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Millimeter-Wave Imaging of Person-Borne Improvised Explosive Devices

A Thesis Presented by

Justin Leigh Fernandes

to

The Department of Electrical and Computer Engineering

In partial fulfillment of the requirements for the degree of

Master of Science

in

Electrical Engineering

In the field of

Electromagnetics

Northeastern University Boston, Massachusetts

January 2010

Acknowledgments

I would like to first thank my family for their support through all my years at Northeastern. Without

their guidance and support I would not have successfully completed this Master’s thesis. I would like to

acknowledge my academic advisor Professor Carey M. Rappaport, his wisdom and technical insight were

extremely helpful and thought provoking. I would like to acknowledge Richard Obermeier for his help in

writing many of the codes necessary to perform the analyses in this thesis. I would like to acknowledge

Manfred Haegelen for his technical and experimental guidance in performing standoff detection experi-

ments at the Fraunhofer Institute for High Frequency Physics. Lastly, I would like to acknowledge Dr.

David M. Sheen for sharing his technical and experimental knowledge in portal based imaging while I

was a student at Pacific Northwest National Laboratory.

I would also like to acknowledge the Gordon Center for Subsurface Sensing and Imaging, their facili-

ties and resources proved to be very helpful in supporting students like myself pursue research in sensing

and imaging technologies. The Department of Homeland Security’s Awareness and Localization of Ex-

plosive Related Threats (ALERT) Center of Excellence funded my research assistant fellowships and gave

me the opportunity network and interact with experts in the field of millimeter wave imaging.

Many thanks to BΓE , Northeastern University’s Engineering fraternity. Thanks for lending a free

place to stay and lots of support in the final days of finishing my thesis.

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1 First Order Scalar Diffraction Tomography 5

1.1 Scalar Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Solving the Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Synthetic Aperture Radar Focusing Techniques 9

2.1 Generalized Synthetic Aperture Focusing Technique (GSAFT) . . . . . . . . . . . . . . . 9

2.2 1D Rectilinear Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Rectilinear Fourier Based Inversion Theory . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 Implementing Rectilinear Fourier Based Inversion . . . . . . . . . . . . . . . . . 12

2.3 Circular Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.1 Circular Fourier Based Inversion Theory . . . . . . . . . . . . . . . . . . . . . . 18

2.3.2 Implementing the Circular Fourier Based Inversion . . . . . . . . . . . . . . . . . 19

2.4 FFT Based Focusing vs GSAFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 LFMCW Signals and Signal Sampling 28

3.1 Time Domain Representation of: Real, Complex, and Analytic FMCW signals . . . . . . . 28

3.1.1 The Real Transmitted Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1.2 The Analaytic Transmitted Signal and Complex Envelope . . . . . . . . . . . . . 29

3.2 Frequency Domain Representation of: Real, Complex, and Analytic FMCW Transmitted

Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 Obtaining Received Signal in Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.1 Obtaining Intermediate Frequency of Ideal Point Target Channel . . . . . . . . . . 33

2

3.3.2 Non-Ideal Channel Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.4 Resolution and Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4.1 Spatial Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4.2 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5 Time-Bandwidth Product (TBP) and Resolution in FMCW Signals . . . . . . . . . . . . 40

3.5.1 Ripple in the Complex Envelope Spectrum . . . . . . . . . . . . . . . . . . . . . 42

3.5.2 Reducing Out-of-Band Spectral Power . . . . . . . . . . . . . . . . . . . . . . . 44

4 Finite Difference Frequency Domain Scattered Field Analysis 46

4.1 Using FDFD to Simulate MMW Scattering Off of Human Bodies . . . . . . . . . . . . . 46

4.1.1 Importance of Using a Full-Wave Analysis For Calculating Scattered Fields . . . . 46

4.2 FDFD Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.3 Description of SAR system simulation using forward model . . . . . . . . . . . . . . . . 52

4.4 FDFD System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.4.1 Measurement vs. FDFD Data Acquisition Times . . . . . . . . . . . . . . . . . . 59

5 Portal Scanning and FDFD Validation 61

5.1 Rectilinear Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.2 Cylindrical Scan Imaging Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2.1 Measurement and Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2.2 Comparing Focused Images Using Data From FDFD Simulation and Actual Mea-

surements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.3 Final Images Obtained with Both Simulated and Experimental Data . . . . . . . . . . . . 89

5.4 Comparing Focused Images Using Measured Data From Nominal Targets with Anomalous

Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.4.1 Dielectric Measurements of Ballistic Gelatin Used For Human Tissue Simulant . . 96

5.4.2 Image Reconstructions of Ballistics Gelatin Cylinders . . . . . . . . . . . . . . . 99

5.4.3 Reconstructions of Ballistic Gelatin Cylinders with Denim Cloth . . . . . . . . . . 100

6 New Multistatic Sensing Configuration 104

7 New Method of Displaying Imaging Data 108

8 Two Dimensional Standoff Scanning 111

8.1 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

9 Image Processing Algorithm for Standoff PBIED Detection 116

10 Summary and Future Work 123

Bibliography 125

List of Figures 130

Abstract

With the recent rise in casualties and threat of casulties resulting from person-borne improvised explo-

sive devices (PBIEDs) there is an urgent need for building imaging systems to perform standoff and portal

detection of such threats. An optimum system that fulfills the requirements of PBIED detection must be

low cost and have a high probability of detection with low probability of false alarm. A standoff detec-

tion system must also be portable while a portal imaging system can be stationary. Currently there are a

variety of modalities being researched to perform standoff detection of PBIED’s including: backscatter X-

ray imaging, infrared imaging, optical detection, terahertz imaging, video analytics, and millimeter-wave

(MMW) imaging. MMW imaging is a perferable modality for full body imaging of PBIEDs for many

reasons. MMWs can propagate through the atmosphere and clothing with very little attenuation, while at

the same time do not cause damage to human skin tissue. MMWs are small enough to build physical and

synthetic aperture systems small enough to have a realistic physical system footprint while also provid-

ing excellent cross-range resolution. Present technology is available to generate very wideband coherent

MMW signals, which can be used to generate very high resolution images of targets at both standoff (> 15

meters) and portal (< 1 meter) distances.

Due to the large expense of building MMW imaging systems there is a large need to accurately model

such systems numerically. With a forward model complex geometries, novel sensor and system configura-

tions can be tested with minimal cost and overhead. Models also allow researchers to carry out extremely

precise and repeatable analyses that have the ability to give extraordinary insight to scattering processes.

The finite difference method in the frequency domain (FDFD) is a forward model which yields itself as

an excellent method to analyze the scattering at MMW frequencies. However, due to the matrix inversion

method of solving, it is not a realistic method for simulating 3D body geometries.

In this thesis two major aspects associated with MMW imaging are discussed: simulating the scat-

tering of MMWs with a forward model and reconstructing MMW field data from both simulated and

experimental continuous wave (CW) radar systems (both portal and standoff scenarios).

Introduction

MMW’s are a proven modality for use in remote sensing applications of whole body imaging for portal

based scenarios [6] and standoff scenarios [8]. MMWs sense reflections associated with changes in con-

stituitive parameters in space. For the application of non-invasive personnel screening and surveillance,

MMWs lend themselves as an excellent modality for many reasons including: they have the ability to

propagate through the atmosphere and clothing with very little attenuation; they are non-ionizing thus do

not cause damage to human skin tissue; they are small enough to build physical and synthetic aperture

systems with realistic physical system footprints; they provide excellent cross-range resolution with rel-

atively small physical or synthetic apertures; present technology is available to generate very wideband

coherent MMW signals, which results in very high resolution images at both standoff (> 15 meters) and

portal (< 1 meter) distances; and with current computing technology MMW scattering can be efficiently

modeled with extremely accurate full-wave forward models.

In the application of full body imaging in portal scenarios Sheen et al have developed an efficient and

effective means to perform concealed weapon detection. However, higher order scattering effects due to

complex imaging geometries lead to the appearance of artifacts in the reconstruction algorithms currently

being employed in [6]. The use of different polarizations has been proposed in [7] to avoid higher or-

der imaging artifacts, however, this would significantly increase the cost of the system due to increased

hardware complexity. A more effective means of avoiding the appearance of higher-order imaging arti-

facts is presented in this thesis. It is proposed that a multistatic measurement configuration may overcome

many problems associated with the current monostatic measurement systems deployed by L3 Commu-

nications/Safeview. These problems include higher-order scattering effects and specular reflections not

being captured by the system.

When building a MMW imaging system there are requirements dictated by certain factors that one

must take into consideration. The geometries of the targets being imaged dictate the necessary range and

cross-range resolution. Certain complex targets may also be hard to image with a monostatic configuration.

For example, a target with many surfaces not normal to direction of illumination may reflect signals in a

manner that a multistatic system would sense better than a monostatic system. This will be explored in

this thesis.

1

With the recent increase in personal computing power, forward models such as FDFD have proven

to give tremendous insight into the scattering processes associated with full body imaging. With this

type of knowledge new sensor configurations can be simulated without the extremely high cost and risk

associated with building such imaging systems. As is shown in Chapter 6, multistatic sensor configurations

have increased system resolution in range and cross-range, increased dynamic range of image power,

and reduced the system susceptibility to specular reflections. Although Fourier techniques have been

developed by [9] for bistatic systems, they fail when the transmit and received angles are very large, such

as in the case of the sensor configuration simulated in Chapter 6. It is also very interesting to point out the

extremely large spatial frequency bandwidth obtained by the multistatic sensor configuration with only a

single frequency.

The benefits of using MMW’s for the portal imaging scenario, high range and cross range resolution

and ability to penetrate clothing, are also a true for the standoff (>15 meters) imaging scenario. In addition

to these benefits, the relatively large wavelength of MMWs, compared to optical and infrared waves, allow

for propagation through various atmospheric states such as dust and/or fog with very little attenuation. For

this reason they are being used to assist helicopters landing in brown-out conditions [13].

One of the main difficulties associated with standoff detection is target movement. Target movement

in standoff imaging scenarios, unlike in portal based imaging where targets are assumed to be relatively

stationary, significantly impairs the ability to perform coherent image reconstruction of signals assumed to

be coming from stationary targets. The reason target movement is not a problem in portal based imaging

scenarios is target cooperation is assumed. Standoff detection systems are expected to work at larger

distances in a personnel surveillance scenario. This is as opposed to a portal based personnel screening

scenario where target movement can be controlled. Therefore, in standoff detection system design, scan

time must be small enough such that target movement does not affect imaging. This can be obtained by

limiting target movement and allowing longer scan times, or simply decreasing scan time.

The next main difficulty associated with the standoff imaging scenario is lack of cross-range band-

width. The lack of cross-range bandwidth implies two different problems. The first is simply the lack of

cross-range resolution. The second difficulty is similar to the appearance of higher order imaging artifacts

in the portal imaging scenario, however, unlike portal based scenarios, where 360o of target information is

obtained, imaging artifacts due to higher order scattering from complex targets have a larger contribution

2

to final reconstructed images. In the portal based scenario, due to the spatial variance of higher order

scattering, when measurements are made over complete 360o azimuth, higher order effects are mostly

averaged out of the final reconstructed image.

One would ask whether it is really necessary to perform standoff imaging as opposed to simply standoff

detection. The reason imaging is necessary is the lack of discovery of a nominal innocent target response

to any type of remote sensing system. For MMWs, target shape is the dominating contribution to the

scattering process. This has been shown in both a forward model and through experimentation. The 2D

FDFD forward model has proven to give great insight into the scattering processes in 2D geometries,

however, a 3D model is necessary to realistically simulate a full-body scattering process. In the standoff

imaging scenario researched in this thesis, it has been found that reflections from the entire body cause

images generated from a 2D imaging system to be very difficult to interpret. Therefore more spatial

bandwidth in elevation is needed to separate target responses in elevation and thus perform full body

imaging.

Humans and possible threat objects take on a virtually infinite number of shapes and sizes. Therefore

a neural network approach of characterizing innocent and threat target responses to perform target classi-

fication has yet to be performed. At the current state of technology and knowledge, only humans have the

ability to distinguish threat targets from non-threats. Even in the portal imaging scenario researchers have

yet to produce a means to perform automatic threat detection. Therefore until a standoff imaging system

has the ability to perform adequate target classification without a human in the loop, automatic standoff

detection will not be possible.

This thesis will discuss millimeter-wave imaging and its applications to portal and standoff imaging

scenarios in the following manner. Chapter 1 gives background information on the foundations of diffrac-

tion tomography which is the basis of the imaging process used in both portal and standoff MMW imaging

systems. Chapter 2 discusses 3 reconstruction techniques. The Fourier based reconstruction techniques

are valid for near field and far field measurements, thus do not rely on uniform plane wave illumination.

The algorithms were first devolped by [9] and extended to three dimensions by [6]. The third reconstruc-

tion technique is based on the generalized synthetic aperture focusing technique (GSAFT) first published

by [14]. This algorithm uses a first order Born approximation to back propagate received fields to recon-

struct images. The two Fourier techniques are methods that evaluate the Born approximation with use of

3

polar reformatting and the Fast Fourier Transform. Polar reformatting is necessary due to target Motion

Through Resolution Cells (MTRC) [36] caused by the large synthetic aperture size used and fine resolu-

tion required of the imaging system. [37] showed that raw data in a circular monostatic SAR (Synthetic

Aperture Radar) system represents spatial frequency samples on a polar grid. Reformatting from a polar

to rectilinear grid allows the use of the Fast Fourier Transform (FFT) to compress measured signal phase

histories. [15] has developed a Fourier based reconstruction algorithm without the computationally inten-

sive interpolation step with the use of frequency scaling. The reason Fourier based imaging techniques

have been developed is because the number of frequency samples associated with a SAR imaging system

is extremely large. As outlined in [14] back propagating all measured frequency samples for all focusing

positions and receiving positions using the GSAFT is computationally expensive. Using FFTs the order

of computation may be significantly reduced.

Chapter 3 discusses modeling an linear frequency modulated continuous wave (LFMCW) communi-

cation system. The use of analytic representations of the real LFMCW signals is also discussed. Sampling

and resolution fundamentals of remote sensing in the frequency domain are derived in chapter 3. Chapter

4 discusses modeling the scattering of MMWs from various two dimensional geometries using the finite

difference frequency domain scattered field analysis. Other radar simulators such as [30] and [5] do not

use full wave forward models and may fail to model certain types of higher order scattering effects.

Chapter 5 validates the FDFD model with measured data in a portal scanning scenario (distance from

sensor to target 1 meter). Both rectilinear and circular scanning system measurements and simulations

are performed. The methods Chapter 6 presents a new sensing system for the portal detection scenario.

A multistatic system is simulated and images are reconstructed. This chapter discusses the capabilities of

obtaining very large spatial bandwidth with multistatic systems.

Chapter 7 presents a new method of displaying reconstructed data. Current body imaging systems, [6]

use a simple maximum value projection of 3D data to produce a 2D image. This simplistic method often

does not show artifacts due to possible threat targets. Chapter 8 describes the results of a measurement

campaign to perform standoff detection (distance from sensor to target 10 meters) of PBIEDs. This chapter

outlines an automatic threat detection algorithm used to process Fourier based reconstructed images from

data measured in the experiment. Chapter 9 shows the results of new imaging and image processing

algorithms to help classify images obtained in the standoff detection scanning scenarios.

4

Chapter 1

First Order Scalar Diffraction Tomography

The use of scalar diffraction theory reduces the complexity of inverting measured signals backscattered

from objects of interest. The use of first order scalar diffraction theory requires the following assumptions.

• There is negligible coupling between electric and magnetic fields and one equation can be used to

approximate the behavior of the electric and magnetic fields.

• The effects of multipath and mutual interaction between scatters can be neglected, thus the total field

interrogating the objects of interest can be approximated with only the incident field.

• Diffraction regions and scatterers are large relative to wavelength.

1.1 Scalar Wave Equation

Scalar wave theory is a simplification of vector wave theory. The fundamentals of vector wave theory start

with Maxwell’s equations. Maxwell’s equations in a source free medium are defined as:

∇× ~E = −µ∂~H

∂t(1.1)

∇× ~H = ε∂ ~E

∂t(1.2)

∇ · ε ~E = 0 (1.3)

∇ · µ ~H = 0 (1.4)

5

µ and ε are the magnetic permability and electric permittivity. × is the vector cross product operator.

· is the vector dot product operater. ∇ = ∂∂xx+ ∂

∂yy + ∂

∂zz. H is the magnetic field. E is the electric field.

The wave equation is obtained by using the vector identity

∇× (∇× ~A) = ∇(∇ · ~A)−∇2 ~A

and applying the curl operation to the left and right sides of 1.1.

(∇2 + n(r)2

c2∂2

∂t2) ~E(r) = 0 (1.5)

where c = 1√µ0ε0

and µ0 and ε0 are the magnetic permability and electric permittivity of free space.

n(r) = √εrµr where εr and µr are the relative permittivity and permeablity. The Hemoltz equation for

source free peicewise inhomogeneous medium is obtained by taking the Fourier Transform of 1.5.

(∇2 + k(r)2) ~E(r) = 0. (1.6)

where k(r) represents the wavenumber of the medium as a function of position r, defined as:

k(r) = k0n(r) = k0(1 + nδ(r)) (1.7)

where k0 = ω√µ0ε0, ω is the radial frequency and nδ(r) =

√(µrεr) − 1, the difference between the

index of refraction and the free space index of refraction.

If the assumptions specified previously are valid then 1.6 is obeyed by all components of the electric

and magnetic fields and a single general equation can be used to describe the behavior of all field compo-

nents [17]. This is the reduction from vector to scalar theory. In this paper the variable for this field value

will be S(r).

1.2 Solving the Wave Equation

To solve for the scattered fields of an object due to some incident field, the following formulation can be

used.

6

S(r) = S0(r) + Ss(r) (1.8)

Which states that the total field is the summation of the incident field with the scattered field. Where

the incident field in free space is the solution to:

(∇2 + k20)S0(r) = 0 (1.9)

Substituting 1.8 and 1.7 into 1.6 one obtains:

(∇2 + k20)(S0(r) + Ss(r)) = −O(r)S(r)

where O(r) can be defined in terms of the index of refraction of the medium by substituting 1.7 into

1.6:

O(r) = −(2k20nδ(r)− k2

0n2δ) (1.10)

and since S0(r) obeys 1.9, the scattered field is the solution to the following:

(∇2 + k20)Ss(r) = −S(r)O(r) (1.11)

Where S(r) on the right side of 1.11 is approximated as the incident field S0(r).

For a 3 dimensional point source in free space the solution to the following scalar Helmotz equation:

(∇2 + k20)G(r, r′) = −δ(r − r′)

is defined in spherical coordinates as the radiation of a point source in free space:

G(r, r′) = G(|r − r′|) = ejk|r−r′|

4π|r − r′|

Such that the scattered field due to a point source can be defined as:

Ss(r) =∫G(r − r′)δ(r′)dr′

7

For a non-ideal point scatterer, the scattered can be approximated as:

Ss(r) =∫G(r − r′)O(r′)S(r′)dr′

Where, by use of the Born approximation, the total field S(r′) in is approximated as only the incident

field S0(r′), thus:

Ss(r) =∫G(r − r′)O(r′)S0(r′)dr′

the scattered field is simply a summation of point sources multiplied by a Greens function. When

discretized:

Ss(rn) =∑m

G(rn − rm)O(rm)S0(rm) (1.12)

Ss(rn) represents the scattered field at position rn due to a collection of point sources at positions rm

with magnitude and phase O(rm)S0(rm) the product of the incident field with the object function. The

scattered fields Ss(rn) will be referred to as the received fields at some finite sized aperture in this thesis.

The product of the incident field with the object function will be defined as:

U(rm) = O(rm)S0(rm) (1.13)

8

Chapter 2

Synthetic Aperture Radar Focusing Techniques

The general method for focusing received fields Ss(rn) to certain regions of interest can be performed

with a brute force method of simply back propagating the fields with the conjugate of the Greens function

specified in Chapter 1. This method is described in the following section.

2.1 Generalized Synthetic Aperture Focusing Technique (GSAFT)

The general back propagation formula used to focus the received field, Ss(rn, rt, kq), for a general bistatic

system with a single transmitter at position rt =< xt, yt >, receiver at position rn =< xn, yn >, and at

operating spatial frequency kq to a point in space rm =< xm, ym > is, (neglecting the change in amplitude

due to distance) [14]:

U(rm, rt) =Q∑q=1

N∑n=1

Ss(rn, rt, kq)e−jkqRn,me−jkqRm,t (2.1)

where kq = 2πfq√µ0ε0 and (xm, ym) are the coordinates received fields are focused to,Rm,t = |rm−rt| =√

(xm − xt)2 + (ym − yt)2 is the distance between transmitter and focal point, and Rn,m = |rn − rm| =√(xn − xm)2 + (yn − ym)2 is the distance between receiver and focal point.

Considering the heavy computational load of numerically evaluating 2.1, some Fourier based imaging

techniques have been developed, including [9] and [6] which are outlined in sections 2.3 and 2.2. With

the recent rise in availability of inexpensive computer memory and Graphics Processing Unit (GPU) com-

puting, 2.1 can be vectorized and evaluated exactly without any approximations or interpolations at very

9

high speeds. The GSAFT does not rely on uniform spatial sampling which can alleviate previous stringent

requirements on sensor hardware due to increased computational power available for image processing.

In addition GSAFT can be crafted to only image certain regions of interest. In the application of full body

imaging, for example, one does not need to image inside of the human body. With thoughtful placement of

sensors and priori knowledge of approximate target location, a minimum number of samples and imaging

pixels can be used to obtain high resolution images limited only by the diffraction limit. An example of an

image produced by the GSAFT and a comparison of the GSAFT with Fourier-based imaging techniques

is shown in section 2.4

2.2 1D Rectilinear Scan

Figure 2.1: Rectilinear Scan: Synthetic aperture width,L = 1 meters; target range, R = 1.09 meters

Figure 2.2: Picture of metal can, 4"diameter.

This section discusses the method of applying a Fourier based focusing technique to data measured in

a rectilinear domain. This method was first developed in two dimensions by [9] and later applied to three

dimensions by [6]. Figure 2.1 depicts the geometry of the measurement setup. Figure 2.2 is a top view

picture of the target measured in the following description of the Fourier based reconstruction. The first

10

subsection will describe the theory of implementing the rectilinear Fourier based inversion. The second

subsection will described each step of implementing the algorithm.

2.2.1 Rectilinear Fourier Based Inversion Theory

The basis of this reconstruction technique starts with modifying the discrete equation 1.12 to a continuous

form and converting to a rectilinear measurement grid. Attenuation in signal amplitude due to distance is

neglected. Figure 2.1 shows the measurement configuration.

Ss(ξ, ω) =∫ ∫

s(x, z)ej2k√

(x−ξ)2+(z−Z)2dxdz (2.2)

Where s(x, y) is represents the product of the object function with the incident field, this is represented

as U(rm) in equation 1.13. The exponential represents the Greens function, where the factor of 2k instead

of k is used to denote the two way travel distance of the signal. This is true for a monostatic measurement

setup. S(ξ, ω) is the received signal, where ξ is receiver position and ω is the angular frequency of the

transmitted signal. See Figure 2.3 for example an LFMCW intermediate frequency signal resulting from

a coffee can, shown in Figure 2.2.

The spherical wave term, ej2k√

(x−ξ)2+(z−Z)2 , in equation 2.2 can be represented by a decomposition

of uniform plane waves in the following form:

∫e−jkξ(x−ξ)−jkz(z−Z)dkξ (2.3)

where kξ and kz represent the spatial wave numbers in the ξ and z directions respectively. Using this

relationship, equation 2.2 can be expressed as:

Ss(ξ, ω) =∫ [ ∫ ∫

s(x, z)e−jkξx−jkzzdxdz]ejkξξ+jkzZdkξ

where kξ and ξ are the spatial frequency and spatial variables associated with Ss(ξ, ω) and kx and x are

the spatial frequency and spatial variables associated with s(x, z). In the case of this imaging algorithm

kξ = kx and x = ξ. The rest of this paper will denote the cross-range spatial and spatial frequency grids

as x and kx respectively.

11

Using the following relationship [9]:

S(kx, kz) =∫ ∫

s(x, z)e−jkxx−jkzzdxdz

Ss(x, ω) can be expressed as:

Ss(x, ω) = F−1kxS(kx, kz)ejkzZ (2.4)

where kz =√

(2k)2 − k2x. Based on equation 2.4, the following relationship is necessary to begin the

inversion process:

Ss(kx, ω)e−j√

(2k)2−k2xZ = S(kx, kz) (2.5)

where the relationship between kz and ω is kz =√

(2ωc)2 − k2

x. The reason this notation is acceptable

is that by demodulating Ss(kx, ω) with the exponential in equation 2.5, the function is now in the spatial

frequency domain kz of the imaging space z. The function Ss(kx, ω) was already in the cross-range

domain, or x and kx space. The reason for this is the signal Ss(x, ω) is within the same limits of the

cross-range imaging grid, but different range position. The x domain is denoted as ξ in the beginning of

this paper to distinguish between the received x position and the imaging x position, however they are

both in the same cross-range imaging domain.

The final equation to describe the inversion is:

s(x, z) = F−1kxF−1

kzFxSs(x, ω)e−jkzZ

2.2.2 Implementing Rectilinear Fourier Based Inversion

This subsection describes in detail the exact steps of implementing the inversion derived above. The first

step in this reconstruction algorithm is to define an imaging grid. In the x direction, which is the ξ direction

in the receiver domain, x = −X2 : ∆x : X

2 where ∆x = XNx

, Nx are the number of spatial samples and

X is the width of the grid. In the z direction z = −Z2 : ∆z : Z

2 where ∆Z = ZNz

, Nz are the number of

spatial samples and Z is the depth of the imaging grid. Based on the imaging grids defined, x and z, the

12

corresponding spatial frequency grids can be defined:

kx = cos(arctan(xczc

))(kc −∆k) + [−kx max : ∆kx : kx max]

where kc = 4π(f0+B2 )

c, f0 starting frequency of transmitted signal, ∆k = 2πB

cand kx max = 2π

2∆x

kz = sin(arctan(xczc

))(kc −∆k) + [−kz max : ∆kz : kz max]

where kz max = 2π2∆z

Figure 2.3: Real portion of received field, Ss(ξ, ω) from coffee can, function of ξ, cross-range receiverposition, and ω angular frequency

The purpose of the next steps of the imaging algorithm is to demodulate the measured data to a low

enough spatial frequency so that the object spectrum can be interpolated to the spatial frequency of the

imaging grid. Taking the forward spatial Fourier Transform along ξ of the received signal we obtain:

Ss(kξ, ω) = FξSs(ξ, ω) (2.6)

As is shown in figure 2.3. Since the imaging grid, denoted as x, is equal to the receiver position grid

ξ and the spatial frequency imaging grid, kx, is also equal to that of the receiver grid, kξ, the spatial and

13

spatial frequency grids in the lateral direction will be denoted as x and kx respectively.

Figure 2.4: Real portion of received field decompressed in cross-range, Ss(kx, ω) from coffee can, functionof spatial frequency kx, and ω angular frequency

Now that the signal is in the frequency domain, spatially in the x direction and temporally in the ω

direction Ss(kx, ω) is then demodulated by the following phase function e−jkz = e−j√

(2k)2−k2x , as is shown

in Figure 2.4.

S(kx, kz) = Ss(kx, ω)e−j√

(2k)2−k2xZ (2.7)

Where k = ω√µ0ε0. ω is the derivative with respect to time of the transmitted radial phase. kx is the

spatial frequency matrix defined previously.

Due to the Fourier relationship between the spatial and spatial frequency domain, demodulation in

spatial frequency, is analogous to shifting the image in space. The next step is to interpolate S(kx, kz)

to a uniformly sampled rectangular spatial frequency imaging grid. Since the signal is already uniformly

spaced in the x direction, and thus sampled uniformly in kx, the interpolation only needs to be performed

along the z or kz direction.

The signal S(kx, kz) represents the sampled spatial frequencies associated with angular frequencies ω,

14

Figure 2.5: Real portion of received field decompressed in cross-range and demodulated in angular fre-quency, S(kx, kz) from coffee can

the derivative of the angular phase of the transmitted signal, defined as:

ω = 2π(f0 + αt) = d

dt

[2π(f0t+ α

2 t2)]

where α = BT

, B, and T are the transmitted signal frequency sweep rate, bandwidth and modulation

period respectively.

S(kx, kz), as is shown in 2.5, needs to be interpolated to the desired angular frequencies, ωd, defined

as:

ωd = c

2√k2x + k2

z

As is shown in Figure 2.6, S(kx, kz) can be interpolated to Si(kx, kz) via a nearest neighbor approach

where the change in index is defined as:

δind = ω0 − ωd∆ω

where ω0 = 2πf0 and ∆ω = 2πBN

and N is the number of frequency samples in S(x, ω).

15

Figure 2.6: Real portion of interpolated received field decompressed in cross-range and demodulated inangular frequency, Si(kx, kz)

To obtain the focused image Si(kx, kz) is compressed in along kx and kz via taking the inverse Fourier

transform in both directions, as is shown in Figure 2.7:

s(x, z) = F−1kxF−1

kzSi(kx, kz)

16

Figure 2.7: Power, 10log10(s(x, z)2), of focus image s(x, z) with truth data of coffee can overlaid in blue

17

2.3 Circular Scan

In this section, a circular ISAR reconstruction algorithm is described. The first subsection will describe

the theory and the second subsection will go step by step through the details of the algorithm. Each

grayscale image in Figures 2.10 through 2.13 contain a snapshot of the circular ISAR signals as they are

processed by the algorithm. Measurements were made over 450o around the target being measured. The

reason for making 450o of measurements is because the data were processed in 8 90o overlapping segments

and then superposed in magnitude. The reason for processing the data in segments is to obtain a smooth

point spread function (PSF) with highest range and cross-range resolution. If the entire spatial frequency

spectrum of a target is processed in one block the PSF contains ripples due to the two separated bands of

spatial frequencies being processed at the same time. Each of the gray scale images contains the final 90o

segment of circular ISAR processed signals.

2.3.1 Circular Fourier Based Inversion Theory

Figure 2.8 shows the system configuration. The received signal from each scatterer at point x, y will be

denoted as Ss(θ, ω). It can be expressed as:

Ss(θ, ω) =∫ ∫

s(x, y)ej2k√

(R cos(θ)−x)2+(R sin(θ)−y)2dxdy (2.8)

where according to equation 7.2.43 in [33], the behavior of the spherical wave on the RHS of 2.8 can

be approximated as a summation of plane waves in the following form:

∫ π2

−π2ej2kR cos(φ)(R cos(θ)−x)+j2kR sin(φ)(R sin(θ)−y)dφ ∀R 6= 0,∀k 6= 0 (2.9)

where φ represents the directions of the plane waves.

Inserting 2.9 into 2.8, the following representation of S(θ, ω) is obtained:

Ss(θ, ω) =∫ π

2

−π2e2kR cos(θ−φ)

∫ ∫s(x, y)ej2kR cos(φ)x+j2kR sin(φ)ydxdydφ (2.10)

where∫ ∫

s(x, y)ej2kR cos(φ)x+j2kR sin(φ)ydxdy is a fourier integral which will be denoted as:

18

S(2k cos(θ), 2k sin(θ)) = S(kx, ky) =∫ ∫

s(x, y)ej2kR cos(φ)x+j2kR sin(φ)ydxdy

which can be mapped to polar coordinates such that S(2k cos(θ), 2k sin(θ)) = Sp(θ, 2k). The follow-

ing definition will also be made:

g(θ, ω) = ej2kR cos(θ) (2.11)

Using Sp(θ, 2k) and g(θ, ω) equation 2.10 can be written in simpler form as a convolution:

Ss(θ, ω) = Sp(θ, 2k) ∗ g(θ, ω)

Using the following Fourier relationship of the convolution operator, where Fθg(θ, ω) = G(ξ, ω),

FθSp(θ, 2k) = Sp(ξ, 2k) and FθSs(θ, ω) = Ss(ξ, ω), the following is true:

Ss(ξ, ω) = G(ξ, ω)Sp(ξ, 2k)

If the amplitude components of Sp(ξ, 2k) can be neglected then the following is also true:

Sp(ξ, 2k) = Ss(ξ, ω)G∗(ξ, ω)

where G∗(ξ, ω) is the complex conjugate of G(ξ, ω). The final inversion can then be defined as:

s(x, y) = F−1kxF−1

kyF−1

ξ FθSs(θ, ω)Fθg(θ, ω)∗

2.3.2 Implementing the Circular Fourier Based Inversion

Figure 2.8 shows the measurement setup. S(θ, ω) is the received signal, where θ is receiver position in

aziumuth, and ω is the angular frequency of the transmitted signal. See Figure 2.10 for example received

signal resulting from a coffee can, shown in Figure 2.9.

The first step is to define an imaging grid. In the x direction x = −X2 : ∆x : X

2 where ∆x = XNx

, Nx

are the number of spatial samples, and X is the imaging grid width. In the y direction y = −Y2 : ∆y : Y

2

19

Figure 2.8: Circular Scan: Synthetic aperture width, 360ometers; target range, R = 1.1 meters

Figure 2.9: Picture of metal can, 4" diam-eter. Not in exact center of rotation.

where ∆y = YNy

, Ny are the number of spatial samples and Y is the depth of the imaging grid. Based on

the imaging grids defined the corresponding spatial frequency grids can be defined:

kx = cos(arctan(xcyc

))(kc −∆k) + [−kx max : ∆kx : kx max]

ky = sin(arctan(xcyc

))(kc −∆k) + [−ky max : ∆ky : ky max]

where kc = 4π(f0+B2 )

c, f0 starting frequency of transmitted signal, ∆k = 2πB

c, kx max = 2π

2∆x and

ky max = 2π2∆y

Taking the forward spatial Fourier Transform along θ of the received signal, as is shown in Figure 2.11,

we obtain:

Ss(ξ, ω) = FθSs(θ, ω) (2.12)

Sp(θ, 2k) is obtained via deomodulating Ss(ξ, ω) with the complex conjugate of G(ξ, ω) and then

taking the inverse FT with respect to ξ:

20

Figure 2.10: Real portion of received field, Ss(θ, ω) from coffee can, function of θ, azimuth receiverposition, and ω angular frequency

Figure 2.11: Real portion of received field decompressed in azimuth, Ss(ξ, ω) from coffee can, functionof a unitless "spatial angular frequency" ξ, and ω angular frequency

21

Sp(θ, 2k) = F−1ξ Ss(ξ, ω)G∗(ξ, ω)

As is shown in Figure 2.12.

Figure 2.12: Real portion of received field decompressed in azimuth and demodulated in angular fre-quency, Sp(ξ, ω) from coffee can

Demodulation in angular frequency, or spatial frequency, towards DC is analogous to shifting the

image in space closer to the origin. The next step is to interpolate Sp(θ, 2k) to a uniformly sampled rect-

angular spatial frequency imaging grid, as is shown in Figure 2.13 . Since the signal is neither uniformly

sampled in the x or y directions, the interpolation needs to be performed along both the x and y directions.

The signal Sp(θ, 2k) represents the sampled spatial frequencies associated with angular frequencies ω,

the derivative with respect to time of the angular phase of the transmitted LFMCW signal, defined as:

ω = 2π(f0 + αt) = d

dt

[2π(f0t+ α

2 t2)]

where α = BT

, B, and T are the transmitted signal frequency sweep rate, bandwidth and modulation

period respectively.

Sp(θ, 2k) needs to be interpolated to the desired angular frequencies, ωd, defined as:

22

ωd = c

2√k2x + k2

y

where kx and ky are the spatial frequencies associated with the imaging grid.

Sp(θ, 2k) can be interpolated to S(kx, ky) via a nearest neighbor approach where the change in column

and row indices are defined as:

δrow ind = ωd − ω0

∆ω

where ω0 = 2πf0 and ∆ω = 2πBN

and N is the number of frequency samples in Ss(θ, ω).

δcol ind = θd − θ∆θ

where θd = arctan(kykx

)

Figure 2.13: Real portion of interpolated received field decompressed in azimuth and demodulated inangular frequency, S(kx, ky)

The focused image is obtained bay compressing S(kx, ky) along kx and ky via taking the inverse

Fourier transform in both directions:

23

s(x, y) = F−1kxF−1

kyS(kx, ky)

As is shown in Figure 2.14.

Figure 2.14: Power, 10log10(s(x, y)2) of focus image s(x, y), with truth data overlaid in blue.

24

2.4 FFT Based Focusing vs GSAFT

This analysis compares the circular FFT Based Focusing Technique with the GSAFT. Figures 2.17 through

2.18 show a 10 dB increase in dynamic range of images obtained using the GSAFT. Although the GSAFT

produces images with a 10 dB larger dynamic range, it has an order of magnitude larger computational

demand in terms of processing time and RAM requirements. However, the GSAFT is extremely paral-

lizable, with use of large memory personal computers in conjunction with GPGPUs (general processing

graphics processing units) processing speeds may be made comparable with that of the FFT based focusing

technique.

Figure 2.16 is a surface plot of two metal cans separated by 2", shown in Figure 2.15. The image was

reconstructed with the circular measurement setup previously described. The following figures are the

same surface plot from a side view.

Figure 2.15: Two metal cans separated by 2" (0.0508 m)

25

Figure 2.16: Surface plot of 2 metal cylinders separated by 2"=(0.0508 m), using GSAFT.

26

Figure 2.17: Using FFT based focusing using nearest neighbor interpolation for polar reformating. 24dB noise floor.

Figure 2.18: Using GSAFT. 35 dB noise floor.

27

Chapter 3

LFMCW Signals and Signal Sampling

3.1 Time Domain Representation of: Real, Complex, and Analytic

FMCW signals

System Parameters

Bandwidth B

Modulation period T

LFM Coefficient α = BT

Time-Bandwidth Product (T )(B)

Frequency Modulated Phase Ω(t)

Frequency Modulated Amplitude a(t)

Transmitted reference phase φt

3.1.1 The Real Transmitted Signal

The transmitted Linear Frequency Modulated (LFM) signal is defined as:

st(t) = a(t)cos(ωot+ παt2 + φt) Rect( tT

) (3.1)

Since st(t) is a real narrowband signal it can be represented in two different ways. First we will look at

the in phase and quadrature phase representation:

28

st(t) = [stI(t) cos(ωot+ φt)− stQ(t) sin(ωot+ φt)] Rect(t

T) (3.2)

where:

stI(t) = a(t) cos(παt2) = a(t) cos(Ω(t))

and

stQ(t) = a(t) sin(παt2) = a(t) sin(Ω(t))

are the in phase and quadrature phase of the baseband transmitted signal st(t). The purpose of splitting

the cosine in 3.2 is to separate the a(t) and Ω(t) from the higher frequency carrier term.

3.1.2 The Analaytic Transmitted Signal and Complex Envelope

There are no analytic signals or systems in the real world. The concept of analytic expressions to the

description of real world systems or signals offers tremendous benefits from the simplicities in the mathe-

matical representations and analyses of real signals and systems [19]. Assuming a(t) = 1, st(t) is defined

as:

st(t) = Resa(t) = Reej(ωot+παt2+φt) Rect( tT

)

sa(t) is the analytic transmitted signal defined as:

sa(t) = sc(t)ej(wot+φt) (3.3)

sc(t) is the baseband complex envelope of the transmitted signal sa(t), defined as:

sc(t) = ej(παt2) Rect( t

T) (3.4)

The concept of the baseband complex envelope will be very helpful with simulating an FMCW radar

system on a computer.

29

3.2 Frequency Domain Representation of: Real, Complex, and An-

alytic FMCW Transmitted Signals

The transmitted waveform st(t) is real, thus it has an even spectral representation, and St(ω) 6= 0 ∀ ω < 0.

This can be obtained by taking the Fourier Transform (FT) of st(t). However, before we look at St(ω) we

will take the FT of sc(t), which represents the baseband complex envelope of the LFM up-chirp.

St(ω) = Fst(t)

The purpose of this section is to compare the spectra of St(ω), Sc(ω) and Sa(ω).

Sc(ω) is plotted below for a time-bandwidth product of 25 ((B)(T ) = 25).

Figure 3.1: Spectral Power of St(ω), Sa(ω) and Sc(ω) for ωo = 2π500 [r], T = 0.5 [s], and B = 2π50 [ rs].

Notics as long as the starting frequency ωo is much larger than the complex envelope bandwidth, thepositive and negative spectrums do not interfere with each other. If this is true, the use of the analyticspectrum for simulations purposes will result in similar signal processing results.

Now that we have Sc(ω) we are ready to look at the spectrum of the real signal st(t). St(ω) is defined as

the FT of st(t):

30

St(ω) = 12[Sc(ω − ωo)ejφt + S∗c (−(ω + ωo))e−jφt

](3.5)

As is shown in figure 3.1, St(ω) has an even spectrum. We can also say that as long as B ωo there

will be little to no interference between Sc(ω − ωo) and S∗c (−(ω + ωo)) and the following equality can

assumed to be true:

Sc(ω − ωo)ejφt = 2St(ω) for ω > 0 ; 0 for ω ≤ 0

Sc(ω − ωo)ejφt can also be expressed as:

Sc(ω − ωo)ejφt = U(ω)St(ω) (3.6)

where U(ω) is the unit step function in the frequency domain. If ωo >> B then we can also say:

Sa(ω) = Sc(ω − ωo) = Sc(ω) ∗ δ(ω − ωo)ejφt (3.7)

3.3 Obtaining Received Signal in Time

Since we can assume that the center frequency of our FMCW system is much greater than the bandwidth

of our system, ωo >> B, the positive and negative frequencies of St(ω) will not interfere with each other,

thus analytic representations of the transmitted and received FMCW signals can be used for analysis.

The real portion of the analytic received signal is obtained using the analytic transmitted signal trav-

eling through an analytic network. The analytic transmitted signal is the baseband complex envelope

modulated by a carrier frequency. The analytic network has a complex impulse response, whose real por-

tion corresponds to the real impulse response of the real network we are trying to model.

The channel has a real impulse response, this real response is modeled with an analytic signal whose

complex spectrum is defined as:

H(ω) = Γ(ω)ejΦ(ω)

31

where the IFT of H(ω) is the impulse response in time of the channel, h(t). The analytic channel

impulse response is represented by:

h(t) = γ(t)ejφ(t)

The received signal is simply the convolution of h(t) with sa(t). The received signal is in the range-

time domain:

sr(t) = sa(t) ∗ h(t)

Where ∗ denotes the convolution operator. Analogous to convolution in the time domain, the received

signal in time can also be obtained via and IFT of the product ofH(ω) and Sa(ω) in the frequency domain:

sr(t) = F−1H(ω)Sa(ω)

The transmitted and real portion of the received signals are then multiplied within the FMCW radar

module.

sm(t) = Resr(t)st(t)

The mixed signals are then lowpass filtered to prevent aliasing of the higher frequency components of

sm(t).

sIF (t) = LLPFsm(t)

where LLPF denotes the lowpass filter operation. The mixing and low-pass filtering operation is com-

monly refferred to as "dechirping" in range. Upon dechirping the received signal, the resulting intermedi-

ate frequency signal is in range-frequency domain [16]. However, it is common practice to visualize the

dechirped signal in the time-frequency domain was well (see 3.9 and 3.10 for this relationship).

32

3.3.1 Obtaining Intermediate Frequency of Ideal Point Target Channel

To obtain the received signal in time, or transmitted pulse echo, we can convolve the transmitted signal

with the channel impulse response.

Resr(t) = Re∞∫−∞

h(t′)sa(t− t′)dt′

where h(t) = δ(t− τ) is the channel impulse response of a point target τ seconds from the transceiver.

The received signal, neglecting amplitude attenuation of channel, will simply be a time shifted version of

the transmitted signal.

sr(t) = sa(t− τ)

The received signal and transmitting signal are mixed producing:

sm(t) = cos(ωot+ παt2)cos(ωo(t− τ) + πα(t− τ)2)[u(t− τ)− u(t− T )] (3.8)

= cos(ωoτ + 2παtτ − πατ 2) + cos(ωo(2t− τ) + παt2 − 2παtτ + πατ 2)[u(t− τ)− u(t− T )]

The mixed signal is lowpass filtered to eliminate higher frequency cosine term:

sIF (t) = cos(ωoτ + 2παtτ − πατ 2)[u(t− τ)− u(t− T )] (3.9)

With a change of variable the intermediate frequency signal can be represented in spatial-frequency

domain as, (neglecting the rectangular function [u(t− τ)− u(t− T )]):

sIF (k) = cos(2kor + 2kαr −4παr2

c2 )

= Reej2rke−j4παr2c2 (3.10)

The second exponential in 3.10 is known as the residual video phase (RVP) and,

33

k = ko + kα

= 2πfoc

+ 2παtc

(3.11)

Where kα is a function of time and sIF (k) is in the spatial frequency domain. The 2kαr term rep-

resents the range rate of the intermediate frequency signal. This term gives us target range information.

The 2kor term is used to obtain cross range resolution. This is intuitive because range resolution is a func-

tion of bandwidth, and cross range resolution is a function of starting frequency, range, and aperture width.

It is important to point out that the sIF (t) obtained above by multiplying the real transmitted and

received signals and lowpass filtering, is also equivalent to:

sIF (t) = Res∗a(t)sr(t) (3.12)

where ∗ denotes the complex conjugate of the analytic transmitted signal. By multiplying the received

signal by the complex conjugate of the analytic transmitted signal, we obtain the same phase terms in

equation 3.9 without implementing the low pass filter operation, or dealing with the sum phases in sm(t).

This is important to note because when simulating these signals on a computer, we must satisfy the nyquist

criterion for sampling signals.

3.3.2 Non-Ideal Channel Response

For a channel containing a distributed set of scatterers the time response is represented as:

h(t) =∑i

γ(τi)ejφ(τi)δ(t− τi) (3.13)

where in this case τi = ric

and ri is the distance from scatterer to sensor.

The received signal is the convolution of the channel impulse response with the transmitted signal:

34

sr(t) = sa(t) ∗ h(t)

= sa(t)[u(t)− u(t− T )] ∗ ∑i

γ(τi)ejφ(τi)δ(t− τi)

=∑i

γ(τi)ejφ(τi)sa(t− τi)[u(t− τi)− u(t− (T + τi))] (3.14)

The received signal is then mixed with the transmitting signal st(t) which is equivalent to:

sIF (t) = Re[s∗a(t)u(t)− u(t− T )

][∑i

γ(τi)ejφ(τi)sa(t− τi)u(t− τi)− u(t− T )]

=∑i

γ(τi)cos(ωoτi + 2παtτi − πατ 2i + φ(τi))[u(t− τi)− u(t− T )] (3.15)

3.4 Resolution and Sampling

This section will be separated into two main parts. Part 3.4.1 will focus on range and cross-range resolu-

tion. Part 3.4.2 will focus on spatial frequency sampling required to obtain certain range and cross-range

resolutions.

3.4.1 Spatial Resolution

Spatial resolution in any type of radar system can be best understood with use of the Ewald Sphere [26].

This paper is concerned with two dimensional imaging, so the Ewald circle will be used. The Ewald

circle represents the two dimensional spatial frequency spectrum of a scatterer, or sometimes referred

to as the k-space spectrum. The axes of the graph are in units of radians per meter in the kx and ky

spatial frequency directions. In theory a three dimensional Fourier transform relationship exists between

the three dimensional k-space spectrum and the three dimensional image of the scene RCS (radar cross

section) ( [16] pg. 102). The radii of the inner and outer circles in Figure 3.2 are a function of the

transmitted signal center frequency. The width of the gray annulus is a function of the total bandwidth of

the transmitted signal. The limits and width of the bandwidth are defined as:

35

kmin = 2ω0 + 2παtc

|t=0

kmax = 2ω0 + 2παtc

|t=T

∆k = kmax − kmin = 2πBc

The k-space graph in 3.2 would represent a monostatic measurement scenario where k-space measure-

ments were made over a 360 degree synthetic circular aperture (see Figure 3.3. In many remote sensing

applications limited K-space information is available due to the limited size aperture of the sensing sys-

tem. A bistatic measurement system example is needed to explain how the Ewald circle is generated in

the most general form. For a single frequency bistatic system shown in Figure 3.5. The corresponding K

space representation would be 3.4. θi and θr are the incident and received positions of the transmitter and

receiver respectively. ∆θr represents the angular width of the receiving aperture (whether it be physical or

synthetic).

Figure 3.2: Spatial frequency representation ofrecorded received field values from monostaticISAR setup with 360 degree synthetic circular aper-ture.

Figure 3.3: Physical ISAR setup for obtaining spa-tial frequency spectrum information in figure 3.2

Figures 3.7 and 3.6 represent a bistatic multi-frequency system setup and the corresponding K-space

36

Figure 3.4: Spatial frequency representation ofrecorded received field values from a single fre-quency bistatic radar setup shown in 3.5.


representation. Instead of a single point width annulus being measured in the single frequency scenario,

we have a finite width annulus of measured points in the Ewald circle. The angular coverage of the annu-

lus is a function of transmitting and receiving aperture size over azimuth. The depth of the annulus in the

radial direction is a function of chirp bandwidth B. It will be referred to as the received spatial bandwidth.

Figure 3.6: Spatial frequency representation ofrecorded received field values from a multi-frequency bistatic radar setup shown in Figure 3.7.

Figure 3.7: Physical ISAR setup for obtaining spa-tial frequency spectrum information in Figure 3.6

If transmitter and receiver are both scanned over a circular aperture of width ∆θ then the angular

coverage in K space is twice as large, thus cross-range resolution is improved twice. Figure 3.8 shows the

increased azimuthal bandwidth obtained by scanning both transmitter and receiver over synthetic aperture

37

of width ∆θr and ∆θi in 3.8 are equal to ∆θ in figure 3.9.

Figure 3.8: Spatial frequency representation ofrecorded received field values from a multi-frequency monostatic radar setup shown in figure3.9, both transmitter and receiver are scanned overcircular aperture of width ∆θ.


The Nyquist criterion states signal with bandwidth B must be sampled such that fs > 2B. Therefore,

the resolution of a signal with spatial bandwidth ∆k has a spatial resolution:

δr = 2π2∆k = 1

2c

B[meterscycles

]

Azimuthal spatial bandwidth is a function of center frequency wavelength λc and total angular extent

of receiving aperture relative to scene being imaged. The following calculations assume a multi-frequency

monostatic setup where both transmitter and receiver are scanned over a circular synthetic aperture. Mea-

surements are taken in the far-field and total size of synthetic aperture is small compared to the range to

the target. This is a typical "standoff" detection scenario. Azimuthal bandwidth is represented as the width

of the semi-annulus representing the spatial frequencies measured, as is shown in figure 3.8. This width is

defined as:

∆klateral = 2(2kc) sin(∆θr2 ) [ radians

meters]

where kc = 2πλc

and resolution is:

38

δlateral =λc2

2 sin(∆θr2 )

substituting sin(∆θr2 ) = L

2R , cross-range resolution is:

δlateral = λcR

4L

3.4.2 Sampling

In this section sampling requirements imposed by system resolutions capabilities is discussed. Resolutions

in range and cross range are:

δr = c

2B

δlateral = λcR

4L

Range resolution is a function of bandwidth. However, the maximum unambiguous distance one is

able to accurately represent scatterer locations is dependent on the frequency sampling interval. This

relationship is:

Dmax = c

2BN

where N is the number of frequencies sampled of the bandwidth B. This relationship can be derived in

time, where the τmax, associated with a maximum two-way distance Dmax, is:

τmax = Dmax

c= 2Rmax

c,

where Rmax = Dmax2 .

To accurately reconstruct a period of length τmax one must sample a signal in time atleast τmax2 . In

frequency, if the bandwidth of a pulse of width τmax is ∆f then the sampling bandwidth associated with

39

pulse of width τmax is 2∆f . Thus the maximum unambiguous range Rmax in terms of ∆f is:

Rmax = τmaxc

2 = 12∆f

c

2 = c

4∆f (3.16)

Resolution in cross-range is a function of the center frequency wavelength of the system, aperture

size, and range to targets being imaged. To obtain a spatial resolution of δx one must sample over spatial

resolution of δx2 . Thus to obtain a cross-range resolution of δlateral = λcR

4L one must sample < δlateral2 . The

minimum sample distance would be λc4 , however, this would only be necessary if the angular extent of the

aperture was close π radians. For a typical "standoff" detection scenario, a minimum sample distance of

λc2 would suffice.

3.5 Time-Bandwidth Product (TBP) and Resolution in FMCW Sig-

nals

The transmitted signal spectrum of a linear FMCW (LFMCW) waveform is the FT of the transmitted signal

in time st(t). In general for radar systems the range resolution is a function of the system bandwidth:

δr = c

2B

This is true no matter how fast the modulation period T is. By reducing the modulation period of the

waveform, the time-bandwidth produce = TB becomes smaller. The reduction of the TBP increases the

sweep rate of the system α = BT

and introduces more ripple in the spectrum of the complex envelope

Sc(ω). We can see this by looking at the FT of the complex envelope.

Sc(ω) = F[sc(t)] = F[a(t)ejπαt2 ]

Due to the t2 term in the exponential, we must use the solution of the Fresnel integral to solve the

equation below. Where, after substituting u =√

T2B

(t− ωT

2πB

), the integral becomes:

40

Sc(ω) =√T

2Be−j ω

2T2πB

x(T2 )∫−x(T2 )

ejπu2

2 du

Figure 3.10: Fresnel integrals: C(x) =x∫0cos(πu2

2 )du and S(x) =x∫0sin(πu2

2 )du

As is show in in figure 3.5 as x increases the deviation in amplitude of the Fresnel integrals decreases.

Since x is proportional to the TBP, decreasing the TBP decreases x and there will be more ripple in the

complex envelope spectrum.

It is also important to point out that a short duration signal will have less energy than a signal of longer

duration but equal average power. Thereby, decreasing the modulation period of a waveform will decrease

the SNR. This is shown in figure 3.5. The same figure also shows the effect on out of band spectrum

is negligible for different TBPs. The reason for this is in all the waveforms there exist discontinuities at

each side of the signal in time. Time discontinuities contain infinite bandwidth and introduce out of band

spectral power in the transmitted signal spectrum. In section 3.5.2 reducing out of band spectral power

will be discussed.

41

Figure 3.11: Complex envelope spectrum for various time-bandwidth products. Notice as the time-bandwidth produt increases, the maximum amplitude deviation across the spectrum is reduced. The totalpower of the spectrum is also increased when the time bandwidth product is increased.

3.5.1 Ripple in the Complex Envelope Spectrum

Having ripples in the complex spectrum increases side lobes on each side of the main lobe of the range

profile. The side lobes are increased because of the phase/amplitude modulation associated with the ripple

(ie. not a flat spectrum), especially for waveforms with time bandwidth products less than 30 [20]. Figure

3.12 shows the transmitted and received complex spectra of a channel with an ideal point target response

at various TBPs.

42

Figure 3.12: Complex envelope spectrum for various time-bandwidth products with corresponding re-ceived signal spectrum of ideal point-target response Ho(ω) = F[sc(t− τ)] for some nominal τ .

Figure 3.13: Complex envelope spectrum for various time-bandwidth products with corresponding re-ceived signal spectrum of ideal point-target response and intermediate frequency spectra (unfiltered)SIF (ω)

43

3.5.2 Reducing Out-of-Band Spectral Power

It is shown that using a Tukey window with 0.1% taper reduced the out of band spectral power by about

50 dB. The following images are of the complex envelope spectrum and intermediate frequency spec-

trum. Windowing either the complex envelope or the intermediate frequency signal both show the effects

windowing has on reducing out of band spectral power in each of the spectra.

Figure 3.14: Real portion of windowed complex envelope for TBP = 100. B = 100. A Taylor window andTukey window were used.

44

Figure 3.15: Magnitude (dB) of windowed complex envelope spectrums Sc(ω) for TBP = 1000. B = 1000.A Taylor window and Tukey window were used.

Figure 3.16: Magnitude (dB) unfiltered intermediate frequency spectrums SIF (ω) generated using win-dowed transmitted and received signals in time. An ideal point-target response is assumed for the receivedsignal. Taylor and Tukey windows were used.

45

Chapter 4

Finite Difference Frequency Domain Scattered

Field Analysis

4.1 Using FDFD to Simulate MMW Scattering Off of Human Bod-

ies

To test the feasibility of using mmw radar to detect irregular contours on a subject’s body, numerical

modeling of the problem was performed. The Finite Difference Frequency Domain (FDFD) numerical

technique was used to model the scattering of a subject wearing conductive materials on their body. FDFD

discretizes Maxwell’s equations in the frequency domain across the entire computational space, and then

solves the resulting simultaneous equations for every pixel in the space [23]. The farfield response is

then determined by applying the Kirchhoff diffraction formula to the electric and magnetic currents on the

surfaces of the box surrounding the computational space.

4.1.1 Importance of Using a Full-Wave Analysis For Calculating Scattered Fields

To show the benefits of using a full wave analysis a transverse magnetic (TM) uniform plane wave incident

on the geometry shown in Figure 4.1 A was simulated. The layered dielectric ellipse (εr ranges from 1 to

2) in the lower left part of the geometry funnels the energy into the PEC rectangle in the upper right part

of the geometry. The received fields were calculated for a 1 meter wide receiving aperture at a 1 meter

46

distance from the center of the geometry. Figure 4.1 B is the focused image using the GSAFT described

in Chapter 2. Figure 4.1 E is focused image using only the layered dielectric ellipse for input geometry.

Figure 4.1 F is focused image using only the PEC rectangle for input geometry.

This analysis shows the importance of taking into account mutual interaction between strong scatterers

when solving for scattered fields from complex geometries. The artifact remaining after subtracting the

superposed image in figure 4.1 C from the image in 4.1 B is a result of the scattering interaction of the

objects in the geometry.

This forward model allows detailed visualization of scattered fields, not just the fields backscattered to

a transceiver in a monostatic measurement scenario. With this information, novel imaging configurations

can be explored, including parametric exploration of potential systems, including parameters such as the

operating frequency bandwidth, scan height, and scan radius. Additionally, modeling allows detailed study

of difficult targets including thin or small targets, dielectric targets, and difficult target placements, such

as under the arms or between the legs. Visualization of they scattered fields may yield new insights and

lead to the development of improved imaging system designs. For example see Figure 4.2. Based on the

scattered fields resulting from the dielectric block in between the metal cylinders, most of the scattered

field energy would not be measured by the sensor, whose azimuthal location is specifed by the blue arrow.

4.2 FDFD Optimization

Previous FDFD simulations of the 2D body cross-cross sections were carried out at 8 points per wave-

length. This discretization proved to be inaccurate and imprecise. This analysis finds the most accurate,

precise and efficient FDFD discretization grid size. To decrease the computational time of each simulation,

the original 2D body cross-section geometries were decimated by a factor of 4. After decimation, the size

of the geometry file matrix was interpolated based upon the desired resolution of the original image (from

8 points per wavelength to 72 points per wavelength). In efforts to eliminate variables that may cause error

to this analysis, X and Y coordinate system of the body was defined in such a way that the origin of the

coordinate system is in the lateral center of the "top most" portion of the human chest (see Figure 4.3).

The distance d was fixed for all simulations. For higher resolution simulations, there are more points in

between the absorbing boundary and front of chest. Each geometry file was then put through the FDFD

47

Figure 4.1: A. Geometry used for input to FDFD scattered field analysis: B. Focused image of geometryin A using GSAFT: C. Superposed images of separate FDFD scattered field analyses of UPW incident oneach part of geometry in A separately: D. Image B subtracted from image A: E. Image produced fromdielectric layered ellipse only: F. Image produced from PEC rectangle only.

48

Figure 4.2: top left: incident field, blue arrow denotes direction of incident field from transceiver. topmiddle: total electric field magnitude, 2 cans separated by 2". top right: scattered electric field magnitude,2 cans separated by 2". bottom left: difference between the scattered fields in top left and bottom left plots.This represents the scattered field resulting from the rexolite block between cans. bottom middle: totalelectric field magnitude, 2 cans separated by 2" with rexolite block in between. bottom right: scatteredelectric field magnitude, 2 cans separated by 2" with rexolite block in between.

simulation with the following input parameters:

FDFD Parameters

Frequency 94GHz

Range 10 meters

Number of elements in planar phased antenna array 13

Array aperture width 0.8 meters

For each iteration, the scattered fields resulting from an incident uniform plane wave were stored

(example shown in figure 4.4). The scattered fields in each iteration were then interpolated to the highest

resolution of 72 ppw. Figures 4.5 and 4.6 are plots of the magnitude and phase of the scattered electric

fields at various positions and ppws.

The scattered field magnitudes begin to converge at about 42 ppw.

49

Figure 4.3: Geometry with distance measurements annotated

Figure 4.4: Scattered electric field polarized in z direction. Red line denotes location where scatteredfields are extracted for near field to near field transformation

50

Figure 4.5: Scattered electric field magnitude as a function of cross-range position on red line in figure 4.4and PPW of FDFD simulation

Figure 4.6: Scattered electric field phase as a function of cross-range position on red line in figure 4.4 andPPW of FDFD simulation

51

4.3 Description of SAR system simulation using forward model

TM uniform plane waves (UPWs) from 13 incident angles over a 1 meter aperture at a range of 10 meters,

a bandwidth of 8 GHz centered at 94 GHz were simulated. The scattered field of each simulation was

superposed and the received fields resulting from the focused beam were calculated. Figures 4.9 a and 4.9

b show the scattered field magnitude resulting from the focused beam on the targets shown in Figures 4.8

and 4.7 respectively.

Superposed received fields were reconstructed using the generalized synthetic aperture focusing tech-

nique (GSAFT) outlined in chapter 2. Figures 4.10 through 4.15 are the reconstructed images using data

from the FDFD forward model simulating 13 uniform plane waves incident from 13 sources uniformly

spaced on a 1 meter wide aperture at a range of 10 meters.

As is shown in the figures, a center frequency of 94 GHz results in enough cross range resolution to

distinguish the groups of metal pipes. However, when TNT pipes were simulated, multipath artifacts due

to higher-order scattering effects associated with the low loss constituitive parameters of TNT appeared in

the first order reconstructions.

Figure 4.7: 2D cross-section of male human wearing metal pipes

52

Figure 4.8: 2D cross-section of male human

53

Figure 4.9: Magnitude of scattered electric field, (a) no pipes, (b) pipes

54

Figure 4.10: Male, no metal pipes, 1 meter wide aperture, range=10meters, 13 transmitters.

Figure 4.11: Male, metal pipes, 1 meter wide aperture, range=10meters, 13 transmitters.

55

Figure 4.12: Male, TNT pipes, 1 meter wide aperture, range=10meters, 13 transmitters.

Figure 4.13: Female, no metal pipes, 1 meter wide aperture, range=10meters, 13 transmitters.

56

Figure 4.14: Female,metal pipes, 1 meter wide aperture, range=10meters, 13 transmitters.

Figure 4.15: Female, TNT pipes, 1 meter wide aperture, range=10meters, 13 transmitters.

57

4.4 FDFD System Requirements

The 3D MMW cylindrical imaging configuration developed by PNNL and licensed to L-3 can be studied

using numerical modeling techniques, however, modeling or simulating realistic full-wave 3-D scattering

data from the cylindrical mm-wave imaging system is a daunting challenge. Accurate simulation of the

3-D data requires simulating a large volume (with each dimension covering 100 - 250 wavelengths) for

every transceiver location and every frequency. For example, A 2D FDFD scattered field analysis requires

O[(L ×M)2] computations, where L ×M represent the number of positions scattered fields are solved

for in a rectangle of size L × M . To extend this analysis to a 3D geometry the total analysis would

require O[(L × M × N)2] computations, or a matrix of size (L × M × N)2. In the case of the 2D

used for this analysis, the rectangle of scattered field points solved for was 850 × 850. This translates

to 8502 = 722500 number of elements being solved for. The fields are being solved for via x = A−1b,

x is 722500 × 1 and A is 722500 × 722500. If each element in matrix A is 8 Bytes then A would take

7225002 × 8 = 4.17605× 1012 bytes , however, A is sparse thus it actually only occupies about 93× 106

bytes in memory, only 0.22% of the initial calculated size. Applying these calculations to solving a 3D

FDFD scattered field analyis for an entire human body of height 1.8288 meters is as follows. The number

of "slices" in elevation at the same discretization size used in the previous 2D analysis would be 3056.

Thus the number of elements being solved for would be 850× 850× 3056 = 2.20796× 109. This would

require an A matrix of size 2.20796×109×2.20796×109 = 4.8750873616×1018, at 8 bytes per element

that is 4.8750873616×1018×8 = 3.90006988928×1019 bytes. Again, due to the sparsity of A, the actual

size in memory is only 0.22% which in this case is 3.90006988928×1019×0.0022 = 8.5802×1016 which

is 8.5802× 107 gigabytes. This is only the actual size of A, to obtain the inverse of a sparse matrix of size

93 MB, 1.3688 GB of memory is required, which is approximately 15 times the actual size of A. Thus to

determine the inverse of a sparse matrix of size 8.5802 × 107 GB, 1.287 petabytes of memory would be

required.

The current L-3 cylindrical system uses on the order of 384 vertical positions, 64 frequency samples,

and 1024 angular samples for a total of over 25 M samples. Each sample would require a full 3-D simula-

tion, and computing 25 M full-wave 3-D simulations is not practical at the present time. However, the 3-D

cylindrical imaging configuration can be effectively simplified using two 2-D cases. A 2-D linear synthetic

58

aperture radar (SAR) imaging configuration effectively simulates the vertical scanning characteristics of

the 3-D cylindrical imaging technique, and a 2-D circular SAR imaging configuration effectively simu-

lates the circular scanning characteristics of the 3-D cylindrical imaging technique. Reducing the problem

to 2-D enables accurate and efficient forward modeling of the full-wave electromagnetic scattering at each

transceiver location using conventional high-performance PCs.

The following table represents the system requirements needed to determine the scattered and received

fields resulting from an incident cylindrical wave on a 0.25 m2 2D geometry. The First column represents

the simulated scenario. 1 Tx 1 Rx represents simulating a single incident wave and calculating the received

field at one receiving position. This process involves calculating the scattered fields due a single incident

wave. Then calculating the received field at a single receiving position based on the scattered fields calcu-

lated. 2 Tx 2 Rx represents simulating two different incident fields from 2 different transmitting positions.

Then calculating the received fields at a single position for each of the 2 scattered fields calculated. Due

to the nature of solving for the scattered fields in FDFD, Ax = b, multiple incident angles can be solved

for with a single matrix inversion via inserting more columns into the b matrix. This eliminates the time

cost of inverting the A matrix per simulated incident field.

FDFD system requirements

Scenario RAM [GB] RAMadditional incident angle [GB] Time [s]

1 Tx 1 Rx 1.2272 NA 37

2 Tx 2 Rx 1.2626 0.0354 42

10 Tx 10 Rx 1.6048 0.0419 80

20 Tx 20 Rx 3.0798 0.0976 131

30 Tx 30 Rx 4.7554 0.1216 167

40 Tx 40 Rx 6.4192 0.1331 222

4.4.1 Measurement vs. FDFD Data Acquisition Times

Assuming the 2D approximation is valid for determining scattered fields from a human body using the

FDFD model, the following time table compares data acquisition times needed for the current L3 Com-

munications full body imaging system, the PNNL system used for this project, and the FDFD model.

System Descriptions:

59

• L3 fully body imaging system: 384 Tx/Rx elements scanned over azimuth

• PNNL System used for AIT summer project: 1 quasi-monostatic transceiver scanned over elevation

and azimuth

• FDFD Simulation on a single Core i7 with 8 GB of DDR3 Tri-channel (1600 MHz Front side bus

speed)

• FDFD Simulation on a single Core i7 with 32 GB of DDR3 Tri-channel (1600 MHz Front side bus

speed)

data acquisition times

System Time

L3 System 1.5 [seconds]

PNNL System 3 [hours]

FDFD, Core i7 w/ 8GB RAM 6 [months]

FDFD, Core i7 w/ 32GB RAM 6 [weeks]

60

Chapter 5

Portal Scanning and FDFD Validation

The current 3D body-scanning system used by L3 Communications/Safeview consists of two booms of

sensors extending about 1.8 meters in height. The booms are each scanned around the target azimuth. The

measured data is focused using a modified combination of rectilinear of a circular focusing techniques

described in this chapter.

5.1 Rectilinear Scan

This section contains images reconstructed from data created by the rectilinear measurement simulated by

the FDFD forward model and obtained the actual measurement system depicted in Figure 5.1. Various

2D targets were measured. The targets were chosen to better understand the imaging artifacts produced

between the legs of the current 3D imaging system employed by L3 Communications/Safeview.

All images displayed in this section are normalized to their maximum value and displayed with a 25

dB dynamic range.

61

Figure 5.1: Rectilinear SAR measurement setup.

62

Figure 5.2: FDFD input geometry. PEC Cylinder, 4" di-ameter

Figure 5.3: Top view of single metal can,4" diameter

Figure 5.4: Reconstruction from simulated data Figure 5.5: Reconstruction from measured data

63

Figure 5.6: FDFD input geometry. 2 PEC Cylinders, 4"diameter, 2" separation

Figure 5.7: Picture of 2 metal cans, 4" di-ameter, 2" separation

Figure 5.8: Reconstruction from simulated data Figure 5.9: Reconstruction from measured data

64

Figure 5.10: FDFD input geometry. 2 PEC Cylinders, 4"diameter, 3" separation.

Figure 5.11: Picture of 2 metal cans, 4"diameter, 3" separation.

Figure 5.12: Reconstruction from simulateddata

Figure 5.13: Reconstruction from measureddata

65

Figure 5.14: FDFD input geometry. 2 PEC Cylinders, 4"diameter, 4" separation.

Figure 5.15: Picture of 2 metal cans, 4"diameter, 4" separation.



66

Figure 5.18: FDFD input geometry. 2 PEC Cylinders, 4"diameter, 2" separation, Rexolite block in between.

Figure 5.19: Picture of 2 metal cans, 4"diameter, 2" separation, Rexolite block inbetween.



67

Figure 5.22: FDFD input geometry. 2 PEC Cylinders, 4"diameter, 2" separation, Rexolite block on side of rightcan.

Figure 5.23: Picture of 2 metal cans, 4" di-ameter, 2" separation, 2" separation, Rex-olite block on side of right can.



68

Figure 5.26: FDFD input geometry. Rexolite block, 5.08cm thick, 31 cm wide.

Figure 5.27: Picture of rexolite block, 5.08cm thick, 31 cm wide.



69

Figure 5.30: FDFD input geometry. Rexolite block, 5.08cm thick, 31 cm wide, with half ground plane.

Figure 5.31: Picture of rexolite block, 5.08cm thick, 31 cm wide, with half groundplane.



70

Figure 5.34: FDFD input geometry. Rexolite block, 5.08cm thick, 31 cm wide, with full ground plane.

Figure 5.35: Picture of rexolite block, 5.08cm thick, 31 cm wide, with full groundplane.



71

The images reconstructed from data produced by the model and measurement setup both show that

when transparent anomalous objects are placed in nominal target scenes, the higher order artifacts signif-

icantly perturbed. As opposed to the first order artifacts representing the nominal targets themselves. It

is concluded that in the scenarios simulated and measured above, automatic target recognition algorithms

should focus on interpreting higher artifacts when classifying targets.

It is concluded that higher order image artifacts are exaggerated in images reconstructed from simu-

lated data. This is due to the discretization of the FDFD input geometry files. Each discretized cylinder

has a flat edge on each side, this results in more normal surface areas for the waves to bounce in between.

This is shown best in Figures 5.12 and 5.16.

5.2 Cylindrical Scan Imaging Results

This section contains images reconstructed from data created by the circular measurement simulated by

the FDFD forward model and obtained by the actual measurement system depicted in Figure 5.38. Various

2D targets were measured. The targets were chosen to better understand the imaging artifacts produced

between the legs of the current 3D imaging system employed by L3 Communications/Safeview.

All images displayed in this section are normalized to their maximum value and displayed with a 25

dB dynamic range.

5.2.1 Measurement and Simulation Setup

Figure 5.38: Circular synthetic aperture size, 450o; target range, R = 1.09 meters.

72

5.2.2 Comparing Focused Images Using Data From FDFD Simulation and Actual

Measurements

The following analysis compares images generated from both simulated and measured data. The final

image is an incoherent (magnitude) summation of each of the following 8 images. It is important to notice

the agreement in locations of the second order artifacts that appear as a late time response behind the

scatters.

Figure 5.39: Picture of single metal can, 4" diameter, top view

Figure 5.40: FDFD input geometry. PEC Cylinder, 4" diameter

73

Figure 5.41: Physical representation of scanning geometry, highlighted section represents actual spacemeasured

Figure 5.42: Simulated data Figure 5.43: Measured data


74



75



76



77

Figures 5.42 through 5.57 are 8 90 degree overlaping image segments. Each image segment was

reconstructed with 90 degrees of spatial frequency spectrum. Each segment of the spectrum was weighted

such that when combined via an incoherent superposition in magnitude, the resulting sum was an accurate

reconstruction of the measured scene.

Combining all of the above images via superposition of image magnitude:

Figure 5.58: Final image generated from simulated data, Target: single metal can 4" diameter

78

Figure 5.59: Final image generated from measured data, Target: single metal can 4" diameter

79

Figure 5.60: Picture of two cans separated by 2" geometryused for input to FDFD simulation

Figure 5.61: Picture of two cans separatedby 2"


Figure 5.64: Simulated data, Target: 2 metalcans separated by 2"

Figure 5.65: Measured data, Target: 2 metalcans separated by 2"

80







81







82

Figures 5.60 through 5.76 are 8 90 degree overlaping image segments. Each image segment was

reconstructed with 90 degrees of spatial frequency spectrum. Each segment of the spectrum was weighted

such that when combined via an incoherent superposition in magnitude, the resulting sum was an accurate

reconstruction of the measured scene shown in Figures 5.78 and 5.79.

Figure 5.78: Final image generated from simulated data, Target: 2 metal cans separated by 2"

83

Figure 5.79: Final image generated from measured data, Target: 2 metal cans separated by 2"

84

Figure 5.80: FDFD input geometry of Two cans separatedby 2" geometry with rexolite block in between

Figure 5.81: Picture of Two cans separatedby 2" with rexolite block in between.



85




86




87

Combining all of the above images via superposition of image magnitude:

Figure 5.98: Final image generated from simulated data, Target: 2 metal cans, 2" separation, rexolite blockin between

Figure 5.99: Final image generated from measured data, Target: 2 metal cans, 2" separation, rexolite blockin between

88

5.3 Final Images Obtained with Both Simulated and Experimental

Data

The following images are a subset of images generated from many different targets containing various

combinations of anomalous objects with nominal target geometries.

Figure 5.100: Simulated: 1 metal can. Figure 5.101: Measured: 1 metal can.

Figure 5.102: Simulated: 2 metal cans only. Figure 5.103: Measured: 2 metal cans only.

It is concluded that the images reconstructed from the model agree with the images reconstructed from

measured data. Note the agreement in location of higher order imaging artifacts circled in Figures 5.106

and 5.107

89

Figure 5.104: Simulated: rexolite block in frontof one metal can.

Figure 5.105: Measured: rexolite block in frontof one metal can.

Figure 5.106: Simulated: rexolite block in be-tween 2 metal cans.

Figure 5.107: Measured: rexolite block in be-tween 2 metal cans.

5.4 Comparing Focused Images Using Measured Data From Nomi-

nal Targets with Anomalous Objects

The following images are generated using the generalized focusing technique, see chapter 2, on measured

data. The higher order artifacts in the images containing anomalous objects are significantly perturbed

when compared with the images containing only the nominal targets. It has been concluded that a quan-

tification of the second order responses in each single image would be the best means of performing

automatic target recognition algorithms. This conclusion is not apparent when analyzing only the final

90

superposed images. Figures below show pictures of the targets measured, and diagrams of geometries

simulated.

Figure 5.108: Picture of Two cans sepa-rated by 2"

Figure 5.109: Picture of Two cans separated by 2" geom-etry used for input to FDFD simulation

Figure 5.110: Picture of Two cans sepa-rated by 2" with rexolite block in between

Figure 5.111: Picture of Two cans separated by 2" withrexolite block in between. Geometry used for input toFDFD simulation.

91

Figure 5.112: 2 metal cans only. Figure 5.113: with rexolite block in between 2metal cans.



92




93



94

Figure 5.128: Final image generated 2 cans only

Figure 5.129: Final image generated 2 cans with rexolite block

95

5.4.1 Dielectric Measurements of Ballistic Gelatin Used For Human Tissue Simu-

lant

Dielectric measurements were made with the Agilent 85070E Dielectric Probe Kit. The probe used was

the high-temperature probe with valid frequency range between 200MHz and 20GHz. The probe shown

in Figures 5.130 and 5.131 has a hermetic glass-to-metal seal. Each of the following graphs displays the

electric constitutive parameters of the ballistic gelatin used for human tissue simulant, rexolite, and water.

The ballistics gelatin was measured 3 times, rexolite was measured 2 times.

Figure 5.130: Picture of probe used for makingdielectric measurements.

Figure 5.131: Schematic of probe used for making dielec-tric measurements.

96

Figure 5.132: ε′ dielectric measurements

Figure 5.133: ε′′ dielectric measurements

97

Figure 5.134: δ = ε′′

ε′= loss tangent calculations

Figure 5.135: γ =1√ε′−1

1√ε′

+1 = reflection coefficient calculations

98

5.4.2 Image Reconstructions of Ballistics Gelatin Cylinders

Figure 5.136: Picture of 1 metal can (left) and 1 ballistics gelatin cylinder. Each is 4" in diameter. Sepa-rated by 4".

Figure 5.137: Reconstruction from measured data. 20dB dynamic range. 1 metal can, 1 ballistics gelatincylinder, 4" separation.

On average over each reconstructed cylinder, the ballistcs gelatin reconstructed power is about 2 dB

99

Figure 5.138: Surface plot of reconstruction from measured data. 20dB dynamic range. 1 metal can, 1ballistics gelatin cylinder, 4" separation. Maximum power in dB of gelatin reconstruction is about 3.5 dBless than the metal can.

less than the metal cylinder. This agrees with the measured reflection coefficient magnitude of about |0.68|

(over the 10GHz-10Ghz bandwidth) 10−0.2 = 0.63.

5.4.3 Reconstructions of Ballistic Gelatin Cylinders with Denim Cloth

This section analyzes the effects of denim cloth covering the ballistics gelatin cylinders. Based on the

reconstructions in this section, the effect of denim cloth is mostly negligible. Due to the slight loss of

denim fabric, the noise floor of the images is slightly increased. However, the relatively lossless dielectric

block of rexolite is still easily visible in both cases.

100

Figure 5.139: Picture of two gelatin cylinders,about 5.5" diameter, separated by 4"

Figure 5.140: Picture of two ballistics gelatincylinders, about 5.5" diameter, covered bydenim cloth, separated by 4"

Figure 5.141: Reconstruction from measureddata. 25dB dynamic range. two ballisticsgelatin cylinders, 4" separation.

Figure 5.142: Reconstruction from measureddata. 25dB dynamic range. two ballisticsgelatin cylinders, covered by denim cloth, 4"separation.

101

Figure 5.143: Picture of two ballistics gelatincylinders, about 5.5" diameter, separated by 4",with rexolite block in between.

Figure 5.144: Picture of two ballistics gelatincylinders, about 5.5" diameter, covered bydenim cloth, separated by 4", with rexoliteblock in between.

Figure 5.145: Reconstruction from measureddata. 25dB dynamic range. two ballisticsgelatin cylinders, 4" separation, rexolite blockin between.

Figure 5.146: Reconstruction from measureddata. 25dB dynamic range. two ballisticsgelatin cylinders, covered by denim cloth, 4"separation, rexolite block in between.

102

Although not pictured, all the following reconstructions are of the targets shown with denim cloth.

Figure 5.147: 2 ballistics gelatin cylinders, 4"separation

Figure 5.148: Picture of two ballistics gelatincylinders, about 5.5" diameter, separated by 4"

Figure 5.149: 2 ballistics gelatin cylinders, 4"separation, rexolite block in between.

Figure 5.150: Picture of two ballistics gelatincylinders, about 5.5" diameter, separated by 4",with rexolite block in between

Figure 5.151: 2 ballistics gelatin cylinders, 4"separation, rexolite block in between coveredby absorber material.

Figure 5.152: Picture of two ballistics gelatincylinders, about 5.5" diameter, separated by 4",with rexolite block in between covered by ab-sorber material.

103

Chapter 6

New Multistatic Sensing Configuration

Using a full-wave forward model, the ability to isolate and visualize scattered fields becomes possible.

As the forward model shows (Figure 6.1), most of the scattered field energy scatters in the front and rear

directions due to presence of the metal cylinders. Using a cicular monostatic scan, the signals from the

object of interest are not measured for the majority of the scan.

Figure 6.1: top left: incident field, blue arrow denotes direction of incident field from transceiver. topmiddle: total electric field magnitude, 2 cans separated by 2". top right: scattered electric field magnitude,2 cans separated by 2". bottom left: difference between the scattered fields in top left and bottom left plots.This represents the scattered field resulting from the rexolite block between cans. bottom middle: totalelectric field magnitude, 2 cans separated by 2" with rexolite block in between. bottom right: scatteredelectric field magnitude, 2 cans separated by 2" with rexolite block in between.

Based on the results picture in Figure 6.1 a new multistatic sensor configuration is simulated, see

104

Figure 6.2. Using the more versatile GSAFT, reconstructing an image using a multistatic system that

combines the benefits of both rectilinear and cyclindrical scanning techniqes is performed.

Figure 6.2: Multistatic sensor configuration. Transmitter is circularly scanned while two static rectilineararrays recieve for every transmitter location.

An interesting result of this multistatic setup, see Figure 6.3, is the extremely large amount of spatial

frequency coverage, even at only a single frequency, see Figure 6.5. Compared to the spatial frequency

coverage, see Figure 6.4, from the monostatic setup in Figure 6.6. In theory, based on the multistatic con-

figuration spatial frequency coverage, very high range and cross-range resolution should be obtainable.

However, due to the non-uniformity of the spatial frequency coverage, certain spatial frequency regions

are more densely sampled than others. It would be interesting to investigate new ways to weight or inter-

polate the sampled spatial frequencies such that images can be reconstructed with only single frequency

measurements.

As is shown in Figures 6.9 and 6.10, the additional spatial frequency coverage creates images with

higher dynamic range, increased range and cross-range resolutions. Due to the targets being measured,

more energy from the object of interest is captured by the sensing systems. Due to the increased combina-

tions of transmit and receive locations, artifacts due to multipath effects have been severely reduced. As

is shown in Figure 6.8, due to multipath effects of the scattering, the reconstructed image fails to show a

scatterer in the location of the rexolite block.

105

Figure 6.3: Multistatic measurement setup. Reddots indicate transmitter positions. Green andBlue dots indicate receiver positions.

Figure 6.4: Monostatic measurment setup. Reddots indicate single transmit/receive locations.

Figure 6.5: Spatial frequency coverage for sin-gle multistatic circular scan using only 1 fre-quency.

Figure 6.6: Spatial frequency coverage for sin-gle monostatic circular scan using only 1 fre-quency.

106

Figure 6.7: Spatial frequency coverage for sin-gle multistatic circular scan using 50% band-width to starting frequency ratio.

Figure 6.8: Spatial frequency coverage for sin-gle monostatic circular scan using 50% band-width to starting frequency ratio.

Figure 6.9: Multi static reconstruction, 25 dBdynamic range.

Figure 6.10: Circular monostatic reconstruc-tion, 20 dB dynamic range.

Figure 6.11: Multi static reconstruction, 30 dB dynamic range.

107

Chapter 7

New Method of Displaying Imaging Data

The current 3D imaging system employed by L3 Communications/Safeview, use a 2D projection of max-

imum values in a 3D image, see Figure 7.1. This 2D maximum value projection is simplied to a 1D

maximum value projection for the 2D images obtained in this analysis.

Figure 7.1: Left: 2D projection generated 3D data set. Middle: Region containing higher order artifacts.Topr Right: 1D Projection of 2D data set. Bottom Right: 2D image crossection of 2D data set

The following three figures are of the two human tissue simulant cylinders separated by 4". The

cylinders are covered with denim cloth. The images on the left are of an innocent case. The images on the

right are of the same case except with a rexolite block in between the cyclinders wrapped in denim cloth.

As is displayed in the following Figures, the imaging artifacts produced by the anomalous object

in between the two human tissue simulant cylinders is behind the images of the cylinders themselves.

When using a maximum value projection, these target signatures are hidden by first order reflections from

nominal targets. It is concluded that using volumetric rendering would result in better anomalous object

108

detection because more anomalous target signatures are displayed.

109

Chapter 8

Two Dimensional Standoff Scanning

Vertical/vertical (VV) polarization measurements were taken across a 4.8 GHz bandwidth, centered at 99

GHz, using a 150 Hz pulse repetition frequency (PRF), while a target person was rotated on the Fraunhofer

Institute for High Frequency Physics and Radar Techniques turntable at 3 degrees per second. Several

initial body orientations were chosen. The data were processed using standard ISAR back projection

techniques described as follows.

18000 individual measurements were obtained as the target was rotated on the turntable 360 degrees, see

Figure 8.1.

The scattering at 99 GHz is dominated by the geometry of the target body. Therefore, to test the

robustness of the system, targets with varying body geometries were chosen as test subjects, see Figure

8.2.

8.1 Signal Processing

Once all of the range profiles are obtained, the data is transformed from the view angle space to image

space by performing a second Fourier Transform over a finite set of range profiles. Care must be taken in

how the Fourier Transform over azimuth is performed. To obtain an accurate image of the target scatterers,

the range and cross-range resolutions must be equal. The maximum resolution in range is limited by the

system bandwidth, B = 4.8GHz.

The range resolution of a continuous wave radar system is ∆Y = c2B = 3.13 [cm]. The cross-range

111

Figure 8.1: Standoff circular ISAR experiment setup.

resolution is ∆X = λ2∆Θ . Where ∆Θ is the size of the azimuthal segment used for imaging and λ is the

free space wavelength of the center frequency. For best imaging results ∆X = ∆Y . Thus ∆Θ is solved

for in terms of ∆X is ∆Θ = λ2∆X = 2.7o.

To go from angular space to spatial space we must perform the second Fourier Transfrom over ∆Θ range

profiles.

Assuming the target of interest is in the farfield of the synthetic aperture, the 2D Fourier transform

over frequency and angular space is used to focus images in range, given by Y , and cross-range, given

by X . The spatial resolution is 3.13 cm. Once the image is obtained, target classification and threat

detection is performed. From the ISAR images created, we have concluded that there are multiple unique

backscattering patterns resulting from a human wearing conductive materials on their body. The largest

distinguishing trait associated with a human wearing metal pipes on their chest is the increase in amount

of forward scattering. To quantify this, a test function is applied to the images created.

The test function finds a best fitting elliptical matrix approximation for the scattering shape within the

image. The elliptical test function is defined as:

112

Figure 8.2: 3 targets used in experiment

T = A

(1 + (xa)2 + (y

b)2)4

Where a defines the semi-major axis and b defines the semi-minor axis. The threat detection algorithm

iteratively varies the a and b parameters and subtracts the test function from the image. The ellipse function

whose ratio of the semi-major and semi-minor axes defining the best fitting elliptical approximation is

recorded and used to determine presence of artificial scatterers on the targets chest. The presence of pipes

on a target chest causes axial ratio, ab, to become smaller than with the presence of pipes.

Figure 4 shows typical reconstructed intensity as a function of target position. The limited view angle

makes detailed imaging impossible, but other discriminating features are clear.

8.2 Results

The best fit ellipse finding algorithm was applied to the ISAR images of human subjects with varying

physical characteristics: male, female, short, tall, thin and corpulent persons were all tested by the radar

113

Figure 8.3: 2 example ISAR images. (a) Subject a (in figure 3) wearing no pipes. (b) Subject a wearingone pipe

system. Figure 5 presents the axial ratio determined for each of the subjects of Figure 3 for different pipe

configurations and aspect angles. It is clear that each subject not wearing pipes has a larger axial ratio

than when he/she is wearing the metal pipes. The probabilities of detection Pd and false alarm Pf for

the system can be established by setting a threshold and computing threat declarations. For example, two

thresholds were established for each aspect angle, denoted as T1 and T2. For the aspect angle of 3 degrees

and T1 threshold: Pd = 83.3% and Pf = 0%, and for T2 threshold: Pd = 91.6% and Pf = 33.3%. For the

aspect angle 61 degrees and T1 threshold: Pd = 58.3% and Pf = 0%, and for T2 threshold: Pd = 100 and

Pf = 33.3%. These results differ from conventional ISAR in that they are derived with a limited aperture

for detection of concealed objects at standoff distances.

114

Figure 8.4: Results: (a) 3o off normal to target chest. (b) 61o off normal to target chest

115

Chapter 9

Image Processing Algorithm for Standoff

PBIED Detection

Due movement, target positions vary ±0.2 meters of center body position. The lack of exact target loca-

tion knowledge combined with limited azimuthal spatial bandwidth measured often makes reconstructed

images hard to interpret because there is no priori basis of estimating the location of imaged scatterers rel-

ative to the targets body. The image processing algorithm presented in this paper uses simulated images of

estimated threat and non-threat target geometries to determine the body center of experimentally obtained

images. After determining a range and cross range adjustment needed to center the experimental image,

an estimated target geometry is overlaid. Once images are superposed onto an estimated body reference,

extracting useful information from the reconstructed images becomes surprisingly easy. The following

equations are the basis of determining the best range and cross range adjustments. First find the y′ that

maximizes f(y′), then find the x′ that maximizes f(x′|y′).

f(y′) =∫

y∈Y

∫x∈X

|US(x, y)|2|UE(x′ − x, y)|2dx δ(y − y′)dy ∀x′ ∈ X (9.1)

where US(x, y) is the simulated image and UE(x, y) is the experimental image.

f(x′|y′) =∫

x∈X

∫y∈Y

|US(x, y)|2|UE(x, y − y′)|2dy δ(x− x′)dx (9.2)

Figure 9.1 shows a flow chart for how the algorithm evaluates equations 9.1 and 9.2. Not only does this

116

Figure 9.1: Image processing flow chart

algorithm make experimentally obtained images much easier to interpret, it may also be used as a basis to

build an automatic threat detection system. Instead of using an estimated geometry of the known threat

target as input to the simulation, an estimated innocent target geometry is used. Target classification is

based on how much the experimental image needs to be shifted and the difference between the experimen-

tal and innocent simulated images. For innocent male targets, both experimental and simulated images

show that the target chest and arms are the dominate scatters within the reconstructed images. If a target

has any artificial scatterers on its body, chest and arms will not be the only dominant scatters and the

algorithm will be forced to shift the experimentally obtained image further to obtain a "best fit". To build

an automatic threat detection algorithm that can perform robustly for many different body types, however,

a much larger set of targets must be measured.

Figures 9.3 through 9.10 are image reconstructions of data obtained from measurements and simula-

tions. All images are displayed in dB with a 25 dB dynamic range. The experimental based images have

been shifted and overlaid onto estimated target geometries with the image processing algorithm presented

in the previous section. All images were created with a 4 GHz system bandwidth and a 2.7o wide aperture

(∼ 0.47 meters) at a range of 10 meters. At a range of 20 meters this would correspond to about a 1 meter

aperture width. The reason for the appearance of late time responses within in the body of the experi-

mental images is that the images are actually a 2D projection of a 3D scattering process. Thus scatterers

117

imaged within the body are most likely reflections from the subject’s neck. The experimental images also

appear to highlight scatters on the left side of the body. This is due to the target not being in the center

of the source antenna’s illuminating beam. This can easily be prevented in future experiments by either

using a smaller antenna or measuring targets at a larger range. Due to having a frequency source based

on a voltage controlled oscillator (VCO), target motion, non-uniform target illumination, and signal phase

noise, experimental images are sometimes hard to interpret. When images are overlaid on to an estimated

target geometry as a reference, however, one can easily extract meaningful information from the image.

Figure 9.2: Incident angle = 90o (normal incidence). Simulated image of innocent male target with simu-lated target geometry overlaid. 25dB dynamic range.

118

Figure 9.3: Incident angle = θ

Figure 9.4: Incident angle = 90o (normal incidence). Experimentally obtained image of innocent male tar-get, automatically shifted to best fitting range and cross range positions, estimated body geometry overlaid.25dB dynamic range.

119

Figure 9.5: Incident angle = 90o (normal incidence). Simulated image of male target with four metal pipeson body with simulated target geometry overlaid. 25dB dynamic range.

Figure 9.6: Incident angle = 90o (normal incidence). Experimentally obtained image male target with 4metal pipes on body, automatically shifted to best fitting range and cross range positions, estimated threattarget geometry overlaid. 25dB dynamic range.

120

Figure 9.7: Incident angle = 115o. Simulated image of innocent male target with simulated target geometryoverlaid. 25dB dynamic range.

Figure 9.8: Incident angle = 115o. Experimentally obtained image of innocent male target, automaticallyshifted to best fitting range and cross range positions, estimated body geometry overlaid. 25dB dynamicrange.

121

Figure 9.9: Incident angle = 115o. Simulated image of male target with four metal pipes on body withsimulated target geometry overlaid. 25dB dynamic range.

Figure 9.10: Incident angle = 115o. Experimentally obtained image male target with 4 metal pipes onbody, automatically shifted to best fitting range and cross range positions, estimated threat target geometryoverlaid. 25dB dynamic range.

122

Chapter 10

Summary and Future Work

MMWs are a proven modality for use in many remote sensing applications. Current full body imaging

systems deployed by L3 Communications/Safeview have proven to be successful in deterring the use of

PBIEDs on airplanes. However, there is still room for improvement. Current focusing methods are very

fast and produce focused images but are limited in imaging certain areas of the body. Current systems

do not use all of the computational power available, so there is room to increase image reconstruction

algorithm complexity without decreasing system throughput. With decreasing cost of MMW sources and

increasing availability of computational power, new sensor configurations can developed without restric-

tions based on the requirements imposed by many Fourier image reconstruction techniques.

With the recent increase in personal computing power, forward models such as FDFD have proven to

give insight into the scattering processes associated with full body imaging. With this type of knowledge

new sensor configurations can be simulated without the extremely high cost and risk associated with

building such imaging systems. As is shown in Chapter 6, multistatic sensor configurations have increased

system resolution in range and cross-range, increased dynamic range of image power, and reduced the

system susceptablity to specular reflections. Although Fourier techniques have been developed by [9] for

bistatic systems, they fail when the transmit and received angles are very large, such as in the case of the

sensor configuration simulated in Chapter 6. It is also very interesting to point out the extremely large

spatial frequency bandwidth obtained by the multistatic sensor configuration with only a single frequency.

This discovery was made very late in the making of this thesis and the author has not had time to further

investigate methods to process the spatial bandwidth obtained.

123

The 2D FDFD forward model has proven to given great insight into the scattering processes in 2D

geometries, however, a 3D model is necessary to realistically simulate a full-body imaging system. In

the standoff imaging scenario researched in this paper it has been found that reflections from entire body

cause images generated from a 2D imaging systems to be very difficult to interpret. A larger physical

aperture, both in azimuth and angle of elevation, must be used to perform target scanning. A large physical

aperture, as opposed to a large synthetic aperture, will create a very small region of illumination, reducing

the interference of multiple scatterers on a target. With this type of target illumination, better agreement

between the 2D forward model and experimental results is hypothesized.

One of the main benefits of using a 3D forward model is the ability to thoroughly investigate the use of

using wave polarization to perform imaging. The human body is made of mostly smooth curves while man

made objects usually have flat sides. Illuminating a target with a circular polarized wave and measuring

vertical, horizontal and circular polarizations would result in multiple advantages. Multipath artifacts that

are produced by only transmitting and receiving rectangularly polarized waves could be avoided. For

example after a circular polarized wave bounces off of a dihedral shaped object, ie a persons legs, the

reflected wave becomes rectangularly polarized. Combining the returns from many different polarizations

gives image reconstruction algorithms the ability to distinguish between first and higher order imaging

artifacts.

Due to the simplistic discretization of the geometries used for the FDFD forward model, a very high

points per wavelength is required to accurately model certain types of objects. For this reason, a finite

element method is recommended for use in the forward model. By using a facet type of geometry, object

shape can be better modeled with fewer calculations and the possibility of using a forward model for a full

body scattering analysis becomes more realistic.

Through standoff scenario experimentation, it has been found that target movement significantly af-

fects images produced using a synthetic aperture measuring technique. Although a synthetic aperture in

theory produces a tight focal point, this is only true if the scene is assumed to be absolutely stationary.

For a scene containing non-cooperative targets (a typical standoff detection scenario), performing MMW

imaging using an distributed array and performing focusing via simple back propagation will fail unless

targets move less than a half wavelength during the entire scan. This may be performed with a switched

antenna system, however, due to the illumination of the entire body by each switched antenna, interference

124

from multiple scatterers would cause artifacts to appear within the focused images. This is more true when

very complicated scattering geometries such as humans are being imaged. In order to perform standoff de-

tection with synthetic apertures, target movement must be known on the order of less than half wavelength

accuracy in order to compensate. Motion compensation is possible for single moving scatters, however,

humans have too many independently moving parts contributing to the scattering which is very difficult

to accurately compensate for. For this reason a multi-element scanned system is the preferred method

of obtaining accurate images of non-cooperative targets at standoff distances. A multi-element scanned

system would have the ability to scan a target fast enough to avoid complications from target movement.

Although if target scanning is not fast enough a scanned system has a better ability to compensate for

target movement through processing Doppler effects resulting from movement in localized regions. Since

the target movement can localized , different motion compensation values could be applied to different

areas of the body.

125

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List of Figures

2.1 Rectilinear Scan: Synthetic aperture width, L = 1 meters; target range, R = 1.09 meters . 10

2.2 Picture of metal can, 4" diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Real portion of received field, Ss(ξ, ω) from coffee can, function of ξ, cross-range receiver

position, and ω angular frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 Real portion of received field decompressed in cross-range, Ss(kx, ω) from coffee can,

function of spatial frequency kx, and ω angular frequency . . . . . . . . . . . . . . . . . . 14

2.5 Real portion of received field decompressed in cross-range and demodulated in angular

frequency, S(kx, kz) from coffee can . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.6 Real portion of interpolated received field decompressed in cross-range and demodulated

in angular frequency, Si(kx, kz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.7 Power, 10log10(s(x, z)2), of focus image s(x, z) with truth data of coffee can overlaid in

blue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.8 Circular Scan: Synthetic aperture width, 360o meters; target range, R = 1.1 meters . . . . 20

2.9 Picture of metal can, 4" diameter. Not in exact center of rotation. . . . . . . . . . . . . . . 20

2.10 Real portion of received field, Ss(θ, ω) from coffee can, function of θ, azimuth receiver

position, and ω angular frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.11 Real portion of received field decompressed in azimuth, Ss(ξ, ω) from coffee can, function

of a unitless "spatial angular frequency" ξ, and ω angular frequency . . . . . . . . . . . . 21

2.12 Real portion of received field decompressed in azimuth and demodulated in angular fre-

quency, Sp(ξ, ω) from coffee can . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.13 Real portion of interpolated received field decompressed in azimuth and demodulated in

angular frequency, S(kx, ky) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

130

2.14 Power, 10log10(s(x, y)2) of focus image s(x, y), with truth data overlaid in blue. . . . . . 24

2.15 Two metal cans separated by 2" (0.0508 m) . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.16 Surface plot of 2 metal cylinders separated by 2"=(0.0508 m), using GSAFT. . . . . . . . 26

2.17 Using FFT based focusing using nearest neighbor interpolation for polar reformating.

24 dB noise floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.18 Using GSAFT. 35 dB noise floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1 Spectral Power of St(ω), Sa(ω) and Sc(ω) for ωo = 2π500 [r], T = 0.5 [s], and B =

2π50 [ rs]. Notics as long as the starting frequency ωo is much larger than the complex

envelope bandwidth, the positive and negative spectrums do not interfere with each other.

If this is true, the use of the analytic spectrum for simulations purposes will result in similar

signal processing results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 Spatial frequency representation of recorded received field values from monostatic ISAR

setup with 360 degree synthetic circular aperture. . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Physical ISAR setup for obtaining spatial frequency spectrum information in figure 3.2 . . 36

3.4 Spatial frequency representation of recorded received field values from a single frequency

bistatic radar setup shown in 3.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37


3.6 Spatial frequency representation of recorded received field values from a multi-frequency

bistatic radar setup shown in Figure 3.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.7 Physical ISAR setup for obtaining spatial frequency spectrum information in Figure 3.6 . . 37

3.8 Spatial frequency representation of recorded received field values from a multi-frequency

monostatic radar setup shown in figure 3.9, both transmitter and receiver are scanned over

circular aperture of width ∆θ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38


3.10 Fresnel integrals: C(x) =x∫0cos(πu2

2 )du and S(x) =x∫0sin(πu2

2 )du . . . . . . . . . . . . . 41

131

3.11 Complex envelope spectrum for various time-bandwidth products. Notice as the time-

bandwidth produt increases, the maximum amplitude deviation across the spectrum is

reduced. The total power of the spectrum is also increased when the time bandwidth

product is increased. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.12 Complex envelope spectrum for various time-bandwidth products with corresponding re-

ceived signal spectrum of ideal point-target response Ho(ω) = F[sc(t − τ)] for some

nominal τ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.13 Complex envelope spectrum for various time-bandwidth products with corresponding re-

ceived signal spectrum of ideal point-target response and intermediate frequency spectra

(unfiltered) SIF (ω) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.14 Real portion of windowed complex envelope for TBP = 100. B = 100. A Taylor window

and Tukey window were used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.15 Magnitude (dB) of windowed complex envelope spectrums Sc(ω) for TBP = 1000. B =

1000. A Taylor window and Tukey window were used. . . . . . . . . . . . . . . . . . . . 45

3.16 Magnitude (dB) unfiltered intermediate frequency spectrums SIF (ω) generated using win-

dowed transmitted and received signals in time. An ideal point-target response is assumed

for the received signal. Taylor and Tukey windows were used. . . . . . . . . . . . . . . . 45

4.1 A. Geometry used for input to FDFD scattered field analysis: B. Focused image of geom-

etry in A using GSAFT: C. Superposed images of separate FDFD scattered field analyses

of UPW incident on each part of geometry in A separately: D. Image B subtracted from

image A: E. Image produced from dielectric layered ellipse only: F. Image produced from

PEC rectangle only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

132

4.2 top left: incident field, blue arrow denotes direction of incident field from transceiver. top

middle: total electric field magnitude, 2 cans separated by 2". top right: scattered electric

field magnitude, 2 cans separated by 2". bottom left: difference between the scattered

fields in top left and bottom left plots. This represents the scattered field resulting from

the rexolite block between cans. bottom middle: total electric field magnitude, 2 cans

separated by 2" with rexolite block in between. bottom right: scattered electric field

magnitude, 2 cans separated by 2" with rexolite block in between. . . . . . . . . . . . . . 49

4.3 Geometry with distance measurements annotated . . . . . . . . . . . . . . . . . . . . . . 50

4.4 Scattered electric field polarized in z direction. Red line denotes location where scattered

fields are extracted for near field to near field transformation . . . . . . . . . . . . . . . . 50

4.5 Scattered electric field magnitude as a function of cross-range position on red line in figure

4.4 and PPW of FDFD simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.6 Scattered electric field phase as a function of cross-range position on red line in figure 4.4

and PPW of FDFD simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.7 2D cross-section of male human wearing metal pipes . . . . . . . . . . . . . . . . . . . . 52

4.8 2D cross-section of male human . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.9 Magnitude of scattered electric field, (a) no pipes, (b) pipes . . . . . . . . . . . . . . . . . 54

4.10 Male, no metal pipes, 1 meter wide aperture, range=10meters, 13 transmitters. . . . . . . . 55

4.11 Male, metal pipes, 1 meter wide aperture, range=10meters, 13 transmitters. . . . . . . . . 55

4.12 Male, TNT pipes, 1 meter wide aperture, range=10meters, 13 transmitters. . . . . . . . . . 56

4.13 Female, no metal pipes, 1 meter wide aperture, range=10meters, 13 transmitters. . . . . . . 56

4.14 Female,metal pipes, 1 meter wide aperture, range=10meters, 13 transmitters. . . . . . . . . 57

4.15 Female, TNT pipes, 1 meter wide aperture, range=10meters, 13 transmitters. . . . . . . . . 57

5.1 Rectilinear SAR measurement setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 FDFD input geometry. PEC Cylinder, 4" diameter . . . . . . . . . . . . . . . . . . . . . . 63

5.3 Top view of single metal can, 4" diameter . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.4 Reconstruction from simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.5 Reconstruction from measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

133

5.6 FDFD input geometry. 2 PEC Cylinders, 4" diameter, 2" separation . . . . . . . . . . . . 64

5.7 Picture of 2 metal cans, 4" diameter, 2" separation . . . . . . . . . . . . . . . . . . . . . . 64



5.10 FDFD input geometry. 2 PEC Cylinders, 4" diameter, 3" separation. . . . . . . . . . . . . 65

5.11 Picture of 2 metal cans, 4" diameter, 3" separation. . . . . . . . . . . . . . . . . . . . . . 65



5.14 FDFD input geometry. 2 PEC Cylinders, 4" diameter, 4" separation. . . . . . . . . . . . . 66

5.15 Picture of 2 metal cans, 4" diameter, 4" separation. . . . . . . . . . . . . . . . . . . . . . 66



5.18 FDFD input geometry. 2 PEC Cylinders, 4" diameter, 2" separation, Rexolite block in

between. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.19 Picture of 2 metal cans, 4" diameter, 2" separation, Rexolite block in between. . . . . . . . 67



5.22 FDFD input geometry. 2 PEC Cylinders, 4" diameter, 2" separation, Rexolite block on

side of right can. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.23 Picture of 2 metal cans, 4" diameter, 2" separation, 2" separation, Rexolite block on side

of right can. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68



5.26 FDFD input geometry. Rexolite block, 5.08 cm thick, 31 cm wide. . . . . . . . . . . . . . 69

5.27 Picture of rexolite block, 5.08 cm thick, 31 cm wide. . . . . . . . . . . . . . . . . . . . . 69



5.30 FDFD input geometry. Rexolite block, 5.08 cm thick, 31 cm wide, with half ground plane. 70

5.31 Picture of rexolite block, 5.08 cm thick, 31 cm wide, with half ground plane. . . . . . . . 70

134



5.34 FDFD input geometry. Rexolite block, 5.08 cm thick, 31 cm wide, with full ground plane. 71

5.35 Picture of rexolite block, 5.08 cm thick, 31 cm wide, with full ground plane. . . . . . . . 71



5.38 Circular synthetic aperture size, 450o; target range, R = 1.09 meters. . . . . . . . . . . . . 72

5.39 Picture of single metal can, 4" diameter, top view . . . . . . . . . . . . . . . . . . . . . . 73

5.40 FDFD input geometry. PEC Cylinder, 4" diameter . . . . . . . . . . . . . . . . . . . . . . 73

5.41 Physical representation of scanning geometry, highlighted section represents actual space

measured . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.42 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.43 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.44 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.45 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.46 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.47 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.48 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.49 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.50 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.51 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.52 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.53 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.54 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.55 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.56 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.57 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.58 Final image generated from simulated data, Target: single metal can 4" diameter . . . . . . 78

5.59 Final image generated from measured data, Target: single metal can 4" diameter . . . . . . 79

135

5.60 Picture of two cans separated by 2" geometry used for input to FDFD simulation . . . . . 80

5.61 Picture of two cans separated by 2" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.62 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.63 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.64 Simulated data, Target: 2 metal cans separated by 2" . . . . . . . . . . . . . . . . . . . . 80

5.65 Measured data, Target: 2 metal cans separated by 2" . . . . . . . . . . . . . . . . . . . . . 80













5.78 Final image generated from simulated data, Target: 2 metal cans separated by 2" . . . . . . 83

5.79 Final image generated from measured data, Target: 2 metal cans separated by 2" . . . . . . 84

5.80 FDFD input geometry of Two cans separated by 2" geometry with rexolite block in between 85

5.81 Picture of Two cans separated by 2" with rexolite block in between. . . . . . . . . . . . . 85

5.82 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.83 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.84 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.85 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.86 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.87 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.88 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

136

5.89 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.90 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.91 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.92 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.93 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.94 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.95 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.96 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.97 Measured data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.98 Final image generated from simulated data, Target: 2 metal cans, 2" separation, rexolite

block in between . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.99 Final image generated from measured data, Target: 2 metal cans, 2" separation, rexolite

block in between . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.100Simulated: 1 metal can. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.101Measured: 1 metal can. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.102Simulated: 2 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.103Measured: 2 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.104Simulated: rexolite block in front of one metal can. . . . . . . . . . . . . . . . . . . . . . 90

5.105Measured: rexolite block in front of one metal can. . . . . . . . . . . . . . . . . . . . . . 90

5.106Simulated: rexolite block in between 2 metal cans. . . . . . . . . . . . . . . . . . . . . . 90

5.107Measured: rexolite block in between 2 metal cans. . . . . . . . . . . . . . . . . . . . . . 90

5.108Picture of Two cans separated by 2" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.109Picture of Two cans separated by 2" geometry used for input to FDFD simulation . . . . . 91

5.110Picture of Two cans separated by 2" with rexolite block in between . . . . . . . . . . . . . 91

5.111Picture of Two cans separated by 2" with rexolite block in between. Geometry used for

input to FDFD simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.1122 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.113with rexolite block in between 2 metal cans. . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.1142 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

137


5.1162 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92


5.1182 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93


5.1202 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93


5.1222 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93


5.1242 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94


5.1262 metal cans only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94


5.128Final image generated 2 cans only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.129Final image generated 2 cans with rexolite block . . . . . . . . . . . . . . . . . . . . . . 95

5.130Picture of probe used for making dielectric measurements. . . . . . . . . . . . . . . . . . 96

5.131Schematic of probe used for making dielectric measurements. . . . . . . . . . . . . . . . 96

5.132ε′ dielectric measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.133ε′′ dielectric measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.134δ = ε′′

ε′= loss tangent calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.135γ =1√ε′−1

1√ε′

+1 = reflection coefficient calculations . . . . . . . . . . . . . . . . . . . . . . . 98

5.136Picture of 1 metal can (left) and 1 ballistics gelatin cylinder. Each is 4" in diameter.

Separated by 4". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.137Reconstruction from measured data. 20dB dynamic range. 1 metal can, 1 ballistics gelatin

cylinder, 4" separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.138Surface plot of reconstruction from measured data. 20dB dynamic range. 1 metal can, 1

ballistics gelatin cylinder, 4" separation. Maximum power in dB of gelatin reconstruction

is about 3.5 dB less than the metal can. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.139Picture of two gelatin cylinders, about 5.5" diameter, separated by 4" . . . . . . . . . . . . 101

138

5.140Picture of two ballistics gelatin cylinders, about 5.5" diameter, covered by denim cloth,

separated by 4" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.141Reconstruction from measured data. 25dB dynamic range. two ballistics gelatin cylinders,

4" separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101


covered by denim cloth, 4" separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.143Picture of two ballistics gelatin cylinders, about 5.5" diameter, separated by 4", with rex-

olite block in between. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.144Picture of two ballistics gelatin cylinders, about 5.5" diameter, covered by denim cloth,

separated by 4", with rexolite block in between. . . . . . . . . . . . . . . . . . . . . . . . 102


4" separation, rexolite block in between. . . . . . . . . . . . . . . . . . . . . . . . . . . . 102


covered by denim cloth, 4" separation, rexolite block in between. . . . . . . . . . . . . . . 102

5.1472 ballistics gelatin cylinders, 4" separation . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.148Picture of two ballistics gelatin cylinders, about 5.5" diameter, separated by 4" . . . . . . . 103

5.1492 ballistics gelatin cylinders, 4" separation, rexolite block in between. . . . . . . . . . . . 103


olite block in between . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.1512 ballistics gelatin cylinders, 4" separation, rexolite block in between covered by absorber

material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103


olite block in between covered by absorber material. . . . . . . . . . . . . . . . . . . . . 103

139

6.1 top left: incident field, blue arrow denotes direction of incident field from transceiver. top

middle: total electric field magnitude, 2 cans separated by 2". top right: scattered electric

field magnitude, 2 cans separated by 2". bottom left: difference between the scattered

fields in top left and bottom left plots. This represents the scattered field resulting from

the rexolite block between cans. bottom middle: total electric field magnitude, 2 cans

separated by 2" with rexolite block in between. bottom right: scattered electric field

magnitude, 2 cans separated by 2" with rexolite block in between. . . . . . . . . . . . . . 104

6.2 Multistatic sensor configuration. Transmitter is circularly scanned while two static recti-

linear arrays recieve for every transmitter location. . . . . . . . . . . . . . . . . . . . . . 105

6.3 Multistatic measurement setup. Red dots indicate transmitter positions. Green and Blue

dots indicate receiver positions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.4 Monostatic measurment setup. Red dots indicate single transmit/receive locations. . . . . . 106

6.5 Spatial frequency coverage for single multistatic circular scan using only 1 frequency. . . . 106

6.6 Spatial frequency coverage for single monostatic circular scan using only 1 frequency. . . 106

6.7 Spatial frequency coverage for single multistatic circular scan using 50% bandwidth to

starting frequency ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.8 Spatial frequency coverage for single monostatic circular scan using 50% bandwidth to

starting frequency ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.9 Multi static reconstruction, 25 dB dynamic range. . . . . . . . . . . . . . . . . . . . . . . 107

6.10 Circular monostatic reconstruction, 20 dB dynamic range. . . . . . . . . . . . . . . . . . 107

6.11 Multi static reconstruction, 30 dB dynamic range. . . . . . . . . . . . . . . . . . . . . . . 107

7.1 Left: 2D projection generated 3D data set. Middle: Region containing higher order arti-

facts. Topr Right: 1D Projection of 2D data set. Bottom Right: 2D image crossection of

2D data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

8.1 Standoff circular ISAR experiment setup. . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.2 3 targets used in experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

8.3 2 example ISAR images. (a) Subject a (in figure 3) wearing no pipes. (b) Subject a wearing

one pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

140

8.4 Results: (a) 3o off normal to target chest. (b) 61o off normal to target chest . . . . . . . . . 115

9.1 Image processing flow chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

9.2 Incident angle = 90o (normal incidence). Simulated image of innocent male target with

simulated target geometry overlaid. 25dB dynamic range. . . . . . . . . . . . . . . . . . . 118

9.3 Incident angle = θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

9.4 Incident angle = 90o (normal incidence). Experimentally obtained image of innocent male

target, automatically shifted to best fitting range and cross range positions, estimated body

geometry overlaid. 25dB dynamic range. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

9.5 Incident angle = 90o (normal incidence). Simulated image of male target with four metal

pipes on body with simulated target geometry overlaid. 25dB dynamic range. . . . . . . . 120

9.6 Incident angle = 90o (normal incidence). Experimentally obtained image male target with

4 metal pipes on body, automatically shifted to best fitting range and cross range positions,

estimated threat target geometry overlaid. 25dB dynamic range. . . . . . . . . . . . . . . 120

9.7 Incident angle = 115o. Simulated image of innocent male target with simulated target

geometry overlaid. 25dB dynamic range. . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

9.8 Incident angle = 115o. Experimentally obtained image of innocent male target, automat-

ically shifted to best fitting range and cross range positions, estimated body geometry

overlaid. 25dB dynamic range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

9.9 Incident angle = 115o. Simulated image of male target with four metal pipes on body with

simulated target geometry overlaid. 25dB dynamic range. . . . . . . . . . . . . . . . . . . 122

9.10 Incident angle = 115o. Experimentally obtained image male target with 4 metal pipes on

body, automatically shifted to best fitting range and cross range positions, estimated threat

target geometry overlaid. 25dB dynamic range. . . . . . . . . . . . . . . . . . . . . . . . 122

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