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Microwave imaging techniques for nondestructive evaluation: Simulation and experimental studies

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MICROWAVE IMAGING TECHNIQUES FOR NONDESTRUCTIVE EVALUATION:
SIMULATION AND EXPERIMENTAL STUDIES
by
JARVIS WARD HILL
B.S., Colorado State University-Fort Collins, 2009
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Electrical Engineering
2014
UMI Number: 1571281
All rights reserved
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UMI 1571281
Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author.
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2014
JARVIS WARD HILL
ALL RIGHTS RESERVED
ii
This thesis for the Master of Science degree by
Jarvis Ward Hill
has been approved for the
Electrical Engineering Program
by
Stephen Gedney, Chair
Yiming Deng, Advisor
Tim Lei
Mark Golkowski
November 21, 2014
iii
Hill, Jarvis Ward (M.S. Electrical Engineering)
Microwave Imaging Techniques for Nondestructive Evaluation: Simulation and
Experimental Studies
Thesis directed by Assistant Professor Yiming J. Deng
ABSTRACT
Microwave imaging is an emerging area of research. Due to its low-cost and simple
system setups, microwaving imaging system(s) (MIS) are growing as alternatives to more
expensive X-ray imaging systems.
This thesis provides background on microwave
imaging and how it’s useful for a broad range of applications. It highlights some of the
design considerations and challenges that can impact the development of an MIS. It also
provides suggestions on how to achieve an MIS with higher resolution, how to eliminate
noise within acquired images and how to optimize scanning execution times without
generating excessive sample vibrations.
The ancillary equipment of an MIS should be catered to the imaging application.
This thesis exposes one to the physical development process of the LEAP Near-field
Microwave Imaging System (NFMWIS). It documents the areas and stages of the system
development and how simulation was used to confirm physical behavior of the system
components prior to purchase and or fabrication. Development efforts show that there is
high importance in the waveguide design of the MIS and a strong need to optimize the
relationship between the MIS hardware and software. The waveguide design should be
conducive to the size, shape and geometry of the desired objects to be imaged.
Waveguides with large apertures are useful in applications that require low resolution.
Waveguides with small apertures help confine the EMF radiation to localized regions on
the sample under test and help achieve high resolution. An MIS is not efficient if it
iv
requires large scanning execution times in order image an object under test but more
importantly image resolution should not be sacrificed for fast scanning times. Ultimately,
there is not a single solution when developing a MIS, all factors must be experimentally
optimized by the design engineer(s).
The form and content of this abstract are approved. I recommend its publication.
Approved: Yiming J. Deng
v
DEDICATION
I would like to dedicate this thesis to the Hill family who made the sacrifices in order
to allow me to complete this task. Many times it takes a village to help someone get to
where they want to be and I’m forever thankful for the lack of complaints,
encouragement and belief. They inspire me to be a better person as each day passes; they
teach me to lead and not follow; and they have instilled in me a hunger to dream big!
vi
ACKNOWLEDGEMENTS
I must thank my program advisor Dr. Yiming Deng for his limitless spirit of humility,
understanding and encouragement. My graduate tenure has truly been a journey and he
has guided me every step of the way.
I would like to thank the Laboratory of
Electromagnetic and Acoustic Imaging and Prognostics Team (LEAP) for their
contribution in developing the Near-Field Microwave Imaging System (NFMWIS).
Special thanks goes to Xiaoye Chen and Salem Egdaire. Salem, thank you for your
collaboration with developing the NFMWIS phase-detection approach and for always
challenging my ideas and experiments during those many late nights in the lab. Xiaoye
Chen, thank you for your significant contributions on the development of the NFMWIS
scanning tip. I would also like to thank our research collaborators at Arizona State
University, Dr. Yongming Liu and Sahil Jain. I would like to offer huge kudos and
thanks to James Merritt, R&D Manager for the U.S. Department of Transportation, for
the funding that allows this program to continue to develop.
vii
TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION ........................................................................................................... 1
1.1 OVERVIEW.............................................................................................................. 1
1.2 THESIS SCOPE ........................................................................................................ 4
1.3 MOTIVATIONS & OBJECTIVES .......................................................................... 6
II. REVIEW OF NEAR-FIELD MICROWAVE IMAGING TECHNIQUES................. 10
2.1 HISTORY OF MICROWAVE IMAGING ............................................................ 10
2.2 NEAR-FIELD & FAR-FIELD EMF RADIATION ............................................... 11
2.3 TIME-HARMONIC ELECTROMAGNETIC FIELDS ......................................... 14
2.3.1 Maxwell Equations ........................................................................................... 14
2.3.2 Constitutive Equations ...................................................................................... 16
2.3.2 Wave Equation ................................................................................................. 17
2.3.3 Helmholtz Wave Equation................................................................................ 17
2.3.4 EM Wave Scattering ......................................................................................... 19
2.4 GENERAL NEAR-FIELD MICROWAVE IMAGING TECHNIQUES ............... 21
2.4.1 Open-ended Waveguide Techniques ................................................................ 21
2.4.2 Near-Field Scanning Tip Techniques ............................................................... 28
2.4.3 Near-field Phase Detection Approach .............................................................. 37
2.5 NEAR-FIELD MEDICAL IMAGING APPLICATIONS ...................................... 40
2.6 SUMMARY ............................................................................................................ 44
III. OPTIMIZATION OF THE LEAP NFMW IMAGING SYSTEM ............................. 47
3.1 MICROWAVE IMAGING PROBLEMS ............................................................... 47
3.1.1 Constructing Valid Numerical Models ................................................................ 47
3.1.2 Real-time NFMW Imaging ............................................................................... 47
3.1.4 Phase Extraction Challenges ............................................................................ 49
3.2 LEAP NFMWI SYSTEM OVERVIEW ................................................................. 50
3.2.1 Approach 1 LEAP NFMWIS Voltage Amplitude Detection System .............. 51
3.2.2 Approach 2 LEAP NFMWI Phase Detection System ...................................... 51
3.3 LEAP NFMWIS OPTIMIZATION METHODS .................................................... 52
3.3.1 System Synchronization ................................................................................... 53
3.3.2 Scan Execution Time ........................................................................................ 53
3.3.3 Antenna (Waveguide) Design .......................................................................... 61
3.3.4 Image Resolution Techniques .......................................................................... 69
3.4 LEAP NFMW PHASE DETECTION APPROACH .............................................. 72
3.4.1 Background Information................................................................................... 73
3.4.3 Analog Mixing Phase Detection Approach ...................................................... 76
3.5 LEAP NFMWI PHASE DETECTION SYSTEM .................................................. 86
viii
3.6 INITIAL LEAP NFMWI PHASE DETECTION ................................................... 92
3.6.1 LEAP NFMWI Phase Detection Measurement Method .................................. 93
3.6.2 Initial Phase Detection Scan Results ................................................................ 94
3.7 SUMMARY ............................................................................................................ 98
IV. CONCLUSION ........................................................................................................ 100
4.1 FUTURE WORK .................................................................................................. 100
4.1.1 Numerical Modeling of LEAP NFMWIS Waveguide ................................... 100
4.1.3 Compressed Sensing Reconstruction.............................................................. 110
4.2 CLOSING REMARKS ......................................................................................... 111
4.3 CONCLUSION ..................................................................................................... 116
REFERENCES ............................................................................................................... 118
APPENDIX A: MATLAB NFMWIS Scanning Code (scan.m)..................................... 121
APPENDIX B: LEAP NFMWIS Scanning Algorithm ................................................. 126
ix
LIST OF TABLES
TABLE
3.1. IF Voltage Frequency Harmonics .............................................................................. 92
x
LIST OF FIGURES
FIGURE
1.1: Some common transmission line waveguides: (a) Two-conductor line; (b) coaxial
line; (c) shielded strip line [1] ............................................................................................. 3
1.2: Some common hollow-pipe waveguides: (a) Rectangular; (b) circular guide; (c) ridge
guide [1] .............................................................................................................................. 4
2.1: EMF Boundary Regions [15]..................................................................................... 12
2.2: Near-field and Far-Field Radiation Behavior [16] ................................................... 13
2.4: LEAP NFMWIS Generation I 1D scan of Hole in a Concrete Sample .................... 22
2.5: Bois Microwave Imaging System for Concrete Cure-State Inspection ..................... 23
2.6: Open-ended Coaxial Line Terminated by a Two Layered Medium .......................... 26
2.7: Magnitude of the reflection coefficient vs. target distance (left); Phase of the
reflection coefficient vs. target distance (right) ................................................................ 27
2.8: Schematic of Microstrip Resonator as Used in a Microwave Evanescent Probe ...... 30
2.9: Measured |S11| of channelized coplanar waveguide probe both with and without a
high resistivity silicon sample near the probe tip.............................................................. 31
2.10: Wang Coaxial Tip Fabrication Process ................................................................... 32
2.11: Micrograph of a Wang Fabricated Silicon Tip ....................................................... 33
2.12: Scan of a 20 pm diameter wire along the x and y-axis using CCPW evanescent
microwave probe ............................................................................................................... 34
2.13: Circuit Schematic for SNMM Scan ......................................................................... 35
2.14: Simultaneous SNMM images by the coaxial tip. (left) AFM internal sensor image;
(right) Microwave amplitude image ................................................................................. 36
2.15: Zhu Spintronic Phase Detection MIS ..................................................................... 38
2.16: Near-field Phase Difference Measurements of Liquid Filled PMMA Grating: (a)
Grating filled with isopropyl alcohol; (b) Grating filled with water ................................ 39
2.17: 3-D Tomographic MIS Examination Chamber: (left) 3-D representation of the
tomographic chamber; (right) Assembled antenna hardware ........................................... 42
2.18: MR Imaged tumor in right breast: (left) Tumor Axial View (right) Tumor axial
View After Baseline Subtraction ...................................................................................... 43
2.19: 3-D Permittivity Breast Image from 3-D Tomographic MIS ................................. 43
2.20: Generic Microwave Imaging System [24] .............................................................. 45
3.1: Block Diagram of LEAP NFMWI Voltage Amplitude Detection System ................ 51
3.2: Block Diagram of LEAP NFMWI Phase Detection System ..................................... 51
3.3: 15” x 12” Aluminum Calibration Sample.................................................................. 52
3.4: Flow Diagram of Initial LEAP NFMWIS Raster Scan Algorithm ............................ 56
3.5: Flow Diagram of Optimized LEAP NFMWIS Raster Scan Algorithm ................... 58
xi
3.6: LEAP NFMWIS Open Ended WG Scan: (left) Calibration sample; (right)
Microwave Image ............................................................................................................. 62
3.7: LEAP NFMWIS Open Ended WG Scan with SA DAQ Device ............................... 63
3.8: LEAP NFMWIS CTA waveguide: (left) waveguide tip and (right) signal spliter and
amplification (annotate picture) ........................................................................................ 64
3.9(a): LEAP NFMWIS Scan Results Calibration sample CTA scan results................... 65
3.9(b): LEAP NFMWIS Scan Results Open-ended WG Scan Results ............................ 65
3.10: Copper Probe Tips .................................................................................................. 66
3.11: CPT Return Loss ..................................................................................................... 67
3.12: Experimental setup with CPT .................................................................................. 68
3.13: Scan result comparison between CPT (left) and CTA (right) ................................ 68
3.14: Histogram of Gen. I Rx Amplitude Data Acquired with SA ................................... 70
3.15: MATLAB Thresholding Algorithm........................................................................ 71
3.16: Binary Thresholding Results: (left) Voltage Amplitude Image using LEAP
NFMWIS Generation I; (right) Image after applying optimized binary thresholding
algorithm ........................................................................................................................... 72
3.17: NFMWI Phase Measurement Simulation: Rx Signal (right); Scalar Spectrum
Analyzer Measurement (left) ............................................................................................ 74
3.18: NFMWIS Phase Measurement Simulation: 90o Phase Shift Rx Signal (left); Scalar
Spectrum Analyzer Measurement (right).......................................................................... 75
3.19: Output Signal Power Displayed on the Function Generator .................................... 76
3.20: Schematic of Product Detector (Analog Multiplier) [27] ....................................... 76
3.21: Plot of Tx and Rx and their frequency spectrums ................................................... 78
3.22: Tx and Rx Product Signal and frequency spectrum ............................................... 79
3.24: VOGX vs. Tx and Rx Phase Difference .................................................................... 80
3.25: Double-balanced Mixer Phase Detection Circuit .................................................... 80
3.26: Screenshot of Double Balanced Mixer Built with LTspice .................................... 82
3.27: LO and RF Phase Detector Input Signals ............................................................... 82
3.28: LO Induced Signal into Phase Detector Circuit...................................................... 83
3.29: Phase Detector IF output without Low-pass Filter ................................................. 83
3.30: Spectrum of Mixer IF Output Voltage ..................................................................... 84
3.31: Phase Detector IF output with Low-pass Filter ...................................................... 84
3.32: Double-balanced Mixer Phase Difference Measurement ....................................... 85
3.33: Detected Phase Differences Actual vs. Calculated ................................................. 85
3.34: MATLAB Phase Detector Product Voltage Results vs. LTspice Double Balanced
Mixer IF Voltage............................................................................................................... 86
3.35: Diagram of Mixer BW measurement setup ............................................................. 88
3.36 Forward voltage gain from the RF input to the IF output ......................................... 89
3.37: RF Mixer IF Voltage Experiment Setup ................................................................. 90
3.38: MATLAB, LTspice and SM1717 RF Mixer IF Voltage Response ......................... 90
xii
3.39: MATLAB, LTspice and SM1717 RF Mixer Phase Difference Approximations ... 91
3.43: SA CXA-N9000A display with 3GHz and 1 GHz fed to the mixer inputs ............. 92
3.43: LEAP NFMWI Phase Detection System ................................................................ 93
3.44: Mid-size Triangle on Aluminum Calibration Sample ............................................ 93
3.45: Phase Detection Feasibility Scan of Mid-size Triangle ........................................... 95
3.46: Image of Calculated Phase Difference..................................................................... 96
3.47: Image of Mixer IF Voltage Measurements .............................................................. 96
3.48: Image of Calculated Phase Difference..................................................................... 97
3.49: Image of Mixer IF Voltage Output Default imagesc Color Map ............................ 97
3.50: Image of Calculated Phase Difference Default imagesc Color Map ....................... 98
4.1: Yee Cell Mesh Grid ................................................................................................ 102
4.2: EMFs at material discontinuity: E-field at PEC boundary (left): H-field at PMC
boundary (right) .............................................................................................................. 103
4.3: FDTD Parallel Plate Computational Parameters .................................................... 104
4.2: Sinusoidal Pulse Stimulus........................................................................................ 106
4.3: Continuous Wave Pulse Stimulus ............................................................................ 106
4.4: 2D and 3D Ez-Field Due to Sinusoidal Pulse Stimulus........................................... 109
4.5: 2D and 3D Ez-Field Due to Continuous Pulse Stimulus ......................................... 109
xiii
CHAPTER I
INTRODUCTION
1.1 OVERVIEW
Microwave energy was exposed to the average consumer when the microwave oven
(microwave) became a common household appliance in the 1970s. The oven generates
electromagnetic radiation at micrometer wavelengths; this micrometer radiation is known
as microwaves. The descriptive term microwaves is used to describe electromagnetic
waves with wavelengths ranging from 1 cm to 1 m. The corresponding frequency range
is 300 MHz up to 30 GHz for 1-cm-wavelength waves [1]. When a material is exposed
to microwave radiation, molecules within the material interact and alter how the waves
transmit through the material. How microwave radiation travels through an object is
described by the materials dispersive and dielectric properties.
Material dispersion
describes how the phase of the microwave radiation propagates through the material. The
dielectric properties of an object are described by the magnetic permeability and electric
permittivity of the material. In electromagnetism, permeability is the measure of the
ability of a material to support the formation of a magnetic field within itself. On the
other hand, Permittivity is the measure of the ability of a material to support the
formation of an electric field.
Materials are anisotropic meaning the dielectric structure of a material is
inhomogeneous and the permittivity and or permittivity are not constant throughout. If
the dielectric structure was constant, the material would be considered isotropic and or
homogenous. Unlike X-rays where the radiation wavelength is much smaller than the
object, EM radiation at microwave frequencies no longer travels in a straight path as the
1
size of the objects is comparable to the wavelength [2].
This phenomenon allows
microwaves to exploit material anisotropies. When an object is exposed to a microwave
field, the field radiates within the material and reflects or scatters/disperses when the field
comes in contact with the anisotropic molecules within the object material.
The
amplitude of the reflected or scattered field can be quantified and measured by employing
microwave imaging techniques. These techniques commonly quantify the amplitude of
radiation by measuring the reflection coefficient or the ratio of the reflected microwaves
to the transmitted microwaves at a localized region on the object.
The larger the
dielectric differences within a material, the larger the amplitude of the reflected or
scattered radiation.
During World War I1, microwave engineering was almost synonymous with radar
(RAdio Detection And Ranging) engineering. There was a great incentive given to the
development of microwave systems due to the need for high-resolution radar capable of
detecting and locating enemy planes and ships. Even today radar, in its many varied
forms, such as missile-tracking radar, fire-control radar, weather-detecting radar, missileguidance radar, airport traffic-control radar, etc., represents a major use of microwave
frequencies [1]. This use arises predominantly from the need to have antennas that will
radiate all the transmitter power into a narrow pencil-like beam similar to that produced
by an optical searchlight [1]. The ability of an antenna to concentrate radiation into a
narrow beam is limited by diffraction effects, which in turn are governed by the relative
size of the radiating aperture in terms of wavelengths [1]. Research has shown that the
ability to concentrate radiation enables the various field amplitudes across a material to
be imaged using microwave imaging systems (MIS). These systems can generate images
2
of a materials dielectric tomography allowing engineers and scientist to evaluate hidden
or embedded flaws within the object structure [3].
In microwave applications waveguides are the most critical component of a
microwave system because they couple the antenna to the microwave energy source.
Waveguides are transmission mediums that are responsible for transmitting as much
microwave energy from the source to the object under test. Ideally a waveguide would
transfer all the energy from the source to an antenna without causing any signal
attenuation. Due to the confined geometries of the waveguide walls, transverse modes
(TEM) are generated within the guide due to the boundary conditions the waveguide
structure imposes on an EMF.
The dominate mode or TEM containing the most
microwave energy is the EMF oscillating at the lowest frequency. Slabs of material with
a specified thickness and dielectric property are often inserted into the waveguide inorder to act as a low-pass filter removing the propagation of these unwanted higher-order
TEMs. Removing unwanted TEMs can increase SNR within a microwave imaging
application and increase imaging resolution. Figures 1.1 and 1.2 show some typical
waveguide geometries.
Figure 1.1: Some common transmission line waveguides: (a) Two-conductor line; (b)
coaxial line; (c) shielded strip line [1]
3
Figure 1.2: Some common hollow-pipe waveguides: (a) Rectangular; (b) circular guide;
(c) ridge guide [1]
There is a wide variety of use for microwave imaging applications and the waveguide
and or antenna of a MIS is dictated by the specificities of the application (i.e. the size and
geometry of the object to be imaged, the required imaging resolution, the imaging
environment and what the system needs to measure). Research has shown that openended rectangular waveguides are useful in applications that warrant the imaging of large
objects and require low imaging resolution [3] [4]. Research shows that open-ended
coaxial waveguides localize EMF on a sample under test and is useful for applications
requiring sub-cm resolution [5]. Research suggests that MIS requiring high-resolution
(greater than sub-mm) should be implemented with a waveguide terminated to a tapered
tip antenna [6] [7].
1.2 THESIS SCOPE
Microwave NDE imaging is a science that provides a quick and nondestructive way to
classify properties of a material. Factors in choosing the right nondestructive evaluation
(NDE) technique depend on the type of material, as well as, the size, orientation and
location of the defect [8]. Whether defects are located on the surface or internally also
affects the selection of the technique [8]. The geometric shape of a material under test
also determines which NDE technique to use [9].
4
All these factors determine the type
and equipment of a MIS. When constructing a MIS there is no ideal solution. The
solution should be optimized based on the material type, geometry, flaw detection
resolution and location of the flaws that need to be imaged [9]. There’s no direct solution,
the final system is optimized through experimentation and evaluation because the
interaction of materials with electromagnetic fields (EMF) is impalpable.
The interaction between EMF and materials may appear ambiguous but researchers
have found ways to quantify it. Near-field microwave imaging techniques have been
employed to classify the material mixture of concrete by scanning the material at predetermined locations and quantifying the reflected field amplitude with a network
analyzer (NA) [4]. Techniques have also been used to achieve microwave breast imaging
[10] and to produce 3-D tomographic microwave images for breast cancer detection [11].
All of these techniques have one thing in common; they are carried out with near-field
microwave imaging techniques. Many microwave imaging techniques exist but like the
MIS, the technique depends on the material under test and the information desired.
Chapter 2 introduces near-field microwave imaging and its interaction with various
object types.
The chapter will also perform literature review highlighting different
strategies to acquire quantized images of material properties using MIS (e.g. conductivity,
dielectric constant or polarization) [9]. The most important component of the MIS is the
waveguide. The size, shape and lift-off distance of the waveguide orchestrates how the
microwaves interact with a material under test [5]. Research has shown that the emitted
microwave radiation and lift-off distance of the material can be optimized through
numerical modeling techniques before MIS construction [12].
The speed and resolution of a microwave imaging technique are two substantial
5
factors that should be considered when developing a MIS.
Chapter 3 shows the
NFMWIS optimization methods and results. The chapter presents a system overview,
phase detection approach to microwave imaging, automated data acquisition algorithms
using MATLAB and initial efforts of MIS image enhancement techniques. Chapter 4
provides a conclusion and summary of future work.
The future work presented in
Chapter 4 provides exposure to the initial efforts made by the LEAP Team to gauge the
response of an open-ended waveguide to EMF radiation using finite-difference timedomain (FDTD) modeling techniques. FDTD modeling is useful because it provides an
approximation of the EMF behavior inside the waveguide. The modeling efforts in
Chapter 4 are incomplete and are a part of the continuous improvement efforts of the
LEAP MIS.
1.3 MOTIVATIONS & OBJECTIVES
If you’re not working on important problems it’s unlikely that you’ll do important work.
-Richard Hamming
Everyone knows that death is imminent. Witnessing the death of a close relative
really puts this into perspective. Death can be graceful when it takes a ninety-year-old
grandmother but it’s quite ugly when it comes in the form of breast cancer plaguing a
vibrant, energetic and loving fifty-year-old woman.
The family’s questions of why
represented denial and the falling tears represented healing. Of course the onset of breast
cancer cannot be completely avoided but it can be mitigated through regularly scheduled
examinations. Microwave imaging is progressing considerably in the areas of early
breast-cancer detection [10] [11] [13]. The effectiveness of imaging contrasts in objects
6
containing sacks of fluid will hopefully translate into imaging tissue with abnormal
coagulates, such as tumors.
Who’s to say that at a time like this you cannot be called forth?
-Wyclef Jean
The nondestructive diagnostic possibilities of microwave imaging are countless but
the techniques that are most impactful are the ones that could potentially save lives. Like
the microwave oven easing the life of the 70s domestic housewife, saving lives matter.
Lives impact other lives. One more day, hour, second for a father, mother, sister, brother
or friend to have that opportunity to make that positive impact on someone’s life, holds
an unquantifiable amount of potential energy. Potential energy that is transferred from
one life to the next; in the right time applied and transformed into kinetic energy to
change the world.
Microwave imaging requires scientists to research, analyze and evaluate in order to
arrive at optimal solutions. The challenge, ambiguity, lack of rules and freedom to create
things is what makes science and engineering fun. The struggle to create superior
imaging diagnostics can lead to fewer lives lost to breast cancer, airplane crash fatalities,
and even hypothermia [14]. The objectives of the LEAP research group is to develop a
near-field microwave imaging technique using open-ended waveguide probes that offer
micron to sub-mm spatial resolution and provides non-contact, one-sided and near realtime measurement capabilities at the same time. This imaging technique is an effort to
satisfy the USDOT CAAP supported research project for the residual strength and
remaining useful life (RUL) analysis of pipeline materials.
7
The USDOT CAAP supported research is a collaborative effort between the USDOT,
University of Colorado Denver and Arizona State University that aims to develop a new
hybrid sensing technique that can identify and proactively characterize injurious pipe
body with superior resolution and high sensitivity.
The detection results from the
proposed nondestructive evaluation (NDE) sensing methodology will be integrated with
probabilistic methods and mechanical analysis for accurate time-dependent reliability
analysis.
Effective reliability analysis using NDE techniques requires a fused
information framework that integrates the residual strength calculation, uncertainty
quantification, propagation analysis, and Bayesian updating. If successful, the pipeline
failure can be significantly reduced with this innovative pipeline defects diagnosis and
prognosis approach.
The overall objectives of this collaborative research are two-fold: diagnosis-find
existing damage at the earliest stage before it becomes failure critical; and prognosisaccurately predict the remaining strength and RUL of pipelining components. The effort
will last 27 months and will establish a prototype concept, composed of mathematical
modeling of the near-field microwave and acoustic interaction, experimental
measurements, feature extraction and pipeline prognosis based on damage quantification
and uncertainty analysis.
Building upon this concept, a sensor prototype with the
integrated diagnosis and prognosis capabilities will be designed, fabricated, and tested at
the last phase of this project.
The works presented in this thesis are personal efforts to contribute to the diagnosis of
existing pipeline damage through the development and optimization of the LEAP near-
8
field microwave imaging technique (LEAP NFMWIS). The objectives of this thesis are
three-fold:
1. Development of an efficient and real-time data acquisition approach for NFMW
imaging.
2. Development of a phase extraction methodology for NFMW imaging.
3. Development and validation of a numerical model for near field microwave
imaging.
9
CHAPTER II
REVIEW OF NEAR-FIELD MICROWAVE IMAGING TECHNIQUES
2.1 HISTORY OF MICROWAVE IMAGING
The existence of microwaves was made clear in the 1860s with the emergence of four
equations that describe the theory of electrodynamics. These equations are known as the
Maxwell’s Equations, named after the great physicist James Clerk Maxwell. Maxwell’s
notable contribution came when he corrected Ampere’s Circuit Law to include a
displacement current term in 1861. This correction aided in formulating the classical
theory of electromagnetic radiation. In 1865 Maxwell published A Dynamical Theory of
the Electromagnetic Field which demonstrated that electric and magnetic fields travel
through space as waves moving at the speed of light. He also demonstrated that light
behaves like the wave motion of electric and magnetic fields which led to the prediction
of radio waves.
The works that supported this paper enabled him to derive the
electromagnetic wave equation (wave equation) which is one of the most fruitful
contributions to physics since Newton’s Laws of Thermodynamics. The wave equation
led to the development of Radio Detection and Ranging or RADAR which can be
considered the forefather of microwave imaging.
The early developments of microwave imaging techniques started with advancements
made in microwave microscopy. Microwave imaging first achieved sub-mm resolution
when Edward Synge proposed using an opaque screen with a small sub-wavelength
diameter hole (10 nm in diameter), held about 10 nm above the surface of a smooth flat
sample. An optically transparent sample was passed just beneath this aperture, and the
transmitted light is collected in a point-by-point scan and raster fashion [Synge et. al].
10
Ash and Nichols utilized the Synge geometry of a small aperture (1.5mm diameter)
scanned over a sample with a microwave signal at 10 GHz. Using a quasi-optical
hemispherical resonator as the detection system, the sample was harmonically distance
modulated at a fixed frequency, and the reflected signal was phase-sensitively detected to
improve sensitivity to sample contrast [Ash and Nichols et. al]. The 1960s marks the first
decade when a transmission line was used to radiate microwave fields from the open end
of a line (coaxial or waveguide). The fringes of the EMF from the aperture interact with
the test sample. Part of the signal is absorbed by the sample, part of it is stored locally in
evanescent and near-zone waves, a portion is reflected back up the transmission line and
some scatters away as far-field radiation [9]. Bryant and Gunn are noted for performing
some of the first experiments with tapered open-ended coaxial probes [Bryant and Gunn
et. al]. They made quantitative measurements of semiconductor resistivity by measuring
the reflection coefficients produced in a coaxial cable probe with an inner diameter of 1
mm. These early experiments led to some of the most fundamental microwave imaging
techniques.
2.2 NEAR-FIELD & FAR-FIELD EMF RADIATION
Electrical engineers define boundary regions to categorize behavior characteristics of
electromagnetic fields as a function of distance from the radiating source. These regions
are: the "Near-Field", "Transition Zone", and "Far-Field". The regional boundaries are
usually measured as a function of the wavelength. Figure 2.1 shows these regions and
boundaries.
11
Figure 2.1: EMF Boundary Regions [15]
Imaging in these regions is specific to the required image resolution, material properties
and geometry of the sample under test [9]. The near-field and far-field are regions of the
EMF around an object (e.g. transmitting antenna, waveguide, and or probe) or the result
of radiation scattering off an object (e.g. metal sample).
Non-radiative near-field
behaviors of electromagnetic fields dominate close to the antenna or scattering object,
while electromagnetic radiation far-field behaviors dominate at greater distances. The
radiative near-field (also called the "Fresnel region") covers the remainder of the nearfield region, from λ∕2π out to the far-field or Fraunhofer distance. The far-field region is
commonly taken to exist at distances from the microwave source that are greater than R =
2D2∕ λ from the source, where D is the overall dimension of the source aperture width and
λ is the wavelength of the EM wave from the source [16]. EMF near-field radiation
strength decreases with distance, R, from the source, whereas far-field strength decreases
with the inverse square of the distance (1/R2) [16]. Figure 2.2 displays the radiation
behavior of near-field EMF and far-field EMF.
12
Figure 2.2: Near-field and Far-Field Radiation Behavior [16]
Near-field and far-field applications can be implemented in order to create microwave
inspection systems.
Near-field microwave imaging techniques are based on the
interaction between evanescent fields generated by an electrically small probe and the
material in the close proximity of the probe. Alterations in the material composition or
the shape of the object near the probe change the near-field distribution. Consequently
the amplitude of the scattered/reflected EMF induced in the waveguide of the MIS
changes. Scanning the probe over an area yields an image corresponding to the material
composition around the probe with sub-mm wavelength resolution [5]. Far-field imaging
techniques are not affected by the scattering and electric charge effects that the near-field
radiation induces on the EMF. The equations describing the fields created about the
antenna (near-field) can be simplified when imaging in the far-field.
The far-field
assumes a large separation between the microwave source and the device under test. In
this region, near-field diffraction provides only a minor contribution to the final field so
these contributions are dropped. In the far-field the EMF radiation becomes plane waves
of constant frequency whose wavefronts are constant in phase and amplitude. These
simplified distributions have been termed the "far-field" and usually have the property
13
that the angular distribution of energy does not change with distance. The simplifications
of EMF radiation in the far-field are very useful in engineering calculations. Microwave
images can be generated in the far-field the same way they are generated in the near-field,
by measuring the amplitude of the reflected EMF.
Researchers have been exploiting experimenting with the microwave images that can
be generated in these regions.
Typical imaging strategies involve generating the
topography of a sample by performing a raster scan of the surface area and measuring the
amplitude of the signal reflection using a data acquisition device (DAQ).
Taking
advantage of material inhomogeneity enables topographic images of a sample’s geometry
and dielectric properties (permittivity, permeability and conductivity) to be imaged with
MIS. The LEAP NFMWIS is a near-field imaging system so this thesis will only focus
on near-field microwave imaging techniques.
2.3 TIME-HARMONIC ELECTROMAGNETIC FIELDS
2.3.1 Maxwell Equations
Electromagnetics (EM) is a fundamental science essential to understand the basic
concepts in physics and electrical engineering. EM theory deals with static, quasi static
and moving charges that causes current flow and maintains electromagnetic fields.
Unlike circuit theory, object dimensions are comparable to the operating wavelength in
electromagnetic field theory and systems are analyzed using distributed parameters and
coupling phenomenon. Electromagnetic field scattering, propagation, radiation, reception
and generation are characterized with the aid of the Maxwell’s equations.
14
Maxwell equations are necessary to understand EM radiation and how it scatters when
it comes in contact with objects. Using curl, divergence and the Stoke’s Theorem, the
Maxwell equations in point form can be derived.
⃗ =
∙
ρv
(2.1)
ε
⃗⃗ = 0
∙
(2.2)
⃗⃗
∂
⃗ = −μ
×
∂t
(2.3)
⃗
⃗⃗ =  + ε ∂
×
∂t
(2.4)
E and H : electric and magnetic fields measured in (V/m) and (A/m)
D and B: electric and magnetic flux densities measured in (C/m2) and (Tesla)
J: electric current density in (A/m3)
ρv: volumetric electric charge density (C/m3)
ε and µ: permittivity (H/m) and permeability (F/m)
The Maxwell equations can describe how EM radiation propagates through time and
space. Consider a vector field V given by,
⃗ = ̂

(2.5)
Maxwell proved that EM radiation propagates as time-harmonic EM waves. So any
component in the vector field can be represented as,
⃗ = V(, , )cos( + )

(2.6)
Applying Euler’s Identity to equation 4.6 yields,
⃗ = [V(, , ) (+) ] = V  

(2.7)
Substituting equation 4.7 into equations 4.1 to 4.4 yields the complex Maxwell equations.
⃗   =
∙
15
ρv  
ε
(2.8)
⃗⃗   = 0
∙
(2.9)
⃗   = −jωμ
⃗⃗  
×
(2.10)
⃗⃗   = ( + jωε
⃗ ) 
×
(2.11)
ω = 2πf: angular frequency or the rate of change of the EMF phase
2.3.2 Constitutive Equations
In the presence of electromagnetic fields, the stable state of the particles inside a
material are altered [2]. The response of the material to an EM field can be approximated
using the constitutive equations [17]. In isotropic media or media where the dielectric
properties (i.e. susceptibility, permeability, permittivity and conductivity) are all the same,
the continuity equations are,
⃗ =

⃗⃗ =

1
εo
+
1
μo
+
1
εo
 
(2.12)
 
(2.13)
1
μo
 = σ
(2.14)
εo and µo: free space permittivity (H/m) and permeability (F/m)
xe = (εr −1) and xm = (μr−1): dimensionless electric and magnetic susceptibilities
εr and µr: dimensionless material relative permittivity and permeability
σ: material electrical conductivity (Siemens/m).
The constitutive equations show how the structure of a material behaves in the presence
of an EMF is described by a materials susceptibility, permeability, permittivity and
conductivity.
These parameters are used to classify materials as dielectric, magnetic,
conductor or semi-conductor. In order to understand this phenomenon one must first
16
understand how EM radiation propagates in space and then how it propagates when it is
obstructed by particles in a material.
2.3.3 Wave Equation
The wave equation describes how EM fields propagate through time and space. It is a
second-order partial differential equation that describes how waves move in time and
space. In order to understand the propagation of EM radiation, first consider the wave
equation in one dimension,
⃗

 2
= 2
⃗

(2.15)
 2
c: is the speed of light in a vacuum (maximum speed particles can travel)
V: EM vector field (see equation 2.6)
Substituting equation 2.7 into 2.15 one can see how the vector field propagates in the xdirection in relation to time.
⃗

 2
⃗

=
()2
2
2
⃗ = − ( ) 
⃗


2

⃗ =0
+( ) 
2


(2.16)
Using the theory of linear differential equations, the general solution of the vector field V
is a linear combination of cosines and sines [linear ODE book].
 2
⃗ =  (  )


+ 
 2

−( ) 
(2.17)
2.3.4 Helmholtz Wave Equation
In order to understand how fields behave within an object, consider a source free
dielectric medium or material, the complex Maxwell Equations become,
17
⃗ = 0
∙
(2.18)
⃗⃗ = 0
∙
(2.19)
⃗ = −jωμ
⃗⃗
×
(2.20)
⃗⃗ = jωε
⃗
×
(2.21)
Taking the curl of equation 2.21 (Farady’s Law) yields the electric field vector wave
equation,
⃗ ) =  × (−jωμ
⃗⃗ )
 × ( × 
⃗ ) − 
⃗ = −jωμ( × 
⃗⃗ )
⇒  ( ∙ 
⃗ ) −  
⃗ = −jωμ(jωε
⃗)
⇒  ( ∙ 
⃗ =  ( ∙ 
⃗ ) − ω2 με
⃗
⇒ 
⃗ = ω2 με
⃗
⇒ 
(2.22)
Similarly taking the curl of equation 2.20 (Ampere’s Law) yields the magnetic field
vector wave equation,
⃗⃗ = ω2 με
⃗⃗
 
(2.23)
Equations 2.22 and 2.23 are known as the homogeneous Helmholtz Wave Equations.
These equations describe how EM radiation propagates in a source free dielectric
medium.
Like the solution of the one dimensional wave equation, the solution to
equation 2.23 will be a linear combination of sine and cosine functions in time (equation
2.17) with angular frequency of ω but also consists of a solution in space. This solution
will depend on the boundary conditions implied by the propagation medium.
18
2.3.5 EM Wave Scattering
As mentioned throughout this thesis microwave imaging exploits the dielectric
differences within materials in order to generate a microwave tomography of a material
under evaluation. In the case of NDE this process is non-invasive. ”Tomography” is a
method of sectional imaging that uses ”projections” or measurements acquired by
illuminating the object from different angles using a penetrating energy source [2]. The
mathematical foundations for image reconstruction from projections dates back to
Radon’s contribution in 1917 [2].
Microwaves are electromagnetic radiation that falls in the range of 30MHz-300GHz.
EM radiation at microwave frequencies, waves no longer travel in a straight path as the
size of the objects is comparable to the wavelength [2]. At these frequencies, the EM
radiation undergoes diffraction or scattering when the radiation waves come in contact
with particles within the material. This scattering can be generalized into two distinct
types of transmission or forward scattering and reflection or back scattering. Figure 2.3
shows the schematic illustration of different microwave tomography measurement
techniques.
The EM waves satisfy the Maxwell’s and continuity equations and the fields are
related to the material property by the constitutive equations [18] [19]. An EM wave
impinging on a penetrable object undergoes diffraction and multiple scattering within the
object resulting in a nonlinear relationship between the measured field and electrical
property of the object at the incident frequency [20]. This behavior is known as the
inverse scattering effect. Inverse scattering problems aim to reconstruct or estimate the
spatial distribution of a materials electrical properties or the scattering potential of the
19
obstacle from scattered field measurements [2].
In microwave imaging these field
measurements are commonly made with a network analyzer.
Figure 2.3: Commonly used Diffraction tomography setup (a)-(b) Transmission or
forward scattered (c) Reflection or back-scattered. [2]
The scattered field generated from an arbitrary shaped object with permeability µr (r,
ω) and permittivity εr (r, ω) can be obtained by substituting the permeability and
permittivity for the arbitrary material into the Helmholtz Wave Equation, equation 2.23.
⃗ () = ω2 μ(, ω)ε(, ω)
⃗ ()

(2.24)
⃗ (): the electric field that can be either the Ex, Ey, Ez component of the electric vector

field
Employing separation of variables on equation 2.24 yields [21] [22],
⃗ () = ω2 μ(, ω)[ε(, ω) − ]
⃗ ()
(  + ω2 μ(, ω)ε(, ω))
⃗ () = −(, )
⃗ ()
⇒ (  +  2 )
k=
2π
λ
(2.25)
: wavenumber which describes how the field disperses/travels within an object for

a given radiation wavelength  = .
20
(, ): forcing function that is only a function of time and describes how the radiated
EMF within the object material is affected based on the permittivity and permeability at a
given location within the object.
⃗  )
In the absence of the material dielectric scatterer, only the incident E-field (
exists everywhere and (2.25) reduces to the form,
⃗  () = 0
(  +  2 )
(2.26)
When the field comes in contact with a material dielectric scatterer, the field is the sum of
the incident E-field and the scattered E-field from the dielectric scatterer within the
⃗ () = 
⃗  () + 
⃗  () . Substituting this E-field quantity into (2.25) yields,
material 
⃗  () = −(, )
⃗ ()
(  +  2 )
(2.27)
Equation 2.27 is the inhomogeneous Helmholtz Wave Equation and the total field that is
scattered by a penetrable dielectric object. The magnitude of this field can be measured
by a microwave imaging system in order to generate the dielectric tomography of an
object under test.
2.4 GENERAL NEAR-FIELD MICROWAVE IMAGING TECHNIQUES
2.4.1 Open-ended Waveguide Techniques
Microwave images can be generated by measuring the amplitude of the reflected
voltage from a sample under test. The LEAP Team generated an image from the MIS
voltage response to a reflected microwave field from a concrete sample. A hole in the
sample was scanned and the resulting image and one dimensional (1D) signal is shown in
Figure 2.3. This image was acquired with the LEAP NFMWIS Generation I proposed in
Chapter 3.
21
Figure 2.4: LEAP NFMWIS Generation I 1D scan of Hole in a Concrete Sample
The measured signal clearly shows the hole in the center of the image and captures its 1
inch diameter geometry, which matches dimensions of the fabricated sample. For this
acquisition, the source frequency was 10 GHz with a scanning step size of 300 microns.
Sample topographies can also be generated by quantifying the amount of signal reflection
from a region on the sample with a network analyzer [4] [3]. These measured reflections
can be translated into images based on the voltage standing wave ratio VSWR,
permittivity [5] and conductivity and phase [23] [11].
In the experiment performed by Karl Bois in the paper Microwave Near-Field
Reflection Property Analysis of Concrete for Material Content Determination [3], an NA
22
and rectangular waveguide were used to perform a near-field and microwave NDE
inspection technique to determine the cure-state of concrete. Bois measured the amount
of signal reflection produced from sample concrete slabs. The amount of reflection was
used to characterize the concretes cure state.
This is an important issue in the
construction industry because being able to detect the cure state of concrete at a
construction site can mitigate days lost in extraneous delays waiting on the concrete to
cure.
Additional structures can be placed on the concrete sooner leading to faster
completion dates. Bois showed that creating this type of inspection system would not
only be useful for the construction field but it can be achieved simply with an NA and an
open-ended rectangular waveguide. Bois’ MIS is can be seen in Figure 2.5.
Figure 2.5: Bois Microwave Imaging System for Concrete Cure-State Inspection
In the Bois MIS the waveguide transferred the microwave radiation to the specimen and
the same waveguide captured the amount of radiation that was reflected back to the
source.
Bois’ MIS is an example of a 1-port system.
The NA can quantify the
waveguide’s signal response to the reflected radiation by comparing the transmitted
23
signal V+ to the reflected signal V- measured at the port of the NA. This ratio of V- to
V+ is called the S11 scattering parameter or the reflection coefficient. The reflection
coefficient tells how much power was transferred from the waveguide and how much was
reflected back to the source from the concrete specimen. Bois shows that the magnitude
of the reflection coefficient is directly proportional to the cure state of the concrete. Bois
shows that two factors affects concretes cure state, the water-content ratio (w/c) and
course-aggregate to cement ratio (ca/c). As the concrete mixture of sand, cement and ca
cures, the reflection coefficient magnitude measured by the NA increases because the
amount of course aggregate increases. The microwave radiation injected into the sample
by the waveguide scatters more when it is incident on the ca versus water or mortar. The
more ca the more the field scatters the larger the amplitude of the reflected field and the
larger the magnitude of the reflection coefficient. In concrete the w/c and ca/c will not be
the same everywhere.
Concrete is very inhomogeneous and due to this fact, the reflection coefficient
amplitude will very as you scan across the concrete specimen. Bois exploited this fact by
conducting two experiments, hitting the specimen with 3GHz (S-band) radiation and
10GHz (X-band) radiation. Instead of performing a raster scan of the entire 8inx8inx8in
slab of concrete which is typical, Bois conducted 20 and 160 independent measurements
on four sides of the concrete slab (excluding the top and bottom).
At 10GHz the
radiation wavelength is λ = 30 mm in free-space and Bois sees that as the concrete cures
the amount of scatter from the increased ca/c increases but the measurements at this
frequency do not provide information on the w/c.
When the Bois MIS generates
radiation at 3GHz the radiation wavelength is λ = 100 mm, Bois sees that the
24
measurements provide information about the background material (everything except the
ca). The background material consists of the cement paste which is an indication of the
w/c. Like the first experiment Bois sees that the amplitude of the reflection coefficient
increases as the ca/c increases and the w/c decreases indicating an increase in cure-state
for the concrete.
Bois’ experiment demonstrates a NDE technique is feasible with a rectangular
waveguide and a NA. The only drawbacks of the experiments is that it does not mention
the geometry of the rectangular open-ended waveguide nor does it mention anything
about the handling of impedance mismatches in Bois’ MIS. Impedance discontinuities in
the MIS system would definitely affect the amplitude of the reflection coefficient and the
concrete cure-state classification.
Bois might not have thought it was necessary to
mention but since he did not mention it, it appears that impedance matching was not
considered, which I’m sure it was in some capacity. Rectangular waveguides are good
for being able to scan and cover larger amounts of sample surface area at a time but their
geometries do not produce high-resolution systems and should not be used for microwave
imaging techniques requiring sub-mm or less resolution.
Muhammed S. Boybay presents analysis of a near-field microwave imaging
experiment that used an open-ended coaxial probe to achieve higher imaging resolution
than Bois. In the paper Open-Ended Coaxial Line Probes with Negative Permittivity
Materials [5], Boybay experiments with a coaxial open-ended waveguide that was
terminated with a two layered medium. The sample under test is sandwiched between a
ε-negative layer and is backed by a perfect electric conductor (PEC). Figure 2.6 shows a
diagram of the coaxial waveguide terminated with the two layered medium.
25
Figure 2.6: Open-ended Coaxial Line Terminated by a Two Layered Medium
Boybay experiments with the optimum target lift-off distance (d) and the thickness and
constitutive parameters of the negative medium ε-negative layer (t).
Boybay’s
motivation stems from recent development in the area of double and single negative
materials. Terminating coaxial probes with negative materials has revealed that the
properties of near-field probes can be improved considerably.
Boybay sees that
optimizing the negative layer thickness and probe to sample lift-off distance gives rise to
significant enhancement in probe sensitivity which allows the probe to have higher
material and detection resolutions.
The dielectric layer of the ε-negative layer is assumed to be infinite in the x-y plane
and the permeability is assumed to be equal to free-space permeability (µo). For different
negative layer thicknesses, the reflection coefficient was analyzed as a function of lift-off
distance. Similar to Bois, Boybay optimizes the lift-off distance and layer thickness by
analyzing the reflection magnitude measurements. One thing that Boybay did that Bois
did not do was he also measured the phase. The reflection magnitude and phase were
26
measured as a function of target distance for difference ε-negative layer thicknesses (see
Figure 2.6).
Figure 2.7: Magnitude of the reflection coefficient vs. target distance (left); Phase of the
reflection coefficient vs. target distance (right)
From the reflection magnitude plot displayed in Figure 2.7, Bombay deduced that the
optimal probe to sample lift-off distance and ε-negative layer thickness was t = 0.8 mm
and d = 0.87 mm. In addition, the phase of the reflection coefficient has the highest slope
at the target distance at which the minimum reflection is observed. At these target
distance and ε-negative layer thickness combinations, the reflection coefficient is
sensitive to the target location such that a small change in the target location causes the
maximum change in the phase of the reflection coefficient. As a result the minimum
reflection magnitude or the highest phase slope conditions correspond to the most
sensitive probe configurations.
Conventional coaxial line probes do not employ a ε-negative layer. Boybay mentions
that the optimum lift-off distance is equal to zero for this case. Meaning, the closer the
target is to the coaxial probe, the more sensitive the probe becomes and higher resolution
is achieved. This is valuable information because the LEAP NFMWIS does not employ a
27
ε-negative layer. The major take-a-way from Boybay’s experiments is that the lift-off
distance from target to probe matters. The lift-off distance can affect the sensitivity or
dynamic range of the MIS reflection magnitude measurements (one of the most typical
measurements made by MIS). It is best to experimentally optimize the target to probe
lift-off distance. Also, Bombay exploits the importance of measuring the reflection
magnitude and aids in showing its effectiveness as a parameter for generating microwave
image topographies. There were several things about Boybay’s experiments that could
have been a little clearer.
The MIS setup that was used to make the reflection
measurements was never divulged. Yes he mentioned that the operation frequency was
5GHz but he never mentioned what device was used to make the reflection measurements.
One would assume that it was a NA but you can also make reflection measurements with
a time-domain reflectometer (TDR). Bois or Boybay did not mention the power level of
the measurements devices which directly correlates to the size of the reflection
coefficient magnitude.
None the less Bois and Bombay show that effective MIS can be
constructed with open-ended waveguides.
2.4.2 Near-Field Scanning Tip Techniques
NDE methods of imaging surface and subsurface structures and material properties are
critical for acceptance testing and failure detection of countless applications including:
semiconductor defect detection, thin film resistivity measurement, continuity of
embedded transmission lines in printed circuit boards (PCB), and substrate epoxy void
detection.
These applications require high detection resolution in order to image their
material properties. Imaging with open-ended rectangular or coaxial cables are adequate
microwave imaging techniques, as demonstrated by Bois [3] and Boybay [5], but they are
28
better for applications that require large scan surface areas and lower resolution. In order
to image defects in semiconductors or the embedded traces of a PCB, a MIS must be built
to achieve µm resolution. G.E. Ponchak [7] and Yaqiang Wang [6] agree that ultra-high
resolution MIS can be achieved with scanning tip waveguides.
Scanning tips are commonly used for near-field imaging applications because they
make great use of the evanescent wave interaction between the sample under test and the
scanning tip. Wang explains how using an open-ended coaxial cables with a protruding
center tapered tip has the advantage of supporting microwave signals with nearly no cutoff limit and producing highly confined electromagnetic fields.
The confined field
confines the measurement area on a sample under test increasing the resolution of the
topographic dielectric measurements. Wang and Ponchak show that there are three
important elements to the fabrication of scanning tip waveguides: length, diameter and
scanning height or lift-off distance. Boybay mentioned that without using matching
layers to match and couple the microwave energy from the waveguide to the sample
under test, probe measurement sensitivity increases as the scanning height decreases.
According to Boybay the ideal scanning height for scanning tip probes would be when
the tip is in contact with the sample. Wang and Ponchak agree with Boybay that
measurement sensitivity increases as the scanning height decreases but explain that with
coaxial tips, parasitic capacitive coupling with the sample material is a problem that
limits coaxial tip microwave imaging techniques.
Parasitic capacitance or stray
capacitance can cause unwanted signal oscillations skewing the dielectric measurements
made by a MIS setup. Wang and Ponchack show two distinct design techniques to
mitigate parasitic capacitive coupling.
29
In scanning tip near-field applications, a microwave signal is sent through a coaxial
cable and radiates as microwave energy through a EMF. Ponchak explains that due to the
close proximity of the scanning probe required by near-filed techniques, the EMF extends
outward from the probe tip a short distance. Ponchak explains that an object that is
brought in close proximity to the tip will interact with the evanescent fields and change
the loading of the scanning tip. Figure 2.8 shows a schematic of the scanning tip and the
equivalent circuit produce between the tip and sample under test.
Figure 2.8: Schematic of Microstrip Resonator Used in a Microwave Evanescent Probe
Ponchak states that the dielectric properties of a sample generates unwanted increases in
the probe capacitance which results in a lower probe resonant frequency. Ponchak
validated this notion by detecting these variations in the probe resonant frequency, fo, by
measuring the reflection coefficient magnitude, |S11|, of the scanning tip resonator with a
NA.
30
Figure 2.9: Measured |S11| of channelized coplanar waveguide probe both with and
without a high resistivity silicon sample near the probe tip
Figure 2.9 shows the plot of the measured reflectivity when the probe is in isolation (no
sample underneath) and it shows the reflection magnitude measured when a silicon
sample was place under the scanning tip. Notice how the resonant frequency of the
scanning tip is shifted from approx. 9.86GHz with no sample placed close to the tip to
approx. 9.82GHz when the silicon sample was placed in close proximity of the scanning
tip.
Ponchak employs a microstrip scanning tip design in order to reduce the unwanted
parasitic capacitive coupling. Two microstrip designs were fabricated. The first uses a
channelized coplanar waveguide (CCPW) fabricated on a 0.3x175 cm (3000x1750000 µm)
thick RT/Duroid (εr = 2.2) substrate. The center conductor width is 0.127 cm (1270 µm)
and the slot width is 0.028 cm (280 µm) except at the probe tip which is tapered to a point.
Copper foil is used to connect the upper and lower ground planes to form the CCPW.
Shorting the ground planes eliminates unwanted transverse electromagnetic modes (TEM)
that result from the electromagnetic wave reflecting off of the boundaries between the
conductor and dielectric insulation in coaxial waveguides. The second probe is a stripline
31
scanning tip fabricated on εr = 3.8 RT/Duroid with a strip width of 0.5 cm. The substrate
provides a dielectric for the scanning strip/tip. This provides noise immunity and reduces
the effect of the parasitic capacitive coupling caused by close sample proximity.
Additionally, both probes have a 20 µm diameter wire tip at the end and are mounted in
an aluminum fixture to eliminate coupling to other probes and decrease the background
noise that would decrease the probe sensitivity.
Wang introduces a new microfabrication method to make silicon coaxial tips. Similar
to Ponchak, Wang employs a scanning tip with a microstrip design. The coaxial silicon
tip microfabrication process is outlined in Fig. 1.
Figure 2.10: Wang Coaxial Tip Fabrication Process
First, a 1-μm-thick thermal oxide is grown on a conductive Si wafer with a resistivity of
0.005 Ω⋅cm [see Figure 2.10(a)].
Then an oxide disk is patterned by standard
photolithography and buffered hydrofluoric (BHF) acid etching [see Figure 2.10(b)]. The
32
exposed Si is etched by a reactive ion etching (RIE) to form a tip precursor [see Figure 2.
10 (c)]. Next, a deep reactive ion etching (DRIE) process is performed using an STS®
Multiplex ICP system to form a tip shaft that determines the length of the tip. The oxide
disc is removed by hydrofluoric (HF) acid after the tip is sharpened using the oxidationsharpening method [see Figure 2. 10 (d)]. To form the inner conductor of the coaxial tip
structure [see Figure 2. 10 (e)], 300-nm-thick Cr film is then deposited on the wafer.
This film is patterned by photolithography using negative-tone SU-8 resist to cover the
tip feature. The insulation layer of the coaxial tip is a 1-μm-thick SiN layer deposited by
plasma enhanced chemical vapor deposition (PECVD) [see Figure 2. 10 (f)]. The outer
shield metal layer is a 1-μm-thick Cr film deposited by sputtering. It is patterned by
another SU-8 photolithography and etched to form the shield pattern [see Figure 2. 10
(g)]. The key step in fabricating the coaxial tip is the tip-exposure process. The final
coaxial tip structure is formed by a Cr wet etch and a SiN RIE. Figure 2.11 is an
micrograph of a coaxial tip with an opening aperture radius of 3 μm fabricated according
to the silicon tip process shown in of Figure 2.10.
Figure 2.11: Micrograph of a Wang Fabricated Silicon Tip
The Wang and Pochnak experiments are good to compare because they used scanning
tip waveguides in two distinct MIS designs. Pochnak uses a scanning tip coaxial cable
33
fed by a 0.5 - 12.5 GHz signal generator through a circulator. A crystal microwave
detector connected to the the circulator produces a DC voltage proportional to the
magnitude of the reflected signal. Samples are mounted on the xy stage platform and are
vibrated in the z-direction by a solenoid at a rate of approximately 100 Hz. This enables
synchronous detection of the signal by a lock-in amplifier to increase the SNR. A
LabVIEW program controls the positioning of the sample in three directions as well as
measuring and monitoring the output voltage of the lock-in amplifier at each position of
the sample.
Near-field scanning tips are characterized by determining the spatial
resolution and minimum detectable sample size.
The spatial resolution is typically
determined by imaging a small sample and reporting the full width of the image at one
half of the maximum signal level [7]. To characterize the resolution of the CCPW, a 20
µm diameter wire resting on a glass plate is imaged along the x and y-axis. The scanned
image of the wire along the x and y-axis for the CCPW at 10GHz is shown in Figure
2.12.
Figure 2.12: Scan of a 20 pm diameter wire along the x and y-axis using CCPW
evanescent microwave probe
34
The CCPW was able to resolve the PCB trace 25.5 µm and 22 µm along the x and y-axis
respectively. Meaning that Pochnak’s microstrip scanning tip approach achieves sub-mm
resolution.
Figure 2.13: Circuit Schematic for SNMM Scan
Wang generated a scanning near-field microwave microscopy (SNMM) system out of
two frequency sweepers, 2.36 GHz and 2.36 GHz + 93 KHz and two mixers. The two
mixers were used to modulate or down convert 2.36 GHz to 90 KHz, which lies in the
working frequency range of a lock-in amplifier. A directional coupler was used to guide
the microwave source from sweeper A to the coaxial tip, and it coupled the reflected
signal from the coaxial tip to one mixer. An atomic force microscope (AFM) probe was
used as the sample under test for his experiment. The output of this mixer contained the
information from the sample (AFM probe). The other mixer mixed direct signals from
sweepers A and B the resulting signal was fed as the reference signal for the lock-in
amplifier. The lock-in amplifier output was delivered to the data acquisition (DAQ)
channel of the AFM system to build up the microwave image of the sample. The SNMM
system that Wang developed was able to image the dimensions of the AFM probe.
35
Figure 2.14: Simultaneous SNMM images by the coaxial tip. (left) AFM internal sensor
image; (right) Microwave amplitude image
The cantilever width is correctly resolved in both AFM and microwave images, around
38 μm as shown in the Figure 2.14. Meaning Wang’s scanning tip approach in the
SNMM system achieved sub-mm resolution like Pochnak’s.
Pochnak and Wang’s design had many similarities and some subtle differences that is
why these two experiments on scanning tip microwave imaging techniques are good
references for designing and implementing scanning tip probes into a MIS.
Both
scientists designed micostrip scanning tip probes in order to reduce measurement noise
caused by RF interference and parasitic capacitive coupling due to the close proximity of
a test sample. Each scientist fabricated scanning tips with µm geometries in order to
achieve sub-mm resolution. The differences come in the form of the MIS used to capture
the topographies of a test sample. Fact, both Wang and Pochnak’s MIS used lock-in
amplifiers (phase-sensitive detector) to improve the system SNR but Pochnak’s system
used a crystal microwave detector connected to the port of a circulator in order to
measure and image the DC voltage that was proportional to the magnitude of the
reflected signal. Wang’s system measured the magnitude of the reflected signal from a
lock-in amplifier with an NA.
36
Lock-in amplifiers are useful for phase sensitive detection techniques (PSD).
The
amplifier locks onto signals with the same frequency as the reference signal input. The
voltage output of the amplifier is directly proportional to the phase difference between
the amplifier’s reference signal and the signal at the RF input. Phase detection is a very
useful inspection technique for microwave imaging systems. Bois [3], Boybay [5], Wang
[6], Ponchak [7] all produced microwave imaging systems that generated topographic
images based on measuring the dielectric variances in inhomogeneous materials. Each
microwave imaging applications previously mentioned imaged samples with relatively
high dielectric constants. As the demand for the medical application for microwave
imaging increases, imaging objects with lower dielectric constants such as laminates,
fluids, and tissue are more desirable. For lower dielectric constant materials sensitivity
and imaging resolution has seen success in measuring not only the magnitude of the
reflection coefficient but also the phase difference between the MIS transmitted signal
(Tx) and the measured received signal (Rx).
2.4.3 Near-field Phase Detection Approach
Xiao Feng Zhu presents a near-field imaging phase detection approach in the paper
Near-field Microwave Phase Imaging by a Spintronic Sensor [23]. Zhu agrees that a MIS
can generate topographic images by measuring a sample’s dielectric properties but
iterates that this can only be done with high accuracy when both the amplitude and the
phase of the radiated and reflected microwave fields are measured. Zhu experiments with
dielectric imaging by measuring the amplitude and phase difference of the Tx and Rx
fields using a spintronic sensor. Zhu’s work presents preliminary imaging using a single
37
sensor scan and shows the sensors capability to achieve both phase and amplitude
resolution on a sub-wavelength scale.
Figure 2.15: Zhu Spintronic Phase Detection MIS
Figure 2.15 shows the PSD experimental setup. The microwave power is split into two
coherently microwave signals that travel two independent paths.
In one path the
microwave signal is directly injected into the sensor from a coaxial cable while in the
other path the microwaves radiate on the sensor from a horn antenna.
The direct
microwave signal driven by the source and the radiated energy from the horn antenna are
coupled at a spintronic sensor. The sensor mixes the source signal and the voltage signal
induced in the spintronic sensor resulting in a homodyne DC voltage that contains
information on the phase difference between the two microwave signals. A lock-in preamplifier is used to measure the microwave induced DC voltage signal from the sensor.
Using the system pictured in Figure 2.15, phase difference measurements were taken
for two different liquids: water and isopropyl alcohol.
The liquids were placed in
channels of a dielectric grating with a period of λ/5 made from a slab of microwave
transparent Methyl Methacrylate (PMMA, ε /ε0=2.9), where channels of λ /12 in the
width and λ /15 in the depth were fabricated with a milling machine. The sensor was
placed a distance of λ /15 behind the grating to measure the near-field response of the
microwave field that transmits through the grating (Rx). Near-field phase difference
38
measurements were captured for the entire grating and imaged by performing a 2D raster
scan over the surface area of the PMMA grating using a 8.1GHz (37 mm wavelength)
microwave source. Zhu’s results for imaging the measured phase difference are shown in
Figure 2.16.
Figure 2.16: Near-field Phase Difference Measurements of Liquid Filled PMMA
Grating: (a) Grating filled with isopropyl alcohol; (b) Grating filled with water
Figure 2.16(a) shows that the spintronic sensor, situated λ /15 behind the grating detects
a periodical modulation in both the amplitude and the phase of near-field microwave
fields when scanning the grating filled with isopropyl alcohol. The dielectric constants
were increased by filling the channels with water, the EMF shifts and a much stronger
contrast in the 2D phase difference image appears as shown in Figure 2.16(b). The
pronounced phase shift due to water significantly enhances the contrast of subwavelength features of the grating, which reveals the power using a spintronic sensor to
detect amplitude and phase difference measurements in liquids with lower dielectric
constants compared to metal samples. Figure 2.16(a) and (b) shows that near-field
phase detection systems can achieve sub-mm resolution.
Compared with traditional transmission line based approaches presented by Wang [6],
Boybay [5] and Ponchak [7], where the parasitic noise from the transmission lines in
39
close proximity of test samples limit the sensitivity of the technique.
Zhu claims
transmission line techniques only provide a qualitative contrast but spintronic sensors can
deduce a quantitative value of the dielectric constant. Physically, both the induced sensor
voltage and the phase difference between the microwave source are related to the
transmission of microwaves in the media and are a representation of the material
dielectric properties. Therefore, the dielectric constant can be precisely determined from
the microwave propagation in comparison with the case for air (ε /ε0=1). The ability of
Zhu’s spintronic sesonsor phase detection approach to detect high dielectric contrasts
between the PMMA and liquids not only shows the superior sensitivity of phase detection
systems over conventional qualitative measurements made by Bois, Boybay, Wang and
Ponchnak but it also puts phase detection approaches at the forefront for microwave
medical imaging applications.
2.5 NEAR-FIELD MEDICAL IMAGING APPLICATIONS
The interaction of electromagnetic waves and matter depends on dielectric properties
which can be directly related to various types of biological elements due to their variable
degree of water content: bone, fat, muscle, etc. This specificity can be exploited in
different tissue types and even offers the rationale for detecting tumors. Permittivity
of biological tissues is normally high at lower frequencies due to the insulating effect
of cell membranes, and decreases over higher frequencies due to dispersion. Fat,
bone and lungs are examples of low water content tissues and muscles, internal
organs, blood and tumors are examples of tissues with high water content. Among
possible applications, breast cancer imaging remains a high research priority
because of its high occurrence. Roughly 200,000 new cases of breast cancer are
40
typically diagnosed in the U.S. every year, with an estimated 25%–30% of women
dying from the disease making it the second largest cause of female cancer deaths in
the U.S [11].
The microwave imaging techniques presently being pursued are generally either
radar or topography [3] [5] [6] [7]. Grzegorczyk presents a 3D imaging system for
generating 3-D tomographic images of breasts in his paper entitled Fast 3-D Tomographic
Microwave Imaging for Breast Cancer Detection [11]. It is not uncommon to wait tens of
hours or even days for a single 3-D microwave tomographic image. Most microwave
breast cancer detection systems are burdened with significant computational times
limiting their clinical utility. Grzegorczyk overcame these limitations by presenting a
MIS which achieves an exam time of less than 2 minutes and produces 3-D
tomographic images in minutes as well.
The 3-D tomographic MIS (see Figure 2.17) employs an array of 16 monopole
antennas is organized in a circular fashion. Each antenna sequentially transmits an
electromagnetic wave which propagates through the breast within the imaging
region. Measurements are collected at the remaining 15 antennas so that those
close to the radiator mainly measure waves reflected off tissue surfaces whereas
those opposite to the transmitter mainly measure transmitted waves. The multiview scattered intensity and phase distributions provide information about the local
dielectric properties of the tissues.
This information is translated into tissue
permittivity and imaged.
41
Figure 2.17: 3-D Tomographic MIS Examination Chamber: (left) 3-D representation of
the tomographic chamber; (right) Assembled antenna hardware
In order to limit reflections off the tank boundaries, a lossy liquid comprised of a
mixture of Glycerin and water provides a biologically sterile medium into which the
patient’s breast can be safely immersed. The system hardware can reliably measure
down to 140 dBm. Such a low noise floor requires an antenna-to-antenna isolation
of 150 dB. Grzegorczyk validates the detection specificity the 3-D tomographic MIS
by comparing breast images of a patient taken with an MR and then comparing it to
3-D tomographic images generated by the DAQ platform. The high resolution MR
image shows a malignant tumor detected in the left breast shown in Figure 2.18.
In order to achieve high resolution the 3-D tomographic system collects a high
number of samples and achieves low examination times by achieving a high sample
rate. The system collects 240 data points (16 transmitters with 15 receivers) in
roughly 1 s. In order to achieve sub-centimeter resolution, an operating frequency
of 1.3 GHz (λ = 230 mm in free space) optimized experimentally and shown to
depend on the breast composition. A mastectomy was performed on the patient in
order to remove the left breast.
The breast was then imaged by the 3-D
42
tomographic breast imaging system. Figure 2.19 shows the 3-D tomographic image
generated when the breast was examined by the 3-D tomographic MIS.
Figure 2.18: MR Imaged tumor in right breast: (left) Tumor Axial View (right) Tumor
axial View After Baseline Subtraction
Figure 2.19: 3-D Permittivity Breast Image from 3-D Tomographic MIS
Figure 2.18 shows a directional averaging of the 3-D permittivity images for each
breast compressed into a single coronal image (similar in concept to that observed
in standard mammograms). Consistent with the previous images and discussions,
43
the tumor is readily visible in the right breast image as an elevated permittivity
zone, with no discerning features visible for the right breast. Grzegorczyk’s 3-D
tomographic breast MIS images the reflection magnitude and phase produced in 16
monopole antennas to an EMF scatted from breast tissue.
His experiments
demonstrate a phase detection approach that enables a MIS to quantitatively
measure and image the dielectric permittivity of breast tissue. Grzegorczyk’s work
confirms Zhu’s experiments [23]of being able to use phase measurements to image
lower dielectric materials such as liquids, tissue and fat.
2.6 SUMMARY
Near-field microwave imaging is concerned with quantitative measurement of the
microwave electrodynamic response of materials on length scales far shorter than the
free-space wavelength of the radiation [9].
Near-field microwave imaging techniques
are very used for NDE inspection techniques. Microwave imaging is performed with a
MIS that can be used to measure material dielectric properties in materials (permittivity,
conductivity, reflectivity) with higher dielectric constants such as concrete [4] [3] and
traces embedded in a PCB [Pochnak.pdf]. MIS generally consists of a microwave source,
waveguide, receiver, data acquisition (DAQ) device, and a computer to process the data
and construct a visual dielectric topographic image of an object under study. Figure 2.20
is an example of a generic MIS. MIS measurements can be acquire data via a 1-port
network [4] [3] [5] [6] or two-port network configuration [23].
44
Figure 2.20: Generic Microwave Imaging System [24]
Three distinct near-field microwave imaging techniques were discussed in this chapter:
open-ended waveguides, scanning tip probes and phase sensitive detection techniques.
Open-ended rectangular or coaxial waveguide techniques should be used for imaging
applications requiring cm resolution [3] but scanning tip waveguides should be employed
in applications that require sub-mm resolution [7] [6]. In order to produce MIS with µm
resolution it is suggested that the phase of the reflected signal induced in the waveguide
be measured and compared to the transmitted signal from the MIS microwave source [23]
[11]. This chapter also suggests that resolution directly relates to the geometry of the
waveguide and the scanning lift-off distance [5] [6] [7].
Reviewing these three near-field imaging techniques was useful because it provides
background on the motivations behind the LEAP NFMWIS development efforts
described in detail in chapter 3. Early developments of the LEAP NFMWIS used an
open-ended rectangular waveguide and a 1-port MIS. The reflected signals from the test
sample were rectified by a crystal detector and used a DMM to capture the root-meansquare (RMS) of the rectified signal from the crystal detector output. This configuration
45
of the LEAP NFMWIS is properly coined Generation I because it was the first system
developed. Generation I of the LEAP NFMWIS generated microwave images using
software running on a PC to move an x-y positioner. The same software would acquire
the DMM voltage measurements at that x-y position and would render a 2D Plot of the
reflected voltage amplitudes when x-y scanning commenced. The desire of the LEAP
NFMWIS is to achieve sub-mm resolution and this was not achieved with Generation I.
Leveraging the ideas of Wang [6] and Ponchak [7] a scanning tip waveguide technique to
spatially confine the EMF radiation to more discrete points on the sample under test was
the motivation behind LEAP NFMWIS Generation II. Generation II used a fabricated
coaxial scanning tip waveguide employed with the same MIS setup as Generation I. An
increase in resolution was witnessed in the images acquired between Generation I and II
systems but Generation II images appeared to have noise attribute to the parasitic
capacitance caused by the close proximity of the sample under test and lossy connections
[6] [7]. Generation III of the LEAP NFMWIS employed a scanning tip waveguide with
a tapered tip following the experiments by Pochnak et. al. Noise was reduced by
terminating the scanning tip to a coaxial cable using SMA connectors. Also additional
shielding was added to reduce the parasitic capacitance coupling caused by the sample
under test and isolated the scanning tip from unwanted RF noise in the testing
environment. A vast improvement in image contrast and resolution has been witnessed
with Generation III.
.
46
CHAPTER III
OPTIMIZATION OF THE LEAP NFMW IMAGING SYSTEM
3.1 MICROWAVE IMAGING PROBLEMS
3.1.1 Constructing Valid Numerical Models
FDTD enables computational modeling and simulation of electromagnetic phenomena.
This is useful when there is a need to understand how EMF behaves in or on an object
(e.g. cell phone antenna, cable dish, transformer coils, etc.). This allows engineers and
scientists to gain information about a component or entire system before fabrication but
constructing a valid numerical model has several challenges,
1. Accurately defining computational domain or object structure for the
simulation.
2. Accurately defining computational boundary conditions
3. Accurately defining material properties (e.g. permittivity, permeability and
conductivity).
4. Modeling the field distribution in the near-field (kz < 1, where z = source-tosample distance and k = 2π/λ is the wavenumber) [12]
3.1.2 Real-time NFMW Imaging
Small signals are typically used in NFMWI techniques and usually amplification is
required to bring these signals into the measurement range of the data acquisition device.
It’s common to use amplifiers to make this translation. The large amplification of signals
attribute more noise to a MIS because the amplifier is going to amplify the noise as well
as the desired signal embedded in it. Noise issues also arise in the waveguide and with
the measurement setup.
47
3.1.2.1 Systematic errors
Several systematic errors can arise when using an MIS to generate the reflection
topography of an object under test.
1. Impedance mismatches between MIS components
2. Flexing of the RF cables [25].
3. Positioning between the sample and waveguide/aperture (in accurate
measurement alignment) [25].
3.1.2.2 Drift Errors
Long measurement times can cause drift errors in measurements due to various wave
propagations in the RF cables used in the MIS. Measurement drift can also occur due to
temperature increases of the internal hardware of the data acquisition device [25]. The
advantages of MIS: ability to focus the energy, relatively low cost, emits non-ionizing
radiation.
The limitations of MIS: hard to achieve high spatial resolution, low
penetration depth, susceptible to EMF interference.
3.1.3 Open-Ended Waveguide (Scanning Tip)
In the case of the NFMWIS a scanning tip was designed to achieve sub-mm resolution
in the near-field, DTip << λ (where DTIP is the aperture diameter or tip curvature) [9]. A
probe tip of this size interacts with the device under test (DUT) in a spatially confined
region. The near-field of an aperture carries with it spatial information on the order of
the aperture size [26]. The spatially confined field distribution near the aperture is
effectively a sampling function of small spatial extent. The tip is placed close to the
sample in order to take advantage of this sampling affect [26]. The aperture of the
scanning tip and its physical performance in the MIS is unknown and should be solidified
48
experimentally. Essentially the scanning tip is an open-ended waveguide that serves as
an antenna radiating and receiving (1 port networks) microwave energy.
Since
microwave imaging techniques typically use small signals, adequate shielding of the
scanning tip is essential for high SNR.
3.1.4 Phase Extraction Challenges
Near-field microwave imaging measurement techniques typically suffer from small
signal-to-noise ratios (SNR). Techniques require instrumentation that provides signal
enhancement, noise reduction, and long-term stability [26]. An arbitrarily high SNR can
be achieved while still preserving long-term stability by implementing phase sensitive
detection (PSD) mechanisms [26].
PSD is often implemented with an RF mixer in
conjunction with a low-pass filter. Mixers are three-port networks (2 inputs, 1 output)
that multiply a local oscillator signal (LO) with an RF signal and the output of the
product is produced at the IF output. A DC signal arises when two sinusoidal signals are
mixed together and the low-pass filter isolates this signal so a device can measure it. The
amplitude of the DC signal is proportional to the phase difference between the two mixed
signals [27]. Problems arise with the PSD approach due to the performance isolation of
the mixer.
RF mixers allow signals from the input ports (LO and RF) to leak to the
output port (IF) contaminating the signal and in turn contaminating the DC signal and
phase measurement. Mathematically, the frequency components generated by a mixer
are,
FIF = nFLO ± mFRF
(3.1)
n and m: are integers
We only want the fundamental output frequency (when n=1 and m=1), the existence of
49
all other harmonic terms creates significant problems [28].
Elimination of these
distortion products is critical in developing an efficient PSD approach.
3.2 LEAP NFMWI SYSTEM OVERVIEW
Following suite of microwave imaging setups, generically the NFMWIS was
composed of an X-Y positioner to perform raster scans; a waveguide to transmit the
microwave radiation to the sample under test; a DAQ device to measure the waveguide’s
response to the returned microwave radiation and a PC to collect the data, perform post
processing and to generate the image. In the LEAP NFMWIS, the waveguide that
transmits the microwave radiation also measures the response of the waveguide to the
received near-field radiation making the NFMWIS a 1-port network.
Figures 3.1 and
3.2 show the current LEAP NFMWIS setup. This thesis covers two main approaches that
were developed during the optimization of the LEAP NFMWIS setup. Approach 1
measures the amplitude of an induced voltage signal produced in a coaxial tip antenna
(CTA) to the reflected microwave energy from a test sample placed a small lift-off
distance away in the near-field. Approach 2 measures the phase difference between the
received AC signal induced in the CTA versus the transmitted signal generated by the
microwave source.
50
3.2.1 Approach 1 LEAP NFMWIS Voltage Amplitude Detection System
Figure 3.1: Block Diagram of LEAP NFMWI Voltage Amplitude Detection System
3.2.2 Approach 2 LEAP NFMWI Phase Detection System
Figure 3.2: Block Diagram of LEAP NFMWI Phase Detection System
51
3.3 LEAP NFMWIS OPTIMIZATION METHODS
As mentioned before microwaves are good at detecting changes in the dielectric
properties of materials and due to their high dielectric constants, metals are some of the
best candidates for microwave imaging applications. In order to monitor the image
quality of each LEAP NFMWIS approach. A calibration sample was fabricated from
aluminum to help gauge the optimization process of each LEAP NFMWIS approach
(calibration sample is shown in Figure 3.3).
Figure 3.3: 15” x 12” Aluminum Calibration Sample (dimensions are in inches)
Assembling an efficient MWIS, a steady development process is required in order to
optimize all the elements of the imaging system.
Chapter 3 discusses the LEAP
NFMWIS optimization efforts that were made in the areas of system synchronization,
scan execution time, antenna design, imaging resolution enhancement and image postprocessing.
52
3.3.1 System Synchronization
When creating accurate dielectric topographies of materials there must be
synchronization between the position and the measurement.
To generate the best
microwave images, the PC, X-Y positioner (scanner) and DAQ device need to be
synchronized. Initial development efforts of the LEAP NFMWIS utilized two computers
to execute a scan. One computer controlled the scanner and the other computer ran a
MATLAB script in order to read measurements from the DAQ device. Each computer
ran as two independent state-machines.
Scans could still be achieved and the system
generated images but when trying to achieve a MWIS with sub-mm resolution,
measurements need to line-up with the current scan location on the sample.
The LEAP NFMWIS scanner is an Arrick Robotics MD2 scanner, which accepts
serial commands through an RS-232 bus. A single MATLAB script (scan.m in appendix)
was developed to issue move commands to the scanner and also coordinated the retrieval
of measurements from the DAQ device. This script ran on one PC alleviating the
dependency of two computers. A Flow Diagram of the imaging algorithm is shown in
Figure 3.4. One can see that the scanner is moved to a desired position, waits, DAQ
occurs and the scanner is moved to the next position, waits, and DAQ occurs and repeat.
DAQ always occurs between positioner movements showing that the synchronization of
NFMWIS components was achieved.
3.3.2 Scan Execution Time
An imaging system is neither effective nor efficient if it takes a day to produce a
microwave image. The benefit of the MATLAB algorithm implemented in Figure 3.4 is
that it synchronizes the positioner movements and DAQ, which yields improved
53
microwave images because there is better identification of sample defect locations. The
downside is that it took a long time to scan test samples. This was unacceptable to the
LEAP Team because without synchronization we were performing scans much faster.
This is an example of where system optimization efforts are required. The algorithm
provides synchronization between sample position and DAQ allowing for better resolved
images, that is a must, but the algorithm leads to long scan times, which shows
inefficiency in the system design. At this stage one must begin to consider all elements
of the MWIS that are involved in the image acquisition process. The two physical
components that could affect scan times are the positioner and the DAQ.
There’s
minimal latency in code execution due to today’s GHz processor speeds.
The positioner of the LEAP NFMWIS is an Arrick Robotics MD2 scanner with two
stepper motors to independently control the 2-axis X-Y movements. The DAQ device
has alternated between a DMM and spectrum analyzer. During initial development, the
positioner motors were ran at very slow speeds. After reviewing the Arrick Robotics
MD2 user manual it was seen that increased motor speeds could be achieved by
prescribing the scanner with a velocity profile.
Since the two scanner motors are
independent, distinct profiles can be issued for each motor. The velocity profile is
provided with a sequence of three numbers separated by semicolons [start velocity of #
steps/s : max velocity of steps/s : acceleration/deceleration slope of # steps/s2].
In order to the positioner drive stepper motors four signals are sent in specific
sequence in order to control clockwise (CW) or counterclockwise (CCW) movements. If
the frequencies of the control signals are too high, the motors fail to interpret them and
motion will not occur.
Thus, the velocity profiles of the positioner motors were
54
experimentally optimized in order to attain the maximum motor velocity that achieves
motion without causing excessive sample vibration.
The optimized velocity profile
moves positioner motors 1 and 2 at a start velocity of 400 steps/s and achieves a
maximum velocity of 600 steps/s with an acceleration/deceleration of 200 steps/s2. From
the positioner user’s manual, the serial bit rate (baud rate) of the positioner controller can
be set to a maximum of 115200 bits/sec. It was thought that issuing commands at the
maximum rate of the controller’s serial buffer could decrease program execution time
considerably. Initial development efforts showed that the bit rate had marginal effect on
overall scanning execution times so it remains at the controller’s default rate of 9600
bits/sec.
Through experimentation it was easy to see that the long execution times of the LEAP
NFMWIS scanning algorithm shown in Figure 3.4 are attributed to two major areas:
1. Object raster scanning algorithm
2. Embedded delays within the DAQ algorithm
For the algorithm in Figure 3.4, the X-position of the scanner corresponds to the sample
length (Xlength) and the Y-position corresponds to the sample width (Ywidth). First, the
scanning algorithm breaks up the designated sample scanning area into rows (x-steps)
and columns (y-steps). The scanner is instructed to traverse the width of the sample by
moving the designated stepper motor a specified number of y-steps and record the DAQ
device measurement into a 2D matrix. Once the scanner has traveled the entire sample
width it will stop DAQ and reverse the y number of steps to return back to top of the
sample, move over a specified sample length (number of x-steps) and began the DAQ
55
process again by traversing the sample width and recording measurements.
Note,
measurements are only recorded when the width of the sample is being scanned.
Figure 3.4: Flow Diagram of Initial LEAP NFMWIS Raster Scan Algorithm
Let the travel time it takes for the positioner to return to the top of the sample be
denoted by YREPOSITION. For the algorithm implemented Figure 3.4, YREPOSITION ≈ 6
seconds (see scan.m script in Appendix). The travel time multiplied by the total number
of x and y-steps (XSTEPS and YSTEPS) it takes to traverse the designated sample scanning
region contributes a considerable amount of time to the overall scanning execution time!
Sample reposition occurs before incrementing an x-step, so the total time it takes to
reposition the sample is,
56
TREPOSITION = YREPOSITION × XSTEPS
(3.2)
For example, if the scanning area of a sample is designated as 100 XSTEPS and 100 YSTEPS,
according to equation 3.2, the algorithm wastes 6 seconds x 100 XSTEPS = 600 seconds
(10 minutes) in sample repositioning time. This latency was removed by removing the
instruction to reposition the sample before incrementing the sample length. The scanning
algorithm in Figure 3.4 was improved by taking measurements as the width of the
scanning region is traversed (top-to-bottom), as before, but once the end of the sample is
reached, instead of stopping DAQ and traveling back to the top of the sample before
reconvening scanning, the DAQ is stopped and the scanner moves a specified sample
length (x-steps), DAQ begins and the width of the scanning region is traversed (bottomto-top). Like the initial algorithm all data is stored in a 2D array with dimensions XSTEPS
by YSTEPS. The improved raster scan algorithm is shown in Figure 3.5 and the MATLAB
code is located Appendix B. This algorithm required data post-processing in order to
yield the appropriate images. Every even column of the 2D data matrix had to be flipped
from bottom-to-top in order to produce an appropriate microwave image (see scan.m in
Appendix A). Eliminating the extraneous sample repositioning movements automatically
improved the execution time of the LEAP NFMWIS by 10 minutes.
57
Figure 3.5: Flow Diagram of Optimized LEAP NFMWIS Raster Scan Algorithm
The algorithm implemented in Figure 3.5 has a sampling rate of approximately 1 square
inch per 20 seconds (1 sq. inch/ 20 seconds). The delays between movements were
optimized in order to limit measurement error due to sample vibration. Initially one
would think that the larger delays to allow for the sample to stop the better. Yes larger
delays lead to minimal vibration and reduced measurement error but it also leads to
longer scanning execution times.
Example, consider the DAQ algorithm of the MATLAB script shown in Figure 3.4.
The course movement of positioner stepper motors causes the sample to move relative to
58
the positioner movements. Fast scanning execution time is desirable but it comes at with
a cost. Not allowing sufficient delays leads to measurement error. It causes the sample
under test to wiggle or vibrate due the momentum the sample builds due to the quick
movements of the positioner. Placing a small delay between the positioner movements
can mitigate vibrations of the sample. Early revisions of the NFMWIS scanning software
the major delays are: a 0.7 second delay between each y-step (YDELAY), a 0.1 second
delay between each lateral x-step (XDELAY) and YREPOSITION time to re-orient the sample
before executing each x-step. These are just the major delays in the algorithm and do not
include the time it takes to execute the MATLAB scanner position code, the DAQ control
code or the data processing code. All major delays in the DAQ process need to be
optimized in order to maximize the trade-off between fastest execution time and minimal
sample vibration.
First, an approximation was performed to determine how much each delay contributes
to the total execution time of the physical scanning process (TotEXC.). Example, consider
a test sample scanning region is defined as 100 XSTEPS by 200 YSTEPS.
The total
execution time of the initial scanning algorithm is approximately,
  ≈ (XDELAY × XSTEPS ) + (YDELAY × YSTEPS ) + TREPOSITION
(3.3)
XSTEPS and YSTEPS: total number of x and y-steps for a scanning region
XDELAY = 0.1 sec and YDELAY = 0.7 sec: delay between each x and y-step
YREPOSITION = 6 sec: time delay to reorient sample before taking another x-step
Using equation 3.2 and 3.3 the approximate total scanning execution time is 750 seconds
(12.5 minutes) for a sample scanning region of 100 XSTEPS by 200 YSTEPS.
59
The impact each major delay has on the total scanning execution time can be
approximated as,
XD.I. ≈
(XDELAY × YSTEPS )
YD.I. ≈
(YDELAY × YSTEPS )
TotEXC
Yrep.D.I. ≈
TotEXC
× 100
(3.4a)
× 100
(3.4b)
(YREPOSITION × XSTEPS )
TotEXC
× 100
(3.4c)
XD.I. and YD.I.: impact of x-step delays on overall scanning execution time
YrepD.I.: impact of sample repositioning delays on overall scanning execution time
Using equations 3.3 and 3.4(a)-3.4(b), for a test sample scanning region of 100 XSTEPS by
200 YSTEPS, the impact of the each major delay on the total scanning execution time is:
XD.I. = 1.3%, YD.I. = 18.7% and YrepD.I. = 80.0%.
The reposition delays were eliminated with the raster scan algorithm developed in
Figure 3.5. This algorithm reduces the total execution time by a minimum of 10 minutes
and but most importantly increases system performance by 80%. Now consider the total
scanning execution time attributed by the x and y-step delays. For a 100 XSTEPS by 200
YSTEPS scanning region, the x-step delays have a minimal 1.3% impact on the overall
scanning execution time but the y-step delay impact of 18.7% is considerable. Since data
measurements are only extrapolated during Y position moves, the y-step delay mitigates
system measurement error attributed to sample vibration. The shorter the delays between
y-step positioner movements, greater are the sample vibrations. High sample vibration
leads to poor microwave images and longer delays between positioner movements leads
to longer execution times. This is another point in the LEAP NFMWIS system where
optimization had to be performed.
Through experimentation the 0.7 second delay
60
between each y-step scan point was reduced to YDELAY = 0.15 seconds, this reduces the
overall scanning execution time for a 100 x 200 point sample scanning region to TotEXC =
(0.1 x 100) + (0.15 x 200) = 40 seconds (0.7 minutes). Optimizing the YDELAY to 0.15
seconds improved the system performance by 26.7% (XD.I. = 40/150).
3.3.3 Antenna (Waveguide) Design
The waveguide is the most import component of a MWIS. It’s the medium that
transmits the microwave energy to the sample under test. The waveguide of the LEAP
NFMWIS has undergone three major design changes during its development. Initial
development (Generation I) used an open-ended rectangular waveguide as the
transmission medium. The second (Generation II) used a coaxial tip antenna (CTA)
made from an RG58U coaxial cable. The the third (Generation III) and most current
setup, is evaluating the using of a tapered scanning tip was fabricated and was terminated
to the end of the coaxial waveguide through an SMA connector.
3.3.3.1 LEAP NFMWIS Generation I
The first LEAP NFMWIS used an open-ended rectangular waveguide to transmit
microwave energy to the test sample.
Rectangular waveguides are good for scanning
samples with a large surface area such as concrete slabs [4] [3]. They’re also good when
high-resolution is not critical. Using the control sample a microwave image a microwave
image was generated with the LEAP NFMWIS Gen. I. This image is pictured in Figure
3.6.
61
Figure 3.6: LEAP NFMWIS Open Ended WG Scan: (left) Calibration sample; (right)
Microwave Image
Initially the phase detection approach involved using the HP8559A spectrum analyzer
(SA). Since the phase development approach was developed in parallel with the LEAP
NFMWIS questions of using various DAQ hardware was posed.
During the early
development effort, a feasibility test was conducted with the Generation I system to see
62
what kind of images would be produced when using the SA as the DAQ device instead of
the Agilent DMM.
Figure 3.7 shows the imaging results of the SA feasibility test.
Figure 3.7: LEAP NFMWIS Open Ended WG Scan with SA DAQ Device
3.3.3.2 Generation II
In near-field applications requiring sub-mm to mm resolution, it’s good to use a
scanning tip waveguide. The diameter of the tip should be much less than the radiation
wavelength [26] and the length of the scanning tip should be equivalent to half the
radiation wavelength in order to transmit all the energy from the source to the test sample.
Tipdiameter ≪ λsource
Tiplength ≤
λsource
2
(3.5)
(3.6)
The second progression of the LEAP NFMWIS used a coaxial scanning tip antenna
(CTA) that was made by removing the dielectric jacket at the end of a RG58U coaxial
cable exposing the copper conductor. This design has the advantages of lower-cost and
easy of fabrication. The diameter of the inner conductor of the co-axial cable is around
63
1.02 mm, which is much smaller than any other kind of probes LEAP had developed to
this point. The length of the antenna was designed to be 1/2 wavelength (1.5 cm) to have
the maximum return loss for the antenna. Figure 3.8(a) shows the CTA tip implemented
in the LEAP NFMWIS and Figure 2.9(b) shows some of the LEAP NFMWIS key
components.
Figure 3.8: LEAP NFMWIS CTA waveguide: (left) waveguide tip and (right) signal
spliter and amplification (annotate picture)
Figure 3.9(a) shows an image generated with the mm CTA and Figure 3.9(b) shows the
image attained with the cm scale open-ended rectangular WG. Better resolution of the
calibration sample defects was achieved using the mm CTA as opposed to the cm scale
open-ended rectangular WG.
64
Figure 3.9(a): LEAP NFMWIS Scan Results Calibration sample CTA scan results
Figure 3.9(b): LEAP NFMWIS Scan Results Open-ended WG Scan Results
Notice the apparent circles around what appears to be the sample defects.
These
functions are caused by the point spread function (PSF) of the scanning tip waveguide
65
aperture. The image clearly shows that shapes are evident but they appear blurred and
unclear. There appears to be a series of circles surrounding each shape of the calibration
sample when imaged by the Generation II of the LEAP NFMWIS.
3.3.3.3 LEAP NFMWIS Generation III
Even though the CTA was able to obtain better scanning results than the open-ended WG,
the inner conductor of the coaxial cable was not mechanically solid enough to implement
contact scanning. Generation III of the LEAP NFMWIS utilized copper tapered scanning
tips. These tips are various diameters and lengths to suit different scanning test frequencies.
Figure 3.10 shows the collection of the prototyped copper probe tips (CPTs) that the LEAP
Team has fabricated.
Figure 3.10: Copper Probe Tips
CPTs are designed to attach to an SMA connector to implement scan testing. The diameter
of each probe tip is 4mm, 3mm and 2mm (from left-to-right). Since the resolution of MWIS
depends on the size of the probe tip, LEAP designed probe tips of various sizes. The probe
tips in Figure 3.10 are for 3GHz ( λ = 100 mm in freespace ) and 10GHz ( λ = 30 mm in
freespace ) scan test frequencies. The designed length the of each antenna are 1/2 of a
wavelength corresponding to the 3GHz and 10 GHz scan frequencies this will direct the EMF
66
at a particular sample location.
This design feature aids in minimizing the return loss of the
antenna. Figure 3.11 shows the return loss of the CPT as it was analyzed with a vector
network analyzer between the frequency range of 500 KHz and 3GHz. The expectation is to
see the strength of the returned signal dip at 3GHz, which means the signal, was purely
transmitted from the tip at 3GHz as it was designed. However, the return loss measurements
indicate that the signal is mostly transmitted at 2.2GHz. This means the probe tip that LEAP
designed is able to transmit and reflect signals, but not at the intended frequency.
Developing the right CPT is an ongoing process that LEAP continues to work towards.
Figure 3.11: CPT Return Loss
We also did the scanning test using the CPT. We put the ground plate at the bottom of the
tip to reduce the noise [pochnak.pdf, Wang.pdf]. Since SMA connectors work better at
high frequencies comparatively, we used SMA cables as transmission lines to transfer the
signals. Figure 3.12 shows the new scan setup using the CPT.
67
Figure 3.12: Experimental setup with CPT
LEAP conducted several experimental scans of calibration sample with the new CPT and
compared the images to the CTA. The results are provided in Figure 3.13.
Figure 3.13: Scan result comparison between CPT (left) and CTA (right)
The result shows that the shapes from the calibrate sample are clear and also reduce the
noise around the shapes, which means the CPT is able to give us a sharper image
compared to the CTA and the rectangular open-ended WG LEAP has implemented thus
far. The finer tip has a smaller aperture and a smaller PSF. Comparing the CTA imaging
results to the CPT results notice that circles or airy disks caused by the CTA are non-
68
existent in the CPT imaging results. The CPT does impose a PSF but it is more confined
and provides little blurring when imaging the calibration sample.
3.3.4 Image Resolution Techniques
Figure 3.7 introduced results of the Generation I imaging system using the SA as the
DAQ device. Notice how there’s not a strong sharpness or distinction between sample
defects and non-defects like the results of the CTA or CPT. Through experimentation
and analysis it was seen that the amplitude measurement data set acquired for the
calibration test samples has a small dynamic range when scanned. The small dynamic
range can be due to multiple things, systematic noise due to the mismatched impedance
of the cables, connectors and equipment of the LEAP NFMWIS, sample vibration due to
positioner movements and the PSF of the open-ended WG. Small dynamic range can
also be attributed to a low SNR of the imaging system. In physical implementations of
any MWIS there will be some noise attributed to system signals.
These imaging
impurities can be filtered out with CPTs or better shielding techniques but noise can also
be filtered out with image thresholding techniques. Image thresholding is a technique
often applied to image pixels but LEAP decided to try it with the Rx amplitude data
acquired with Generation I of the LEAP NFMWIS using the SA as the DAQ device. The
goal is to make this distinction as sharp as possible so a binary thresholding technique
was applied. Binary thresholding is an image processing technique to improve the
contrast between foreground objects and the background in an image. Consider the
simple binary thresholding algorithm,
1, TLOW ≥ Ii ≤ THIGH
Oi = {
0, otherwise
69
(3.7)
Where Oi is the value of the output data point i, Ii is the value of input data point i and
TLOW and THIGH are the high and low threshold values. If the data point is within the
threshold values it makes that data point appear white in the image (Oi = 1). If the data
point falls outside the thresholding values then the algorithm makes the data point appear
black in the image (Oi = 0). In image processing a histogram of an image is produced in
order to algorithmically determine thresholding values. Using MATLAB a histogram of
the acquired Rx amplitude dataset imaged in Figure 3.14 was produced.
Figure 3.14: Histogram of Gen. I Rx Amplitude Data Acquired with SA
Instead of deriving the TLOW and Thigh thresholding values algorithmically, they were
derived experimentally based on analysis of the histogram data. The optimum low and
high threshold was set to TLOW = -50.05dB and THIGH = -47.5dB. Figure 3.15 shows a
flow chart of the binary thresholding algorithm applied in MATLAB.
70
Figure 3.15: MATLAB Thresholding Algorithm
The binary double thresholding technique was applied to bring the sample defects to the
foreground and place all other data points in the background. The binary thresholding
results can be viewed in Figure 3.16. Notice how there binary thresholding technique
creates a strong contrast between defect and non-defect areas. It also helps remove the
PSF of the open-ended WG. This feasibility study shows the power of imposing image
processing techniques in order to optimize the imaging results of the MWIS. It also helps
to limit cost and time in refining the MWIS components if sufficient image processing
algorithms can be applied.
71
Figure 3.16: Binary Thresholding Results: (left) Voltage Amplitude Image using LEAP
NFMWIS Generation I; (right) Image after applying optimized binary thresholding
algorithm
3.4 LEAP NFMW PHASE DETECTION APPROACH
The purpose of the phase detection approach is to develop an approach to measure
phase difference between the transmitted (Tx) and received (Rx) signals of the LEAP
NFMWIS to see if plotting the phase difference improves system resolution.
The
difference in phase between transmitted signal (Tx) and the reflected signal (Rx) is a
fruitful area for research and investigation besides the magnitude information collected
by Approach 1 of the LEAP NFMWIS. The goal of Approach 2 of the LEAP NFMWIS
is to collect the phase difference information between Tx and the reflected signal Rx.
Phase information aids in material characterization and imaging materials with smaller
dielectric constants such as composite materials, liquids or tissue [23].
Composite
materials are quickly replacing materials because their strong degradation resistance and
light weight. The necessity of imaging liquids and tissue is strongly driven by the desire
to develop adequate medical microwave imaging applications.
72
3.4.1 Background Information
It was thought the phase difference between the transmitted signal, Tx, and received
signal, Rx, in the LEAP Near-Field Microwave Imaging System (NFMWI) could be
acquired using a HP8559A spectrum analyzer. This is not possible because the HP559A
is a scalar spectrum analyzer. Scalar spectrum analyzers only measure and report the
amplitude vs. frequency of the input signals over a specified frequency span. In the
NFMWI system the transmitted signal is a 10GHz sinusoidal signal of the form,
Tx (t) = A cos(ωt + Φ)
(3.8)
Φ: phase of the transmitted signal
A: Tx signal amplitude
ω: angular frequency = 2πf, where f =10GHz
A = Vrms =
Vpp
(3.9)
2√2
Vrms: root-mean-square voltage
Vpp: voltage peak-to-peak
Scalar spectrum analyzers often present the amplitude in terms of signal power
referenced to 1mW or Decibels-milliwatts (dBm),
Vrms2
dBm = 10log10 (
R Po
)
(3.10)
R: signal input impedance = 50Ω (typical)
Po: reference power, 1mW for dBm, 1W for dB
The amplitude measurement displayed by a scalar spectrum analyzer contains no phase
information about the sinusoidal input signal. Therefore, using the HP8559A, only the
amplitude, power and frequency of the NFMWIS Rx signal can be extrapolated.
73
3.4.1.1 HP8559A Phase Measurement Simulation
Consider the following feasibility test. A Tektronix AFG3102 arbitrary function
generator was used to simulate the Rx signal of the NFMWI system. The function
generator was configured to supply a 100MHz, 1 Vpp, 0 phase shift sinusoidal signal.
The signal was supplied to an Agilent 8463E scalar spectrum analyzer. Using equations
3.9 and 3.10 the amplitude of the signal is A ≈ 0.353 Vrms (3.98dBm). Figure 3.17
shows the screenshots of the function generator signal and the frequency vs. amplitude
curve measured by the Agilent 8463E. The red boxes on Figure 3.17 highlight the
properties and measurements of the simulated Rx signal on their respective devices. The
Agilent 8463E measured an input signal with amplitude of 3.64 dBm and a frequency of
100MHz. Notice, the screen of the spectrum analyzer reports no information on the
phase of the input signal.
Figure 3.17: NFMWI Phase Measurement Simulation: Rx Signal (right); Scalar
Spectrum Analyzer Measurement (left)
Due to the inverse scattering produced by the test sample, there will be a phase
difference between the Tx and Rx signals in the NFMWIS. In order to simulate this, a
phase shift of 90 degrees was added to the signal produced by the function generator.
Figure 3.18 shows the screenshots of the function generator signal with added 90 degrees
74
phase shift and the corresponding amplitude vs. frequency curve measured by the Agilent
8463E. The red boxes on Figure 3.18 highlight the properties and measurements of the
simulated Rx signal on their respective devices. Though a 90 degrees phase difference
was added to the input signal, the spectrum analyzer makes the exact same measurements
seen in Figure 3.17. There’s a discrepancy between the calculated power of the Rx
signal and what was measured by the Agilent 8463E. This measurement is potentially
caused by variances in the impedance of the output port of the signal generator and or the
input port of the spectrum analyzer.
Both ports are listed at 50Ω.
Also, power
discrepancy could be related to user error. Nevertheless, the function generator was
configured to display the power of its output signal seen in Figure 3.19.
Figure 3.18: NFMWIS Phase Measurement Simulation: 90o Phase Shift Rx Signal (left);
Scalar Spectrum Analyzer Measurement (right)
The Agilent 8463E interprets the simulated Rx signal with and without phase difference
exactly the same. The scalar spectrum analyzer does not preserve the phase or temporal
information of an input signal. Since the HP8559A is a scalar spectrum analyzer it is
strongly inferred that it won’t capture this information either. Alternate approaches are
required in order to measure the phase information of a test sample scanned by the
NFMWI system.
75
Figure 3.19: Output Signal Power Displayed on the Function Generator
3.4.2 Analog Mixing Phase Detection Approach
Frequency mixing is an analog phase detection technique that is used to measure
phase difference between two signals with same frequency. For our purpose these two
signals are the transmitted signal (Tx) and the reflected signal (Rx). This approach is
achieved by feeding these two amplitude-limited signals into a product detector and the
output of the detector will represent the phase difference between the signals after
filtering out high frequency harmonics [27].
Figure 3.20: Schematic of Product Detector (Analog Multiplier) [27]
Analog mixing can be performed with an RF or microwave mixer. Typically mixers
have 2 inputs (LO, RF) and 1 output (IF). In the NFMWIS LO will be generated by Tx,
RF will be generated by Rx and are expected to oscillate the same frequency. When two
76
analog signals are mixed, a voltage proportional to the detected phase difference is
generated at the IF output of the mixer (VIF) [27].
VIF =
KV1 V2
2
[cos(2ωt − θ) + cos θ]
(3.11)
V1 and V2: amplitudes of Tx and Rx
K: gain caused by the analog mixer circuitry
ω = 2πf: angular frequency of Tx and Rx
θ = (θTx – θRx): phase difference between Tx and Rx
VIF is a mixed sinusoidal signal that oscillates at twice the frequency of the input signals
with a DC offset [27].
The DC component is roughly proportional to the phase error
[27]. The AC signal is composed of the fundamental frequency of Tx and Rx but also
possess some higher unwanted harmonics. Mathematically, the frequency harmonics
generated by a mixer are,
FIF = nFLO ± mFRF
(3.12)
m and n: integers
For phase detection, the fundamental output frequency (when n=1 and m=1) is desired,
the existence of all other harmonic terms distorts the IF output signal of the mixer
causing significant problems in accuracy [28]. Normally, these unwanted frequency
harmonics are filtered out by a low-pass filter leaving the DC offset:
VIF =
KV1V2
2
cos θ
(3.13)
Rearranging equation 3.13, the phase difference between Tx and Rx can be computed.
2Vo
180
θ ≈ cos−1 ( KV1V2 ) (
77
π
) degrees
(3.14)
Generally, the response of phase detectors is non-linear and repeats over a limited phase
range. However the response is usually very nearly linear in a narrow phase range [27].
Two simulations were performed to gain the theoretical and physical understanding of
phase detectors utilizing analog mixers. These simulations aided in optimizing the LEAP
NFMWIS phase detection approach before purchasing the phase detection hardware.
3.4.2.1 MATLAB Phase Detector Simulation
An analytical simulation for phase detection using analog mixing was performed using
a MATLAB. The script Phase_Detector_Simulation.m (see Appendix A) generates the
following sinusoidal signals to simulate Tx and Rx.
Tx (t) = A cos(2π × 10x109 × t)
R x (t) = B cos(2π × 10x109 × t + Φ)
Figure 3.21: Plot of Tx and Rx and their frequency spectrums
Figure 3.21compares the Tx, Rx and their frequency spectrums. The script calculates the
product of Tx and Rx which is a sinusoid at twice the fundamental frequency that
78
oscillates with a DC offset proportional to the phase difference between Tx and Rx. The
product signal, Gx is shown in Figure 3.22.
Figure 3.22: Tx and Rx Product Signal and frequency spectrum
The script applies a low-pass filter to isolate the DC offset of the resultant signal. Using
equation 3.14 the phase difference between Tx and Rx was plotted versus the DC offset
of the product signal Gx (VOGX) in Figure 3.24.
79
Figure 3.24: VOGX vs. Tx and Rx Phase Difference
3.4.2.2 LTspice Phase Detector Simulation
Using LTspice, a phase detector circuit was created. The circuit consists of 2 RF input
signals, 1 RF output signal, a double-balanced mixer and a first-order low-pass filter.
Figure 3.25: Double-balanced Mixer Phase Detection Circuit
In order to measure the phase signal between Tx and Rx they should oscillate at the same
frequency, so RO=LO=100MHz.
Each signal is coupled into the mixer by a 1:1
transformer to not amplify either signal and to keep both input signals isolated from one
80
another. To remove distortion in the phase detector, a first order low pass filter was add
to the IF output of the mixer to remove unwanted higher-order harmonics. A first-order
low-pass filter has the following cut-off frequency,
fc =
1
2πR1 C1
(3.15)
R1: filter resistor
C1: filter capacitor
The cut-off frequency of the phase detector circuit in Figure 3.25, fC ≈159KHz, which is
well below the double-frequency component 2*f = 200MHz.
Using LTSpice the
performance of the phase detector circuit was analyzed. Figure 3.26 is a screenshot of
the LTspice simulation circuit. The LO and RF inputs are driven by two sinusoidal 1
VAC @ 100 MHz voltage sources. The 1:1 transformer that couples the LO signal into
the phase detector is center tapped to ground so a voltage at half the amplitude of LO is
induced into the secondary coil of the transformer.
Figure 3.29 shows the unfiltered 1 VAC @ 200 MHz IF output signal from the
double-balanced mixer. The IF output signal is twice fundamental frequency of the LO
and RF input AC voltage sources. The IF output also oscillates with a DC offset of 250
mV. Figure 3.30 shows the harmonics of the IF output signal and why a low-pass should
be used in order to isolate the frequency component of interest. In the case of phase
detection it’s appropriate to use low-pass filter that isolates the DC component of the
product signal and eliminates all higher order harmonics because they cause signal
distortion. The double-frequency AC component in IF is filtered out by the first-order
low-pass filter (see Figure 3.25) leaving the DC offset. The C1 capacitor in the low-pass
filter takes approximately 5 time-constants (5τ = 5*RC ≈ 5µs) to charge up to the value
81
of the DC offset. The minimum time it takes for the capacitor to charge up to the DC
voltage needs to be considered. The delay between each acquired data point would need
to be 5τ minimum. The effect the low-pass filter has on the mixer IF voltage output is
shown in Figure 3.31.
Figure 3.26: Screenshot of Double Balanced Mixer Built with LTspice
Figure 3.27: LO and RF Phase Detector Input Signals
82
Figure 3.28: LO Induced Signal into Phase Detector Circuit
Figure 3.29: Phase Detector IF output without Low-pass Filter
83
Figure 3.30: Spectrum of Mixer IF Output Voltage
Figure 3.31: Phase Detector IF output with Low-pass Filter
The phase difference between the RF and LO signals was varied between 0 to 180
degrees by increments of 9 degrees.
At each phase increment the IF voltage was
measured. Figure 3.32 shows the phase detector output voltage measured at each phase
84
increment.
The phase difference was calculated using equation 3.14.
Figure 3.33
compares the calculated and theoretical phase difference.
Phase Detector Voltage Response
500
400
IF Voltage [mV]
300
200
100
0
Phase Detector
Output Voltage
-100
-200
-300
-400
-500
0
30
45
60
90
120
135
150
180
Phase Difference [degrees]
Figure 3.32: Double-balanced Mixer Phase Difference Measurement
Phase Difference:
Calculated vs. Theoretical
200
Phase Difference [degrees]
180
160
140
120
Theoretical Phase Diff.
100
80
Calc. Phase Diff.
60
40
20
0
1
2
3
4
5
6
7
8
9
Measurement #
Figure 3.33: Detected Phase Differences Actual vs. Calculated
85
Phase Detector Voltage Response:
MATLAB Mixer, LTspice Mixer
0.6000
IF Voltage [mV]
0.4000
Phase Detector IF Voltage
MATLAB Simulation
0.2000
0.0000
Phase Detector IF Voltage
LTSPICE Simulation
-0.2000
-0.4000
-0.6000
0
18
36
54
72
90
108
126
144
162
180
Phase Difference [degrees]
Figure 3.34: MATLAB Phase Detector Product Voltage Results vs. LTspice Double
Balanced Mixer IF Voltage
Figure 3.34 compares the IF output voltages for the MATLAB and LTspice phase
detector models for phase differences ranging from 9 to 180 degrees. The two traces in
the plot of Figure 3.34 show vertical lines between the IF voltages of each phase detector
model for a given phase difference between the input signals LO and RF. These lines
highlight the difference between the MATLAB and LTspice phase difference simulation
models. Part of the disparity is because the LTspice model requires that the voltage
sources LO and RF have some internal series resistance and MATLAB does not.
Modeling voltage sources with internal series resistance is a real and more accurate
assessment.
3.5 LEAP NFMWI PHASE DETECTION SYSTEM
After performing two simulations, physical components to implement phase detection
were purchased. Two components were needed, an RF mixer and a low-pass filter but
only the RF mixer has been purchased at this time. Distortion plays are large role when
86
creating systems that can measure small signals. Amplifiers can be used to amplify small
signals but the amplifier does not isolate and only amplify the desired signal, it amplifies
the signal distortions and noise as well. Riding the measurement signal of distortions is
key when using RF mixers for phase detection [28]. Several issues arise when using a
mixer for phase detection, LO-to-IF leakage and improper filtration of high-order
harmonics in the IF output signal. In order to develop an effective phase detection
approach, the performance of the RF mixer had to be analyzed.
The RF mixer is a SigTek SM1717 RF Mixer. The mixer has a specified bandwidth
of 4-12GHz for the RF inputs LO and RF. The mixer also has a 7dB conversion loss
(10*log[Pin/Pout]), this is the amount of loss incurred between the input signal (RF) and
output signal (IF). When the mixer was purchased a WAVETEK 809A was used as a
10GHz microwave source in the LEAP NFMWIS but after experimentation this source
was proved to be noisy. The WAVETEK 809A was replaced by a more modern Agilent
N5181A arbitrary waveform generator and the source signal (Tx) was adjusted to 3GHz.
Figure 3.35 shows the setup used to make bandwidth measurements of the mixer to see if
driving the mixer with a 3GHz source was feasible or would the mixer attenuate the
signal too much so phase detection was not possible.
87
Figure 3.35: Diagram of Mixer BW measurement setup
An Agilent E5062A network analyzer (NA) configured to make throughput
measurements (S12) was used to analyze the frequency response of the mixer. To see
how much the mixer inputs would attenuate the 3GHz signal and determine if the 3GHz
signal generated by the Agilent signal generator could be used to drive the LO input of
the mixer during scanning. The Agilent generator was used to generate a +17dBm @
3GHz microwave signal. Figure 3.36 shows the forward voltage gain from the RF input
to the IF output from 300 KHz to 3 GHz. Three frequency points are marked in the
figure showing the amplitude of the transmitted signal from the SM1717 RF Mixer
Bandwidth Analysis. Notice that the amplitude of the signal is -10.462 dB (+19.583 dBm)
at 3 GHz.
88
Figure 3.36 Forward voltage gain from the RF input to the IF output
Before integrating the mixer into the LEAP NFMWIS the mixing behavior of the RF
mixer was compared to IF voltage simulation data from the SPICE and MATLAB and
simulation. Using the setup in Figure 3.37 the IF voltage output of the mixer was
analyzed. A phase difference was generated by adjusting the phase difference on one
signal generator and leaving the other one constant at 0 degrees. The phase was adjusted
between the range of 0-180 degrees and the resulting IF voltage was measured at 9
degree increments to agree with the MATLAB and LTspice simulations. Figure 3.38
shows the measured IF voltage compared to the IF voltage seen in the MATLAB and
SPICE simulations and Figure 3.39 compares the phase difference approximations
between the MATLAB and LTspice simulations to the approximations made with the
physical mixer.
89
Figure 3.37: RF Mixer IF Voltage Experiment Setup
Phase Detector Voltage Response:
MATLAB Mixer, LTspice Mixer, SM1717 Mixer
0.6
IF Voltage [mV]
0.4
Mixer IF Voltage MATLAB
(V)
0.2
Mixer IF Voltage LTSPICE (V)
0
SigTek 1717 Mixer IF Voltage
(V)
-0.2
-0.4
-0.6
0
18
36
54
72
90
108
126
144
162
180
RF & LO Phase Difference [degrees]
Figure 3.38: MATLAB, LTspice and SM1717 RF Mixer IF Voltage Response
90
Calculated Phase Difference:
Calculated vs. Theoretical
Calculated Phase Difference [degrees]
180
160
Calc. Phase Diff. 1717
SigTek Mixer [degrees]
140
120
Calc. Phase Diff. LTSPICE
[degrees]
100
80
Calc. Phase Diff. MATLAB
[degrees]
60
40
20
0
0
18
36
54
72
90
108
126
144
162
180
Theoretical Phase Difference [degrees]
Figure 3.39: MATLAB, LTspice and SM1717 RF Mixer Phase Difference
Approximations
There are two common noise modes when using analog mixers, signal leakage
between the input and output ports of the mixer and harmonic distortion. Signal leakage
can occur between the LO and RF port (Isolation LO-RF) and between the LO and IF
ports (Isolation LO-IF). Per the SM717 specification the LO-RF isolation is 25dB min.
and the LO-IF isolation is 20dB min. The spectrum of the IF output of the mixer was
analyzed with a CXA-N9000A spectrum analyzer.
When two analog AC signals are
mixed the output is a mixed signal consisting of an AC signal that oscillates with a DC
offset.
As mentioned before, the AC signal is composed of harmonics of the general
form FIF = n FLO ± FRF.
Two Agilent NXA signal generators were used to drive the RF and LO input signals to
the SM1717 RF mixer. One signal generator was set to output a 17dBm @ 3GHz signal
to the LO input; the other one was set to provide 17dBm @ 1 GHz signal to the RF input.
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Table 3.1: IF Voltage Frequency Harmonics
FIF Harmonics
Frequency (GHz)
0*FRF + FLO
3
FRF + 0*FLO
1
FRF + FLO
4
FRF - FLO
2
The output from the mixer was fed to the spectrum analyzer to study the spectrum of the
IF voltage output signal. The measured IF signal harmonics are presented in the SA
screenshot provided in Figure 3.43.
Figure 3.43: SA CXA-N9000A display with 3GHz and 1 GHz fed to the mixer inputs
3.6 INITIAL LEAP NFMWI PHASE DETECTION
Figure 3.43 shows annotated pictures of the physical LEAP NFMWI Phase Detection
System, the block diagram of the measurement setup is located in Figure 3.2.
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Figure 3.43: LEAP NFMWI Phase Detection System
3.6.1 LEAP NFMWI Phase Detection Measurement Method
Here are the initial results from the LEAP NFMWI Phase Detection Approach.
Measurements were taken with a coaxial scanning tip waveguide positioned a lift-off
distance of approx. 3mm (0.1”) from the aluminum calibration sample. Feasibility of the
setup was determined by measuring the triangle in the middle of the sample (see Figure
3.44). The output of the microwave generator was externally set to +0.9dBm @ 7.33GHz
with an analog voltage of +0VDC using an HP DC power supply (see WAVETEK 907A
User’s Manual for external control of power output).
Mid-size triangle
Figure 3.44: Mid-size Triangle on Aluminum Calibration Sample
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The microwave source was routed to a +20dBm amplifier and then split into two
signals with a power splitter. One of the signals drives the LO input of the mixer and the
other is routed to a directional coupler and fed to the CTA. The Rx signal induced in the
CTA from the signal reflection produced by the sample under test is fed to the RF input
of the mixer. The mixer takes the products of two Tx and Rx sinusoidal signals and
produces a mixed signal at its IF output (see equation 3.11). The current phase detection
setup does not have a low-pass filter. LEAP wanted to perform initial testing in order to
test the feasibility of the phase detection approach before purchasing additional hardware.
Even without a low-pass filter, the DC offset that resides in the mixed signal IF output
can be measured with a DMM but there will be distortion in this signal due to the higherorder harmonics of the AC signal.
This distortion will cause errors in the phase
difference calculation but the approximate phase difference between the two analog
signals can still be computed using equation 3.14. After preliminary the test results are
analyzed and the setup is a little more refined, study of adding a low-pass filter to
improve phase measurement accuracy will be implemented.
3.6.2 Initial Phase Detection Scan Results
Figure 3.45 shows the IF output voltage of the mixer measured by the DMM for the
mid-size triangle on the calibration sample.
Figure 3.46 shows an image of the
calculated phase difference using Eq. 2. From the feasibility phase detection scans there
is noticeable contrast between the fabricated triangle hole and the surrounding aluminum
material. Due to the success of the phase detection feasibility scan taken of the mid-size
triangle on the calibration sample, a scan of the entire aluminum calibration sample was
performed. Figure 3.47 shows the results of the mixer’s IF output votlage and Figure
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3.48 is an image of the calculated phase difference using Eq. 2.
When the phase
difference calculations were imaged in Figure 3.48, there is minimal contrast between
the defects and non-defect material. This is because the information was plotted using
MATLAB’s imagesc function with the hot color map.
The imagesc function scales
image data to the full range of the hot color map. To improve image contrast, the IF
voltage and phase difference data were imaged using the default color map of the
imagesc function. The results can be seen in Figures 3.49 and 3.50.
Figure 3.45: Phase Detection Feasibility Scan of Mid-size Triangle
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Figure 3.46: Image of Calculated Phase Difference
Figure 3.47: Image of Mixer IF Voltage Measurements
96
Figure 3.48: Image of Calculated Phase Difference
Figure 3.49: Image of Mixer IF Voltage Output Default imagesc Color Map
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Figure 3.50: Image of Calculated Phase Difference Default imagesc Color Map
3.7 SUMMARY
The major components of the LEAP NFMWIS are a PC, microwave generator,
waveguide, DAQ device and X-Y positioner.
The waveguide is used to transmit the
microwave radiation to the sample under test, the DAQ device is used to measure the
waveguide’s response to the returned microwave radiation and the PC is used to collect
the data, post process and generate the image. In the LEAP NFMWIS the waveguide that
transmits the microwave radiation also measures the response of the waveguide to the
received near-field radiation making the NFMWIS a 1-port network.
Currently there are two main approaches to optimizing the LEAP NFMWIS setup.
Approach 1 is an amplitude detection approach that measures the received DC signal
produced in the waveguide scanning tip waveguide to the reflected microwave energy
from a test sample in the near-field. Approach 2 is a phase detection approach that
measures the phase-difference between the received AC signal produced in the CTA
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waveguide versus the transmitted AC signal from the microwave source. Any MWIS
requires optimization in order to refine its imaging capability.
Chapter 3 shows
optimization in the areas of system synchronization, raster scanning algorithms, DAQ
algorithm, waveguide design and image post-processing techniques.
This chapter expresses that MWIS should have the shortest execution time but not at
the expense of poor image resolution.
It also demonstrates that there is a strong
correlation between image resolution and waveguide design. LEAP NFMWIS Gen. I
reaffirms that rectangular open-ended waveguides are good for microwave imaging
applications but not for systems that require sub-mm resolution. LEAP NFMWIS Gen. II
reaffirms that sub-mm resolution can be achieved with coaxial scanning tip waveguides.
LEAP NFMWIS Gen. III reaffirms that EMF can be localized and directed using a
tapered scanning tip waveguide which generates higher-quality images. Chapter 3 also
provided insight on the LEAP Teams parallel development process of a phase detection
system in hopes of imaging materials with lower dielectric constants (i.e. composite
materials, liquids, body tissue). There are a lot of improvements and optimizations that
can still be made to the LEAP NFMWIS but the information presented in Chapter 3
shows that the team is headed in a feasible and good direction.
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CHAPTER IV
CONCLUSION
4.1 FUTURE WORK
4.1.1 Numerical Modeling of LEAP NFMWIS Waveguide
The most essential component of any imaging system is the channel which the energy
is transferred to the object. In the case of MIS, the waveguide is the channel that
transfers EMF intensity to the sample to be imaged. The more intensity that can be
transferred from the source to the object or the higher the efficiency of the system, better
the imaging quality. Modeling waveguides using FDTD can be beneficial in deciding
what waveguide shape and material will work for a particular system. Ideally, you want
the applied source field to be the field that reaches the target without loss. Physically,
this is not the case. FDTD can be used to model how the EMF will interact within the
waveguide to determine its efficiency.
In summer 2012 a simple FDTD model was
constructed on the Generation I LEAP NFMWIS during a NSF Research Internship
conducted at the Indian Institute of Technology-Madras.
4.1.1.1 Algorithm
Finite Difference Time-Domain is a numerical modeling technique for computational
electrodynamics. FDTD makes possible algorithmic modeling of electromagnetic wave
(EMW) interaction in physical structures.
EMW is modeled the same way as acoustic
waves, with the wave equation (see Chapter 2). With given initial conditions the EMF
amplitude can be approximated at any point in time and space. Instead of solving
complex partial differential equations in order to obtain field intensity, you can apply an
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FDTD algorithm to reduce solutions to algebraic equations. It does this by systemically
turning time-dependent Maxwell equations into finite-difference equations via Taylor
Series Expansion. Mathematically the process is represented with equation 4.1.
∂u2
∂t 2
= c 2 ∇2 u → ′ () ≈
(+ℎ)− ()
ℎ
(4.1)
If u is the input field or microwave source, equation 4.1 explains that the approximation
of a wave at any point and time in space is nothing more than the derivative of the source
wave at the specified point. Central or finite difference equations describe the velocity or
rate of change of a wave as it moves through space. The solutions to these difference
equations yield an approximation of the EMF intensity at particular instance in time and
space within the modeled structure.
Most commonly FDTD modeling is performed with Yee Cells and the Yee algorithm,
named after the originator Kane Yee. Yee Cells are a form of model meshing that is used
to spatially define the electric and magnetic fields propagating within a structure. A
cluster of Yee Cells is appropriately termed a Yee Mesh.
Figure 4.1 shows the
geometry of a FDTD Yee Cell in 3D. Notice that the Yee Cell resembles a cube that
describes the Magnetic field (H-field) and Electric field (E-field) components at discrete
points along the surface of the cell, these points are called nodes (similar to nodes in an
electric circuit).
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Figure 4.1: Yee Cell Mesh Grid
The E and H-fields at each node can be numerically solved using the Yee Algorithm.
The algorithm yields an approximation of the EM radiation at any point in time and space
inside a structure. Generally, these are the steps to simulate a FDTD Yee Algorithm: (1)
Define computational domain for the simulation in terms of Yee Cells. (2) Define the
permittivity, permeability and conductivity of each cell within the modelling domain. (3)
Excite the Yee Mesh (cluster of Yee Cells) an AC source. (4) Compute the H-field
vector components in the cell at a given instant in time. (5) Compute the E-field vector
components in the same cell at the next instant in time. (6) Repeat the process over and
over again until the desired transient or steady-state electromagnetic field behavior is
fully calculated.
4.1.1.2 Boundary Conditions
Quality FDTD models impose boundary conditions (BCs).
Dissimilar material
interfaces and sources along boundaries result in discontinuous field behavior. At such
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boundaries, the solutions to Maxwell’s Equations are meaningless and cannot be used to
define the EMF behavior [2]. Instead, the field behavior is given by the BCs that
examine the field vectors themselves at discontinuous boundaries. Accounting for BCs
permits the construction of accurate numerical models for diverse structural geometries.
These BCs describe how the EMF propagates at the walls of a structure and correctly
account for the TEM modes that are produced at these boundaries. To reduce model
complexity, Perfect Magnetic Conducting (PMC) or Perfect Electric Conduction (PEC)
are two common BCs that are imposed to develop decent FDTD numerical models. PEC
and PMC BCs describe how the E-field and H-fields flow on the surface boundary of a
material. Consider two distinct spaces in a material where the dielectric properties are
not the same (anisotropic). PEC and PMC BCs imply that the tangential field component
Et and Ht that propagates on the surface between the medium boundary is equal to zero
(Et = 0 and Ht = 0) and only the normal field components propagate from medium 1 to 2.
Figure 4.2: EMFs at material discontinuity: E-field at PEC boundary (left): H-field at
PMC boundary (right)
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4.1.1.3 Simulation Results
A simple FDTD simulation of a parallel plate waveguide was conducted in C++. In
the simulation ‘Waveguide3DFDTD.cpp’ a parallel plate waveguide with interior width =
2.29 cm and height = 1.02 cm was modeled. The waveguide was defined by a Yee Mesh
of 132 x 20 x 9, 23,760 total Yee Cells with 25 cells defined per wavelength. The guide
is modeled in a vacuum so the permittivity and permeability equal that of free space (εo =
8.85 x 10-12 F/m, µo = 1.26 x 10-6 H/m) and the wave velocity equals the speed of light (ν
= 3.00 x 108 m/s). The program models EMF interaction within the parallel plate
waveguide due to two types of time-varying stimulus sources S(t), a sinusoidal pulse or a
continuous wave (CW) pulse. The source emanates from the x = 0 face of the waveguide.
The time-varying excitation generates an E and H-field inside the waveguide. The
simulation propagates the EMF for 1,000 steps through the waveguide/meshes which
equated to 2.19ns of simulation time. Figure 4.3 summarizes the computational model
parameters.
Figure 4.3: FDTD Parallel Plate Computational Parameters
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Exciting a parallel plate waveguide with a time-varying source, induces an E-field
between the top and bottom plates. Waveguide3DFDTD.cpp simulates EMF behavior to
understand how the field propagates due to the various dielectric properties (i.e.
permittivity, permeability) throughout the waveguide. Doing this gives an idea of how
effective and efficient the waveguide will be at transmitting microwave energy. The
simulation applies the Yee FDTD scheme and first computes the H-field for the cell at
each time step and then computes the corresponding E-field for that cell at the next
instance in time for the inner meshes. Finally, the fields at the wall boundaries of the
waveguide are computed imposing PEC BCs on the faces of the Yee Mesh that are along
the y-axis of the waveguide meaning Ex and Ey components in Figure 4.1 are equal to
zero and the Ez component completely reflects because no E-field propagates in
waveguide wall.
The initial step in validating the simulation was to ensure the source signals supplied
to the waveguide are accurate. In the case of exciting the wave with a sinusoidal pulse,
the source signal is in equation 4.2.
1
S(t) = 2 (1 + sin(ωt − π))
(4.2)
t: current simulated time (0 to 2.19ns).
In the case of a continuous pulse source signal, view equation 4.3.
S(t) = sin(ωt)
(4.3)
C doesn’t have a visual plotting tool, in order to plot the two stimulus waves, the
amplitude versus time data was placed into a text file. The data is then passed to a
MATLAB script, ‘FDTD3D_Sim.m’, which parses the data from the text file and
generates a 1000 x 2 array from the data and produces a plot. Figures 4.2 is a graph of
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the sinusoidal pulse and Figure 4.3 depicts the CW pulse. As you can see the two
stimulus pulses are accurate.
Figure 4.2: Sinusoidal Pulse Stimulus
Figure 4.3: Continuous Wave Pulse Stimulus
FDTD is all about describing the field behavior within the waveguide. So a visual
representation had to be constructed in order to analyze whether the field behavior
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appeared reasonable. FDTD can describe the EMF intensity at any point and time in
space. With a 120x20x9 for the x,y and z dimensions respectively, you can approximated
the field amplitude at any combination of these points. The simulation provides field
intensity data for six field components (Ex, Ey, Ez, Hx, Hy, Hz) were each component is
a 3-dimensional array consisting of the electric field intensity vector for every point (e.g.
Ez[i][j][k]) in the mesh for that component at a given time step, including the field
intensity at the boundaries.
Since the source emanates from the x = 0 face of a parallel plate waveguide the only
concern is the E-field intensity component in the direction of the height of the waveguide,
Ez. This is because the sides of the waveguide are open and the guide sits in a vacuum.
The intensity of the field at the boundary walls of the waveguide are computed using
PEC boundary conditions. Thus, the surfaces that make up the top and bottom of the
waveguide or Yee Mesh (combination of 120x32x9 Yee cells) completely reflect the
electromagnetic waves without creating phase change in the electric field (E-field). After
the inner mesh E-Field intensity data is computed, the intensities at the PEC boundaries
are computed. The data for each field intensity component, per time step is placed into a
text file. The text file was then parsed into 132x20x9 3D arrays via the MATLAB
FDTD3D_Sim.m script. The MATLAB script also plots each fields text file at each time
step one right after another. When FDTD3D_Sim.m is executed the Ez component
actually appears to propagate through the waveguide mesh.
After multiple simulations,
I found out picking a point that is in the center of the mesh/waveguide, Ez[66][15][5],
provides the best results.
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Figure 4.4 displays the 2D (x and y) and 3D (x,y and z) Ez-Field intensity in the
parallel plate waveguide due to a sinusoidal pulse excitation at 10GHz. You can see that
the stimulus pulse in Figure 4.2 matches the pulse that emanates at x=y=0 in the ‘2D EzField propagated for 2.12ns’ plot of Figure 4.4. In the same plot you see that the
sinusoidal pulse appears to reflect and go negative and reflect and return positive again.
This behavior is due the PEC boundary conditions imposed at the walls along the height
of the waveguide implying the Ez-field is completely reflected. Also in Figure 4.4 is a
volumetric representation of the Ez-Field intensity at three different time steps: 0.292ns,
1.092ns and 1.53ns.
There were some challenges in plotting the 3D Ez-field intensity
per time step. It would be nice to see the field propagate through a volumetric space.
This is achievable with additional work. Figure 8 displays the Ez-Field intensity in a
parallel plate waveguide due to a CW pulse stimulus at 10GHz as well. You can see that
the stimulus pulse in Figure 4.3 matches the pulse that emanates at x=y=0 in the ‘2D EzField propagated for 2.12ns’ plot of Figure 4.5. In the same plot you see that the Ez-field
produced by the CW pulse appears to peter out periodically through the waveguide. This
is attributed to the stimulus field destructively interfering with the reflected fields
produced by the PEC boundaries. Also in Figure 4.5 is a volumetric representation of
the Ez-Field intensity at three different time steps: 0.292ns, 1.092ns and 1.53ns.
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Figure 4.4: 2D and 3D Ez-Field Due to Sinusoidal Pulse Stimulus
Figure 4.5: 2D and 3D Ez-Field Due to Continuous Pulse Stimulus
4.1.1.4 Simulation Summary
FDTD enables computational modeling and simulation of electromagnetic phenomena.
This is useful when there is a need to understand how EMF behaves in an object. It
reduces complex differential equations, time-dependent Maxwell equations, into finitedifference equations via Taylor Series Expansion allowing approximations of EMF
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behavior. FDTD is applicable to a vast set of applications that utilize EMF fields for
functionality.
Numerical simulations allow fabricators to get an idea of the waveguide geometry,
size and material that works well for a particular imaging system prior to purchasing the
actual product. FDTD algorithms are easy to use and easy to understand. It works well
for simple applications. For more complex applications or waveguide geometries the
FDTD implementation could take a considerable amount of time. The fact that FDTD
requires that the entire computational area be describe by a combination of Yee cells
means that very large computational domains can be developed, which results in long
simulation times. Future work would be to implement the FDTD algorithms on a GPU to
see the benefits in accelerated execution times.
4.1.3 Compressed Sensing Reconstruction
4.1.3.1 Background and Challenges
The existing data acquistion (DAQ) system using Agilent 34401A DMM approach is
not efficient and the sampling rate is limited. The maximum sampling rate of the DMM
is 1000 samples per second maximum. Achieving a high-sampling rates is a challenge
using the DMM as the DAQ device.
In order to overcome this issue, LEAP ordered a
high speed National Instrument (NI) 6341 PCIe DAQ module which has a analog input
sampling rate of 500,000 samples a second. Theoretically the LEAP NFMWIS can
achieve a higher data collection rate with the PCIe card because it is 500 times faster than
the DMM. Decreased scanning execution times can be achieved with the increased data
transfer rate of PCIe bus vesus the universal serial bus (USB) of the DMM. USB has a
bit rate of 60 MB/sec, which is slow compared to the 250 MB/sec rate achieved by the
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PCIe v1.1 compliant bus of the NI 6341 card. A NI BNC-2110 Shielded Connector
Block was purchased to compliment the PCIe card. This connector block breaks out all
of the I/O pins on the PCIe card to BNC female conncetors for easy connection with the
ancillary LEAP NFMWIS equipment.
4.1.3.1 Compressed Sensing Approach
Compressive sensing is typically an image processing technique for efficiently
acquiring and reconstructing signals with relatively few measurements. The LEAP Team
is currently working on a continuous DAQ approach to decrease scanning times that will
leverage the fast sampling rate of the NI PCIe card. This approach will perform random
sampling at a few discrete locations on the sample under test. Compressed sensing based
reconstruction will be investigated in order to generate microwave images from relatively
small amounts of acquired data. Implementing this technique in the LEAP NFMWIS
would allow for entire microwave images to be constructed by only scanning a small set
of discrete locations on the sample under test.
If perfected, this approach would
significantly reduce the imaging time of the LEAP NFMWIS.
4.2 CLOSING REMARKS
Microwave energy was exposed to the average consumer when the microwave oven
(microwave) became a common household appliance in the 1970s. The oven generates
electromagnetic radiation at micrometer wavelengths or microwaves.
The water
molecules in the food absorb the microwaves, heating the food and essentially cooking it.
Reducing the dependency on the conventional oven, the microwave created an easier
way-of-life for the 70s domestic housewife. The impact of the microwave oven was
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tremendous to modern society but it wasn’t the first valuable application of microwave
energy.
Prior to the microwave oven, the most common application of microwaves was in
RADAR. Microwave radiation is emitted from an antenna to determine the range,
altitude, direction, size, shape and velocity of an object in its path. Microwaves either
reflect or scatter when they travel from one medium, air, to a second medium, the object
material. This is due to the drastic dielectric difference between air and the object
material. The dielectric difference between air and metal is considerable. The larger the
dielectric differences between two mediums, the larger the amplitude of the reflected
microwave radiation. This is why RADAR is superb at detecting aircrafts, tanks, and
even missiles.
The amount of radiation is commonly classified by the reflection
coefficient or the ratio of the reflected microwaves to the transmitted microwaves. Since
no material is homogenous and neither are its dielectric properties, microwave radiation
can exploit these dielectric differences. Research has shown that by measuring the
various reflection coefficients across a material, microwave imaging systems (MIS) can
evaluate hidden or embedded flaws within its structure [29]. This thesis shows how this
can be accomplished with near-field microwave imaging techniques.
Near-field microwave imaging is concerned with quantitative measurement of the
microwaves electrodynamic response to materials on length scales far shorter than the
free-space wavelength of the radiation [9].
Near-field microwave imaging techniques
are very useful for NDE inspection techniques. Microwave imaging is performed with a
MIS that can be used to image material dielectric qualities (permittivity, conductivity,
and reflectivity).
MIS generally consists of a microwave source, waveguide, receiver,
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data acquisition (DAQ) device, and a computer to process the data and construct an
image of the dielectric tomography of a test object. Figure 2.19 is an example of a
generic MIS. MIS measurements can be acquired data via a 1-port network [4] [3] [5] [6]
or multi-port networks [11].
Chapter 2 introduced three distinct near-field microwave imaging techniques: openended waveguides, scanning tip probes and phase sensitive detection techniques (PSD).
Open-ended rectangular or coaxial waveguide techniques should be used for imaging
applications requiring cm resolution [5] but scanning tip waveguides should be employed
in applications that require sub-mm resolution [7] [6]. In order to produce MIS with µm
resolution it is suggested that the phase of the reflected signal induced in the waveguide
be measured and compared to the transmitted signal from the MIS source [23] [11]. This
chapter also suggests that resolution directly relates to the geometry of the waveguide and
the scanning lift-off distance [5] [6] [7].
Reviewing these three near-field imaging
techniques is useful because it provides background on the motivations behind the LEAP
NFMWIS development efforts described in detail in Chapter 2.
Early developments of the LEAP NFMWIS used an open-ended rectangular
waveguide and a 1-port MIS. The reflected signals from the test sample were rectified by
a crystal detector. The root-mean-square (RMS) voltage of the rectified signals from the
crystal detector output was measured with a DMM. This configuration of the LEAP
NFMWIS is properly coined Generation I because it was the first system developed. Gen.
I of the LEAP NFMWIS generated microwave images using software running on a PC to
move an x-y positioner.
The same software would acquire the DMM voltage
measurements at the current x-y position and would render a 2D Plot of the reflected
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voltage amplitudes when object scanning commenced.
The desire of the LEAP
NFMWIS is to achieve sub-mm resolution and this was not achieved with Generation I.
Leveraging the ideas of Wang [6] and Pochnak [7] a scanning tip waveguide technique to
spatially confine the EMF radiation to more discrete points on the sample under test was
the motivation behind LEAP NFMWIS Generation II. Generation II used a fabricated
coaxial scanning tip waveguide employed with the same ancillary equipment used in
Generation I. An increase in resolution was witnessed in the images acquired between
Generation I and II systems but Generation II images appeared to have noise. This noise
could originate from several areas, the parasitic capacitance from the close proximity of
the sample under test to the waveguide, the waveguide PSF and or lossy connections
within the system [6] [7]. Generation III of the LEAP NFMWIS employed a scanning
tip waveguide with a tapered tip following the experiments by Pochnak et. al [7]. Noise
was reduced by terminating the scanning tip to a coaxial cable using SMA connectors.
Also additional shielding was added to reduce the parasitic capacitance coupling caused
by the sample under test and also isolated the scanning tip from unwanted RF noise in the
testing environment. A vast improvement in image contrast and resolution has been
witnessed with Generation III.
The major components of the LEAP NFMWIS are a PC, microwave generator,
waveguide, DAQ device and X-Y positioner.
The waveguide is used to transmit the
microwave radiation to the sample under test, the DAQ device is used to measure the
waveguide’s response to the returned microwave radiation and the PC is used to collect
the data, post process and generate the image. In the LEAP NFMWIS the waveguide that
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transmits the microwave radiation also measures the response of the waveguide to the
received near-field radiation making the NFMWIS a 1-port network.
Currently there are two main approaches to optimizing the LEAP NFMWIS setup.
Approach 1 is an amplitude detection approach that measures the received DC signal
produced in the waveguide scanning tip to the reflected microwave energy from a test
sample in the near-field. Approach 2 is a phase detection approach that measures the
phase-difference between the received AC signal produced in the CTA waveguide versus
the transmitted AC signal from the microwave source. Any MWIS requires optimization
in order to refine its imaging capability. Chapter 3 shows optimization in the areas of
system synchronization, raster scanning algorithms, DAQ algorithm, waveguide design
and image post-processing techniques.
Chapter 3 expresses that MWIS should have the shortest execution time but not at the
expense of poor image resolution. It also demonstrates that there is a strong correlation
between image resolution and waveguide design. LEAP NFMWIS Gen. I reaffirms that
rectangular open-ended waveguides are good for microwave imaging applications but not
for systems that require sub-mm resolution. LEAP NFMWIS Gen. II reaffirms that submm resolution can be achieved with coaxial scanning tip waveguides. LEAP NFMWIS
Gen. III reaffirms that EMF can be localized and directed using a tapered scanning tip
waveguide which generates higher-quality images. Chapter 3 also provided insight on
the LEAP Teams parallel development process of a phase detection system in hopes of
imaging materials with lower dielectric constants (i.e. composite materials, liquids, body
tissue). There are a lot of improvements and optimizations that can still be made to the
115
LEAP NFMWIS but the information presented in Chapter 3 shows that the team is
headed in a feasible and good direction.
Microwave research is growing in NDE applications due to its, relatively low cost,
high-imaging contrast and timely results compared to X-ray imaging.
Microwaves
exploit the dielectric properties of materials and since materials anisotropic, a dielectric
tomography of objects under test can be imaged with MIS. The hardware and software
used in the MIS have to be optimized in order to produce the most efficient system. Fast
classifications of objects under test are important but the most important aspect of an MIS
is the image resolution. This thesis shows that there’s a relationship between these two
factors that needs to be optimized in order to produce a useful MIS. The waveguide used
in an MIS should be very application specific, depending on what you want to measure.
The waveguide utilized depends on the size and geometry of the object to be imaged.
Microwave imaging is ever increasing in popularity due to its broad application range.
Microwave imaging has proven effective in imaging concrete [4] [3], PCB traces [7] and
even body tissue [11]. Some of the LEAP NFMWIS development efforts presented in
this thesis are respectable and show signs that the project is moving towards a
considerable MIS that will consistently achieve sub-mm resolution.
4.3 CONCLUSION
The LEAP NFMWIS has accomplished sub-mm resolution. Experimental studies
presented in this thesis demonstrate that the system image resolution correlates to the
sensor aperture size. The experimental results presented in Chapter 3 align with the
existing research presented in Chapter 2 in that the smaller the aperture, the higher the
MIS resolution.
Models assisted in the development of the LEAP NFMWIS phase
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detection framework.
The MATLAB and LTspice mixer simulations helped develop
understanding and reaffirm physical behavior of the phase detector element. The LEAP
NFMWIS amplitude and phase detection approaches have undergone respectable
optimization efforts.
The amplitude approach has proven good for characterizing
materials and the phase detection method is useful for depth estimation and defect
profiling.
Both approaches have proven feasible at achieving sub-mm resolution but
there are still areas for improvement. The LEAP Team will continue to develop these
areas in order to produce a quality NFMWIS.
117
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120
APPENDIX A: MATLAB NFMWIS Scanning Code (scan.m)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
Scan.m
%
%Written By: Jarvis Hill, University of Colorado-Denver
%
%Purpose: This code will perform a scan on test material using the
%
%LEAP %NFMWIS System set-up (Arrick Robotics Scanner + Agilent 3401A %
%DMM)Call function by typing 'filename(obj_len,obj_width)' where
%
%'filename'= name of MATLAB script and 'obj_len' and 'obj_width' are %
%integers representing the dimensions of the test object in inches
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function main(obj_len,obj_width)
%Declare table scanning region
steps_inch = 180; %approx. steps per inch
region_width = 33; %inches
region_length = 33; %inches
center = 33;
%# of total steps to
length limit
length_steps = steps_inch*region_length;
%Establish COMs with Arrick Robotics Scanner
scanner = init_scanner();
%Establish COMs with Agilent 34405A DMM
dmm = init_dmm();
%Home motors 1 & 2
home_motors(scanner);
%Center test object on scanner
center_scanner(scanner, region_length, region_width, steps_inch);
%Position object for scanning
obj_scan_pos(scanner, obj_len, obj_width, steps_inch);
%Scan test object
scan_step = 10; %achieves ~1.4mm moves
scan_obj(scanner, dmm, obj_len, obj_width, steps_inch, scan_step)
%Plot acquired image
figure;
imagesc(data_array);colormap(hot);
axis equal;
%Home motor 1 and then motor 2
home_motors(scanner);
%End communication with scanner
fclose(scanner);
%End communication with dmm
fclose(dmm);
121
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
Function: init_scanner()
%
%Purpose: Configures serial object for COMs with
%
%Arrick Robitics C4/MD2 scanning system
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function scanner_device = init_scanner()
%Serial COM parameters
Port ='COM1';
Baud = 9600;
%Create scanner object
scanner_device = serial(Port, 'BaudRate',Baud,'Terminator','LF');
%Open serial comm. with scanner (C4 controller & MD2 Driver)
fopen(scanner_device);
pause(.1)
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
Function: init_dmm()
%
%Purpose: Configures visa object for usb COMs
%
%with Agilent 34405A DMM and begins COMs with deivce %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function device = init_dmm()
%%Establish serial COM with Instrument (Agilent 34450A)
dmmadr = 'USB0::0x0957::0x0618::my52320004::0::INSTR';
device = visa('agilent',dmmadr);
fopen(device)
set(device,'EOSMode','read&write')
set(device,'EOSCharCode','LF')
fprintf(device,'*CLS;*RST');
%%Identify Instrument
idn= query(device,'*IDN?');
disp(['IDN? = ' idn(1:end-1)])
%%Configure DMM to measure DC voltage
fprintf(device,'CONF:VOLT:DC')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
Function: home_motors()
%
%Purpose: Sends home commands to Arrick Robotics C4 %
%controller to home motors 1 & 2.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function home_motors(scanner)
%Clear command memory buffer on controller
fprintf(scanner,'!1bc')
122
move_ack = ' '
%Ensure that motors 1 & 2 start from home position
%Set motion parameters
%velocity
fprintf(scanner,'!1wv1,1000,2000,500')
pause(.1)
%Provide time to set all parameters
fprintf(scanner,'!1wv2,1000,2000,500')
pause(.1)
%Provide time to set all parameters
%Ensure that motors 1 & 2 start from home position
fprintf(scanner,'!1h12')
pause(.1)
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',11) %It appears # needs to = the
exact number of characters in the buffer
end
%C4 controller command
buffer is cleared after every read (fscanf)
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
Function: center_scanner()
%
%Purpose: Places scanning platform and test object %
%in center of scanning table.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function center_scanner(scanner, region_length, region_width,
steps_inch)
%Move scanning platform to center of scanning region
center_length = ceil(region_length/2);
center_width = ceil(region_width/2);
%Convert numbers to strings
str_clength = num2str(center_length*steps_inch)
str_cwidth = num2str(center_width*steps_inch)
%Create scanner center commands with length and width
center_cmdlength = strcat('!1m1f',str_clength);
center_cmdwidth = strcat('!1m2f',str_cwidth);
center_cmdlength = strcat(center_cmdlength,'n');
center_cmdwidth = strcat(center_cmdwidth,'n');
%Center scanning table in scanning region
move_ack = ' '
fprintf(scanner,center_cmdwidth)
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2); %It appears # needs to = the
exact number of characters in the buffer
end
move_ack = ' '
fprintf(scanner,center_cmdlength)
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2); %It appears # needs to = the
exact number of characters in the buffer
end
123
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
Function: obj_scan_pos()
%
%Purpose: Positions object under test for raster %
%scan by LEAP NFMWI system.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function obj_scan_pos(scanner, obj_len, obj_width, steps_inch)
%Move scanning platform to top left corner of object scanning
region
center_length = ceil(obj_len/2);
center_width = ceil(obj_width/2);
%Convert numbers to strings
str_clength = num2str(center_length*steps_inch);
str_cwidth = num2str(center_width*steps_inch);
%Create scanner center commands with length and width
center_cmdlength = strcat('!1m1r',str_clength);
center_cmdwidth = strcat('!1m2r',str_cwidth);
center_cmdlength = strcat(center_cmdlength,'n');
center_cmdwidth = strcat(center_cmdwidth,'n');
%Move scanner
move_ack = ' '
fprintf(scanner,center_cmdwidth)
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2);
end
move_ack = ' '
fprintf(scanner,center_cmdlength)
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
Function: scan_obj()
%
%Purpose: Performs raster scan on test object collecting %
%Voltage DC measurements from DMM DAQ
%
% Initial LEAP NFMWIS Raster Scan Algorithm
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function scan_obj(scanner, dmm, obj_len, obj_width, steps_inch,
scan_step)
move_ack = ' '
fprintf(scanner,'!1wv1,400,600,200')
pause(.1)
%Provide time to set all parameters are set
fprintf(scanner,'!1wv2,400,600,200')
pause(.1)
while(move_ack(end) ~= 'a')
124
move_ack = fscanf(scanner,'%s',2)
end
%Formulate steps in y direction and y start pos. commands
x_limit = ceil(((obj_width*steps_inch))/scan_step);
y_limit = ceil(((obj_len*steps_inch))/scan_step);
y_step = strcat('!1m1f',num2str(scan_step));
y_step = strcat(y_step,'n');
x_step = strcat('!1m2f',num2str(scan_step));
x_step = strcat(x_step,'n');
y_start = strcat('!1m1r',num2str(scan_step*y_limit));
y_start = strcat(y_start,'n');
%Perform scanning of object
%motor 2 = x position, motor 1 = y position
for x = 1:x_limit
for y = 1:y_limit
data_array(x,y) = str2num(query(dmm,'READ?'));
pause(.5)
fprintf(scanner,y_step)
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2)
end
end
fprintf(scanner, y_start)
pause(6)
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2)
end
fprintf(scanner,x_step)
pause(.5)
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2)
end
end
end
125
APPENDIX B: LEAP NFMWIS Scanning Algorithm
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
Function: scan_obj()
%
%Purpose: Performs raster scan on test object collecting %
%Voltage DC measurement from NFMWI crystal detector.
%
%Initial LEAP NFMWIS Raster Scan Algorithm
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function data_array = scan_obj(scanner, dmm, obj_len, obj_width,
steps_inch, scan_step)
%Set motor velocities for performing scan on test object
move_ack = ' ';
fprintf(scanner,'!1wv1,400,600,200');
pause(.1)
%Provide time to set all parameters are set
fprintf(scanner,'!1wv2,400,600,200');
pause(.1)
while(move_ack(end) ~= 'a')
move_ack = fscanf(scanner,'%s',2);
end
%Formulate steps in y direction and y start pos. commands
x_limit = ceil(((obj_width*steps_inch))/scan_step);
y_limit = ceil(((obj_len*steps_inch))/scan_step);
y_step_down = strcat('!1m1f',num2str(scan_step));
y_step_down = strcat(y_step_down,'n');
y_step_up = strcat('!1m1r',num2str(scan_step));
y_step_up = strcat(y_step_up,'n');
x_step = strcat('!1m2f',num2str(scan_step));
x_step = strcat(x_step,'n');
tic %Start scan time
%Perform scanning of object
%motor 2 = x position, motor 1 = y position
for width = 1:x_limit
%Indexes rows of data array
for length = 1:y_limit
%Indexes columns of data array
%Measure DC voltage and store into 2D data array
%Each time loop iterates a column in the data array gets
%populated
data_array(length,width) = str2num(query(dmm,'READ?'));
pause(.1)
%Check to see if column # even
if mod(width,2) == 0
%Move scanner up to next y-position
fprintf(scanner,y_step_up);
pause(.05)
%Wait for scanner to finish move
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2);
end
126
%If column # is odd
else
%Move scanner down to next y-position
fprintf(scanner,y_step_down);
pause(.05)
%Wait for scanner to finish move
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2);
end
end
end
%Delay at end of each column
pause(.1)
%Move scanner to next x position
fprintf(scanner,x_step);
%Wait for scanner to finish move
while(move_ack(end) ~= 'o')
move_ack = fscanf(scanner,'%s',2);
end
end
%Display how long it took to scan test object
scan_stop = toc;
%Represent scan time in hrs:min:secs
%Code snippet from Stackoverflow
hours = floor(scan_stop / 3600);
scan_stop = scan_stop - hours * 3600;
mins = floor(scan_stop / 60);
secs = scan_stop - mins * 60;
hrs = fprintf('Scan Elapsed Time(hrs:mins:secs.ms):
%02d:%02d:%05.2f\n', hours, mins, secs);
%Notify user that scan is complete
fprintf('Scan complete...\n');
pause(2)
end
127
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