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Optical fiber based microwave-photonic interferometric sensors

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OPTICAL FIBER BASED MICROWAVE-PHOTONIC INTERFEROMETRIC
SENSORS
A Dissertation
Presented to
the Graduate School of
Clemson University
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
Electrical Engineering
by
Jie Huang
August 2015
Accepted by:
Hai Xiao, Committee Chair
John Ballato
Liang Dong
Lin Zhu
ProQuest Number: 3722386
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ABSTRACT
Optical fiber interferometers (OFIs) have been extensively used for precise
measurements of various physical/chemical quantities (e.g., temperature, strain, pressure,
rotation, refractive index, etc.). However, the random change of polarization states along
the optical fibers and the strong dependence on the materials/geometries of the optical
waveguides are problematic for acquiring high quality interference signal. Meanwhile,
the difficulty in multiplexing has always been a bottleneck on the application scopes of
OFIs. Interrogated in optical domain, FOIs are commonly implemented using singlemode fibers with tightly-controlled state of polarization (SOP) to obtain high quality
interference signals.
Here, we present a new sensing concept of optical carrier based microwave
interferometry (OCMI) by reading optical interferometric sensors in microwave domain.
It combines the advantages from both optics and microwave. The low oscillation
frequency of the microwave can hardly distinguish the optical differences from both
modal and polarization dispersion making it insensitive to the optical polarization and
waveguides/materials. The phase information of the microwave can be unambiguitly
resolved so that it has potential in fully distributed sensing. The OCMI concept has been
implemented in different types of interferometers (e.g., Michelson, Mach-Zehnder,
Fabry-Perot) among different optical waveguides (e.g., singlemode, multimode, and
sapphire fibers) with excellent signal-to-noise ratio (SNR) and low polarization
dependence. A spatially continuous distributed strain sensing has also been demonstrated.
ii
ACKNOWLEDGMENTS
Upon finishing this dissertation, first and foremost, I would like to present my
sincere gratitude to my advisor Dr. Hai Xiao, who gave me a precious opportunity to
work with him. Without his encouragement, patience and generous supports, I would not
have been able to finish my Ph.D. program. His profound and selfless guidance not only
inspired me greatly during my graduate study, but also lighted my way to a brighter
future. He is my greatest mentor and friend.
I would like to thank Drs. John Ballato, Liang Dong, and Lin Zhu for being my
Ph.D. committee and for the encouragements, valuable insightful questions and
suggestions that I received from them.
I would also like to express my acknowledgement to my peers and friends that I
have worked in this project with in the Photonics Technology Lab: Tao Wei, Xinwei Lan,
Lei Yuan, Liwei Hua, Lei Hua, Yang Song, Yanjun Li and other members help me with
the project.
I would like to give special thanks to my wife Lingyu Chi who has been
supporting me continuously for the last 5 years.
iii
TABLE OF CONTENTS
Page
TITLE PAGE .................................................................................................................... i
ABSTRACT..................................................................................................................... ii
ACKNOWLEDGMENTS ..............................................................................................iii
LIST OF FIGURES ........................................................................................................ vi
CHAPTER
I.
INTRUDUCTION ......................................................................................... 1
1.1 Optical interferometry........................................................................ 1
1.2 Microwave interferometry ................................................................. 3
1.3 Mixing microwave with optics .......................................................... 5
1.4 Motivations of OCMI ........................................................................ 6
1.5 Organization of the dissertation ......................................................... 8
II.
OPTICAL CARRIER BASED MICROWAVE INTERFEROMETRY ..... 10
2.1 OCMI concept .................................................................................. 10
2.2 OCMI Systems ................................................................................. 13
2.21 External modulation based OCMI system ............................... 13
2.22 Direct modulation based OCMI system ................................... 15
2.3 Demonstration of the OCMI concept ............................................... 17
2.31 SMF-OCMI .............................................................................. 17
2.32 MMF-OCMI ............................................................................ 20
III.
MATHEMATICAL MODEL OF OCMI .................................................... 24
3.1 Modeling of the OCMI under generalized conditions ..................... 24
3.2 The Microwave interferogram - the amplitude and phase spectra ... 31
3.3 Demonstration of the OCMI concept ............................................... 34
IV.
OCMI FOR SENSING APPLICATIONS ................................................... 38
4.1 SMF based OCMI for sensing applications ..................................... 38
4.11 Strain measurement using a SMF
based Fabry-Perot OCMI ......................................................... 38
iv
Table of Contents (Continued)
Page
4.12 Characterization of Sensing Performance
at High Temperature ................................................................ 41
4.121 SMF based Michelson OCMI ........................................ 41
4.122 Sensitivity characterization ............................................ 42
4.123 Stability and Reversibility Test ...................................... 44
4.2 Special optical fiber based OCMI for sensing applications ............. 47
4.21 Single crystal sapphire optical fiber
for high temperature application .............................................. 47
4.22 Polymer optical fiber for large strain measurement ................. 60
V.
OCMI BASED DISTRIBUTED SENSING ................................................ 68
5.1 Review of the state-of-the-art technologies ..................................... 68
5.2 Spatially continuous distributed fiber optic sensing using OCMI ... 72
5.21 Concept of the spatially continuous distributed sensing .......... 73
5.22 Modeling and simulations ........................................................ 77
5.23 Experimental demonstration .................................................... 85
5.3 Microwave assisted reconstruction of optical interferograms ......... 95
5.31 Microwave assisted multiplexing of interferometric sensors .. 96
5.32 System realization and concept demonstration ........................ 99
5.33 Demonstration of distributed sensing .................................... 103
VI.
CONCLUSION AND FUTURE WORK .................................................. 108
6.1 Conclusion ..................................................................................... 108
6.2 Future work .................................................................................... 110
REFERENCES ............................................................................................................ 113
v
LIST OF FIGURES
Page
Figure
1.1
Schematic of an optical fiber based FPI ........................................................ 2
1.2
Schematic of an optical fiber based FPI ........................................................ 4
2.1
Conceptual illustration of the optical carrier based
microwave interferometry. ..................................................................... 11
2.2
Schematic of the OCMI system used to support
proof-of-concept experiments. ............................................................... 15
2.3
Schematic of an OCMI interrogation system............................................... 16
2.4
(a) Schematic of SMF based Michelson OCMI
(b) Measured interferogram in microwave domain ............................... 18
2.5
Schematic of a Mach-Zehnder OCMI implemented using SMFs ............... 19
2.6
(a) Schematic of a Michelson OCMI implemented using graded
index MMFs (Corning, InfiniCor-300). (b) Microwave
interferogram of the Michelson OCMI, showing a visibility
exceeding 40 dB and a FSR of 536.3 MHz. ........................................ 20
2.7
(a) Schematic of a Fabry-Perot OCMI implemented using graded
index MMFs (Corning, InfiniCor-300). (b) Time domain signal
after applying a complex and inverse Fourier transform to the
microwave amplitude and phase spectra (c) Microwave
interferogram of the Fabry-Perot OCMI, showing a visibility
exceeding 20 dB. .................................................................................... 21
2.8
(a) Schematic of a Fabry-Perot OCMI implemented using a single
crystal sapphire optical fiber. (b) Time domain signal after
applying a complex and inverse Fourier transform to the
microwave amplitude and phase spectra (c) Microwave
interferogram of the Fabry-Perot OCMI, showing a visibility
exceeding 20 dB. .................................................................................... 22
3.1
Simulation of an OCMI implemented using single-mode fibers. ................ 33
vi
List of Figures (Continued)
Figure
Page
3.2
Simulation of an OCMI implemented using step-index multimode fibers. . 36
3.3
Simulation of an OCMI implemented using graded-index
multimode fibers. ................................................................................... 37
4.1
One simply way to construct OCMI-FPI ..................................................... 38
4.2
SMF extrinsic Fabry-Perot OCMI for strain sensing. .................................. 40
4.3
(a) Schematic of a Michelson OCMI implemented using SMFs.
(b) Time domain signal after applying a complex and inverse
Fourier transform to the microwave amplitude and phase spectra
(c) Microwave interferogram of the Michelson OCMI, showing a
visibility exceeding 40 dB. .................................................................... 42
4.4
Interference spectra at various surrounding temperature increase from
50 to 900 °C. .......................................................................................... 43
4.5
Temperature-induced resonant frequency shifts of the OCMI
based optical fiber Michelson interferometer. ....................................... 44
4.6
Stability test of the OCMI based optical fiber Michelson
interferometer at different temperatures (100 ~ 1100 °C). .................... 46
4.7
Repeatability test of the OCMI based optical fiber
Michelson interferometer.. ..................................................................... 47
4.8
Schematic of an OCMI interrogation system............................................... 51
4.9
Time domain signal after applying a complex and inverse Fourier
transform to the recorded microwave spectrum (S21). ........................... 53
4.10
Microwave interferogram of the sapphire fiber Michelson OCMI
showing a visibility exceeding 40 dB at the microwave
frequency of about 3500 MHz. .............................................................. 54
4.11
Interference fringes of the sapphire fiber based OCMI at
different temperatures during (a) increasing and (b)
decreasing steps, respectively. ............................................................... 56
vii
List of Figures (Continued)
Figure
Page
4.12
The center frequency of the interferogram valley at about
4300 MHz at different ambient temperatures during the
temperature increasing and decreasing cycles. ...................................... 58
4.13
(a) Stability test of the sapphire fiber based Michelson OCMI
at (a) 800 °C and (b) 1000 °C.. .............................................................. 59
4.14
Polymer optical fiber based OCMI-FPI ....................................................... 63
4.15
Microwave interferogram of the POF Fabry-Perot OCMI
showing a visibility exceeding 15 dB at the microwave
frequency of about 4000 MHz.. ............................................................. 66
4.16
Frequency shift as a function of applied strain. The inset
shows the microwave spectra at various applied strain. ........................ 66
5.1
Joint-time-frequency domain interrogation of multi-point FPI
in a single coaxial cable for distributed sensing with
high spatial resolution. ........................................................................... 75
5.2
Schematic illustration of the fundamental concept of the spatially
continuous distributed sensing using cascaded FPIs ............................. 76
5.3
Simulation of 8 reflectors along a single-mode fiber................................... 85
5.4
Validation of the distributed sensing capability of OCMI.. ......................... 88
5.5
Schematic illustration of the experiment setup to validate
the distributed strain sensing capability of OCMI. ................................ 92
5.6
Schematic illustration of the microwave assisted multiplexing
of fiber optic interferometric sensors. PD: photo-detector .................... 97
5.7
Schematic of the system configuration and implementation
for concept demonstration.................................................................... 100
viii
List of Figures (Continued)
Figure
Page
5.8
(a) Time domain signal after applying a complex inverse
Fourier transform to the microwave spectrum with the
center wavelength of the tunable filter set to be 1552 nm,
(b), (c) and (d) Normalized microwave-reconstructed optical
interferograms of the three EFPIs in comparison with their
spectra measured individually using an OSA, respectively.. ............... 103
5.9
(a) Distributed strain measurement using three multiplexed EFPI
sensors, where strain is applied on EFPI #2 only, (b) Interferogram
shift of the EFPI #2 as a function of applied axial strain. Inset:
Interferograms of EFPI #2 at various applied strains. ......................... 105
6.1
(a) Schematic illustration of the experiment setup to validate the
OCMI based cavity ring-down concept. (b) Time/distance
resolved ring-down delay curve with excellent SNR. ......................... 112
ix
CHAPTER ONE
INTRODUCTION
1.1 Optical interferometry
Optical interferometry has been widely used for accurate measurement of various
physical, chemical and biological quantities [1-4]. Optical interference superposes two or
more coherent optical waves of certain propagation delays to generate periodic patterns in
time, space, or frequency domain. The information embedded in the periodic patterns
such as the phase, the amplitude, and the frequency positions of the waves can be utilized
to compute the propagation delays. An interferometer can be designed to encode the
information to be measured into the propagation delays. Thus, an interferometric sensor
can be used to measure various parameters. Optical interferometric sensors and
measurement techniques have high sensitivity, high response frequency, immunity to
electromagnetic interference (EMI), remote operation, low optical attenuation and the
ability to be transmitted over the long distance.
The principle has been implemented into various sensors and instruments. Based
on the different ways of generating, separating, and combining the coherent optical waves,
various types of optical interferometers have been implemented into optical
interferometric systems including the Fabry-Perot interferometer (FPI) [5, 6], Fizeau
interferometer [7, 8], Michelson interferometer (MI) [9, 10], Mach-Zehnder
interferometer (MZI) [11, 12] and Sagnac interferometer [13, 14]. These interferometers
have found a wide variety of applications in various scientific and engineering fields.
1
With many well-known advantages such as small size, light weight, high
resolution, and immunity to electromagnetic inference (EMI), fiber optic interferometers
(FOIs) have been widely used as sensors for measurement of various physical, chemical
and biological quantities by encoding the information of interest into the optical path
difference (OPD) of the interferometer [15-20]. Their applications have been found in
many important areas such as infrastructure health monitoring [21], astronomy [22], high
resolution biomedical imaging [23], harsh environment sensing [24], etc. Fig. 1.1 shows
an example of a fiber inline FPI. An optical fiber based FPI consists of a cavity formed
by two reflectors with a typical separation of tens to hundreds of micrometers. Light
waves reflected at the two reflectors have a different time delay, resulting in an
interference signal (e.g., an interferogram in spectrum domain) that can be demodulated
to find the optical length of the cavity. The variations in ambient temperature and/or
strain will change the physical length or material properties of the medium between the
two reflectors, leading to a shift in the interference pattern. This shift can be measured to
find the ambient temperature or strain change.
Fiber core
Optical fiber FPI
Fiber cladding
Fig. 1.1. Schematic of an optical fiber based FPI.
To obtain a high quality interference signal in optical domain, an FOI prefers to
use singlemode fibers (SMFs) to minimize the fringe visibility reduction caused by
2
multimodal influences 8. The SOPs of the interference beams need to be tightly
controlled to avoid the so-called polarization fading issue 9. If reflectors are used in the
interferometer, they must be fabricated with high precision, preferably within a fraction
of the optical wavelength. Furthermore, it is difficult to multiplex a large number of FOIs
in optical domain for distributed sensing. The combination of the aforementioned issues
has placed a bottleneck on the technology advancement and further expansion of the
application scopes.
1.2 Microwave interferometry
Governed by the same electromagnetic theories, microwave and optics have many
characteristics in common but significant differences in properties and applications.
From the electromagnetic point of view, a microwave waveguide (e.g., a coaxial cable)
performs a similar function as an optical fiber by transmitting an electromagnetic signal
over a long distance. A typical coaxial cable consists of an inner and outer conductor
sandwiched by a tubular insulating layer with a high dielectric constant. The EM wave
frequencies supported by them are quite different. The optical frequency is orders of
magnitude higher than the radio frequency (RF). Over the years, optical fiber and coaxial
cable technologies have evolved along quite different paths, resulting in unique devices
of their own right.
Two microwave beams can also be coherently superimposed to generate an
interference pattern similar to two optical beams [25-30]. Due to the large wavelength
(low frequency) of microwave, the size of a microwave interferometer is larger than that
of an optical interferometer. Construction of a microwave interferometer thus does not
3
necessarily require a manufacturing accuracy as high as that required by an optical
interferometer.
In addition, the stringent requirements on optical waveguides (e.g.,
geometry, dispersion, modal and material characteristics) for making an optical
interferometer can be relieved significantly in a microwave interferometer. Unlike an
optical signal whose fundamental frequency is too high to be resolved, the phase of a
microwave signal can be accurately measured. Let’s take a microwave FPI as an example.
In comparison with the aforementioned optical fiber based FPI in Fig. 1.1, we can
similarly engineer partial reflectors inside a microwave waveguide like a coaxial cable to
construct a coaxial cable FPI (CCFPI) [31]. As shown in Fig. 1.2, a CCFPI consists of a
pair of partial reflectors separated by millimeters to centimeters. The EM wave traveling
inside the cable is partially reflected at the first reflector while the remaining energy
transmits through to reach the second reflector. At the second reflector, the EM wave is
again partially reflected. The two reflected waves travel backwards and interfere
coherently to generate an interference signal in microwave domain. When observed in the
spectrum domain, the interference signal manifests itself as an interferogram.
Outer conductor
Reflector
U2
U1
Coaxial cable FPI
Inner conductor
Dielectric layer
Fig. 1.2. Schematic of an optical fiber based FPI.
However, microwaves cannot transmit over a long distance in a waveguide
because of the large dielectric loss of the medium used for construction of the waveguide
4
(e.g., a coaxial cable). Meanwhile, microwave waveguides are usually large in size (e.g.,
the most commonly used coaxial cable has a typical diameter on the order of several
millimeters). In addition, a microwave beam is difficult to be manipulated with high
precision (e.g., focused, collimated or redirected). Microwave devices in general have
low quality (Q) factors compared to optical devices and are susceptible to EMI [32-36].
Although pure microwave interferometers have been successfully used for point
measurement of various parameters, their applications in distributed measurement has
been rather limited.
1.3 Mixing microwave with optics
In an effort to bring together the strengths from both microwave and optics, a
research area known as the microwave-photonics has been explored over the past 30
years.
The combination of microwave and optics has indeed found many unique
applications in optical communication, broadband wireless access network, radar and
satellite instrumentation [37-42]. In general, the microwave photonics techniques cover
the following topics: 1) photonic generation of microwave signals, 2) photonic processing
of microwave signals, 3) photonic distribution of microwave signals, and 4) photonic
analog-to-digital conversion. Some successful examples include high-quality microwave
sources [43-45], high-performance analog links [46-48], phased array antennas [49-51],
frequency-tunable high-Q microwave filters [52-54] and high-speed analog-to-digital
convertors [55-57]. These successes have intrigued us to explore the possibility of
combining microwave and optics for sensing applications, which has led to the new
5
concept of optical carrier based microwave interferometry (OCMI) to be reported in this
dissertation [58, 59].
1.4 Motivations of OCMI
The essence of OCMI is to read optical interferometers using microwave. As
such, it combines the advantages from both optics and microwave. When used for
sensing, it inherits the advantages of optical interferometry such as small size, light
weight, low signal loss, remote operation and immunity to EMI. Meanwhile, by
constructing the interference in microwave domain, the OCMI has many unique
advantages that are unachievable by conventional optical interferometry, including:
1)
Excellent signal quality. OCMI uses coherent detection in which the
modulation, detection and demodulation are all synchronized and phase-locked to the
same microwave frequency. As a result, OCMI has a higher signal-to-noise ratio (SNR)
comparing to the conventional all-optical interferometers. Our results have shown that
clean interference spectra with excellent visibility can be routinely obtained in the
microwave domain.
2)
Distributed sensing with spatial continuity and reconfigurable gauge
length: Time-resolved reflections can be easily obtained by complex Fourier transform of
the microwave signals with phase and amplitude information. Distributed sensing can be
achieved with spatial continuity by taking consecutive measurement between two
adjacent reflectors. In addition, the gauge length can be varied by taking measurement
between two arbitrary reflectors.
6
3)
Insensitivity to the types of optical waveguides. The differences in optics
(e.g., dispersion and modal interference) have little influences on the OCMI signal. High
quality interference signals can be conveniently obtained using highly multimode
fibers/waveguides (e.g., glass, plastic, quartz or sapphire fibers and rods). For instance,
with large strain capability, the plastic fiber based OCMI distributed sensors can be very
useful in structural health monitoring. With tolerance to high temperatures, the sapphire
fiber OCMI sensors can be used for measurement of very high temperatures.
4)
Insensitivity to variations in optical polarizations. In OCMI, the
interference is a result of coherent superposition of the microwave envelops. The
polarization fading issue, commonly confronted in all-optical interferometers, is no
longer a concern in OCMI. Polarization maintaining optical fibers are no longer required
to construct high quality OCMI based FOIs.
5)
Relieved fabrication requirements.
In order to obtain a high-quality
interference signal, the surface smoothness of the reflectors needs to be smaller than 1/20
of the wavelength. All-optical interferometers need to be fabricated with very high
precision (within a fraction of the optical wavelength). In comparison, OCMI can be
fabricated with lowed precision because the interference is observed in microwave region
whose wavelength is much longer than that of an optical wave. In a sense, currently
available micromachining techniques can easily satisfy the precision requirements of
OCMI.
7
1.5 Organization of the dissertation
The dissertation is organized into five chapters with their contents briefly
described below:
Chapter 1 provides a brief introduction of interferometry technique for sensing
applications in both optical and microwave domains, where their unique features and
drawbacks are generally introduced and analyzed. A new concept of reading optical
interferometry in microwave domain has been proposed based on the successful
exploration of microwave-photonics technology, which has led to an interferometric
technique called OCMI. The motivations and unique advantages of OCMI have also been
introduced.
Chapter 2 starts with a general introduction of the proposed OCMI technology
including the design, development and demonstration to uncover the full potentials and
explore the full capabilities of OCMI. Different designs of OCMI system have been
introduced with different modulation techniques. Various types of OCMIs on different
types of optical fibers (e.g., singlemode, multimode, sapphire, polymer fibers, etc.) have
been experimentally demonstrated with good SNR.
Chapter 3 mainly focuses on a rigorous mathematical model including
contributions from both optics and microwave in order to gain a fundamental
understanding of the underlying physics of OCMI. The quality of the OCMI signal and
its dependence on various optical and microwave parameters (e.g., modal dispersion,
optical polarization, modulation depth, coherent and incoherent superposition, optical and
microwave path differences, etc.) have been comprehensively studied.
8
Chapter 4 experimentally demonstrates that optical fiber based OCMI can be used
for sensing applications (e.g., temperature and strain measurement). In particular, OCMI
has been successfully implemented on some special optical fibers such as a single crystal
sapphire fiber and a polymer optical fiber for extremely high temperature (up to 1400 °C)
and large strain measurements (up to 5%), respectively. It has been proved that the OCMI
concept has low dependence on optical waveguides/materials.
Chapter 5 presents one of the unique advantages of OCMI, which is its ability for
spatially continuous distributed sensing. This unique feature was experimentally
validated using cascaded optical fiber intrinsic FPIs. Mathematical illustration of the
novel signal processing method and experimental results are both presented. In addition,
a new way of reconstruction of optical interferograms assisted in microwave domain is
also investigated and presented.
Chapter 6 summarizes the dissertation works and recommends future works in
terms of potential applications.
9
CHAPTER TWO
OPTICAL CARRIER BASED MICROWAVE INTERFEROMETRY
2.1 OCMI concept
The essence of OCMI is to read an optical interferometer in microwave domain as
described in Fig. 2.1. A low-coherence optical source is modulated by a microwave
signal. The microwave modulated signal is sent through an optical interferometer. A high
speed photo-detector is used to receive the signal and strip off the optical information to
obtain the microwave information. Inside the optical interferometer, the incident
microwave modulated signal is split into two or more paths with certain propagation
delays. The optical path difference of the interferometer is longer than the coherence
length of the optical source but shorter than the coherence length of the microwave
source. As such, the optical carrier waves build up incoherently while the microwave
signals (envelopes) build up coherently to form an interferogram in microwave domain.
A photo-detector is then used to receive the output from the optical interferometer and
convert it to an electrical signal. The photo-detector has a limited bandwidth so that the
optical carrier frequency cannot be resolved and only the microwave modulation can be
determined. One method to obtain a microwave interferogram in spectrum domain is to
sweep the frequency of the microwave signal and record the demodulated microwave
signals by the photo-detector. The OCMI, now interrogated in microwave domain, can be
used for sensing by correlating its optical path difference to the parameters of interests.
10
Optical broadband
source
Intensity
Modulator
Path 1
Δλ
Path 2
Optical interferometer
Vector microwave
detector
Microwave source
Sync
High-speed optical detection
Frequency
scanning
Data acquisition
Control
OPD
Fourier
transform
+
(c) Propagation delay
Fig. 2.1. Conceptual illustration of the optical carrier based microwave
interferometry. The light from an optical broadband source is intensity modulated by a
microwave signal, and sent into an optical interferometer whose output is recorded by a
high-speed photodetector. The optical detection is synchronized at the modulation
frequency. By scanning the frequency, the microwave amplitude spectrum (a) and phase
spectrum (b) are acquired. The Fourier transform of the microwave complex spectrum
shows the propagation delays of the two paths (c).
For simplicity we assume two-beam interference with equal amplitude (A
rigorous mathematical expression can be found in Chapter 3. The complex amplitudes of
the two intensity-modulated optical waves are given by
11
  W + LO1  

 L 
E1 (t , LO1 )= A 1 + M cos W  t +
⋅ exp  − jω  t + O1  


c
c 


 

  W + LO 2
E2 (t , LO 2 )= A 1 + M cos W  t +
c
 


 LO 2
  ⋅ exp  − jω  t + c



(2.1)



where t is the time; A and M are the amplitudes of the optical carrier and microwave
envelope, respectively; ω and Ω are the optical and microwave angular frequencies,
respectively; c is the speed of light in vacuum; W is the electrical length of the common
microwave path; LO1 and LO2 are the two optical path lengths, respectively. The power of
the superimposed optical waves is thus given by
Microwave term
Optical term
(2.2)
where ωmin and ωmax are the minimum and maximum frequencies of the light source,
respectively.
The detected signal given in Equation 2.2 includes three terms: the DC,
microwave and optical terms. When the OPD = LO1 – LO2 is sufficiently larger than the
coherence length of the optical source, the integral term of the optical contribution
approaches zero. The synchronized detection at the microwave frequency eliminates the
DC term to provide the amplitude and phase of the microwave signal in Equation 2.2. By
scanning the frequency, the microwave amplitude and phase spectra can be acquired as
12
shown in Fig. 2.1 (a) and (b). The microwave amplitude spectrum (i.e., microwave
interferogram) can be analyzed to determine the OPD and/or its changes for the purpose
of sensing. In addition, the microwave phase is a function of the total length (i.e., the
summation of the electric and optical lengths) between the microwave source and
detector. As shown in Fig. 2.1 (c), the Fourier transform of the complex microwave
spectrum provides the propagation delays of the two paths, which can be used to
determine the location of the interferometer.
2.2 OCMI Systems
2.21 External modulation based OCMI system
Modulation of the light intensity by a microwave signal can be achieved by either
direct modulation or external modulation. In direct modulation, the microwave signal
directly regulates the driving current of the light source so that the optical power changes
correspondingly. Direct modulation can be easily and inexpensively implemented on a
semiconductor laser or LED with a modulation depth close to 100%. However, the
maximum modulation frequency is limited (<10 GHz) and there might be time jitters and
excess intensity noises. External modulation uses an Electro-optic modulator (EOM, e.g.,
the Lithium Niobate Modulator used in our current system) to externally control the light
intensity. An EOM based modulation can reach very high frequencies (e.g., 40 GHz).
However, it is polarization dependent and the modulation depth is smaller than that of
direct modulation.
13
While there are many ways to implement the OCMI concept, Fig. 2.2 illustrates
an example system configuration based on an external modulator. A microwave vector
network analyzer (VNA) is used as the microwave source and signal detector. A
broadband light source with the bandwidth of 50 nm is intensity modulated using an
electro-optic modulator (EOM) driven by the microwave signal from the Port 1 of a VNA
(HP 8753es). The VNA output is DC-biased and amplified to achieve a high modulation
index. The modulated light is then sent into an FOI (or FOIs) whose outputs are detected
by a high speed photodetector. For a reflection type FOI (e.g., a Fabry-Perot or
Michelson interferometer), a fiber circulator is used to route the input light into and the
output signal out of the FOI (solid lines in Fig. 2.2 (b)). For a transmission type FOI (e.g.,
a Mach-Zhender interferometer), its output is directly connected to the photodetector
(dashed lines in Fig. 2.2 (c)). An optional erbium doped fiber amplifier (EDFA) can be
used for additional signal amplification. After DC-filtering and RF amplification, the
photodetector output is connected to the Port 2 of the VNA, where the amplitude and
phase of the signal are extracted. By sweeping the VNA frequency, the microwave
spectrum of the interferometer is obtained.
14
VNA
Port 2
Port 1
Optical broadband
source
RF
Amplifier
RF
Amplifier
Bias-T
Optical fibre
DC
DC-Filter
Polarization controller
Coaxial cable
EOM
Photodetector
Polarizer
Output
Input
Fibre circulator
1
(a)
3
2
Sensor head
3 dB coupler
(c)
(b)
Reflection type
Transmission type
Fig. 2.2. Schematic of the OCMI system used to support proof-of-concept
experiments. A broadband light source (bandwidth of 50 nm) is intensity-modulated
using an electro-optic modulator (EOM) driven by the microwave output (DC-biased and
amplified) from Port 1 of a VNA (HP 8753es). The output from the FOI is detected by a
photodetector whose signal, after DC-filtering and RF amplification, is recorded at Port 2
where the amplitude and phase of the signal are extracted. By sweeping the VNA
frequency, the microwave spectrum of the interferometer is obtained (i.e., the S21 of the
VNA). (a) For a reflection type FOI (e.g., Michelson or Fabry-Perot), a fiber circulator is
used to route the optical input and output. (b) For a transmission type FOI (e.g., MachZehnder), its output is directly connected to the photodetector.
2.22 Direct modulation based OCMI system
15
Another way to implement the OCMI system is to use a direct modulated laser
source. Fig. 2.3. illustrates a simple OCMI system where a microwave VNA is also used
as the microwave source and signal detector. A laser diode (Agilent/HP 83402A) is
directly modulated by the microwave signal from the Port 1 of the VNA. The center
wavelength and bandwidth of the light source we used are 1300 nm and 1 nm,
respectively. It can be directly modulated in the frequency range from 300 KHz to 6 GHz.
The microwave-modulated light is then sent into a fiber optic inerferometer, whose
outputs are detected by a high speed photodetector (HP/Agilent 83411C). The
photodetector has a detection bandwidth of 6 GHz and a detection area of 62.5 μm in
diameter. A 3dB fiber coupler is used to route the input microwave-modulated light into
and the output signal out of the fiber sensor. After DC-filtering, the photodetector output
is connected to Port 2 of the VNA, where the amplitude and phase of the signal are
extracted. By sweeping the VNA frequency, the microwave spectrum of the sensor is
obtained (i.e., the S21 of the VNA).
Fig. 2.3. Schematic of an OCMI interrogation system. VNA: Vector network
analyzer. LD: Laser diode. PD: Photodetector.
16
2.3 Demonstration of the OCMI concept
2.31 SMF-OCMI
In principle, the OCMI concept can be implemented in most types of FOIs. It was
first tested using singlemode fiber (SMF) interferometers. The external modulation based
OCMI system was used to interrogate the interference pattern in microwave domain. Fig.
2.4 (a) shows the schematic construction of a SMF Michelson interferometer with a
length difference of 14.38 cm (measured by a caliper). The Michelson interferometer was
made by a 3 dB SMF coupler. The two ends of the fiber couplers were cleaved as two
partial reflectors.
The incident microwave-modulated light is first split into two paths through a 3
dB 2×2 SMF coupler. One beam is reflected from the endface of a SMF fiber; the other
beam is reflected from the other endface. The two reflected beams are then recombined
through the fiber coupler. The superposition of the two beams results in an interference
signal that is a function of the OPD between the two different paths. The OPD of the
proposed interferometer is longer than the coherence length of the optical source but
shorter than the coherence length of the microwave source. As such, the optical carrier
waves build up incoherently while the microwave signals (envelopes) build up coherently
to form an interferogram in the microwave domain. The microwave interference
spectrum is shown in Fig. 2.4 (b). The fringe visibility exceeded 30 dB, indicating an
excellent SNR. The free spectrum range (FSR) of the interferogram was found to be
715MHz. The calculated length difference was 14.37cm based on Equation 2.2, which
was in good agreement with the value measured by the caliper.
17
Fig. 2.4. (a) Schematic of SMF based Michelson OCMI (b) Measured
interferogram in microwave domain
Fig. 2.5 (a) shows a Mach-Zehnder FOI implemented using SMFs (Corning SMF28e) with a length difference of 18.10 cm. Fig. 2.3 (b) shows the microwave
interferogram in the frequency range of 0-3.5 GHz. The fringes are clean with a visibility
exceeding 45 dB. The free spectral range (FSR) was found to be 1.125 GHz. Based on
Equation 2.2, the OPD was found to be 26.67 cm. Using the effective refractive index of
the fiber core of 1.468, the length difference was calculated to be 18.16 cm, which agreed
well with the value measured by the caliper. An optical fiber polarization controller was
inserted in Path 1 to test the polarization dependence. As shown in Fig. 2.5 (c), the
interferogram showed very little dependence on the polarization, with a maximum
variation of 0.12 dB at the interference peak.
18
Fig. 2.5. Schematic of a Mach-Zehnder OCMI implemented using SMFs
(Corning SMF28e). (b) Microwave interferogram of the Mach-Zehnder OCMI showing a
visibility exceeding 45 dB. Using the effective refractive index of the fiber core of 1.468,
the length difference was calculated to be 18.16 cm, which agreed well with the value
(18.10 cm) measured by the caliper. (c) Variation of an interference peak at different
polarization states. A maximum intensity variation of 0.12 dB was observed at all
polarizations.
The OCMI concept has also been validated using a multimode fiber (MMF,
Corning InfiniCor-300) Michelson interferometer as shown in Fig. 2.6 (a). The acquired
microwave interferogram (Fig. 2.6 (e)) has an excellent quality with a visibility over 40
dB. Again, the calculated path difference was in excellent agreement with the value
measured by the caliper. The experiment results prove that the OCMI concept is
insensitive to multimodal influences and can be conveniently implemented using various
19
MMFs such as plastic and single crystal sapphire fibers. Some application examples of
the OCMIs can be found in chapter 4.
Fig. 2.6. (a) Schematic of a Michelson OCMI implemented using graded index
MMFs (Corning, InfiniCor-300). (b) Microwave interferogram of the Michelson OCMI,
showing a visibility exceeding 40 dB and a FSR of 536.3 MHz. Using the fiber core
effective index of 1.488 at 1550 nm, the path difference was found to be 18.81 cm, in
excellent agreement with the value (18.70 cm) measured by the caliper.
2.32 MMF-OCMI
Fig. 2.7 (a) shows the schematic construction of a MMF Fabry-Perot OCMI with
a length difference of 13.8 cm. Again, the fringe visibility is pretty good with an excellent
SNR. A time domain signal is plotted in Fig. 2.7 (b) by applying a complex and inverse
20
Fourier transform to the recorded amplitude and phase spectra in microwave domain as
described in Fig. 2.1. It is clear that two time-resolved reflections along this MMF can be
identified. Fig. 2.7 (c) plots the microwave interference spectrum from this MMF FabryPerot OCMI. There are many methods to implement inline reflectors along the fiber. For
this experiment, we intentionally misaligned the fibers during fusion splicing, creating a
reflector R1 as shown in Fig. 2.7 (a) and R2 is a reflection from a cleaved fiber.
Fig. 2.7. (a) Schematic of a Fabry-Perot OCMI implemented using graded index
MMFs (Corning, InfiniCor-300). (b) Time domain signal after applying a complex and
inverse Fourier transform to the microwave amplitude and phase spectra (c) Microwave
interferogram of the Fabry-Perot OCMI, showing a visibility exceeding 20 dB.
21
Fig. 2.8 (a) shows the schematic construction of a sapphire fiber based FPI with a
length of 1 m. The diameter of sapphire fiber is 125 μm. The time resolved reflections
from two endfaces of sapphire fiber are shown in Fig. 2.8 (b). Fig. 2.8 (c) plots the
microwave interference spectrum from this sapphire fiber based FPI. The fringe visibility
is more than 20 dB showing an excellent SNR. The lead in multimode fiber (105/125 μm)
and sapphire fiber are both with 125 um diameter, and they are placed face-to-face in a
~126 μm wide v-shape channel (~4 cm length) fabricated on a silicon wafer. By varying
the surrounding refractive index, the reflectivity from the first sapphire fiber endface can
be modified. This easy modification facilitate the reflectivity matches with each other
from both fiber endfaces to obtain good interference spectrum, shown in Fig. 2.8 (b) and
(c).
22
Fig. 2.8. (a) Schematic of a Fabry-Perot OCMI implemented using a single crystal
sapphire optical fiber. (b) Time domain signal after applying a complex and inverse
Fourier transform to the microwave amplitude and phase spectra (c) Microwave
interferogram of the Fabry-Perot OCMI, showing a visibility exceeding 20 dB.
The proof-of-concept results clearly demonstrates that the OCMI inherits the
advantages of optical interferometry and offers many unique features including high
signal quality, insensitivity to SOP variations, low dependence on multimodal influences,
and relieved requirement on fabrication. Although FOIs were used in demonstrations, the
OCMI concept can be implemented in free space and other forms of optical waveguides.
23
CHAPTER THREE
MATHEMATICAL MODEL OF OCMI
3.1
Modeling of the OCMI under generalized conditions
Chapter 2.1 illustrates a simplified model of OCMI by assuming two-beam
interference with equal amplitude, equal state of polarization, and single mode only. In
order to gain a fundamental understanding of the underlying physics of OCMI, a rigorous
mathematical model needs to be developed to include contributions from both optics and
microwave. Equation 2.2 presents a simplified OCMI model that provides an intuitive
understanding of the concept. However, the quality of the OCMI signal and its
dependence on various optical and microwave parameters (e.g., dispersion, polarization,
wavelength stability, modulation depth, phase detection error, optical/electrical loss,
amplitude fluctuation, etc. deserves more comprehensive studies. In addition, the various
assumptions made during the derivation of Equation 2.2 also need to be verified and
tested. A rigorous mathematical model of OCMI is shown below.
Assume a polarized optical wave given by:



=
Eo Eox a x + Eoy a y
{
}
{
}


= Ax exp − j ωt + j x  a x + A y exp − j ωt + j y  a y




(3.1)
where, t is the time; Eox and Eoy are electric fields in the x and y directions, respectively;
Ax and Ay are the amplitudes and φx and φy are the phases of the corresponding electric
24


fields, respectively; ω is the angular optical frequency; ax and a y are the unit vectors
along x and y directions, respectively.
The microwave signal used to modulate the optical wave is given by:
s(t ) M cos ( Ωt + φ )
=
(3.2)
where M is the amplitude, Ω is the angular frequency, and φ is the phase.
The electric field of the light wave modulated by the microwave becomes:



=
E m x (t ) Eox a x + m y (t ) Eoy a y
(3.3)
where mx(t) and my(t) are the amplitude modulation terms, given by
m x (t )=
1 + h x s(t ) = 1 + h x M cos ( Ωt + φ )
m (t )=
1 + h s(t )=
(3.4)
y
1 + h M cos ( Ωt + φ )
y
y
where hx and hy are the modulation index in the x and y direction, respectively. Note that
the microwave modulations may be different in the x and y directions.
The microwave modulated light is split into two optical paths. These two light waves
propagate through different paths (z1 and z2), excite different optical modes, experience
different polarization evolutions (φx and φy), and eventually superimpose to generate the
interference signal.
The complex electric field amplitudes of the two microwave-modulated light waves
propagating in the i-th mode are given by
25



=
E1,i ( t , z1 ) E1,xi ( t , z1 ) a x + E1,yi ( t , z1 ) a y


= m1,xi ( t , z1 ) Eox1,i ( t , z1 ) a x + m1,yi ( t , z1 ) Eoy1,i ( t , z1 ) a y



=
E2,i ( t , z2 ) E2,x i ( t , z2 ) a x + E2,y i ( t , z2 ) a y


= m2,x i ( t , z2 ) Eox2,i ( t , z2 ) a x + m2,y i ( t , z2 ) Eoy2,i ( t , z2 ) a y
(3.5)
Note that in Equation 3.5, both the optical and microwave components are functions
of their corresponding optical path lengths.
The optical components (i.e., electric fields of the i-th optical mode in the x and y
directions) in Equation 3.5 are given by

z1neff ,i 
  
x 
Eox1,i ( t , z1 )= A1,xi exp  − j ω  t +
 + j1,i  
c 
 
  
z1neff ,i
  
Eoy1,i ( t , z1 )= A1,yi exp  − j ω  t +
c
  
Eox2,i
( t, z2 )=
A2,x i


y 
j
+

 1,i 

 

z2 neff ,i 
  
x 
exp  − j ω  t +
 + j 2,i  
c 
 
  
(3.6)

z2 neff ,i 
  
y 
Eoy2,i ( t , z2 ) = A2,y i exp  − j ω  t +
 + j 2,i  
c 
  
 
where A1,ix, A1,iy, A2,ix, A2,iy are the electric field amplitudes of the optical waves; c is the
speed of light in vacuum; z1 and z2 are the lengths of the two optical paths, respectively;
neff,i is the effective refractive index of the i-th optical mode; ϕ1,xi , ϕ1,yi , ϕ2,x i , ϕ2,y i are the
polarization phase terms.
26
The microwave amplitude modulation terms in Equation (3.5) are
m1,xi ( t , z1 ) =
  W z1neff ,i  W x 
  W z1neff ,i
x
1 + h x M cos W  t + +
 + ϕ1,i  ≈ 1 + h M cos W  t + +
c
c  ω
c
c
 

 


 
m1,yi ( t , z1 ) =
  W z1neff ,i
1 + h y M cos W  t + +
c
c
 
  W z1neff ,i
 W y
y
 + ϕ1,i  ≈ 1 + h M cos W  t + +
c
c
 ω

 


 
m2,x i ( t , z2 ) =
  W z2 neff ,i  W x 
  W z2 neff ,i
x
1 + h x M cos W  t + +
 + ϕ 2,i  ≈ 1 + h M cos W  t + +
c
c  ω
c
c
 

 


 
m2,y i ( t , z2 ) =
  W z2 neff ,i
1 + h y M cos W  t + +
c
c
 
  W z2 neff ,i  
 W y 
y
 + ϕ 2,i  ≈ 1 + h M cos W  t + +

c
c  

 
 ω
(3.7)
where the microwave envelopes include two delay terms. The first is the delay associated
with the common electrical length (W) of microwave system and this delay is the same
for all the paths. The second delay term is the contributions from the optical propagation
delays along the different optical paths. It is interesting to notice that the polarization
phase contributions are reduced by a factor of ω/W, becoming negligible because ω is at
least 5 orders magnitude larger than W. As such, the variations in optical polarization
have very little influence on the microwave signals.
Assume that the optical source has a spectrum width from ωmin and ωmax, the total
optical power of the superimposed optical waves of all modes is thus given by
27
d
2
E=
total
x
E total
ωmax
2
+ Ey
2
total
2
ωmax N
x
x
E1,i + E2,i d ω +
=
1
i
=
=
ωmin
ωmin i 1
N
∫ ∑(
∫ ∑(
)
+
E1,yi
E2,y i
)
2
(3.8)
dω
where N is the total number of optical modes.
The total optical power in x direction can be further derived as follow,
N
E total =
E1,xi E1,xi* +
=i 1 =i 1
x
N
∑(
2
) ∑(
ωmax N
N

x
x*
E2,i E2,i +
E1,xi E2,x*i +

 i 1 =i 1
=
ωmin 
) ∫ ∑(
) ∑( E
x* x
1,i E2,i

) d ω

(3.9)
where the first two terms are the self-products and the last two terms are the crossproducts.
Let’s first examine the cross-products in Equation (3.9)
ωmax
N
 N

E1,xi E2,x*i +
E1,xi* E2,x i  d ω

 i 1 =i 1

=
ωmin 
∫ ∑(
) ∑(
)
(3.10)
ωmax



 x x x x

ω
x
x 
m
A
m
A
z
z
n
ϕϕ
d
ω
2
cos
=
−
+
−
(
)
 1,i 1,i 2,i 2,i


1,i
2,i  
 c 1 2 eff ,i

 
i =1 
ωmin 


N
∑
(
∫
)
It is interesting to notice that the cross-product terms is the optical interference signal
similar to a conventional all-optical interferometer. In the OCMI, the OPD is chosen to be
sufficiently
( z1 − z2 ) neff ,i
larger
>>
than
the
coherence
length
of
the
optical
source,
i.e.,
2π c
. As a result, the integral term in Equation 3.10 approaches
ωmax − ωmin
zero. The optical variations (e.g., variations in polarization states and modal
interferences) commonly seen in an all-optical interferometer have much reduced
28
influences on the OMCI. In our experimental OCMI system, we used a light source with
a spectral width of 50 nm at the center wavelength of about 1550 nm, whose coherence
length was about 48 mm. A typical OCMI has an OPD of a few centimeters that is much
larger than the coherence length of a broadband light source.
Let’s examine the self-product terms in Equation 3.9.
∑(E
) ∑(E
N
N
x x*
+
E
1,i 1,i
=i 1 =i 1
x
x*
2,i E2,i
N

2
 x 2
x
+
+
A
A
h x M  A1,xi
2,i
 1,i

1 =i 1

∑( ) ( )
N
=
=i
x
1,i
2
x
2,i
( )
∑
∑ ( A ) + ( A )  + A
N
=
)
2
x
(
2
cos Wt + Φ x
i =1
  W + z1neff ,i
cos W  t +
c
 

x
  + A2,i
 
( )
2
  W + z2 neff ,i
cos W  t +
c
 
  
  
  
)
(3.11)
Equation 3.11 is easy to calculate using the Phasor method. As such, we have
N
=
Ax
∑A
x
x
eff ,i Aeff , j
(
x
x
cos ff
eff ,i − eff , j
)
(3.12)
i, j



x
arctan 
=
Φ



N

x
sin feff
,i 

,
x
x
Aeff ,i cos feff ,i 


(
∑A
x
eff ,i
i
N
∑
i
)
(
)
Φ x ∈ {−π , π }
(3.13)
x
 neff

,i
cos Ω
( z1 − z2 )
c


(3.14)
and
x
A
=
hx M
eff ,i
( ) ( )
A1,xi
4
+ A2,x i
4
(
+ 2 A1,xi A2,x i
29
)
2
 x 2
  W z1neff ,i  
  W z2 neff ,i   
2
x
 A1,i sin W  +
  + A2,i sin W  +
 
c  
c   

  c
  c
x
x
ff
arctan 
,
eff ,i
eff ,i ∈ {−π , π }




2
2
z
n
z
n




W
W
 x

1 eff ,i
2 eff ,i
x
 A1,i cos W  c + c   + A2,i cos W  c + c   
 
  
 
 

( )
( )
( )
( )
(3.15)
Similarly, the total optical power in y direction is found to be
2
=
E
y
total
N
∑ ( A ) + ( A )  + A
y 2
1,i
y 2
2,i
y
(
cos Ωt + Φ y
i =1
)
(3.16)
where
N
=
Ay
∑A
y
y
eff ,i Aeff , j
(
y
y
cos ff
eff ,i − eff , j
)
(3.17)
i, j



y
=
Φ
arctan 



y
A
=
eff ,i
y
h M
N

y
sin feff
,i 

,
y
y
Aeff ,i cos feff ,i 


∑A
y
eff ,i
i
N
∑
i
( ) +( )
A1,yi
4
A2,y i
(
)
(
4
+2
(
Φ y ∈ {−π , π }
)
A1,yi A2,y i
)
2
y
 neff

,i

cos Ω
( z1 − z2 )
c


(3.18)
(3.19)
 y 2
  W z1neff ,i  
  W z2 neff ,i   
2
y
 A1,i sin W  +
  + A2,i sin W  +
 
c  
c   

  c
  c
y
y
ff
arctan 
,
eff ,i
eff ,i ∈ {−π , π }




2
2
z
n
z
n




W
W
 y

1 eff ,i
2 eff ,i
y
 A1,i cos W  c + c   + A2,i cos W  c + c   
 
 
 
  

( )
( )
( )
( )
(3.20)
The OCMI uses synchronized detection to eliminate the DC term in Equation 3.11
and 3.16 and record only the amplitude and phase of the microwave signal at the
30
microwave frequency W. As a result, the total signal after optoelectronic conversion (with
an optical gain of g) and synchronized microwave detection is found by summing the
powers in x and y directions, given by
)
(
(
)
=
S g  Ax cos Ωt + Φ x + A y cos Ωt + Φ y 


= A cos ( Ωt + Φ )
(3.21)
where
A g
=
Φ
3.2
(A ) +(A )
x 2
(
y 2
+ 2 Ax A y cos Φ x − Φ y
( )
( )
( )  ,
( ) 
 A x sin Φ x + A y sin Φ y
arctan 
 A x cos Φ x + A y cos Φ y

)
Φ ∈ {−π , π }
(3.22)
(3.23)
The Microwave interferogram – the amplitude and phase spectra
Numerical simulations were performed to understand Equation 3.21 and study the
amplitude and phase of the signal as functions of the optical parameters.
First, let’s examine the case of a singlemode fiber (SMF) based OCMI. Assume the
fiber used is Corning SMF-28e with the effective refractive index of the core of neff =
1.468 according to the datasheet from the manufacturer. The optical power is equally
split into the two paths. The lengths of the two optical paths are z1 = 0.1 m and z2 = 0.2 m,
respectively. The common electric length is W = 1 m. The two polarization states are
evenly excited. Based on the assumption, the microwave signal in Equation 3.21 becomes
31
 z −z
=
S 2 A2 gM cos W 1 2 neff
2c

  2W + ( z1 + z2 ) neff

 cos W  t +
2c

 
  2W + ( z1 + z2 ) neff
 OPD 
= 2 A2 gM cos W
cos
W  t +
2c 
2c

 

 
 

 
 
(3.24)
where OPD = L01 − L02 = ( z1 − z2 ) neff . Lo1 and Lo2 are the optical path lengths of the two
optical paths, respectively.
Equation 3.24 indicates that the amplitude of the signal varies as a sinusoidal function
of the microwave frequency and OPD, and the phase of the microwave signal is a
function of the summation of the electric and optical lengths. Fig. 3.1 shows the
simulated microwave amplitude and phase spectra of the OCMI in the frequency range of
0 – 6 GHz. The free spectral range (FSR) of the spectrum is a function of the OPD, given
by
FSR =
c
OPD
Similar to an optical interference spectrum, the microwave amplitude spectrum in the
OCMI can be used to find the optical path difference of an interferometer. It can also be
used to find the change in OPD based on the interference fringe shift.
By applying complex Fourier transform of the signal shown in Equation 3.21, one can
find the propagation delays of the microwave signal. As shown in Fig. 1 (c), the common
electric length (W) and the two optical path lengths can be clearly identified, allowing the
OCMI to locate the position of the interferometer and enabling its unique capability of
distributed sensing.
32
1
4
0.9
3
2
Phase (radians)
Amplitude(a.u.)
0.8
0.7
0.6
0.5
0.4
0.3
1
0
-1
-2
0.2
FSR
0.1
2.044 GHz
-3
0
0
1
2
4
3
6
5
Frequency(Hz)
x 10
-4
0
1
2
3
4
5
Frequency(Hz)
9
(a) Amplitude spectrum
(b) Phase spectrum
OPD
= ( z1 − z2 )neff
0.8
0.7
W + z1neff
Amplitude
0.6
W + z2 neff
0.5
0.4
0.3
0.2
0.1
0
1
0.5
1.5
Distance(m)
(c) Delay diagram
Fig. 3.1. Simulation of an OCMI implemented using single-mode fibers. The
optical power is equally split into the two paths. The lengths of the two optical
paths are z1 = 0.1 m and z2 = 0.2 m, respectively. The common electric length is
W = 1 m. (a) Amplitude spectrum (i.e., interferogram), (b) Phase spectrum, (c)
Delay diagram obtained by applying complex Fourier transform on the amplitude
and phase spectra.
33
6
x 10
9
3.3
Multimodal influences of OCMI
The influence of multiple optical modes on the OCMI signal is clearly shown in
Equations 3.12 and 3.17, where the effective refractive indices of the optical modes are
different. In addition, the multimodal influences also depend on the lengths of
propagation (z1 and z2). In essence, the multimodal dispersion generates phase differences
among the different optical modes and reduces the fringe visibility of the interferogram.
In reality, the number of modes excited inside the fiber strongly depends on how the
light is coupled into the fiber. In addition, the optical power usually is not evenly
distributed among the various modes. The detailed analysis is quite involved. Here for the
purposes of gaining a qualitative understanding of the multimodal influences, we simplify
the case by assuming that all optical modes are evenly excited and the power is evenly
distributed among them.
The number of modes supported in a multimode optical fiber can be estimated by
Nm ≈
V2
V2
for a step-index fiber and N m ≈
for a graded-index fiber. V is the normalized
2
4
=
frequency, given
by V
2π a
l
ncore 2 − nclad 2 . The effective refractive index neff of a guided
mode in a multimode fiber is bounded between the core and cladding refractive indices.
That is ncore < neff < nclad , where ncore and nclad are the refractive index of the core and
δ neff neff ,max − neff ,min ) of the
cladding, respectively. The actual effective index range (=
multimode fiber can be estimated based on the group delay of the optical fiber, given by
[60]
34
d=
tSI
Ld neff , SI
c
2
L∆ ncore
≈
⋅
, for a step-index multimode fiber,
c nclad
(3.25)
L 2
∆ ⋅ ncore , for a graded-index multimode fiber
8c
(3.26)
and
=
δ tGI
where=
∆
Lδ neff ,GI
c
( ncore − nclad )
≈
ncore is the index difference between the core and cladding,
∆<<1; L is the length of the fiber. The ranges of the effective indices of the modes
supported in multimode fibers are thus found to be
δ neff , SI ≈ ∆ ⋅ ncore for a step-index multimode fiber,
(3.27)
∆neff ,GI ≈ ∆ 2 ⋅ ncore / 8 for a graded-index multimode fiber.
(3.28)
and
Simulations were performed to study the multimodal influence on OCMIs and its
dependence on the fiber type and length. Fig. 2 shows the simulated interferograms of an
OCMI implemented using a step-index multimode fiber. The step-index multimode fiber
had core and cladding diameters of 62.5 and 12.5mm, respectively. The refractive index
of the core is ncore = 1.488, and the index difference is ∆ = 0.01. Based on Equation 3.27,
the maximum effective refractive index difference is found to be δ neff , SI = 0.01ncore . The
lengths of the two optical beams varied but their difference was kept the same (z1 – z2 =
0.3 m). It is noticed that the contrast of the interferogram reduces as the optical length
increases, indicating that the multimodal influence is accumulative along the fiber length.
35
In addition, the contrast reduction becomes more noticeable in the high frequency region.
The peak-to-peak value at 3 GHz and 10 m fiber length reduces by half compared with
that at 1 m fiber length. It is anticipated that the fringes may completely disappear when
1
1
0.9
0.9
0.8
0.8
0.8
0.7
0.7
0.7
0.6
0.5
0.4
0.3
0.6
0.5
0.4
0.3
0.2
0.2
0.1
0.1
0
0
1
2
3
4
frequency(Hz)
5
6
x 10
9
Amplitude(a.u.)
1
0.9
Amplitude(a.u.)
Amplitude(a.u.)
the length exceeds a certain value.
0
0.6
0.5
0.4
0.3
0.2
0.1
0
1
3
2
frequency(Hz)
4
6
5
x 10
0
0
1
9
2
3
4
6
5
frequency(Hz)
x 10
9
Fig. 3.2. Simulation of an OCMI implemented using step-index multimode fibers. All
optical modes are equally excited. The core and cladding diameters of the fiber are 62.5
and 125 mm, respectively. The refractive index of the core is ncore = 1.488, and the index
difference is ∆ = 0.01. The common electric length is W = 1. (a) Amplitude spectrum
when z1=1 m and z2=1.3 m. (b) Amplitude spectrum when z1=5 m and z2=5.3 m. (c)
Amplitude spectrum when z1=10 m and z2=10.3 m.
Fig. 3.3 shows the simulated interferograms of an OCMI implemented using a
graded-index multimode fiber with core and cladding diameters of 62.5 and 12.5 mm,
respectively. The common electric length is W = 1. The refractive index of the core is
ncore = 1.488, and the index difference is ∆ = 0.02. Based on Equation 3.28, the maximum
effective refractive index difference is found to be δ neff ,GI= 7.4 ×10−5 ncore which is
significantly smaller than that of a step-index multimode fiber. As shown in Fig. 3.3, the
36
contrast of the interferograms reduces slowly as the fiber length increases. The peak-topeak value around 3 GHz reduces by half after propagating through 1 km of graded-index
fiber. In comparison, it only takes 10 m step-index multimode fiber to decrease by half
1
1
1
0.9
0.9
0.9
0.8
0.8
0.7
0.7
0.7
0.6
0.5
0.4
0.3
Amplitude(a.u.)
0.8
Amplitude(a.u.)
Amplitude(a.u.)
from its original peak-to-peak value.
0.6
0.5
0.4
0.3
0.6
0.5
0.4
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0
0
1
2
3
frequency(Hz)
4
5
6
x 10
9
0
0
0
1
2
3
frequency(Hz)
4
6
5
x 10
0
1
9
2
3
frequency(Hz)
4
6
5
x 10
9
Fig. 3.3. Simulation of an OCMI implemented using graded-index multimode
fibers. All optical modes are equally excited. The core and cladding diameters of
the fiber are 62.5 and 125 mm, respectively. The refractive index of the core is
ncore = 1.488, and the index difference is ∆ = 0.02. The common electric length is
W = 1. (a) Amplitude spectrum when z1=10 m and z2=10.3 m. (b) Amplitude
spectrum when z1=100 m and z2=100.3 m. (c) Amplitude spectrum when z1=1000
m and z2=1,000.3 m.
The simulation results indicate that OCMI can be implemented using multimode
fibers. However, the modal dispersions will lower the quality of the interferogram by
decreasing the contrast of the fringes. The larger the modal dispersion is, the lower the
fringe contrast becomes. The dispersion effect is also accumulative along the fiber length.
The contrast decreases as the length of the multimode fiber increases.
37
CHAPTER FOUR
OCMI FOR SENSING APPLICATIONS
4.1
4.11
SMF based OCMI for sensing applications
Strain measurement using a SMF based Fabry-Perot OCMI
Optical fiber based FPI have been widely used in sensing application in the past
[61-65]. The two reflections at the two end surfaces of the FP cavity form an interference
pattern that is a function of the length and refractive index of the cavity. The length of the
cavity could be tens of micrometers so that the interferogram of the FPI could be better
resolved via optical instrumentation. If the length could be enlarged into tens of
millimeters, the interferogram of the FPI would be located into microwave region and it
might be clearly observed via microwave instrumentation. As a result, an OCMI based
FPI (OCMI-FPI) over optical fiber is developed. The novel OCMI-FPI can be applied
into specific applications, such as structural health monitoring, pressure sensor, liquid
level sensor or distributed sensing network.
Microwave modulated light
Optical partial
reflector #2
Optical partial
reflector #1
Path #1
Path #2
Fig. 4.1. One simply way to construct OCMI-FPI
There exist several ways to create OCMI-FPIs. One simple way is shown in Fig.
4.1. Two optical FPIs are connected with a separation of 2 meters. Each FPI consists of a
38
section of capillary tube with length of tens of micrometers, which is sandwiched
between two single mode fibers. The end faces of the two sections of optical fibers are
vertically cleaved before splicing to the capillary. Each FPI could be considered as one
reflector to the microwave signals travelling inside the fiber since the wavelength of the
microwave is way larger than the length of the tube. Seen by microwave, the optical FPI
is indeed a single reflector independent to microwave frequency although it has an
interferogram in optical spectrum.
A more simple way of implementing a FP based OCMI is shown in the inset of
Fig. 4.2 (b). The FPI had a cavity length (i.e., the distance between the two reflectors) of
about 2 m with both ends cleaved. The lead-in fiber was angle cleaved to eliminate its
own reflection and connected to the EFPI sensor using a capillary tube [66]. Experiments
were carried out to demonstrate the strain sensing capability of sensor. In these
experiments, the VNA was configured to record the S21 signal with 16001 equally
sampled data points. The intermediate frequency bandwidth (IFBW) was set to be 500 Hz.
The frequency sweeping range was from 1 to 3 GHz. One end of the SMF was fixed to a
motorized stage (PM500, Newport) through all-purpose glue, and the other end was fixed
to a 3D adjustable stage. The distance between the two fixing points was set as 2 m. The
S21 spectra were constantly captured by the VNA as the distance between the two points
was increased step by step. Time domain response was obtained by applying a complex
and inverse Fourier transform to the S21. A width of 24-ns time domain band pass filter,
centered at the middle point of the two time domain pulses, was applied to the signal.
39
The inset of Fig. 4.2 (a) shows the amplitude spectrum of the S21 after the filtering
when there was no applied strain to the sensing arm. A high quality microwave
interferogram was obtained, with fringe visibilities exceeding 40 dB and a FSR of about
40 MHz. The long interferometer was tested as a strain sensor. Fig. 4.2 (a) shows the
interference fringes at different applied axial strains. The fringe moved towards the low
frequency regime as the strain increased, indicating the optical length of the
interferometer increased correspondingly. Fig. 4.2 (b) plots the frequency shift as a
function of the applied strain at a step of 100 µε. The frequency shift varied with the
applied strain linearly with a slope of -2.37 kHz/µε. This monotonic, linear relation
0.0
Increasing steps
Iinear fit
-0.2
0 me
100 me
200 me
300 me
400 me
500 me
600 me
700 me
-30
-40
-50
-60
-70
1000
1100
1200
1300
1400
Spectral shift (MHz)
-30
-35
-40
-45
-50
-55
-60
-65
-70
-75
-80
Amplitude (dB)
Amplitude (dB)
clearly demonstrated the potential of using the OCMI for strain sensing.
1742
Slope: 2.37 KHz/me
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
1500
Frequency (MHz)
1740
-0.4
1744
1746
1748
Frequency (MHz)
0
100
200
300
400
Strain (me)
500
600
700
Fig. 4.2. SMF extrinsic Fabry-Perot OCMI for strain sensing. (a) Zoom-in
microwave interferograms under various applied axial strain (inset: interferogram
observed in the frequency range of 1 - 1.5 GHz, (b) Spectral shift as a function of
applied strain (inset: schematic of the Fabry-Perot interferometer with a length of
2 m.
40
4.12
Characterization of Sensing Performance at High Temperature
4.121 SMF based Michelson OCMI
SMF Michelson OCMI configuration was used for temperature sensing
characterization. Fig. 4.3 (a) shows the schematic construction of a SMF Michelson
OCMI with a length difference of 29 cm. The light is first splitted into two paths by a
3dB 2x2 SMF coupler. The two light beams travels along a distance and are reflected
back by two reflectors of the two paths. The two reflected beams are then recombined at
the coupler. The superposition of the two beams results in an interference signal that is a
function of the OPD between the two different paths. The time resolved reflections from
two endfaces of these fibers are shown in Fig. 4.3 (b). It is clear that the reflections from
two the endfaces are very close to each other. Fig. 4.3 (c) plots the microwave
interference spectrum from this SMF Michelson interferometer. The fringe visibility is
30~40 dB showing an excellent signal to noise ratio (SNR). There are many methods to
create the reflectors, and we directly use the two endfaces of the SMF fibers as reflectors.
The fringe visibility of the interference pattern is controlled by the fact if the two
reflected intensity is balanced.
Fig. 4.3 (b) clearly shows two balanced reflection
resulting in a high fringe contrast shown in Fig. 4.3 (c).
41
Input
2x2 coupler
R1
29 cm fiber
R2
(a)
Output
(c)
(b)
Fig. 4.3. (a) Schematic of a Michelson OCMI implemented using SMFs. (b) Time
domain signal after applying a complex and inverse Fourier transform to the microwave
amplitude and phase spectra (c) Microwave interferogram of the Michelson OCMI,
showing a visibility exceeding 40 dB.
4.122 Sensitivity characterization
The single mode fiber Michelson interferometer was characterized by placing it
into a programmable tube furnace. The whole part of Michelson interferometer
(difference of the two reflection path lengths) works as a sensing element, which can
survive at high temperature. Fig. 4.4 shows one interference fringe valley at different
temperatures from 50 to 900 °C at an increment of 50 °C. The fringe moved towards the
low frequency regime as the temperature increased, indicating the optical length of the
42
interferometer increased correspondingly. The sensitivity is defined as the relative
frequency shift in response to certain temperature variation. Based on the observation
from these high quality spectra in Fig. 4.4, we believe that SMF based Michelson OCMI
has a relatively high sensitivity and thus a high measurement accuracy can be obtained
due to the high measurement resolution provided by VPN system.
Fig. 4.4. Interference spectra at various surrounding temperature increase from 50
to 900 °C.
A fourth order polynomial curve fit was used to find the minimal point of each
fringe. The resonant frequency shift of the OCMI based Michelson interferometer as a
function of ambient temperature is shown in Fig. 4.5. Linear regression was used to fit
the response curve function and the slope of the fitted line was computed to find the
temperature sensitivity. The temperature sensitivity of this particular interferometer was
43
estimated to be -37.38 kHz/°C in terms of frequency shift versus temperature at
resonance frequency around 3770 MHz. The bandwidth for VNA frequency sweeping
was 30 Hz and the sampling point in this test was 1600 points. It is expected that higher
sensitivity can be achieved using larger resonance frequency and better resolution can be
obtained using dense sampling points. This temperature test demonstrates our proposed
OCMI fiber interferometer can be used as a high temperature sensor with excellent signal
quality and high temperature sensitivity. This monotonic, linear relation clearly
demonstrated the capability of using the OCMI system for temperature sensing.
Fig. 4.5. Temperature-induced resonant frequency shifts of the OCMI based
optical fiber Michelson interferometer.
4.123 Stability and Reversibility Test
44
The stability of the SMF Michelson interferometer was characterized by
programming the tube furnace. In our test, the temperature heat-up speed was set to be
100 °C per 15 minutes, and the dwelling time at each specific temperature was 80
minutes during the temperature increasing process. For temperature decreasing process,
due to the fact that much longer recovery time is needed for relatively lower temperature,
the temperature decrease speed was set at 100 °C per 30 minutes for 400 and 300 °C and
dwelling time at 200 °C was set to 120 minutes in order to fully stabilize the temperature
in tube furnace. Some abrupt temperature changes are due to the limited programmable
steps from our tube furnace.
Fig. 4.6 shows the stability test results of the OCMI Michelson interferometer
during the whole temperature increasing and decreasing procedure. The resonant
frequency of each spectrum was recorded constantly every minute. It is clear that the
temperature increasing, decreasing and stabilizing process can be easily and clearly
distinguished shown in this figure. Based on the experimental data, the sensor stability
can be characterized by reading the frequency variation values directly from Fig. 4.6. It is
estimated that the temperature variation range is around3 °C during the whole test
process, demonstrating that the OCMI Michelson interferometer has a relatively high
stability even under very high temperature environment.
45
Fig. 4.6. Stability test of the OCMI based optical fiber Michelson interferometer at
different temperatures (100 ~ 1100 °C).
The reversibility of OCMI Michelson interferometer was also characterized by
recording and comparing the resonance frequency shifts during temperature increasing
and decreasing process. The experimental data was acquired from Michelson
interferometer, with maximum temperature reaching 900 °C and the experimental result
was plotted in Fig. 4.7.
The OCMI Michelson interferometer was firstly tested at temperature increasing
condition, and before the temperature was decreased, this device was kept under 900 °C
for 24 hours, with resonance frequency shifted a little bit to lower frequency region.
Basically, the recorded decreasing temperatures matched well with those taken at
increasing procedure, meaning good reversibility can be realized for this temperature
sensor, and no obvious optical hysteresis was found.
46
Fig. 4.7. Repeatability test of the OCMI based optical fiber Michelson
interferometer.
4.2
4.21
Special optical fiber based OCMI for sensing applications
Single crystal sapphire optical fiber for high temperature application
Silica glass optical fibers have been extensively used for sensing applications in
the past few decades, showing advantages such as low loss, light weight, immunity to
electromagnetic interference, and resistance to corrosion [67]. However, when used in
harsh environments, especially in high temperatures above 1000 °C, the softening of the
silica glass material and the diffusion of the dopants (e.g., Germanium) inside the fiber
core raised a concern on the long-term stability of the sensors. For better survivability
and stability in high temperatures, single-crystal sapphire optical fibers have been used
for sensor development due to their high melting point (2040 °C) and hardness [68-70].
47
Sapphire material has low transmission loss in a wide spectrum range and a large
numerical aperture [71]. The early sapphire optical fiber sensors utilized these features
for temperature measurement by coating the fiber tip with a thin layer of metal and
monitoring the blackbody (thermo) radiation [72-75]. The blackbody radiation based
temperature measurement worked well at high temperatures but had low resolution at the
low temperature region. Later, various sensor devices, e.g., fiber Bragg gratings [76-78]
and Fabry-Perot interferometers [79-83], have been developed using sapphire fibers
aiming to enhance the measurement resolution as well as for measurements of other
parameters such as strain and pressure.
However, sapphire fibers are highly multimode owning to their large core
diameters, uncladded structure and large numerical apertures. As a result, it is generally
very difficult to make sapphire sensors with satisfactory performance. Despite high
temperature coatings [84] have been developed to improve the waveguiding properties by
decreasing the numerical aperture to a certain degree, the optical mode number was still
as large as the conventional multimode fiber. Because of the multimodal influence, it is
difficult to fabricate a Bragg grating or an interferometer using a sapphire fiber with good
signal quality. For example, to construct a Fabry-Perot interferometer on a sapphire fiber,
the two reflectors must be precisely fabricated with good smoothness and aligned exactly
in parallel. An angle of 10-2 misalignment could reduce the fringe visibility significantly
[85]. In addition, the input light source must be well collimated to reduce the number of
excited optical modes. While most of the sapphire fiber sensors are based on optical DC
detection, the background blackbody radiation in the sapphire material at high
48
temperatures may severely interfere with the sensors’ signals. In summary, the
combination of multimodal influence, requirement of high fabrication precision and
interference of background blackbody radiation have placed a bottleneck on the
development of high quality sapphire fiber sensors.
By interrogating an optical interferometer in microwave domain, the OCMI
concept integrates the strengths of optics and microwave, providing several unique
features that are particularly advantageous for sensing application, including low
dependence on the types of optical waveguides, insensitive to variations in optical
polarizations, high signal quality, relieved fabrication requirements, and spatially
continuous distributed sensing. In addition, OCMI uses coherent detection in which the
modulation, detection and demodulation are all synchronized and phase-locked to the
same microwave frequency. The influence of background blackbody radiation can be
drastically reduced when the sensor is used in high temperatures.
In this section, a microwave interrogated sapphire fiber Michelson interferometer
is reported for high temperature sensing using OCMI technology. Unlike the traditional
two-tap optical interferometers which are primarily implemented on single-mode fibers
for sensing or microwave filtering applications [86], we have successfully demonstrated
its possibility on a highly multimode optical fiber (i.e., sapphire fiber) and proven its
effectiveness for sensing applications. The OCMI concept can also be implemented for
other types of sapphire fiber interferometers such as a Fabry-Perot or Mach-Zehnder
configuration. Other than the optical fiber based sensors, the OCMI concept could be
49
potentially used in free space. The interferometric sensor can also be used for
measurement of other parameters such as strain and pressure in high temperatures.
While there are many ways to implement the OCMI concept, Fig. 4.8 illustrates
an example system configuration where a microwave VNA is used as the microwave
source and signal detector. A broadband light source (BBS) with the bandwidth of 50 nm
is intensity modulated using an electro-optic modulator (EOM) driven by the microwave
signal from the Port 1 of a VNA (HP 8753es). The VNA output is amplified to achieve a
high modulation index. A fiber inline polarizer and a polarization controller are used for
better modulation. The modulated light is then sent into an optical interferometer (the
sapphire fiber sensor) whose output is detected by a high speed photodetector. The
photodetector has a detection bandwidth of 6 GHz and a detection area of 62.5 μm in
diameter. A 3 dB fiber coupler is used to route the input microwave-modulated light into
and the output signal out of the fiber sensor. After DC-filtering, the photodetector output
is connected to Port 2 of the VNA, where the amplitude and phase of the signal are
extracted. By sweeping the VNA frequency, the microwave spectrum of the sensor is
obtained (i.e., the S21 of the VNA).
A single crystal sapphire fiber based OCMI Michelson interferometer was
demonstrated for measurement of high temperatures. As shown in the inset of Fig. 1, the
Michelson interferometer was made by fusion splicing two sapphire fibers onto the two
leads of a 3 dB, 2×2 multimode fiber coupler. The fiber coupler was made of gradedindex fibers with core and cladding diameters of 62.5 and 125 μm, respectively. The
50
single crystal sapphire fibers (MicroMaterials, Inc.) were uncladded with a diameter of
125 μm. The two leads of the multimode fiber couplers were cleaved to have the same
length. The lengths of the two sapphire fibers were about 70 and 85 cm, respectively. The
far ends of the sapphire fibers were fine polished.
Fig. 4.8. Schematic of an OCMI interrogation system. VNA: Vector network
analyzer. BBS: Broadband source. PC: Polarization controller. EOM: electro-optic
modulator. MA: Microwave amplifier. PD: Photodetector. Color inset: Schematic of the
sapphire fiber based Michelson OCMI.
The incident microwave-modulated light is first split into two paths through the
fiber coupler. One beam is reflected from the endface of the sapphire fiber #1; the other
beam is reflected from the endface of sapphire fiber #2. The two reflected beams are then
recombined at the fiber coupler. The superposition of the two beams results in an
interference signal that is a function of the OPD between the two different paths. The
51
OPD of the proposed interferometer is longer than the coherence length of the optical
source but shorter than the coherence length of the microwave source. As such, the
optical carrier waves build up incoherently while the microwave signals (envelopes)
build up coherently to form an interferogram in the microwave domain.
The detected signal given in Equation 2.2 includes three terms: the DC,
microwave and optical terms. When the OPD = LO1 – LO2 is sufficiently larger than the
coherence length of the optical source, the integral term of the optical contribution
approaches zero. The synchronized detection at the microwave frequency eliminates the
DC term to provide the amplitude and phase of the microwave signal in Equation 2.2. By
scanning the frequency, the microwave amplitude and phase spectra can be acquired. The
microwave amplitude spectrum (i.e., microwave interferogram) can be analyzed to
determine the OPD and/or its changes for the purpose of sensing.
To reduce the reflection and the transmission attenuation of the joint of silica and
sapphire fibers, the sapphire fibers were permanently fusion spliced to the two lead silica
fibers of the coupler. A large-core fusion splicer (3SAE) was used to precisely push the
sapphire fiber step by step while heated. Then the joint was gradually annealed to release
the stress caused by the fusion.
In the experiment, the intermediate frequency bandwidth (IFBW) and the
sampling point of the VNA were set to be 700 Hz and 16001, respectively. The IFBW
stands for the spectral resolution of VNA. The driving power from port 1 was 4 dBm.
The microwave frequency was swept from 2 to 5 GHz. Without taking averages in data
52
acquisitions and processing, it took about 7 seconds to acquire a microwave spectrum
(S21). Fig. 4.9 shows the time domain signal after applying a complex and inverse Fourier
transform to the recorded microwave spectrum. The first peak represents the reflections
from the fusion points between silica and sapphire fibers. Because the two splice points
have almost the same length measured from the coupler, the two reflections generated at
the splice points were inseparable in the time domain.
1.4
Reflection (mUnit)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
80
90
100
110
120
130
Time (ns)
Fig. 4.9. Time domain signal after applying a complex and inverse Fourier
transform to the recorded microwave spectrum (S21).
The two other two peaks, representing the reflections from the two sapphire
endfaces at the far end, can be clearly identified. As illustrated in Fig. 4.9, a gate function
was applied in the time signal to cut out the two reflections from the sapphire fibers and
eliminate the reflections from the silica-sapphire joints. Then the cut-out data was
complex Fourier transformed to reconstruct the interferogram as shown in Fig. 4.10. This
53
interferogram is the result of the coherent superposition of the two far-end sapphire fiber
reflections in the microwave domain, i.e., the OCMI interferogram of the sapphire fiber
Michelson interferometer. The fringes are clean with a visibility exceeding 40 dB at the
microwave frequency of about 3500 MHz. It is obvious that the multimodal interference
in a sapphire fiber does not influence the interferogram in microwave domain, indicating
that the OCMI technology is basically insensitive to the multimodal influences. The
optical waves built up incoherently through which the OPD is much larger than the
coherence length of the light source, which could partially explain that OCMI has low
dependence on the multimode interference. The FSR was measured to be 571.5 MHz.
Based on the Equation 2.2, the OPD of the interferometer was calculated to be 52.50 cm.
Assuming 1.74 to be the effective refractive index of sapphire fiber, the length difference
of the two interferometer arms was estimated to be 15.08 cm, which agreed well with the
15 cm measured by a caliper.
54
Fig. 4.10. Microwave interferogram of the sapphire fiber Michelson OCMI showing a
visibility exceeding 40 dB at the microwave frequency of about 3500 MHz.
To avoid breakage and keep them in parallel during test, the two sapphire fiber
arms of the interferometer were inserted into a ceramic tube with an inner diameter of 0.5
mm. The ceramic tube hosted sensor was then placed in a programmable tubular electric
furnace for characterization of its capability for high temperature sensing. The
temperature was increased from 100 to 1400 °C and then decreased back to 100 °C at an
incrementing/decrementing step of 100 °C. As the surrounding temperature increased, the
OPD of the two beams increased due to the combination of the thermo-optic effect and
the thermal expansion of the sapphire material. The increase of OPD induced an
interference spectrum shift towards the lower frequency region.
Fig. 4.11 (a) and (b) show the interference fringes at different temperatures during
increasing and decreasing steps, respectively. The fringe moved towards the low/high
frequency regime as the temperature increased/decreased, indicating the optical length of
the interferometer increased/decreased correspondingly. It is interesting that the fringe
visibility and intensity did not change too much at temperatures lower than 1000 °C,
while it dropped dramatically when the temperature is above 1000 °C. One possible
reason is that heating over 1000 °C could have caused high-temperature oxidation of the
sapphire fiber, which resulted in a temperature-dependent scattering loss mechanism [87].
An interesting thing is that the oxidation will recover at cooling cycles indicated in Fig.
4.11 (b), where the fringes went back to their original waveforms indicating a good
55
repeatability. The deceasing of the fringe visibility at high temperatures is mainly due to
the unbalanced reflection from the two arms where they have different lengths in the
heated region experiencing different attenuation in high temperatures. It is clear that the
blackbody radiation of the sapphire fiber under high temperature did not influence the
interferogram in microwave domain. Although the large blackboard radiation will
influence the optical spectrum from visible to IR range, it functions as a DC-component
which could be eliminated during coherence detection.
100 °C
200 °C
300 °C
400 °C
500 °C
600 °C
700 °C
800 °C
900 °C
1000 °C
1100 °C
1200 °C
1300 °C
1400 °C
-50
Reflection (dB)
-60
-70
-80
-90
-100
-110
3600
3800
4000
4200
4400
Frequency (MHz)
1400 °C
1300 °C
1200 °C
1100 °C
1000 °C
900 °C
800 °C
700 °C
600 °C
500 °C
400 °C
300 °C
200 °C
100 °C
-50
Reflection (dB)
-60
-70
-80
-90
-100
3600
3800
4000
4200
Frequency (MHz)
56
4400
Fig. 4.11. Interference fringes of the sapphire fiber based OCMI at different
temperatures during (a) increasing and (b) decreasing steps, respectively.
Fig. 4.12 plots the center frequency of the interferogram valley at about 4300
MHz at different ambient temperatures. A non-linear relation was observed. The higher
the ambient temperature, the slightly larger the temperature sensitivity became. The
average temperature sensitivity of the sapphire fiber sensor was estimated to be -64
kHz/°C, demonstrating that the developed sapphire fiber Michelson OCMI could be used
as a high temperature sensor with good sensitivity. The temperature responses at the
increasing and decreasing cycles also agreed well and showed no obvious hysteresis,
indicating a good reversibility of the temperature sensor. The stability of the sapphire
fiber sensor was also characterized. The sensor was placed inside the furnace at room
temperature. The resonant frequency of the sensor was constantly recorded for several
hours and the standard deviation was calculated to be ± 30 KHz, corresponding to a
temperature variation of ± 0.5 °C, or a relative measurement resolution of 1.4×10-5
around 4300 MHz. The results demonstrate good stability of the proposed sensor for high
temperature sensing.
57
Fig. 4.12. The center frequency of the interferogram valley at about 4300 MHz at
different ambient temperatures during the temperature increasing and decreasing cycles.
The stability of the sapphire fiber sensor was also characterized. The sensor was
placed inside the furnace with temperature rising rate of 200 °C per 30 minutes. The
dwelling time at each temperature step was set to be 4 hours during the temperature
increasing process. Parts of the experimental results of the stability test. Fig. 4.13 (a) and
(b) show the recorded sensing data in the duration of more than one hour at 800 and
1000 °C, respectively. Based on the experimental data, the standard deviation of
frequency at 800 and 1000 °C were calculated to be ± 0.13 MHz, corresponding to a
temperature variation of ± 2.9 °C, or a relative variation of 3.47×10-3. The standard
deviation of frequency at 1000 °C was calculated to be ± 0.12 MHz, corresponding to a
58
temperature variation of ± 2.7 °C, or a relative variation of 3.20×10-3. The results
demonstrate good stability of the proposed sensor for high temperature sensing.
Fig. 4.13. (a) Stability test of the sapphire fiber based Michelson OCMI at (a)
800 °C and (b) 1000 °C.
In summary, a microwave interrogated sapphire fiber Michelson interferometer
was demonstrated for high temperature sensing. Using the OCMI technology, a high
quality interference spectrum of the sapphire fiber interferometer was obtained with a
fringe visibility exceeding 40 dB in microwave domain. The sensor was tested from 100
to 1400 °C, showing good sensitivity, reversibility and stability for high temperature
59
sensing. By interrogating the optical interferometer in microwave domain, the OCMI
technique offers many unique features including low dependence to the multimodal
influences, high signal quality, relieved fabrication precision, and insensitivity to
background blackbody radiation when the sensor is used in high temperature. It is
envisioned that the proposed technique can be implemented in other types of sapphire
fiber interferometers for measurement of various parameters in high temperature harsh
environments.
4.22
Polymer optical fiber for large strain measurement
Fiber optic strain sensors have unique advantages such as high signal-to-noise
ratio, light weight, small size, and insensitivity to ambient electromagnetic fields. Many
fiber optic strain sensors have been reported [88, 89] and some of them are commercially
available [90]. So far, glass singlemode optical fibers have been exclusively used to
implement the aforementioned distributed sensing techniques due to their low loss and
well-defined optical characteristics. However, glass optical fibers are fragile and can
easily break when they are subjected to a large strain and/or a shear force due to their
small size and brittleness, causing serious challenges for sensor installation, embedment
and operation. As a result, glass optical fibers have to be rigorously packaged when they
are used for SHM. In addition, glass optical fiber sensors have small dynamic range
(~4000 µɛ) due to the limited deformability of silica materials. As a result, optical fiber
strain sensors have limited applications, especially in some highly loaded engineering
structures, such as bridges, buildings, pipelines, dams, offshore platforms, etc. A fiber
optic strain sensor with large dynamic range is highly demanded.
60
Recently, polymer optical fibers (POFs) as strain-sensing substrates have attracted
many attentions. POFs, also commonly referred to as plastic optical fibers, have been
explored for sensor development by taking the advantage of their inelasticity. Comparing
to glass fibers, POFs have much better flexibility and deformability. As a result, POF
based sensors are expected to have the necessary robustness and large strain capability
desired for SHM. It has been shown that POF sensors can measure strain up to 15.8%
[91-96]. However, most of commercially available POFs are multimode, making it
impossible to be utilized in the aforementioned distributed sensing technologies due to
the strong multimode interference and large modal dispersion. New sensing concepts are
required to harvest the unique properties of POFs for distributed sensing. Aside from
their great optical performance as optical fibers, their flexibility and deformability make
them possible to sustain a large strain load. Similar fiber sensor structures have been
successfully implemented using POFs. For example, Liu et al implemented a Bragg
grating structure in a single mode POF with a >28 dB signal-to-noise ratio [97]. The
Bragg wavelength shifted a 52 nm in response to a 3.61% axial strain. Recently, a Bragg
grating has also been successfully fabricated on a microstructured POF for large strain
measurement [98] with high resolution. In addition, the dynamic characterization of the
POF has also been investigated. It was found that the POF based strain sensor has a
limited frequency response due to its viscoelastic property.
Although great efforts have been made to improve the performance of POF, the
commercially available single mode POFs currently are still expensive. Microstructured
POFs are even more difficult to fabricate. As such, it is desired to use regular multimode
61
POFs for sensor construction. The optical time domain reflectometry (OTDR) response
of standard multimode POFs has been investigated and a detailed analysis to understand
the optical loss mechanism has been performed [99]. A Time-of-flight measurement was
conducted in order to monitor the strain in an aircraft using multimode POF [100]. More
recently, a singlemode-multimode-singlemode fiber structure was proposed to realize
large strain sensing using multimode POF [101].
So far, most of the existing strain sensors based on multimode POFs use timedomain signal analysis by measuring the transmission loss. In general, optical loss based
measurement is difficult to achieve high accuracy. Here we discuss a new type of
multimode POF strain sensor which uses OCMI technology. An axial tensile strain
applied to the MMF would produce a shift in the microwave spectrum of the POF based
OCMI as a result of the photoelastic effect. The OCMI provides a high resolution and
low dependence to the multimodal influence while the multimode POF offers a large
dynamic range. The combination of these two might provide a solution for some
challenging issues faced in many applications.
The interrogation system was based on the aforementioned one shown in Fig. 2.2.
The POF has a core of 240 µm and a cladding of 10 µm in diameter. A section of POF
without buffer layer with a length of 160 mm was vertically cleaved on both ends by a
commercial preheated blade. A piece of silica MMF (core/cladding 105/125 μm) with the
end face cleaved was spatially aligned to one end face of the POF with a separation of
several micrometers using a motorized 3D translation stage. A drop of optical adhesive
62
(Norland optical adhesive, NOA 85, refractive index ~1.46 @1550 nm) was used to fill
the gap to reduce the transmission loss. By exposing the optical adhesive to ultraviolet
light for 30 seconds, the NOA was solidified and the MMF was attached to the POF. The
same method was used to attach the other end face of the POF to a second MMF. The
two attach points can be considered as two partial reflectors forming a FPI structure as
shown in Fig. 4.14.
R2
R1
Polymer optical fiber
Superglue
Fig. 4.14. Polymer optical fiber based OCMI-FPI
The applied strain in the POF will induce a change in the length (ΔL), core radius (Δa),
and refractive index of the core (Δnco) in microwave domain, which can be expressed as [102],
∆L =Lse
∆a =−vae
n3
∆nco =
− co [ p12 − v( p11 + p12 ) ] e =
−nco Peff e
2
(4.1)
where Ls is the sensing length of the POF; ɛ is the applied strain; a is the core radius; v is
the Poisson ratio of the POF; nco is the RI of the core; p11 and p12 are the Pockel’s coefficients of
the stress-optic tensor; Peff is the effective strain-optic coefficient.
When an axial force is applied to the POF, a wavelength shift will be introduced because
of the changes in fiber dimension and refractive index. The strain induced frequency shift ΔfS can
be expressed as follow (based on Equation 4.1),
63
∆f S =−
Ls
Lt
 ∆nco
Ls
∆a ∆L 
 n + 2 a + L  f =− L ( Peff + 2v + 1) e f
s 
t
 co
(4.2)
where f is the interrogated wavelength; Lt is the total length of POF. The typical values of
Peff and v for PMMA based POF are 0.099 (±0.0009) and 0.35-0.45, respectively. The negative
sign indicates that the axial strain to the POF will cause a blueshift in the transmission spectrum.
A quick calculation based on Equation 4.2 revealed that the anticipated slope of the strain
response at the wavelength of 1570 nm is -2.82 pm/µɛ (assume Ls / Lt = 1, v = 0.35).
The strain-temperature crosstalk is always a concern for strain sensors. The frequency
shift ΔfT caused by temperature variations is
dn 

fT f  α n +
∆=
 ∆T
dT 

(4.3)
where α (~3.3×10-5 /°C for PMMA) is the coefficient of thermo expansion (CTE); dn/dT
(~1×10-5 /°C for PMMA) is temperature induced dielectric constant change of the POF; n is the
effective reflective index of the core of the POF in microwave doamin; ΔT is the change in
temperature. An increase in temperature will cause a redshift in the transmission spectrum, and
the slope is determined by the characteristics of the POF. Assuming ΔfS = ΔfT, the temperaturestrain crosstalk of the sensor is given by
dn 

×106
Lt  α n +

µe
dT 
= − 
∆T
Ls ( Peff + 2v + 1)
64
(4.4)
Using typical parameters of PMMA POF, the crosstalk µɛ/ΔT is calculated to be about 33
µɛ/ºC (assume Lt / Ls = 1). As a result, the temperature-strain crosstalk is an issue for the POF
sensor and it may introduce a measurement error in a temperature-uncontrolled environment.
The reconstruction microwave interferogram of the POF-OCMI is shown in Fig. 4.15.
The fringe visibility is around 15 dB which is lower than other type of OCMIs. It is because it is
difficult to make the two reflections balanced based on the mentioned fabrication method. Other
methods of engineering built-in reflectors need to be investigated.
The POF was tightly attached to two translation stages at two points using all-purpose
glue. The length between two attaching points, considered as the sensing length, was precisely
controlled to 100 mm. The microwave spectra of the POF based OCMI structure were recorded
and the distance between the two points was increased step by step. The inset of Fig. 4.16 shows
the spectral shift as the tensile strain increased at a step of 0.3%. The increasing strain did not
incur any significant loss in the microwave spectra. The increasing axial strain induced a shift to
the lower frequency region as predicted by Equation 4.2.
By applying a 4th order polynomial curve-fitting and monitoring the notch of the
microwave spectra, the frequency shift was plotted as a function of the axial strain. Fig. 4.16
shows the frequency shift at a total applied strain of 2.1×104 µɛ (2.1% without break) with an
increasing step of 3000 µɛ. The strain-wavelength response was quite linear, indicating that it can
be used as a strain sensor after proper calibration. The total shift in interference spectra was ~67
MHz in response to the 2.1% strain. The slope of the strain-wavelength was -3.19 KHz/µɛ
interrogated at the frequency of 4000 MHz, which agreed with the theoretic predicting according
to Equation 4.2. The sensitivity of the POF based OCMI sensor was similar to that of the POF-
65
based Bragg gratings [8, 9]. With good linearity, decent sensitivity and a large dynamic range, the
POF based OCMI may find many applications in structural health monitoring after proper
calibration and temperature compensation.
-57
Reflection (dB)
-60
-63
-67
-70
-73
-77
-80
3000
3500
4000
4500
5000
Frequency (MHz)
Fig. 4.15. Microwave interferogram of the POF Fabry-Perot OCMI showing a
visibility exceeding 15 dB at the microwave frequency of about 4000 MHz.
10
0.0%
0.3%
0.6%
0.9%
1.2%
1.5%
1.8%
2.1%
-62
0
Reflection (dB)
-64
-10
∆ƒ (MHz)
-20
-66
-68
-70
-72
-30
-74
3900
3950
4000
4050
4100
Frequency (MHz)
-40
-50
Slope = 3.16 KHz/µe
-60
-70
0.0
0.5
1.0
1.5
Strain (%)
66
2.0
2.5
Fig. 4.16. Frequency shift as a function of applied strain. The inset shows the
microwave spectra at various applied strain.
67
CHAPTER FIVE
OCMI BASED DISTRIBUTED SENSING
5.1
Review of the state-of-the-art technologies
Critical civil infrastructures in the U.S. are deteriorating at an alarming rate. They
are also in a state of disrepair due to inadequate maintenance, excessive loading and
adverse environmental conditions. The safety and reliability of critical civil
infrastructures have become a major public concern. In addition to handling the normal
loads, civil structures are also potentially subject to unexpected forces from nature and
human disasters such as earthquakes, hurricanes, tornados, floods and terrorist attacks.
These excess loads and lack of maintenance could potentially lead to structural
failures/collapses. Catastrophic failures can be prevented by detecting intermediate
damage such as fatigue, structural cracking and excessive deformations using structural
health monitoring (SHM) techniques [103-105].
Oftentimes, comprehensive assessments of the structural health status require
distributed sensing techniques with high measurement resolution, large dynamic range,
robustness, and spatial continuity. In general, spatially distributed information can be
acquired by either grouping/multiplexing a large number of discrete sensors or by
sending a pulsed signal to probe the spatially resolved information as a function of timeof-arrival. The following summarizes a number of existing techniques and their latest
advancements as well as limitations for distributed sensing.
68
A large number of point sensors (e.g., hundreds) can be grouped together to form
a monitoring network, in which the sensors are deployed at different locations, uniquely
indexed, and connected/ interrogated through wireless or wired links [106-109]. For
example, the dynamic behavior of large scale civil infrastructures has been monitored
under normal and post-disaster conditions using dense deployment of wireless smart
sensors [110]. The unique advantages of networked sensors include the flexibility in
sensor deployment, heterogeneity in the sensor functions (i.e., inclusion of different types
of sensors), and hierarchy in group formation. On the other hand, networked sensors
only provide discrete sampling of the space, leaving dark zones in SHM. In addition,
such a monitoring network is complex, data massive and difficult to manage.
A number of sensors can be cascaded along a single cable (e.g., an optical fiber, a
coaxial cable or a twisted-pair wire). These sensors have their unique signatures (e.g.,
different frequency or wavelength) that can be unambiguously identified using a single
interrogation unit [111-113].
sensing.
This method is commonly referred to as multiplexed
Multiplexed sensing has the advantages of straightforward and fast signal
interrogation, and flexible choice of sensor functions. However, multiplexed sensing
only provides discrete sampling of the space. In addition, the number of sensors that can
be multiplexed in a system is constrained due to the limited bandwidth available. For
example, multiplexed fiber Bragg gratings (FBGs) have been widely used in SHM to
acquire spatially sampled information with high measurement resolution [114-116].
However, the maximum number of FBG sensors along an optical fiber is limited by the
bandwidth of the light source and the required frequency interval per sensor for
69
prevention of overlapped signals and crosstalks. Very recently, a wavelength scanning
time division multiplexing method has been demonstrated to interrogate 1000 ultraweak
FBGs for distributed temperature sensing [117, 118]. However, the measurement was
still quasi-distributed or spatially interrupted. In addition, the spatial resolution of the
system was 0.2 m limited by the pulse width and crosstalks.
In the past few decades, optical fibers have been widely used for various sensing
applications due to their low loss, light weight, immunity to electromagnetic interference
(EMI), and resistance to corrosion. One of the most attractive features of optical fiber
sensing is its capability of measurement of spatially distributed parameters. In general,
optical fiber based distributed sensing can be implemented either by multiplexing a large
number of discrete sensors to form a spatially-distributed measurement network or by
sending a pulsed signal to probe the spatially-resolved information as a function of timeof-arrival.
In multiplexed sensing, or the so-called quasi-distributed sensing, many discrete
sensors are cascaded in series along a single optical fiber. The signals of the sensors are
unambiguously demodulated either in time or frequency domain. For example, fiber
Bragg gratings (FBGs) have been cascaded along a single fiber for multiplexed sensing.
The cascaded FBGs can have different Bragg wavelengths so that their spectral shifts can
be unambiguously determined. Thousands of weakly reflecting FBGs can also be made
of the same resonant wavelength and interrogated using either optical time domain
reflectormetry (OTDR) [119] or optical frequency domain reflectometry (OFDR) [120].
70
In addition to FBGs, fiber optic interferometers (FOIs) can also be multiplexed. For
example, fiber Fabry-Perot interferometers (FPIs) of different cavity lengths have been
multiplexed onto a single fiber. Identification of the cascaded FPIs can be achieved by
Fourier transform of the optical interferogram in the spectral domain to obtain their
individual optical path differences [121-124]. Recently, it has been demonstrated that
cascaded FPIs with the same or similar cavity lengths can be discriminated using
microwave assisted separation and reconstruction of the individual optical interferograms
in the spectrum domain [125]. One unique feature of the multiplexed sensing is that each
point sensor along the optical fiber can be flexibly encoded to measure different physical,
chemical and biological quantities. However, the current multiplexed sensing techniques
were still quasi-distributed or spatially interrupted, only providing discrete sampling of
the space, leaving dark zones among the sensors.
Another technique, known as the time domain reflectometry (TDR), has also been
widely explored for spatially continues sensing of various parameters in SHM. In TDR, a
pulsed signal is sent along a cable and the time/space resolved reflections are collected
and analyzed. The reflections can be from Rayleigh, Brillouin and Raman scatterings.
For example, a long-range spatially continuous Brillouin optical time-domain analysis
(BOTDA) measurement system was demonstrated with a spatial resolution of 2m over a
sensing length of 100km [126,127]. The unique advantages of TDR based distributed
sensing include long span of coverage and spatial continuity. However, the measurement
resolution of TDR is generally low due to the inherently weak scatterings. In addition,
71
the spatial resolution of TDR is about 0.5m limited by the pulse width of the interrogation
signal.
To improve the signal-to-noise ratio (SNR) and the spatial resolution of TDR,
OFDR has been proposed. In OFDR, a frequency-scanning, highly coherent source and a
Michelson interferometer are used to encode the time-of-arrival information into
frequency domain signals, which can be Fourier-transformed back to time/space domain.
The SNR and spatial resolution of OFDR are noticeably higher than the traditional TDR
method.
OFDR based Brillouin sensors have been successfully demonstrated for
distributed measurement of strain and temperature with good performance and excellent
spatial resolution. However, the measurement accuracy has been limited by the power
fluctuations and/or random changes in polarizations.
In addition, the measurement
distance of OFDR is about several hundred meters due to the availability of high-quality
light sources with both long coherence length and fine frequency scanning intervals.
5.2
Spatially continuous distributed fiber optic sensing using OCMI
Here we report our studies on using the OCMI technique for spatially continuous
distributed sensing [128]. Intrinsic FPIs formed by cascaded weak reflectors in an optical
fiber are used for the purpose of demonstration. It is expected that the proposed technique
can also be used for multiplexing other types of fiber interferometers. Distributed strain
sensing is used as an example in this paper. However, we believe that the interferometry
based system can be easily modified for distributed measurement of other physical,
chemical and biological parameters.
72
5.21
Concept of the spatially continuous distributed sensing
Fig. 5.1 shows the device and method of signal processing for distributed sensing.
Assume an optical cable comprises multiple reflectors. The first step is to obtain the
reflection spectrum of the whole cable including magnitude and phase information. For
example, the complex spectrum can be obtained from a conventional VNA). The next
step is to achieve its time domain information through a complex and inverse Fourier
transform to the measured reflection spectrum. This process functions as a joint-timefrequency domain reflectometry. Multiple reflected pulses (sinc-shaped pulses) could be
observed in time domain, and these reflections are corresponding to the location of each
reflector
along the cable. Select any two consecutive reflections through a gating
function in time domain to filter out or isolate the unwanted signals. The two reflections
in the applied window define a microwave FPI at a specific location. The interferogram
in spectral domain of the selected FPI can be obtained after applying another complex
Fourier transform to the time domain signal with gating. As such, the interferograms of
any FPI along the cable can be reconstructed and used for sensing application. The
sampling rate or total sampling point of the reconstructed spectrum must be drastically
decreased due to the applied observation window in time domain. This will further
influence measurement resolution. In order to get the same sampling rate or number of
point for the reconstructed spectrum, zero-padding needs to be added in time domain
after adding a gating function. Zero-padding in time domain will give better resolution in
spectrum domain and this is proved to improve the sensing performance in terms of
measurement resolution. The cable with multiple FPIs can be considered as a linear
73
superposition of many isolated FPIs with different initial distance. The applied
observation window is used for isolating the FPI of interest or suppressing/filtering out
the unwanted signal. Most of the information of the FPI is confined inside the applied
window in time domain. The applied zero-padding in time domain is just to recover the
original information of one isolated FPI on the entire length of the cable. In a sense, the
interferogram in spectral domain of each FPI can be reconstructed through this device
and method, and it can be used for sensing by correlating its path difference to the
parameters of interests. The FPIs can be designed to share the same bandwidth in spectral
domain so that the bandwidth of the source required frequency interval per sensor is not a
concern to this device and method. The maximum number of sensors is only determined
by the total transmission loss of the sensors and the cable. As a result, this device and
method combine the unique features of both conventional frequency domain
measurement and time domain multiplexing including a large capacity sensing network
and high measurement resolution.
74
Fig. 5.1. Joint-time-frequency domain interrogation of multi-point FPI in a single coaxial
cable for distributed sensing with high spatial resolution.
To implement the joint-time-frequency interrogation method on OCMI, Fig. 5.2
illustrates the fundamental concept of the spatially continuous distributed sensing
technique using cascaded inline OCMI-FPIs. The essence of OCMI is to read an optical
interferometer in microwave domain with its detailed description given in [59, 60].
As shown in Fig. 5.2, the light from a broadband optical source is intensitymodulated by a microwave signal whose frequency can be scanned via computer control.
The microwave-modulated light, where the optical is the carrier and the microwave is the
envelope, is then sent into (via a fiber optic circulator) an optical fiber with cascaded
weak reflectors. The optical reflections travel backwards, pass the fiber circulator and are
detected by a high-speed photodetector. The optical detection is synchronized with the
75
microwave frequency by a phase lock loop (PLL) so that the amplitude and phase of the
reflected signal can be resolved. After scanning the microwave frequency through the
entire available range, the reflection spectrum (with both amplitude and phase) is
obtained.
The inverse complex Fourier transform of the reflection spectrum provides the
time-resolved discrete reflections along the optical fiber. A time gating function with two
opening windows is then applied to the time series so as to “cut out” two arbitrary
reflections (e.g., Γi and Γj in Fig. 1) while suppressing other values to zero. These two
reflections are then Fourier transformed back to frequency domain to reconstruct a
microwave interferogram, which can be used to find the OPD between the two reflectors
(e.g., dij). The change in the OPD between these two reflectors (e.g., Δdij) can be
calculated based on the frequency shift of the microwave interferogram.
Light
Source
Microwave-modulated optical beam
Cascaded weak reflectors along
an optical fiber
Circulator
Modulator
Microwave
System
Synchronized PD
detection
Amplitude & phase
Signal processing
Γi
Time-resolved
reflections
along the POF
Γj
dij
Time gating to select
two arbitrary
reflections
Reconstructed
interference spectra in
microwave domain
Δf ∝ Δdij
Fig. 5.2. Schematic illustration of the fundamental concept of the spatially continuous
distributed sensing using cascaded FPIs. The segmentation is achieved by implementing a
time-gating function with two windows to isolate two arbitrary reflections (e.g., Γi and Γj)
76
for reconstruction of the microwave interferogram, whose spectral shift is proportional to
the length change of the segment between the i-th and j-th reflectors (i.e., Δdij).
Because any two reflectors can be chosen to form an OCMI interferogram,
spatially continuous distributed sensing can be realized by consecutively selecting two
adjacent reflectors along the cable. In addition, the base length of the interferometer can
be varied by choosing any two arbitrary reflectors (e.g., select 2 and 5 and suppress the
other reflectors). As such, the gauge length can be flexibly reconfigured during
measurement.
5.22
Modeling and simulations
Let’s start with an optical wave in the form of
Eo = A exp {− j [ωt + j ]}
(5.1)
where, t is the time; Eo is the electric field; A is the amplitude; φ is the phase; ω is the
angular optical frequency.
The microwave signal used to modulate the optical wave is given by
=
s(t ) M cos ( Ωt + φ )
(5.2)
where M is the amplitude, Ω is the microwave angular frequency, and ϕ is the phase.
The electric field of the light wave modulated by the microwave becomes
E = m(t ) Eo
where m(t) is the amplitude modulation term, given by
77
(5.3)
m(t )=
1 + hs(t ) = 1 + hM cos ( Ωt + φ )
(5.4)
where h is the modulation index, which falls in the range of 0 to 1.
The microwave-modulated light, in which the optical is the carrier and the
microwave is the envelope, is then sent into an optical fiber with cascaded reflectors. The
reflection of each reflector can be designed to be weak enough so that the light can be
transmitted over many sensors and the multiple reflections are negligible. The electric
field of the total reflected light wave is given by
N
=
Etotal
∑
=
Ei ( t , zi )
N
∑ m ( t, z ) E
i
i
o ,i
( t , zi )
(5.5)
=i 1 =i 1
where N is the total number of the reflectors. zi represents the location of the i-th reflector.
Note that in Equation 5.5, both the optical and microwave components are functions of
the locations (zi) of the reflectors.
The optical component (i.e., the electric field of the i-th optical reflection) in
Equation 5.5 is given by
   2 z n   
Eo,i ( t , zi ) =
Γi A exp  − j ω  t + i   
c   
  
(5.6)
where Γi is the amplitude reflection coefficient of the i-th reflector seen by the
photodetector; c is the speed of light in vacuum; n is the effective refractive index.
The microwave amplitude modulation term in Equation (5) is
78
  W 2 z n 
1 + hM cos W  t + + i  
c
c 
 
m ( t , zi ) =
(5.7)
where the microwave envelopes include two delay terms. The first is the delay associated
with the common electrical length (W) of the microwave system and this delay is the
same for all the paths. The second delay term is the contribution from the optical
propagation delays at different reflectors.
Assume that the optical source has a broad spectrum width from ωmin to ωmax, the
total power of the superimposed optical waves of all the reflections is given by
ωmax
2
Etotal
=
2
N
∫ ∑
ω
Ei ( t , zi ) d ω
=
=i 1
min
ωmax N
ωmax
N
∫ ∑ E ( t, z ) dω + 2ω∫ ∑
ω
2
i
min
=i 1
min
=i 1, =j 1,i ≠ j
(
)
E ( t , zi ) E t , z j d ω
(5.8)
where the first integral is the self-product term and the second integral is the crossproduct term.
Let’s first examine the cross-product term in Equation 5.8
ωmax
N
∫ ∑
(
N
=
∑
)
E ( t , zi ) E t , z j d ω
ωmin =i 1, =j 1,i ≠ j
(
)
m ( t , zi ) m t , z j Γi Γ j A
=i 1, =j 1,i ≠ j
2
ωmax
∫
ωmin


 2ω
( z1 − z2 ) n   d ω
2 cos 
 c


(5.9)
It is interesting to notice that the cross-product term is the optical interference
signal similar to a conventional all-optical interferometer. In the OCMI, the optical path
difference (OPD) is chosen to be sufficiently larger than the coherence length of the
optical source, i.e., ( z1 − z2 ) n >> 2π c (ω
max
− ωmin )
79
. Under this condition, the integral term in
Equation 5.9 approaches zero. In our experimental OCMI system, we used a light source
with a spectral width of 50 nm at the center wavelength of about 1550 nm, whose
coherence length was about 48 μm. A typical OCMI has an OPD of a few centimeters
that is much larger than the coherence length of a broadband light source. As a result, the
contribution from pure optical interference as depicted in Equation 5.9 is negligible in a
typical OCMI system.
The self-product term in Equation (8) is found to be
ωmax N
∫ ∑E (
ω
=
i 1
min
N
2 2
t , zi d ω =
Γi A +
=i 1 =i 1
)
2
N

∑ Γ A hM cos W  t + c +
∑
2
i
2
W
2 zi n  
c  
(5.10)
which includes a DC term and the summation of a series of sinusoids at the microwave
frequency of W .
The OCMI system uses synchronized detection to eliminate the DC term (first
term) in and record the amplitude and phase of the microwave signal (second term) in
Equation 5.10. As a result, the total signal after optoelectronic conversion by the
photodetector (with a gain of g) and synchronized microwave detection is given by
(
=
S Aeff cos Ωt + Φ eff
)
(5.11)
where
N
=
Aeff g
∑A
eff ,i Aeff , j
i, j
80
(
cos ff
eff ,i − eff , j
)



=
Φ eff arctan 


N
∑Γ
2
i sin
i
N
∑
Γi2

(feff ,i ) 
(
cos feff , j
i
)

,


Φ eff ∈ {−π , π }
Aeff ,i = Γi2 A2 hM , Aeff , j = Γ 2j A2 hM
And
 W 2z jn 
 W 2 zi n 
Γ 2j A2 hM  +
+
, feff , j =


c 
c 
 c
 c
feff ,i =
Γi2 A2 hM 
In Equation 5.11, Aeff and Φeff are the amplitude and phase of the microwave
signal, respectively. After scanning the microwave frequency through the entire available
range (from Ωmin to Ωmax), the complex microwave reflection spectrum (with both
amplitude and phase) is obtained. By applying a complex and inverse Fourier-transform
to the microwave spectrum, a series of cardinal sine functions are obtained at discrete
reflectors, given by:
1
=
Χ (t )
2p
=
1
2p
W max
∫
S exp ( jWt ) d W
W min
W max N
 
∫ ∑ Γ A hM cos W  t + c +
2
i
2
W min i =1
N
=
∑ Γ A hM sinc ( W
2
i
2
max
i =1
where τ=i
W 2 zi n
+
c
c
W
2 zi n  
  exp ( jWt ) d W
c 
(5.12)
− W min )( t + t i ) 
is the propagation delay of the signal corresponding to the i-th
reflector.
In Equation 5.12, the maximum amplitudes of the discrete sinc functions are
proportional to the reflectivity of the cascaded reflectors. In addition, Equation 5.12 also
81
provides the location information of the reflectors along the optical fiber. The peaks of
the sinc functions are at the specific reflector locations (zi) that can be found when the
delays (τi) are determined. The frequency bandwidth (Ωmax -Ωmin) determines the spatial
resolution, i.e., the minimum distance between two adjacent reflectors to avoid an overlap
of the two pulses in the time domain. The larger the microwave bandwidth, the narrower
is the pulse width (sinc function) in time domain and the higher is the spatial resolution.
A time gating function with two windows is then applied to time domain signal
given in Equation 5.12 so as to isolate two arbitrary reflections. The gate functions could
be designed to have different shapes such as rectangular, Hanning, Turkey, etc. Here we
generalize the gate function as g(t). The time domain signal after applying a gate function
is thus given by X(t)g(t). The gated signal is then Fourier transformed back to the
frequency domain to reconstruct the microwave interferogram, which can be used to find
the optical distance between the two reflectors (e.g., dij). The reconstructed OCMI-FPI
interferogram is thus given by
SOCMI = S ∗ G ( Ω ) exp ( −iΩτ 0 )
(5.13)
where G(Ω) is the inverse Fourier transform of the gate function g(t); τ0 is the
time delay of the gate function. As shown in Equation 5.13, the reconstructed microwave
FPI interferogram in spectrum domain is in essence a convolution of the microwave
signal S and G(Ω). Here we define the optical path difference (OPD) of the OCMI-FPI is
(
)
OPD= d=
2 zi − z j n
ij
82
(5.14)
The free spectral range (FSR) of the reconstructed interference spectrum is a
function of the OPD, given by
FSR =
c
OPD
(5.15)
Similar to an optical interference spectrum, the microwave amplitude spectrum in
the reconstructed OMCI-FPI can be used to find the OPD of an interferometer. It can also
be used to find the change in OPD based on the interference fringe shift.
Numerical simulations were performed to gain an intuitive understanding of using
the OCMI technique for distributed sensing. In the simulation, the fiber used was a
Corning SMF-28e singlemode fiber with the effective refractive index of the core of
1.468 according to the datasheet from the manufacturer. The microwave frequency was
chosen to be in the range of 0-6 GHz with 20000 equally-spaced sampling points. 8 weak
reflectors with equal reflectivity of 1% were implanted in the fiber at the discrete
locations of 0.30, 0.40, 0.60, 0.75, 0.80, 0.90, 1.20, 1.60 m, respectively. The common
electrical length of the microwave system was chosen to be 0.20 m.
Fig. 5.3 (a) and (b) plot the calculated amplitude (Aeff) and phase (Φeff) spectra
based on Equation (11). Fig. 5.3 (c) and (d) plot the calculated results based on Equations
5.12) and 5.13, respectively. As shown in Fig. 5.3 (c), the 8 reflectors can be clearly
identified at the corresponding locations. A Hanning window function was applied to the
time-domain signal shown in Fig. 5.3 (c) to cut out a section including the 4th and 5th
reflectors. The center of the Hhanning window was located at the center between the two
reflectors and the width of the window was chosen to be 1.22 ns. The cut-out section of
83
the time-domain signal was then Fourier transformed back into the frequency domain as
shown in Fig. 5.3 (d), where an interferogram can be clearly identified. The reconstructed
interferogram is the result of the microwave interference of the two reflected signals at
the 4th and 5th reflectors. The FSR was found to be 1.005 GHz, which matched well with
that calculated based on Equation 5.15.
In a similar way, any two reflectors can be cut out by applying a proper
windowing function. In essence, the two cut-out reflectors and the fiber section between
them defines a low-finesse fiber intrinsic FPI whose interferogram can be reconstructed
in the frequency domain. The reconstructed microwave interferogram can be processed to
find its OPD or changes in OPD for sensing applications. The location of the cut-out FPI
is also known because the positions of the two reflectors can be found in the time-domain.
Spatially continuous distributed sensing can be realized by consecutively selecting two
adjacent reflectors along the optical fiber. In addition, any two arbitrary reflectors on the
optical fiber can be selected to construct the interferometer. As such, the gauge length can
be flexibly reconfigured during measurement.
84
0.09
4
(a)
0.08
2
Phase (radians)
Magnitude (a.u.)
0.07
0.06
0.05
0.04
0.03
1
0
-1
0.02
-2
0.01
-3
0
(b)
3
0
1
2
3
4
frequency (Hz)
x 10
-3
5
-4
0
6
x 10
1
9
2
3
4
5
frequency (Hz)
6
x 10
9
-35
10
8
Amplitude (dB)
Amplitude (a.u.)
-40
6
4
2
1.5
-55
FSR
(d)
1.005
GHz
0
1
-50
-60
(c)
0.5
-45
-65
2
0
1
2
3
frequency (Hz)
Location (m)
4
5
6
x 10
9
Fig. 5.3. Simulation of 8 reflectors along a single-mode fiber. The optical reflectivity is
equally distributed. The locations of the reflectors are 0.5, 0.6, 0.8, 0.9, 1, 1.1, 1.4, 1.8m,
respectively. (a) Calculated amplitude spectrum (Aeff) based on Eq. 11. (b) Calculated
phase spectrum (Φeff) based on Equation 5.11. (c) Calculated time/spatial domain result
based on Equation 5.12. (d) Calculated microwave interferogram of the 4th and 5th
reflectors based on Equation 5.13.
5.23
Experimental demonstration
According to the aforementioned modeling and simulation results, the OCMI
interferogram of any two reflectors can be unambiguously reconstructed for spatially
85
continuous distributed sensing. To validate the proposed concept, we designed two
experiments based on cascaded optical fiber FPIs.
5.231 Strain measurement using OCMI-FPIs
As shown in Fig. 5.4 (a), 6 weak reflectors were implemented on a singlemode
fiber (SMF-28e) by intentionally misaligning the fibers during fusion splicing. The 6
reflectors divided the entire fiber into 5 measurement sections of different lengths as
schematically shown in Figure. The sensors were interrogated using the preliminary
OCMI system described in Chapter 2 except that an Erbium doped fiber amplifier (EDFA)
was inserted before the photodetector for additional signal amplification. The microwave
interference spectrum of the distributed sensors was first acquired and then complex
inverse Fourier transformed to obtain the time resolved reflections along the optical fiber
as shown in Fig. 5.4 (b), where the 6 reflections can be clearly identified at the time
intervals matching the section lengths. Using a time gating window, we isolated the two
reflectors defining Section 3 and reconstructed its microwave interferogram by complex
Fourier transform as shown in Fig. 5.4 (c), where interference fringes are clean and has a
visibility exceeding 25 dB, indicating excellent signal quality.
Distributed sensing
capability was tested by applying axial strains to Section 3 only. Fig. 5.4 (d) plots the 3D
view of the frequency shift of the interferogram as a function of the applied strain, where
the frequency decreases linearly as the strain increases. In contrast, the other sections
were left unstressed. As a result, no frequency shifts were observed along the fiber
86
outside Section 3. As shown in Fig. 5.4 (e), the FPI defined by Section 3 had a linear
response to the applied axial strain with a sensitivity of 2.26 KHz/με.
It is worth noting that the reflectors created by fiber misalignments had large
losses. As a result, the reflections were not even and their amplitudes dropped quickly. A
reflector with controlled reflectivity and negligible losses is needed so that better fringe
visibilities can be obtained for each section and the number of reflectors can be
significantly increased (thus a much longer monitoring span). Nevertheless, the
experiment results clearly show the capability of using OCMI-FPI for strain sensing and
the capability of locating the spatial position of the interferometer using the OCMI
technique.
87
Fig. 5.4. Validation of the distributed sensing capability of OCMI. (a) SMF distributed
sensors with 6 reflectors implanted to divide the entire length into 5 sections, (b) Time
resolved reflections along the optical fiber and time gating window to isolate Section 3,
(c) Reconstructed microwave interferogram of Section 3, (d) 3D view of the distributed
OCMI fiber sensor in response to axial strains applied to Section 3 only, and (e)
Frequency shift as a function of the applied strain.
88
5.232 Spatially continuous measurement of distributed strains
We also experimentally validated the spatially continuous distributed sensing
capability using cascaded optical fiber intrinsic Fabry-Perot interferometers (IFPI) as
illustrated in Fig. 5.5 (a), where 10 weak reflectors were inscribed inside the core of a
SMF using femtosecond (fs) laser micromachining. The fs laser is a regeneratively
amplified Ti: Sapphire laser (Coherent, Inc.). The central wavelength, pulse width and
repetition rate of the laser are 800 nm, 180 fs and 250 kHz, respectively. The maximum
output power of the laser is 1 W. The actual power used for fabrication was controlled by
adjusting the laser beam optics. The laser operation is fully controlled by a computer. A
microscopic video system is included in the system to observe the fabrication process in
real time. During fabrication, the lens and fiber were immersed in deionized water. The
focused fs laser beam penetrated into the fiber and ablated a small cuboid shape with the
dimension of 5 µm × 30 µm × 20 µm in the fiber core as shown in Fig. 5.5 (f). The
typical reflectivity of such a structure was about -45 dB and the loss was about 0.02 dB
measured by an optical power meter. The weak reflectivity and very small loss allow us
to cascade many reflectors along a fiber, enabling distributed sensing over a long distance.
The reflectors divided the fiber into 9 consecutive measurement sections. Each
section was an IFPI with a length of about 12 cm. The IFPI sensors were epoxied on the
surface of an aluminum cantilever beam with its length, width, and thickness of 1,250, 80,
and 9.10 mm, respectively. One side of the beam was clamped in a vice. The other side
was pushed by a micro-actuator to bend the beam and apply strain to the attached sensors.
89
The distance between the clamp and the micro-actuator was 1.14 m. As the cantilever
beam deflected, the amounts of axial strain seen by the IFPI sensors were different. The
mathematical model of the cantilever beam used to calculate the strain distribution can be
found in [83].
The complex microwave spectrum (amplitude and phase spectrum) of the
distributed sensors was first acquired as shown in Fig. 5.5 (b) and (c). Then complex
inverse Fourier transform was performed to obtain the distance-resolved reflections along
the fiber as shown in Fig. 5.5 (d), where the 10 reflections can be clearly identified and
their separations match the corresponding section lengths. Using a Hanning window, we
isolated the two reflectors defining Section 8 and reconstructed a microwave
interferogram by applying complex Fourier transform to the window-gated data. As
shown in Fig. 5.5 (e), the reconstructed interferogram is clean and has a visibility
exceeding 25 dB.
The weak reflectors were inscribed inside the core of a SMF using femtosecond
(fs) laser micromachining. The fs laser is a regeneratively amplified Ti: Sapphire laser
(Coherent, Inc.). The central wavelength, pulse width and repetition rate of the laser are
800 nm, 180 fs and 250 kHz, respectively. The maximum output power of the laser is 1
W. The actual power used for fabrication was controlled by adjusting the laser beam
optics. The laser operation is fully controlled by a computer. A microscopic video
system is included in the system to observe the fabrication process in real time. During
fabrication, the lens and fiber were immersed in deionized water. The focused fs laser
90
beam penetrated into the fiber and ablated a small cuboid shape with the dimension of 5
µm × 30 µm × 20 µm in the fiber core. The typical reflectivity of such a structure was
about ‒45 dB and the loss was about 0.02 dB measured by optical power meters.
The cantilever beam used for distributed strain measurement was made of an
aluminum plate. The length, width, and thickness of the plate were 1.25 m, 0.08 m, and
9.10 mm, respectively. One side of the beam was clamped in a vice. The other side was
pushed by a micro-actuator to bend the beam and strain the attached sensors. The
distance between the clamp and the micro-actuator was 1.14 m. The fs laser inscribed
cascaded IFPIs were epoxied onto the surface of the cantilever beam with a pre-strain of
about 300 μm. The amounts of axial strain seen by the IFPI sensors were different. The
deflections of the aluminum plate were increased at a step of 5 cm, measured by a caliper.
The mathematical model of the cantilever beam used to calculate the strain distribution
can be found in 20. An Erbium doped fiber amplifier (EDFA) was inserted before the
photodetector for additional signal amplification. No average was used in data
acquisitions and data processing.
91
x 10
-3
4
16
3
2
12
PhMse (rMdiMns)
MMgnitude (M.u.)
14
10
8
6
4
0
-1
-2
2
-3
0
1
2
3
4
5
frequency (Hz)
-4
0
6
x 10
1
2
3
4
5
frequency (Hz)
9
1.6
-60
1.3
-65
1.1
Aµplitude (dB)
Reflection (µUnit)
1
0.9
0.7
0.4
6
x 10
9
-70
-75
-80
-85
0.2
0.0
-90
1423
1462
1500
1538
DistMnce (cµ)
1577
500
1000
1500
2000
2500
3000
Frequency (MHz)
Axial strain
Measurement data
Fig. 5.5. (a) Schematic illustration of the experiment setup to validate the distributed
strain sensing capability of OCMI. (b) Amplitude spectrum and (c) phase spectrum of the
92
distributed sensor systems. (d) Time/distance resolved reflections along the optical fiber
where the 10 weak reflections can be clearly identified with excellent SNR. (e)
Reconstructed microwave interferogram of Section 8, where clean interference fringes
shows excellent visibility exceeding 25 dB. (f) Confocal microscopic image of a weak
reflector fabricated by femtosecond laser micromachining. Using water immersion
fabrication, the focused fs laser beam penetrated into the fiber and ablated a very small
region inside the fiber core. The reflector has a typical reflectivity of about -45 dB and a
typical loss of about 0.02 dB. (g) Measured strain distribution at the different sections
along the beam under different amounts of deflections. The strain increased at the
location that was closer to the clamped end of the beam. The strain also increased at the
same location as the deflection increased.
The deflections of the aluminum plate were increased at a step of 5 cm, measured
by a caliper. As the strain increased, the interferogram of each IFPI shifted
correspondingly. By tracking the frequency shift of the individual interferogram, the
changes in OPDs (thus the physical lengths) were calculated for all the consecutive
sections. The strain value of each section was calculated by dividing the physical length
change with respect to its initial length calculated based on the FSR of the interferogram.
Fig. 5.5 (e) shows the measured strains (black dots) of various sections along the
cantilever beam at the deflections of 5, 10 and 15 cm, respectively. The measurement
data agreed well with the statics model predictions, i.e., the mesh grids in Fig. 5.5 (g).
The strain increased at the location that was closer to the clamped end of the beam. The
strain also increased at the same location as the deflection increased.
93
In our preliminary OCMI system, the microwave bandwidth was about 6 GHz,
which provided a theoretical spatial resolution of about 3 cm. The pulses shown in Fig.
5.5 (d) indicated no obverse overlap for the reflectors separated by about 12 cm. Given
that modern microwave instrumentation can easily reach 50 GHz bandwidth, the spatial
resolution can be as high as a few millimeters.
In conclusion, a new distributed fiber optic sensing technique using optical carrier
based microwave interferometry was developed. Many optical interferometers with the
same or different optical path differences are interrogated in the microwave domain and
their locations can be unambiguously determined. The concept is demonstrated using
cascaded weak optical reflectors along a single optical fiber, where any two arbitrary
reflectors are paired to define a low-finesse Fabry-Perot interferometer. Spatially
continuous (i.e., no dark zone), fully distributed strain measurement was used as an
example to demonstrate the capability of the proposed concept. The spatial resolution is
inversely proportional to the microwave bandwidth. With a microwave bandwidth of 6
GHz, the spatial resolution can reach 3 cm. Although distributed strain measurement
using cascaded FPIs was used as a demonstration, the proposed concept may also be
implemented on other types of waveguide or free-space interferometers. In addition to
strain measurements, it can also be flexibly designed to measure other physical, chemical
and biological quantities by encoding the parameters to be measured into the OPDs of the
interferometers. As presented in [59], by reading the fiber optic interferometers in
microwave domain, the system offers many unique features including high signal quality,
relieved requirement on fabrication, low dependence on the types of optical waveguide,
94
and insensitive to the variations of polarization. It is also envisioned that the proposed
technique could be implemented in special optical fibers (e.g., multimode, single crystal
sapphire and polymer fibers), optical waveguides and free space. The new distributed
sensing concept may enable many important applications that are long-desired but
currently unavailable.
5.3
Microwave assisted reconstruction of optical interferograms
In multiplexed sensing, many sensors can be trained in series on an optical fiber
to sample the spatially distributed information. These cascaded sensors have their unique
signatures that can be unambiguously identified. For example, a number of fiber Bragg
gratings (FBGs) can be cascaded along an optical fiber and uniquely identified by their
different resonant wavelengths in spectrum domain. However, the maximum number of
FBG sensors multiplexed along a fiber is limited by the bandwidth of the light source and
the required frequency interval per sensor for prevention of overlapped signals and
crosstalks. Recently, a wavelength scanning, time division multiplexing method has been
demonstrated to interrogate 1000 ultraweak FBGs for distributed temperature sensing
[129]. However, the time domain signal was noisy and multiple measurements were
required to achieve an acceptable signal-to-noise ratio (SNR).
Among many types of sensors, fiber optic interferometers are known for their
high resolution and design flexibility for measurement of various physical, chemical and
biological parameters. One can imagine that multiplexed fiber optic interferometers
would have broad applications in many fields. Multiplexing several fiber interferometers
95
has been demonstrated in wavelength domain by designing large differences in their
initial OPD. As such, the superimposed spectral interferogram can be separated by
frequency analysis, e.g., by Fourier transform. However, the number of sensors to be
multiplexed is limited by the spectral width of the light source as well as the differences
in OPD.
Here we report a new method to multiplex fiber optic interferometers for
distributed sensing through microwave assisted separation and reconstruction of optical
interferograms in spectrum domain. Cascaded fiber optic extrinsic Fabry-Perot
interferometers (EFPI) sensors are used for the purpose of demonstration. It is expected
that the proposed technique can also be used for multiplexing other types of fiber
interferometers.
5.31
Microwave assisted multiplexing of interferometric sensors
The proposed approach is schematically shown in Fig. 5.6. The light from a
broadband source is launched into a tunable optical filter and then intensity-modulated by
a microwave signal whose modulation frequency can be scanned via computer control.
The intensity of the microwave modulated light can be expressed as:
=
I I 0 1 + M cos (ωt ) 
(5.16)
where I0 is the intensity of the light source, M is the modulation depth, and ω is the
frequency of the microwave signal.
96
Low
Coherent
Source
Microwave
modulated
optical signals
λ₁
Tunable
Filter
λn
Cascaded sensors along an
optical fiber
Circulator
Modulator
PD
Microwave
System
Synchronized
detection
Sensor2
Sensor3
Reflection
Sensor1
Amplitude &
phase
Location
Computer
Microwave reconstructed optical spectra for each sensor
Fig. 5.6. Schematic illustration of the microwave assisted multiplexing of fiber optic
interferometric sensors. PD: photo-detector
The microwave-modulated light, where the optical is the carrier and the
microwave is the envelope, is then sent into an optical fiber with cascaded reflective
EFPI sensors through a fiber optic circulator. The reflection of each EFPI sensor can be
designed to be weak enough so that the light can be transmitted over many sensors and
the multiple reflections within each sensor is negligible. The coherence length of the
light, which is determined by the bandwidth of the tunable filter, is much larger than the
OPD of the EFPI sensors but much smaller than the distance between two adjacent
sensors. As a result, optical interference occurs within one sensor while the optical
interference between sensors is avoided. The optical interference signal Γj of the j-th
EFPI can be written as:
97
I 0 1 + M cos (ω (t + t j ) )  R j ,
Γ=
j
(5.17)
 2π

⋅ OPD j + φ j 
R j (λm ) = R j1 + R j 2 + 2 R j1 R j 2 cos 
 λm

(5.18)
and
where Rj(lm) is the optical interference signal; Rj1 and Rj2 are the optical reflectivity of
the two endfaces of the cavity, respectively; lm is the optical wavelength set by the
optical tunable filter; OPDj is the optical path difference; φj is the initial phase; tj is the
propagation delay of the microwave envelope of the j-th EFPI, which can be calculated
using the following equation,
τj =
2D j
v
(5.19)
where Dj is approximately the distance between the j-th sensor and the photodetector
(PD), v is the group velocity of the microwave-modulated light transmitted inside the
optical fiber.
The optical interference signals of the sensors travel backwards, pass the fiber
circulator and are detected by a high-speed photodetector. The optical signal is the
superposition of all the cascaded EFPIs, given by,
Y=
N
∑Γ
=
N
∑I R
j
=j 1 =j 1
0
j
1 + M cos (ω (t + t j ) ) 


(5.20)
where N is the total number of EFPIs cascaded along the fiber.
The optical detection is synchronized with the microwave modulation frequency
(ω) so that the amplitude and the phase of the AC term (i.e., the cos(ωt) term in Equation
98
5.20) are obtained. After scanning the microwave frequency through the entire available
range, the complex microwave reflection spectrum (with both amplitude and phase) is
obtained. By applying a complex and inverse Fourier-transform to the microwave
spectrum, a series of delta functions are obtained at discrete time positions, given by:
=
y j AMI 0 R j
=
at t t=
1, 2,...N
j and j
(5.21)
where A is the gain of the microwave detection.
As indicated in Equation 5.21, the discrete time domain signals are proportional to
the optical interference signals (Rj) of the cascaded EFPI sensors at a particular optical
wavelength (lm) determined by the tunable filter. In addition, Equation 5.21 also provides
the locations of the sensors along the optical fiber because it has nonzero values only at
the specific propagation delays (tj) corresponding to the sensor locations (Dj) as given by
Equation 5.19.
By sweeping the optical wavelength and repeating the microwave measurement,
we can obtain the discrete optical interference signals (separated in the time domain) at
different wavelengths. These data points can then be used to construct the optical
interferograms of the cascaded EFPI sensors.
5.32
System realization and concept demonstration
Fig. 5.7 shows an example system to verify the proposed concept. The broadband
light source used was an amplified spontaneous emission (ASE) source emitting in the
spectrum of 1530-1560nm. The tunable filter had a full width at half maxima (FWHM) of
about 1nm, corresponding to a coherence length of about 1 mm. The intensity modulation
99
of the bandpass filtered light was performed through an electro-optic modulator (EOM).
An optical polarizer and an optical polarization controller are placed before the EOM to
enhance the modulation efficiency. The microwave source and detection were realized
through a vector network analyzer (VNA). The EOM was driven by the output from the
Port 1 (P1) of the VNA. The microwave signal from VNA was amplified to obtain a
desirable modulation index. The modulated light was then routed to the cascaded EFPI
sensors via an optical circulator. By fine tuning the polarization controller and the driving
power to the EOM, we obtained a modulation index of 100% at 3GHz.
Broadband
Source
Tunable
Filter
Polarizer
Polarization
Controller
Capillary Tube
Input
Driving
P1
Air
E
O
M
RF-AMP
Vector
Network
Analyzer
Output
1
P2
Core
Cladding
2
PD
3
Coaxial Cable
EFPI
EDFA
Circulator
Optical Fiber
Fig. 5.7. Schematic of the system configuration and implementation for concept
demonstration. RF-AMP: radio frequency-amplifier, EOM: electro-optic modulator,
EDFA: Erbium-doped fiber amplifier, PD: photo-detector, EFPI: extrinsic Fabry-Perot
interferometer, P1/P2: Port 1/Port 2
The reflected signals from the EFPIs were first amplified by an EDFA and then
received by a high speed photo-detector (100 MHz to 6 GHz), which was connected to
the Port 2 (P2) of the VNA. To further improve the signal quality, a microwave amplifier
100
could be placed after the photodetector to amplify the converted microwave analog signal.
By sweeping the modulation frequency of the VNA, the amplitude and phase information
of the received microwave signals (i.e., the scattering parameter S21 of the VNA) were
recorded to reconstruct the microwave spectrum.
For the purpose of concept demonstration, three EFPI sensors were used. The
EFPIs were made by fusion-splicing a capillary tube between two singlemode fibers, with
cavity lengths of approximately 80, 70, and 140 µm, respectively. They were separated
by a distance of about 100 mm apart along a single mode fiber. The intermediate
frequency bandwidth (IFBW) of the VNA was set to 300 Hz. The microwave power at
Port 1 of VNA was set to -11 dBm and pre-amplified to 27 dBm for all frequency range
to drive the EOM.
By scanning the microwave frequency from 100 MHz to 6 GHz with 1601
sampling points and recording their amplitude and phase information from Port 2 of
VNA, the microwave reflection spectrum (S21) was obtained. After applying a complex
and inverse Fourier transform, the time-resolved discrete reflections of the three EFPIs
were obtained. The tunable filter was then scanned from 1545 to 1560 nm with an
interval of 0.5 nm. The whole procedure took about 1 minute, which included the time
required for the VNA to scan through the entire available frequency span, data
acquisition, signal analysis, stepping the wavelength of the tunable filter through the
spectrum range, and interferogram reconstruction.
Fig. 5.8 (a) plots the time-resolved discrete reflections where the optical carrier
wavelength was tuned to 1552 nm. Three reflections (three EFPIs) can be clearly
101
observed in time domain with good signal-to-noise ratio. Although the two air/glass
interfaces in each capillary tube had two optical reflections, they could not be resolved in
microwave domain due to the large wavelength of microwave comparing with the cavity
lengths of the EFPIs. The observed microwave reflections is proportional to the total
optical reflection of the EFPI structure, which was a result of optical interference when
the coherence length of the light source was much large than the cavity length. The
distance between two consecutive EFPIs was far larger than the coherence length of the
input light source so that there was no interference between two EFPIs.
Fig. 5.8 (b)-(d) plot the reconstructed optical interferograms of the three EFPIs,
respectively.
The
red
curves
represent
the
microwave
reconstructed
optical
interferograms, and the blue curves are the interference spectra recorded individually
using an optical spectrum analyzer (OSA). The microwave intensities were all
normalized based on their corresponding optical intensities for comparison. The
reconstructed optical interferograms matched well with those measured by the OSA. We
believe that the difference is mainly resulted from the uneven gain spectrum of the EDFA
used in the experiments.
102
Fig. 5.8. (a) Time domain signal after applying a complex inverse Fourier transform to
the microwave spectrum with the center wavelength of the tunable filter set to be 1552
nm, (b), (c) and (d) Normalized microwave-reconstructed optical interferograms of the
three EFPIs in comparison with their spectra measured individually using an OSA,
respectively.
5.33
Demonstration of distributed sensing
To demonstrate the proposed method for distributed sensing, a strain test was
performed. The axial strain was applied to the second EFPI while the other two sensors
were relaxed. The two ends of the second EFPI sensor were tightly attached to a
103
motorized translation stage and a fixed stage using all-purpose glue, respectively. The
length between two attaching points was precisely measured to be 100 mm. The
interferograms of the three EFPIs were recorded using the microwave method as the
distance between the two points was increased step by step. The distance was increased at
a step of 5 µm, corresponding to a strain increment of 50 µɛ per step.
By applying the 4th order polynomial curve-fitting to all the reconstructed spectra
and monitoring the center wavelength of the interference valleys, the wavelength shift of
each sensor was plotted as a function of the axial strain. Fig. 5.9 (a) shows the 3D plot of
the spectral shift of the three multiplexed EFPIs along the optical fiber as a function of
the applied strain. The second sensor had an obvious response to the applied strain while
the other sensors had no responses, indicating that the proposed distributed sensing
method had little crosstalk among sensors. Fig. 5.9 (b) plots the second sensor in
response to the applied axial strain, where the wavelength shift of the interferogram
increases linearly as a function of the applied strain with a slope of 0.0024 nm/µε. The
inset of Fig. 5.9 (b) plots a few examples of reconstructed spectra as the applied strain
increased. The increasing strain did not incur noticeable loss in the reflection spectra. The
spectra of the other two sensors had no any observable shift.
104
Fig. 5.9. (a) Distributed strain measurement using three multiplexed EFPI sensors, where
strain is applied on EFPI #2 only, (b) Interferogram shift of the EFPI #2 as a function of
applied axial strain. Inset: Interferograms of EFPI #2 at various applied strains.
The spatial resolution ∆Dmin (i.e., the minimum distance between two adjacent
sensors) is determined by the microwave frequency bandwidth according to the following
equation,
105
1
DDmin = v
2 BRF
(5.22)
where BRF is the bandwidth (i.e., the maximum scanning frequency range) of the
microwave source. A larger bandwidth results in a better spatial resolution. For example,
if the bandwidth of the microwave source is 6GHz, the minimum distance between two
adjacent sensors is about 1.7cm. Of course as stated earlier, the separation between two
sensors needs to be significantly larger than the coherence length of the spectrally filtered
optical source to avoid the optical interference between two adjacent sensors.
Because the cascaded EFPIs are uniquely identified in the microwave domain,
they can be made to have the same OPD. On contrast, the typical optical spectral domain
Fourier transform based multiplexing method requires the multiplexed sensors to have
significantly different OPDs. The maximum number of sensors can be multiplexed
depends on the insertion loss (including reflection) of each sensor, the dynamic range of
the microwave instrument, and the dynamic range of the photodetector. In general, the
cascaded EFPIs can be made to have weak reflectivity to reduce the insertion loss. The
optical signals can be further amplified by using EDFAs. It is expected that the reported
microwave method is able to multiplex much more interferometers than the typical
optical spectral domain Fourier transform based multiplexing method.
To summarize, a microwave based method was studied for multiplexing fiber
optic interferometers for distributed sensing. By sending a microwave-modulated optical
signal through cascaded fiber optic interferometers, the microwave signals are used to
resolve the position and reflectivity of each sensor along the optical fiber. The coherence
106
length of the optical source is chosen to be larger than the optical path differences of the
cascaded interferometers but smaller than the spatial separation between sensors. As such,
the cascaded interferometers can be uniquely identified by complex Fourier transform of
the microwave spectrum. By sweeping the optical wavelength, the optical spectrum of
each sensor can be reconstructed. Three cascaded EFPIs along an optical fiber were used
to demonstrate the concept. The optical interferograms of the EFPIs were reconstructed
unambiguously and they matched well with those measured individually using an OSA.
Distributed strain sensing was conducted to prove the system’s effectiveness in sensing
applications. It is necessary to note that although three EFPIs are used for the purpose of
concept demonstration; other types of fiber interferometric sensors can also be
implemented using the method. The reported microwave method can multiplex
interferometric sensors with the same OPDs. In comparison with the traditional optical
spectral domain Fourier transform based multiplexing approach, the reported method has
the advantages of multiplexing much more sensors because it is not limited by the
bandwidth of the optical source. It is expected that the proposed multiplexing technique
may find many applications for distributed measurement of various physical, chemical
and biological parameters.
107
CHAPTER SIX
CONCLUSION AND FUTURE WORK
6.1
Conclusion
The dissertation work clearly demonstrated the feasibility of the OCMI concept
for sensing applications on SMF, MMF, POF, single crystal sapphire fiber, and its
promising potential for spatially-uninterrupted distributed sensing with high measurement
resolution. Two types of interrogation systems have been proposed and investigated. A
rigorous mathematical model has also been studied to uncover the full potentials and
explore the full capabilities of OCMI. The essence of OCMI is to read optical
interferometers using microwave. As such, it combines the advantages from both optics
and microwave.
When used for sensing, it inherits the advantages of optical
interferometry such as small size, light weight, low signal loss, remote operation and
immunity to EMI. Meanwhile, by constructing the interference in microwave domain, the
OCMI has many unique advantages that are unachievable by conventional optical
interferometry, including:
1)
High measurement resolution: OCMI uses coherent detection in which the
modulation, detection and demodulation are all synchronized to the same microwave
frequency. As a result, OCMI has a higher SNR comparing with the traditional alloptical interferometers that use DC detection. In addition, the measurement of distance
change is based on tracking the spectral shift of the interferogram. As such, the
measurement resolution is expected to be high.
108
2)
Distributed sensing with spatial continuity and reconfigurable gauge
length: Time-resolved reflections can be easily obtained by complex Fourier transform of
the microwave signals with phase and amplitude information. Distributed sensing can be
achieved with spatial continuity by taking consecutive measurement between two
adjacent reflectors. In addition, the gauge length can be varied by taking measurement
between two arbitrary reflectors.
3)
Insensitivity to the types of optical waveguides. The differences in optics
(e.g., dispersion and modal interference) have little influences on the microwave signal.
As such, multimode waveguides (e.g., POFs) can be used to construct OCMI for
distributed sensing.
4)
Insensitivity to optical polarizations. In OCMI, the interference is a result
of coherent superposition of the microwave envelops. As such, OCMI does not have the
polarization fading issue commonly faced by all-optical interferometers.
5)
Relieved fabrication requirements.
In order to obtain a high-quality
interference signal, the surface smoothness of the reflectors needs to be smaller than 1/20
of the wavelength. The wavelength of microwave is much larger than that of an optical
wave. In a sense, currently available micromachining techniques can easily satisfy the
precision requirements of OCMI.
Although in this particular project our efforts are focused on the design and
demonstration of the new OCMI based distributed sensing technology, the fundamental
knowledge of OCMI and the modeling/manufacturing/interrogation methodologies
developed in this research are transferrable to many other extended applications in SHM
109
such as distributed monitoring of force, bending, fatigue and corrosion. In addition, the
new OCMI distributed sensing concept could be modified to measure chemical and
biological species, which may have numerous applications beyond SHM, such as
pollution monitoring, environmental management and detection of chemical/biological
warfare agents. As such, the fundamental studies in this project may promise a broader
societal impact on human welfare and national security.
The innovative idea of combining microwave and optics for sensing application
and the successful demonstration of the OCMI concept will inspire similar
interdisciplinary ideas, encourage broader participations of various disciplines in sensing
research, and foster a wider range of collaborations. Our pioneering research may open a
new exciting research area of mixing microwave with optics for sensing and
consequently contribute to advancing the state-of-the-art.
6.2
Future work
By reading optical interferometers in microwave domain, OCMI combines the
advantages from both optics and microwave. When used for sensing, it inherits the
advantages of optical interferometry and offers many unique features including high
signal quality, insensitivity to SOP variations, low dependence on multimodal influences,
relieved requirement on fabrication, and distributed sensing capability with spatial
continuity. In addition to strain and temperature measurements demonstrated in this letter,
the OCMI can be flexibly designed to measure other physical, chemical and biological
quantities. The new OCMI concept may revolutionize the fiber optic sensing field and
enable many important applications that are long-desired but currently unavailable.
110
Although FOIs were used in demonstrations, the OCMI concept can be implemented in
free space and other forms of optical waveguides. Example applications include optical
carrier based microwave metamaterials, superlens, tomographic imaging, spectroscopy,
antennas, etc.
One example of extending the OCMI applications will be distributed spectroscopy
where the optics will provide the spectroscopic information and the microwave will
provide the location information. It could be implemented in distributed Raman,
fluorescence, or absorption spectroscopies. Here is an example of fiber optic cavity ringdown spectroscopic sensor based on OCMI technology. Fig. 6.1 (a) shows the schematic
of a system to demonstrate the OCMI based cavity ring-down concept. A semiconductor
diode laser source with a 3dB bandwidth of about 1nm is intensity-modulated using an
EOM driven by the microwave output (DC-biased and amplified) from the Port 1 of a
VNA. The microwave modulated light is sent to an optical fiber ring constructed by two
fiber couplers with the split ratio of 98%. The output from the fiber ring is detected by a
high-speed photodetector (Wavecrest, OE-2). The output of the photodetector, after DCfiltering and RF amplification, is recorded at the Port 2 of the VNA where the amplitude
and phase of the signal are extracted. By sweeping the VNA frequency, the microwave
spectrum of the interferometer is obtained (i.e., the S21 of the VNA). As shown in Fig. 6.1
(b), the complex inverse Fourier transform of the microwave spectrum resulted in a
cavity ring-down curve with excellent SNR and time/space resolution.
The high sensitivity and specificity of cavity ring-down spectroscopy are well
proven [130-132]. However, the traditional all-optical cavity ring-down concept can only
111
interrogate a single ring and does not have the distributed sensing capability. It is
envisioned that the OCMI technology could potentially provide spatially distributed
continuous monitoring capability for cavity ring-down spectroscopy.
Fig. 6.1. (a) Schematic illustration of the experiment setup to validate the OCMI based
cavity ring-down concept. (b) Time/distance resolved ring-down delay curve with
excellent SNR.
112
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