Electromagnetic Induction Systems for Discrimination among
Metallic Targets
Except where reference is made to the work of others, the work described in this
dissertation is my own or was done in collaboration with my advisory committee.
This dissertation does not include proprietary or classified information.
Venkata Sailaja Chilaka
Certificate of Approval:
Jitendra K. Tugnait
Professor
Electrical and Computer Engineering
Lloyd S. Riggs, Chair
Professor
Electrical and Computer Engineering
Stuart M. Wentworth
Associate Professor
Electrical and Computer Engineering
Michael E. Baginski
Associate Professor
Electrical and Computer Engineering
Prathima Agrawal
Professor
Electrical and Computer Engineering
Stephen L. McFarland
Dean
Graduate School
Electromagnetic Induction Systems for Discrimination among
Metallic Targets
Venkata Sailaja Chilaka
A Dissertation
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Doctor of Philosophy
Auburn, Alabama
May 11, 2006
Electromagnetic Induction Systems for Discrimination among
Metallic Targets
Venkata Sailaja Chilaka
Permission is granted to Auburn University to make copies of this thesis at its
discretion, upon the request of individuals or institutions and at their expense. The
author reserves all publication rights.
Signature of Author
Date of Graduation
iii
Vita
Venkata Sailaja Chilaka, daughter of Suryanarayana Chilaka and Rajaratnam
Chilaka, was born on June 5, 1976 in Srikakulam, India. She received the Bachelor of
Technology degree in Electrical and Electronics Engineering from Jawaharlal Nehru
Technological University in June 1998. She earned the Master of Electrical Engineer
ing degree from The University of Texas at Dallas in May 2001. She entered graduate
program at Auburn University in Spring 2002 and later went on to accept an Auburn
University Graduate Research Fellowship and VodafoneUS Foundation Fellowship.
She is married to Raveendra B. Amara from July 20, 2000.
iv
Dissertation Abstract
Electromagnetic Induction Systems for Discrimination among
Metallic Targets
Venkata Sailaja Chilaka
Doctor of Philosophy, May 11, 2006
(M.S.E.E., The University of Texas at Dallas, 2001)
(B.Tech., Jawaharlal Nehru Technological University  Hyderabad, India, 1998)
94 Typed Pages
Directed by Lloyd S. Riggs
This dissertation discusses the ability of time and frequencydomain electro
magnetic induction (EMI) systems to discriminate unexploded ordnance (UXO) from
clutter. The chief contribution of this work is to demonstrate the importance of ex
tremely low frequency (ELF) data in discrimination of thick and thinwalled ferrous
UXOlike targets that are otherwise visually identical. It is demonstrated that when
data in the 30 Hz to 24 kHz range is extended down to 1 Hz discrimination per
formance improves by a factor of 1.5. Improved discrimination performance reduces
false alarms and ultimately lowers remediation costs.
v
Acknowledgments
First and foremost the author would like to thank Dr. Lloyd Riggs for his
inspiration and extensive guidance. For his friendship and invaluable help she will
forever be grateful. Special thanks to Daniel Faircloth for his FEM model which gave
a better insight into the research problem. She would like to extend her thanks to
Dr. Jitendra Tugnait for his valuable suggestions on statistical part of the research,
and to Dr. Stuart Wentworth and Dr. Michael Baginski for providing constructive
comments on her dissertation. She thanks her research team for the wonderful work
environment and funfilled lunch hours.
She is grateful to Dr. Prathima Agrawal and VodafoneUS foundation for sup
porting her through fellowship, and Strategic Environmental Research and Develop
ment (SERDP) for funding the research.
To all her friends, the author is thankful for their constant support. She expresses
her gratitude to her parents for their prayers, for putting her on the right path, and
teaching her to dream big and chase it. She thanks her parentsinlaw for their
immense understanding. She is indebted to her husband Ravi for his love, sacrifice,
patience and persistent encouragement. Last but most important she is thankful to
Almighty God who gives her the best always.
vi
Style manual or journal used IEEE Transactions on Geoscience and Remote
Sensing(together with the style known as ?auphd?).
Computer software used The document preparation package TeXnicCenter and
LATEXwith the stylefile auphd.sty.
vii
Table of Contents
List of Figures x
List of Tables xiii
1 Introduction 1
2 Electromagnetic Induction Theory 8
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Circuit Representation of EMI system . . . . . . . . . . . . . . . . . . 8
2.3 EMI Response of a Conducting Loop . . . . . . . . . . . . . . . . . . 11
2.4 EMI Response of a Conducting Sphere [35] . . . . . . . . . . . . . . . 18
2.5 EMI Response of a Conducting Spherical Shell . . . . . . . . . . . . . 23
2.6 EMI Response of an Arbitrary Permeable Conducting Target . . . . . 27
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 EMI Sensor Description 30
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 CW System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.2 Pulsed System . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Transmitter and Receiver Coil Characteristics . . . . . . . . . . . . . 34
3.3.1 Various Tradeoffs Considered in Coil Construction . . . . . . 35
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Measurements 48
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Test Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 FrequencyDomain Measurements . . . . . . . . . . . . . . . . . . . . 50
4.3.1 Comparison between FEM and Measured Responses . . . . . . 50
4.3.2 Effect of Target Size . . . . . . . . . . . . . . . . . . . . . . . 50
4.3.3 Effect of Wall Thickness . . . . . . . . . . . . . . . . . . . . . 52
4.3.4 Effect of Driving Bands . . . . . . . . . . . . . . . . . . . . . 55
4.3.5 UXO Measurements . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 TimeDomain Measurements . . . . . . . . . . . . . . . . . . . . . . . 58
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
viii
5 Statistical Analysis 64
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Noise Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Discrimination Problem . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.1 Square of Mean Error (SME) . . . . . . . . . . . . . . . . . . 66
5.3.2 Mean Squared Error (MSE) . . . . . . . . . . . . . . . . . . . 67
5.3.3 ErrortoNoise Ratio (ENR) . . . . . . . . . . . . . . . . . . . 68
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6 Conclusions 73
Bibliography 75
ix
List of Figures
2.1 Typical EMI system . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Circuit Model of (a) CW EMI system (b) pulsed EMI system . . . . . 10
2.3 Frequency response of a thin copper loop (simple first order target) . 13
2.4 Current and voltage waveforms at different stages of the pulsed EMI
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Conducting sphere in a uniform magnetic field . . . . . . . . . . . . . 18
2.6 Response function of a sphere in uniform magnetic field . . . . . . . . 23
2.7 (a) Magnitude (b) Phase responses of a sphere . . . . . . . . . . . . . 24
2.8 Conducting spherical shell in a uniform magnetic field . . . . . . . . . 25
2.9 (a) Real and imaginary (b) Magnitude responses of ferrous (? = 70?0,
? = 5.82?106 S/m) spherical shells with fixed outer radius (a = 5 cm)
and different inner radii . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1 Block Diagram of a CW EMI system . . . . . . . . . . . . . . . . . . 31
3.2 Hardware setup of a CW EMI system . . . . . . . . . . . . . . . . . . 32
3.3 Block Diagram of pulsed EMI system . . . . . . . . . . . . . . . . . . 33
3.4 Hardware configuration of pulsed EMI system. (1) Oscilloscope (2) DC
power supply for pulser (3) Transmit coil (4) Receive coil (5) Pulser
(6) Gagescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 Components of the pulser on a printed circuit board . . . . . . . . . . 35
3.6 Transmitter and receiver coil pair used in CW and pulsed EMI mea
surements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
x
3.7 Magnetic field along the axis (zaxis) of a square loop for side of 10,
25, 50 and 100cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.8 Static sensitivity maps superimposed on a line diagram of the EMI
sensor. Plots over 0.5m ? x ? 0.5m, 0.5m ? y ? 0.5m at z = 1, 10,
20, 50cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.9 Transfer characteristics of a highpass filter: (j?/10)/(1+j?/10). Solid
line is the magnitude response and dashed line is the phase response . 42
3.10 Operational amplifier connected in a noninverting configuration to the
receiver coil. The parasitic capacitance of the receiver coil distorts
measurements of the object?s response. . . . . . . . . . . . . . . . . . 43
3.11 Operational amplifier connected in an inverting configuration to the
receiver coil as a currenttovoltage converter. . . . . . . . . . . . . . 45
4.1 Test targets used in the measurements. . . . . . . . . . . . . . . . . . 49
4.2 Comparison of response obtained by FEM and measurements for 1B
cylinder with centered copper ring. . . . . . . . . . . . . . . . . . . . 51
4.3 Measured responses of four solid steel cylinders of varying size. . . . . 52
4.4 FEM Response of four solid steel cylinders of varying size. . . . . . . 53
4.5 Extremely low frequency FEM response of the four solid steel cylinders 53
4.6 Measured responses of visually identical steel cylinders with differing
wall thicknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.7 FEM response of visually identical cylinders. . . . . . . . . . . . . . . 55
4.8 Low frequency FEM response of visually identical cylinders. . . . . . 56
4.9 Effect of driving band on targets Measured response. . . . . . . . . . 56
4.10 Effect of driving band on targets FEM response. . . . . . . . . . . . . 57
4.11 UXO items from left to right 155mm, 105mm, and 107mm shell . . . 58
4.12 Measured Response of (a) 155 mm shell (b) 105 mm shell (c) 107 mm
shell in the 1Hz to 10kHz frequency range. . . . . . . . . . . . . . . . 59
4.13 Theoretical, FEM and Measured TimeDomain response of 18 AWG
5? Copper loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
xi
4.14 Measured decays for ?2 series? cylinders identical except for wall thick
ness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.15 FEM decays for ?2 series? cylinders identical except for wall thickness 61
4.16 FEM decays for ?A series? cylinders of different sizes and same wall
thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.1 Noise distribution at (a) 1Hz and (b) 100Hz . . . . . . . . . . . . . . 65
5.2 Distribution of test statistics (a) SME (b) MSE and (c) ENR . . . . . 69
5.3 Performance of SME, MSE and ENR in for 22dB SNR over two fre
quency bands 30Hz to 24kHz and 1Hz to 24kHz . . . . . . . . . . . . 71
5.4 Comparison of the performance of 30Hz to 24kHz data and 1Hz to
24kHz data in identifying the cylinder correctly for three SNRs . . . . 71
xii
List of Tables
1.1 Strengths and limitations of UXO detection technologies [3]  [9] . . . 3
4.1 Size details of the test targets . . . . . . . . . . . . . . . . . . . . . . 49
xiii
Chapter 1
Introduction
Unexploded ordnance (UXO) are devastating weapons (bombs, mortars, shells,
grenades, etc.) that did not explode when they were employed [1]. These remnants
of ongoing conflicts, past wars (as far back as the First World War) and military
training have contaminated vast areas all over the world. UXO pose a threat to
the environment and lives of innocent civilians, thus leaving millions of acres of land
uninhabitable. It is not a problem being faced by third world countries alone, it
is one of the most pervasive environmental problems faced by the U.S. Department
of Defense (DOD). In the United States, 6 million acres of land is contaminated
with UXO, most of which is a result of past and present military ranges or training
sites [2]. Due to their high metallic content, UXO are much easier to detect than to
discriminate. It is estimated that 70% of UXO remediation costs are going toward the
investigation of false positives (nonUXO items and ?dry holes?). Clearly effective
discrimination between UXO and clutter is necessary to reduce remediation costs [3].
The discrimination problem has captured the attention of many researchers in
the past decade and the detection technologies currently being used or proposed for
this purpose include acoustic sensors, biological odor sensors (dogs and bees), elec
tromagnetic induction (EMI), ground penetrating radar (GPR), infrared (IR), mag
netometry, synthetic aperture radar (SAR), trace gas analysis and combinations of
these technologies [3]  [9]. Moreover, research and development efforts are underway
1
in exploring new technologies and in combining current technologies [6]. Table 1.1
summarizes strengths and limitations of four different detection/discrimination tech
nologies. The performance of each of these technologies depends on different factors
such as the dimensions and constitution of the UXO, the depth at and medium in
which it is buried. Prominent among all ordnance detection technologies are mag
netometers and EMI sensors, as they are fairly simple, cheap and reasonably well
understood. A magnetometer is a passive sensor which uses the earth?s magnetic
field as excitation source to measure an object?s magnetic susceptibility. On the other
hand an EMI sensor is an active device that carries an excitation source and mea
sures magnetic susceptibility and electrical conductivity depending on the frequency
of excitation [10].
The Multisensor Towed Array Detection System (MTADS) developed by Naval
Research Laboratory, comprising of magnetometers and EMI sensors achieved a detec
tion rate of 95% [11]. However, it still suffers a high falsealarm rate, thus presenting
a need for a more efficient and costeffective discrimination system. The work pre
sented in this dissertation is part of a project funded by the Strategic Environmental
Research and Development Program (SERDP) to develop an ordnancespecific EMI
sensor that combines detection with discrimination [12].
2
Table 1.1: Strengths and limitations of UXO detection technologies [3]  [9]
Technology Strengths Limitations
Acoustics ? Immune to metallic clutter
? Good for plastic mine detec
tion
? Best suited to underwater de
tection
? Inability to detect deep tar
gets
? Limited discrimination be
tween high metallic targets
like UXO
Electromagnetic Induction ? Relatively immune to geologic
noise
? Ability to determine target
shape, size and orientation
? False alarms due to metal
fragments
? Sensitive to sensor orientation
? Inability to determine target
depth
Magnetometry ? Easy to use
? Ability to detect deep targets
? Prone to geologic noise
? Inability to determine target
shape
Ground Penetrating radar ? Ability to determine target
depth and shape
? Reduces false alarm when
used with other sensor tech
nologies
? Reduced efficiency in wet
and/or clay rich soils
? Not proven to be a stand
alone UXO sensor
3
Many researchers have proved that electromagnetic induction (EMI) has poten
tial for classification and identification [13]  [32]. Based on the operating mode,
EMI sensors can be classified as time domain (TD) (pulsed induction, PI) systems
or frequency domain (FD) (continuous wave, CW) systems. A time domain sys
tem operates by employing short pulses of current with rapid turnoff time and the
target information lies in the decay characteristics of the received signal [15]  [22].
The simplest time domain EMI sensor is a metal detector and it has been in use
for subsurface target detection for many decades [33] . On the other hand, a fre
quency domain system operates at a single or discrete set of frequencies and the
received signal (spectrum) provides target information [23]  [32]. The basic concept
of Electromagnetic Induction Spectroscopy (EMIS) for the purpose of subsurface tar
get identification has been introduced by Won et al [33]. It is a wellknown fact that
the time and frequencydomain responses form a Fourier transform pair [34], [16]
and therefore, both responses should contain the same information. However, due to
practical constraints, it is difficult to acquire certain information using one system or
the other. Therefore, the relative limitations of each system will affect their respective
discrimination capabilities.
The goal of this research is to study the discrimination capabilities of both time
and frequencydomain EMI systems and in particular, to evaluate the importance
of extremely low frequency CW EMI response in improving the discrimination of
visually identical UXOlike targets of different wall thicknesses.
Wait derived the EMI response of a conducting sphere [34] in a uniformly time
varying magnetic field. Grant and West [35] showed that this response can be ex
pressed as a product of a coupling term and response function, where the coupling
4
term depends on geometry and orientation of the object, and the response function
depends on frequency and the object?s material properties. In order to study the
effect of wall thickness on the response of visually identical targets, the work of Grant
and West has been extended to a conducting and permeable spherical shell and its
analytical response is derived. In Chapter 2, the theoretical response of a conducting
loop, and solid and hollow spheres are presented in order to acquaint the reader with
the general response characteristics of conducting and/or permeable targets.
The response of the spherical shell indicates that extremely low frequency mag
netic fields in the range of 1 to 30Hz can be used to penetrate deep into ferrous targets
and thereby reveal their subsurface characteristics. The subsurface information can
in turn be used to improve discrimination performance over what can be achieved us
ing a commercial system with a typical EMI spectrum extending from ?30Hz up to
?24kHz. Similarly, differences in the timedomain EMI response of visually identical
objects due to difference in wall thickness are not observable until many milliseconds
after the transmitter current turn off. Therefore, to improve discrimination over what
is currently available with commercially available EMI instruments, there is a need
for a CW system with its bandwidth extended to extremely low frequencies or equiv
alently a pulsed system with its time capture range extended to latetime. Time
and frequencydomain EMI systems with respective extended ranges were built and
a careful study of different practical difficulties and tradeoffs involved in their design
are described in Chapter 3.
The prototype CW and pulsed systems are used to measure the response of
various targets including loops, spheres, thin and thickwalled cylinders and inert
UXOs. The measurements are validated using a numerical model (finite element
5
method) as illustrated in Chapter 4. It was observed that the responses of thin
and thick walled cylinders were practically indistinguishable above 30Hz (the low
frequency limit of the popular Geophex GEM3 sensor). However, variations among
the responses were easily discernible if the operating frequency was extended down
to 1Hz due to the significant skin depth at those frequencies. Likewise, numerical
simulations show that similar information might be available from a timedomain
system if very latetime data is captured. However, discrimination based on the late
time data is hindered by low signaltonoise ratio. Therefore, efforts are currently
underway to construct a timedomain EMI sensor with improved sensitivity and noise
characterization at latetimes (more than 10ms after the transmitter current turn off).
The key contribution of this work is to provide a statistically based quantitative
measure of the improvement in discrimination performance obtained by extending
the EMI frequency response downward to 1Hz relative to what can be achieved using
the typical EMI spectrum that extends from ?30Hz upward to ?24kHz. Specifically,
in Chapter 5 three statistical tests are developed to discriminate between UXOlike
targets. Applying this inferencebased statistical test shows that at a probability
of false alarm of 20%, probability of correct identification is only 60% using the
restricted bandwidth whereas using the extended frequency range the probability of
correct identification improves to 90% at the same false alarm rate.
Although extending the typical EMI spectrum to extremely low frequencies sub
stantially improves discrimination performance, a price must be paid for the addi
tional information acquired. A single point collected at 1Hz takes 1 second but often
many data records must be averaged to achieve adequate signaltonoise ratio so in
general it is very timeconsuming indeed to collect a sufficient number of data points
6
in the 1Hz to 30Hz frequency range to adequately represent a target?s (especially a
ferrous target?s) low frequency spectrum. A slow data acquisition rate causes the
EMI data acquisition to be sensitive to motion and therefore, when acquiring very
low frequency data, it is necessary for the system to remain stationary with respect to
the target. This and other practical implementation issues are discussed in Chapter
6 along with suggestions for possibly fruitful future research.
7
Chapter 2
Electromagnetic Induction Theory
2.1 Introduction
In this chapter the reader is first introduced to the basic concept of electromag
netic induction theory. Next, time and frequency responses of a conducting loop are
derived using a simple circuit analysis of the EMI system and significant features of
the response are explained. After that, EMI response of a solid sphere is derived
as a boundaryvalue problem to show that the features presented in simple loop re
sponse are still valid for a threedimensional object. By examining the response of
the solid sphere one can observe the effect of permeability on the object?s response.
The response of a hollow sphere is derived to study the effect of wall thickness on an
object?s response. The general form of the response of an arbitrarily shaped object is
also presented.
2.2 Circuit Representation of EMI system
According to Faraday?s law, timevarying electric current through a transmitter
coil radiates a primary magnetic field. This field may in turn induce eddy currents
in any nearby conductive and/or permeable object. The eddy currents in turn ra
diate a secondary magnetic field which is sensed using a receiver coil. The received
signal may be used to acquire information regarding the target and ultimately used
8
for detection and discrimination purposes. When source frequencies are low or the
transmitter currents do not change too rapidly the above electromagnetic interaction
may be referred to as electromagnetic induction (EMI) thus emphasizing magnetic
(or quasimagnetostatic) processes. Typical components of an EMI system are shown
in Figure 2.1 and include a transmitter and receiver coil and buried object or objects.
Object
Transmitter Coil Receiver Coil
Buried Metallic
I T I R
I O
Figure 2.1: Typical EMI system
Figure 2.2 represents the equivalent frequency and timedomain circuit models
of the EMI system shown in Figure 2.1. In Figures 2.2(a) and 2.2(b) the transmitter,
receiver and object are represented by their equivalent resistance and inductance
pairs (R, L) [35] . The subscripts T, R and O represent transmitter, receiver and
object respectively. Note that this circuit representation of an object is exact only
for a simple first order target like a qcoil (thin copper loop) and does not hold for
complex objects like spheres and cylinders. Further, IT, IR and IO correspond to
the transmitter, receiver, and object currents. Note that IT is a sinusoidal signal
in CW EMI but would manifest as a short duration pulse of current in pulsed EMI
9
(a) (b)
Figure 2.2: Circuit Model of (a) CW EMI system (b) pulsed EMI system
systems. The mutual coupling between transmitter and object, object and receiver,
and transmitter and receiver isMTO, MOR and MTR respectively. Because of magnetic
coupling between the transmitter and object (MTO) a current IO is induced in the
buried object. Similarly, coupling between the object and receiver coil, MOR, results
in a voltage VOBJECT. Finally, because of direct coupling between the transmitter
and receiver coils, MTR, a direct (as opposed to object coupled) voltage exists at
the receiver, termed VDIRECT. The direct coupled voltage is usually undesirable and
efforts are often made to reduce its magnitude with respect to that of the object
coupled voltage (i.e. it is best to have VDIRECT << VOBJECT). By superposition, the
net voltage at the receiver is VOUT= VOBJECT+ VDIRECT. It is desirable to reduce
VDIRECT such that the output voltage is almost equal to the voltage due only to the
object. This can be achieved by using a figure8 receiver coil, also known as a bucking
coil. This configuration consists of two N turn coils of opposite polarity, connected in
10
series such that equal flux passing through them will produce an equal and opposite
voltage in each coil. The net voltage is therefore theoretically zero in the absence of
an object. The figure8 receiver coil is represented in the circuit diagram by splitting
the receiver coil inductance each half with inductance LR/2.
In the case of a pulsed system it is desirable to turn off the transmitter current
as rapidly as possible without oscillations because the induced voltage in the object is
proportional to the derivative of the transmitter current. A shunt resistance RX may
be used to dampen oscillations due to second order interaction between the parasitic
capacitance and the transmitter coil inductance. The resistance RX insures a rapid
and smooth turnoff of the transmitter current. Similarly, RY reduces the oscillations
in the receiver coil. Further, ZR and ZL are the input impedances of the receiver coil
amplifiers for the CW and pulsed systems respectively.
TheEMIresponsesofaloopandaconductingspherehavebeenderivedbyseveral
authors including Wait [34], and Grant and West [35]. These will be presented here in
the same order to provide the reader with an understanding of the response function
for relatively simple objects.
2.3 EMI Response of a Conducting Loop
First, assuming that ZR is infinity (open circuit), and applying Kirchoff?s Voltage
Law to the circuit in Figure 2.2(a) yields
IO(RO +j?LO) +j?MTOIT = 0 (2.1)
VOBJECT = j?MORIO (2.2)
11
VDIRECT = j?MTRIT (2.3)
Simple manipulation of these three equations results in
VOBJECT
VDIRECT =
parenleftbigg?M
TOMOR
LOMTR
parenrightbiggparenleftbigg?2 +j?
1 +?2
parenrightbigg
(2.4)
where ? = ?/?O = ?LO/RO is the response parameter, ? is the radian frequency and
?O is the radian break frequency. VOBJECT/VDIRECT represents the response of the
EMI system to an object where
parenleftBig
?MTOMOR
LOMTR
parenrightBig
is the coupling coefficient and
parenleftBig
?2+j?
1+?2
parenrightBig
is the response function. As Mij = kijradicalbigLiLj, the coupling coefficient reduces to
parenleftBig
kTOkOR
kTR
parenrightBig
and equation (2.4) is now given by
VOBJECT
VDIRECT =
parenleftbigg?k
TOkOR
kTR
parenrightbigg
bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright
Coupling
Coefficient
parenleftbigg?2 +j?
1 +?2
parenrightbigg
bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright
Response
Function
(2.5)
In equation (2.5), only the response function depends on the frequency of the current
and electrical properties of the loop, and the coupling coefficient depends on the
physical size and location of the loop with respect to the transmitter and receiver
coils. The real and imaginary parts of the response function are shown in Figure
2.3(a) and magnitude and phase are shown in 2.3(b). As ? ? 0 the real part of
response function shown in Figure 2.3(a) tends to zero faster than the imaginary part
resulting in a purely imaginary response for small ? which is given by
lim??0 VOBJECTV
DIRECT
= ?j?LR kTOkORk
TR
. (2.6)
12
10?2 10?1 100 101 102
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Response Parameter (?)
Response Function
Real
Imaginary
(a)
10?2 10?1 100 101 102
?40
?35
?30
?25
?20
?15
?10
?5
0
Response Magnitude
Response Parameter (?)
0
10
20
30
40
50
60
70
80
90
Response Phase
?3 dB
45?
(b)
Figure 2.3: Frequency response of a thin copper loop (simple first order target)
and is referred to as the resistive limit. Similarly, as ? ? ?, the imaginary part of
the response function vanishes, and the real part asymptotically approaches unity.
Under this condition the response is given by
lim??0 VOBJECTV
DIRECT
= ?kTOkORk
TR
(2.7)
which is referred to as the inductive limit. The crossover frequency in Figure 2.3(a)
or equivalently 45? frequency in Figure 2.3(b) is where the real and imaginary parts
of the response function are equal. The quadrature peak as the name suggests is
where the imaginary response is maximum. Observe from Figure 2.3(b) that the
thin copper loop acts like a high pass filter with a break (3dB) frequency at ? = 1
or fbreak = RO/(2piLO). In this particular case, crossover frequency and quadrature
peak coincide with the break frequency, which may not be true for three dimensional
permeable targets as shown in subsequent sections.
Now, if a finite ZR is assumed, finite currents flow in the receiver circuit. If we
also assume that receiver coil currents are much less than currents in the transmitter
13
coil, then only the transmitter current will induce a voltage in the object. This
assumption results in
VOBJECT
VDIRECT =
?kTOkOR
kTR
parenleftbigg?2 +j?
1 +?2
parenrightbigg Z
R
ZR +ZCOIL (2.8)
where ZCOIL = RR+j?LR. If ZR is a simple resistor, the object response is modified
by the lowpass filter function (1 +j?/?B)?1 where ?B = R/LR is the radian break
frequency of the lowpass filter. This means R should be large enough such that ?B
is much greater than the highest frequency of interest. However, R cannot be too
high as this will force current to flow through the parasitic capacitance of the receiver
coil. Therefore, it is desirable for the parasitic capacitance to be as small as possible
so that R can be increased. This, in turn, will result in an increased measurement
bandwidth.
As stated earlier, time and frequency domain responses form a Fourier transform
pair, and therefore the time domain response can be derived by taking an inverse
Fourier transform (IFT) of the frequency domain response. However, for a loop, it
is straightforward to solve the circuit model directly in time domain and which also
provides better insight into the problem.
Kirchhoff?s voltage law applied to the object loop yields
bracketleftbigg
RO +LO ddt
bracketrightbigg
IO(t) = ?MTOdIT(t)dt (2.9)
14
where IT(t) is given by
IT(t) =
??
????
?
???
???
II t < 0
II parenleftbig1? tTparenrightbig 0 ? t < T
0 t > T
(2.10)
where II is the initial current. Substituting equation (2.10) in equation (2.9) and
solving for IO(t) gives
IO(t) =
?
????
??
???
???
0 t < 0
MTOII
ROT
parenleftbig1?e?t/?parenrightbig 0 ? t < T
MTOII
ROT
parenleftbig1?e?T/?parenrightbige?(t?T)/? t > T
(2.11)
where ? = LO/RO is the time constant of the exponential decay. Note that the
object eddy currents and receiver voltage are inversely proportional to the turnoff
time of the transmitter current and thus, assuming a constant noise level, detec
tion/discrimination improves as the turnoff time of the transmitter current decreases.
Therefore, the turnoff time should be much smaller than the object time constant
(T << ?), in order to achieve good signaltonoise ratio. If t < T then t << ?.
Substituting the small value approximation into a Taylor series expansion for the
exponential functions (ex = 1 +x for small x) in equation (2.11) yields
IO(t) =
?
???
???
????
??
0 t < 0
MTOII
LOT t 0 ? t < T
MTOII
LO e
?t/? t > T
(2.12)
15
Furthermore, the voltage at the receiver due to direct coupling with the transmitter
current (equation (2.10)) is
VDIRECT = ?MTR ddtIT(t) =
?
????
??
???
???
0 t < 0
MTRII
T 0 ? t ? T
0 t > T
(2.13)
Similarly, the voltage at the receiver due to the object current (equation (2.12)) is
VOBJECT = ?MOR ddtIO(t) =
?
????
??
???
???
0 t < 0
?MORMTOII
LOT 0 ? t ? T
MORMTOII
LO? e
?t/? t > T
(2.14)
The resulting total receiver output voltage is VOUT = VOBJECT +VDIRECT.
VOUT =
??
????
?
????
??
0 t < 0
MTRII
T ?
MORMTOII
LOT 0 ? t < T
MORMTOII
LO? e
?t/? t > T
(2.15)
Figure 2.4 shows the normalized current and voltage waveforms of a TD system. VOUT
is not given in since it is simply the sum of the object voltage and the direct voltage.
For t < T, VOUT may vary depending on the magnitude of both object and direct
voltages. However, VOUT for t > T is of primary interest, and it is ideally due only
to the object eddy currents.
It is worthwhile to mention the relationship between time and frequency domain
responses. For a simple first order target like a thin copper loop, the time constant
16
?0.5 0 0.5 1 1.5 2 2.50
0.5
1
?0.5 0 0.5 1 1.5 2 2.50
0.5
1
?0.5 0 0.5 1 1.5 2 2.50
0.5
1
?0.5 0 0.5 1 1.5 2 2.5?1
0
1
t
t
t
t
0 T
0 T
0 T
0 T
Transmitter Current
VDIRECT
Object Current
VOBJECT
II
MTOII/LO
MTRII/T
MTOMORII/LO
MTOMORII/LOT
?
Figure 2.4: Current and voltage waveforms at different stages of the pulsed EMI
system
(? = LO/RO) of the exponential decay is the inverse of the radian break frequency
or crossover frequency (?O = RO/LO) of the frequency response. For complex ob
jects like the ferrous sphere or cylinder, the time domain response is not a simple
exponential decay and in the frequency response, the quadrature peak and crossover
frequencies do not coincide with the break frequency. However, the response of a
ferrous sphere is in the form of a powerlaw in early time followed by an exponential
decay that reflects the residual signal due to the lowest mode eddy currents [23].
Moreover, the transition from powerlaw to exponential decay corresponds approxi
mately to the quadrature peak in the frequency response [23].
17
2.4 EMI Response of a Conducting Sphere [35]
A simple circuit model representation of (RO + j?LO) is not valid for objects
like the sphere and cylinder. Therefore, in this section a boundary value problem
is solved to derive the response of a conducting and permeable sphere in a uniform,
timevarying magnetic field [35, 36]. Figure 2.5 shows a sphere with its center located
Figure 2.5: Conducting sphere in a uniform magnetic field
at the origin of a spherical coordinate system and the primary field in the direction
of the polar axis. With these assumptions the primary field can be expressed as
H(P) = H cos??r?H sin??? =?? 12Hrsin??? (2.16)
and H(P) =??A(P), which means that the primary field H(P) can be obtained from
a vector potential
A(P) = 12Hrsin??? (2.17)
18
The vector potential must satisfy the diffusion equations
?2A?j???A = 0 ??A = 0 (2.18)
where A = A(r,?)?? = ?A(r,?)sin??x+A(r,?)cos??y.
Operating the Laplacian operator separately on each of the rectangular compo
nents of A and recombining them gives
?2A =
parenleftbigg
?2A? Ar2 sin2 ?
parenrightbigg
?? (2.19)
which is a linear scalar equation that can be solved by the method of separation of
variables, where it is assumed that there exists a solution such that
A(r,?) = R(r)?(?) (2.20)
Substituting equation (2.20) into equation (2.19), results in two ordinary differential
equations  a modified Bessel equation and an associated Legendre equation, which
are expressed as
(1?u2)d
2?
du2 ?2u
d?
du ?
bracketleftbigg 1
(1?u2) ?n(n+ 1)
bracketrightbigg
? = 0 (2.21)
and
d2R
dr2 +
2
r
dR
dr ?
bracketleftbigg
k2 + n(n+ 1)r2
bracketrightbigg
R = 0 (2.22)
where u = cos?, k2 = j??? and n is the separation constant. Equation (2.21) has a
solution of the formP1n, and Equation (2.22) has two possible solutionsr?1/2In+1/2(kr)
19
and r?1/2I?n?1/2(kr) when k negationslash= 0, and when k = 0 (i.e., ? = 0), equation (2.22)
reduces to
d
dr
parenleftbigg
r2dRdr
parenrightbigg
?n(n+ 1)R = 0 (2.23)
which has the solution
R(r) = Crn +Dr?(n+1) (2.24)
Since P11(u) = sin?, the vector potential in equation (2.17) can be written as
A(P) = 12HrP11(u)?? (2.25)
where P11 is the Legendre polynomial with separation constant n = 1. The general
solutions of equation (2.18) can now be written for region 1 (outside sphere) and region
2 (inside sphere). In region 1, the field must be the sum of a primary field (equation
(2.25)) and an induction field (with n = 1) that vanishes at infinity. Therefore, the
vector potential in region 1 is given as
A1 = A(P) +A(S) = 12HrP11(u) +Dr?2P11(u) (2.26)
and in region 2, as there can be no singularities, the potential is given as
A2 = FP11(u)r?1/2I3/2(kr) (2.27)
The boundary conditions to be applied at the surface of the sphere (r = a) are
20
1. the magnetic field tangential to the interface is continuous
n?(H1 ?H2) = 0 (2.28)
2. the magnetic flux density normal to the interface is continuous
n?(?1H1 ??2H2) = 0 (2.29)
These two boundary conditions in terms of the vector potential are
A1 = A2
1
?0
?
?r(rA1)=
1
?
?
?r(rA2) (2.30)
Substituting equations (2.26) and (2.27) in equation (2.30), and solving for D yields
D = ?a
3?0H
2
bracketleftbigg(?
0/2?2?)I?3/2(ka) +?0kaI?3/2(ka)
(?0/2 +?)I?3/2(ka) +?0kaI?3/2(ka)
bracketrightbigg
(2.31)
The derivatives of the Bessel functions are
I?n(x) = In?1 ? nxIn(x) = In+1(x) + nxIn(x) (2.32)
which reduce the Bessel functions in equation (2.31) to I?1/2 and I??1/2 which are
expressed in terms of hyperbolic functions as
I1/2(ka) =
radicalbigg 2
pika sinh(ka) and I?1/2(ka) =
radicalbigg 2
pika cosh(ka) (2.33)
21
Substituting these into equation (2.31) yields
D = ?a
3?0H
2
braceleftbigg[?
0(1 +k2a2) + 2?]sinh(ka)?(2?+?0)kacosh(ka)
[?0(1 +k2a2)??]sinh(ka) + (???0)kacosh(ka)
bracerightbigg
(2.34)
Therefore,
A(S) = Dr?2P11(u)?? = ??0 sin?4pir2 2pia3H
?
braceleftbigg[?
0(1 +k2a2) + 2?]sinh(ka)?(2?+?0)kacosh(ka)
[?0(1 +k2a2)??]sinh(ka) + (???0)kacosh(ka)
bracerightbigg
?? (2.35)
If the complex quantity in the braces is represented as (X + jY), then the moment
of magnetic dipole oriented in the direction of the polar axis is
m = ?2pia3H(X +jY) (2.36)
Note that (X+jY) is the only term in equation (2.35) which depends on the frequency
ofthefieldandelectrical propertiesofthesphere. So, (X+jY)istheresponsefunction
of a sphere and is plotted for different values of relative permeability and presented
in Figure 2.6. The response function of a nonpermeable sphere is similar to that of
a copper loop except that the real part of the response reaches its inductive limit
at frequencies higher than that of the loop. For a relative permeability greater than
one (e.g. ferrous target), the real part of the response tends to some negative value
as the response parameter tends to zero. This DC asymptote becomes increasingly
negative with increasing permeability and approaches 2 for ?r ? ?. Also, the
lowfrequency asymptote for permeable sphere is not reached until frequencies well
below 30Hz and therefore cannot be captured with 30Hz to 24kHz band commercial
22
10?1 100 101 102 103
?2
?1.5
?1
?0.5
0
0.5
1
Frequency (Hz)
Response Function
Re(?r=1)
Im(?r=1)
Re(?r=5)
Im(?r=5)
Re(?r=10)
Im(?r=10)
Re(?r=50)
Im(?r=50)
Re(?r=100)
Im(?r=100)
Re(?r=500)
Im(?r=500)
radius = 1"
30 Hz
Figure 2.6: Response function of a sphere in uniform magnetic field
systems. Figure 2.7 shows the magnitude and phase responses of spheres. Note
from Figures 2.7(a) and 2.7(b) that only the nonpermeable sphere has a highpass
response like a copper loop and all permeable spheres have a predominantly lowpass
response. Moreover, the phase response of the nonpermeable sphere starts at 90?
and asymptotes to 0? at high frequencies (Figure 2.7(c)), while that of the permeable
sphere starts at 180? and asymptotes to 0? at high frequencies (Figure 2.7(d)).
2.5 EMI Response of a Conducting Spherical Shell
As UXOs are hollow objects filled with an explosive, the response of a spherical
shell is derived to study the effect of wallthickness on a target?s response. The
sphere problem in the previous section is extended to a spherical shell by satisfying
boundaryconditions at both the boundaries (between regions 1 and 2, and 2 and 3)
as shown in Figure 2.5. For this problem, the vector potential in each region is given
23
10?2 100 102 104 106
?70
?60
?50
?40
?30
?20
?10
0
Frequency (Hz)
Response Magnitude (dB)
?r=1
(a)
10?2 10?1 100 101 102 103
?6
?4
?2
0
2
4
6
Frequency (Hz)
Response Magnitude (dB)
?r=5
?r=10
?r=50
?r=100
?r=500
(b)
10?2 100 102 104 106
0
10
20
30
40
50
60
70
80
90
Frequency (Hz)
Response Phase (degrees)
?r=1
(c)
10?2 10?1 100 101 102 103
0
20
40
60
80
100
120
140
160
180
Frequency (Hz)
Response Phase (degrees)
?r=5
?r=10
?r=50
?r=100
?r=500
(d)
Figure 2.7: (a) Magnitude (b) Phase responses of a sphere
24
Figure 2.8: Conducting spherical shell in a uniform magnetic field
by
A1 =
bracketleftbigg1
2?0H0r +Dr
?2
bracketrightbigg
P11(u)
A2 = bracketleftbigFI3/2(kr) +GK3/2(kr)bracketrightbigr?1/2P11(u) (2.37)
A3 = CrP11(u)
Note that A1 is same as A1 for the solid sphere because fields should vanish at infinity.
A2 is chosen to avoid singularities and A3 is chosen such that fields are zero at the
origin. The boundary conditions at r = a and r = b are
A1 =A2r=a
A2 =A3r=b
1
?0
?
?r(rA1)=
1
?
?
?r(rA2)r=a (2.38)
1
?0
?
?r(rA2)=
1
?
?
?r(rA3)r=b
25
Solving these boundary conditions for D yields
D = ??0Ha
3
2
bracketleftbiggn
11n12 ?n21n22
d11d12 ?d21d22
bracketrightbigg
(2.39)
where
n11 =
parenleftBig?0
2 ?2?
parenrightBig
I3/2(ka) +?0kaI?3/2(ka)
n21 =
parenleftBig?0
2 ?2?
parenrightBig
K3/2(ka) +?0kaK?3/2(ka)
d11 =
parenleftBig
?+ ?02
parenrightBig
I3/2(ka) +?0kaI?3/2(ka)
d21 =
parenleftBig
?+ ?02
parenrightBig
K3/2(ka) +?0kaK?3/2(ka)
d12 =n12 =
parenleftBig?0
2 ?2?
parenrightBig
K3/2(kb) +?0kbK?3/2(kb)
d22 =n22 =
parenleftBig?0
2 ?2?
parenrightBig
I3/2(kb) +?0kbI?3/2(kb)
This equation can be verified by considering b ? 0 (i.e., solid sphere) where n22 and
d22 tend to 0
Db?0 = ??0Ha
3
2
bracketleftbiggn
11
d11
bracketrightbigg
=?a
3?0H
2
bracketleftbigg(?
0/2?2?)I?3/2(ka) +?0kaI?3/2(ka)
(?0/2 +?)I?3/2(ka) +?0kaI?3/2(ka)
bracketrightbigg
(2.40)
which is the same expression as in equation (2.31) for the solid sphere.
The secondary vector potential A(S) can be derived just as in the sphere problem.
The response of a ferrous spherical shell is plotted for different values of inner radius
in Figure 2.9. The values for ? and ?r are chosen to match those of ferrous cylinders
that will be addressed in Chapter 4. Observe that above 30Hz it is hard to distinguish
26
even the thinnest wall shell (b = 2.75??) from the solid sphere (b = 0??). Clearly at very
low frequencies, nominally below 30Hz, the wall thickness can be clearly discerned.
Therefore, for large ferrous targets, valuable target information for discrimination
purposes exists at very low frequencies.
10?2 100 102 104
?1.5
?1
?0.5
0
0.5
Frequency (Hz)
Response Function
b=0" Real
b=0" Imag
b=2.5" Real
b=2.5" Imag
b=2.75" Real
b=2.75" Imag
30 Hz
a=3"
?=5.82e6 S/m
?r=70
(a)
10?2 100 102 104
?6
?4
?2
0
2
4
6
Frequency (Hz)
Response Magnitude (dB)
b=0" Real
b=0" Imag
b=2.5" Real
a=3"
?=5.82e6 S/m
?r=70
(b)
Figure 2.9: (a) Real and imaginary (b) Magnitude responses of ferrous (? = 70?0,
? = 5.82?106 S/m) spherical shells with fixed outer radius (a = 5 cm) and different
inner radii
2.6 EMI Response of an Arbitrary Permeable Conducting Target
The sphere and spherical shell are objects with threedimensional symmetry and
therefore, have analytical models. In contrast, rotationally symmetric objects like fi
nite cylinders do not have a simple closed form analytical solution. Liao and Carin [45]
give
M(?) = diag[mp0 +
summationdisplay
k
?mpk
??j?pk,mp0 +
summationdisplay
k
?mpk
??j?pk,mz0 +
summationdisplay
k
?mzk
??j?zk] (2.41)
27
as the magnetization tensor of a rotationally symmetric object with the zdirection
taken as the axis of rotation. (The object?s scattered field is proportional to its
magnetization tensor.) Observe that each component of the magnetization tensor
is composed of an infinite sum of terms of weight mzk and mpk for the component
along and perpendicular to the object?s axis of rotation, respectively. Unlike the
objects treated above, the frequency response of arbitrarily shaped conducting bodies
is represented by a superposition of high pass terms, but in many cases only the lowest
order component has significant strength allowing one to replace the summation in
M(?) with a single term which will be the object?s response function. If the excitatory
magnetic field is aligned with the axis of the object, then all mpk are zero and vice
versa. In general, though, both components will be excited. Also, mp0 and mzp give
the DC (zero frequency) response and both are zero for nonmagnetic targets.
Although equation (2.41) is valuable for general expository purposes, actual com
putation for mzk, mpk, ?zk, and ?pk is not at all straightforward. Therefore, numer
ical methods have to be used to compute the scattered field for bodyofrevolution
geometries. Several numerical methods previously applied to the UXO problem in
clude Integral Equations (IE) [40], [46] [52], Method of Moments (MoM) [53] [56],
and Finite Element MethodBoundary Element Method (FEMBEM) [37]. In order
to ensure that the results (presented in chapter 4) obtained using our EMI sensor
are correct, the measured responses of steel cylinders are compared with the Finite
Element Method (FEM) model developed by Faircloth [57].
28
2.7 Summary
A typical electromagnetic induction system has a transmitter coil, receiver coil
and a buried metallic target, andoperates according to Faraday?s law. A simple circuit
analysis of the EMI system yields transient and frequency responses of a conducting
loop where the transient response is exponential and the frequency response is high
pass.
The EMI response of a solid sphere presents the effect of permeability on the
object?s response. The frequency response is highpass for a nonpermeable sphere
(just like that of the conducting loop) whereas it is lowpass for a permeable sphere.
The response of a hollow sphere was derived and it was shown that the responses
of spherical shells with fixed outer radius but different wall thicknesses are identical
above 30Hz. However below 30Hz, the responses are distinct because the fields at low
frequencies penetrate into the object and reveal its inner structure.
Therefore, frequencies below 30Hz are necessary to acquire the information nec
essary to discriminate among visually identical objects with varying wall thicknesses.
29
Chapter 3
EMI Sensor Description
3.1 Introduction
Analytical responses of permeable solid and hollow spheres presented in Chap
ter 2 show that important target information is contained in the extremely low fre
quency or equivalently in the late time EMI response. The CW and pulsed EMI
systems designed to acquire extended data ranges are explained in this chapter. Also,
major design tradeoffs germane to the development of such systems are discussed.
3.2 Experimental setup
The operation of CW and pulsed EMI systems is described utilizing block di
agrams and digitized photographs of the corresponding hardware configurations are
also presented.
3.2.1 CW System
Figure 3.1 presents a generic block diagram of the CW measurement system. The
Hewlett Packard 89410A Vector Signal Analyzer forms the heart of the measurement
system and provides stimulus and measures the coherent response of any test target.
The analyzer?s source is programmed to provide excitation at a discrete number (51,
101, 401, or 801) of uniformly spaced frequencies anywhere within the operating range
from near DC to 10 MHz.
30
Figure 3.1: Block Diagram of a CW EMI system
Theanalyzer?ssourcedrivesaPowertronModel250APowerAmplifier(250Watts)
which boosts the current flowing in the transmitter coil. The current flowing through
the transmitter coil is measured using a Tektronix TM502A current probe and fed
to channel one of the analyzer. The resistance R is used to limit the transmitter
current due to low coil impedance at low frequencies. The receiver coil consisting of
N clockwise and N counterclockwise turns should ideally have zero output voltage
when symmetrically located with respect to the transmitting coil. Any object that is
not symmetrically located with respect to the transmitter coil will induce a voltage
at the output of the receiver coil. This voltage, representing the object response,
is amplified by the receiver coil amplifier that in turn is connected to channel two
of the analyzer. In order to determine the object transfer function the analyzer is
programmed to compute the frequency response (ratio of voltage at channel two to
31
the current at channel one) divided by j? over the range of frequencies of interest
(refer to equation (2.4)).
Figure 3.2 shows the hardware configuration corresponding to Figure 3.1.
Figure 3.2: Hardware setup of a CW EMI system
3.2.2 Pulsed System
In a pulsed EMI system the four major components are the sensor coils, pulser,
signal conditioning unit and data acquisition package as shown in Figure 3.3. The
sensor coils are the same as in the CW system and are described in next section. A
PIC Microcontroller PIC16F88 is used to generate a pulse waveform, which switches
the insulated gate bipolar transistor (IGBT) on and off. When the pulse waveform is
?high? the switch closes and allows current IT to flow through the transmitter coil for
the duration of the pulse. When the pulse falls below a characteristic ?low? the switch
is opened. The pulse duration is chosen to be 800?s, which is sufficient time for the
32
Figure 3.3: Block Diagram of pulsed EMI system
transmitter currentto reach a steady maximum value (? 18A with 24V power supply).
As mentioned in the previous chapter, rapid transmitter current turnoff is necessary
for inducing large object currents. Rapid turnoff is insured by driving the IGBT with
a MOSFET/IGBT driver chip IXDN404PI from IXYS Corporation. The transmitter
current falls to zero in approximately 0.5?s. It is also important that the current pulse
remains ?off? long enough to permit the receiver coil to capture the object?s response
which may be of significant amplitude for tens of milliseconds. Hence, the pulse
repetition rate is chosen to be 50Hz (20ms period). The object?s response captured
by the receiver coil is passed through the signal conditioning unit which consists of a
currenttovoltage converter, and an amplifier with lowpass filter characteristics (3dB
frequency = 10 kHz). The signal conditioning unit converts the receiver coil current
into a voltage with more gain, and also filters out high frequency noise. The amplified
and filtered analog receiver voltage is then digitized using analogtodigital (AD) data
acquisition card, Compuscope (CS)1602. The Gagescope software is used to display
the waveform and record the data. The hardware configuration for the pulsed system
33
is shown in Figure 3.4. The ?pulser box? in Figure 3.5 contains various components
including IGBT, MOSFET driver, PIC Microcontroller and receiver amplifier.
Figure 3.4: Hardware configuration of pulsed EMI system. (1) Oscilloscope (2) DC
power supply for pulser (3) Transmit coil (4) Receive coil (5) Pulser (6) Gagescope
3.3 Transmitter and Receiver Coil Characteristics
The transmitter and receiver coil pair used in the measurements is presented in
Figure 3.6. The 1m?1m transmitter coil consists of 10 turns of 18 AWG magnetic
wire. Each 0.33m?0.33m coil of the figure8 receiver consists of 14 turns of 18 AWG
magnetic wire. Square coils were chosen because they are easier than round coils to
construct. The receiver coils are glued to a Plexiglas sheet that is designed to slide
atop another Plexiglas sheet that has been glued to the top of the transmitter coil
frame. While transmitting over the band of frequencies of interest, the receiver coil
output voltage is minimized by carefully positioning the receiver coil with respect to
the transmitter coil.
34
Figure 3.5: Components of the pulser on a printed circuit board
3.3.1 Various Tradeoffs Considered in Coil Construction
The response of an EMI system not only depends on the physical and material
characteristics and the location of the target, but also on the characteristics of the
transmitter and receiver coils. There are many tradeoffs that must be addressed
regarding coil design some of which are described in the next section.
Coil Dimensions
A good coil design requires tradeoffs among competing objectives. For example,
Figure 3.7 plots the magnetic field along the axis (zaxis) of a square loop for side of
10, 25, 50 and 100cm (HZ = Ia2/
bracketleftBig
2pi(h2 +a2/4)radicalbigh2 +a2/2
bracketrightBig
, I = 1 ampere). The
magnetic field at the center of the loop (z=0) decreases with increasing loop size, but
the magnetic field along the axis of a large loop diminishes more slowly than that of a
smaller loop. Therefore, transmitter coil dimensions are chosen as 1m?1m to provide
35
Figure 3.6: Transmitter and receiver coil pair used in CW and pulsed EMI measure
ments
good depth sensitivity without sacrificing system sensitivity to closein (close to the
plane of the coils) sensitivity.
Direct Coupling
Direct coupling between the transmitter and the receiver coils is another setback
in the measurements as the direct coupled signal can be much larger than the object
response and therefore may mask the weak object response. For this reason, the
receiver is chosen to be wound in a bucking fashion where two coils with equal number
of turns and of opposite polarity are connected in series. Equal flux passing through
each coil that theoretically cancel. The dimensions of each of the two receiver coils
is 0.33m?0.33m. Note that a bucking configuration can be used on the transmitter
instead of receiver and GEM3 sensor sold by Geophex is an example of an EMI
36
Figure 3.7: Magnetic field along the axis (zaxis) of a square loop for side of 10, 25,
50 and 100cm
sensor that utilizes just such configuration [58]. Another approach commonly used
in pulsed system is to wait until the transmitter current falls below the noise level
to acquire the object response. Once the transmitter current decays sufficiently the
captured response will be due only to the object.
Sensitivity Maps
One way to evaluate the sensor coil pair without involving the target character
istics is by static sensitivity maps as first introduced by Silvester [59]. ?The static
sensitivity can be interpreted physically as the ratio of opencircuit output voltage
change to the input voltage, per unit volume of perfectly conducting sphere, assuming
37
the sphere to be infinitesimally small and the coils to consist of one turn each? [59].
And, static sensitivity is directly proportional to HT ?HR, where HT and HR are
the magnetic fields due to transmitter and receiver coils respectively and each can
be computed using the BioSavart Law. Figure 3.8 presents the sensitive maps cor
responding to a 1m?1m transmitter coil and 0.33m?0.33m figure8 receiver coil pair
superimposed on a line diagram of the sensor coils. The plots are over the xy plane
at various heights and the dot (x ?0.2m, y = 0,z) represents the center of one coil of
figure8 receiver. The contours represent sensor sensitivity in dB (where 0dB corre
sponds to the maximum sensitivity).
Important observations made from these sensitivity maps are
1. The sensitivity is minimum at the center of the sensor (x = 0, y = 0) as the
fields cancel out due to the symmetry of the figure8 receiver.
2. For small z, the point of maximum sensitivity is at the center of each coil (y = 0
and x ?? 0.2m) of figure8 receiver and drifts away from the center (dot) as z
increases.
3. With a 10cm increase in z the sensitivity diminishes by ?10dB at the center of
receiver coil (dot).
Optimal Number of Transmitter Coil Turns for VOUT/VS Measurement
Another tradeoff in coil design exists between system bandwidth and gain, both
of which depend on the number of transmit coil turns NT. In section 2.3, the
frequencydomain transfer function of a conducting loop is determined by solving
a magnetically coupled circuit representation of an EMI system. In this section, the
38
?0.5 0 0.5
?0.5
0
0.5 ?55
?55
?50
?50
?50
?50
?45
?45
?45
?45
?45
?45
?45
?45
?40
?40
?40
?40
?40
?40
?40
?40
?35 ?35
?35
?35
?35
?35 ?35
?35
?35
?35
?35
?35
?30
?30 ?30 ?30
?30
?30 ?30 ?30
?30
?30
?30
?30
?25 ?25 ?25
?25
?25?25?25
?25
?25
?25
?25
?25
?20
?20 ?20
?20
?20
?20
?20
?20
?20
?20
?20
?20
?20
?20
?20
?20
?15 ?15 ?15
?15
?15?15?15
?15
?15
?15
?15
?10 ?10
?10
?10
?10
?10
?10
?10
?10
?10
?10
?10
?5
?5
?5?5
?1
?1
?1
?1
x axis
y axis
(a) z = 1 cm
?0.5 0 0.5
?0.5
0
0.5
?80
?80
?80
?80
?80?80
?80
?80
?75
?75
?75
?75
?75
?75
?75
?75
?75
?75
?75
?75 ?75?75
?70
?70
?70
?70
?70
?70
?70
?70
?70 ?70?70
?70 ?70?70
?65
?65
?65
?65
?65
?65
?65
?65
?65
?65
?65
?65
?65
?65
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?60
?55
?55
?55
?55
?55 ?55
?55
?55
?55
?55 ?55
?55 ?55
?55
?55
?55
?55 ?55
?50
?50 ?50
?50
?50
?50 ?50
?50
?50
?50
?50
?50
?50
?50
?50
?50
?45
?45 ?45
?45
?45
?45 ?45
?45
?40 ?40 ?40
?40 ?40 ?40
?35 ?35 ?35 ?35
?35
?35 ?35
?35
?30 ?30 ?30
?30
?30?30
?30
?25
?25
?25
?25
?25
?25
?25
?25
?20
?20
?20
?20
?20
?20
x axis
y axis
(b) z = 10 cm
?0.5 0 0.5
?0.5
0
0.5 ?70
?70
?65
?65
?60
?60
?60
?60
?60
?60
?60
?60
?55
?55
?55
?55
?55
?55
?55
?55
?50 ?50
?50
?50
?50
?50 ?50 ?50
?45
?45 ?45 ?45
?45 ?45 ?45 ?45
?40
?40
?40
?40
?40 ?40
?40
?40
?40 ?40
?35
?35
?35
?35
?35
?35
?35
?35
?30
?30
?30
?30?30
?30
x axis
y axis
(c) z = 20 cm
?0.5 0 0.5
?0.5
0
0.5 ?85
?85
?80
?80
?75
?75
?75
?75
?70
?70
?70
?70
?70
?70?70
?70
?70
?70
?65
?65
?65
?65
?65
?65
?65
?65
?65
?65
?60
?60
?60
?60
?60
?60
?60
?60
?55
?55
?55?55
x axis
y axis
(d) z = 50 cm
Figure 3.8: Static sensitivity maps superimposed on a line diagram of the EMI sensor.
Plots over 0.5m ? x ? 0.5m, 0.5m ? y ? 0.5m at z = 1, 10, 20, 50cm
39
physical characteristics of the transmitting coil are included in the aforementioned
analysis. Referring to Figure 2.2(a), the object current of equation (2.1) can be
rearranged as
IO = ? j?MTO(R
O +j?LO)
IT (3.1)
where transmitter current IT is the source voltage divided by the transmitter coil
impedance
IT = ? VS(R
T +j?LT)
(3.2)
Substituting equation (3.2) in equation (3.1) yields
IO = ? j?MTOVS(R
O +j?LO)(RT +j?LT)
(3.3)
The receiver current is given by
IR = ? j?MOR(Z
R +RR +j?LR)
IO (3.4)
Eliminating IO in the above equation results in
IR = ?j?MORj?MTOVS(Z
R +RR +j?LR)(RO +j?LO)(RT +j?LT)
(3.5)
The output voltage is the product of the receiver current, IR and the load impedance
ZR and is given by
VOUT = ? ZRj?MORj?MTOVS(Z
R +RR +j?LR)(RO +j?LO)(RT +j?LT)
(3.6)
40
The system transfer function VOUT/VS is then given by
VOUT
VS = ?
ZRj?MORj?MTO
(ZR +RR +j?LR)(RO +j?LO)(RT +j?LT) (3.7)
First assuming that the receiver coil is open circuited, i.e., ZR = ?, equation (3.7)
reduces to
VOUT
VS = ?
j?MORj?MTO
(RO +j?LO)(RT +j?LT) (3.8)
Iftheobjectandtransmittercoilradianbreakfrequenciesaredefinedtobe?O =RO/LO
and ?T = RT/LT respectively, equation (3.8) can be expressed as
VOUT
VS = ?
MORMTO
LTLO
j?/?T
(1 +j?/?T)
j?/?O
(1 +j?/?O) (3.9)
The highpass filter (frequency dependent) terms in equation (3.9) are associated
with the transmitter coil (?T) and object (?O) in the same order. For a highpass
filter, it can be noticed from Figure 3.9 that for operating frequencies above the
break frequency the magnitude of the response approaches unity (0dB), at the break
frequency is 3dB below (1/?2 times) its high frequency asymptote Furthermore, the
response decreases by a factor of 10 (20dB) per decade decrease in frequency. The
phase starts at 90? close to DC, is 45? at the break frequency and asymptotes to 0?
for frequencies well above the break frequency.
The transmitter coil resistance RT is proportional to NT and inductance LT is
proportional to N2T resulting in a transmitter coil break frequency (?T = RT/LT)
that is inversely proportional to NT. The transmitter coil resistance is Rcoil=917m?
41
10?1 100 101 102 103
?40
?30
?20
?10
0
Response Magnitude dB
0
10
20
30
40
50
60
70
80
90
Response Phase Degrees
Frequency Radians/second
45? at Break Frequency
?3 dB at Break Frequency
Break Frequency
?B=10 rads/sec
Figure 3.9: Transfer characteristics of a highpass filter: (j?/10)/(1 + j?/10). Solid
line is the magnitude response and dashed line is the phase response
and its inductance is Lcoil=357?H (measured at 1kHz). Therefore 3dB break fre
quency of the coil is approximately 400Hz. At 4Hz the overall system response is
attenuated by 40dB compared to what it would be if this coil had enough turns to
drop the break frequency by two decades.
Certainly, the system would be improved in terms of bandwidth if NT is increased
to shift the transmitter coil break frequency close to the lowest frequency of interest;
however, there is an important tradeoff to be considered. VOUT/VS of equation (3.9)
is proportional to MORMTO/LTLO which in turn is proportional to radicalbigLR/LT (since,
Mij = kijradicalbigLiLj). Therefore, VOUT/VS is proportional to NR/NT. So, for a fixed
numberofreceivercoil turnsNR, theamplitudeoftheresponsedecreaseswith increase
in NT. NR can be increased along with NT to maintain the amplitude, but this will
lead to additional more tradeoffs that are addressed subsequently.
42
Receiver Coil and Receiver Coil Amplifier Considerations for VOUT/VS
Measurement
The weak signals induced in the receiver coil by the eddy currents in the buried
metallic object are boosted using an operational amplifier shown in Figure 3.10. It is
+

+V CC
V CC
R R
C R L R V
OUT
R 1 R 2
V IN
Figure 3.10: Operational amplifier connected in a noninverting configuration to the
receiver coil. The parasitic capacitance of the receiver coil distorts measurements of
the object?s response.
connected in a noninverting configuration and provides a voltage gain VOUT/VIN =
1 + R2/R1. In noninverting configuration the operational amplifier has a very large
(many mega ohms) input impedance. Because of this, currents will begin to flow
through the parasitic capacitance CR above a certain frequency. Due to the resonant
circuit formed by LR, RR and CR the input voltage VIN will increase proportional to
frequency at 20dB/decade up to the first selfresonance of the receiver coil (typically
around 10kHz) which will in turn distort the output voltage and make it difficult
to recover the object response. Equivalently, the transfer function (equation (3.9))
is now multiplied by a new frequency dependent factor that takes into account the
resonant nature of the receiver coil
?2n
s2 + 2??ns+?2n (3.10)
43
which is a closedloop transfer function for the standard secondorder system where
thenaturalresonantfrequency?n = 1/?LRCR andthedampingconstant? =0.5RR?LRCR.
The resulting system transfer function becomes
VOUT
VS = ?
MORMTO
LTLO
j?/?T
(1 +j?/?T)
j?/?O
(1 +j?/?O)
?2n
s2 + 2??ns+?2n
parenleftbigg
1 + R2R
1
parenrightbigg
(3.11)
The resonance effect of the receiver coil can be avoided by measuring the cur
rent in the receiver coil (instead of the voltage) and using a currenttovoltage con
verter [60], [61].
Optimal Number of Transmitter Coil Turns for Object Current Measure
ment
The case in which the object current IO is measured (instead of the voltage
proportional to the object response) is considered in this section. Rearranging the
terms in equations (3.1) and (3.2) yields
IO = ?MTOL
O
j?/?O
(1 +j?/?O)IT (3.12)
and
IT = ? VS/RT(1 +j?/?
T)
(3.13)
Since there is no extra j? term in equation (3.13), IT is a single pole low pass filter.
Hence, the transmitter coil break frequency should be much higher than that of object
?T >> ?O. As ?T is inversely proportional to NT, theoretically it appears to be
44
desirable to use as few turns as possible so that the transmitter coil impedance is low
enough so that transmitter amplifier can supply rated current. However practically
speaking, a reduced number of transmitter coil turns decreases the field strength
at the target thereby weakening the overall response. Note that more transmitter
turns can be used to improve the field strength if a resistor is added in series with the
transmitter. However, a series resistor will reduce the current through the transmitter
coil which but can be overcome by using a more powerful amplifier. In short, a large
number of transmitter coil turns along with a series resistor and increased power can
be used to achieve both bandwidth and sensitivity.
Receiver Coil and Receiver Coil Amplifier Considerations for Object Cur
rent Measurement
The operational amplifier shown in Figure 3.11 is connected in an inverting con
figuration (input into negative terminal) as a currenttovoltage converter, so that
VOUT = IRRF where IR is the receiver coil current and RF is the feedback resistor
that sets the gain.
+

+V CC
V CC
R R
C R L R
V OUT
R F
V IN
j M OR I O
Figure 3.11: Operational amplifier connected in an inverting configuration to the
receiver coil as a currenttovoltage converter.
45
The voltage induced in the receiver coil due to object eddy currents is given
by j?MORIO. Receiver current IR is induced voltage divided by the receiver coil
impedance
IR = j?MORIOR
R +j?LR
= MORL
R
j?/?R
1 +j?/?RIO (3.14)
As the receiver coil break frequency is ?R = RR/LR, the operational amplifier output
voltage may be written as
VOUT = RFIR = RF MORL
R
j?/?R
1 +j?/?RIO (3.15)
Manipulation of equations (3.12), (3.13) and (3.15) yields an object response
VOUT
VS =
RF
RT
parenleftbiggM
TOMOR
LOLR
parenrightbiggparenleftbigg 1
1 +j?/?T
parenrightbiggparenleftbigg j?/?
O
1 +j?/?O
parenrightbiggparenleftbigg j?/?
R
1 +j?/?R
parenrightbigg
(3.16)
which is undistorted over the range of frequencies from ?R to the first resonance
frequency of the receiver coil. Once the transmitter has been developed as explained
in previous section and the coil dimensions of the receiver have been determined, the
number of receiver coil turns should be chosen to fix the 3dB frequency to ?R.
In the development of equation (3.15) the effect of the parasitic capacitance CR
is ignored as the input impedance of the currenttovoltage converter is negligible..
3.4 Summary
In this chapter laboratory setups of CW and pulsedEMI systems are described
and several factors affecting system design have been described. Most importantly,
46
using a currenttovoltage converting operational amplifier to measure the ?short
circuit? receiver coil current allows one to avoid problems introduced by parasitic
capacitance.
47
Chapter 4
Measurements
4.1 Introduction
Time and frequencydomain EMI responses of UXOlike ferrous targets acquired
using the systems described in Chapter 3 are presented. The measured responses are
validated by comparing them with numerical simulations. Effects of target size, wall
thickness, and the presence of copper bands on the response characteristics are dis
cussed. Special attention is given to the target response characteristics at extremely
low frequencies or equivalently very late times. The next chapter presents a quan
titative measure of discrimination performance enhancement provided by extremely
low frequency target and latetime features
4.2 Test Targets
Figure 4.1 shows the ferrous cylinders used for simulations and measurements.
The cylinders are of four different sizes and three different wall thicknesses and the
copper bands model the driving bands on real UXO. The number on each cylinder
represents its size and the letter represents its wall thickness. The dimensions of these
twelve cylinders are given in table 4.1.
48
Figure 4.1: Test targets used in the measurements.
Table 4.1: Size details of the test targets
WallTarget
Thickness (in) L (in) D (in)
1A 1/4 8 2
1B 1/2 8 2
1C Solid 8 2
2A 1/4 12 3
2B 1/2 12 3
2C Solid 12 3
3A 1/4 16 4
3B 1/2 16 4
3C Solid 16 4
4A 1/4 24 6
4B 1/2 24 6
4C Solid 24 6
49
4.3 FrequencyDomain Measurements
The CW system presented in Figure 3.2 is used to acquire the frequency responses
of the targets. Results presented here are for axial excitationof the target (i.e., vertical
orientation of target with respect to the sensor).
4.3.1 Comparison between FEM and Measured Responses
Due to lack of threedimensional symmetry, the finite cylinder does not have
an analytical solution and therefore, a numerical method has to be employed to de
termine its scattered field. In this work, the Finite Element Method (FEM) model
developed by Faircloth is chosen to pursue a direct numerical computation of the
bodyofrevolution (BOR) response for axial excitation [57]. Good agreement be
tween the analytical and FEM computed response for the sphere is demonstrated.
As the error in the FEM results is negligible, a least squared error minimization al
gorithm is used to effectively normalize the measured data with respect to the FEM
results for comparison purposes. Excellent agreement between measurements and
FEM simulation were achieved when the conductivity and permeability of the ferrous
cylinders were taken as 5.82?106 S/m and 70 respectively. The normalized FEM and
measured responses of cylinder 1B with a centered copper driving band are compared
in Figure 4.2. Note that the results are in close agreement as anticipated.
4.3.2 Effect of Target Size
To evaluate the importance of extremely lowfrequency response of UXOlike tar
gets, an initial comparison of steel cylinders of varying size was performed. Figure 4.3
shows normalized responses of solid cylinders for all four sizes. Clearly, the overall
50
100 101 102 103 104
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
Frequency (Hz)
Normalized Response
Measured
FEM
Real
Imag
Figure 4.2: Comparison of response obtained by FEM and measurements for 1B
cylinder with centered copper ring.
trends of the responses are quite similar with the exception of a downward frequency
shift of the lowfrequency real asymptote and quadrature peak with increasing cylin
der size. In particular, note that the inphase responses of cylinders 1C and 2C start
approaching their lowfrequency limit around 1Hz and due to higher metallic content
of cylinders 3C and 4C, their responses tend to their lowfrequency asymptotes at
frequencies below 1Hz.
The frequency range for FEM simulation is extended downward to 1mHz in
order to study the target response behavior at extremely low frequencies. Figure 4.4
compares FEM responses for different sized steel cylinders. The FEM responses
shown in Figure 4.4 displays the same trends as the measured response of Figure 4.3.
Of particular interest is the fact that none of the cylinders reach their inphase low
frequency asymptotic limit until well below the typical EMI frequency band (30Hz to
51
100 101 102 103 104
?1.5
?1
?0.5
0
0.5
Frequency (Hz)
Normalized Response
1C2C
3C4C
Real
Imag
30 Hz
Figure 4.3: Measured responses of four solid steel cylinders of varying size.
24kHz). Since each of the cylinders has its own unique point at which the asymptotic
limit is reached, valuable discrimination information is neglected if one collects data
only in the 30Hz to 24kHz range. Figure 4.5 gives a detailed viewof the lowfrequency
asymptotic behavior of the real part of the response for different size cylinders. The
low frequency asymptote of the largest cylinder (4C) is not reached until ?10mHz
which is well below the lowest operating frequency of commercially available CW
EMI systems. Similarly, the asymptote of the smallest cylinder (1C) is not reached
until ?300mHz which is two decades below the lowest operating frequency (30Hz) of
commercial systems.
4.3.3 Effect of Wall Thickness
Next, the effect of wall thickness on target response is compared for a variety of
cylinders. Figure 4.6 shows the measured response of three ?2 Series? cylinders that
52
10?2 100 102 104
?2
?1.5
?1
?0.5
0
0.5
Frequency (Hz)
Normalized Response
Real
Imag
1C
4C 3C
2C
30 Hz
Figure 4.4: FEM Response of four solid steel cylinders of varying size.
10?3 10?2 10?1 100 101
?1.95
?1.9
?1.85
?1.8
?1.75
?1.7
?1.65
?1.6
?1.55
?1.5
Frequency (Hz)
Normalized Response
1C
2C
3C
4C
Figure 4.5: Extremely low frequency FEM response of the four solid steel cylinders
53
have different wall thicknesses. A line at 30Hz divides the figure into lowfrequency
100 101 102 103 104
?1.5
?1
?0.5
0
0.5
Frequency (Hz)
Normalized Response
30 Hz
2C
2B 2A RealImag
Figure 4.6: Measured responses of visually identical steel cylinders with differing wall
thicknesses
band and typical EMI band. Above 30Hz, there is very little difference between the
responses of the three cylinders. Therefore, discrimination using only the information
above 30Hz would prove most difficult at low SNRs. However, below 30Hz, there is
a notable difference among the responses.
FEM responses of cylinders 2A, 2B and 2C for the frequencies from 1mHz to
100kHz are presented in Figure 4.7. FEM responses show the same trends as de
termined from the measured responses presented in Figure 4.6. Once again, the
difference in the responses is only significant below 30Hz. Another point to be noted
here is that the imaginary part of all the three responses asymptote to zero while
the real part asymptotes to a distinct negative value, just as in the analytical hollow
54
sphere case shown in Figure 2.9. It is clear from Figure 4.8 that the thinwalled cylin
der reaches its lowfrequency asymptote at ?1Hz whereas the other cylinders have
asymptotes below ?200 mHz. Obviously, the lowfrequency information should be
helpful in discerning UXOlike targets from flat plates or other thin metallic debris.
10?2 100 102 104
?2
?1.5
?1
?0.5
0
0.5
Frequency (Hz)
Normalized Response
30 Hz
2A
2B
2C
Real
Imag
Figure 4.7: FEM response of visually identical cylinders.
4.3.4 Effect of Driving Bands
Actual UXO targets are often equipped with metallic rings known as driving
bands. The bands are usually made of highly conductive, nonpermeable metals such
as copper. For the vertical (axial) excitation, presence of the driving band should
significantly affect the response of a target. The effect of centered copper driving
band on ferrous cylinder response is presented in Figures 4.9 and 4.10 using measured
responses and FEM simulated data. When a copper driving band is placed around
the cylinder its quadrature peak shifts down in frequency. The most significant fact
is that the quadrature peak of the banded case is now well below the 30Hz lower
55
10?2 10?1 100 101 102
?1
?0.9
?0.8
?0.7
?0.6
?0.5
?0.4
?0.3
Frequency (Hz)
Normalized Response
2C
2B
2A
Figure 4.8: Low frequency FEM response of visually identical cylinders.
100 101 102 103 104
?1.5
?1
?0.5
0
0.5
Frequency (Hz)
Normalized Response
30 Hz
Without Ring
With Ring
Real
Imag
Figure 4.9: Effect of driving band on targets Measured response.
56
10?2 100 102 104
?2
?1.5
?1
?0.5
0
0.5
Frequency (Hz)
Normalized Response
With Ring
Without Ring
Real
Imag
Figure 4.10: Effect of driving band on targets FEM response.
limit of typical EMI measurement systems. Using only the typical EMI measurement
spectrum could adversely affect discrimination performance since quadrature peak
frequency is used as a parameter in discrimination algorithms [38].
4.3.5 UXO Measurements
Figure 4.11 shows three UXO targets that are measured with the incident mag
netic field along the long axis of the targets. Figure 4.12 presents the responses of
these three UXOs in the 1Hz to 10kHz range. Note that the data in this range does
display the expected lowfrequency asymptotic behavior (e.g.  the real part converges
to a constant negative value and imaginary part converges to zero). In general the
response of the UXOs is similar to that of the test cylinders.
57
Figure 4.11: UXO items from left to right 155mm, 105mm, and 107mm shell
4.4 TimeDomain Measurements
A comparison of theoretical, FEM, and measured timedomain response of an
18 AWG 5? copper loop is presented in Figure 4.13. It can be seen from the figure
that the measured time responses are in close agreement with FEM and theoretical
results.
Figure 4.14 shows the measured timedomain response of the ?2 series? (3? di
ameter ? 12? height) cylinders with same diameter and height but different wall
thicknesses. The response has a steep slope in early time and a gradual slope later.
The early time response corresponds to higher frequencies that do not penetrate the
object. Therefore, the responses of the three cylinders are almost identical in early
time. As the fields penetrate deeper into the object at late time (low frequencies),
the response reveals information regarding the target?s inner geometry. The late time
target information can be used to improve discrimination performance. However, it
58
100 101 102 103 104
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
Frequency (Hz)
Normalized Response
Real
Imag
(a)
100 101 102 103 104
?1
?0.5
0
0.5
Frequency (Hz)
Normalized Response
Real
Imag
(b)
100 101 102 103 104
?1
?0.5
0
0.5
1
Frequency (Hz)
Normalized Response
Real
Imag
(c)
Figure 4.12: Measured Response of (a) 155 mm shell (b) 105 mm shell (c) 107 mm
shell in the 1Hz to 10kHz frequency range.
is very difficult to measure the late time data as the magnitude of the signal falls
below the noise level. Hence, only the data up to 17ms is shown in Figure 4.14. Im
provements to the timedomain EMI system described in section 3.2.2 are currently
underway to acquire latetime data beyond 17ms. In order to observe the nature of
the response beyond 17ms, timederivative of the FEM magnetic field responses are
presented in Figure 4.15. The figure shows that there is a clear difference in the decay
behavior depending on the wall thickness. The response of cylinder 2A decays faster
and has a pure exponential decay starting at about 4ms. Whereas cylinder 2B goes
59
0 50 100 150 200
10?1
100
Normalized Voltage
Time (?s)
Measured
FEM
Theory
Figure 4.13: Theoretical, FEM and Measured TimeDomain response of 18 AWG 5?
Copper loop
into a pure exponential regime at around 20ms and the exponential portion of the
response for cylinder 2C would have been noticeable, if the response was extended
beyond 40ms. Similar trends are observed in the cylinders of other series (1, 3 and
4) also.
Another interesting feature of the FEM data is the ?powerlaw to exponential
transition? of cylinders with different dimensions but same wall thickness. Figure 4.16
presents the transient response of ?A? cylinders (1/4?? wall thickness) of different sizes.
As anticipated, the decay slows down with increase in the cylinder size, however, it can
be noticed that all four cylinders enter a pure exponential regime at ?4ms. Similarly,
?B? cylinders (1/2?? wall thickness) are noticed to start decaying exponentially at
?20ms. From the time responses presented in Figure 4.16 it can be inferred that the
transition time is a characteristic of wallthickness only (and not size).
60
0 5 10 15
10?3
10?2
10?1
100
Time (ms)
Normalized Voltage
2A
2B
2C
Figure 4.14: Measured decays for ?2 series? cylinders identical except for wall thick
ness
0 10 20 30 40
10?6
10?4
10?2
100
Time (ms)
Normalized Voltage
2A
2B
2C
Figure 4.15: FEM decays for ?2 series? cylinders identical except for wall thickness
61
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1510
?3
10?2
10?1
100
Time (ms)
Normalized Voltage
1A
2A
3A
4A
Figure 4.16: FEM decays for ?A series? cylinders of different sizes and same wall
thickness
It is important that of a timedomain EMI sensor be able to measure the transi
tion from powerlaw to exponential decay. As seen in Figure 4.15, for cylinder ?2C?
this transition does not occur in the 0 to 40ms time window and it is very difficult
to measure the data beyond 40ms. However, as mentioned earlier, transition from
powerlaw to exponential decay (inflection time) is related to the quadrature peak
of the frequency response which can be acquired with much greater ease using a
frequencydomain EMI system.
The timedomain system was tested at Blossom Point Test field and currently
efforts are continuing toward improving the system for sensitivity and duration of the
acquisition. For further details readers are refered to [62].
62
4.5 Summary
Measured and FEM responses of cylinders in frequency and timedomain show
that extremely low frequency or equivalently latetime data provides valuable target
information which can improve discrimination relative to what can be achieved using
the usual spectral content available from commercial systems. However, high fidelity
lowfrequency is easier to obtain with a CW system than a pulsed system. Discrimi
nation improvement provided by ELF frequencies will be statistically analyzed in the
next chapter.
63
Chapter 5
Statistical Analysis
5.1 Introduction
Chapters 2 and 4 show that frequency responses of UXOsize visually identical
ferrous targets are not distinct until below 30Hz. Discrimination performance of an
EMI system can be improved by extending the lower bound from 30Hz downward to
1Hz. A quantitative measure of improvement in discrimination performance provided
by ELF data is presented in this chapter. Three statistical tests are analyzed using
data in 1Hz to 24kHz and 30Hz to 24kHz ranges.
5.2 Noise Statistics
As noise characteristics are necessary to represent received the data set, noise
is measured 150 times for frequencies over the entire 1Hz  24kHz band. The noise
distribution at each frequency point appears to be approximately Gaussian. The
Gaussian assumption is confirmed by measuring the noise again this time 1000 times
over the 1Hz to 100Hz range. The noise distribution at 1Hz and 100Hz based on
the second measurement is shown in Fig. 5.1. Important observations are (i) noise
is complex Gaussian, (ii) noise variance is frequency dependent and decreases with
increasing frequency, and (iii) the variances of the real and imaginary parts at each
frequency are approximately equal.
64
?0.6 ?0.4 ?0.2 0 0.2 0.4 0.60
20
40
60
80
100
Noise value (mV)
Number of Occurences
Real
Imag1 Hz
(a)
?0.1 ?0.05 0 0.05 0.10
20
40
60
80
100
120
Noise value (mV)
Number of Occurences
Real
Imag100 Hz
(b)
Figure 5.1: Noise distribution at (a) 1Hz and (b) 100Hz
5.3 Discrimination Problem
Measured EMI responses of the twelve cylinders shown in Figure 4.1 were used
for statistical analysis. Measurements taken with 50 averages provide high SNR data
and forms the target library data set. Noise is added to the library data set in order
to represent the received data set.
The received signal (or response), r(f) is complex and is represented as
r(f) = yi(f) +e(f) i = 1,2,...,N (5.1)
where yi(f) is the expected response of the ith cylinder and e(f) is noise. As the data
is not continuous and is obtained for M discrete frequencies, (5.1) can be written as
rj = yij +ej i = 1,2,...,N
j = 1,2,...,M (5.2)
65
where ej ?NC(0,?2j) as explained in section 5.2. For simplicity, ej?s are assumed to
be independent which implies that the rj?s are also independent.
Let error, zj be defined as
zj = rj ?yi0j i0 = 1,2,...,N
j = 1,2,...,M (5.3)
where
zj =
?
??
??
ej i = i0
(yij ?yi0j) +ej i negationslash= i0
(5.4)
And, the discrimination problem can be represented as a binary hypothesis prob
lem where z is an observation, and alternate and null hypotheses are represented by
H0 : Different target (i negationslash= i0)
H1 : Same target (i = i0) (5.5)
which is analogous to the ?no target? (null) and ?target? (alternate) hypotheses in a
radar detection problem.
Three error functions are evaluated as a statistic for the decision rule involving
the hypotheses defined in equation (5.5).
5.3.1 Square of Mean Error (SME)
According to a variant of the central limit theorem (CLT) [63], if Y1, ..., Yn,
are n independent random variables each with probability density function Pk(xk),
mean ?k and variance ?2k, the distribution of sample mean of random variables (i.e.,
66
1
n
summationtextn
k=1 Yk) rapidly approaches Gaussian distribution with a mean ? =
1
n
summationtextn
k=1 ?k
and a variance ?2 = 1n summationtextnk=1 ?2k as n ? ?. Therefore, if Xi = 1M summationtextMj=1 zj, then by
the central limit theorem
Xi CLT?
??
?
??
?NC(0,?2) i = i0
?NC(mi,?2) i negationslash= i0
(5.6)
where the variance ?2 and mean mi are given by
?2 = 1M
Msummationdisplay
j=1
?2j
mi = 1M
Msummationdisplay
j=1
(yij ?yi0j)
If a test target ?i0 ( ?i0 = 1,2,...,N) is picked and X?i0 is calculated, then 2X?i0
2
?2 is
X2(2) (central chisquare function with two degrees of freedom) for i0 = ?i0. The test
now can be defined as
2X?i02
?2
H0
greaterlessequal
H1
? (5.7)
where ? is the threshold.
5.3.2 Mean Squared Error (MSE)
If Xi is defined as a sample mean of zj2 instead of a sample mean of zj as in
section 5.3.1, i.e., if Xi = 1/M summationtextMj=1zj2, then again by central limit theorem,
Xi CLT?
?
??
??
?N(?2,V0) i = i0
?N(mi,V1) i negationslash= i0
(5.8)
67
where
?2 = 1M
Msummationdisplay
j=1
?2j
mi = 1M
Msummationdisplay
j=1
(yij ?yi0j2) mi negationslash= ?2
V0 = 1M
Msummationdisplay
j=1
?2ej2
V1 = 1M
Msummationdisplay
j=1
(?2ej2 + 4(yij ?yi0j)2?2j)
Therefore, if a test target ?i0 ( ?i0 = 1,2,...,N) is picked and X?i0 is calculated, then
X?i0??2?
V0 ?N(0,1) (normal distribution). Hence, the test can be written as
X?i0 ??2?
V0
H0
greaterlessequal
H1
? (5.9)
5.3.3 ErrortoNoise Ratio (ENR)
If z = [z1,z2,...,zM] and x = [Re(z),Im(z)]T, then a covariance matrix is defined
as ? = diag(?2x) and the statistic for this test is defined as xT??1x which can also be
written as summationtext2Mj=1 x2j?2
j
. The test in this case can be written as
xT??1x
H0
greaterlessequal
H1
? (5.10)
where ? is the threshold. Note that xT??1x has been used as a discriminant func
tion for multivariate binary hypothesis problems [65] and multiple hypothesis prob
lems [29].
The distributions of the three test statistics are presented in Figure 5.2.
68
0 1 2 3 4 5 6
x 10?10
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Distribution
Square of Mean Error
(a)
0 0.5 1 1.5 2
x 10?8
0
0.02
0.04
0.06
0.08
0.1
Mean Square Error
Distribution
(b)
0 0.5 1 1.5 2 2.50
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Error to Noise Ratio
Distribution
(c)
Figure 5.2: Distribution of test statistics (a) SME (b) MSE and (c) ENR
The expression for zj in equation (5.3) is valid only if the target position is known.
However, as the target depth is unknown, a series of measurements with the targets
at various depths were performed, and the normalized responses were found to be the
same. Therefore, to mitigate uncertainty due to the target depth, the received signal
was normalized, and the new expression for rj is given as
rj = yij2(y
i)qp
+ej i = 1,2,...,N
j = 1,2,...,M (5.11)
69
where (yi)qp is the quadrature peak. Then zj is given by
zj = rj ? yij2(y
i)qp
i = 1,2,...,N
j = 1,2,...,M (5.12)
Using normalized data changes the means and variances of the abovementioned three
methods, namely SME, MSE and ENR, but the decision rules in equations (5.7), (5.9)
and (5.10) are still valid.
As shown in Figure 5.1, the noise variance is frequency dependent. So, signal
tonoise ratio (SNR) is defined at the quadrature peak and is given by
SNR (dB) = 10log10 (yi)
2
qp
?2qp (5.13)
Figure 5.3 shows the performance of SME, MSE and ENR over restricted (30Hz
to 24kHz) and extended (1Hz to 24kHz) bands in the presence of 22dB SNR. ENR
performs better than other two methods because actual noise variance is included in
ENR unlike mean of variances in SME and MSE.
As ENR performs the best of three methods, it is used to analyze the discrimina
tion performance of the two frequency bands at different noise levels and is presented
in Fig. 5.4. It can be noticed that for SNR above approximately 18dB, 1Hz to 24kHz
band gives perfect performance and neither band performs well below 2dB. At a SNR
of 8dB, for a probability of false alarm of 0.2, the probability of correct identification
for 30Hz to 24kHz band is 0.6 and that for 1Hz to 24kHz is 0.9  improvement by a
factor of 1.5.
70
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of False Alarm
Probability of Detection
1 Hz ? 24 kHz (MENR)
30 Hz ? 24 kHz (MENR)
1 Hz ? 24 kHz (SME)
30 Hz ? 24 kHz (SME)
1 Hz ? 24 kHz (MSE)
30 Hz ? 24 kHz (MSE)
Figure 5.3: Performance of SME, MSE and ENR in for 22dB SNR over two frequency
bands 30Hz to 24kHz and 1Hz to 24kHz
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
Probability of False Alarm
Probability of Correct Identification
1Hz?24kHz (18dB)
30Hz?24kHz (18dB)
1Hz?24kHz (8dB)
30Hz?24kHz (8dB)
1Hz?24kHz (?2dB)
30Hz?24kHz (?2dB)
Figure 5.4: Comparison of the performance of 30Hz to 24kHz data and 1Hz to 24kHz
data in identifying the cylinder correctly for three SNRs
71
5.4 Summary
In this chapter, the discrimination problem is defined as a binary hypothesis
problem and noise characteristics are presented. Performance of three test statistics,
SME, MSE and ENR is evaluated which shows that ENR performs the best due to
the knowledge of noise. Performance of ENR for 8dB SNR shows that extended band
performs 1.5 times better than the restricted band for 0.2 probability of false alarm.
72
Chapter 6
Conclusions
Even though there is a considerable (factor of 1.5) performance gain by using
ELF band in CW systems, there is a price to pay for this improvement. It is time
consuming to obtain very low frequency target data especially when many averages
are required to achieve adequate SNR. For example, 100 averages at 1Hz will require
at least 100 seconds which would also result in averaging over different orientations
if the sensor is moving with respect to the target under test. One recognizes imme
diately, that it is not practical to operate a CW EMI system as a survey (towed or
vehicular) sensor at very low frequencies. Alternatively, static measurements at pre
defined locations would eliminate sensormotion noise as well as sensor location and
orientation uncertainties [27]. In this ?cued? approach, target locations would be
marked using another detection technique (e.g. a simple totalfield magnetometer)
and the low frequency CW EMI system would be deployed to these known target
locations for classification. An alternative deployment strategy is to use an EMI
sensor operating in detection mode and shift to classification mode when a target is
detected. This process will obviously lengthen the survey period but does not require
intermediate marking for target reacquisition.
The research efforts presented is a first step towards showing the effectiveness
of extremely low frequency data in discriminating the targets. The following are
some suggestions for future research. An entire target response is used for statistical
73
analysis in Chapter 5. The work can be extended to extract target features like
quadrature peak frequency, peak width, low frequency asymptote, and 3dB frequency
that might serve to efficiently discriminate among the targets. Besides, the data used
in discrimination are from vertically oriented (axially excited) objects whereas in
reality, the buried UXO are arbitrarily oriented. Therefore, ELF data for different
orientations of the target should be studied to extract orientation dependent and
independent parameters. The extracted parameters can be analyzed statistically to
present a quantitative measure of discrimination improvement provided by adding
ELF data. A similar analysis in timedomain by extracting features like powerlaw
to exponential transition time and decay rate should also be investigated.
74
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