347
Optical Fiber S
14. Optical Fiber Strain Gages
Chris S. Baldwin
14.1 Optical Fiber Basics ............................... 348
14.1.1 Guiding Principals for Optical Fiber 348
14.1.2 Types of Optical Fibers ................. 349
14.2.3
14.2.4
14.2.5
14.2.6
Advantages of Fiber Optic Sensors .
Limitations of Fiber Optic Sensors ..
Thermal Effects ...........................
Introduction to Strain–Optic Effect
352
353
354
354
14.3 Interferometry .....................................
14.3.1 Two-Beam Interference ...............
14.3.2 Strain–Optic Effect.......................
14.3.3 Optical Coherence .......................
14.3.4 Mach–Zehnder ...........................
14.3.5 Michelson ..................................
14.3.6 Fabry–Pérot ...............................
14.3.7 Polarization................................
14.3.8 Interrogation of Interferometers ...
354
355
355
356
357
357
357
358
358
14.4 Scattering ............................................ 359
14.4.1 Brillouin Scattering...................... 359
14.4.2 Strain Sensing Using Brillouin
Scattering................................... 359
14.5 Fiber Bragg Grating Sensors ..................
14.5.1 Fabrication Techniques ................
14.5.2 Fiber Bragg Grating Optical
Response ...................................
14.5.3 Strain Sensing Using FBG Sensors ..
14.5.4 Serial Multiplexing ......................
14.5.5 Interrogation of FBG Sensors,
Wavelength Detection..................
14.5.6 Other Grating Structures ...............
361
361
362
363
364
14.6 Applications of Fiber Optic Sensors .........
14.6.1 Marine Applications.....................
14.6.2 Oil and Gas Applications ..............
14.6.3 Wind Power Applications .............
14.6.4 Civil Structural Monitoring ............
367
367
367
368
368
366
367
14.2 General Fiber Optic Sensing Systems....... 351
14.2.1 Strain Sensing System Concept ...... 351
14.2.2 Basic Fiber Optic Sensing
Definitions ................................. 351
References .................................................. 369
Many optical fiber sensors are based on classical bulk
optic arrangements, as discussed in Chap. 18 – Basics
of Optics. These arrangements are named after the in-
ventors who are credited with their invention. Other
optical fiber sensors are based on physical phenomenon
such as scattering effects that are inherent to the optical
14.7 Summary ............................................. 368
Part B 14
Optical fiber strain sensing is an evolving field in
optical sciences in which multiple optical principles
and techniques are employed to measure strain.
This chapter seeks to provide a concise overview
of the various types of optical fiber strain sensors
currently available. The field of optical fiber strain
sensing is nearly 30 years old and is still breaking
new ground in terms of optical fiber technology,
instrumentation, and applications. For each sensor
discussed in the following sections, the basic
optical layout is presented along with a description
of the optical phenomena and the governing
equations.
Comprehensive coverage of all aspects of optical fiber strain sensing is beyond the scope of
this chapter. For example, each sensor type can
be interrogated by a number of means, sometimes based on differing technology. Furthermore,
these sensors are finding applications in a wide
variety of fields including aerospace, oil and gas,
maritime, and civil infrastructures. The interested reader is referred to the works by Grattan
and Meggit [14.1], Measures [14.2], and Udd [14.3]
for more-detailed descriptions of interrogation
techniques and applications of the various sensors.
348
Part B
Contact Methods
fiber material. In general, fiber optic sensors function
by monitoring a change in an optical parameter as the
optical fiber is exposed to the strain field.
The three main types of optical fiber strain gages are
•
•
•
interferometry (changes in optical phase)
scattering (changes in optical wavelength)
fiber Bragg grating (changes in optical wavelength)
Other optical phenomena such as intensity variations
are exploited for optical fiber sensors measuring other
quantities such as chemical concentrations, applied
loads/pressure, and temperature. The strain sensing
mechanisms listed above are explored in the sections
below, but first an introduction to optical fibers and
a general overview of the basic layout, advantages, and
disadvantages of optical fiber strain sensors is provided.
14.1 Optical Fiber Basics
Part B 14.1
The first thought many people have when introduced to
optical fiber is of a thin, fragile piece of glass. On the
contrary, the ultrapure manufacturing that goes into producing the low-loss optical fiber of today creates a thin
glass structure essentially free of defects with tensile
strength values near 800 ksi (5.5 GPa) [14.2]. The following sections discuss the optical guiding properties of
optical fiber and provide a brief description of the various types of optical fiber commercially available for
sensing applications.
14.1.1 Guiding Principals for Optical Fiber
Before any discussion of fiber optic strain sensors can
be realized, an understanding of the light guiding principles of optical fiber should be presented. The basic
material for optical fiber is fused silica [14.2]. Standard
optical fiber consists of two concentric glass portions.
The inner portion is called the core and the outer portion is called the cladding. The core region of the optical
fiber typically contains dopants such as germanium (Ge)
or boron (B) to increase the refractive index of the core
(n core ) to a slightly higher value than that of the cladding
(n clad ), which is pure fused silica. Optical fiber also
uses protective layers of polymer coatings to protect the
glass surface from damage. For most strain sensing applications, one of two coatings is applied to the optical
fiber. Acrylate-coated optical fibers have a final outer
diameter of 250 μm. Polyimide-coated optical fibers are
available in a range of final outer diameters, typically
around 180 μm.
Standard telecommunications optical fiber has
a germanium-doped core. The optical transmission
spectrum for Ge–Si is shown in Fig. 14.1 [14.2]. The
transmission spectra displays the characteristic decay of
the Rayleigh curve (1/λ4 ); at higher wavelengths the
transmission is limited by the absorption of energy by
the silica structure. The multiple peaks in the attenua-
tion curve are due to OH− (hydroxyl) scattering in the
optical transmission curve. The effect of the hydroxyl
peaks is the creation of transmission windows for optical fiber. The telecommunications industry makes use of
the wavelength regions around 1550 nm due to the lowloss properties and the availability of optical sources
and detectors. This is commonly referred to as the Cband. The region around 1300 nm, termed the S-band,
is also used for data transmission, but typically is reserved for shorter-length applications such as local area
networks (LANs).
A schematic diagram of standard single-mode optical fiber is shown in Fig. 14.2. The size of the core
(radius = a) is dependent on the wavelength of light the
optical fiber is designed to guide. For single-mode operation in the C-band, this value is around 4 μm. The
cladding diameter is standardized at 125 μm for many
optical fiber types. This allows for the use of common
optical fiber tools such as cleavers, strippers, and fusion
splicers to be used on different optical fiber types from
different optical fiber vendors.
In the simplest sense, light is guided via total internal reflection (TIR) between the core and cladding
Attenuation (dB/km)
S-band
0.6
0.8
1
1.2
C-band
1.4
1.6
1.8
Wavelength (μm)
Fig. 14.1 Optical transmission windows for optical fibers
Optical Fiber Strain Gages
1
250 μm
a
J0 (V )
0.75
349
V = 2.405
J1 (V )
0.5
125μm
14.1 Optical Fiber Basics
0.25
0
Fig. 14.2 Schematic of typical optical fibers
–0.25
Therefore, the modal propagation of light in a stepindex optical fiber is dependent on the core size (a),
the refractive index difference between the core and
cladding, and the wavelength of light propagating in the
core. The V number value to ensure single-mode operation is 2.405. If the V number is larger than 2.405 then
Acceptance
cone
α
Cladding
Core
Fig. 14.3 Total internal reflection between core and
cladding
–0.5
–0.75
–J1 (V )
0
2
4
Singlemode region
6
8
10
Fig. 14.4 Bessel solution space for modal operation of op-
tical fiber
light in the optical fiber is not propagating as singlemode. Based on the formulation given in (14.1), a cutoff
wavelength value can be determined for the optical
fiber, which defines the lower limit of single-mode operation with respect to wavelength. The cutoff wavelength
is given by:
2πa
n 2core − n 2clad .
(14.2)
λcutoff =
V
Any wavelength of light lower than the cutoff wavelength will not propagate as single-mode in the optical
fiber. Likewise, to determine the appropriate core size
to ensure single-mode operation at a given wavelength,
(14.1) can be written as
(14.3)
a = 2.405λ/2πV n 2core − n 2clad .
The vast majority of optical fiber strain sensors
employ standard single-mode optical fiber or similar
constructed optical fiber. The following section provides a brief description of optical fiber types that may
be encountered in the field of strain sensing.
14.1.2 Types of Optical Fibers
For the most part, fiber optic strain sensors make use
of readily available, standard optical fiber and components. Optical fiber sensing has experienced a new
thrust of interest and development in recent years. Much
of the current research has been focused on the field
of biosensing with the development of new optical
fiber types and sensing techniques. Optical fiber strain
sensing has been steadily finding and being integrated
Part B 14.1
of the optical fiber, as illustrated in Fig. 14.3. TIR was
introduced in Chap. 18. Figure 14.3 shows a slab waveguide description for optical fiber. Based on the slab
waveguide formulation, the standard Snell’s law can
be employed to determine the guiding principles for
the structure. This analysis leads to an acceptance cone
where light entering the core within this angle will result in a guiding condition. In optical fiber terms, this is
related to the numerical aperture (NA).
Of course, the explanation of TIR for the guiding
principles of optical fiber is very limiting. The derivation for the propagation of light through an optical fiber
is based on a solution of the electromagnetic wave equation (18.1), as discussed in Chap. 18. This derivation
is beyond the scope of this chapter. The important result from the derivation is that the propagation of light
through the core is based on Bessel functions (Ji (x)).
Single-mode propagation in optical fiber is defined by
a parameter known as the V number, which is the argument of the Bessel function solution for guided core
modes [14.2]. The solution plots of the first few Bessel
functions are shown in Fig. 14.4. The V number for
standard single-mode optical fiber is expressed as
2πa
n 2core − n 2clad . (14.1)
V = ka n 2core − n 2clad =
λ
350
Part B
Contact Methods
a) Singlemode
b) Multimode
c) PM-elliptical core
d) PM-bowtie
Part B 14.1
Fig. 14.5a–d Cross-section views of various types of opti-
cal fiber
into more application areas including civil infrastructure monitoring, oil and gas application, embedded
composite sensing, and maritime sensing. As discussed
in Sect. 14.2.3, optical fiber sensing possesses some inherent advantages over traditional sensing techniques
for these and other application areas.
The development of low-loss optical fibers in the
1970s began a period of innovation in both telecommunications and sensing applications. The first optical
fibers designed for telecommunication applications
were manufactured by Corning in 1970 and possessed
attenuation values just less than 20 dB/km [14.2]. Current attenuation values for telecommunication grade
optical fiber are of the order of 0.2 dB/km [14.2]. Although the vast majority of fiber optic sensors use
standard communications-grade single-mode optical
fiber, it should be noted that multiple varieties of optical fiber exist and are being explored for various sensing
applications. Figure 14.5 shows a cross-section view of
several types of optical fiber. For example, a variety of
polarization-maintaining optical fibers exist that possess
an induced birefringence throughout the fiber length,
thus maintaining two principal polarization axes for optical transmission. Various dopants and fiber structures
have been explored throughout the past few decades to
decrease the influence of bend losses and improve signal
quality within optical fiber.
Using Fig. 14.2 as a reference, the optical fibers displayed in Fig. 14.5 can be compared to the standard
single-mode optical fiber. Multimode optical fiber (illustrated in Fig. 14.5b) possesses a much larger core
size compared to single-mode fiber. This aspect was
discussed in Sect. 14.1.1 in terms of the V number dictating single-mode operation. Multimode optical fiber
may either have a step index core (like the single-mode
optical fiber) or a graded refractive index core. If the
multimode fiber is step index, then the various propagation modes travel different path lengths due to the
oscillatory nature of the propagation. Graded-index optical fibers allow the various modes propagating in the
fiber to have equivalent path lengths.
Figure 14.5 also displays two types of polarizationmaintaining fiber (PM fiber). Polarization of light is
covered in both Chaps. 18 and 25 of this Handbook.
The polarization-maintaining aspect is induced either
through a geometric structure of the core (elliptical
core fiber – Fig. 14.5c) or by inducing a permanent
mechanical load within the fiber structure (such as
bow-tie fiber – Fig. 14.5d). PM fiber develops two polarization states (fast and slow axis) whose responses
to mechanical loads are slightly different. PM fiber
has found applications in strain sensing, as discussed
in Sect. 14.3.7.
Most recently, the development of photonicbandgap (PBG) fiber and photonic-crystal fiber (PCF)
has generated great interest in the sensing community,
particularly in the field of chemical and biosensing.
These optical fibers are commonly referred to as “holey
fibers” because the core and cladding regions are developed by manufacturing a structured pattern of voids
(holes) that traverse the entire length of the optical
fiber. For more information on this type of optical fiber,
the reader may visit www.crystal-fibre.com. In general,
PCFs use a patterned microstructure of voids along
the length of the optical fiber to create an effective
lower-index cladding and guide light in a solid core by
modified total internal reflection (M-TIR)[14.4]. PBG
fibers guide light within a low-index region (longitudinal void) by creating a photonic bandgap based on the
structure and pattern of the voids [14.4].
Optical Fiber Strain Gages
14.2 General Fiber Optic Sensing Systems
351
14.2 General Fiber Optic Sensing Systems
14.2.1 Strain Sensing System Concept
Interrorgation unit
Fiber optic sensor
Source
Optics
Feedback
Data acquisition
Demodulator
Fig. 14.6 Basic configuration of an optical fiber sensor sys-
tem
a) Distributed
b) Discrete
Fig. 14.7a–c Fiber optic sensor classifications
14.2.2 Basic Fiber Optic Sensing Definitions
Due to the wide variety of fiber optic sensors, some definitions of optical fiber strain sensing are required. Fiber
optic sensors can be classified into distributed, discrete,
or cumulative strain sensors, as illustrated in Fig. 14.7.
A distributed strain sensor provides a measure of strain
at potentially every point along the sensing optical fiber.
Distributed sensors typically have a spatial resolution of
approximately 1 m due to the resolution of the measurement systems. A discrete strain sensor provides a strain
measurement at one location often based on a smallgage-length fiber optic sensor. By serially multiplexing
these sensors, a distributed sensor array can be fabricated with the strain measurements being at discrete
points instead of an average of the spatial resolution.
A cumulative strain sensor provides a measure of strain
that is an average strain value over the entire sensing
length of the optical fiber.
The selection of a fiber optic strain sensor for a particular application is driven by the sensing requirements
for the application. For example, measurement of the
hoop strain of a pressure vessel may use a distributed
sensor to obtain strain values at multiple locations
around the circumference. A discrete sensor can provide a single strain measurement at a single location on
the circumference or multiple measurements if serially
multiplexed. A cumulative strain sensor would provide
a single strain measurement based on the overall strain
induced in the fiber bonded to the circumference of the
vessel. Cumulative sensors provide the highest sensitivity and are often employed when very small strain
signals are of interest such as the measurement of acoustic fields.
In many cases, the optical fiber serves as both the
conduit for the optical signal and the sensing mechanism. In this situation, the sensor is referred to as an
intrinsic sensor. An extrinsic sensor is the case where
the optical fiber delivers the optical signal to the sensc) Cumulative
Part B 14.2
The basic building blocks of a fiber optic strain sensor system can be compared to the building blocks
of a resistance strain gage (RSG) system discussed
in Chap. 12. A resistance strain gage circuit requires
a voltage supply, Wheatstone bridge, electrical wires
connecting to the RSG, a voltmeter to monitor the circuit output, and a data-acquisition system to record the
voltage changes. In terms of fiber optic sensors, an
equivalent arrangement can be drawn where the voltage supply is equivalent to the light source (laser, light
emitting diode, or other optical source). The Wheatstone bridge is equivalent to the optics that guide the
light to and from the sensors or sensing region of the optical fiber. The wires that connect to the RSG are simply
the lead optical fiber to the fiber optic sensors. In some
cases, a single strand of optical fiber is used to monitor
multiple (potentially thousands) fiber optic strain sensors (see multiplexing below). This is vastly different
from RSG circuits where each uniaxial gage requires
at least two conductors. The voltmeter for a fiber optic sensor system is the interrogation unit (also called
a demodulator). The interrogation units typically have
one or more photodetectors to transfer the optical signal
to a voltage signal proportional to the optical intensity. The data-acquisition system is the one component
that may be an exact duplicate between the RSG circuit and the fiber optic sensor system. This is typically
a personal computer (PC) or laptop device with appro-
priate interface cards/boards to record the data from the
interrogation unit.
352
Part B
Contact Methods
A
A/2
B/2
B
A/2
B/2
Fig. 14.8 Bidirectional optical fiber coupler
Part B 14.2
ing mechanism such as an air cavity. In both cases, the
applied strain induces a physical change in the geometry of the sensor. For the case of an intrinsic sensor,
a strain–optic effect is also induced and must be considered when determining the calibration coefficient (gage
factor) of the sensor.
Another differentiation between types of optical
fiber sensors is whether the sensor works as a reflective
or a transmission element. The majority of fiber optic
strain sensors function in reflection mode, where light
traveling in the optical fiber is reflected back towards
the optical source from reflective elements or from inherent scattering of the optical fiber material. In order
to direct the back-reflected light to the interrogation
instrumentation, an optical fiber coupler device is employed. A bidirectional coupler is typically used in these
applications, as shown in Fig. 14.8. The commercially
available standard bidirectional coupler is termed a 3 dB
coupler because it divides the optical signal equally into
the two output arms as indicated in Fig. 14.8.
14.2.3 Advantages of Fiber Optic Sensors
Optical fiber sensors offer many advantages over traditional electrical-based strain sensors. Many of these
advantages stem from the pure optical nature of the
sensor mechanisms. Traditional sensors depend on the
measurement of variations of resistance or capacitance
of the electrical sensors. Optical fiber sensors depend on
changes to optical parameters of the optical fiber or the
light traveling within the optical fiber. This difference
leads to many advantages, including
•
•
•
•
immunity to electromagnetic interference
long transmission lead lines
no combustion danger
serial multiplexing
The following discussion expands on each of the advantages stated above.
Immunity to Electromagnetic Interference
Optical fiber sensors function by measuring changes to
the light that is traveling within the optical fiber. Unlike
low-level voltage signals, resistance changes, or other
electrical phenomena used for traditional sensors, electromagnetic influences do not cause measurable levels
of noise. Therefore, when dealing with optical lead
lines and cabling, no special shielding is required, thus
greatly reducing the cabling weight compared to traditional sensors.
Long Transmission Lines
With the advances made in the telecommunications field
for optical fiber transmission, current standards for optical signal transmission allow the light signal to be
transmitted many kilometers without a detrimental level
of signal degradation. Optical power loss in current
communications grade optical fiber are on the order of
0.2 dB/km. Other factors that affect the transmission of
optical signals in fibers such as chromatic and material
dispersion have also experienced improvements.
No Combustion Danger
In some applications, there exists a risk of ignition
or explosion of combustive materials from sparks or
electrical potentials from sensors. The optical power
guided within the core for fiber optic sensors is typically
less than 1 mW, essentially eliminating any potential of
spark or ignition danger. Without the requirement of
a voltage potential at the sensor location and the ability
to have long lead lines, optical fiber sensors are regarded
as being immune to combustion danger. This is one reason why fiber optic sensors are being heavily explored
for various oil and gas industry applications [14.5].
Multiplexing
Some of the optical fiber sensors discussed in this
chapter have the ability to be multiplexed (multiple
sensors interrogated by a signal instrumentation system). The two main types of multiplexing are parallel
and serial multiplexing. In parallel multiplexing (also
called spatial multiplexing), the light source is separated
into multiple optical fiber channels, with each channel
containing an optical sensor. Typically, each sensor in
a parallel multiplexing scheme will have its own detector and processing instrumentation. If the light source is
guided to the multiple channels via a fiber optic switch
component (as shown in Fig. 14.9), then the optical
sensor signals are not monitored simultaneously but sequentially depending on the timing of the optical switch.
In this case, a common detector and processing instru-
Optical Fiber Strain Gages
Optical switch
Source
Coupler
Demodulation and
data acquisition
Sensor
arrays
Switch control signal
Fig. 14.9 Parallel multiplexing employing an optical
switch
Coupler
#1 #2 #3
#n–1 #n
Sensor
array
Instrumentation
Fig. 14.10 Serially multiplexed sensors
mentation may be employed for all the sensors. If the
optical source is divided to all the sensors via a fiber
optic coupler arrangement, then all the fiber optic sensors can be interrogated simultaneously through each
sensor’s individual processing instrumentation.
Serial multiplexing is a major advantage of some
types of optical fiber sensors (in particular the fiber
Bragg grating, Sect. 14.5). In serial multiplexing techniques, multiple sensors are positioned along a single
optical fiber lead (in serial fashion), as illustrated
in Fig. 14.10. The strain signals from each of these sensors are separated through optical means or via the
processing instrumentation. The sensing system may
also contain a secondary fiber sensor to provide reference and/or gating signals to decouple the serially
multiplexed signals.
14.2.4 Limitations of Fiber Optic Sensors
In most texts dealing with optical fiber sensors, the
reader can find a similar list of advantages as displayed
in Sect. 14.2.3. What is often omitted from these texts is
a list of their limitations. For the reader (and potential
user of these systems), it is imperative that these factors
be discussed and explained so the strain sensing community achieves a common understanding of the present
limitations of fiber optic strain sensors. The following
lists the major limitations of fiber optic sensing technology. The degree to which each limitation affects fiber
optic sensing technology is dependent on the particular
style of fiber optic sensor
1
1.5
2
2.5
Bend radius (cm)
Fig. 14.11 Attenuation due to bend radius for SMF-28 optical fiber with one complete wrap 1550 nm (marks data,
solid line theory)
•
•
•
•
limited bend radius
precise alignment of connections
cost
varying specifications
Limited Bend Radius
In order to maintain optimum transmission of the optical power, the limited bend radius of the optical fiber
must be adhered to. This is much more restricted compared to traditional electrical sensors where bending the
electrical wires through a 90◦ turn does not damage
the electrical wire. Thus placing optical fiber sensors
near physical boundaries requires some consideration.
A general rule of thumb is to keep the bend radius
greater than 2 cm. When the optical fiber bend radius
decreases below 2 cm, the level of attenuation sharply
increases, as shown in Fig. 14.11. Manufactures have
been developing new classes of optical fiber for various applications. Some of these are considered bend
insensitive.
Precise Alignment with Connections
Unlike traditional electrical sensors, where twisting two
copper conductors together is all that is needed to make
a connection, optical fiber requires precise alignment of
the two end-faces to ensure proper transmission of the
optical power. For single-mode optical fiber, the alignment of the adjoining cores is critical. The end-faces
of the fiber optic connectors must also be polished and
cleaned to ensure low losses at the connection. Issues
with misalignment can cause signal loss and also reduce
signal-to-noise levels with the introduction of backscat-
353
Part B 14.2
Source
Power loss (%)
100
90
80
70
60
50
40
30
20
10
0
0
0.5
14.2 General Fiber Optic Sensing Systems
354
Part B
Contact Methods
tered light from the interface. Fortunately, a number of
fiber optic connectors have become industry standards
and these provide quality connections.
Part B 14.3
Cost
In some cases, the cost of the optical fiber sensor is
equivalent to the price of standard telecommunication
fiber and components. With the high-volume production
of optical fiber and certain optical components, these
items are reasonably priced. However, the instrumentation systems required to interrogate these sensors are
high-precision electro-optic systems that are relatively
expensive, especially compared with RSG instrumentation.
Varying Specifications
As mentioned earlier, there are multiple choices for
instrumentation systems for each fiber optic strain sensor type. This level of variability in the marketplace
has led to a lack of industry standards, with companies continuing to market a particular technology to
various application areas. This issue is of greatest importance for the fiber Bragg grating sensor discussed in
this chapter where various types of the FBG sensors can
be used to measure strain with different interrogation
techniques.
respect to temperature. With RSG sensors, proper selection of materials and fabrication of the foil allows
for the manufacture of sensors that are thermally compensated for a particular material. This same process
of developing thermally self-compensating sensors cannot be implemented with fiber optic sensors. There
is a definite limit on the material property selection
for optical fibers, and the fabrication procedures for
optical fibers do not allow for the development of
material property variations that occur with metal coldworking processes. There are some athermal packages
of fiber optic sensors available commercially, but these
are not designed for strain measurement. The sensors
are bonded into self-contained housings (not suited for
bonding to other structures) that are typically composed
of materials of differing thermal expansion coefficients,
thus counteracting any expansion or contraction due to
thermal variations. For the most part, thermal compensation is accomplished by using a secondary sensor to
measure the temperature and subtract this effect from
the measured strain reading of the fiber optic sensor. Often, the secondary sensor is another fiber optic sensor
of similar design, but isolated from the strain field such
that the sensor thermal response is well characterized
for the application.
14.2.6 Introduction to Strain–Optic Effect
14.2.5 Thermal Effects
Most fiber optic sensors also experience issues of thermal apparent strain readings. Extrinsic sensors, whose
strain sensing is accomplished in an air gap or comparable structure, may have negligible thermal issues.
Intrinsic sensors suffer from thermal influences due to
the thermal expansion of the optical fiber and changes in
the refractive index with respect to temperature. These
quantities are comparable to the elongation and the resistance change of electrical resistance strain gages with
Central to many fiber optic strain sensors is the influence of the strain–optic effect. As a mechanical load
is applied to the optical fiber, the length of the optical
fiber changes and the refractive index also changes as
a function of the strain field. The change in the refractive
index is similar to the change in specific resistance of
electrical strain gages with respect to the applied strain.
Similar to the thermal effects, extrinsic sensors do not
experience this influence due to the use of an air cavity
as the sensing region.
14.3 Interferometry
As low-loss optical fiber became more readily available, researchers in the late 1970s and 1980s began
exploring the uses of optical fiber as a sensing medium.
Some of the first sensors to be explored were optical
fiber equivalents of classical interferometers such as
those of Michelson and Mach–Zehnder (MZ) [14.1].
Another interferometer, the Sagnac fiber optic sensor,
has enjoyed commercial success as the fiber optic gyroscope [14.6].
Many of the basic concepts employed in fiber optic interferometry are discussed in Chap. 18 in this
Handbook. Each interferometer discussed in this section makes use of fiber optic components to create two
optical paths that interfere to provide a measurement
of strain. Similar to full-field strain measurement discussed in other chapters of this Handbook, fiber optic
interferometers must extract the strain data from the
resulting fringe information. In the case of fiber op-
Optical Fiber Strain Gages
tic interferometers, the resulting interference signal is
detected via a photodetector and transformed to a voltage signal, which is processed via an instrumentation
system.
14.3.1 Two-Beam Interference
where nd is the optical path length for the wave, ω
is the frequency of the light wave, and φ is the phase
of the optical wave. Interference is generated by the
combination of two coherent light waves with different optical phases. In general, the phase difference is
created by having the two optical waves travel different paths forming a path length difference (PLD) as
discussed in Chap. 18.
The derivation of the intensity response of a general
interferometer begins with two coherent light waves that
differ by the optical phase term, as given in (14.6).
E1 = A1 cos(φ1 − ωt) ,
E2 = A2 cos(φ2 − ωt) .
(14.6)
The intensity that results from the interference of these
two electric field vectors is given by
I = |E1 + E2 |2 .
identity: 2 cos(α) cos(β) = cos(α + β) + cos(α − β). Applying these two considerations to (14.8), the intensity
function becomes
I = Ā + A1 A2 cos(φ1 + φ2 − 2ωt) + . . .
A1 A2 cos(φ1 − φ2 ) .
I = A21 cos2 (φ1 − ωt) + A22 cos2 (φ2 − ωt) + . . .
(14.8)
2A1 A2 cos(φ1 − ωt) cos(φ2 − ωt) .
The first two terms in (14.8) are the intensity of the
two individual electric field vectors and only contribute
an effective constant to the measurement signal as
described in Chap. 18. The final term in the above expression can be replaced by the product of cosines
(14.9)
The second term in (14.8) is at twice the optical frequency and only adds to the constant term in the
equation. The final term in (14.8) provides a means for
measuring the difference in optical phase between the
two coherent light waves with intensity. Equation (14.8)
can now be written in the more familiar form for interferometers
I = A + B cos(Δφ) ,
(14.10)
where the phase difference (Δφ) contains the strain
information of interest in the terms of a PLD. The
differences between the types of fiber optic interferometers are based on how the two coherent beams are
derived from the system and where the two optical paths
are recombined. In classical interferometers, the output of a light source is split via a beam-splitter and
the two paths are recombined on a screen. In fiber optic interferometers, the beam splitting and recombining
are accomplished within the optical fiber components
so that the optical signals are always guided. The
interference signal is then coupled to one (or more) photodetectors for signal acquisition and data processing.
14.3.2 Strain–Optic Effect
The following derivation examines how the change in
optical phase is related to the strain on the optical fiber.
Where the stress–optic law discussed in Chap. 25 examines the optical effect on a two-dimensional structure
(i. e., plate) under a state of plane stress, the strain–optic
effect discussed here examines the influence of a strain
state on an optical fiber. Light traveling in an optical
fiber can be classified by an optical modal parameter
called the propagation constant β given by [14.7]
(14.7)
Substituting (14.6) into (14.7) yields:
355
β = nkw =
2πn core
,
λ
(14.11)
where n core is the refractive index of the core of the optical fiber and kw is the wavenumber associated with the
wavelength of light propagating in the optical fiber. The
optical phase (φ) of light traveling through a section of
optical fiber is given by
φ = βL =
2πn core
L.
λ
(14.12)
Part B 14.3
As discussed in Chap. 18, the basic equation for the
electric vector of a light wave is given by (18.1) and
is rewritten here for convenience in (14.4):
2π
(14.4)
(z − vt) ,
E1 = A cos
λ
where A is a vector giving the amplitude and plane of
the wave, λ is the wavelength, and v is the wave velocity. Since the wave is traveling in the optical fiber, the
refractive index of the core is included in the path length
and wave velocity as
2π
c nd − t
E1 = A cos
λ
n
2π
2π
nd −
ct
= A cos
λ
nλ
(14.5)
= A cos(φ − ωt) ,
14.3 Interferometry
356
Part B
Contact Methods
When a mechanical load is applied to the optical fiber,
a phase change is experienced due to changes in the
length of the optical fiber (strain) and due to changes
to the propagation constant (strain–optic). These influences are the basis for interferometric strain sensors.
The change in optical phase (Δφ) can be written
as [14.8]
Δφ = βΔL + LΔβ .
(14.13)
Part B 14.3
The influence of the βΔL term is directly related to
the strain on the optical fiber (ε), as a change in length
and can be written as βεL. The change in the propagation constant is attributed to two sources. One is
a waveguide dispersion effect due to the change in the
optical fiber diameter. This effect is considered negligible compared to the other influences on the optical
phase change [14.8]. The other source is the change in
the refractive index, written as
dβ
(14.14)
Δn .
LΔβ = L
dn
The dβ/ dn term is reduced to the wavenumber, kw ,
but the Δn term is related to the optical indicatrix,
Δ[1/n 2 ]2,3 , as [14.8, 9]
n3
1
(14.15)
,
Δn = −
Δ 2
2
n 2,3
where light is propagating in the axial direction of the
optical fiber as indicated in Fig. 14.12. For the case of
small strains, the optical indicatrix is related to the strain
on the optical fiber as:
1
= pij ε j ,
(14.16)
Δ 2
n eff i
where pij is the strain–optic tensor of the optical fiber
and ε j is the contracted strain tensor. In the general
case, the strain–optic tensor will have nine distinct elements, termed photoelastic constants related to the
normal strains (shear strain is neglected).
Fortunately, for a homogenous, isotropic material
(such as optical fiber), the strain–optic tensor can be
2
Fig. 14.12 Indicial directions for optical fiber
For the case of a surface-mounted sensor, it has been
shown that the contracted strain tensor with zero shear
strain may be written as [14.2, 9]
⎛ ⎞
1
⎜ ⎟
(14.18)
ε j = ⎝−ν ⎠ εz ,
−ν
where ν is Poisson’s ratio for the optical fiber. If transverse loads are of interest, they may be incorporated
through the strain tensor. Due to the symmetry of the
optical fiber, the optical indicatrix is equivalent for i = 2
or 3. Incorporating the contracted strain tensor into
(14.16) leads to the following expression for a surfacemounted optical fiber sensor
1
= εz [ p12 − ν( p11 + p12 )] .
(14.19)
Δ 2
n eff 2,3
After substituting (14.19) into (14.13), the result is
Δφ = βεz L −
2π L n 3
εz [ p12 − ν( p11 + p12 )] .
λ 2
(14.20)
Reducing the above equation leads to:
n2
Δφ = βL 1 − [ p12 − ν( p11 + p12 )] εz .
2
(14.21)
Normalizing (14.21) by (14.12) yields the standard form
of the phase change with respect to the original phase:
n2
Δφ
= 1 − [ p12 − ν( p11 + p12 )] εz . (14.22)
φ
2
14.3.3 Optical Coherence
1
3
represented by two photoelastic constants p11 and p12
as [14.9]
⎞
⎛
p11 p12 p12
⎟
⎜
pij = ⎝ p12 p11 p12 ⎠ .
(14.17)
p12 p12 p11
Another important concept for fiber optic interferometers is optical coherence. Interference of optical waves
can only occur if the two waves are coherent, meaning that the phase information between the two waves
is related. When light is emitted from a source, it is
composed of coherent packets of energy. Coherence of
Optical Fiber Strain Gages
Fig. 14.13 Optical
source spectrum
λ 20
Lc ≈
Δλ
357
Sensing path
Δλ
λ0
14.3 Interferometry
Reference path
Fig. 14.14 Basic Mach–Zehnder fiber optic sensor arrangement
λ
14.3.5 Michelson
Lc ≈
λ20
Δλ
.
(14.23)
14.3.4 Mach–Zehnder
As optical fiber and optical fiber components became available for sensing purposes, the recreation of
classic interferometers was the first choice for early researchers. The first reported fiber optic strain gage by
Butter and Hocker was an optical-fiber-based Mach–
Zehnder [14.8]. In this early version, the output from
two optical fibers was recombined on a screen to monitor the resulting interference pattern. As displayed
in Fig. 14.14, light from a coherent light source is split
into two optical paths via a 3 dB coupler. A second
3 dB coupler is used to recombine the optical paths and
create the interference signal. The interference signal
passes through both outputs of the second 3 dB coupler to the photodetectors. The use of both outputs is
beneficial to some interrogation techniques. The path
length difference for the Mach–Zehnder interferometer is dependent on the strain applied to the sensing
path.
The history of the Michelson interferometer was discussed in the basic optics chapter of this handbook
(Chap. 18). Like the Mach–Zehnder interferometer, the
Michelson interferometer is constructed in a similar
fashion to its classical namesake. The Michelson interferometer, illustrated in Fig. 14.15, uses a 3 dB coupler
to divide the optical source into two optical paths. Each
optical path has a mirror that reflects the optical signal
back to the 3 dB coupler where the two paths interfere. The intensity of the interference signal is then
monitored via the photodetector. The reference path is
usually isolated from strain, so changes to the sensing
path due to the applied load create an optical phase
change with respect to the reference path.
14.3.6 Fabry–Pérot
The basis of a Fabry–Pérot interferometer is the interference of a light wave reflected from a cavity. French
physicists Fabry and Pérot analyzed this type of optical
structure in the 19th century. As displayed in Fig. 14.16,
the basic fiber optic Fabry–Pérot sensor functions from
the interference of a reflection from a first surface, fiber
to air, and a second surface, air to fiber. The air–glass
interface leads to a reflection of approximately 4% of
the input intensity. With such a low reflectivity percentage, the Fabry–Pérot interferometer can be assumed
to be a two-beam interferometer. If higher-reflectivity
coatings are applied, then a multipass interferometer
is created. The particular Fabry–Pérot sensor displayed
in Fig. 14.16 is an extrinsic Fabry–Pérot interferometer
Sensing path
Reference path
Fig. 14.15 Basic Michelson fiber optic sensor
Part B 14.3
an optical source is a measure of the length of the optical wave packets. Each wave packet can be thought
to have a different starting optical phase; thus, light
from two different wave packets have different starting phases and will not produce an interference pattern.
For very narrow-band sources such as lasers, the coherence length is very long. For broadband optical sources
such as light bulbs, the coherence length is very short.
In order for an interferometer to function and produce
an interference signal, the coherence length of the optical source must be greater than the resulting PLD of
the interferometer. A general rule of thumb for determining the coherence length (L c ) of an optical source
is to divide the square of the center wavelength (λ0 ) by
the bandwidth of the source (Δλ), as given by (14.23).
A depiction of the optical source spectrum is shown
in Fig. 14.13.
358
Part B
Contact Methods
signal is generated when the output of the PM fiber is
launched back into standard single-mode fiber.
It should be noted that PM fiber and PM optical
components are also used to make Michelson, Mach–
Zehnder, and Fabry–Pérot interferometers with the light
being restricted to a single polarization axis. This type
of construction alleviates issues due to polarization
fading that are common among the optical fiber interferometers.
Fig. 14.16 Schematic of a fiber optic Fabry–Pérot sensor
14.3.8 Interrogation of Interferometers
Part B 14.3
(EFPI). The sensor is extrinsic because the sensing region is the air cavity formed by the two optical fiber end
faces. There are intrinsic Fabry–Pérot sensors where the
sensing cavity is formed between partial mirrors fused
within an optical fiber. These sensors are much more
difficult to fabricate and have not experienced the same
commercial availability as the EFPI sensors.
The low-finesse interferometer allows for a twobeam interferometer to be assumed for mathematical
analysis. With the sensing region taking place in an air
cavity for the EFPI, the influence of the strain–optic effect can be neglected and the refractive index is assumed
to be equal to 1. Thus, the optical phase change with
respect to applied strain can be written as
Δφ = βΔL =
4π L FP
ε.
λ
(14.24)
For the case of intrinsic Fabry–Pérot sensors, the strain–
optic effect will be included in the phase change
formulation.
14.3.7 Polarization
As discussed in Sect. 14.1.2, there exist specialty optical fibers that are designed to preserve the polarization
of light as it is guided along the optical fiber. These
polarization-maintaining (PM) fibers induce a birefringence state in the optical fiber where the refractive
index along the two principal axes of polarization are
different. Thus, light traveling in the optical fiber will
travel faster along the lower index axis (fast axis) than
the higher-index axis (slow axis). In the simplest form,
the polarization interferometer functions by taking light
from a standard single-mode optical fiber and launches
it into a length of PM fiber such that light travels down
both the fast and slow axes. These two paths represent
the two paths for the interferometer. Any applied load
to the PM fiber will induce an optical phase change
between the two paths due to the difference in the refractive index between the two axes. The interference
Phase Detection
There exist a number of means for interrogating interferometric fiber optic strain sensors. Each of these
techniques is focused on extracting the optical phase
change from the cosine function given in (14.10). Some
techniques use an active modulation scheme where the
reference path is perturbed by a sinusoidal or ramp function. Other forms of modulation include varying the
optical source wavelength (optical frequency modulation). These active modulation techniques have different
attributes in terms of frequency response and strain
range. The selection of the phase detection technique is
dependent on the selected interferometric sensor and the
sensing application requirements. Passive interrogation
techniques for interferometric sensors are concerned
with optically deriving a sin(Δφ) and cos(Δφ) function
from the sensing system. Then, an arctangent operation
can be used to obtain the phase change.
Another form of phase detection is based on
low-coherence interferometry, also called white-light
interferometry. These techniques use a broadband optical source with a coherence length shorter than the
optical path difference (OPD) of the interferometer.
In order to achieve an interference signal, the optical output of the sensing interferometer is passed
through a reference interferometer, also called a readout interferometer. The resulting OPD between the two
Intensity
Strain
Time
Fig. 14.17 Phase ambiguity with respect to change in strain
(dashed line)
Optical Fiber Strain Gages
interferometers is less than the coherence length of the
optical source leading to an interference signal. The reference interferometer can then be tuned to the sensing
interferometer as a means of interrogation. This method
is advantageous because it allows the use of lower cost
and longer-life broadband optical sources such as lightemitting diodes (LEDs).
Phase Ambiguity
One of the main difficulties with interferometric detection is the issue of phase ambiguity. As an increasing
strain field is applied to the sensor, the intensity signal is a cosine function given by (14.10). With this
14.4 Scattering
type of response, differentiating between an increasing
strain and a decreasing strain is difficult. As shown in
Fig. 14.17, the intensity response looks the same for increasing and decreasing strain. The crossover point can
be identified by the change in the intensity pattern. If
this change occurs at a maximum or minimum of the
intensity function the crossover becomes difficult to detect. Some interrogation techniques limit the intensity
response (and thus the phase change) to a single linear
portion of the cosine function. Other interrogation techniques must account for multiple fringes in the response
function. This is similar to fringe counting as discussed
in Chap. 25.
where Va is velocity of sound in the optical fiber and
λ is the free-space operating wavelength. The Brillouin
frequency shift is dependent on the density of the optical
fiber, which is dependent on strain and temperature.
14.4.2 Strain Sensing
Using Brillouin Scattering
Measuring strain with Brillouin scattering requires the
generation of a narrow-line-width short-duration pulse.
As the pulse travels down the optical fiber, scattering
occurs at the Brillouin frequency. The location along
the optical fiber is determined by gating the optical
pulse and measuring the time of flight of the returned
scattered signal. The standard spatial resolution for
these sensor systems is approximately 1 m. This level
Intensity
E = hν =
hc
λ
3 – 5 orders
of magnitude
Anti-Stokes
14.4.1 Brillouin Scattering
Brillouin scattering is a result of the interaction between
light propagating in the optical fiber and spontaneous
sound waves within the optical fiber. Because the sound
wave is moving, the scattered light is Doppler-shifted to
a different frequency. The Brillouin frequency shift (ν B )
is determined by:
Temperature
dependent
Pump wavelength
Rayleigh
scattering
Brillouin
scattering
Fluorescence
Stokes
Raman
scattering
Wavelength
Fig. 14.18 Picture of various scattering effects with respect to the
νB = 2nVa /λ ,
(14.25)
pump wavelength
Part B 14.4
14.4 Scattering
As light travels through optical fiber, scattering mechanisms displayed in Fig. 14.18 come into play that can
be exploited for sensing purposes. In order to achieve
measurable scattering effects, a relatively high-powered
optical source is required. Rayleigh scattering results
from elastic collision between the phonons and the optical fiber material. The scattered wavelength (which will
be guided back towards the optical source) is equivalent to the pump or excitation wavelength. Rayleigh
scattering is extensively used with pulsed laser sources
and time-gated detectors to monitor long lengths of
optical fiber for attenuation sources such as connections, optical splices, tight bend locations, and breaks
in the optical fiber. Raman scattering involves the inelastic scattering effect of the optical energy interacting
with molecular bonds. Raman scattering is used extensively for distributed temperature monitoring. The
Raman scattering effect is immune to strain effects,
making it ideal for these applications. Brillouin scattering results from reflections from a spontaneous sound
wave propagating in the fiber [14.10]. The Brillouin
scattering effect is sensitive to both strain and temperature variations.
359
360
Part B
Contact Methods
a) Brillouin gain
1.016
1.012
Data acquisition
1.008
1.004
1
0.996
–100 0
Part B 14.4
100 200 300 400 500 600 700
Position along the fibre (m)
b) Gain
1.02
1.01
1
12.7
c) Brillouin frequency shift (GHz)
12.83
12.82
12.81
12.8
12.79
12.78
12.77
12.76
12.75
12.74
–100 0
12.75
12.8
12.85
700
600
500 Distance (m)
400
300
200
100
12.9 0
Frequency (GHz)
Data analysis
100 200 300 400 500 600 700
Position along the fibre (m)
Fig. 14.19 Illustration of a typical measurement from a Brillouin scattering system [14.11] (Courtesy of OmniSensTM )
of spatial resolution is adequate for applications on
long structures such as pipeline monitoring. In order
to construct the Brillouin frequency response along the
optical fiber, the optical pulse is scanned through the
frequency range of interest. In this manner, each pulse
provides a measurement of the scattered intensity along
the optical fiber at a particular frequency, as depicted
in Fig. 14.19. A three-dimensional plot is generated
with respect to optical frequency and position along the
optical fiber, with each pulse producing an intensity response at a single frequency. The Brillouin frequency
shift is then computed from this plot by taking the max-
imum gain intensity at each position along the optical
fiber.
Since Brillouin scattering is sensitive to both strain
and temperature, a means for performing temperature
compensation is required. In most cases, a secondary
optical fiber is deployed in a loose tube fashion such
that no strain is coupled and temperature can be monitored along this fiber and compensated for in the strain
measurement, as discussed in Sect. 14.2.5. In these
cases, an alternative optical method such as Raman
scattering may also be used to monitor the temperature.
Optical Fiber Strain Gages
14.5 Fiber Bragg Grating Sensors
361
14.5 Fiber Bragg Grating Sensors
Because of these difficulties, sensing applications with
fiber gratings were not realized until a novel manufacturing technique was developed in 1989 [14.15].
In the case of Bragg grating formation, the change
of the refractive index of an optical fiber is induced by
exposure to intense UV radiation (typical UV wavelengths are in a range from 150 to 248 nm). To create
a periodic change in the refractive index, an interference pattern of UV radiation is produced such that it is
focused onto the core region of the optical fiber. The refractive index of the optical fiber core changes where
the intensity is brightest in the interference pattern to
produce a periodic refractive index profile [14.12]. The
manner in which the refractive index change is induced has been linked to multiple mechanisms over
the past 15 years of research. The various mechanisms
are dependent on the intensity of the UV source, the
exposure time, and any pretreatment of the optical
fiber. The resulting FBG from each mechanism displays
slightly different properties related to the optical spectrum response, sensitivity to strain and temperature, and
performance at elevated temperatures. The most common type of FBG sensor (type I) is a result of short
exposure times to relatively low-intensity UV radiation
to standard telecommunications optical fiber. There exist other FBG sensor types (type IIa, type II, chemical
composition) that have been researched for sensing applications. The discussion in this section will be limited
to the standard type I FBG sensor.
The length of a single period for the grating
structure is called the grating pitch, Λ, as shown
in Fig. 14.20. The pitch of the grating is controlled durCladding
14.5.1 Fabrication Techniques
Fiber Bragg grating sensors are unique compared to
the strain sensors discussed thus far in this chapter.
The sensors up to this point have been fabricated from
a combination of standard optical fibers or making use
of inherent properties of optical fibers. The FBG sensor
is fabricated by altering the refractive index structure of
the core of an optical fiber. The refractive index change
is made possible in standard communications-grade
optical fiber due to a phenomena known as photosensitivity discovered in 1978 by Hill [14.13]. Hill-type
gratings are limited in practicality because they reflect
the UV wavelength that was used to induce the refractive index change and are difficult to manufacture.
Λ
Core
n
neff
ncore
z
Fig. 14.20 Schematic of an FBG sensor
Part B 14.5
Fiber Bragg gratings (FBGs) have become an integral part of the telecommunications hardware, used
in applications such as add/drop filters, fiber lasers,
and data multiplexing [14.12]. Since the discovery of
the photosensitive effect in optical fiber [14.13] by
which ultraviolet (UV) light is used to induce a permanent change in the refractive index of optical fiber,
researchers have been discovering new applications
for this unique optical phenomena. Because of the
widespread use and development of this technology,
several textbooks dedicated to FBGs and their applications have been published [14.2, 12, 14]. In recent
years, the FBG sensor has become a popular choice
for fiber optic sensor applications for many reasons.
As will be seen in this section, the optical response
of the FBG sensor is wavelength-encoded, allowing
many FBG sensors to be serially multiplexed via wavelength division multiplexing techniques. FBG sensors
may also be time division multiplexed, allowing approximately 100 FBG sensors to be monitored along
a single fiber strand. There exist other multiplexing
techniques for FBG sensors that allow thousands of
FBG sensors to be serially multiplexed and monitored
with a single instrumentation system. Many commercially available interrogation systems have also come
to market, making these types of sensors and systems
readily available and relatively less complex for the enduser. Unfortunately, many of these systems use different
technologies for interrogation of the FBG sensors, leading to different sensor specifications as well as different
requirements for the fabrication of the FBG sensor. An
overview of the different interrogation technologies is
presented in Sect. 14.5.5.
362
Part B
Contact Methods
Lloyd mirror
Focused UV
Focused UV
Optical fiber
Phase mask
Optical fiber
–1
Interference
pattern
+1
Interference pattern
Reflective surface
Fig. 14.21 Phase mask fabrication technique
Part B 14.5
ing the manufacturing process, and is typically on the
order of ≈ 0.5 μm, while the amplitude of the index
variation is only on the order of 0.01–0.1% of the original refractive index [14.12].
Many methods are used to create the periodic interference pattern (e.g., phase masks [14.16],
Mach–Zehnder interferometers [14.15], and Lloyd mirrors [14.14]). Phase masks are corrugated silica optical
components, as shown in Fig. 14.21. As laser radiation
passes through the phase mask, the light is divided into
different diffraction beams. The diffracted beams in the
example are the +1 and −1 beams, which create an interference pattern that is focused on the optical fiber
core. Other orders of diffraction are designed to be minimized in these passive optical devices. The interference
pattern induces a periodic refractive index change along
the exposed length of the optical fiber, thus creating the
Bragg grating. Phase masks provide a stable, repeatable interference pattern and are used for high-volume
production of FBG sensors at a common wavelength.
The Mach–Zehnder interferometer technique uses
a bulk optic Mach–Zehnder interferometer to create
an interference pattern on the optical fiber. The optical arrangement for a basic Mach–Zehnder technique
is shown in Fig. 14.22. Light from the laser emission is
passed through focusing optics and is split via an optical beam splitter. The two divergent laser beams are
Focused UV
Mirror
Interference
pattern
Beam splitter
Mirror
Optical fiber
Fig. 14.22 Mach–Zehnder interferometer technique
Fig. 14.23 Lloyd mirror technique
redirected via mirrors to combine at the optical fiber
location, resulting in an interference pattern from the
combination of these two optical paths. The focusing
optics are designed to focus the laser energy at the
optical fiber location. This technique allows for the fabrication of FBG sensors with different pitches through
adjustment of the angle of incidence of the interference
beams.
The Lloyd mirror technique uses a Lloyd mirror to
create an interference pattern on the optical fiber, as
shown in Fig. 14.23. Light from the laser emission is
passed through focusing optics and transmitted to the
Lloyd mirror arrangement. The Lloyd mirror causes the
input laser beam to split into two beams. These beams
are recombined and focused at the optical fiber location, which creates an interference pattern and forms the
FBG sensor.
14.5.2 Fiber Bragg Grating Optical Response
Light traveling in an optical fiber can be classified by
an optical modal parameter β, as discussed in Sect. 14.3
and given by [14.7]
2πn core
(14.26)
,
λ
where n core is the refractive index of the core of the
optical fiber and kw is the wavenumber associated
with the wavelength of light propagating in the optical
fiber. The function of the Bragg grating is to transfer
a forward-propagating mode (β1 ) into a backwardpropagating mode (−β1 ) (i. e., reflect the light) for
a particular wavelength meeting the phase-matching criterion. The phase-matching condition is derived from
coupled-mode theory and is given by
β = nkw =
βi − β j =
2πm
,
Λ
(14.27)
Optical Fiber Strain Gages
14.5 Fiber Bragg Grating Sensors
363
Fig. 14.24 Schematic of an FBG sensor with reflected and transmitted
spectra
Reflected
spectrum
Incoming
spectrum
Transmitted
spectrum
Λ
λB = 2n eff Λ ,
(14.29)
(ΔT ), so that the Bragg wavelength shifts to higher
or lower wavelengths in response to applied thermalmechanical fields. For most applications, the shift in the
Bragg wavelength is considered a linear function of the
thermal-mechanical load. The treatment of FBG sensors
here will ignore the thermal effects, because the thermal effects can be modeled as an independent response
of the Bragg grating. The shift in the Bragg wavelength
due to an incremental change of length (ΔL) is given
by [14.9]:
∂Λ
∂n eff
(14.30)
+ n eff
ΔL .
ΔλB = 2 Λ
∂L
∂L
Assuming that the strain field is uniform across the
Bragg grating length (L), the term ∂Λ/∂L can be replaced with Λ/L. Likewise, the term ∂n eff /∂L can
be replaced by Δn eff /ΔL in (14.30). The terms Λ
and L are physical quantities that are determined by
the interference pattern formed during fabrication and
are known. The change in the effective refractive index (Δn eff ) can be related to the optical indicatrix,
Δ[1/n 2eff ], as discussed in Sect. 14.3 [14.9].
Δn eff = −
n 3eff
1
.
Δ 2
2
n eff
(14.31)
where the subscript ‘B’ defines the wavelength as the
Bragg wavelength. Equation (14.29) states that, for
a given pitch (Λ) and average refractive index (n eff ), the
wavelength λB will be reflected from the Bragg grating,
as illustrated in Fig. 14.24.
In the case of small strains, the optical indicatrix is
related to the strain on the optical fiber as:
1
Δ 2
= pij ε j ,
(14.32)
n eff i
14.5.3 Strain Sensing Using FBG Sensors
where pij is the strain–optic tensor of the optical fiber
and ε j is the contracted strain tensor. The directions associated with the indices in (14.32) are illustrated in
Fig. 14.25. In the general case, the strain–optic tensor
will have nine distinct elements, termed photoelastic
constants. Fortunately, for a homogenous, isotropic material (such as optical fiber), the strain–optic tensor can
be represented by two photoelastic constants p11 and
Bragg gratings operate as wavelength selective filters
reflecting the Bragg wavelength λB which is related to
the grating pitch Λ and the mean refractive index of
the core, n eff , given by (14.29). Both the effective refractive index (n eff ) of the core and the grating pitch
(Λ) vary with changes in strain (ε) and temperature
Part B 14.5
where m is an integer value representing the harmonic
order of the grating [14.12]. From (14.27), multiple
propagation modes can be used to satisfy the phasematching condition. Therefore, a single FBG sensor will
reflect multiple wavelengths with respect to the order of
the integer m. Most optical sources do not have a large
enough bandwidth to excite multiple wavelength reflections from a single FBG sensor. Some research has
been performed using multiple optical sources to excite
more than the first-order Bragg condition as a means of
providing a temperature and strain measurement with
a single FBG sensor [14.17]. For all practical applications to date, only the first-order Bragg condition of
m = 1 is employed for standard uniform Bragg gratings.
For this case, the backward-propagating mode (−β1 ) is
substituted into (14.27) for β j , and the following equation is derived
π
2πn eff
(14.28)
β1 = =
.
Λ
λ
The index of refraction is now noted as an effective
(or average) refractive index, n eff , for the Bragg grating, due to the periodic change across the length of
the optical fiber. Solving (14.28) for the wavelength (λ)
provides the Bragg wavelength equation
364
Part B
Contact Methods
2
1
3
Fig. 14.25 Indicial directions for an FBG optical fiber
Part B 14.5
p12 as [14.9]:
⎞
⎛
p11 p12 p12
⎟
⎜
pij = ⎝ p12 p11 p12 ⎠ .
p12 p12 p11
Transverse loads may also be modeled using this analysis by choosing the proper contracted strain tensor
formulation. For example, the measurement of a uniform pressure field on the optical fiber can be modeled
with the following contracted strain tensor
⎛ ⎞
εz
⎜ ⎟
(14.39)
ε j = ⎝εr ⎠ .
εr
Using (14.39) in the above formulation leads to the following response function for the FBG sensor response:
(14.33)
For the case of a surface mounted FBG sensor, it has
been shown that the contracted strain tensor may be
written as [14.2, 9]:
⎛ ⎞
1
⎜ ⎟
(14.34)
ε j = ⎝−ν ⎠ εz ,
−ν
where ν is Poisson’s ratio for the optical fiber. Due to
the symmetry of the optical fiber, the optical indicatrix
is equivalent for i = 2 or 3. Incorporating the strain tensor into (14.32) leads to the following expression for
a surface-mounted optical fiber sensor:
1
(14.35)
Δ 2 = εz [ p12 − ν( p11 + p12 )] .
n eff
n2
ΔλB
= εz − eff [εz p12 + εr ( p11 + p12 )] .
λB
2
(14.40)
For other strain states, such as diametric loading, the
analysis of the FBG response becomes more complicated. This is due to the induced polarization effects and
nonuniform loading on the optical fiber. In extreme diametric loading cases, the FBG sensor response will split
due to the reflection from the different polarization axis
and nonuniform strain on the grating structure [14.18].
Research is continuing in this field for the development
of transversely sensitive FBG sensors with emphasis on
using FBG sensors written into PM optical fiber to take
advantage of the pre-existing polarization properties.
14.5.4 Serial Multiplexing
One of the main advantages of FBG sensors is the ability to measure multiple physical parameters. This ability
combined with serial multiplexing of FBG sensors alAfter substituting (14.31) and (14.35) into (14.30), the lows for multiple parameters to be monitored not only
result is
by a single instrument, but also with all the data transmitted on a single piece of optical fiber [14.19]. This is
n3
ΔλB = −2Λ eff εz [ p12 − ν( p11 + p12 )] + 2n eff Λεz . advantageous in applications where minimal intrusion
2
into an environment is required. Many applications of
(14.36)
FBG sensors concern measuring strain and/or temperNormalizing (14.36) by the Bragg wavelength demon- ature. In these applications, many sensors (from fewer
strates the dependence on the wavelength shift of the than ten to over a hundred) are multiplexed to provide
FBG sensor on the refractive index, strain–optic coeffi- measurements across the structure. Examples of these
applications are monitoring civil infrastructure [14.20],
cients, and Poisson’s ratio for the optical fiber.
naval/marine vessels [14.21, 22], and shape measure
n 2eff
ΔλB ment of flexible structures [14.23].
= 1−
[ p12 − ν( p11 + p12 )] εz . (14.37)
The ability to serially multiplex FBG sensors is arλB
2
guably the most prominent advantage of this sensor
The terms multiplying the strain in (14.37) are constant type. With over a decade of development, researchers
over the strain range of the Bragg grating, and (14.37) have devised three main techniques for serial multiis often written in simplified form as
plexing FBG sensors: wavelength-domain multiplexing
(WDM), time division multiplexing (TDM), and optical
ΔλB
= Pe εz .
(14.38)
frequency-domain reflectometry (OFDR).
λB
Optical Fiber Strain Gages
Wavelength response
of FBG #2
Λ1
Λ2
Λ3
Thermomechanical
load
Reflected spectrum
Fig. 14.26 Serial multiplexing of FBG sensors
from which sensor. The default is to place the lowerwavelength signal with the previous lower-wavelength
sensor signal. If the lower-wavelength signal completely overwhelms the higher-wavelength signal, as is
depicted in Fig. 14.27, then the instrumentation records
the wrong wavelength data for each of these sensors
after the overlap event.
Knowledge of the potential measurement range for
each sensor is required to prevent sensor overlap issues. When this is not provided, conservative estimates
should be used to select sensor wavelength separations.
In cases where the FBG sensors are expected to experience similar responses, such as thermal measurements,
the wavelength spacing of the sensors may be more
tightly spaced.
Time Division Multiplexing
TDM uses a time-of-flight measurement to discriminate
the FBG sensors on a fiber. The basic TDM architecture
is shown in Fig. 14.28. A light source generates a short
pulse of light that propagates down the optical fiber
to a series of FBG sensors. All the FBG sensors initially have the same wavelength and reflect only a small
portion of the light at the Bragg wavelength. The light
source has a somewhat wide spectrum that is centered
about the unstrained Bragg wavelength of the FBG sensors. Each FBG sensor generates a return pulse when
it reflects the light at its particular Bragg wavelength,
which is dependent upon the strain/temperature state of
the FBG. For the example shown in Fig. 14.28, there are
five return pulses generated by the FBG sensors. These
pulses propagate back along the fiber and are coupled
to a high-speed photodetector, which measures when
each pulse was detected. The FBG sensors must be separated by a minimum distance along the fiber to allow
accurate measurement of the difference in arrival time
of the reflected pulses, often by 1 m or more. An additional wavelength measurement system is needed to
measure the Bragg wavelength of each sensor as it is
detected. TDM systems have become more popular in
ε, T
λB1
λB2
λB1 λB2
λ
λ
ε, T
FBG #1
FBG #2
λB2 λB1 λ
Fig. 14.27 Wavelength shift description and sensor overlap for WDM
systems
365
Part B 14.5
Wavelength Division Multiplexing
As shown in Fig. 14.26, WDM is accomplished by producing an optical fiber with a sequence of spatially
separated gratings, each with different grating pitches,
Λi = 1, 2, 3, . . .. The output of the multiplexed sensors
is processed through wavelength selective instrumentation, and the reflected spectrum contains a series of
peaks, each peak associated with a different Bragg
wavelength given by λi = 2nΛi . As indicated in the
figure, the measurement field at grating 2 is uniquely
encoded as a perturbation of the Bragg wavelength λ2 .
Note that this multiplexing scheme is completely based
on the optical wavelength of the Bragg grating sensors. The upper limit to the number of gratings that can
be addressed in this manner is a function of the optical source profile width and the expected strain range.
WDM was the first form of multiplexing explored for
the FBG sensor and is common in commercially available systems.
A major concern for WDM FBG systems is sensor
wavelength overlap. This occurs when two neighboring sensors in wavelength space experience loads that
cause the reflected Bragg wavelengths from each sensor to approach each other and overlap. During the
overlap event, the monitoring instrumentation cannot
process both sensors independently and will record
only a single senor. After the overlap event when both
sensors can be resolved, the instrumentation cannot distinguish which of the reflected Bragg wavelengths is
14.5 Fiber Bragg Grating Sensors
366
Part B
Contact Methods
I (t)
Light source
FBG sensors
t
S-1 S-2 S-3 S-4 S-5
3 dB coupler
I (t)
t1
Detector 1
t2
t3
t4
t5
t
Time delayed signals
from each of the sensors
Light dump
Fig. 14.28 Time division multiplexing technique
Part B 14.5
recent years due to advances in optical sources, data
acquisition, and computing technology.
determine the Bragg wavelength of that particular sensor [14.24].
Optical Frequency-Domain Reflectometry
OFDR is a more complex interrogation technique then
the other systems discussed. The basic concept of an
OFDR system is to create a response function from the
serially multiplexed FBG sensors that spatially isolates
the individual FBG sensor response in the frequency
domain of the system response [14.24]. A schematic
of a typical OFDR optical system layout is shown
in Fig. 14.29. Light from a tunable laser source is coupled into an optical arrangement containing the FBG
sensors and a reference interferometer. The reference
interferometer is used to trigger the sampling on detector 1, thus ensuring that the response from the FBG
sensors is sampled at a constant wavenumber interval. The FBG sensors are low reflectivity, typically at
a common wavelength, and can be very closely spaced
(on the order of 1 cm). Each sampled set of FBG data
from detector 1 is initially processed via a Fourier
transform. The frequency spectrum obtained from the
Fourier transform displays a collection of peaks at the
physical distance of each FBG along the sensing array.
Each peak is then bandpass filtered in the frequency
spectrum and an inverse Fourier transform is used to
14.5.5 Interrogation of FBG Sensors,
Wavelength Detection
As the popularity of using FBG sensors has grown in recent years, so has the number of techniques to perform
interrogation. Of course, the method of interrogation
used depends on the type of multiplexing, the sampling
rate requirements, and the measurement resolution requirements. The existing technologies for interrogating
FBG sensors include scanning lasers, tunable filters, linear optical filters, and spectroscopic techniques. The
end-user must ensure the instrumentation system chosen meets the requirements for the application.
In terms of sampling rate, the response of FBG
sensors is very fast; unfortunately, all instrumentation
systems are limited by the speed of the electronics,
data acquisition, and data processing. This is especially true for serially multiplexed systems. In most
cases, the sampling rate for individual sensors is not
selectable. The instrumentation records data at one sampling rate for all sensors interrogated by the system. The
end-user may design additional data-acquisition software to store the data into separate files with different
Detector 1
Coupler
Tunable laser
source
FBG sensors
Coupler
R
Li
Coupler
R
R
Detector 2
Lref
Reference
interferometer
Fig. 14.29 Schematic of typical
OFDR interrogation design
Optical Fiber Strain Gages
14.5.6 Other Grating Structures
Although not commonly employed for the measurement
of strain, there do exist other fiber grating structures that
are founded upon the variation of refractive index in the
core of the optical fiber. Two structures in particular are
the chirped grating and the long-period grating.
The chirped grating is an FBG with a linear
variation of the periodicity (Λ(z)). Without a uniform periodicity, the reflected spectrum of the grating
structure becomes spread out. This device is commonly used as a linear wavelength filter. Although
the chirped grating has similar sensitivities to strain
as the FBG sensor, it is almost never used as such
because of the difficulty in obtaining a wavelength
peak detection value, as well as increased fabrication
costs.
A long-period grating (LPG) is similar to the Bragg
grating such that the periodicity is uniform, but the periodicity is much larger, on the order of Λ = 1 mm.
Examination of the phase-matching condition (14.27)
for the Bragg grating permits interaction between allowable optical modes (β y i). For the case of an LPG,
the forward-propagating optical mode in the core is
transferred to cladding modes, which are attenuated
from the optical fiber, leading to wavelength-dependent
attenuation in the transmitted signal. Once the light
gets beyond the LPG structure, the various modes are
coupled back to the core region and the wavelength attenuated signal is transmitted through the optical fiber.
The attenuation mechanisms for the cladding modes
are highly dependent on the boundary condition of the
cladding. Therefore, LPG sensors have been examined
for potential use as chemical sensors with the presence
of a chemical species inducing wavelength attenuation
shifts [14.25].
14.6 Applications of Fiber Optic Sensors
Although fiber optic strain sensors are not widely used
in any industry, they have been tested in many applications. Often, these applications have attributes that
make traditional sensing technologies ineffectual or difficult to implement. With advantages of long lead lines,
embedding, and multiplexing, fiber optic sensors have
proven their ability to perform measurements were traditional sensors cannot. The following sections provide
a brief overview of some of the applications. References [14.2, 3, 14] provide additional applications. With
new applications of fiber optic sensors occurring regularly, a quick internet search will provide information
on the latest and greatest applications.
14.6.1 Marine Applications
In a marine environment, fiber optic sensors have
the advantage of not requiring extensive waterproof-
ing for short-duration tests. Also, many sensors can be
multiplexed to achieve a high sensor count for large
structures such as ships and submarines. FBG sensors
have been used to monitor wave impacts and loads
on surface ships [14.21, 22] and for American Bureau
of Shipping (ABS) certification of a manned submarine [14.26].
14.6.2 Oil and Gas Applications
Fiber optic sensing in the oil and gas industry has made
great strides in recent years. Of particular use are distributed temperature sensing (DTS) systems based on
Raman scattering [14.27, 28]. For structural monitoring, the area that has witnessed use of fiber optic strain
sensors is in riser monitoring. Risers are long structural components used on offshore platforms for many
applications including drilling, water injection, and col-
367
Part B 14.6
sampling rates. Alternatively, postprocessing the oversampled data through averaging or filtering techniques
may provide improved results.
Some WDM multiplexed instrumentation systems
require the FBG sensors to have certain nominal
wavelengths to fit within the instrument’s wavelength
filtering windows. This limits the flexibility of the
wavelength spacing discussed previously and limits the
number of FBG sensors that can be serially multiplexed
with these instrumentation systems. Other WDM instrumentation systems allow for the wavelength spacing of
neighboring FBG sensors to be less than 1 nm, allowing
for over 100 FBG sensors to be serially multiplexed, but
issues of sensor wavelength overlap must be taken into
consideration. For TDM and OFDR systems, the special
design of the FBG sensors in terms of low reflectivity
and physical spacing requirements limits the availability
of commercial vendors to provide these sensing arrays.
The end-user can typically only purchase FBG sensors
that function with the systems from the system vendors
themselves.
14.6 Applications of Fiber Optic Sensors
368
Part B
Contact Methods
lection of the oil. Tidal currents are known to induce
vibrations in these structures, and fiber optics sensors
have recently been used to gain an understanding of
the structural effects the vibrations have on the risers [14.29, 30].
14.6.3 Wind Power Applications
Part B 14.7
With the upswing in oil prices, more effort is being
expended on research and development of alternative
energy sources, including renewable energy sources
such as wind power.
Wind power turbines are large structures that make
use of composite blades. Wind turbine manufacturers
are examining ways in which to improve the efficiency
of these devices and are turning to fiber optic sensing to
provide load monitoring and control data [14.31]. Other
wind turbine applications using fiber optic sensors include health monitoring of the wind turbine [14.31] and
shape measurement of the wind turbine blade [14.32].
Attributes that make fiber optic sensors attractive
for these applications include multiplexing, immunity
to radiofrequency (RF) noise, and immunity to damage
caused by the electrical charge from lightning strikes.
Fiber optic sensors also have the ability to be embedded
into these composite structures.
14.6.4 Civil Structural Monitoring
The application area that has received the most interest in fiber optic strain sensing has been civil structure
monitoring. Using the attributes of long lead fibers and
sensor multiplexing, monitoring the loads and structural health of these large structures has been an ideal
application for fiber optic sensors.
FBG sensors have been used to monitor bridge
structural components including bridge decks [14.2],
composite piles [14.20], and stay-cables [14.2]. In each
of these cases, the FBG sensor has been embedded into
the structural component. As the growth of FBG sensor
applications continues, many more examples of FBG
sensors being employed in civil structural monitoring
will be realized.
Michelson-interferometer-based systems have also
been used for civil structural monitoring purposes
including bridges [14.33], dams [14.34], and buildings [14.35]. The Michelson interferometer has a long
sensor gage length, which is beneficial when measuring the deformation of these large structures. The
reference arm of the Michelson can also be packaged
alongside the sensing arm, allowing for straightforward temperature compensation of the measured
signal.
Brillouin scattering sensor systems are also finding
applications in civil structures, including pipeline monitoring and dam monitoring [14.36]. Again, the ease
of embedding these sensors directly into the structure
is leveraged for these applications. Furthermore, the
distributed sensing nature of Brillouin-based sensors allows for a strain measurement at approximately every
meter along the optical fiber, making Brillouin scattering appealing for these applications.
14.7 Summary
Optical fiber sensing is a growing field, full of potential. In general, fiber optic sensing is a viable technology
for strain monitoring applications in many industries.
Advancement of this technology is dependent on leveraging its many advantages over traditional sensors.
Arguably the key aspect of fiber optic sensors is the
ability to multiplex many sensors or obtain distributed
measurements using a single strand of optical fiber. This
allows for a vast number of sensing points with reduced
cabling weight and minimal intrusion into the application environment. The ability to embed optical fiber into
composite structures is also a primary driver for fiber
optic sensing in the composite structures field.
As discussed in this chapter, there are many different types of fiber optic strain sensors. Some of
these sensor types have their roots in classical optics,
while others take advantage of the special properties of optical fiber. There exist single-point sensors
(EFPI, FBG), cumulative strain sensors (MZ, Michelson), and distributed strain sensors (Brillouin). The
selection of a strain measurement technique is highly
dependent on the application requirements. Just as there
are multiple types of fiber optic strain sensors, there
are often multiple interrogation techniques for each of
the sensor types. This leads to a very complex design space for the novice engineer tasked with selecting
the appropriate sensing system. Careful consideration
of measurement resolution, sampling rate, and number
of sensors will assist in making an informed decision.
Optical Fiber Strain Gages
References
369
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14.1
14.2
14.3
14.4
14.5
14.7
14.8
14.9
14.10
14.11
14.12
14.13
14.14
14.15
14.16
14.17
14.18
14.19
14.20
14.21
14.22
14.23
14.24
14.25
14.26
14.27
14.28
14.29
14.30
14.31
14.32
14.33
14.34
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