable. Another drawback associated with these two types of interferometric
sensors is the polarization-fading problem, which refers to the interference fringe visibility
as a function of the polarization status of the light transmitted inside the fibers. The
temperature instability and the polarization fading problem both render the Mach- Zehnder
and Michelson interferometric sensors unsuitable for the long-term measurement of DC
pressure signals where the sensor drift must be kept to a very small level.
4.2 Fabry-Perot interferometer sensors
The Fabry-Perot interferometer is a very useful tool for high precision measurement, optical
spectrum analysis, optical wavelength filtering, and construction of lasers. It is a high resolution,
high throughput optical spectrometer that works on the principle of constructive
interference. The Fabry-Perot interferometer is a very simple device that is based on the
interference of multiple beams. It consists of two partially transmitting mirrors that form a
![Page 22: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/22.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 17
reflective cavity. Incident light enters the Fabry-Perot cavity and experiences multiple reflections
between the mirrors so that the light can produce multiple interferences.
According to the different behaviors of the incident light, fiber optic Fabry-Perot sensors
can be classified into two types æ extrinsic F-P sensors and intrinsic F-P sensors. In
extrinsic sensors, the light can be allowed to exit the fiber and be modulated in a
separate zone before being relaunched into either the same or a different fiber. They form
an interferometric cavity outside the fiber, and the fiber just acts as a medium to transmit light
into and out of the Fabry-Perot cavity. In intrinsic sensors, the light can continue within the fiber
and be modulated. A Fabry-Perot cavity is formed by a section of fiber with its two end faces
cleaved or coated with reflective coatings.
4.2.1 Intrinsic Fabry-Perot Interferometer Sensor
In intrinsic sensors the fiber construction materials are deliberately chosen in order to give
sensitivity to one or more parameters. Often it is not cost effective to make highly specialized
fibers for sensing applications; therefore intrinsic sensors may utilize readily available
fiber in specialized configurations and in conjunction with sophisticated instrumentation.
Usually an Intrinsic Fabry-Perot Interferometer (IFPI) sensor is fabricated by splicing a section
of special fiber with its two endfaces coated with reflective films to regular fibers. The
interferometric superposition of multiple reflections at the two special fiber’s end faces
generates the output signal, which is a function of the F-P cavity length, the refractive
index of the special fiber, and the reflectance of the coating. The change of the F-P cavity
length or the refractive index of the special fiber can be detected by tracking the
interference output (either through the reflection or the transmission). Various physical or
chemical parameters such as temperature, pressure and strain can be measured with a high
resolution using an IFPI sensor.
4.2.2 Extrinsic Fabry-Perot Interferometer Sensor
In extrinsic sensors the performance of the device should be independent of the fiber and
depend only on the nature of the sensing element, hence it offers the flexibility to design the
Fabry-Perot cavity to accommodate different applications. A typical EFPI sensor configuration
is shown in Fig.7. It consists of a cavity that is formed between an input optical fiber and a
reflecting optical fiber. Although the two reflectors of forming the Fabry-Perot cavity can
be the surfaces of any optical components, a very simple way to form an EFPI will be using the
well-cleaved end faces of two fibers.
![Page 23: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/23.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 18
Fig. 6 Illustration of an EFPI fiber optic sensor
As shown in Fig. 6, the light from an optical source propagates along the input optical
fiber to the Fabry-Perot cavity that is formed by the input optical fiber and the reflecting optical
fiber. A fraction of this incident light R1, approximately 4%, is reflected at the end face of
the input optical fiber backward the input optical fiber. The light transmitting out of the input
optical fiber projects onto the fiber end face of the reflecting optical fiber. The reflected
light R2 from the reflecting optical fiber is partially recoupled into the input optical fiber.
Optical fiber Extrinsic Fabry-Perot interferometers (EFPI) have also been developed into
pressure sensors. Compared to the Mach-Zehnder and Michelson sensors, the EFPI sensor has
advantages such as high sensitivity, small size, simple structure, polarization independence,
and great design flexibility; EFPI fiber optic sensors are therefore attractive for many
sensing applications. Moreover, because the optical fibers are packed very closely together,
there is a potential advantage to minimize the temperature dependence of the sensor.
In summary, optical fiber interferometric sensors usually have the reputation of design flexibility
of the sensing element, large dynamic range, and extremely high resolutions. However, due
to the non- linear periodic nature of the interference signal, the accurate detection of the
differential phase change of an interferometer becomes a real challenge. Very often, the
complexity of the phase demodulation part of the interferometric sensor contributes the most
to its high cost.
4.3 Fiber optic engine pressure sensors
Fiber optic pressure sensors are capable of working in hostile environments such as
turbine engines. Compared with hollow cylinder based pressure sensors for static pressure
measurement, diaphragm based configurations are more suitable for both static and dynamic
pressure measurements . However, these diaphragm based pressure sensors are still not
suitable for applications above 500ºC. Also, the large coefficient of thermal expansion
(CTE) mismatch will cause severe stress between different materials used in sensor
![Page 24: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/24.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 19
construction. This stress will degrade the sensor performance or lead to a failure. Even if the
same material is used to fabricate the sensor elements, the bonding adhesive used,
especially if epoxy-based, is still a major concern for the sensor’s performance. For example,
epoxy will exhibit a time-dependent viscoelastic dimensional change and will decompose at
high temperatures. Also, the bonding adhesive having a different CTE from the sensor
elements will cause a large temperature dependence in the pressure measurement or cause
the sensor to fail. Although anodic bonding is adhesive free bonding, it cannot be used for
bonding fused silica glass, which has a higher softening point and much lower CTE than other
glass and is the most compatible material to silica optical fiber.
The goal of this research was to develop a new diaphragm based fiber optic EFPI engine
pressure sensor, which has high sensitivity, high temperature capability, large bandwidth and
low thermal- induced measurement error. Also, the sensor must be reliable and anticorrosion.
In general, the fiber optic engine pressures have to satisfy several special requirements as
explained below.
4.3.1. High temperature capability
High temperature is very often involved in many harsh environments. For example,
temperatures in turbine engines can reach 500°C or much hotter depending upon which
region of the turbine. The high temperature is the main reason that renders most electronic
sensors inapplicable. Although optical fibers can sustain temperatures as high as 800°C
before the dopants start to thermally diffuse appreciably, extra attention must be paid to the
design and fabrication of the fiber sensor in order to maintain the desirable performance at
such high temperature.
4.3.2. High pressure capability
Pressures as high as 500 psi can be encountered in turbine engines. In order to be able to survive
in such high pressure environments, fiber optic pressure sensors must be designed and
fabricated with enough mechanical strength and with their optical paths hermetically sealed to
provide the necessary protection.
4.3.3. High Bandwidth
Dynamic pressures with frequency up to 50kHz exist in turbine engines. The pressure sensor
must have very high frequency response.
4.3.4. Good thermal stability
Fiber optic pressure sensors designed for high temperature applications must be thermally
stable or have the capability of compensating for temperature variations. Otherwise the
temperature fluctuation of the environment can easily introduce large errors in the pressure
measurement results.
![Page 25: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/25.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 20
4.3.5. Absolute measurement and self-calibration capability
Fiber optic pressure sensors with absolute readouts are much more attractive in
applications for harsh environments because of their exemption from initialization and/or
calibration when the power is switched on. In addition, the sensors are required to have self-
calibration capability so that the fiber loss changes and the source power fluctuations can be
fully compensated, or absolute measurement becomes meaningless.
4.3.6. Cost-effectiveness
As the market for fiber optic pressure sensors for harsh environment opens rapidly, the cost of
the sensors and instrumentation is becoming a concern of increasing Importance. In order
to achieve successful commercialization, fiber optic pressure sensor systems must be robust
as well as low cost. This requires that the complexity of the fiber sensor system must be kept to
the minimum and the technique and process of fabricating sensor probes must have the potential
of allowing mass production.
4.3.7. Installability
Fiber optic pressure sensors designed for harsh environment applications must be capable
of remote operation and flexible enough for easy installation. This requires the sensor size to
be small enough to fit in the limited space where the sensor will be located. Also, the
sensor packaging must be compatible with the standard installation ports.
4.4 Operating Principle of FOPS
Optical fibers are also attractive for applications in sensing, control and instrumentation. In these
areas, optical fibers have made a significant impact. For these app lications fibers are made more
susceptible and sensitive to the same external mechanisms against which fibers were made to be
immune for their effective operation in telecommunications.
An optical fiber sensing system is basically composed of a light source, optical fiber; a sensing
element or transducer and a detector (see Fig. 7). The principle of operation of a fiber sensor is
that the transducer modulates some parameter of the optical system (intensity, wavelength,
polarization, phase, etc.) which gives rise to a change in the characteristics of the optical signal
received at the detector.
![Page 26: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/26.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 21
Fig. 7 Basic elements of an optical fiber sensing system
The fiber sensor can be either an intrinsic one - if the modulation takes place directly in the fiber-
- or extrinsic, if the modulation is performed by some external transducer as depicted in Fig. 8
Fig. 8 Classification of optical fiber sensors
![Page 27: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/27.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 22
4.5 Advantages of fiber optic pressure sensors
Compared with conventional electronic sensors, fiber optic sensors have many advantages
including small size, light weight, high sensitivity, large bandwidth, high reliability, immunity
to electromagnetic interference and anti-corrosion and absence of a spark source hazard for
flammable environments. Fiber optic sensors can also survive at much higher temperatures
than conventional pressure sensors.
The inherent advantages of fiber optic sensors which include their ability to be lightweight, of
very small size, passive, low power, resistant to electromagnetic interference, high sensitivity,
wide bandwidth and environmental ruggedness were heavily used to offset their major
disadvantages of high cost and unfamiliarity to the end user.
Optical fiber sensors offer attractive characteristics that make them very suitable and, in some
cases, the only viable sensing solution.
Fiber optic pressure sensors have been shown to possess advantages of high sensitivity, wide
bandwidth, high operation temperature, immunity to EMI, lightweight and long life.
4.6 Applications Of FOPS
Fiber optic sensors are being developed and used in two major ways. The first is as a direct
replacement for existing sensors where the fiber sensor offers significantly improved
performance, reliability, safety and/or cost advantages to the end user. The second area is the
development and deployment of fiber optic sensors in new market areas.
For the case of direct replacement, the inherent value of the fiber sensor, to the customer, has to
be sufficiently high to displace older technology. Because this often involves replacing
technology the customer is familiar with, the improvements must be substantial.
The most obvious example of a fiber optic sensor succeeding in this arena is the fiber optic gyro,
which is displacing both mechanical and ring laser gyros for medium accuracy devices. As this
technology matures it can be expected that the fiber gyro will dominate large segments of this
market.
Significant development efforts are underway in the United States in the a rea of fly-by-light
where conventional electronic sensor technology are targeted to be replaced by equivalent fiber
optic sensor technology that offers sensors with relative immunity to electromagnetic
interference, significant weight savings and safety improvements.
In manufacturing, fiber sensors are being developed to support process control. Oftentimes the
selling points for these sensors are improvements in environmental ruggedness and safety,
especially in areas where electrical discharges could be hazardous.
![Page 28: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/28.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 23
One other area where fiber optic sensors are being mass-produced is the field of medicine,
where they are being used to measure blood gas parameters and dosage levels. Because these
sensors are completely passive they pose no electrical shock threat to the patient and their
inherent safety has lead to a relatively rapid introduction.
The automotive industry, construction industry and other traditional users of sensors remain
relatively untouched by fiber sensors, mainly because of cost considerat ions. This can be
expected to change as the improvements in optoelectronics and fiber optic communications
continue to expand along with the continuing emergence of new fiber optic sensors.
New market areas present opportunities where equivalent sensors do not exist. New sensors,
once developed, will most likely have a large impact in these areas. A prime example of this is
in the area of fiber optic smart structures. Fiber optic sensors are being embedded into or
attached to materials (1) during the manufacturing process to enhance process control systems,
(2) to augment nondestructive evaluation once parts have been made, (3) to form health and
damage assessment systems once parts have been assembled into structures and (4) to enhance
control systems.
![Page 29: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/29.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 24
Chapter 5
Analytical Treatment of Three Layer Optical Fiber
We consider the meridional cross-section of a three- layer fiber. The outermost layer is
considered as the infinitely extended free-space having an RI of n3 = 1. RIs of the other different
layers are represented as n1 and n2 with n1 > n2. The analysis of the fiber structure essentially
needs the use of the cylindrical polar coordinate system ( , , z ); z-axis being the optical axis
of the fiber along which the propagation takes place. There are two interfaces in the fiber
separating the different regions, and the parametric boundaries of the different layers are
considered to be = 1 and = 2 with 1 < 2.
Solutions of the wave equation with cylindrical symmetry for axial components of the
electric/magnetic fields Ez and Hz are sought for the three regions, and then matched at the
interfaces for continuity conditions. The wave equation is
(2/2) + (/)/ + (2/2)/2 + q2 = 0 (1)
Where stands for either Ez or Hz, as the case may be. Also
q2 = 2 - β2
Where
is the angular frequency of the wave in the unbound medium,
β is the axial component of the propagation constant, and
and , respectively, are the permeability and permittivity of the medium.
5.1 Fiber without coating
For three- layer dielectric fibers, the electric/magnetic fields in the central core section can be
taken in the form of Bessel function Jʋ (·) of the first kind, whereas those in the inner clad can
be represented by the linear combination of Bessel functions of the first and the second kinds,
i.e., Jʋ(·) and Yʋ(·). In the outer clad section, field essentially has decaying character with
increasing radial parameter, and therefore, the most suitable solution in this region can be
represented by the modified Bessel function Kʋ(·) of the second kind. The axial components of
the electric/magnetic fields (i.e., Ez and Hz ) for the different regions of the fiber can be written
on the basis of these considerations.
Region I: core (0 <= ρ <= 1)
Ez1 = C1Jʋ(1ρ)ejʋ (2a)
![Page 30: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/30.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 25
Hz1 = C2Jʋ(1ρ)ejʋ (2b)
Region II: inner cladding (1 <= ρ <= 2)
Ez2 = C3Jʋ(2ρ) + C4Yʋ(2ρ)}ejʋ (3a)
Hz2 = C5Jʋ(2ρ) + C6Yʋ(2ρ)}ejʋ (3b)
Region III: outer cladding (ρ >= 2)
Ez3 = C7Kʋ(3ρ)ejʋ (4a)
Hz3 = C8Kʋ(3ρ)ejʋ (4b)
In Eqs. (2a) – (4b), C1– C8 represent unknown constants to be determined by the boundary
conditions. Also 1, 2 and 3 are the quantities corresponding to the different regions of the
fiber, and may be given as
12 = k1
2 - β2 = 21 - β2 (5b)
22 = β2 - k2
2 = β2 - 22 (5c)
32 = β2 – k3
2 = β2 - 23 (5d)
Where 1, 2 and 3 are the dielectric constants, and is the relative permeability of the medium.
Also ni = ( i)1/2, where
i is the relative dielectric permittivity of medium i,
β is the longitudinal component of the propagation constant.
Those axial components can be used to determine the transverse field components (i.e., E , H
and E, H) corresponding to the different regions of the fiber. These field components are not
explicitly stated in the text, but used to develop the equations that can be obtained after
implementing the continuity conditions at the layer interfaces. As there are two interfaces in the
fiber, there can be eight equations generated altogether after implementing the boundary
conditions at the layer interfaces with the parametric coordinates = a and = b (with a < b).
In order to simplify the situation, the outermost region is considered to be infinitely extended.
The form of this set of eight equations is as
A1Jʋ(1a) – A3Jʋ(2a)- A4Yʋ(2a) = 0 (6)
A2Jʋ(1a) – A5Jʋ(2a)- A6 Yʋ(2a) = 0 (7)
![Page 31: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/31.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 26
A1(βʋ/q12a) Jʋ(1a) + A2(j /q1
2) 1Jʋ’(1a) - A3(βʋ/q2
2a) Jʋ(2a)
– A4(βʋ/q22a) Yʋ(2a) - A5(j /q2
2) 2Jʋ’(2a) - A6(j /q2
2a) 2Yʋ’(2a) = 0 (8)
- A1(j /q12) 1Jʋ
’(1a) + A2(βʋ/q12a) Jʋ(1a) +A3(j/q2
2) 2 Jʋ’ (2a)
+ A4(j /q22) 2Yʋ
’(2a) - A5(βʋ /q22a) Jʋ’(2a) – A6(βʋ/q2
2a) Yʋ(2a) = 0 (9)
A3Jʋ(2b) + A4Yʋ(2b) - A7Kʋ(3b) = 0 (10)
A5Jʋ(2b) + A6Yʋ(2b) - A8Kʋ(3b) = 0 (11)
A3(βʋ/q22b) Jʋ(2b) + A4(βʋ/q2
2b) Yʋ(2b) + A5(j/q22) 2Jʋ
’ (2a)
+ A6(j/q22) 2Yʋ
’ (2b) – A7(βʋ/q3
2b) Kʋ(3b) - A8(j/q32) 3Kʋ
’ (3b) = 0 (12)
– A3(j/q22) 2 Jʋ
’ (2a) – A4(j/q2
2) 2 Yʋ’ (2b) + A5(βʋ/q2
2b) Jʋ(2b)
+ A6(βʋ/q22b)Yʋ(2b) + A7(j/q3
2) 3Kʋ’ (3b) – A8(βʋ/q3
2b) Kʋ(3b) = 0 (13)
In Eqs. (6) – (13), A1 - A8 are unknown constants to be determined by the boundary conditions.
Primes (‘) are first differentiation of the Bessel function. Also, 1, 2 and 3 are the quantities as
defined in Eq. (5). For Eqs. (6) – (13) to be consistent, the determinant (2) formed by the
coefficients A1 - A8 must vanish, i.e.,
2 = 0 (14)
2 is essentially a 8 × 8 determinant, the explicit form of which is not incorporated into the text.
Eq.(14) determines the dispersion relation for the three- layer dielectric fiber without Au-
coating, the solutions of which will provide the actual values of modal propagation constants
satisfied by the fiber. Once again the form of 2 is complex, and therefore, one may rewrite Eq.
(14) as
21 + j22 = 0 (15)
![Page 32: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/32.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 27
where 21 and 22 are, respectively, the real and the imaginary parts of 2. Obviously, the valid
propagation constants of the sustained modes in the fiber will be only those for which both 21
and 22 simultaneously vanish.
![Page 33: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/33.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 28
Chapter 6
Result
As already stated that present project will be completed by using Bessel function of first kind,
second kind and Hankel function. Bessel function of first kind and second kind has been studied
and implemented by MATLAB. It is now possible to interpret the wave equation (1) in
numerical terms. This will give us an insight into the model properties of our waveguides. By
putting the particular values of n1, n2 and λ into equation (14) , one can obtain different values of
2 for a large number of equispaced values of β, in the range of n1k > β > n2k, where k is the free
space propagation constant.
6.1 Bessel function of first kind (integer value)
Fig. 9 Bessel function of first kind (integer value 0, 1)
![Page 34: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/34.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 29
6.2 Bessel function of first kind (non-integer value)
Fig. 10 Bessel function of first kind (non- integer value 0.5, 1.5)
![Page 35: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/35.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 30
6.3 Bessel function of Second kind (integer value)
Fig. 11 Bessel function of second kind (integer value 0, 1)
![Page 36: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/36.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 31
6.4 Bessel function of second kind (non-integer value)
Fig. 12 Bessel function of second kind (non- integer value 0.5, 1.5)
![Page 37: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/37.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 32
Chapter 7
Summary and Future Work
7.1 Summary
Bessel Function of first and second kind has been studied and implemented by using MATLAB.
Characteristics of Bessel Function of first and second kind have been shown. It is now possible
to interpret the wave equation (1) in numerical terms. This will give us an insight into the model
properties of our waveguides. By putting the particular values of n1, n2 and λ into equation (14) ,
one can obtain different values of 2 for a large number of equispaced values of β, in the range of
n1k > β > n2k, where k is the free space propagation constant.
7.2 Future Work
Future work requires more complex steps, in future we will study and implement Fiber with Au-
coating in helical fashion, and thus design our main pressure sensor. So brief introduction for
future work has been given here
Fiber with Au-coating (Four-layer Fiber)
In the case of such a fiber, in the central core section, the solution can be taken in the form of
Bessel function Jʋ(·) of the first kind; ʋ representing the azimuthal periodicity, which can take
only discrete values. Essentially the symbol ʋ represents the mode index. In the outermost clad
region, the field has a decaying character as one moves away from the fiber axis, and
therefore, the solution can be best represented by the modified Bessel function Kʋ(·) of the
second kind. In the remaining two intermediate regions, the solutions must be formed by
linear combinations in the region next to the fiber core, by Bessel function of the first and the
second kinds, i.e., Jʋ(·) and Yʋ(·), and in the remaining region before the outermost clad, by
the modified Bessel function of the second kind and Hankel function, i.e., Kʋ(·) and Hʋ(1)(.).
![Page 38: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/38.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 33
References
[1] H. Xiao, Self-Calibrated Interferometric/Intensity Based Fiber Optic Pressure Sensors. 2000,
Ph.D. Dissertation of Virginia Tech.
[2] J. Xu, et al., "A Novel Temperature-Insensitive Optical Fiber Pressure Sensor For Harsh
Environments," IEEE Photonics Technology Letters, 17, pp. 870- 872, 2005.
[3] B.G. Clarke, Pressuremeters in geotechnical design: Blackie Academic & Professiona 1995.
[4] Y.J. Rao and D.A. Jackson, "Prototype fiber optic based pressure probe with built- in
temperature compersation with signal recovery by coherence reading," Applied Optics, 32,
pp. 1993.
[5] A. Arie, B. Lissak, and M. Tur, "Static fiber-Bragg grating strain sensing using frequency-
locked lasers," Journal of Lightwave Technology, 17, pp. 1849-1855, 1999.
[6] M.G. Xu, H. Geiger, and J.P. Dakin, "Fiber grating pressure sensor with enhanced sensitivity
using a glass-bubble housing," Electronics Letters, 32, pp. 128-129, 1996.
[7] D.J. Hill and G.A. Cranch, "Gain in hydrostatic pressure sensitivity of coated
fiber Bragg grating," Electronics Letters, 35, pp. 1268-1269, 1999.
[8] J.W. Berthold, "Historical review of microbend fiber-optic sensors," Journal of
Lightwave Technology, 13, pp. 1193-1199, 1995.
[9] B.P. Samoriski. "Fabry Perot Interferometers Theory," in
http://www.burleigh.com/Pages/opticalTech.htm, 2000,
[10] J. Dakin and B. Culshaw, Optical Fiber Sensors: Principles and Components:
Artech House, Inc, 1988.
[11] Y.J. Rao, et al., "Development of prototype fibre-based Fizeau pressure sensors
with temperature compensation," J. Lightwave Technol., 12, pp. 1685-1695,
[12] M.I. Belovlov, M.M. Bubnov, and S.L. Semjonov. "High Sensitive Fiber Interferometric
Pressure Sensor," in Lasers and Electro-optics Europe, 1996, 192.
![Page 39: A Dissertation Preliminary Report On - AJAY KUMAR …ajaykmga.weebly.com/uploads/2/2/1/5/2215854/m._tech_primary.pdf · A Dissertation Preliminary Report On ... highly corrosive agents](https://reader031.vdocuments.us/reader031/viewer/2022030411/5a9d7c447f8b9a21688b90cc/html5/thumbnails/39.jpg)
A Design of High Temperature High Bandwidth Fiber Optic Pressure Sensors
S V National Institute of Technology – Surat Page 34
[13] W.F. Cullinane and R.R. Strange. "Gas Turbine Engine Validation Instrumentation:
Measurements, Sensors, and Needs," in Proc. of SPIE, Harsh Environment Sensors II,
1999, 3852.
[14] K.A. Murphy, et al., "Quadrature phase shifted extrinsic Fabry-Perot optical fiber sensors,"
Opt. Lett., 16, pp. 273-275, 1991.
[15] J. Zhou, et al., "Optically Interrogated MEMS Pressure Sensors for Propulsion
Applications," Opt. Eng, 40, pp. 598-604, 2001
[16] D.C. Abeysinghe, et al., "Novel MEMS Pressure and Temperature Sensors Fabricated
on Optical Fibers," Journal of Micromechanics and Micro engineering, 12, pp. 229-135,
2002.
[17] http://electron9.phys.utk.edu/optics421/modules/m9/Optical%20Wave%20Guides.htm
[18] http://www.techweb.com/encyclopedia/defineterm.jhtml?term=Dispersion
[19] http://www.tpub.com/neets/tm/106-9.htm
[20] http://zone.ni.com/devzone/cda/ph/p/id/129
[21] http://www.iec.org/online/tutorials/fiber_optic/topic02.asp
[22] http://www.poly-optical.com/tech_manual.html
[23] http://www.math.sfu.ca/~cbm/aands/toc.htm
[24] http://www.wikipedia.com