TERAHERTZ REFLECTION TIME-DOMAIN SPECTROSCOPY FOR
IMAGING AND IDENTIFYING CONCEALED INTERFACES IN
MULTILAYERED SYSTEMS

by

Seth Lowry
B.Sc., University of Northern British Columbia, 2017

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
IN
PHYSICS

UNIVERSITY OF NORTHERN BRITISH COLUMBIA
August 2020

© Seth Lowry, 2020

Abstract
This thesis reviews multiple forms of terahertz spectroscopy and imaging, and
exploits a combination of aspects from the techniques involved to undertake a
novel method. With the use of this method, subsurface interfaces within a practical, insulated system are spatially imaged and identified. Initially, transmission spectroscopy is used to select the insulating material of the system based
on favourable dielectric properties, followed by the use of dove prism reflection
spectroscopy to understand and qualitatively contrast the responses of the interfaces to reflecting terahertz pulses. After constructing a reflection imaging system,
multiple interface materials concealed by insulation are successfully located and
identified by coloured overlays in a 100 by 100 image. Further exploration of applications involving the proposed method is also discussed.

ii

TABLE OF CONTENTS

Abstract

ii

Table of Contents

iii

List of Tables

iv

List of Figures

v

List of Abbreviations

viii

List of Contributions

ix

Acknowledgements

x

Introduction

1

1

Terahertz Imaging & Spectroscopy
1.1
Terahertz Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
Applications of THz Radiation for NDE . . . . . . . . . . . . . . . .
1.3
Reflection Spectroscopy in the Lab . . . . . . . . . . . . . . . . . . . .
1.4
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
3
5
11
13

2

THz Time-Domain & Reflection Spectroscopy
2.1
Generation & Detection of THz Pulses with Photoconductive Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
THz Time-Domain Spectroscopy . . . . . . . . . . . . . . . . . . . . .
2.3
Modelling a THz Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4
THz Transmission Spectroscopy . . . . . . . . . . . . . . . . . . . . .
2.5
THz Dove Prism Reflection Spectroscopy . . . . . . . . . . . . . . .

16
17
19
21
24
29

Experimental Methods
3.1
Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Pulsed Terahertz Controller . . . . . . . . . . . . . . . . . . . .
3.1.2 Dove Prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Imaging Sample . . . . . . . . . . . . . . . . . . . . . . . . . . .

33
34
34
35
37

3

iii

3.2

Transmission Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . .
Dove Prism Reflection Spectroscopy . . . . . . . . . . . . . . . . . .
3.3.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . .
THz Reflection Imaging . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Automation of the Image Measurements . . . . . . . . . . . .
3.4.2 Preparation of the Concealed Samples . . . . . . . . . . . . . .
3.4.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . .

40
41
45
48
56
59
61
64

Discussion and Future Work
4.1
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2
Discussion of the Key Results . . . . . . . . . . . . . . . . . . . . . . .
4.3
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77
77
78
81
83

3.3
3.4

4

Bibliography

85

iv

LIST OF TABLES

3.1

The passing conditions for each interface-specific image filter. . . .

v

75

LIST OF FIGURES

2.1
2.2
2.3
2.4
2.5

A top and side view of a PCA emitting a THz pulse. . . . . . . . . .
A schematic of a typical THz-TDS system. . . . . . . . . . . . . . . .
The propagation of an electromagnetic wave at an interface. . . . .
An illustration of Fabry-Pérot reflections in a sample. . . . . . . . .
The propagation of a THz pulse in a dove prism. . . . . . . . . . . .

3.1

A photograph of the pulsed THz controller and emitter/detector
heads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
The blueprint of the dove prism used for reflection spectroscopy. . 36
A photograph of the dismantled imaging sample. . . . . . . . . . . 37
The calculated index of refraction of UHMW. . . . . . . . . . . . . . 42
The calculated index of refraction and absorption coefficient of glass. 43
Schematics of the alignment of the dove prism. . . . . . . . . . . . . 45
Predicted THz reflections from multiple UHMW-sample interfaces
in TE and TM polarizations. . . . . . . . . . . . . . . . . . . . . . . . 51
Predicted and measured THz reflections from each UHMW-sample
interface in the TM polarization. . . . . . . . . . . . . . . . . . . . . . 52
Predicted and measured THz reflections from UHMW-gold and
UHMW-aluminum interfaces. . . . . . . . . . . . . . . . . . . . . . . 54
A photograph of the complete reflection imaging system. . . . . . . 57
The propagation of a THz pulse through the reflection imaging system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
An illustration of the incremental positions of the imaging sample
during a raster scan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
A photograph of the imaging sample containing sample inserts. . . 62
Measured THz pulses reflected from different samples, along with
the amplitude of the corresponding fast-Fourier transforms. . . . . 65
A brief outline for calculating pixel intensity values for the amplitude image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
A 100 by 100 amplitude image of the concealed interfaces. . . . . . 67
A brief outline of a single pixel intensity calculation for the phase
image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
A 100 by 100 phase image of the concealed interfaces. . . . . . . . . 70
Characteristics of a THz pulse in the time-domain. . . . . . . . . . . 71

3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19

vi

18
20
22
25
30

3.20

3.21

3.22

A collection of 100 by 100 images displaying the integrated electric
field amplitude, maximum and minimum electric fields, and the
peak-to-peak time-width of the THz pulse. . . . . . . . . . . . . . . .
A collection of 100 by 100 images displaying the FWHM of minimum and maximum peaks, and the slope and y-intercept of the
phase data from the THz pulse. . . . . . . . . . . . . . . . . . . . . .
The resulting image from the applied filters for the identification
of each interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

73

74
76

LIST OF ABBREVIATIONS

APT Automatically programmed tool. 59
cw Continuous-wave. 5
EM Electromagnetic. 21
F-P Fabry-Pérot. 26
FFT Fast-Fourier transform. 20
fs Femtosecond (10−15 s). 5
FWHM Full width at half maximum. 72
GHz Gigahertz (109 Hz). 3
LT-GaAs Low temperature grown gallium arsenide. 19
MDMA Methylenedioxymethamphetamine. 7
NDE Non-destructive evaluation. 4
PCA Photoconductive antenna. 17
POI Plane of incidence. 21
ps Picosecond (10−12 s). 5
RDX Royal Demolition eXplosive, or cyclonite. 7
TE Transverse electric. 22
THz Terahertz (1012 Hz). 3
THz-TDS THz time-domain spectroscopy. 6
TM Transverse magnetic. 22
TNT Trinitrotoluene. 7
UHMW-PE, or UHMW Ultra-high molecular weight polyethylene. 33
UNBC University of Northern British Columbia. 37
viii

LIST OF CONTRIBUTIONS

Journal Articles
[A1] B. D. Price, S. N. Lowry, I. D. Hartley, and M. Reid, ”Subterahertz refractive
flat-top beam shaping via 3D printed aspheric lens combination,” Applied Optics, vol. 59, no. 18, pp. 5429-5436, 2020.
[A2] E. Lozowski, M. R. A. Shegelski, M. Hawse, S. N. Lowry, C. Sample, and
M. Reid, ”Comment on ’A Scratch-Guide Model for the Motion of a Curling
Rock’,” Tribology Letters, vol. 68, no. 2, 2020.
Conference Presentations
[C1] S. N. Lowry and M. Reid, ”Terahertz Reflection Imaging for Concealed Interface Inspection [PowerPoint Presentation],” UNBC Interdisciplinary Weekly
Seminar Series, Prince George, BC, Canada. October 2019.
[C2] B. D. Price, S. N. Lowry, and M. Reid, ”THz refractive top-hat beam shaping
via 3D-printed aspheric lens combination,” Poster presented at the 2018 Canadian Undergraduate Physics Conference, Edmonton, AB, Canada. August 2018.
[C3] B. D. Price, S. N. Lowry, I. D. Hartley, and M. Reid, ”THz Michelson Interferometer for measuring properties of engineered wood products,”, Poster
presented at the 2017 Canadian Undergraduate Physics Conference, Ottawa, ON,
Canada. October 2017.
[C4] S. N. Lowry, P. Kilcullen, and M. Reid, ”Towards a Digital Micro-Mirror
Array-based, Broadband Single Pixel Camera,” Poster presented at the 2016
Canadian Undergraduate Physics Conference, Halifax, NS, Canada. October
2016.

ix

Acknowledgements
I am delighted to extend my sincere thanks towards those who have made this
project possible. Foremost, I cannot begin to express my thanks to my supervisors, Dr. Matthew Reid and Dr. Mark Shegelski. It is with their patient guidance,
knowledge and genuine support that has given me the chance to not only become
the researcher I am, but to profoundly enjoy my first few years of research. I am
deeply indebted to Dr. Reid for providing me with research opportunities in a
novel field for many years throughout my education, introducing me to exciting
projects to be a part of, and managing my first visit to the east coast to share my
research at a conference. I am also extremely grateful to Dr. Shegelski for allowing me to gain experience and confidence giving lectures in numerous physics
courses, and especially for the continuous, valuable advice and support over the
years. They are the key reasons why my passion for physics is so great, in regards
to both research and teaching.
Particularly helpful to me during the beginning of my studies was my third
committee member, Dr. Alex Aravind, who encouraged stimulating conversations
regarding the generalities of research, as well as Dr. Ian Hartley and his vast supply of interesting questions and ideas towards a project. I would also like to thank
everyone from the Physics Department at UNBC and those at the Wood Innovations Research Lab for their interest in assisting in this project.
Finally, I must express my deepest appreciation and gratitude for my friends
and family who have never wavered in their support, specifically throughout the
duration of this project. My utmost appreciation goes to my parents, who have
always pushed me to excel in my passions and interests and have never stopped
believing in me, to my sister, who has never failed to help through the more difficult times, and to Sophie for her endless patience and friendship through all of
the ups and downs of my research. I want to also extend my thanks to friends and
family I did not mention, who have consistently shown interest in my work and
research.

x

Introduction
Recent advancements in terahertz (THz) technology have led to innovations in
imaging, spectroscopy, and non-destructive evaluation (NDE) techniques. This
stable access to a new frequency range of light has led to cutting-edge advancements and diversified strategies in this field of research. Measuring the interaction
between matter and differing frequencies of light allows for characterizations of
that material; this is classified as a form of spectroscopy. For NDE purposes, measuring the reflectance of light from matter can be a useful form of spectroscopy,
which is called reflection spectroscopy. This allows interfaces of differing materials to be examined and evaluated.
The purpose of this thesis is to review important contributions made in the field
of imaging, NDE, and reflection spectroscopy at THz frequencies of light to determine the most appropriate implementation for conducting concealed interface
inspection. Further, this work realizes such an implementation and exploits it to
demonstrate an example of subsurface interface imaging appropriate for NDE. The
scope includes analyzing current NDE techniques that implement THz reflection
spectroscopy for imaging, quality assessment, and characterization of materials
and interfaces, identifying limits in current NDE techniques where THz imaging
may present a feasible alternative, and demonstrates a functional system suitable
for further work to expand NDE methods in THz technology.

1

Outline of this Thesis
Chapter 1 contains a brief overview of the history of THz radiation as well as
its involvement in various forms of spectroscopy. THz applications are explored
from research in controlled environments to applied, practical systems in industry.
A comparison of techniques from each area is undertaken to set the stage for the
project of this thesis.
Chapter 2 details a common mechanism for the generation and detection of pulsed
THz radiation, as well as its operation in THz time-domain spectroscopy (THzTDS). Two theoretical models regarding different forms of spectroscopy for the
extraction of material dielectric properties are also developed.
Chapter 3 reports the experimental methods involved in transmission and reflection spectroscopy, as well as the implementation of a reflection imaging system for
the identification of subsurface interfaces within an insulated system. A collection
of images are displayed based on various amplitude and phase characteristics of
the reflected THz pulses. Interface-specific image filters are described and applied
to a reflection image, successfully locating and identifying each interface material.
Chapter 4 conclusively summarizes the experimental results of this thesis, and
emphasizes its importance to broadening the use of THz in NDE, followed by suggestions for future direction.

2

Chapter 1
Terahertz Imaging & Spectroscopy
1.1

Terahertz Radiation

Terahertz (THz) radiation, sometimes referred to as far-infrared radiation or submillimeter waves, corresponds to a frequency range of the electromagnetic spectrum between microwaves and the infrared range of light [1]. Inherent from the
prefix tera (T), these frequencies usually exist upwards to approximately 3 THz
(1012 Hz) and can reach as low as 300 GHz (109 Hz). Until recent technological
advancements, the stable production of electromagnetic waves in this range of frequencies has been difficult to access in a compact setting [2]. For many years, the
electromagnetic frequencies produced by conventional electronic methods have
not extended up to terahertz frequencies, nor have they been accessible by optical methods involving lasers and semiconductors [3]. The frequency roll-off from
these common methods creates a gap in the electromagnetic spectrum, commonly
referred to as the ’THz gap.’ This technological impasse poses a substantial practical challenge for the production of radiation in this range of frequencies, and also
serves to define the characteristic range of frequencies in the THz region.
The rising interest in exploring THz frequencies over the years has been driven

3

by this phenomenon, and has given rise to novel methods since the 1970’s for the
stable production and coherent detection of THz radiation by borrowing concepts
from both optical and electronic domains. Following this technological leap, significant progress has been made in improving THz technology, thus increasing the
accessibility of frequencies within the THz gap. Now, with a growing expanse
of experimental methods and diverse production of THz equipment, the regular conduction of THz research in a compact setting is no longer a challenging
task. Recent applications of THz science span many areas of non-destructive evaluation (NDE) [4], food inspection [5], security screening [6], art preservation [7],
medicine [8], as well as imaging [9].
THz radiation retains numerous appealing qualities regarding its interactions
with some materials. These unique properties are driving the pursuit for new applications in the constantly evolving THz field. THz radiation propagates through
a vast selection of dry, non-conducting materials, such as plastics, foams, and
composites, with minimal absorption, motivating a range of applications towards
the quality testing of packaged materials and detection of corrosion under insulation [10]. With applications heavily involved in NDE techniques, competition
between THz and the previously prominent X-ray technology naturally exists. In
applications for which the use of THz technology is applicable, it has proven to excel due, in part, to the inherent safety of using this type of radiation since THz frequencies are non-ionizing and do not have the required photon energy to directly
damage DNA structures within a biological system, as opposed to X-rays [11]. The
sub-millimetre wavelength provides sufficient resolution for many imaging applications, and demonstrates unique interactions upon reflection with water [12, 13].
These qualities are limited by the heavy absorption of THz frequencies in atmospheric moisture, restricting propagation distances to tens of meters, which is still
suitable for many applications.

4

With innovation in technology, the methods of producing and detecting THz radiation have diversified over the years, lending different varieties of THz sources
for a given application. Common continuous-wave (cw) THz sources take advantage of photomixing two laser modes of a different frequency of light in order
to produce a monochromatic THz beam at the difference frequency [14]. These
lasers exhibit a high power density for a given frequency, but are limited in bandwidth and solely rely on intensity-based measurements. These cw sources are often
adapted to specific applications for NDE in industry. With the rapid commercialization of femtosecond (fs) laser sources in the early 1990’s, the development of
ultrafast THz systems has enabled the coherent detection of THz pulses [15]. In
these systems, femtosecond laser pulses interact with an emitter, releasing a range
of THz frequencies in a pulse. The bandwidth of these pulses consists of frequencies as low as 0.1 THz up to 5 THz. The femtosecond laser is also used to gate
the receiver, which allows for direct time-domain mapping of the electric field on
a sub-picosecond (ps) time scale. Even though compact sources and detectors for
THz frequencies are readily available for a laboratory setting, research in THz technology continues to discover more cost-efficient systems and designs.

1.2

Applications of THz Radiation for NDE

Since the advancements in electronics and photonics that led to the access of the
THz gap, there have been numerous applications for THz imaging. These range
from moisture content and concealed object imaging in biological materials [16,17],
to absorption spectroscopy for the identification of drugs/explosives [18], to security screening applications [11], and finally to the detection of flaws in materials
within insulated systems such as submarine hulls [19] and the NASA space shuttle foam insulation [20]. Imaging with THz can be performed in a transmission

5

or reflection geometry, each of these methods specialized for certain applications
based on their respective strengths and weaknesses. Transmission imaging with
THz provides information regarding the full complex dielectric function (index of
refraction and absorption coefficient) of a sample, whereas reflection imaging can
provide unique surface and interface information which may be difficult or even
impossible to obtain via transmission.
For example, the complex dielectric characteristics of liquid water and other
polar liquids cannot be extracted by the use of transmission spectroscopy, due to
the heavy absorption of THz radiation by polar liquids [21]. By containing a liquid
water sample below a silicon window, the multiply reflected THz pulse (at the
surface of the window, and the silicon-water interface) contains amplitude and
phase information of the electric field of the reflected THz pulse. Analysis of the
effects of liquid water on these measured quantities allows the determination of
the dielectric properties of the sample.
One of the important aspects of these configurations is the delay line that enables THz time-domain spectroscopy (THz-TDS). This allows each delayed pulse
to be paired with its associated reference pulse, in order to determine the relative
time delay of the pulse travelling through the sample. There are many characteristic changes in pulse shape and position of the THz pulse in the time-domain that
are used to determine the properties of the sample transmitted through or reflected
from. Transmission imaging is generally used in materials in which THz radiation will propagate in order to detect the pulse on the opposite side of the sample. Reflection imaging is often used in multilayered systems where propagation
through the sample is not possible, and this technique becomes extremely effective with concealed objects/interfaces that are highly reflective. Examples utilizing
transmission imaging are the imaging of food products low in water content [17],
the imaging of water content in a leaf [22], automobile dashboard inspection of

6

the foam padding between plastic parts [1], and security screening for weapons,
drugs or explosives [23, 24]. By taking measurements with a pulsed THz spectrometer through chocolate bars contaminated with glass splinters, small stones,
and screws, Jördens and Koch find sudden intensity drops in the transmitted pulse
used to determine the presence of these contaminants [17]. An image of the contaminated chocolate bar still in its original packaging is produced, identifying the
intrusive objects. A small stone embedded in the chocolate bar is identified by
a drop in transmitted intensity from the image scan due to increased scattering
or absorption of the THz pulse. This report demonstrates the ability of THz-TDS
imaging to detect foreign bodies in chocolate bars and suggests the applicability of
THz imaging to food products in low moisture environments.
THz transmission spectroscopy can also be applied to the detection of illicit
drugs and explosives. Due to the specific structure of the chemicals involved in
drugs and explosives, the absorption spectra in the THz range for different materials can vary significantly. Reports from Kawase et al. and Kemp conclude that the
identification of drugs and explosives with THz transmission spectroscopy is possible, even when these powders are concealed by materials transparent to THz frequencies, such as envelopes and cloth [18, 23]. By measuring the absorption spectra for methylenedioxymethamphetamine (MDMA), aspirin and other methamphetamines separately, these drugs are detectable within an envelope packaging,
and a spatial image is produced, visually classifying each substance. It can be noticed that absorption peaks at certain frequencies are very distinguishable for a
given material. In many materials that interact minimally with THz radiation, the
absorption curve increases with frequency, and peaks along the absorption curve
can be specific to certain substances. A similar technique is used to identify explosive powders such as Semtex, trinitrotoluene (TNT), and Royal Demolition eXplosive (RDX), also known as cyclonite [18]. Taking security applications further,

7

recent progress has been made by moving towards merging microwave and THz
imaging for security screening in airports [6]. The high resolution of THz radiation
and the lesser absorption in the atmosphere of microwaves allows for the detection
of metallic objects concealed underneath clothing.
Mittleman et al. exercise the use of a THz-TDS system for the identification of
various individual gases as well as gas mixtures [25]. Absorption lines at specific
frequencies illustrate absorption fingerprints that are used for gas identification.
Closely related gases are also distinguished by exploiting the time delay of THz
pulse ”commensurate” echoes to examine characteristic rotational energies.
Applications for reflection spectroscopy and imaging at THz frequencies expand into the field of NDE of manufactured materials. In many manufactured
products, errors often occur in mouldings, sealant, and insulation, and over time
these materials can wear down. With NDE techniques, these flaws and defects
can be located without removal of insulation or destruction of the product. For
some reflection spectroscopy applications, the lack of the ability to perform transmission spectroscopy makes the identification of concealed objects by their optical properties difficult since absorption spectra, or absorption ’fingerprints’, may
not be present in reflections. It is also complicated by the fact that a well-defined
reference, required for spectroscopy, is not always possible to collect. THz-TDS
reflection imaging is involved in art conservation [7], under paint corrosion detection [26], and concealed interface inspection such as foam insulation defect detection in the NASA space shuttle [20] and void detection in submarine acoustic tiles [19]. Fukunaga and Picollo demonstrate the impact that THz reflection
spectroscopy could have on art conservation [7]. Although they find that the
interaction between THz radiation and many art materials is difficult to model,
they demonstrate the impact this form of imaging can have on art conservation
and restoration processes. A THz-TDS reflection image of a painting is generated

8

which identifies gold foil and lead paint used on the panel by the reflectance of
each material. The materials involved in each layer of the painting are also identified based on the time delay and intensity of the THz pulse, essentially quantifying the materials in terms of their corresponding reflections. Reflections from an
interface at a further depth correlate to a measurement at a later time delay due
to its increased time-of-flight, indicating the depth position of that interface. The
addition of a wooden structural enforcement on the back of the painting is also
identified in this manner. By performing THz spectroscopy with numerous art
materials, identification of paints, binders, and other art materials can be utilized
for restoration purposes.
Taking THz-TDS imaging for NDE further, a field of interest is discovering hidden areas of corrosion or damage in metals and composites. Anastasi and Madaras
investigate the detection of corrosion underneath varying thicknesses of paint [26].
This report relies on the changes in paint thickness and shape as a result of corrosion of the underlying metal. When the painted metal corrodes, the paint can swell
and take on a rough shape. This changes the optical path and reflectance, thus affecting the detected time delay of the signal. It is found that when the paint layer
becomes thin, the surface reflections become indistinguishable as the time delays
of the reflected pulses from the surfaces of the paint and metal approach a common value. Nonetheless, chips and holes are detected with certainty, while corrosion detection may require further signal processing methods. These methods are
utilized in THz reflection spectroscopy, discussed further in Section 1.3.
Numerous reports have studied the evaluation of damaged high strength composites involved in lightweight aircraft manufacturing. Stoik et al. report on the
identification of voids, delaminations, paint removal and damage on layered composite systems important for aircraft production [27]. For multi-layered systems,
where multiple back-reflections are expected from the layered system composed

9

of various media, the reflection from the interface remains consistent if the dielectric contrast between the two media (i.e. sample-air) is consistent throughout the
scanned sample. Changes in the amplitude or phase of the interface reflection provides information on how the interface has changed. Stoik et al. identify how
this reflection changes with delaminations, damage and burns at an interface [27].
Detecting these flaws in manufactured composites before use in aircraft is of vital
importance to the quality and structure of the aircraft.
In a similar apparatus, NDE for foam insulation and shuttle tiles on the NASA
space shuttle has shown to be suitable with THz frequencies. Anastasi et al. compare the THz reflection images of corroded aluminum with the same sample concealed by the shuttle tiles [20]. It is concluded that the newfound ability to detect
corrosion in a layered system from access to only one side of the sample is more
difficult to detect with shuttle tiles that absorb heavily at THz frequencies. Two
images are produced of the corroded region from spatial plots of the peak-to-peak
value of the THz pulse and of the amplitude of a chosen frequency. Similar images
have previously been produced for inspecting voids in the foam insulation in the
NASA space shuttle as well.
Kilcullen et al. produce reflection images for the detection of water-filled voids
between acoustic tiles surrounding the hull of a submarine [19]. The strong reflection from the rubber-water interface is relied on to locate the presence of water
before corrosion can occur. Similar to the shuttle tiles, the acoustic tiles heavily
absorb THz radiation, and make it difficult to gather a detectable back-reflection.
It suggests that for any system in which the layered sample has a small dielectric contrast among the media, regions of high dielectric contrast can be used for
detection of water or metals.
What all of these examples have in common is that reflection imaging is not
amenable to reflection spectroscopic imaging because a well defined reference pulse

10

has not been available or has been impossible to achieve. In this thesis, we identify, construct and demonstrate a system that can be used to identify materials at a
concealed interface by exploiting the spectrum of reflected THz pulses.

1.3

Reflection Spectroscopy in the Lab

There are numerous industrial applications of spectroscopic testing and NDE using THz radiation, and with state-of-the-art technology allowing the use of new
electromagnetic frequencies in the THz range, there are many applications for THz
reflection spectroscopy and the collection of dielectric properties of materials. By
measuring the electric field of reflected THz pulses in the time-domain with a THzTDS system, the Fourier-transformed data provides access to both amplitude (used
traditionally in reflection imaging) and phase information (which is exploited in
this work) to determine dielectric properties for the purpose of identifying materials at a concealed interface. These material-specific functions are expected as the
THz pulses respond in reflection to the underlying dielectric function ˜ (ω), complex index of refraction ñ(ω) =

p
˜ (ω) and absorption coefficient α(ω) [28]. In

order to work with amplitude and phase information most effectively, a reference
reflection measurement must be performed without the sample in the THz-TDS
system, as well as a sample reflection measurement. The ratio of the two measurements transformed into the frequency domain is used to determine amplitude and
phase shifts required for comparison to calculations. Results of this kind have been
published for various dielectric materials, therefore calculating dielectric properties allows the probed sample to be identified. The ability of identifying materials
in the lab setting is simplified by close-range detection and controlled humidity for
minimally disturbed THz pulses, as opposed to the real environment required for
most applications [29]. For this reason, most reflection imaging at THz frequencies

11

has exploited amplitude-only information. Where the phase is also used to study
full dielectric functions, a well-defined reference is used. In this work, the gap between lab-based reflection spectroscopy and practical industrial imaging is tackled
with promising initial results.
Lab-based reflection spectroscopy shares the same principles as spectroscopy
in transmission mode, discussed briefly in Section 1.2. The key difference is that
position-sensitive measurements now pose a challenge since any change in position of the sample introduces a change in time-of-flight of the pulse and an associated change in phase. To avoid this, a fixed window can be introduced to
hold the sample without affecting the point of reflection. Thrane et al. introduce
a reflection spectroscopy technique for the extraction of dielectric properties of
highly absorbing liquids such as liquid water, performing index of refraction and
absorption coefficient measurements [30]. In agreement with previous theoretical
models, THz reflection spectroscopy also shows that water molecules can change
orientation while maintaining hydrogen bonds. Uhd Jepsen and Fischer present
the quantification of the dynamic range of the absorption coefficient detected for
dielectric materials [31]. It is concluded that by using reflection spectroscopy, as
opposed to transmission spectroscopy, larger absorption coefficients can be more
reliably measured. It has been noticed that higher frequencies of spectrometers are
less dependable in transmission modes for absorption peaks, whereas reflection
modes are limited mostly by laser fluctuations.
In summary, there are some key points to be outlined regarding two perspectives of reflection spectroscopy. In the case of lab-based experiments for which
the determination of dielectric properties of liquids, gases or materials leads to its
identification, the use of a reference beam or measurement is required. Due to
changes in amplitude and phase between this reference and the sample measurement, unique spectral features can be located, inferring the materials used in the

12

sample under study. Contrasting with applied reflection spectroscopy for NDE,
surveyed in Section 1.2, the reliability of spectroscopic information in this area is
limited since the required reference measurement for spectroscopy is not available.
With limited spectral information from a sample, some amount of previous knowledge of possible materials present may be required. Because of this, applications
often revolve around detecting irregularities and delaminations from immediate
changes in the scanning waveform. The time delay of a signal is primarily inspected to detect changes in position, thickness, and refractive index. In addition,
some materials are less reactive to THz frequencies, leaving no sharp, detectable
spectral features in this range.

1.4

Motivation

The reports discussed throughout this review have outlined common limitations
to THz imaging and spectroscopy for practical purposes. Since the development
of stable THz sources, the common problem has been favouring the implementation of THz sources for imaging over other frequencies of radiation for NDE. THz
frequencies can be more easily absorbed than microwaves, especially in thick materials or in materials having a high moisture content. The high absorption from
atmospheric moisture hinders applications for long distance imaging with THz.
Regarding the application of THz imaging for corrosion NDE beneath rubber tiles,
the high absorption of THz frequencies has limited the practicality of these applications. A similar issue is found in evaluating wooden building products with
THz radiation. In the papers reviewed, a repeated limitation of the experiments
for reflection imaging and spectroscopy is the lack of a better signal processing
technique. In many of the papers investigating reflection imaging of concealed interfaces, the reflected pulses detected provide a large amount of information, that

13

is not always analyzed to its full extent.
In many cases, a change in the amplitude or phase of the signal suggests a
change in the material or quality of material at the interface. Most often, water or
metal is detected based on a large reflection, or a larger absorption. It is expected
that there exists a spectroscopy technique that can gather information from the
reflected signals to distinguish between different metals, water or other materials.
This is often not regarded in the field of NDE of concealed interfaces for corrosion.
In other words, in most systems, there is no need to distinguish between a highly
reflective metal and highly absorbent water sample. In a similar manner, there
has been plenty of research investigating the detection of damage or corrosion,
but less research on identifying areas filled with water or of high moisture content
before corrosion takes place.
The ability to detect failing systems involving metallic articles or structures due
to indications of pre-corrosion is a cost-effective and conservative step crucial for industrial applications of THz in NDE, which this thesis aims to explore. In Section
1.2, an application of THz reflection imaging towards the identification of waterfilled gaps within submarine tiles is outlined. Based on the expectation of detecting one of two materials, water or air gaps, the detection of water intrusion in a
dielectric system protecting a vulnerable metallic system is performed before corrosion can take place. This is an appealing conceptual example of a proactive NDE
technique that may substantially benefit applicable industrial systems involving
insulated metallic structures and water.
This thesis aims to focus on identifying the difference between metallic and
water interfaces, along with identifying other dielectric materials, in an insulated,
layered system in order to display the practicality of detecting indicators of precorrosion, as well as emphasizing the importance of these proactive NDE measures
to industry. By combining techniques from lab-based THz reflection spectroscopy

14

as well as those from the applications in THz NDE, the goal of this thesis is to
explore the ability to conduct reflection imaging at an interface while trying to
identify the interface material without the use of a reference measurement.

15

Chapter 2
THz Time-Domain & Reflection
Spectroscopy
For many years, there has existed a slow progression in research involving frequencies constrained by the existence of the THz gap [32]. However, the advancements in optics and electronics technologies towards the 1990s have catalysed the
leap of certain technologies leading to the commercialization of THz spectroscopic
and imaging systems [33]. The main cause of this leap is the development and implementation of the fs laser source [34]. These extremely short-pulsed laser sources
have opened the gate for a novel means of THz pulse generation and coherent detection, generating a surge in publications throughout the 2000s. With access to
time-domain information regarding the changing electric field of an electromagnetic pulse, more accurate measures have been discovered for the determination
of optical properties of materials using THz radiation. With the use of these spectrometers [35] beginning in the early 2000s, new means of stable THz generation
and detection have been adopted. Originally, these methods have relied on photoconducting switches or antennas [36–38] to generate and detect this form of radiation, and have subsequently expanded to include the use of optical rectification

16

and electro-optic sampling [39, 40]. These two methods are not the only forms of
generating and detecting this range of wavelengths, but they are quite common in
THz-TDS systems. Since the Picometrix® THz-TDS system involved in this thesis
revolves around the generation of THz pulses using photoconductive antennas,
this is the sole mechanism discussed.

2.1

Generation & Detection of THz Pulses with Photoconductive Antennas

The Picometrix® THz-TDS system employed in this work performs pulsed THz
generation and detection by illuminating photoconductive antennas (PCA). For
the generation of THz pulses specifically using a PCA, an ultrafast fs laser produces a pulse of radiation having a duration of less than 1 ps [41]. Femtosecond
lasers typically operate in the near-infrared, usually around 800 nm wavelengths.
These ultrashort optical pulses are incident on a PCA, and the resulting THz pulse
emitted is a result of the structure of a PCA and the carrier dynamics within a
biased semiconductor [42].
The structure of a PCA is comprised of an electronically biased metallic dipole
antenna prepared on a semiconductor substrate, as seen in Figure 2.1. The characteristic distances of the antenna such as the dipole length, D, and the gap width,
G, directly affect the wavelengths of the radiation emitted. The dipole length is

often around 100 µm, and the gap width can be as low as several microns [43].
The absorbed optical pulse supplies sufficient photon energy exceeding the band
gap of the semiconductor resulting in excited electrons from the valence band to
the conduction band, generating photocarriers within the semiconductor. These
photocarriers are accelerated by the electric field of the bias, transmitting a transient electric current density, J. This short-lived, rapidly changing current density
17

(b)

(a)
Vbias

+

-

+

Vbias
-

fs pulse

Metallic Dipole
G

fs pulse

Silicon
Lens

D

Radiated
THz Pulse

Semiconductor Substrate

Figure 2.1: (a) A top view of the metallic dipole prepared on the semiconductor
substrate with dipole length, D, gap width, G and electronic bias, Vbias . The optical
femtosecond pulse pumps the center of the antenna. (b) A side view of the PCA
emitting a THz pulse focussed by a silicon lens.
dJ
[42].
drives the dipole antenna which emits a THz pulse, where ET Hz ∝ dt

The coherent detection of THz pulses with a PCA can be understood comparably to the way it is used for THz generation. The main difference is that the electric
field of the THz pulse incident on the detecting PCA works as the bias for the
antenna which creates a photocurrent. This current is gated by ultrashort optical
pulses on the opposite side of the PCA which samples the electric field of the THz
pulse. Incidence of these sampling pulses on the PCA allows for conduction of the
transient photocurrent, creating the THz signal, which is a current proportional to
the THz electric field, when the optical pulse-width is sufficiently short and the
carrier lifetime of the antenna substrate is also short. In order to sample the entire
18

electric field of the THz pulse, multiple optical pulses used for gating the PCA are
given different time delays along a delay line relative to the optical pulses used for
generation [42], which allows the THz electric field amplitude to be mapped out
in time.
The most common semiconductor material for use in PCAs with THz pulses
is low temperature grown GaAs (LT-GaAs). The role of this semiconducting substrate is well established in ultrashort pulse photonics due to its adequate carrier
mobility and sub-picosecond carrier lifetime. Minimizing the carrier lifetime is of
high interest for the creation of quickly changing transient pulses, increasing the
bandwidth of emitted THz pulses and associated detection [44]. A frequent interest in emitter/detector systems is the reduction of noise. A primary source of noise
within PCAs is Joule heating, a consequence of the conduction of electrical current.
Collier et al. studies the application of textured semiconductors in PCAs to reduce
charge-carrier lifetimes, minimizing the degree of Joule heating [45]. With the generation of THz pulses and its coherent detection using PCAs, the implementation
of THz-TDS is made possible.

2.2

THz Time-Domain Spectroscopy

The emergence of THz-TDS techniques sets the stage for the most common practice
of examining optical properties of materials and sampling the interaction of THz
frequencies with matter by analyzing spectral information. From the prominence
of THz-TDS, many publications in THz science involve the cataloguing of absorption spectra, refractive indices, and other optical properties of dielectrics, gases
and metals. As discussed in Section 2.1, the generation and coherent detection
of THz pulses using PCAs results in the sampling of the electric field waveform
in the time-domain. Measurements of an electric field pulse with respect to time

19

can provide spectral information from the pulse by applying a fast-Fourier transform (FFT) of the time-domain data. This transforms the data into the frequencydomain, providing an individual look at the interaction of specific frequencies with
a sample within the bandwidth of the broadband THz pulse [46].

THz Detec�ng PCA

THz Emi�ng PCA

Sample

Lens

Lens

Pump Pulse

fs Laser

BS

Probe Pulse
Delay Line

Figure 2.2: A schematic for a typical THz-TDS system using PCAs for the generation and detection of THz pulses. [BS - beam splitter.]

The schematic in Figure 2.2 summarizes a simplified THz-TDS system. Beginning at the ultrafast fs laser, a pulse on the order of 100 fs is split by a beam splitter
into two identical pulses: the generating pulse directed towards the emitting PCA,
and the sampling pulse directed towards an optical delay line before reaching the
detecting PCA. The THz pulse emitted by the emitting PCA transmits or reflects
from a sample towards the detecting PCA. As the delay line is adjusted, different
points along the THz waveform are measured and plotted in the time-domain [47].
For each different delay line position, the time value of the electric field data point
20

is altered accordingly. Optics such as lenses and mirrors for redirecting or focussing optical pulses are excluded from the diagram to clearly illustrate the operation of the system. The THz-TDS is capable of performing in the transmission
and reflection modes. This spectroscopic system is often used in THz imaging as
well. By raster scanning a sample within the apparatus described above, these THz
pulse measurements can be gathered in a spatial configuration. Signals are often
converted to the frequency-domain to obtain spectroscopic information from the
THz pulse for each pixel of the gathered image. Not only can spatial spectroscopic
information be gathered, but given the time-domain measurements, time-of-flight
analysis can be performed to determine depth characteristics of the given imaging
sample [48].

2.3

Modelling a THz Pulse

Electromagnetic (EM) radiation, or EM waves, are represented in terms of the cor~ , respectively, which are in phase,
responding electric and magnetic fields, ~E and B

simultaneously varying in time, and perpendicular to each other in space. The
electric field of a plane wave can be represented in time in terms of the amplitude
Eo , the wave number k, and angular frequency ω.

~E = ~Eo ei(~k~r−ωt) = ~Eo eiφ

(2.1)

~ indicates the direction of the
The direction of the cross product between ~E and B

wave propagation, parallel to ~k. For an EM wave given by equation (2.1), it is essential to define the orientation of the wave with respect to the plane of incidence
(POI) along which reflection and transmission of the EM wave occurs. The POI
is defined as the plane containing the wavevector ~k and the surface unit normal
vector n̂ of the boundary plane where reflection and transmission occur. At the
21

(b)

(a)

ETE

ETM n1 n2

n1 n2
BTM

k TE

BTE

kTM
θr

θr
θt E
t

Br

Er

kt
Er
kr

θt
Br

Bt

Bt

Et
kt

kr

Figure 2.3: The propagation of an electromagnetic wave at an interface between
two media, n1 and n2 . For the (a) TE and (b) TM polarizations, the reflected and
~ are shown as vectors, along
transmitted electric fields ~E and magnetic fields B
~
with the corresponding wavevectors k. The POI is parallel with the page, and
the boundary plane is perpendicular to the page.
intersection of the POI and the boundary plane, the boundary conditions (inherent
from Maxwell’s equations) are applied to the electric and magnetic fields of the
incident wave to determine the behaviour of the resulting electromagnetic waves,
following incidence with the boundary. Since these boundary conditions require
the continuity of the portion of the electric field that is parallel to the boundary
plane, as well as the portion of the magnetic field that is perpendicular to the
boundary plane, two unique (and convenient) polarization modes of an EM wave
are introduced [49]. If ~E is perpendicular to the POI, then this is referred to as
~ is perpendicular
transverse electric (TE) polarization. Conversely, in the case that B

to the POI, the EM wave has transverse magnetic (TM) polarization.
Upon reflection at an interface between two different media, the Fresnel equa-

22

tions determine the fraction of the electromagnetic field amplitude reflected and
transmitted. Since the reflectance and transmittance of an electromagnetic wave
at an interface are sensitive to polarization, the reflection coefficients are given for
both TE and TM polarizations. For an incident EM wave having an electric field
Ei , the reflected electric field Er ≡ rEi is determined by the amplitude reflection

coefficient r given below for the TE polarization

rT E =

cos θ −

p

n2 − sin2 θ

cos θ +

p

n2 − sin2 θ

,

(2.2)

as well as the TM polarization
p
−n2 cos θ + n2 − sin2 θ
p
,
rT M =
n2 cos θ + n2 − sin2 θ

(2.3)

where θ is the angle of incidence on the boundary, and n ≡ nn12 is defined by the
fraction of the refractive indices n1 for medium 1 (incident) and n2 for medium 2
(transmitted), which form the interface. Similarly, for the transmitted portion of
the EM wave, transmission coefficients are used to determine the transmitted electric field amplitude. The equations for the amplitude transmission coefficients can
be simplified for normal incidence (wave propagation orthogonal to the surface
plane). Only the simplified transmission coefficient equation with θ = 0 is shown
as this thesis deals primarily with the reflected waves.

t12 =

2ñ1
ñ1 + ñ2

(2.4)

In equation (2.4), ñ1 and ñ2 are the complex refractive indices for medium 1 and
2, which are generally defined in terms of the real refractive index n(ω) and the
extinction coefficient κ(ω) as in equation (2.5).

ñ(ω) = n(ω) + iκ(ω)

23

(2.5)

The extinction coefficient is dominant in metals and conducting materials, and it
is directly related to the absorption coefficient α(ω) of the medium as follows:

κ(ω) =

α(ω)c
2ω

(2.6)

where c is the speed of light in a vacuum (c = 3 × 108 m/s).
These equations are often used in various methods of reflection spectroscopy in
order to determine optical and material properties of a sample medium present at
the reflecting interface because THz spectroscopy is sensitive to the electric field directly, and consequently probes the complex index of refraction directly (both real
and imaginary parts). Conventionally, a common focus in spectroscopy is the use
of a reference and sample measurement. By controlling all components of an optical system for a reference measurement, followed by the introduction of a sample
into the optical system for the sample measurement, a ratio of these two measurements can reveal optical information for the sample material by mathematically
inverting the Fresnel equations in combination with the measured data. This technique allows for the determination of optical and material properties of a sample,
as well as the identification of materials. This general method is explicitly outlined
in the following sections, first by a simplified transmission spectroscopy model,
and next, in the context of a unique form of reflection spectroscopy involving a
dove prism.

2.4

THz Transmission Spectroscopy

The use of THz-TDS in the transmission mode excels in the extraction of dielectric
properties of many insulating materials, in which THz frequencies can propagate
with low losses. As the noise floor is approached at higher frequencies within the
bandwidth of a spectrometer, transmission spectroscopy becomes less reliable [31].
24

This causes heavily absorbing materials to be difficult to determine via transmission spectroscopy. In this field, outlining the assumptions made for a given transmission spectroscopy technique is important. Typically, it is assumed that material properties are homogeneous with respect to position and direction, and that
interfaces between media are flat and parallel to each other, also neglecting scattering [50]. Unless otherwise specified, the atmosphere is assumed to be dry and
uniform in temperature, and its absorption is ignored. One key assumption that
allows the use of the simplified transmission coefficient given by equation (2.4) is
taking the angle of incidence θ to be zero, or assuming normal incidence. This allows
the change in path of propagation introduced by refraction to be ignored. The last
assumption to be made for this transmission spectroscopy technique is introduced
as the thick sample approximation.

Tx

n1

Sample
n2
n1
E0samp

Einc

Rx

E1samp
E2samp

Tx

d
Eref

Rx

Figure 2.4: An illustration of Fabry-Pérot reflections from an incident electric field
Einc transmitting through a sample having a refractive index of n2 surrounded
by air, n1 = 1. These F-P reflections cause multiple THz pulses to be detected at
different time delays. The electric field at the bottom of the figure represents a
reference measurement Eref . [Tx - transmitter, Rx - receiver.]

As an electric field approaches a sample with optically flat and parallel edges,
25

a portion of the electric field is reflected and transmitted into the sample. The
transmitted portion undergoes multiple reflections within the sample, referred to
as Fabry-Pérot (F-P) reflections. At each consecutive reflection, a weaker electric
field is transmitted outside of the sample as sketched in Figure 2.4. In the context of
detecting THz pulses transmitting through a sample at normal incidence, multiple
pulses are detected at different time delays. For the case of a thin sample, these
pulses are separated by a very small time delay, calling for complex analytical
methods to interpret the measured electric field. In the case of a thick sample,
these reflections have relative time delays such that the first transmitted pulse can
be captured and isolated within the time window of the THz-TDS system, and the
more simple analytical method can be used. Assuming thick samples are used for
this method in this thesis, modelling of only the 0th transmitted pulse in Figure 2.4
is sufficient for the determination of ñ(ω) and α(ω), as in Duvillaret et al. [51].
In order to determine the index of refraction n(ω) and the absorption coefficient α(ω) of a sample, a reference THz pulse Eref (t) as well as a sample THz pulse
Esamp (t) need to be collected to measure the effect of the sample on the propagation

of the THz pulse. The fast-Fourier transform of the pulses are then taken, giving
Eref (ω) and Esamp (ω), and since dielectric properties are dependent on frequency,

the spectroscopic information from these pulses are analyzed. Since the propagation of an electric field through the system is complicated, the construction of a
transfer function experimentally Hexp (ω) and theoretically Hth (ω) is a vital aspect
to creating a solvable problem:

Hexp,th (ω) =

exp,th
Esamp
(ω)

,th
(ω)
Eexp
ref

.

(2.7)

The reference and sample measurements allow Hexp (ω) to be calculated, however
Hth (ω) remains to be evaluated.

In order to build the physical representation of the reference and sample elec26

th
tric fields, Eth
ref and Esamp , propagation effects must be included. When an initial

electric field propagates some distance in any medium, the resulting electric field
is determined by a propagation coefficient [52]. For an electric field Eo propagating
a distance z through medium 1, the propagation coefficient P(ñ1 , z) is as follows:

P(ñ1 , z) = exp


−iωñ1 z
.
c

(2.8)

Applying this coefficient to the initial electric field Eo gives the resulting electric
field E(z) in the following equation:

E(z) = Eo P(ñ1 , z).

(2.9)

Using propagation coefficients and transmission coefficients and referring to
th
Figure 2.4, Eth
ref and Esamp can be built to determine Hth (ω). Since the reference

pulse Eth
ref propagates solely through air (n1 = 1) over an arbitrary distance L between the source and detector, it can be given simply by Eth
ref = Eo P(ñ1 , L). For the
sample pulse Eth
samp , the pulse propagates through a width d in the sample medium
2, as well as propagating in air for a distance L − d. Transmission from medium 1
to 2 and back to 1 also introduces coefficients, t12 and t21 , given by equation (2.4).
The sample pulse can then be given as Eth
samp = Eo P(ñ1 , L − d)t12 P(ñ2 , d)t21 , thus the
theoretical transfer function is constructed as follows:

Hth (ω) =

Eth
samp
Eth
ref

= P(ñ1 , −d)t12 P(ñ2 , d)t21

(2.10)

since P(ñ1 , L − d)/P(ñ1 , L) = P(ñ1 , −d).
After equating equations (2.7) and (2.10) to set Hexp (ω) = Hth (ω), then using
equation (2.8) to insert the propagation coefficients, the following equation arises:



−iωd
Hexp (ω) = t12 t21 exp
(ñ2 − 1) .
c

27

(2.11)

It should be noted that ñ1 = 1 for air, t12 and t21 do not have complex components
throughout this configuration, and ñ2 = n2 + iκ2 from equation (2.5). By using a
form of Euler’s equation to express equation (2.11) as Hexp (ω) = A(ω)eiφ(ω) , the
absolute value |Hexp | and the argument arg(Hexp ) of equation (2.11) can be used to
extract the index of refraction n2 (ω) and absorption coefficient α2 (ω) of the sample.
The representation of the index of refraction is a consequence of analyzing the
phase φ(ω) of the transfer function, letting φ(ω) = arg[Hexp (ω)]. From equation
(2.11) it is evident that this phase φ(ω) becomes

φ(ω) =

ωd
[n2 (ω) − 1]
c

(2.12)

which can then be rearranged to give the following relationship for the index of
refraction n2 (ω):

n2 (ω) =

c
φ(ω) + 1.
ωd

(2.13)

Similarly, the absorption coefficient can be determined by inspecting the amplitude A(ω) of the transfer function, letting A(ω) = |Hexp (ω)|. Again, from equation
(2.11), and substituting Fresnel’s transmission coefficients and complex index of refraction with equation (2.4) and (2.5), respectively, the following equation emerges:


κ2 (ω)ωd
4n2 (ω)
|Hexp (ω)| =
.
exp
c
[n2 (ω) + 1]2

(2.14)

Note that in the determination of Fresnel’s transmission coefficients, the approximation n  κ is used. For optically transparent (low absorption) materials at THz
frequencies, this approximation holds. Finally, by using the relationship between
the extinction coefficient κ2 (ω) and absorption coefficient α2 (ω) in equation (2.6),

28

the relationship yielding the absorption coefficient becomes
[n2 (ω) + 1]2
2
α(ω) = − ln A(ω)
d
4n2 (ω)

.

(2.15)

To conclude, the determination of the index of refraction n2 (ω) depends strictly
on the phase φ(ω) of the transfer function constructed by the reference and sample
measurements in the frequency domain, as well as the angular frequency ω and
thickness of the sample d. Adding a small amount of complexity, the absorption
coefficient essentially depends on the angular frequency ω, thickness d, amplitude
A(ω) and phase φ(ω) of the same transfer function. As a reminder, the thick sample

approximation assumes roughly that 2n2 (ω)d/c > twindow , where twindow is the
length of the spectrometer time window, thus thick or high index materials are
sufficient.

2.5

THz Dove Prism Reflection Spectroscopy

The use of a dove prism in THz-TDS is a common technique when exploring reactive optical properties of materials. A dove prism is a component of an optical
system that takes the geometrical form of a trapezoidal prism, in which the two angled, rectangular faces can be described as the input and output for incident plane
EM waves. Throughout the course of this thesis, THz pulses in the time-domain
spectrometer are modelled similarly to a plane wave. Each pulse is a superposition
of plane waves at different frequencies, thus for analysis, a fast-Fourier transform
is often applied to measured pulses in order to study the electric field at each frequency. Provided by its shape and orientation displayed in Figure 2.5, there are
many convenient features of dove prisms for determining reflecting properties of
a sample. After a horizontal EM wave propagates through the dove prism, it is
returned to its initial propagation direction, allowing for quick alignment. The flat
29

top face also simplifies the testing of sample materials, especially liquids.

TE

Eo

ETM
o

ET2
n3
θprism

Eo

ER3
ER2 = r23ET1

ET1 = t12Eo

ET3 = t21ER2

n2
n1

ER1

Incident pulse: Eo
Detected pulse: ET3 = t12r23t21Eo
Figure 2.5: The path of propagation of a THz pulse within a dove prism (n2 ) used
for reflection spectroscopy of a sample (n3 ). Reflected and transmitted electric
fields are expressed with respect to the appropriate Fresnel coefficient. The detected pulse is determined in terms of the initial electric field Eo . The key purpose
of this diagram is to draw attention to the cause of changes in the detected pulse
when only the sample (n3 ) is changed.

Figure 2.5 illustrates the optical path of propagation of a THz pulse as a plane
EM wave within the dove prism. In a typical THz-TDS apparatus, the measured
current or voltage directly relates to the electric field of the THz pulse, so the focus is on the determination of the electric field of a given THz pulse throughout
the dove prism. Considering a THz pulse travelling horizontally with an electric
field Eo in medium 1 incident on the first angled face of the dove prism, a small
amount is reflected downwards giving ER1 and the remainder is transmitted from
medium 1 into medium 2 giving ET 1 = t12 Eo , refracting towards the top face of the
dove prism. The next boundary involves the interface of the dove prism and the
sample, medium 2 and medium 3. Upon reflection at this interface, the THz pulse
30

ER2 = r23 ET 1 = r23 t12 Eo travels along a path symmetric to its previous propagation.

Following the refraction back into medium 1 from medium 2, the electric field Ef
(re-labelling ET 3 from Figure 2.5 for convenience) of the output (horizontally travelling) THz pulse is detected.

Ef = ET 3 = t21 ER2 = t21 r23 t12 Eo

(2.16)

In order to model reflections within a dove prism, or to use reflections to determine optical properties of a sample material, the use of a type of transfer function
is vital. By taking a reference measurement, as well as a measurement with the
sample on the top face of the dove prism, the ratio of these measurements results
in the cancellation of unnecessary components from equation (2.16). Considering
these two measurements, the only part of the optical system that is not kept controlled is medium 3, thus the theoretical transfer function Hth can be constructed
as shown below

Hth =

t21 rsam23 t12 Eo
Esam
,
=
Eref
t21 rref23 t12 Eo

(2.17)

and the simplified relationship for dove prism reflection spectroscopy is illustrated as follows:
Esam (ω)
rsam (ω)
=
.
Eref (ω)
rref (ω)

(2.18)

It is noted that the reflection coefficients for the interface between medium 2 and
medium 3 have been renamed rref and rsam for the reference and sample measurements, respectively.
In the simplified equation (2.18), the ratio of the measured reference and sample
electric fields is equivalent to the ratio of the corresponding reflection coefficients.
Using this approach, the equation is rearranged to solve for Esam (ω) in order to
31

predict the reflected electric fields from a sample material. Equation (2.18) becomes

Esam (ω) =

rsam (ω)
Eref (ω)
rref (ω)

(2.19)

where rsam (ω) and rref (ω) are calculated using equations (2.2) or (2.3). This requires a reference measurement as well as the refractive index of the dove prism
material n2 (ω) and that of both the reference and sample material n3 (ω) for the
appropriate angular frequency ω.
This approach can also be used to solve for rsam (ω) in order to determine the reflectance of a sample material of unknown optical properties. Equations (2.2) and
(2.3) can then be used to calculate the refractive index of the unknown sample. It is
important to note that in spectroscopy and NDE applications, the transfer function
detailed in equation (2.17) is often used to detect subtle differences in two measured waveforms, one being the reference. From equation (2.1), relative changes
in amplitude and phase can be easily calculated and illustrated using a ratio of the
corresponding electric fields. This is often the main focus in many practical cases
since a single measurement of an electric field from a complex system is difficult
to analyze. For the identification of a sample material, a reference measurement is
required, and in this way, the index of refraction and absorption coefficient of the
sample can be calculated.

32

Chapter 3
Experimental Methods

After establishing a theoretical model for the reflection of an electromagnetic
wave at a concealed interface, a dove prism is used to compare measured reflections to predicted reflections for varying interfaces. The geometry of a dove prism
allows for convenient and quick testing of different samples in search of significant,
qualitative differences in the reflections at a selected interface. Those interfaces that
result in reflections having drastic inversions or changes in shape relative to a reference reflection can then be implemented in a similar configuration to be imaged
(e.g. a layered system concealing the corresponding interfaces). For a given sample
in contact with the face of an ultra-high molecular weight polyethylene (UHMWPE, or UHMW) dove prism, the measured THz pulse at the output of the dove
prism represents the reflection of the incident pulse from a UHMW-sample interface. Not only can this configuration distinguish between contrasting reflecting
33

interfaces, but it can also reveal which polarization configuration will be most sensitive for this purpose. The dove prism simplifies reflection measurements from a
UHMW-sample interface as opposed to repetitively swapping samples concealed
by layers of UHMW which introduces errors in time-domain measurements from
moving the interface in between measurements. The use of a dove prism in the
first part of the experimental methods is of great importance in order to determine
which interfaces are to be involved in the imaging sample in the later section of
the experiment and in what polarization the imaging beam is to be aligned. After
determining four materials that each produce a differing reflected waveform in the
dove prism, these materials are concealed within a layered UHMW system to imitate a system in an applied, real-world setting. Using THz frequencies, the layered
sample is imaged by means of a raster scan in order to spatially locate and identify
the concealed materials.

3.1

Apparatus

3.1.1

Pulsed Terahertz Controller

The THz-TDS source and detection system used in this thesis is a modified T-Ray®
4000 pulsed THz controller patented by Picometrix® . The enclosed system produces and detects THz pulses on the order of picosecond durations by the use of a
1064 nm fs laser with fiber-coupled emitter and detector heads as shown in Figure
3.1. The heads allow for the propagation of THz pulses through an experimental
system before detection in order to examine properties of the system at THz frequencies. Broadband THz pulse measurements from 0.02 THz to 2 THz can be
measured within an 80 ps time window with a data collection rate of 1000 Hz.
The T-REX computer software displays and analyzes detection measurements for
real-time monitoring or recording of THz waveforms for experimental analysis. A
34

Figure 3.1: A photograph of (a) the pulsed THz controller and (b) an emitter and
detector head. The optical cables couple each head to the corresponding transmitting/receiving plug. The dual-channel setup allows two emitter/detector pairs to
be operating simultaneously.
newer model of this system is the T-Ray® 5000 available through Picometrix® , a
subsidiary of Advanced Photonix Inc [53]. The system is used in a transmission
(Section 3.2) and two separate reflection geometries (Section 3.4) throughout this
thesis.

3.1.2

Dove Prism

The dove prism is designed in order to conveniently create and examine interfaces
that are to be concealed in an imaged sample in a later section of the experiment.
The dove prism is constructed from a solid block of UHMW material because of its
extremely low absorbing properties, which is investigated in Section 3.2 via THz
transmission spectroscopy. The block of UHMW has been cut with a band saw to
the shape of a 45◦ trapezoidal prism, and the top face has been sanded to provide
a smooth surface. The surface roughness is estimated to be approximately 30 µm,
or in terms of wavelength, λ/10 (at λ = 0.3 mm wavelength or 1 THz). The specific
dimensions of the dove prism are outlined in Figure 3.2. The height and width of 6
cm provide a sufficient area on the angled face of the prism to contain the incident
beam of the THz source. The index of refraction of UHMW is 1.52 for frequencies
in the range of 0.1 THz to 0.6 THz. Given this value, the selection of an angle of
35

Top View

Side View
25.29 cm
o

45

6.00 cm

Side View:
6.00 cm

13.29 cm

6.00 cm

25.29 cm

Top View:

6.00 cm

Figure 3.2: The blueprint of the UHMW dove prism used to inspect reflections
at chosen UHMW-sample interfaces. Important dimensions and the angle of the
prism are outlined and selected such that the input/output THz pulses remain
horizontal, considering an index of refraction of 1.52.

36

incidence of 45◦ leads to an angle of reflection at the top face of the prism of 73◦ for
these frequencies. The dove prism is mounted onto a secured mechanical jack in
the experiment for convenience in alignment.

3.1.3

Imaging Sample

Figure 3.3: A photograph of the dismantled imaging sample at its actual size. The
top and bottom sections are shown respectively on the left and right. Each division
of the scale bar represents 2.54 cm (1 inch).

The imaging sample is constructed from a slab of UHMW that is 1.27 cm thick.
Using a band saw, two identical rectangular pieces, 24.1 cm by 22.9 cm, have been
cut from the slab. After dividing one of the pieces into four quadrants, small square
sections, 3.2 cm by 3.2 cm, have been milled out at the center of each of the four
quadrants at a depth of 0.64 cm as seen in Figure 3.3. The computer numerical
control machine at the UNBC Wood Innovation Research Labs is used to create
the uniform, square pockets. Next, the two pieces of UHMW are stacked with
the edges aligned and clamped together such that the milled-out sections were
concealed. Holes are drilled at each corner and in the center of the sample, so the
37

top and bottom pieces in Figure 3.3 can be bolted together. This allows for quick
and convenient manipulation of the materials being concealed within the pockets
of the sample for imaging purposes later in this thesis. A larger drill bit is used
to countersink the bolt heads on the top piece of the imaging sample to provide a
smooth top surface.
UHMW-PE is an exceptionally high molecular weight thermoplastic that is extremely abrasion, impact and chemically resistant, the highest among plastics [54].
The surface has very low adhesion, friction and water absorption properties. The
material is also very ductile, and it absorbs energy and sound well, although when
heated, it maintains a high resistance to deformation, even past its melting point
[55]. Many attributes of UHMW hold up even at cryogenic temperatures.
The impressive qualities of UHMW lead it to be a favoured material for many
insulating applications, even replacing steel in some applications. Due to its selflubrication and impact resistant properties, it has been originally used in the handling of bulk materials like grain, cement and gravel, as well as in the mining industry. UHMW can be used in dumping trucks, silos, large bins, conveyor systems,
chutes, dry bearings, and so forth [54]. UHMW combined with other substances,
such as oil, can be crafted into a fibrous form, which is found in bulletproof vests
and protective gloves. Since UHMW is well-established in protective applications
involving large amounts of harsh, gritty materials or chemicals, its involvement in
the field of NDE is not surprising. Due to its advantageous characteristics, UHMW
mostly exists on the outermost layer of many industrial systems in order to prevent wear or damage to the underlying structure of the system. The use of various
metals within the underlying structure of these types of systems is also common,
posing many risks such as the infiltration of elements from the outside environment, such as water. In Section 3.2, the determination of the dielectric properties
of UHMW at THz frequencies is outlined. One key result is the minimal absorp-

38

tion of UHMW at these frequencies. This prompts the investigation of UHMW,
in this thesis, for use as the outer material of a layered system imitating a realistic, industrial system, in which various concealed interfaces are imaged in space
and identified. The practical importance of the identification of different materials, especially metals and water, concealed by UHMW is also evident from the
applications surveyed.

39

3.2

Transmission Spectroscopy

The analytical method used for transmission spectroscopy of insulating materials
such as UHMW and glass is outlined in Section 2.4. Results of transmission spectroscopy include plots of the index of refraction as a function of frequency for the
dielectric materials used through the course of this thesis, as well as the inspection
of the absorbing properties of UHMW, which motivates the selection of UHMW
as the dove prism constructing material. The measurement of the refractive index
of glass allows modelling of glass reflections in the reflective mode, described in
the later Section 3.3. By taking a set of reference and sample measurements of THz
pulses for both materials, illustrated in Figure 2.4, spectroscopic functions for index of refraction and the absorption coefficient are calculated. For an explanation
of the setup, the schematic involved in the sketch from Figure 2.4 can be followed.
Setting up the apparatus for the transmission mode is straight-forward, since
it involves mounting the transmitting and receiving THz pulse heads with only
a sample and aperture in between. After aligning the emitter and detector, the
sample and aperture are mounted nearest to the detector, in the respective order.
The sample is mounted in the THz pulse path, and a carpenter square is used to
align the sample normal to the propagation of the THz pulse.
For the determination of dielectric properties for UHMW, a reference electric
field measurement of the THz pulse is taken at a time delay of 1610 ps, captured
within an 80 ps time window by the T-REX software in real-time. Three consecutive measurements immediately follow as part of the same reference measurement,
each with a time delay translated 80 ps further. The full measurement consists of
four 80 ps wide electric field plots, each at 1610 ps, 1690 ps, 1770 ps and 1850 ps,
respectively. This allows for a higher resolution in the frequency domain, increasing the degree of accuracy for measuring the dielectric properties. The averaging
setting in the T-REX software also automatically averages 1000 THz waveforms
40

for each sampled waveform before recording, in real-time. The reference measurement corresponds to an empty region between the emitter and detector. This
technique of data collection is repeated for every measurement in this section. For
the sample measurements, the electric field of the transmitted THz pulse through
the sample at normal incidence is captured in the same time window as the reference measurement. The sample measurements are taken immediately following
the reference measurements to avoid errors from fluctuating temperatures within
the optical fibers of the pulsed THz controller that may cause detected values to
slightly drift in the time-domain. A 12.7 mm thick sample of UHMW is placed
between the emitter and detector during the sample measurements. Following the
first two measurements, a total of two measured electric fields are obtained for the
reference and the sample, across a time range of 360 ps.
This is repeated five times for averaging purposes. The entire process is repeated for a 6 mm thick glass sample. With the set of measured THz pulse electric
fields, the time-domain waveforms need to be analyzed in order to determine the
dielectric properties of UHMW (and glass). In Section 3.3, a dove prism can then
be constructed according to the optical properties at THz frequencies of UHMW
in order to analyze spectral features of materials in the reflection mode, with confidence, which then establishes the foundation of the main focus of this thesis, a
deeper look into reflection imaging.

3.2.1

Experimental Results

The analytical method introduced in Chapter 2.4 is implemented in a MATLAB®
script in order to calculate values to construct the index of refraction n(ω) and absorption coefficient α(ω) at various frequencies in the low-THz range for UHMW
and glass. By taking the fast-Fourier transform of the time-domain electric field
data E(t), the reference and sample electric field waveforms Ẽ(ω) are calculated
41

along the frequency domain. The transfer function Hexp (ω) from equation (2.7) is
constructed by taking the ratio of the transformed electric fields for the sample and
reference measurements. Finally by taking the argument and absolute value of the
complex data points that generate the transfer function, φ(ω) and A(ω) are obtained and used in equations (2.13) and (2.15) to determine the index of refraction
n(ω) and absorption coefficient α(ω) with respect to frequency.

Index of refraction

2

1.5

1

0.5
0.2

0.4

0.6

0.8

1

Frequency (THz)
Figure 3.4: The calculated index of refraction n(ω) of UHMW from 0.1 THz to 1
THz using transmission TDS. The index of refraction is constant at approximately
1.52 from 0.1 THz to 1 THz.

Figure 3.4 displays the index of refraction of UHMW which is essentially constant, around 1.52 over frequencies between 0.1 THz and 1 THz. The absorption
coefficient is excluded from Figure 3.4 since it falls to the noise floor over the same
frequency range, leading to the conclusion that THz radiation is minimally absorbed by UHMW. Motivated by the interest in designing a dove prism for reflection spectroscopy in Section 3.3, a material which has minimal absorption and a
constant index of refraction for frequencies within the bandwidth of the THz-TDS
system is ideal for use in the construction of THz optics. To emphasize the im-

42

portance of low absorption in UHMW, the path of propagation in a dove prism
designed for THz frequencies is longer than in most optical instruments, such as
lenses and other beam shaping devices, leading to a larger amount of absorption
which diminishes the accuracy of spectroscopic information within the THz pulse.
The use of UHMW as the primary material of a dove prism for reflection spectroscopy is predicted to be sufficient based on the consistent refractive properties
at THz frequencies, as well as its minimal absorbance.

Absorption coefficient (cm -1)

Index of refraction

3
2.5
2
1.5
1
0.5
0.1

0.2

0.3

Frequency (THz)

10
8
6
4
2
0
0.1

0.2

0.3

Frequency (THz)

Figure 3.5: The calculated index of refraction n(ω) (left) and absorption coefficient
α(ω) (right) of glass from 0.1 THz to 0.35 THz. The refractive index is constant
around 2.56. The large absorption of glass at higher THz frequencies prevents
the attainment of accurate spectroscopic information for dielectric characteristics
above 0.35 THz.

The index of refraction and absorption coefficient α(ω) of the glass sample used
in Section 3.3 is also calculated and plotted in Figure 3.5. The index of refraction
of glass is constant at approximately 2.56 from 0.1 THz to 0.35 THz. Due to the
depletion of frequencies above 0.35 THz by transmitting through glass, accurate
information regarding the index of refraction cannot be determined past 0.35 THz
43

with this method. This large absorption in glass at high frequencies is displayed in
the plot of its absorption coefficient in Figure 3.5.

44

3.3

Dove Prism Reflection Spectroscopy

The UHMW dove prism designed in Section 3.1.2 is used to examine and compare
reflections at UHMW-sample interfaces, as well as test the reflection spectroscopy
analysis. Figure 3.6 details the alignment of the dove prism. The dove prism is
placed between the THz-TDS transmitter (Tx ) and receiver (Rx ), which are oriented
in the TE polarization. It can be noticed that the dove prism acts as an optical
black box, returning the THz pulse to its original propagation after one reflection
at the interface of interest. This simplifies reflection measurements for different
UHMW-sample interfaces by constraining the propagation of the THz pulse to a
plane parallel to the mounting table.

A1

(a)
Tx

L2

L1
1.4 cm

f2= 10 cm

f1= 20 cm
20 cm
(b)
Tx

Rx

L1

20 cm
L2

S

Rx

9.9 cm

9.9 cm

Figure 3.6: (a) Schematic of the THz beam spot measurement. Silicon lenses (L1,L2)
have focal lengths, f1 and f2 , respectively. The aperture (A1) is used to measure the
beam spot. (b) Schematic of the dove prism alignment (not to scale). The beam
spot is centered on the top face of the dove prism. Dotted lines represent the path
of propagation for the detected pulse.

45

To ensure the measured reflection solely represents the reflection at the interface, the THz pulse is focussed to a beam spot of approximately 1.9 cm by using
silicon lenses of focal lengths 200 mm and 100 mm, respectively. The 200 mm focal
length lens is required to provide sufficient distance between the lens and the focal
point, to ensure the focal point occurs at the top surface of the large dove prism.
The latter 100 mm focal length lens is used for a quick focus at the receiver (Rx ). Silicon lenses also have a favourable bandwidth in this spectral range consequential
of the absence of absorption lines and dispersive effects at THz frequencies [56].
The beam spot is measured with an optical aperture (replacing the dove prism)
at a distance approximately the focal length of the lens (200 mm) away from the
lens, L1. The diameter of the aperture at which the electric field amplitude of the
THz beam drops by 1e of its initial electric field peak (open aperture) gives the beam
diameter at the focal point [57]. The electric field amplitude of the THz pulse is directly observed using the T-REX software. Once the THz pulse measurement is
located in the time-domain and plotted via the software, the electric field amplitude is displayed. After recording the distances between the lenses (L1,L2) and the
focal point (A1), the dove prism is put in place of the aperture, A1. Introducing
the dove prism increases the optical path length, so the lenses are brought closer
together accordingly such that the focal point is incident with the top face of the
dove prism. This minimizes the beam diameter at the reflecting interface of interest. The introduction of the dove prism also leads to an increased time delay of the
THz pulse, so the 80 ps time window observing the THz pulse in real-time via the
T-REX software must be adjusted to relocate the pulse.
Previously, the beam diameter at the focal point has been measured, but the size
of the beam spot projected onto the face of the dove prism needs to be calculated.
This gives the approximate size of the surface required to form an acceptable interface with the top face of the UHMW dove prism. Due to the geometrical change

46

of the optical path induced by refraction in the dove prism, the THz beam spot
is elongated along the interface by a factor of cos1 θr ≈ 3.42, where θr = 73◦ is the
angle of reflection at the interface. For example, assuming an original beam spot of
1.9 cm without the dove prism as discussed above, the elongated beam spot with
the introduction of the dove prism is expected to be a factor of 3.42 larger, giving
a 6.5 cm focussed beam spot. This helps describe the absolute minimum size of
an interface, or the minimum size of a sample in contact with the top face of the
UHMW dove prism, to give a reliable reflection.
Once the dove prism is aligned in the TE polarization mode of the THz-TDS
optical system, measurements of the electric field of the reflected THz pulse with
respect to time can be made. By placing a flat sample on the top face of the dove
prism, a UHMW-sample interface is made. These samples consist of varying materials including different metals and wood products, water, air, a stack of paper
towel with varying water content, a gold-plated mirror, glass, and other plastics.
The first stages of measurements include monitoring qualitative aspects of the reflected THz signal using T-REX computer software for terahertz pulse signal processing and analysis. By resting a sample on the top face of the dove prism, an
interface is created with the UHMW, and the real-time signal corresponding to the
new reflection is collected. This is repeated for the materials mentioned above. All
reflections are compared to the reference UHMW-air interface reflection, for convenience. Contrasting reflections include signal inversions, delays (translations in
time), and even entire changes in shape.
Interfaces that produce the most contrasting reflections are then inspected more
carefully. Before placing each sample on the dove prism, reference measurements
are taken to record the reflection at the UHMW-air interface. Next, a sample is
placed on the dove prism in order to record the reflection at each UHMW-sample
interface. Reference measurements are of vital importance in this section in order

47

to theoretically predict the reflection from a UHMW-sample interface, and to verify the MATLAB® script written to calculate these predictions based on Fresnel’s
equations. In Chapter 2.5, Fresnel’s equations are used to develop a theoretical
model to predict the reflected signal at an interface with a known dielectric function or index of refraction (˜ = ñ2 ) given only a reference signal from the dove
prism. A script has been written in MATLAB® to calculate and plot these predicted
signals. It is shown in equation (2.19) that the electric field of a reflection from a
UHMW-sample interface Esam (ω) can be written in terms of Fresnel’s reflection
coefficients and the electric field of the reflection at a reference interface Eref (ω)
(UHMW-air), provided all other parameters are fixed. The Fast Fourier Transform
or Inverse Fast Fourier Transform functions in MATLAB® are used to express the
electric fields in either the frequency or time domain, respectively [58]. The measured UHMW-sample reflections are plotted with their corresponding predicted
reflections in the interest of testing the model outlined in Chapter 2.5.
These measurements are repeated to align the TM polarization mode of the
THz-TDS receiver and transmitter. To obtain a TM polarization, the emitter and
receiver heads are rotated by 90◦ . It is noted that the reflections contrast at a substantially higher degree, in this configuration, thus the interfaces are more distinguishable. This provides motivation to continue the rest of the experiment in this
thesis using the TM configuration. Nonetheless, in the remaining sections of this
thesis, the TE configuration is employed.

3.3.1

Experimental Results

By following the above procedure, a collection of measured waveforms in the time
domain is obtained from UHMW-sample interfaces created by the dove prism and
a selection of samples. Reference waveforms (UHMW-air reflections) are recorded
immediately following each reflection measurement of a sample on the dove prism.
48

Samples examined on the dove prism exhibiting contrasting THz reflections among
the group include a gold-plated mirror, water, and glass, along with the reference
air reflection. Using transmission spectroscopy, the refractive indices for UHMW
and glass have been determined. Similar to reflection spectroscopy, the calculation
of the index of refraction of a material through transmission spectroscopy relies
on reference and sample measurements of a THz pulse. The amplitude and phase
changes of the THz pulse due to the introduction of the sample provide information to determine the refractive index and absorption of the sample. Chapter 2.4
details this method used to determine the refractive indices for UHMW and glass
as in Section 3.2. The empirical dielectric function of water is calculated using the
double Debye model with the parameters discussed by Uhd Jepsen et al. [59]. The
empirical dielectric functions of gold and aluminum are calculated using a similar
Drude model and parameters presented by Zeman et al. [60].
In order to determine which UHMW-sample interfaces produce contrasting reflections, a qualitative form of spectroscopy in the time-domain is used to directly
observe changes in amplitude, delay or shape of the pulse. By plotting THz pulse
reflections from each interface in the time-domain (with respect to its time delay),
these changes in pulse properties are identified, thus revealing contrasting interfaces to be used in the imaging sample in Section 3.4.
Once the refractive indices or dielectric functions of the samples are determined, the script written in MATLAB® is used to calculate and plot the associated predicted THz pulse reflected from the UHMW-sample interface, given the
reference reflection from a UHMW-air interface and an angle of reflection of 73◦ .
Figure 3.7 shows the reflected THz pulse from each UHMW-sample interface of
the dove prism for the TE and TM polarizations. The reflected waveforms for each
interface examined in the TE polarization appear to differ primarily by amplitude.
The lack of substantial changes in shape or form of the reflected pulses suggest

49

minimal phase change upon reflection at these interfaces. It is speculated that distinguishing between four differing interfaces solely by amplitude changes upon
reflection may be exceptionally challenging in a more practical setting; in such a
setting, fewer parameters of the system can be held fixed.
Upon plotting the reflections from identical interfaces in the TM polarization,
the problem outlined above is resolved. Figure 3.7b displays the significant change
in shape of every interface examined in the TM polarization. In contrast to the
UHMW-air interface, the reflection from the UHMW-gold interface undergoes an
inversion of the waveform as well as a small degree of attenuation. The UHMWwater and UHMW-glass reflections are heavily attenuated while displaying some
difference in form such as the small peak at approximately 2063 ps exhibited by
the UHMW-water reflection. This suggests a common phase shift between the
reflections at the two interfaces created by water and glass. Due to these significant qualitative amplitude and phase changes between the differing interfaces, it is
suggested that TM polarized reflections are more distinguishable, and the identification of these interfaces concealed by UHMW in a practical setting may be more
definitive and efficient using TM polarization rather than TE polarization.
Following the comparison of TE and TM polarization for this system, it is essential to verify the theoretical reflections modelled earlier with the corresponding
measured reflections. This allows for a similar model to be used for imaging concealed interfaces in a practical setting in the next section of this thesis. Figure 3.8a
shows the measured reflected THz pulses from the interface of the UHMW dove
prism and the sample in the TM polarization, once again displaying the distinguishability between each reflection in this mode. Figure 3.8b-d plots, side-by-side,
the measured and predicted reflected THz pulses from a UHMW-glass, UHMWgold, and UHMW-water interface of the dove prism. The predicted reflections
for the UHMW-glass and UHMW-water interfaces agree with the measured wave-

50

0.4

(a) Predicted UHMW-sample reflection waveforms
from dove prism in TE polarization.
UHMW-glass
UHMW-gold
UHMW-water
UHMW-air

Amplitude (arb.units)

0.3
0.2
0.1
0
-0.1
-0.2
-0.3
2010

2020

2030

2040

2050

2060

2070

2080

Time (ps)

Amplitude (arb.units)

0.4

(b) Predicted UHMW-sample reflection waveforms
from dove prism in TM polarization.
UHMW-glass
UHMW-gold
UHMW-water
UHMW-air

0.2

0

-0.2

-0.4
2010

2020

2030

2040

2050

2060

2070

2080

Time (ps)

Figure 3.7: Predicted THz waveforms output by the UHMW dove prism system
with a reflecting UHMW-sample interface, using (a) TE and (b) TM polarizations.
Given one reference measurement (UHMW-air) for each configuration, reflections
at other UHMW interfaces are calculated.
51

Amplitude (arb.units)
Amplitude (arb.units)

0

-0.2
2000

UHMW-glass
UHMW-gold
UHMW-water
UHMW-air
2010

0.02

2020

2030

2040

2050

2060

2070

2080

2070

2080

2070

2080

2070

2080

Time (ps)
(b) UHMW-glass reflections

0.04

Prediction
Measurement

0
-0.02
2000

Amplitude (arb.units)
Amplitude (arb.units)

0.2

(a) Measured UHMW-sample reflection waveforms
from dove prism in TM polarization.

2010

2020

2030

2040

2050

2060

Time (ps)
(c) UHMW-gold reflections
0.1

Prediction
Measurement

0
-0.1
2000

2010

2020

2030

2040

2050

2060

Time (ps)
(d) UHMW-water reflections

0.05

Prediction
Measurement
0

-0.05
2000

2010

2020

2030

2040

2050

2060

Time (ps)

Figure 3.8: (a) Measured THz waveforms output by the UHMW dove prism system with a reflecting UHMW-sample interface (TM polarization). Predicted and
measured THz waveforms output by the dove prism from a (b) UHMW-glass interface, (c) UHMW-gold interface, (d) UHMW-water interface (TM polarization).
52

forms.
The measured reflection for the UHMW-gold interface does not have as strong
an agreement with the predicted reflection as compared to the other interfaces,
however, both of these measured and predicted waveforms are of similar form
and are distinguishable among the reflections plotted in Figure 3.8. This weak
agreement can be explained by the nature of the sample used for the UHMW-gold
interface. Firstly, a 76.2 mm protected gold mirror is used for the gold sample,
which is the largest one available. The dielectric overcoat on the gold-plating of
the mirror may have reduced the quality of the UHMW-gold interface, however
typical thicknesses for these coatings are well below the order of magnitude of
the wavelength of THz radiation, so its measurable effect in this configuration is
unlikely [61].
The factor that is most likely diminishing the quality of the UHMW-gold interface is the size of the mirror. Earlier in this section, an expected focussed beam
size incident at the top surface of the dove prism has been estimated. When constructing a sample for forming an interface with UHMW, it is favourable to select
dimensions that considerably exceed the beam spot size since the electric field amplitude is e1 of its initial maximum at the beam waist. This ensures that a large
fraction of the incident electric field reflects from the supposed interface. Because
the beam spot (6.5 cm) and gold mirror diameter (7.62 cm) are close, it is suspected
that the entire THz pulse does not reflect at the designated UHMW-gold interface.
Other samples used throughout this section are also substantially larger than the
beam spot, explaining the better agreements with theory of the other reflections.
To verify the speculation above, Figure 3.9 displays the contrast in the agreement with theory between the reflections from the UHMW interfaces with the
small gold sample and the larger aluminum sample. The reflection from the sufficiently large sample (aluminum) agrees with theory, while the reflection from the

53

gold sample is not a perfect match with the predicted pulse. It can be noted that
the predicted reflected pulse from both metal samples are identical, illustrating
the expected reflection from any sample possessing an extreme dielectric contrast

Amplitude (arb.units)

Amplitude (arb.units)

to UHMW.

UHMW-gold reflections
0.1

Prediction
Measurement

0
-0.1
2000

2010

2020

2030

2040

2050

2060

2070

2080

2070

2080

Time (ps)
UHMW-aluminum reflections
0.1

Prediction
Measurement

0
-0.1
2000

2010

2020

2030

2040

2050

2060

Time (ps)
Figure 3.9: Predicted and measured THz waveforms output by the dove prism
from a UHMW-gold interface (top) and UHMW-aluminum interface (bottom). The
aluminum sample is larger than the gold sample, thus reflecting a greater amount
of the THz pulse, and strengthening the agreement with theory.

Nonetheless, the reflection spectroscopy model written earlier supports the
measured reflections at each interface. The four samples that have been examined in this section also provide identifiable and distinguishable reflections at THz
frequencies for each respective UHMW-sample interface.
Also, for measurements in the TM mode, the force exerted on the sample affects
the measured reflection. The greater the force is on the sample creating the inter-

54

face with the dove prism, the better the agreement is between the predicted and
measured reflections. This is not the case for the TE mode since the force exerted
on the sample does not significantly affect the measured reflection. This reduction
of accuracy for measurements in the TM mode can be explained by the considerable contrast between UHMW-air interface reflections and other interface reflections within the imaging sample, exclusively during operation in the TM mode, as
seen in Figure 3.7. It is expected that interfaces in practical systems are not perfect interfaces whereas the intrusion of small air gaps between two media may be
present. In this case, a small portion of the THz pulse reflects as if the interface
was a UHMW-air interface, affecting the detected waveform by the combination
of contrasting reflections. In the TE mode, where the UHMW-air interface reflection is identical in form (but not amplitude) to the other interface reflections, small
air gaps at the interfaces may not be easily detectable due to the lesser degree of
contrast of its reflection, as opposed to the TM mode. By exerting a force on the
sample, small air gaps are mostly eradicated, but still may have affected accuracy
in the measurements seen in Figure 3.8.

55

3.4

THz Reflection Imaging

After validation of the reflection model for a UHMW system involving varying
interfaces, a THz reflection imaging system must be set up and aligned in order
to explore the possibility of spatially locating and identifying materials concealed
within a UHMW layered system in an applied setting. A similar imaging apparatus to the Brewster’s angle reflection imaging system designed by Kilcullen et al.
is used [19]. Figure 3.10 is a labelled photograph of the reflection imaging system
in operation. Figure 3.11 displays the THz pulse path of propagation throughout
the imaging system. The entire system is aligned optically, using a mounted green
laser pointer.
In order to align all four mirrors and sample with the transmitter (Tx ) and receiver (Rx ) heads, the imaging sample is replaced with a flat gold-plated mirror
(S). For the purpose of suspending the mirrors in such a way that the incident horizontal THz pulses from the transmitter are directed downwards onto the imaging
sample and allowing the sample to be translated in space below the mounting system, all four mirrors are mounted onto a raised crosspiece constructed from four
stacked dovetail rails. For sufficient clearance of the apparatus above the imaging
sample plane, on each side of the rail crosspiece, one pillar post is attached beneath a post holder and post, which is ultimately attached to the crosspiece. The
post holder allows for height adjustments of the entire reflection apparatus.
Next, two gold-plated parabolic mirrors (PM1 and PM2) are mounted against
the underside of the rail crosspiece to focus horizontally incident light vertically
downwards. By mounting a pair of gold-plated flat mirrors (M1 and M2) directly
below the parabolic mirrors, the focussed light is redirected downwards and towards the center of the table. The flat mirrors are angled and positioned such that
the focal point lands below the lowest mirrors, centered above the table and at the
imaging sample plane (S). It is important for the focal point of the propagating
56

PM1

M1

PM2

S

Tx

M2

Rx

Figure 3.10: The complete reflection imaging system used to raster scan the imaging sample at a selected depth. [Tx - transmitter, Rx - receiver, PM1/PM2 - parabolic
mirrors, M1/M2 - flat mirrors, S - imaging sample.]
light to be centered because the reflected focussed light from the sample is then
redirected and collimated towards the receiver by the flat and parabolic mirrors
on the opposing side of the apparatus. In this way, the symmetry of the apparatus
and of the path of propagation of the incident THz pulses dictates the quality of
the imaging measurements. The gold mirror in place of the imaging sample (S)
for alignment is mounted on a mechanical jack to adjust its height. After raising
this gold mirror to a top surface height of 14.5 cm above the table, the reflected
THz pulses are successfully collimated into the receiver head. At this height, the
detected THz pulse, which is monitored via the T-REX software, is at its strongest.
The angle of reflection at the surface of the gold mirror in place of the sample is

57

S

Tx

Rx

Figure 3.11: The path that a measured THz pulse propagates through the reflection
imaging system. [Tx - transmitter head, Rx - receiver head, S - imaging sample.]
approximately 60◦ .
Following the construction and alignment of the reflection measurement apparatus, the optimal height of the imaging sample above the mounting table needs
to be determined. By inspecting concealed interfaces underneath the top layer of
the imaging sample, a change in the path of propagation by refraction of the THz
pulses is introduced as compared to a direct reflection from air to the gold mirror. This requires the top surface of the imaging sample to be raised a height, ∆h,
higher than the original focal point height in air of 14.5 cm. This change in height
is calculated in the following equation utilizing the geometry of the paths of light

58

in air as well as the refracted path through the top layer of the imaging sample:

∆h = √

dcosθ
n2 − sin2 θ

.

(3.1)

Given the thickness of the top layer of the UHMW imaging sample (d=1.27 cm), the
refractive index of UHMW (n=1.52), and the angle of incidence at the top surface
(θ=60◦ ), the surface of the imaging sample must be raised by about 0.5 cm above
the focal point in air.
After this calculation, the mechanical jack used to mount the imaging sample
is adjusted such that the top surface of the imaging sample is 15.0 cm above the
mounting table. All reflection measurements in the remainder of this thesis are
collected with the surface of the imaging sample at this height. Only precise lateral translations of the imaging sample are to be executed for imaging purposes.
Now that the focal point of the THz pulses occur at the first interface below the
surface of the imaging sample, the output THz pulses that are detected from the
reflection imaging system contain accurate information regarding the properties
of that concealed interface. By analyzing these reflections, spatial and material
properties of the interfaces concealed within the sample can be determined.

3.4.1

Automation of the Image Measurements

In order to automate the reflection measurements for imaging purposes, two motorized translation stages are mounted beneath the imaging sample and perpendicular to each other. This allows for precise positioning of the imaging sample for
automated measurements of a reflected THz pulse to construct an accurate spatial
image. Using a USB cable, the motorized translation stages contain integrated electronic controllers that are controlled by a computer via Thorlabs’ APT™ software.
MATLAB® scripts, in combination with macros, have been written to control the

59

Figure 3.12: An illustration of the incremental positions of the imaging sample
within the reflection imaging system for a 10 by 10 raster scan. The starting position, (Xi , Yi ), is given by the large white triangle, the finishing position, (Xf , Yf ), is
given by the large white circle, and directions are indicated.
APT™ and T-REX software in order to laterally position the imaging sample and
to collect THz pulse data at that position, respectively. To obtain a spatial image
of the concealed interfaces within the imaging sample, imaging measurements are
obtained in the form of a raster scan. After centering the top-right corner of the
imaging sample under the reflection imaging system, the positions of the translation stages are recorded as (Xi ,Yi ). This is repeated for the bottom-left corner of the
imaging sample, recording (Xf ,Yf ). For an image of a desired resolution, m by n,
−Xi
i
and Yf −Y
the incremental position changes are given by Xfm
n . The imaging sam-

ple is scanned using these positional increments in order to consistently space the
reflection measurements over the entire sample to create an m by n depth image of
the interfaces within the sample. Figure 3.12 illustrates the starting and finishing

60

points of an example raster scan as well as the incremental positions of the sample which is kept stationary for the duration of each measurement. Following the
scan, in-depth analysis algorithms written in MATLAB® are used to spatially plot
the amplitude and phase, as well as other spectroscopic features, of the measured
THz pulses for these images.
Following the construction of the reflection imaging apparatus, it is observed
that a front reflection from the top surface of the imaging sample interferes with
the reflection measurements of the subsurface interface of interest. This small airUHMW reflection occurs approximately 100 ps before the measured reflection, introducing noise within the system. The original design of this imaging system is
intended to minimize these front reflections by operating near Brewster’s angle as
the angle of reflection of the first UHMW-air interface at the top of the imaging
sample (approximately 60◦ ) [62]. The front surface back reflection is only reduced
for the TM polarization. As a result, for TE polarization, front surface back reflections need to be minimized using a beam block to improve signal quality. In order
to prevent this signal interference, a front reflection blocker is constructed from
a thin, flat strip of aluminum foil. It is mounted and centered directly above the
imaging sample, as close as possible to its top surface without impeding motion of
the sample during imaging. The introduction of this front reflection blocker successfully diminishes the amplitude of the top reflection such that the addition of
the signal is negligible to the reflection from the concealed interface.

3.4.2

Preparation of the Concealed Samples

Before imaging of the concealed interfaces inside the UHMW imaging sample is
performed, three different samples are prepared for containment in each of the
milled 3.2 cm square sections of the bottom layer of the imaging sample. In Section
3.3 reflections from various interfaces are examined by use of the UHMW dove
61

(b) Complete imaging sample.
(a) Bottom layer of imaging sample.

Figure 3.13: A photograph of (a) the bottom layer of the imaging sample with sample inserts and (b) the imaging sample fully enclosing the sample inserts. The topleft section (M) contains steel, the top-right section (G) contains glass, the bottomleft section (A) contains air, and the bottom-right section (W) contains water.
prism. Based on the substantial qualitative contrast of the reflections from the
gold-mirror, glass, water, and air, all but one of these materials are selected as a
sample insert.
Figure 3.13a illustrates the corresponding location for each sample insert inside
the imaging sample. The reference air sample requires minimal preparation since
an empty square section within the imaging sample creates the desired UHMW-air
interface. The glass sample is prepared by cutting a 3.2 cm square from a 0.64 cm
thick glass sheet. The edges are carefully sanded to a flush fit into one of the milled
sections of the imaging sample. In place of the gold sample, a 3.2 cm steel sample
is cut from steel flat bar using an angle grinder. This significantly minimizes the
cost of the materials while the conducting, metallic properties of the sample insert
remains sufficient for the aim of this experiment. The steel sample is filed and
polished to a flush fit into a milled section of the imaging sample.
The final sample consists of tap water. A glass pipette is used to fill its corre62

sponding section to the desired amount. One issue that continuously arises in this
part of the experiment is the problematic leaking of water into other regions of the
imaging sample. The intrusion of water into other regions of the imaging sample
is detrimental to the integrity of the surrounding reflection measurements. In order to minimize the intrusion of water from its designated section, a 3.2 cm square
absorption inlay constructed by numerous square paper towels of a similar size is
used to fill the milled section to absorb and contain the water within its assigned
section. Water is then added until the section is full. The optimal thickness of the
absorption inlay is such that without force or contact, the water-saturated absorber
slightly overfills the pocket. Upon contact with the top layer of the imaging sample for concealment, the saturated absorber is slightly compressed until flush with
the interface, thus releasing a small amount of water to create the UHMW-water
interface. It is crucial to add the optimal amount of water to ensure the surfacing
of water upon compression of the absorber, but not such an amount that may lead
to the leakage of water into other regions.
The approach to the containment of water in this thesis requires the acknowledgment that the interface created by the saturated absorber may not be identical
to the interface that is created by only water. There is a large contrast, however,
between the dielectric properties of water and paper that leads to the following assumption. First, the absorbing properties of water are large enough to completely
prevent the transmission of THz radiation through a single damp paper towel [63].
Second, paper towels, which make up the absorber, are nearly transparent at THz
frequencies, thus speculations on principles from effective medium theory indicate that the medium resulting from the combination of water and paper towels
respond almost identically to a water medium, with respect to its optical properties [64].

63

3.4.3

Experimental Results

After bolting together the top and bottom layers of the imaging sample, the completed sample with various concealed interfaces is imaged as detailed in Section
3.4.1. After acquiring the time-domain measurements representing the electric
field of the reflected THz pulses for a 100 by 100 image, the collection of reflection measurements must be analyzed in order to construct spatial images, which
represents the spatial distribution of the amplitude and phase of the reflected THz
pulses. To quickly summarize, first, a base THz image must be constructed, which
accurately represents the spatial features of the concealed interface within the layered system. Subsequently, an in-depth analysis of the THz waveforms is used to
inspect the 100 by 100 image data, thus determining specific properties of the THz
reflections that are unique to a given interface. For example, the UHMW-metal
interface is expected to be highly reflective due to the large dielectric contrast and
conductivity of metallic objects, suggesting a substantial reflecting amplitude from
this interface, which may be a unique property for identification among the other
concealed interfaces. Using these properties, interface-specific image filters are
designed in MATLAB® , which are used to create a ’filtered’ copy of the original,
base image for each interface. Each interface-specific filter overlays a different set
of coloured pixels on a spatial THz reflection image of the concealed interfaces,
identifying the spatial distribution of each interface by its analogous pixel colour.
The first phase of interpreting the THz reflection image data involves mathematically inverting the domain of the data points by use of the fast-Fourier transform. Figure 3.14 compares the electric field E(t) of the THz pulse in the timedomain with the complex amplitude of the same electric field |Ẽ(ω)| in the frequency domain for each concealed interface. Since the transformation of the electric field to the frequency-domain yields a complex-valued function, it is commonly visualized by plotting the complex amplitude. In this form, the variation
64

(a)

Electric Field (arb. units)

0.2

UHMW-metal
UHMW-glass
UHMW-water
UHMW-air

0

-0.2

-0.4

-0.6
1690

1700

1710

1720

1730

1740

1750

1760

1770

Time (ps)

(b)

Electric Field (arb. units)

2.5

UHMW-metal
UHMW-glass
UHMW-water
UHMW-air

2

1.5

1

0.5

0
0

0.2

0.4

0.6

0.8

1

Frequency (THz)

Figure 3.14: (a) Detected time-domain THz pulses reflected from the imaging sample with different interfaces. (b) The amplitude of the fast-Fourier transform,
|Ẽ(ω)|, of each detected pulse.

65

(a)

(b)

2.5

0.15

Electric Field (arb. units)

Electric Field (arb. units)

0.2

0.1
0.05
0
-0.05
-0.1

2

1.5

1

0.5

-0.15
0
1700

1720

1740

1760

0

0.5

Time (ps)

Frequency (THz)

0.377 THz

2

0.628 THz

(c)

2.5

Electric Field (arb. units)

1

1.5

1

0.5

0
0

0.2

0.4

0.6

0.8

1

Frequency (THz)

Figure 3.15: A brief outline for calculating pixel intensity values for the amplitude
image. (a) The time-domain THz pulse undergoes a fast-Fourier transform to give
Ẽ(ω), which is shown in (b) as |Ẽ(ω)|. (c) This curve is integrated over 0.377 THz
to 0.628 THz to obtain the pixel value at the spatial location of the corresponding
reflection.
66

% of max.
100

20

80

y (cm)

15

60
10
40
5

20

0

0
0

5

10

15

20

x (cm)

Figure 3.16: A 100 by 100 amplitude image of the concealed interfaces within the
imaging sample. The pixel intensities represent the amplitude of the reflected electric field. These values are averaged over the frequency range 0.377 THz to 0.628
THz.

67

of the electric field amplitude with respect to each frequency can be observed. By
selecting a frequency, a single value is obtained for each reflection measurement,
indicating the amplitude of the electric field detected for that frequency. By repeating this for each spatial measurement of the amplitude, an image containing the
electric field amplitudes at the selected frequency as pixel values is constructed.
For the purpose of creating an initial image which accurately depicts the structure
and locations of the concealed interfaces, the sum of amplitudes is calculated over
a frequency interval and used as the pixel intensity of the image. This is similar
to integrating the electric field |Ẽ(ω)| over a range of frequencies to reduce noise
in the image. Figure 3.15 provides a detailed summary of the results of each step
involved in determining each pixel value for an amplitude image integrated from
0.377 THz to 0.628 THz. The resulting integrated amplitude image is presented in
Figure 3.16.
With an image constructed that conveys spectral amplitude information from
a range of frequencies, the spectral phase information from the measured THz
pulses is yet to be investigated. Given complex electric field values from Euler’s
formula, Ẽ(ω) = |Ẽ(ω)|eiφ(ω) , the phase of the electric field of a THz pulse is calculated by taking the argument of each complex data point, φ(ω) = arg[Ẽ(ω)]. The
phase φ(ω) uniformly increases with frequency, but when the phase rises above
π, the value immediately jumps to −π and continues its growth (φ(ω) is naturally

restricted to a range of [−π, π]). Because of this, the phase data is difficult to analyze and various frequencies return identical phase values, which is not physically
accurate. The use of the unwrap function in MATLAB® vertically translates the
remaining phase values by 2π, following each drop in the phase data. The unwrapped phase data consists of a set of values linearly increasing with frequency.
Due to high noise levels on each end of the bandwidth of the THz pulses, phase
values at frequencies less than 0.07 THz are cropped prior to unwrapping the

68

(b)
0.07 THz

(a)

0.15
3
0.1

Phase (rad)

Electric Field (arb. units)

0.2

0.05
0

0

-0.05
-0.1
-3

-0.15
1700

1720

1740

1760

0

0.5

Time (ps)

1

Frequency (THz)

(c)

120

80
0.07 THz

Unwrapped Phase (rad)

100

60
40
20

0.251 THz

0
-20
0

0.2

0.4

0.6

0.8

1

Frequency (THz)

Figure 3.17: A brief outline of a single pixel intensity calculation for the phase
image. The measured time-domain THz pulse is displayed in (a). (b) The phase
is determined by calculating arg(Ẽ(ω)). To limit effects of noise, only phase data
past 0.07 THz is unwrapped to give the trend in (c). The phase value at 0.251 THz
gives the pixel intensity for the measured pulse.
69

% of max.
100

20

80

y (cm)

15

60
10
40
5

20

0

0
0

5

10

15

20

x (cm)

Figure 3.18: A 100 by 100 phase image of the concealed interfaces within the imaging sample. The pixel intensities represent the phase of the reflected electric field
at 0.251 THz.

70

phase. With the extracted phase of the electric fields at each frequency, a phase
image can be constructed at a chosen frequency. Figure 3.17 reveals the calculated
phase plots (both original and unwrapped phases) used to produce a spatial image of the phase distribution of the THz pulses reflected from concealed interfaces
within the imaging sample. Phase values at 0.251 THz are designated as pixel
intensities for the phase image exhibited in Figure 3.18.

0.2
max

Electric Field (arb. units)

E(t)
0.15
0.1

Δtmax

0.05
0

Δtp-p

-0.05

Δtmin
-0.1
min

E(t)
1690

1700

1710

1720

1730

Time (ps)
Figure 3.19: A collection of THz pulse characteristics used to create multiple spatial images of concealed interfaces. Features include the maximum and minimum
electric field E(t)max and E(t)min , peak-to-peak (maximum peak to minimum peak
time point) time-width of the pulse ∆tp−p , FWHM on either side of [E(t) = 0] ∆tmax
and ∆tmin .

After testing the analysis of the amplitude and phase of the reflected electric
field measurements by creating spatial images illustrating the distribution of the

71

corresponding values, a closer look at the characteristics of a reflected THz pulse
is required to differentiate between the concealed interfaces. Figure 3.19 reveals
several quantities which can be used to help summarize a THz pulse. Variations
in these characteristic quantities are analyzed to develop a collection of features
specific to one interface, for the purpose of distinguishing each concealed interface
from the rest. Some of the features of the THz pulse include the maximum and
minimum value of the electric field in time E(t)max and E(t)min , the time-width
of the pulse from peak-to-peak ∆tp−p , and the time-width of the pulse given by
the full width at half maximum (FWHM) on either side of the time axis [E(t) = 0]
given by ∆tmax and ∆tmin . There are also two other features of interest, which
are determined by expanding the analysis of the phase data of the electric field.
An additional step is added following the unwrapping of the phase data, which
consists of fitting a line to the unwrapped phase data and extracting the corresponding slope (phase shift) mφ and y-intercept (phase offset) φo . By fitting a line
to the phase data, the expected noise introduced into the phase data (due to its
high sensitivity to changes in position or thickness) is reduced. The entirety of
the previously mentioned THz pulse characteristics are quantified and each trait is
used as a pixel intensity for its corresponding spatial image. A diverse selection of
THz pulse traits is intended to give multiple dissimilar images displaying different aspects of its spectroscopic information. The collection of images fabricated by
these quantities is organized throughout Figures 3.20 and 3.21. It is noted that in
Figure 3.20a, the base image produced above from integrating the amplitude from
0.377 THz to 0.628 THz is shown again, for comparison.
The collection of images given by the quantification of numerous THz pulse
characteristics allows for the assignment of conditions unique to each interface
that establish the image filters for each concealed interface. Specific ranges of values, unique to a given interface, for each quantified characteristic of a THz pulse

72

Figure 3.20: A collection of 100 by 100 spatial images with pixel intensities dictated
by (a) the integrated electric field amplitude from 0.377 THz to 0.628 THz, (b) the
maximum and (c) minimum value of E(t), and (d) the peak-to-peak time-width of
the electric field pulse ∆tp−p . For convenience and ease in comparison, the colormap ranges from the minimum (blue) to maximum (yellow) pixel value of each
image; the centre and corner regions are ignored in this range, since extreme noise
values are expected here (where the imaging sample is bolted).

73

Figure 3.21: A collection of 100 by 100 spatial images with pixel intensities dictated
by (a),(b) the FWHM on either side of [E(t) = 0] given by ∆tmin and ∆tmax , (c) the
slope of the phase data (phase shift) mφ , and (d) the y-intercept of the fitted line
to the phase data (phase offset) φo . For convenience and ease in comparison, the
colormap ranges from the minimum (blue) to maximum (yellow) pixel value of
each image; the centre and corner regions are ignored in this range, since extreme
noise values are expected here (where the imaging sample is bolted).

74

are carefully applied to each interface in order to identify a concealed interface
throughout the reflection image. An image filter for each interface is built by designating passing conditions, of which all were required to succeed, to identify a
given measurement (pixel) as a specific interface. For all of the pixels which pass
the conditions of any filter, the correlated coloured pixel is overlaid on the base
image. The previously mentioned passing conditions, which are the structure of
each filter, are given in Table 3.1.

UHMW-sample
interface

Filter
colour

Filter
condition(s)

Metal

Red

E(t)max > 0.1 (arb. units)

Air

Yellow

∆tp−p ⩽ −1.75 ps

Water

Blue

∆tp−p ⩾ 2.20 ps
R0.628 T Hz
0.377 T Hz |Ẽ(ω)|dω ⩽ 2.25 (arb. units)
−8.0 ⩽ φo ⩽ −5.4 (rads)

Glass

Green

0.06 ⩽ E(t)max ⩽ 0.09 (arb. units)
−0.0551 ⩽ E(t)min ⩽ −0.0400 (arb. units)
−0.20 ⩽ φo ⩽ 0.20 (rads)

Table 3.1: The passing conditions for each interface-specific image filter. For any
pixel which pass all conditions of any filter, that pixel assumes the filter colour and
overlays the base spatial image of the concealed interfaces.

The set of measurements contained by the reflection image data is analyzed by
the image filters specifically outlined in Table 3.1, and the resulting overlays are
individually applied to the base amplitude image (integrated from 0.377 THz to
0.628 THz). The resulting spatial images from each filter are presented in Figure
3.22.

75

Figure 3.22: Each concealed interface filter applied to the spatial image of the electric field amplitude, integrated from 0.377 THz to 0.628 THz, identifying UHMWmetal (red), UHMW-glass (green), UHMW-air (yellow), and UHMW-water (blue)
interfaces.

76

Chapter 4
Discussion and Future Work
4.1

Summary

The main results obtained in Chapter 3 demonstrate the clear distinction between
different concealed interfaces within a layered, insulated system by means of a
100 by 100 spatial THz reflection image in conjunction with a filtering technique
for the identification of the interface materials. Initially, transmission spectroscopy
of UHMW and glass is performed which extracts the index of refraction of each
material, confirms the applicability of UHMW as the insulating layer of the imaging sample, and validates the developed reflection spectroscopy technique. The
implementation of dove prism reflection spectroscopy allows for the convenient
testing of different interfaces, and illustrates the contrasts among reflections from
the interfaces. It also allows the choice of the most sensitive polarization configuration. Following the collection of the concealed interface image data, the amplitude and phase images display key differences between some interfaces. In
order to generate the interface-specific filters, numerous amplitude and phase features of the reflected electric fields are analyzed and categorized with respect to
each UHMW-sample interface. The construction of each interface-specific image

77

filter relies on the visual comparison of these quantified electric field traits of reflected THz pulses by developing spatial images from these calculated values. In
each image generated from a THz pulse trait, observations are made suggesting
the distinguishability of one interface from the remaining interfaces. Identification
conditions, based on the quantification of the pulsed electric field characteristics,
are established for each interface, and they are applied to the collection of measurements composing the reflection image to successfully identify regions of each
concealed interface investigated in this thesis.

4.2

Discussion of the Key Results

The application of each interface-specific image filter yields four 100 by 100 images of the spatial locations of all interfaces with coloured pixels overlaying the
corresponding region containing the successfully identified concealed interface.
Each concealed interface (UHMW-metal, UHMW-glass, UHMW-air, and UHMWwater) is spatially identified within the imaging sample (even with multiple sources
of noise in specific areas of the imaging sample) by its indicated colour.
The identification of the UHMW-metal and UHMW-air interfaces makes use of
a single filter condition. From the large reflectance of polished metal, the trait that
discriminates the metal interface from the rest is the large reflected electric field
amplitude. This is sufficient to successfully identify the region of metal throughout
the entire imaging sample.
Due to the decrease in refractive index from UHMW to air, this interface reflects incident electric fields internally, rather than externally, introducing an expected relative π phase shift with respect to the other interfaces. This phase shift
is identified by the characteristic time-width of the THz pulse from peak-to-peak
∆tp−p . Since these values are calculated by the difference of the time delays of the

78

maximum and minimum peaks, the π phase shifted UHMW-air reflection gives
a large negative value for the time-width, as opposed to positive values for the
other interfaces. The UHMW-air interface is also identified by ∆tp−p throughout
the noise given by small air gaps within the expected UHMW-UHMW interfaces
(which often consist of small air gaps, i.e. less uniform UHMW-air interfaces). The
reflections from these unwanted interfaces reflect with the same phase shift, however due to the non-uniformity and small size of the air gaps, the reflected electric
field is lesser in amplitude, thus ∆tp−p is smaller in magnitude. As it turns out,
the characteristic peak-to-peak time-width ∆tp−p identifies and substantially diminishes the noise introduced by unwanted air gaps within the entire image, for
all concealed interfaces. Collectively, the unique phase shift and relatively large
amplitude of the concealed UHMW-air interface allow for its identification.
The identification of UHMW-water and UHMW-glass interfaces is more convoluted, in comparison, each consisting of three unique conditions to be satisfied
to map out the respective image filter. The detection of water within the layered
system is based on a lesser amplitude within the amplitude image integrated over
a small range of frequencies, as well as a unique range among the values of the
initial phase offset φo . The UHMW-glass interface is similarly identified, by specifying ranges of values for the amplitudes of the minimum and maximum peaks,
as well as the phase offset.
The incorrect identification of some pixels among the spatial image must be
addressed. Due to the significant distinction between the reflecting amplitude
from the UHMW-metal interface and others, there are no pixels misidentified as
a UHMW-metal interface. For the other interfaces, however, some pixels near the
far right edge of the image or the borders of a region are improperly identified.
The locations of the misidentified pixels are not surprising since at these edges or
borders, it is expected that THz pulses are reflecting from two interfaces, simulta-

79

neously. For example, if the pulses are aligned such that half of the pulse is incident on a UHMW-air interface, and the other half is incident on a UHMW-metal
interface, then the detected reflection is a superposition of the two reflected electric
fields. In this case, the two reflections are out-of-phase, so the resulting reflection
may appear to be a single reflection from a different interface.
It is assumed that a similar effect is dominant on the far right of the images,
for example, at the edge of the imaging sample, a portion of the pulse may have
reached the reflecting interface of the imaging sample from its side, without initially refracting through the top layer of the sample. This essentially clips the
detected THz pulse, reflecting with a lesser amplitude, leading to its misidentification.
Known sources of noise are also recognized at the center and corners of the images. At these locations, the imaging sample is bolted to the translation stage. In
these regions, the noise floor of the THz-TDS system is detected, thus creating a
dark region in amplitude images and leading to extreme values for the determination of the phase. Nonetheless, these regions do not interfere with the imaging
and identification of concealed interfaces.
The temperature-dependence of the time delay of a THz pulse may have been
observed in the phase image selected at 0.251 THz. On the right side of the image,
the average phase value between the UHMW-glass and UHMW-water interfaces
is noticeably inconsistent with that on the left side of the image. It is noted that
temperature fluctuations may cause internal drift of the extracted time delay of a
THz pulse. Since the phase of an electric field is extremely sensitive to changes in
time delay, the effects of temperature fluctuations have surfaced after generating
the phase image. It seems that along a given vertical line in the image, the phase
values are rather consistent (or gradually changing), as opposed to the sudden
shifts in phase values along a horizontal line. This horizontal sectioning of phase

80

values also supports the above conclusion since from the nature of the raster scan
in this thesis, the y-axis is traversed much more frequently than the x-axis, thus the
phase fluctuations caused by long-term temperature shifts are more pronounced
along the x-axis.
Another possible source of the sudden transition in phase of the reflected electric fields on the right side of the image is the design of the instrument used to
block the front reflection at the top surface of the imaging sample. Since this thin
metal object is fixed directly above the imaging sample, along the y-axis, as the
imaging sample is translated along the x-axis, any small changes in thickness or
height of the imaging sample introduce a small gap between the front reflection
blocker and the surface of the sample. Therefore in some regions, a portion of the
unwanted reflected THz pulse at the top surface of the imaging sample may have
been detected, in superposition with the reflection of interest from the concealed
interfaces, which affects the calculated phase.

4.3

Future Work

In the THz reflection imaging experiment, a 100 by 100 set of reflection measurements, selected for the depth of the concealed interfaces, are collected with the
use of a THz-TDS system. By averaging 1000 waveforms per measurement, and
pausing reflection collection over the duration of sample translation between measurements, the image data acquisition lasts approximately 12 hours for a single 100
by 100 image.
The next logical step would be to repeat the experiments for the TM configuration, which is shown in Section 3.3, to potentially demonstrate a higher degree
of contrast between the concealed materials. This is also necessary to refine the
coloured filters based on considerations of physical theory. There are also many

81

variables that can be adjusted to maximize the efficiency of the imaging system for
the purpose of concealed interface identification, now that the concept has been
demonstrated successfully. This may involve averaging over fewer waveforms or
reducing the resolution of the collected image data, as appropriate for a given industrial setting in order to test these principles for a specific application.
The duration of the image data collection also has an impact on the consistency of the reflection measurements since temperature fluctuations in the THzTDS system, introduce a small time delay drift in the measurements. The greater
the duration is of the imaging process, the greater the likelihood is of temperature
impacting the measured time delay of a THz pulse. This is observed in the phase
images since the calculated phase is extremely sensitive to the delay, thus sensitive
to the drift.
In order to accurately determine the phase data, the reliability of the front reflection blocker, used to prevent detection of the THz pulses reflected from the top
surface of the imaging sample, must be ensured. The stationary mounting of a
thin metal piece directly above the sample works for a perfectly flat and uniformly
thick sample, however in practice, this may not be a realistic approximation. As the
thickness changes, the distance between the blocker and the surface of the sample
also changes. In order to fully prevent front reflections from being detected, a simple adjustment can be made, such as a constant force supplied downwards against
the reflection blocker while restricting its motion along the z-axis (up and down).
By exploring the implementation of other materials, as opposed to UHMW,
as the insulating material in the layered system, a different range of identifiable
interfaces may arise, assuming that the identification of an interface among other
materials can be based on the contrast in dielectric features. A steep change in
refractive index of the insulating medium may significantly alter the possibility of
identifying interfaces composed of materials with a low index of refraction.

82

With the success of identifying each interface within the layered system with
minimal false identifications, this experiment can be repeated with a more diverse
and larger selection of concealed interfaces. In this revised experiment, a focus
may be drawn on discovering the required limit of contrast (or difference) between
the dielectric properties of two materials in order to identify the interfaces formed
in the imaging sample. Since the UHMW-metal interface is simply identifiable,
a deeper look at metallic interfaces may be undertaken. Remaining in the realm
of applications related to identifying indicators of corrosion before it takes place,
various samples of painted and corroded metal can be imaged to test the distinguishability between the respective UHMW-sample interfaces within the layered
system. Referring to the work of Anastasi and Madaras [26], the ability to detect
corrosion under painted surfaces with THz reflection imaging is available by the
determination of surface roughness and response to paint thickness. By inspecting rough, corroded or painted metals within the layered system, identification of
these differences among other interfaces, along with precursors of corrosion, may
be possible.

4.4

Conclusion

The experiment and techniques performed within this thesis have validated the
feasibility of conducting THz reflection imaging to spatially map the structure of
concealed interfaces at a given depth, while simultaneously identifying each interface material without the use of a reference beam, commonly required for reflection spectroscopy. The specific involvement of water and metal, among other
interfaces, demonstrates the applicability of this technique for the detection of precorrosion within a practical system. Initially, the employment of THz transmission
spectroscopy establishes UHMW as a suitable coating in a system probed by radi-

83

ation at these frequencies. The subsequent development of a dove prism reflection
spectroscopy system aids in understanding THz reflections at different interfaces
and realizing contrasting reflections for different materials, thus identifying materials likely to be distinguished in a layered UHMW system. Concealed interfaces are then imaged with the construction of a reflection imaging system using
TE polarization. Guided by the results from dove prism reflection spectroscopy,
numerous pulsed electric field characteristics from the image measurements are
investigated, and interface-specific filters are developed. Applying these filters
produces a colourmap of the interface materials, overlaying the spatial image. The
spatial location and identification of each interface material is performed with minimal false identifications. The filtered images demonstrate the ability to apply reflection spectroscopy techniques to a practical, insulated, system to spatially map
and identify various concealed interfaces (without using a reference measurement)
based on electric field amplitude and phase properties (despite the sensitivity of
phase to minuscule changes in position or thickness), including the detection of
water among other metallic and dielectric materials. The identification of water
(and other dielectric materials) in this manner suggests further exploration of this
method towards a variety of relevant industrial applications for the purpose of
identifying precursors to the corrosion of a protected, insulated structure, which
may significantly impact the cost, duration, and intricacies of repair.

84

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