Microwave Object Detection and imagereconstruction with a synthetic circular

aperture

Master thesis

Jan Joseph Estrada

Thesis submitted for the degree ofMaster in Nanoelectronics

60 credits

Department of InformaticsFaculty of mathematics and natural sciences

UNIVERSITY OF OSLO

Autumn 2018

Microwave Object Detection andimage reconstruction with a synthetic

circular aperture

Master thesis

Jan Joseph Estrada

© 2018 Jan Joseph Estrada

Microwave Object Detection and image reconstruction with a synthetic circular aperture

http://www.duo.uio.no/

Printed: Reprosentralen, University of Oslo

Abstract

The use of microwave imaging in the medical field is promising. The advantagesover conventional methods such as X-ray, MRI, is cost-effective, non-ionizing signals.Microwave tomography is complex but promising in soft tissue imaging. Largerwavelengths are more affected by diffraction. Therefore assumptions of straightpropagation in a dielectric are only valid for frequencies at ultraviolet to gamma rayspectrum. By using a circular radar aperture to image an object and with post-processingimage reconstruction techniques improves the performance of the total imaging system.The simulation showed using an ultrawideband (UWB) enhances increasing the depthresolution while angular resolution enhances cross-range resolution and was able todistinguish targes location and range. A tradeoff occurs between attenuation andresolution as a function of frequency, especially in a lossy dielectric. The importance ofa stable imaging system for the consistency of measurements is crucial when performingartefact removal, which was my reason of failure at recreating an image of measureddata since the error margin of the phase difference to high and highly susceptible forinconsistencies.

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Contents

I Introduction 1

1 Introduction 31.1 Brief history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Medical imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Motivation and goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Background 72.1 Wave equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Maxwell’s equation in free space . . . . . . . . . . . . . . . . . . . . 72.1.2 Finite difference method for solving Maxwell’s equation . . . . . . 9

2.2 Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.1 Free space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.2 Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.3 Dielectric Phantom . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Radar principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Reflection and transmission . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Radar Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.3 Electromagnetism in biologic tissue . . . . . . . . . . . . . . . . . . 15

2.4 Antenna Aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4.1 Array Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4.2 Angular resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4.3 Uniform circular array . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.4 Synthetic aperture radar . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5 Ultra wide band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5.1 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.6 Image Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.6.1 Delay and sum reconstruction . . . . . . . . . . . . . . . . . . . . . 192.6.2 Adaptive Image recontruction . . . . . . . . . . . . . . . . . . . . . 202.6.3 Delay Multiply and sum . . . . . . . . . . . . . . . . . . . . . . . . . 202.6.4 Inverse scattering problem . . . . . . . . . . . . . . . . . . . . . . . 20

2.7 S-parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7.1 Vector Network Analyzer . . . . . . . . . . . . . . . . . . . . . . . . 232.7.2 Frequency and time domain . . . . . . . . . . . . . . . . . . . . . . . 23

2.8 Microwave imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.8.1 Microwave tomography . . . . . . . . . . . . . . . . . . . . . . . . . 24

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2.8.2 Microwave imaging using s parameters . . . . . . . . . . . . . . . . 242.8.3 Microwave tomography for Brain imaging . . . . . . . . . . . . . . 242.8.4 Realistic wave propagation . . . . . . . . . . . . . . . . . . . . . . . 25

II The project 27

3 Implementation/Method of approach 293.1 Hardware and Software tools . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.1.1 GPRmax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.2 SolidWorks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.3 MERIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.4 Other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 Choice of input pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2.1 Pulse modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2.2 VNA signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.3 Truncating Window function . . . . . . . . . . . . . . . . . . . . . . 323.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3 Phantom design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.1 Simulated phantom . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.2 Design Properties of a phantom . . . . . . . . . . . . . . . . . . . . 333.3.3 Measurments of solutions . . . . . . . . . . . . . . . . . . . . . . . . 353.3.4 Expected total attenuation . . . . . . . . . . . . . . . . . . . . . . . . 353.3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4 Imaging System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.4.1 Rotary controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.4.2 VNA settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.4.3 Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.4 Chamber construction . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5 Post proscessing rawdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.5.1 Artefact removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.5.2 Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.5.3 Image reconstruction algorithm . . . . . . . . . . . . . . . . . . . . . 423.5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Results 454.1 Imaging system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.1 Detection and location of an object . . . . . . . . . . . . . . . . . . . 484.2.2 Noise reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2.3 Multiple object detection . . . . . . . . . . . . . . . . . . . . . . . . . 504.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.3 Measured data on real phantom . . . . . . . . . . . . . . . . . . . . . . . . . 514.3.1 Reflection coefficient based imaging . . . . . . . . . . . . . . . . . . 51

4.4 MERIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

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4.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.5.1 Possible cause of Error . . . . . . . . . . . . . . . . . . . . . . . . . . 554.5.2 Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.5.3 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.5.4 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

III Conclusion 594.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.6.1 Last remark and thoughts . . . . . . . . . . . . . . . . . . . . . . . . 61

A gprMAX 67

B Matlab simulation 69

C Matlab Measurements 77

D Servo script 85

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List of Figures

1.1 Early era flouroscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Yee cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Radar cross section vs relative frequency . . . . . . . . . . . . . . . . . . . . 142.3 General multiportnetwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4 General S-port network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1 Illustration of approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Excited pulse and its frequency response . . . . . . . . . . . . . . . . . . . 313.3 Comparing 3 window function and its frequency transform . . . . . . . . 333.4 (a) center positioned object, (b) off-center position object . . . . . . . . . . 343.5 Dielectrics of gray tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.6 (a) real permittivity, (b) complex permittivity . . . . . . . . . . . . . . . . . 363.7 Illustration of imaging system setup . . . . . . . . . . . . . . . . . . . . . . 373.8 Monopole Antenna soldiered on a rigid coax . . . . . . . . . . . . . . . . . 393.9 3d construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.10 Artifact removal on simulated data . . . . . . . . . . . . . . . . . . . . . . 413.11 Enveloped signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.12 Signal from different receivers . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1 Final setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2 Final setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3 Final setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.4 (a) center positioned, (b) off center position . . . . . . . . . . . . . . . . . . 484.5 Location off center (a) 8 antenna DAS, (b) 8 Antenna DMAS, (c) 16 Antenna

DAS, (d)16 antenna DMAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.6 2 objects present 5 cm apart (a) 8 antenna DAS, (b) 8 Antenna DMAS, (c)

16 Antenna DAS, (d)16 antenna DMAS . . . . . . . . . . . . . . . . . . . . 504.7 Reflection based imaging, location at (a) center, (b) off center, (c) side . . . 524.8 Tomopgraphy based imaging, location (a) center, (b) off center, (c) side . . 534.9 Merit based . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

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List of Tables

3.1 Ingredients for each solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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Preface

A variety of scanning and imaging systems are used for different purpose, from rangingand allocation to biomedical imaging. Application of systems in the medical field employdifferent imaging techniques such as CT, PET, MRI, ultrasonography.

The awareness of radiation exposure and cost-effectiveness has increased since thetime of invention. It exists, therefore, a demand for a safer and mobile imagingtechnology with high accuracy. The potential of microwave imaging is knownamong scientists, and conducted research exists but only to the extent of optimizingsegments of the technique itself. Microwave tomography was limited due to numeroustechnical reasons, including high costs of unique hardware components and insufficientcomputing power. The motivating factor for this thesis the is the contribution of afunctioning imaging system accurate enough to be an applicant in medical diagnostics.Since the existing imaging systems have such a high cost, to accomplish the same tasks ata much lower cost would benefit mankind, especially for the underdeveloped countrieswith the limited economy.

According to LHL and National Centre for Biotechnology Institute, Norway hasapproximately 40000 cases of brain stroke each year, more or less in countries worldwiderelative to the population. Stroke is one of many diagnoses were administeringemergency aid is vital. The preferred medicine for stroke caused by a blood clot could befatal if given to stroke caused by bleeding. A fast diagnostic is essential to differentiatebetween the two types. The real-time aspect of the imaging can truly benefit the acutediagnostic aspect.

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Acknowledgements

Dedicated to my daughter Leah and wife for the love and support and the source of ded-ication.

I would like to thank my supervisor Mathias Tømmer for his assistance and his know-ledge that helped me throughout this thesis. A true inspiration of what I as a futurescientist should aim for.

To my co-supervisor Tor Sverre Lande, for his invaluable feedback, and as a true mo-tivator towards the end.

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Part I

Introduction

1

Chapter 1

Introduction

In this project, I will attempt to reconstruct an image of an object due to back-scatteredmicrowave signals. The main object of this thesis is using radar ranging and detectionprinciples to locate a change in dielectrics in a homogeneous background. The final 2Dimage will be a representation of the location of the object. I will introduce why it ispossible to do so, and the underlying phenomena. This thesis is organized starting withan introductory history, background theory applicated in this thesis will be presented inthe next chapter. Following chapter is the experiments and simulation done in order tocreate the final results, which will be presented in the last chapter. I summarize with aconclusion.

1.1 Brief history

Since the conclusion of the existence of Electromagnetic waves by Hertz, earlier theorizedby James Clerk Maxwell, huge progress has been made in its application in multiplefields in the last 150 years. Medical imaging began in 1897 with the invention of X-ray by Roentgen. Not long after the famous Marie Courie got her Noble Prize forher research in radiation. The invention of fluoroscope with sufficient image intensityfor commercial purpose came shortly after when Thomas Edison began investigatingfluorescent material properties. The ability to inspect bone-tissue was a medicalbreakthrough, soon to be adopted internationally. It wasn’t until 1940 the long termseffects of radiation exposure began to surface and the acknowledgement of the damage[1]. The Radon transform, mathematic operations which in essential imaging techniqueshas long been theorized, but not experimented on due to equipment has not beeninvented yet.

The first evidence of radar principle had its origin in wireless technology as early as1897 when Alexander Popov observed interference by a passing ship while transmittingwireless signals. The first operating device, the telemobiloscope, was built in 1904 byGerman Christian Hülsemeyer. A continuous wave device operating at 650MHz, capableof detecting the presence of ships within 2 miles dense fog. Its performance was limiteddue to lack of effective electronics and antennas.

The idea of radar was introduced by Nicola Tesla in 1914, most known for his work onmodern alternating currents (AC) electricity supply. Not long after, Guglielmo Macroni,

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a Nobel Prize winner in physics, lectured on principles of radar in 1922. Research onradar began to arise almost simultaneously in all war participating nations, hence thecontribution from scientists across multiple nations [2].

Figure 1.1: Early era flouroscope

First radar built using the Doppler Principlewas in 1935. Intended use was positioning ondetection of vehicles pre World War II era [3].

By the end of WWII, radar systems had ad-vanced to a level inconceivable before the war andcontinued to be refined post-war era. Hence thefast development of the electronic market todaywhen Microwave technology was introduced.

Radar technology was not fully implementedfor medical application until the early 70s. Meas-urements of organ movements and qualitative de-tection of water condensation in human lungs wereamong the first uses in medical diagnostic [4].

1.2 Medical imaging

Over the last two decades, microwave imaging (MWI) has been investigated as a differentimaging and diagnostics technique for tumour detection [5].

Development of EM imaging techniques for the purpose of detecting and evaluatinghidden objects in a structure has been the focus of investigation in the field ofnondestructive testing and evaluation. EM-techniques may be based on imagingfrequency band. Microwave band covering 300MHz - 30 GHz, millimetre wave covering30GHz -300GHz, or terahertz covering the range of 300GHz - 3THz [6]. This project willmainly be utilizing the microwave band between 300MHz - 30GHz even thou using onlythe lower part between 1GHz and 6GHz. The reason behind this choice of the bandwill be elaborated in the next chapter, and what properties that make the best suitablefrequency-band for imaging.

A general view of an imaging system is composed of two parts, the hardware andthe signal processing (imaging algorithm). The hardware is composed of instrumentsetup, antenna, measurement instruments and recording tools. While the signalprocessing part is the utilization of the "collected data" and determines the electricaland geometrical parameters of an object under test. Equally essential for high-qualityimage reconstruction. In general, the techniques can be classified as quantitative imagingtechniques or qualitative imaging techniques[7].

Today’s computers are faster and can handle more complex mathematical functionslike the inverse scattering problem, which was/still is a constraint. The problem isresolved by redefining the original problem into a suitable optimization problem eventhough it comes with drawbacks in terms of validity and misrepresenting the actualphysics.

There are numerous approaches which in their mission to detect, locate, and mapdifferent tissue [8] [9] [10] [11].

Although microwave imaging has the potential to offer improved resolution, a

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number of challenges exist. Biological tissue is heterogeneous, resulting in a complexfield distribution in the body. Efforts should be made to suppress signals due to theinterference of common artefacts surrounding the area of interests. Will it be the skull,skin and fat layers, cerebral fluid when imaging brain, or skin nipple, chest wall etc.when imaging breasts. Embolisms and early-stage tumours are usually in mm sizes sohigh resolution is required. The losses introduce a trade-off between spatial resolutionan depth penetration.

The high resolution imposes an enlarged size of computation required to reconstructan image. In addition, the individual anatomical features of patients also add a certaindegree of complexity to the process. Relative to the imaging scenario, a rise in specificchallenges occurs. Different methods of approach and system configuration related tothe different physical effects of a specific area [12].

1.3 Motivation and goals

As I have a background in the medical field, medical technology is of great interest.Imaging systems today are a majority of large expensive systems and invasive in termsof radiation exposure and the use of fluorescent contrast fluid. Today we possessreliant diagnostic tools in the medical field but has some inconveniences such asionizing radiation related to cancer, large size and high power consumption, thus furtherimprovements will most likely be a contribution in this technology. Third world countriescould have great benefits with cheap and reliant medical systems. The contribution ofa cost-effective and reliant medical imaging system could improve international publichealth. Quick diagnostics is crucial at ambulant scenarios such as stroke and can be life-saving if a correct classification of stroke (internal bleeding or thrombus), and treatedwithin a couple of hours.

My goal in this thesis is to prove the concept of high-resolution ultra wideband radardetection of an object inside biological tissue. A commercial application of a microwave-based imaging technology does not exist as of today, even thou microwaves are widelyused(Ground/wall penetration, heartbeat monitoring). I can achieve this by mimickinga UWB excited signal into a simulated phantom, read of the backscattered signals andperform a synthetic focus algorithm in order to create an image. I will further test on aliquid phantom with realistic dielectric properties of a human brain.

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Chapter 2

Background

In this section, I elaborate the theory and formulas I used throughout this project. Thisinvolves physics of wave propagation, basic antenna aperture theory and applications,and signal processing.

2.1 Wave equation

In Physics, a wave is a disturbance that transfers energy through matter or space andconsist of oscillations or vibrations of a physical medium or a field. Sound wavespropagate via air molecules colliding and the kinetic energy is transported in terms ofpressure. This is classified as mechanical waves whereas electromagnetic waves do notrequire a medium. Instead, they consist of periodic oscillations of electrical and magneticfields originally generated by charged particles. These types vary in wavelength. Wavesare described by a wave equation which explains how the disturbance proceeds overtime. The occurrence and travel of electromagnetic field operate in waves as it differs inboth time and space.

2.1.1 Maxwell’s equation in free space

The physics of propagation is described by the wave equation for the appropriatemedium and boundary conditions. For example, James Clerk Maxwell developed atheory of propagation of electromagnetic fields in free space

∇× ~E = −δ(µ~H)

δt∇ · (ε~E) = 0 Faradays law (2.1)

∇× ~H =δ(ε~E)

δt∇ · (µ~H) = 0 Ampere’s law (2.2)

Where ~E is the electric field intensity,~H is the magnetic field intensityε is the electric permitivityµ is the magnetic permeabilityand ∇ represent the gradient vector operator [13] [7].

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The wave equation derived from Maxwell’s equation is

∇2~E =1c2

δ2~Eδt2 (2.3)

where c is the speed of propagation,and ∇2 represents the Laplacian operator

δ2

δx2 +δ2

δy2 +δ2

δz2 (2.4)

A general propagating signal in 3D space can be represented as s(x,y,z,t), the spatialvalues x, y and z amplitude displacement and how it evolves in time t. The signalcharacteristic has fundamental importance such as the direction of propagation, thespeed of propagation, and its frequency content, spatial as well as temporal. Whiletemporal contains an energy spectrum as a function of frequency cycles/s, ie. numberof periods per unit of time, spatial frequency is measured as a function of cycles/meter,the number of periods per unit of distance.

Due to linearity of the wave equation in free space, it is possible to build morecomplicated solutions of the equation by expressing them as sums or integrals of acomplex exponential, i.e., we can use Fourier Theory to form an integral of complexexponentials to represent any wave shape.

We can assume a signal s(x,y,z,t) has a complex exponential form of

s(x, y, z, t) = Aexp(j(wt− kxx− kyy− kzz)) (2.5)

where (kx, ky, kz) =~k is the wavenumber vector, the same way ω represents temporalfrequency,~k represents spatial frequency. In order to satisfy the wave equation , the signalmust satisfy a constraint of

~k2 =ω2

c2 (2.6)

The wavenumber vector points in the direction of propagation and its magnitudewhere the slowness vector~α =~k/ω [13] [14].Solving Maxwell’s equation in order to determine the electric field ~E form the

knowledge of the source, obstacles and the object of interest’s dielectric properties, iscalled the forward scattering problem. Inversely, determining the mediums dielectricproperties from the knowledge of the electric field and source is called the inversescattering problem [7]. One can solve the inverse scattering problem by makingassumptions about the wave propagation which leads to error if not appropriately takenhandled. This possesses a great challenge in the RF field which is still being unsolvedtoday.

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2.1.2 Finite difference method for solving Maxwell’s equation

Finite difference method (FDTD)is the idea of replacing all derivatives in a differentialequation with approximations. Solution to the time-dependent Maxwell’s equations ingeneral form is unknown except for a few special cases. The difficulty is mostly due to theimposition of the boundary conditions. In order to obtain a solution, one has to define aninitial condition and allow for the resulting fields to propagate through space reaching azero value at infinity. By specifying a boundary which limits the geometry of the problemand where EM fields can take a predetermined value can give a prediction of how anEM field propagates in different environments. The FDTD approach to the numericalsolution of Maxwell’s equations is to discretize both space and time. The FTDT relationof spatial step size at a given time interval is

∆t =1

c0√

∆x2 + ∆y2 + ∆x2(2.7)

Kane Yee [15], a pioneer of the FDTD method, illustrated the discretized FDTDgrid(Yee cell) and a way to numerical interpret the EM wave propagation.

Figure 2.1: Yee cell

Simulation results will always contain some numerical error. It is important tounderstand some of the sources of numerical error and steps that can be taken to reducethe error to an acceptable level. Common errors are related to the calculation of wavepropagation with a coarse mesh. As non-straight contour of objects will get a "staircase"approximation. This results in an inaccurate description of the EM field distribution. Byincreasing, grid resolution would lower the inaccuracies but will drastically increase thedata and calculation time [16].

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2.2 Attenuation

In reality, all medium of which a wave passes through has a certain amount of loss. Withattenuation taken into account, the wave equation for the electric field changes to

∇2~E =1c2

δ2~Eδt2 + (εµ + σ)

δ~Eδt

(2.8)

where σ is the conductive properties in S/m−1 What differs from the wave equation infree space is the dampening term (εµ + σ) δ~E

δt There are multiple phenomena on why anEM wave loses its power from travelling from one transmitter to a receiver. The net totalattenuation of the receiving signal is the summation of all the attenuation coefficientsα . I will only discuss the path loss most relevant to microwave imaging. When amaterial has parameters such as permittivity, conductivity, and/or permeability varyingas a function of frequency, it is said to be dispersive. Evaluating dielectric dispersionconsists in considering the variation of the properties as a function of frequency.

2.2.1 Free space

Friis equation is one the most fundamental equations in antenna theory. It is used tocalculate the power transmitted and received between two antennas and is a function ofthe distance between the antennas and the operating frequency. The main ideology isthe power of an isotropic wave at a constant power will dissipate as the spherical wavesexpand, thus lowering the power density of the wave at the receiving end.

Assume PT Watts of total power are delivered to the transmit antenna. For themoment assume that the antenna is omnidirectional, lossless and that the receiverantenna is in the far field of the transmit antenna. Then the power density p(Watts persquare meter) of the plane wave incident on the receiver antenna a distance from theequation

PR =PTGTGRλ2

(4πR)2 (2.9)

Where GT and GRis the gain of the transmitting and receiving antenna respectivelyPR is the power measured at the receiving antennaλ is wave length of the signal with the relation c

fc being the speed of light, and f for frequency in Hz.

A useful form of the Friis equation is to insert the relation of λ in equation 2.9 whichgives

PR =PTGTGRc2

(4πR f )2 (2.10)

Note that higher frequency and speed of propagation is factors that affect total powerreceived. When isolating the loss factor by ignoring the individual antenna propertiessuch as gain Gt and GR and express it as a power gain of an antenna system Friis equationcan be altered to

Pr

Pt=( λ

4πd

)2(2.11)

10

Since the path loss formula expresses a loss value that is reciprocal of the gain in termsof dB

αiso = 10 ∗ log((4πd

λ

)2)(2.12)

[17] The equation can be used to describes the expected loss at per unit of distance in freespace.

2.2.2 Dielectrics

The definition of dielectrics (or dielectric materials) is the electromagnetic propertiesof a medium. The wave equation is a function of electric permittivity ε, magneticpermeability µ. In general, the velocity of propagation is

c =1

√µ0µrε0εr

(2.13)

whereµ0 = 1.261̇0−6Hm−1, absolute magnetic permeability of free spaceε0 = 8.861̇0−6Fm−1, absolute electric permittivityµr relative magnetic permability of the mediumεr reltive electric permittivity of the medium

In free space, these dielectric constants that are independent of frequency and themedium is not hence dispersive (εr = 1, µr = 1) simplifies the equation to the velocity oflight

c =1

√µ0ε0

(2.14)

[18]In reality is that the dielectrics are not perfect which results in a slightly different

effect. Free or bound carriers can result in both heating and losses. Dissipation can becharacterized as an imaginary component with a relative permittivity

ε = ε′ + jε′′ (2.15)

[19]where ε′′ is called the dielectric absorption as it intervenes in the equation for the

electrical energy. And is usually expressed in terms of loss tangent δ with the relation

tanδ =ε′′

ε′(2.16)

Multiple phenomena are responsible for this dielectric absorption. These principlesare important when creating and designing a controlled substance of dielectric forRF purposes. Analyzing the equation in electric field dielectrics 2.8 states that theconductivity, permittivity and permeability all is responsible for the loss. I will not gointo detail on loss due to conductivity as is less relevant in the process of phantom designin the following subsection.

11

2.2.3 Dielectric Phantom

Phantoms are often used in medical imaging and are a substance that mimics theproperties of environments surrounding the object of interests. It is specially designedtowards its intent of use, and is more readily available and provides more consistentresults than the use of a living object or cadaver, and prevents the exposure of direct risktowards a living organism. But a large variety of different phantoms exists dependingon the purpose of use, and field of use. As velocity is dependent on the properties of themedium. Absorption of the signal is in general, the energy converted to heat. Absorptionof microwave energy in involves primary two mechanisms: ionic interaction and dipolarrotation. Salt, for example, is composed of positive sodium and negative chloride ionsin dissociated form. The net electric field will accelerate the particle in one direction andthe oppositely charged particle in the other direction. The accelerating particle collidesand it will impart kinetic energy to an adjacent particle which again will interact withtheir neighbouring particles, causing heat and heat transfer. The physically separatedcharges are caller dipoles, such as water and exhibit strong dipole moments. When watermolecules are placed in an alternating electric field, they will experience a rotational forceattempting to orient them in the direction of the field. As molecules attempt to orientthemselves in the field direction, they collide randomly with their neighbours. The fieldreverses and they try to line up with the reversed direction and further collision occurscauses thermal agitation.

Liquid water is polar and easily absorb microwave energy based on the mechanismof dipolar rotation. Water can exist in either free or bound state. Bound water is when themolecules physically adsorbed to the surface of dry material making it less susceptiblefor dipolar rotation, thus effecting dielectric loss factor.

Loss factor from ionic conduction increases with temperature due to the decreasedviscosity of the liquid and increased mobility of the ions. At higher temperatures, ionsbecome more mobile and not tightly bound to water, and thus the loss factor from ionicloss component increases with temperature [20].

This can be a problem when applied to living beings as human consists of 60% ofwater. Rules and regulations applies and set by national committees.

Dielectric phantom’s purpose is to mimic the dielectric properties of biological tissuein a certain bandwidth.

The idea behind the phantom design is thinning out water in order to lower the ε′ andε′′ relative to deionized water, pure H20, which has a known permittivity characteristicand loss. It is, in fact, a calibration process when measuring dielectric properties ofa sample. Consumable tap-water has gone through the mineralization process whichaffects the dielectric properties. Comparison between tap water(depending on quality)and de-ionized water is not so noticeable [21].

Chew et al [22] conducted an experiment to model the human brain in terms ofrelative permittivity dielectric properties. It is possible to mimic brain tissue dielectricswith a mixture of sugar, water and agar-agar. Sugar plays an important role in stabilizingthe permittivity values of the model. They concluded that further improvements isneeded but indeed possible with low cost materials.

12

2.3 Radar principles

Electromagnetic scattering is the physical phenomenon that occurs when an EM wavehits a discontinuity or an object. The deviation of the wave trajectory is known asscattering. Radar signals reflect or scatter in different ways depending on the wavelengthof the EM wave and the shape of the object. If the wavelength of the EM wave is muchsmaller than the size of the scatterer. This type of scattering is often called scattering in theoptical region and the dominant scattering phenomenon is usually forward scattering. Ifthe EM wave is of comparable size of the scatterer, such as within a few wavelengths,some resonances may occur and the scattering intensity may fluctuate for differentfrequencies. This particular scattering type is called Mie scattering or resonant, and theamount of scattering is mostly forward and some backward scattering. If the EM waveis much longer than the size of the scatterer, the wave is dispersed around the scatterer,meaning scattering trajectory in all directions. This type of reflection is named Rayleighsscattering [23]. The different regions are illustrated in figure 2.2 relative to a sphere.

Cross section of σ of a sphere of radius a can be shown as a function of thecircumference. In large spheres the asymptotic expression is given by

σsphere = πa2, λ� a (2.17)

For small spheres(Rayleigh region) the asymptotic expression is

σsphere = πa29(ka)4, a� λ (2.18)

where k is the wave number which is defined as

k =2π

λ(2.19)

It is worth to note the cross section of a cylinder is

σcylinder =2aπL2

λ(2.20)

2.3.1 Reflection and transmission

Reflection and transmission of light are often oversimplified to a phenomenon ofdirection change of an incoming ray and opacity of an object, which is true but thereis a reason of why reflections and transmission take place. From an incident wavestriking a discontinuity in results in a reflected wave and a transmitted wave due to asudden change in speed of propagation. As the properties of two media have unequalpermittivity, the speed of wave propagation is unique to the material. The sudden changein velocity creates a congestion of photons as light transitions into a new medium. Henceresulting into photons "bouncing off" and continues in a new direction depending onthe angle of incidence, and photons travel through. The angles of reflection equal theangle of incidence, while the angles of refraction of the transmitted wave obey Snell’sLaw. This principle is the reasons why it is possible to utilize an electromagnetic field todetect distant or hidden objects. Since the transmitted and the reflected wave experiencea certain amount of loss, directional changes, information of the second medium can be

13

Figure 2.2: Radar cross section vs relative frequency

derived given that we know the properties of the first medium. This is oversimplifiedas there are multiple factors of loss and direction change of an incident wave hitting acomplex structure. But in the essence describes the basis of radio detection and ranging.

2.3.2 Radar Equation

Friis equation is the fundamental principles of the radar equation. The radar equationdiffers with taking a scattering object into account when estimating received power.

Power density =PT

4πR2 (2.21)

PT = transmitted signal with power from the antennaR = distance to the object of interest

When the transmitted signal bounces and reflects, the power of reflected signal canbe modeled in the following equation

Reflected power =PTGσ

4πR2 (2.22)

G = antenna gain, σ = the effective area of isotropic target. Since the power is reflectedisotropically (same power in all directions) only a small portion of power is reflected backand the density can be modeled as

Reflected power density =PTGσ

(4πR2)2 (2.23)

14

PR =PT AGσ

(4πR2)2 (2.24)

A = antenna aperture size, the effective area of an receiving antenna. The relationshipbetween the antenna gain G and its effective area A is given by

A =Gλ2

4π(2.25)

Inserting the definition of effective area A in the reflected power density functionyields the basic radar equation

PR =PTG2λ2σ

(4π)3R4 (2.26)

The radar equation assumes a target with area σ and with an isotropic reflectionpattern. Most targets are not isotropic. In able to use the radar equation, we replaceeach real target with an isotropic target and change the area of the isotropic target untilit produces the same return power as the original target. Thus validness of the effectivearea σ still being isotropic is true [24].

2.3.3 Electromagnetism in biologic tissue

There are safety concerns regarding the biological effects of electromagnetic radiation.The field has become rather sophisticated an established safety recommendations or rulesand making adequate measurements.

Even though RF is not considered ionizing, energy is still transferred and absorbed inhuman and other potentially harmful effects can take place if not being cautious. Peopleare being constantly being exposed to microwave sources. Standards for public safetyhas been developed

Specific absorption rate (SAR) is a measure of the rate at which energy is absorbedby the human body when exposed to an EM field in RF band. It is defined as powerabsorbed per mass of tissue with the equation

SAR =1V

∫sample

σ(r)|E(r)|2ρ(r)

dr (2.27)

whereσ is he sample electrica conductivityE is the root mean squared(RMS) electric fieldρ is the sample densityV is the volume of the sample.

The SAR value given in Watts per meter and can be related to temperature differences.A set of standards has been developed by different commissions to ensure safetyfor the public by testing and research [25]. American standards are set by FederalCommunication Commission (FCC). Europe has its own set of standards set by theEuropean Telecommunications Standards Institute (ETSI).

15

There are currently no specific standards for Ultra-wideband radar scanner of thismoment as it has never been realized, but regulations for a generic UWB applications[26]. Ultra-wideband radar scanner of this moment as it has never been realized, butregulations for a generic [26]

2.4 Antenna Aperture

In order to represent waveforms from a physical signal, a sensor must be designed suchthat it interacts with propagating energy. Because propagating waves vary in spaceand time, sensors are designed such that it has a spatial characteristic relative to thepropagating signal.

A single sensor element has a continuous surface and shape, can be interpreted like awindow through which we observe the wavefield. The aperture function is easily derivedfrom the physical appearance of the aperture, by defining the function to take any valuebetween 0 and 1 within the aperture. Let us take square-shape sensor with side lengthsD would let us define

w(x, y) =

{1 if x,y < D0 else

(2.28)

This can be done by any antenna shapes. The effect of multiple sensors that gathersignal energy over a finite area is known as spatial sampling, while the set of sensorsor the sensor physical appearance is known as aperture [13]. This is known as a sparsearray, or antenna array.

2.4.1 Array Gain

Array gain is defined as the ratio of the array signal-to-noise ratio and the sensor signal-to-noise ratio.

G =SNRarray

SNRsensor(2.29)

In general, the array gain depends only on applied weighting on the sensor outputs.In a simple case with uniform weighting, an array with M sensors can increase the SNRratio by a factor of M [13].

2.4.2 Angular resolution

Angular resolution is the ability to distinguish two objects next to one another and is adependant of the antennas beamwidth. Narrow beamwidth results in a better resolution.The beamwidth is dependent on aperture size with the relation

θL =λ

d(2.30)

Note this that this is only for the linear aperture. To keep it simple I will not providedetails of why a circular array aperture has a resolution is

θC = 0.61λ

R(2.31)

16

0.61 is related to the first order Bessel function. They both show dependencies ofwavelength, thus stating that higher frequencies lead to better angular resolution.

2.4.3 Uniform circular array

The size of the sparse aperture array determines the resolution with which two planewaves can be separated. The larger the aperture is, the more focused it can be on the onany specific direction.

Compared to a continuous aperture, a sparse array consists of multiple individualsensors or transceivers that sample the environment at discrete spatial locations. It givesan idea of the beamwidth of the total antenna array. Sampling theorem specific for auniform linear array state if a continuous-variable signal is band-limited to frequenciesbelow k0, then it can be periodically sampled without loss of information so long asthe inter-element spacing has d ≤ π/k0 = λ/2. The effect of spatial undersamplingis the appearance of deceptive main lobes in the aperture smoothing function, underthe name grating lobes. Thus making signals propagating from the main lobe directionindistinguishable from the signals propagating from the grating lobes correspondingspatial frequency [13].

Space sampling characteristics of circular array and linear array have some differ-ences. Consider the number of array N elements can be defined as spatial sampling rateM with an aperture of 2R, R being the radius of the circular array. N is the number ofelements which the circular array should consist of

N =4πR

λ(2.32)

Note that since antenna aperture occupies physical space, there is a limitation of howclose one could spatially sample. Small sized aperture is better suited for a circular arraydepending on the field of use. Thou there are techniques that can overcome this limitationpresented in the following subsection. [27]

2.4.4 Synthetic aperture radar

A synthetic aperture radar is an active imaging system which achieves improvedspatial/cross-range resolution through the exploiting of relative movement betweensensor and target. The idea behind this technique is with multiple measurementsfrom different locations will, in reality, simulate a sparse array with a larger aperture.Commonly used for terrain mapping from an aircraft. It is best understood from itsoriginal intents of use. As previously mentioned, larger aperture improves angularresolution and limited to aperture size. By simulating a larger aperture by a movingantenna increases the angular resolution only on the along a track parallel to the movingdirection, this is known as the cross-range resolution [24]. The relationship betweendistance travelled and the cross range resolution is

θcr =λR0

2L(2.33)

where R0 is the distance between the antenna and the illuminated area,L is the distance traveled and is limited by the antenna beamwidth with the relation

17

θ =Lmax

R0(2.34)

With SAR principles follow with post-processing techniques to compensate for thetime delay due to sequential measurements depending on the sampling frequency. Theessence of SAR principles is that it is possible to synthetically create a larger array ifsampled at the different location. [24]

2.5 Ultra wide band

Ultra wideband wireless(UWB) technologies spread signals over a wide spectrum andhave numerous application for military, security, civilian, commercial and medical. Thereare multiple advantages to UWB. It is better in applications that experience multipathpropagation problems because of the wider the bandwidth, the better the resistance toreflections and related propagation problems. Multiple signals can be placed on top ofone another thus increasing the data rate. It is less of an interference with other signalsin the same spectrum due to their low power which makes them appear more like noisethan as interference. It is also more secure as it is has a low probability of interceptionand signal recovery.

UWB signals can be defined as signals having a bandlimit, also known as fractionalbandwidth at 20-25% of its center frequency, or those occupying 0.5GHz or more of thespectrum, standards and regulations defined by international committees such as FCCand ITEAS. Fractional bandwidth B f is defined by

B f = 2fh − fl

fh + fl(2.35)

Where, B f = Fractional Bandwidth in Hzfh = the highest -10dB frequency point of the signal spectrumfl = The lowest -10dB frequency point of the signal spectrum [28].

One proposed methods to increase resolution with wide-band data processingconsists of to first estimate the signal subspace at a number of frequency channels.Merging the information for different frequencies by dividing the bandwidth into severalnarrow bands. This would depreciate sidelobes when the objective is to make thetransformed steering matrices A at different frequencies as identical as possible. Theside effect of this is an elevated noise floor relative to the main lobe [14].

2.5.1 Resolution

Range resolution is the ability to distinguish an object at from their range relative tothe parallel distance from the transmitter/receiver, meaning the same axis or depth. Asimilar meaning is depth perception. It is determined as a function of pulse duration τ

Sr =cτ̇

2(2.36)

18

Where c is the speed of lightSr is the angular resolution. The division by 2 stems from the reflected signal propagationdistance.

The relationship between the bandwidth B and a pulse duration τ is

B =1τ

(2.37)

A large bandwidth would result in a narrow pulse duration. Which is why UWB hasa fine time resolution which makes it a technology suitable for accurate ranging only. Itis worth to mention that this is not dependant on wavelength unlike angular resolutionand cross-range resolution.

Since UWB signals are able to penetrate the human body among various materialsand are non-ionizing, the potential non-invasive techniques are wide. Different tissueand body mass have different reflection indices, to exploiting the narrow time signalinto detecting different tissues. Health monitoring, health examination of patients anddetection and imaging of tumours for instance [28] [29].

2.6 Image Reconstruction

In array signal processing the word beamforming is usually associated with a transmit-ting beam. Throughout this thesis, I associate it with image reconstruction as I use thesame principles to create the final image with the basis of receiving signals beam. It hasalso been referred to as synthetic focusing.

2.6.1 Delay and sum reconstruction

Delay and sum (DAS) beamforming is a processing algorithm that implies if apropagating signal is present in an array’s aperture, the sensor outputs reinforce thesignal with respect to noise or waves propagating in different directions by summationacross all sensors. Given that the sensors are delayed related to the time it takes forthe signal to propagate between sensors, hence delay and sum. Delay and sum is anattempt to automatically localize signal sources using antenna array. The idea is to aimthe array in one direction and measure the power output. The steering angle whichyields the maximum power is estimated to be the direction of an arriving signal. Thearrays response is steered by forming a linear combination of the sensor outputs. Themathematic expression DAS algorithm is

z(t) =M−1

∑m=0

wmym(t− ∆m) (2.38)

where z(t): beamformer outputm: elementM: number of sensor elementswm : amplitude weightym : signal at sensor m∆m : delay of signal at sensor m

19

DAS is the standard algorithm in terms of beamforming is limited by the arraybeamwidth. [13] [14]

2.6.2 Adaptive Image recontruction

The conventional delay-and-sum makes specific assumptions on the form of thepropagating signal. Such as the relation between the direction of propagation anddelay per sensor must be known. It does not depend on signal characteristics or onnoise characteristics. By modifying conventional beamforming algorithms to incorporatespatial correlation, improves the resolution without tampering with the physical aperturesize. With techniques derived from optimal detection and estimation theory, we adoptthe computations to the characteristics of the observations. Adaptive methods modifysensor output weights and delays according to several aspects of the observation.Such as signal frequency content, spatial and temporal noise characteristics and signalnumber. If enough observations are available, these algorithms have a superiorcapability of yielding signal processing performances than the conventional delay-and-sum. One exception is the special purpose algorithms tailored to specific signal and noisesituations.[13] [14]

2.6.3 Delay Multiply and sum

In the Delay Multiply and Sum (DMAS) algorithm, the backscattered signals at allantennas are time-shifted according to the focus point, similar to DAS. Then an additionalprocessing step that involves pairing multiplications with adjacent time shifted sensorelement before summed to create a synthetic focal point. The multiplication of adjacentreceivers attenuates the data when mismatched. This occurs when the reflecting objectis closer to one of the antenna pair. The signal will arrive at the closest antenna first,implying that a perfect match will amplify the data of where the object is at equal distancerelative to the pair

z(t) =M−1

∑m=0

N

∑n=m+1

wmym(t− ∆m) ∗ yn(t− ∆n) (2.39)

The Delay multiply and sum should in theory not improve angular resolution butreduce noise. [30]

The known superior algorithms, previously mentioned, that enhance angularresolution, are MUSIC and CAPON [13], which uses statistical properties of the signal.But in reality, the optimal algorithm is its adaptability for specific scenarios in order tomaximize resolution. This implies that it is possible, due to signal post-processing alone,to further improve the imaging system. Thus not being limited by the physical propertiesof the antenna.

2.6.4 Inverse scattering problem

In an inverse scattering problem, the goal is to determine the dielectric properties in theimaging domain from the back projection. There is a nonlinear relationship between thefield and material properties. Another reason for nonlinearity is the multiple reflections

20

Figure 2.3: General multiportnetwork

from different boundaries. Significant absorption of the incident signal may occur in aninhomogeneous object with high conductivity. The shape of the original waveform canbe distorted in a dispersive object. All of the abovementioned makes the inverse problemnonlinear and complicated to solve. There might be several arrangements of scatterersthat will have very similar back projections when diffraction due to inhomogeneity hasto be considered[19].

2.7 S-parameters

The ability to reduce most passive and active devices, regardless of circuit complexity andtheir nonlinear behaviour, to simple input-output relation has many benefits. "Black box"method of approach is important in RF and MW circuits, where complete field solutionsto Maxwell’s equation are either too difficult to derive or provide more information thanis needed in order to design systems such as filters and resonators. The basic conceptof this method is measuring ports for its current and voltage while applying knownconditions at other ports, often termination like shown in fig 2.3 [31].

Since we know the relation of current and voltage(Ohms law), it is possible to extractthe impedance of the device under test.

At higher frequencies, it is nearly impossible to create an ideal short/open circuit dueto parasitic properties in components 1.

With respect to figure 2.4 By defining an incident normalized power wave an and areflected power wave bn as

an =1

2√

Z0(Vn + Z0 In) (2.40)

bn =1

2√

Z0(Vn − Z0 In) (2.41)

1Passive components are not only created by wires, coils and plates as depicted in conventional low-frequency electronics. It possesses frequency dependencies that can change its behaviour at high frequencies[31]

21

Figure 2.4: General S-port network

where Z0 is input impedance,VN Voltage at port n,IN Current at port n.

Given that both input and output impedance is equal, leads to the following voltageand current expressions

Vn =√

Z0(an + bn) (2.42)

In =1√Z0

(an + bn) (2.43)

Isolating forward and backward traveling wave components, results to the expression

an =V+

n√Z0

=√

Z0 I+n (2.44)

bn =V−n√

Z0= −

√Z0 I−n (2.45)

Based on the direcotnal convention shown in fig 2.4, it is possible to define S-parameters

b1b2...

bn

=

S11 S12 · · · S1nS21 S22 · · · S2n

......

. . ....

Sn1 Sn2 · · · Snn

a1a2...

an

(2.46)

S -parameters can only be determined under perfect input/output conditions. Forinstance, in order to measure S11 and S21, one must ensure that the line impedanceis matched for a2 = 0. Snn is interpreted as the reflection of the signal, while Snmis interpreted as transmission of the signal. Instruments to measure the scatteringparameters exist and utilized in electronics. Vector Network Analyzer will be explainedin the following subsection.

22

2.7.1 Vector Network Analyzer

The vector network analyzer(VNA) is a form of RF network instrument widely used forRF design application. It is a test system that evaluates the RF performance of radiofrequency and microwave devices in terms of complex S-parameters, as it measures boththe amplitude and phase of the single/multi-port network. The information providedby the VNA is crucial as it provides the designer with a view of the components andcircuits that would not be possible with any other form of test equipment. It is aninstrument that can measure voltages in terms of magnitude and phase. It sweeps over aspecified frequency range by measuring the response transmission and reflection relativeto incident signal at each frequency., thus manage to calculate the Snm parameters. Sincethe measurement includes both phase and amplitude, far more information lies in thedata which makes it possible to perform time-dime domain characterization from thefrequency response [31].

2.7.2 Frequency and time domain

The frequency domain is the domain of mathematical functions or signals with respectto frequency rather than time in electronics, control systems engineering and statisticsfield. Its graph shows how much of the signal lies at each given frequency band over agiven range. A change of a signal over time is able to be identified form time-domaingraph. Time domain and frequency domain represents the different entity but can beconverted between them using a mathematical operator transforms. One example, theFourier transform decomposes a function into the sum of a potentially infinite numberof sinewave frequency components, which is the frequency domain representation of agiven time signal. Like other transforms, it can be inverted to represent a given frequencyfunction in the time domain. [22]

F(ω) =∫

f (t)e−2πωδt (2.47)

To investigate the effect of physical sources, one has to operate in the time domain,where the phenomena are described as a function of time, and are real and physicallymeasurable. The interaction of RF/MW fields with biological tissues is investigatedmostly in the frequency domain, with sources considered as sinusoidal. It is usefulbecause many sources are almost monochromatic [25].

23

2.8 Microwave imaging

Microwave imaging can be divided mainly into radar imaging and microwave tomo-graphy. While in MWT, a nonlinear inverse scattering2 problem must be solved to predicta map of the dielectric properties of the target, radar approach is a simpler computationalproblem, mainly a linear inverse problem.

Radar approaches can provide an image of the location of contrasts in the imagingmedium. It cannot retrieve the values of dielectric properties. Radar method involvesanalyzing reflections of the object of interest to identify the presence of target. Syntheticaperture radar (SAR) is a signal processing technique which involves a single elementtransmitter being in motion in order to mimic a larger aperture thus improvingresolution. SAR is based on measuring the phase shift of the reflected signal, ignoring theamplitude in classical SAR signal processing. The reason is that amplitude attenuationdepends on factors such as radar cross section, the distance between the antennas andthe target, and electromagnetic loss in the media [13] [14] [7].

2.8.1 Microwave tomography

Current clinical tomographic imaging methods. including the three most widely usedones is computed tomography (CT), positron emission tomography(PET) and magneticresonance imaging(MRI). Each contributes with useful information on various tissueproperties related to ischemia and infarct, hypoxia, metabolism and malignancies. Allwith strengths and weaknesses, CT presents superior spatial resolution, while lessinformative in soft-tissue imaging than PET [8].

Microwave tomography is an active wave-based noninvasive imaging method andgives us an ability to see inside and through objects with radiation other than light. Itis the process of creating the image of dielectric properties from measured electric fieldqualities, i.e. permittivity and magnetic permeability.

The dielectric properties and measured field are related by a nonlinear relationshipthat is modelled by Maxwell’s equation [7].

2.8.2 Microwave imaging using s parameters

The scattering parameters essentially is the reflection coefficient and transmissioncoefficients in frequency domain.

2.8.3 Microwave tomography for Brain imaging

There are promising results of MWT for brain imaging [9] but not near to becommercialized. Semenov [32] used nonlinear Newton approach for imaging, and wasable to produce a meaningful biological map of the dielectric layers in a pig’s hind in asalt solution. The best spatial resolution can be achieved at high frequencies, however,the attenuation of EM radiation in biological objects is in inverse ratio with the frequency,with decreasing SNR at high frequencies. The aim was to find the highest frequencies

2Scattering is how the particles are forced to deviate from a straight trajectory through the medium dueto non-uniformity(heterogeneity) in the medium

24

possible at which the receivers will still able to detect signal with good SNR and notcompromise the temporal resolution. He used the same imaging algorithm on a 2Dcomputer generated model of the brain, containing an area of a simulated stroke. Stroke-affected brain tissue deviates in dielectrics relative to healthy tissue. Results in this casewhere also interpretable. The author managed to detect and locate the affected areawhere the minimum size detectable was at 2cm. Some of the challenges included softtissue encapsulated in a bone tissue with low dielectric properties. Note that the latterexperiment was a noiseless case with a circular antenna array of 32 x 32 Tx/Rx and 64 x64. Iterating one tx at the time while receiving the back projection at oppositely faced Rx.

Noghanian [7] introduces a genetic algorithm (GA) as a potential solution for theinverse scattering problem. GA is a robust stochastic population-based global searchtechnique. It is inspired by the Darwinian theory and contains principles of geneticsand evolution in order to solve the problem. It is an iterative process which containsa solution with an array of "genes", where the gene is the parameter to be optimized.It adjusts and measures fitness to the scatterer. It is well suited for parallel algorithms,however, it takes a long time to converge to a perfect fitness. Some of the steps in thealgorithm uses forward solving scattering equation. And illustrates how it can be usedto map the dielectric properties of a heterogeneous medium such as the breast. Imagesof GA based solvers are comparable with the test profiles used proving GA effectiveness.Noghanian successfully created a very low-resolution image of a breast phantom. Intheory, possess great accuracy at high resolution but not realistic due to computationalheavy and the complex structure of a brain.

2.8.4 Realistic wave propagation

Rays of light and sound may deviate from a straight line propagation if the medium isinhomogeneous. Refraction and diffraction are names given to two physical phenomenathat cause rays to bend. Refraction is typically caused by spatial changes in the medium’sspeed of propagation. For electromagnetic radiation, changes in the medium, causechanges in the dielectric permittivity ε or the magnetic permeability µ, which results indifferent speeds of light through the medium. Reflection based imaging assumes wavepropagation perpendicular to the object resulting signal propagating back to where itcame from.

Diffraction describes the phenomenon of waves bending around objects. For lightand sound-waves that have wavelengths comparable with the structures they meet, thuscause the wave to deviate from straight-line propagation. Diffraction theory attempts toexplain why the edges of shadow are not perfectly sharp and how we can hear aroundcorners [13].

When the wavelength of the imaging beam is large compared to the size of the imagedobject, diffraction cannot be neglected and the assumptions of classical tomography areinvalid. The property that is responsible for diffraction at an object is its complex-valued refractive index distribution. The real part of the refractive index accountsfor refraction of light and the refractive index accounts for refraction of light and theimaginary part causes attenuation. Features in the refractive index distribution that arecomparable in size to the wavelength of the light cause diffraction. Approximating thepropagation of light in straight lines for CT is valid because organic tissue does not affect

25

the directional propagation of x-ray. Diffraction tomography takes wave propagationinto account. Diffraction tomography requires imaging techniques that quantify sample-induced phase changes since single cells do not absorb significant amounts of light.Radon transform, Fourier slice theorem, all proofs of the back projection algorithmassumes light propagating along straight lines. Which makes them not suitable forinhomogeneous tomography [33].

26

Part II

The project

27

Chapter 3

Implementation/Method of approach

My goal is to image an object in a homogeneous substance within the RF spectre, henceneglecting diffraction of the signal. My method consists of a image reconstructionof simulation data collection and experimental measurement data from a phantom.Through simulation, I can implement different imaging reconstruction algorithms fornoise reduction purposes, verify resolution enhancement due to the number of elementson various object location, and test the algorithm, before attempting on a phantom withthe same principles of simulation. By doing a simulation first would help me prepareand define an approach towards designing an imaging device.

Figure 3.1: Illustration of approach

Figure 3.1 illustrates my approach in attempting to build a imaging system andrecreate an image. It has with different topics of focus at each stage. Imagingreconstruction algorithm is what the simulation stage and trial stage has in common.

Test measurements involve a chamber filled with the dielectric liquid similar to thehuman brain. As blood has slightly higher permittivity than brain tissue it should bedetectable if the blood is big enough relative to the aperture resolution.

Some alterations were made during the project due to findings during simulationthat resulted in changing the method of approach, but the basics still remain the same.The following sections provide the process of designing an imaging system and with

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underlying important factors reasons behind the choices I took.

3.1 Hardware and Software tools

The tools I had at disposal during this project is listed in the subsections below.

3.1.1 GPRmax

GprMax is an python based, open-source wave propagation simulator. It simulateselectromagnetic wave propagation and solves Maxwell’s equations in 3D using Finite-difference Time-Domain(FDTD) method [15]. Environment characteristics such as objectscan manually be edited in form of defining dielectric parameters.

It requires multiple predefined parameters in order to reenact the real world, but forthe sake of the localization, 2D is sufficient, making it a slice of the object. Location, formand substance of an object are defined by the user. Location of source and receivers, andthe ability to apply a custom input pulse. One of FDTD limits is a time difference as afunction of the spatial discretization.

3.1.2 SolidWorks

SolidWorks is a Computer-assisted design (CAD) tool, that assists the user for parameterconstraint 3D structure design and assembly. It assisted me for high accuracy positioningof the antenna and dimensions of the construction material needed for the imagingsystem.

3.1.3 MERIT

MERIT is an open source microwave imaging toolbox in and uses the same principlesof image reconstruction from scattering parameters in 3D. Its intent of use is mainly onbreast cancer detection thus assuming a homogeneous environment in a non-dispersivemedia.

3.1.4 Other

• Matlab: for signal processing and creating generic bash script and .in- files andtext files for gprMax. Matlab that the university provides has a set of toolboxesin multiple cross disciplines, such as Digital Signal Processing, Digital ImageProcessing and RF.

• Ultimaker 3+ / Cuda: for 3D printed parts to mount, fixture antennas and motor tothe supporting structure with high precision.

• MERIT: open source Microwave Radar based imaging toolbox for matlab. Its anoptimized for efficient image reconstruction for tumor detection for breast.

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3.2 Choice of input pulse

Range resolution is only dependent on pulse duration, as stated in the previous chapter,and is the inverse of signal bandwidth. It is therefore desired to simulate a time pulsewith the same principles.

3.2.1 Pulse modulation

The Gaussian function is the probability density function of the normal distribution, andcan be modified to be a function of time,

G(t) =1

σ√

2πe−(t−t0)

2/(2σ2) (3.1)

The scaling is ignored, leaving only the exponential function to be used to envelop asine function. The equation applied for excited pulse s(t) is

s(t) = Vamp ∗ e−(t−t0)2/(2τ2)cos(2π fc(t− to f f )) (3.2)

where Vamp is the amplitude of 1,t0 is pulse center in timeτ which determines the temporal width of the pulsefc being the center frequency of 3.2 GHz

The excitation pulse is a Gaussian enveloped sine with a duration of 2ns with a timedelay t0 at 1ns.

Figure 3.2: Excited pulse and its frequency response

To simulate a UWB radar signal, the impulse response of choice is important. Shortimpulse durations translates to wide bandwidth in the frequency domain. The choice ofinput pulse must be Gaussian enveloped sine wave with a total temporal width of 2ns.

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Fig 3.2 shows the excited pulse from each transmitter. When inspecting the frequencyresponse, we clearly see a bandwidth spanning from 2GHz-5GHz which would beclassified as UWB according to FCC and ITEAS regulations.

3.2.2 VNA signal

Scattering parameters received from the 4-port network gives 16 outputs where Snn is thereflected signal relative to incident signal and Snm/Smn are the transmitted signal relativeto the incident signal. VNA signal modulation is not as intuitive as in time domain, as itsweeps frequencies across a bandwidth and frequency step of choice. By inverse Fouriertransforming the S parameters, I clearly see that the wavelet is of Gaussiandot waveletwhich is characterised by a single zero crossing point which is very ideal. Truncatingthe frequency changes the wavelet pulse character closer to a known width. This isimportant as to accurately decide he centre of a wavelet, for correctly estimation of anobjects range when calculating reflected wave and signal delay. A frequency sweep1GHz-6GHz would imply a total transient time of

time =Nsamplesbandwidth

(3.3)

This is used when to correctly scale the time axis after performing an IFFT [34].

3.2.3 Truncating Window function

By truncating the frequency response attenuates the unwanted frequency in thefrequency band, keeping as much of the center frequency as possible. With truncationcomes problems in terms of sidelobes height when transformed to another domain,depending on the window of choosing. Generally, a Fourier transform of a bell-shapedcurve gives a sinc function. Figure 3.3 shows 3 different types evaluated accordingto their main lobe width and side lobe suppression. Even thou the figure shows thefrequency response of a window in the time domain, it is trivial due to the convolutionproperties of the Fourier transform. The expected response from truncating in frequencyspectre is a sinc function in the time domain. Wide frequency spectre is desired in orderto simulate a UWB signal while attenuating other frequencies [34]. I chose Hammingwindow with 3.5GHz center frequency as it is known to have low sidelobe levels relativeto the main lobe. 3.5GHz is well within the antennas operating range, the downsideis attenuation as the loss is frequency dependent. In theory, Hamming window hasspecial properties in terms of its low sidelobes and narrow main lobe domain transformcompared to other.

3.2.4 Summary

With the restriction of the module of intended use, the incident wavelet has a characterof a Gaussian enveloped sine. This is applied in the gprMax software when calculatingthe wave propagation in a media. For simplicity and optimal simulation results, σ is seta very low value. A UWB signal simulated had a central frequency at 3.2GHz, spanningapprox 2GHz-5GHz at -10dB mark.

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Figure 3.3: Comparing 3 window function and its frequency transform

The VNA signal response is truncated with a central frequency at 3.5GHz in order toinspect the desired frequency band.

3.3 Phantom design

The goal is to make a liquid phantom with similar dielectric characteristics to the humanbrain tissue. Since water content is the main factor of the permittivity in a material,a liquid phantom can be designed solely on nontoxic, non-hazardous and inexpensivematerial found at a store. Thou there are risks of contamination as grocery store boughtmerchandise contain an uncertainty.

3.3.1 Simulated phantom

I create an environment 0.3m x 0.3m with sensors of circular orientation with a radius of0.075m. While the surroundings consist of a homogeneous matter. I simply submergedreceiver elements in a material with same dielectrics as a human brain tissue. By reducingthe complexity of the environment will increase the possibility of imaging in the post-processing part. Being successful in imaging with simulated data will conclude that myimplementation of the imaging algorithm is correct.

The object of choice is a circular blood clot with a permittivity of 57 of the size 1cm indiameter [35].

3.3.2 Design Properties of a phantom

There are multiple ways of creating a dielectric phantom. It differs from complexity andingredient composition to achieve a controlled test environment. My intentions are tomake it instantly applicable, environmentally friendly and cost-effective way to simulatedielectrics tissue. There are many options in how to create a phantom. There are someadvantages in using a liquid phantom opposed to a solid phantom. Making liquid basedphantom is less time consuming as solid phantoms has to harden, thus limiting the abilityto alter object location. It is cost-effective and easily disposable.

Chew et al [36] used a liquid brain phantom composition based on 200ml water, 5gagar-agar and 20g sugar. Agar is a jelly-like substance which is extracted from red algae.

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(a) (b)

(c)

Figure 3.4: (a) center positioned object, (b) off-center position object

The application of it is widely known in impression material, and modelling clay forchildren and biofertilizer component in organic farming. Its purpose in phantom designis solidifying a liquid. It is possible to create a phantom with household items. Theyalso concluded that de-ionized water and regular tap water showed slight differences inpermittivity [37]. Small enough to be ignored as my intention is to alter the permittivityusing other household products. In order to recreate a dielectric liquid, I do an altercationto the composition in hope to improve permittivity and lower attenuation.

The object of choice is a brass cylinder with the diameter of 1.2cm, and length of 25cm.The idea behind this instead of another liquid is mounting purposes as it will be hard toencapsulate another liquid and for it to stay motionless. It solves trivial challenges forconstruction and the main object of this thesis is to distinguish dielectric properties.

Tissue dielectrics used for the simulation is provided by The Foundation for Researchon Information Technologies in Society [35]. This is used for calculating for wavepropagation speed in a dielectric media, its frequency response is showed in figure 3.5.

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Figure 3.5: Dielectrics of gray tissue

Solution IngredientLiquid 1 200ml water, 100g Sugar , 10ml 75%ethanol, 8g saltLiquid 2 150ml water, 15g SugarLiquid 3 200ml water, 100g SugarLiquid 4 150ml water, 15g Sugar 50ml 75%ethanolLiquid 5 200ml water 100g sugar, 10ml 75%ethanol

Table 3.1: Ingredients for each solution

3.3.3 Measurments of solutions

The VNA utilized was a Rohde and Schwarz calibrated with a known substance, highquality short and open. The known substance would be deionized water. I did 5 sampledissolved sugar liquids shown in table 3.1

Figure 3.6 shows the frequency response of the permittivity both real and imaginary,Loss tangent should be lower than de-ionized water itself in order to improvepenetrability. rising the temperature will lower the loss and increase penetration depth.The reason behind the choice of ethanol solution as water dilution is because of the lowloss property, similar molecular structuring to oil thus lower molecular dipole moment,and water soluble. Oil has a lower permittivity and low loss. Other imaging systems haveused an oil-based phantom [36]. A hypothesis why it showed higher loss than water maybe the contamination of 25% of an unknown ingredient is the colluding factor.

When comparing liquid 1 and liquid 5, the effect of salt is highly present due to ionicinteraction ie. making the phantom more conductive.

3.3.4 Expected total attenuation

It is possible estimate the expected bath loss form the radar equation and path lossattenuation where the dielectric properties are based on the phantom made in previous

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(a) (b)

Figure 3.6: (a) real permittivity, (b) complex permittivity

subsection, ε′ = 50 and ε′′ = 15. Cross-section of a cylinder is

σcylinder =2aπL2

λ(3.4)

By using the radar equation 2.26 and insert for the cross section for R = 1m.

PR =PTG2λ2σ

(4π)3R4

The gain gives me the equation

PR

PT=

PTG2λ2σ

(4π)3R4 (3.5)

and attenuation due to cross range of the object is

αcr/100cm =(4π)3R4

PTG2λ2σ(3.6)

This gives me a dB loss off 2.1dB/cm.Calculation for path loss in dielectric is given by the equation

αd =27.3√

ε′ tan( ε′′

ε′ )

λ0= 696dB/m = 6.96dB/cm (3.7)

The expected loss can be calculated with the radar equation givenThe total sum of attenuation is

αTOT = αcr + αd = 9.06db/cm (3.8)

for the frequency at 3.5GHz.If the noise floor is -120dB would mean any signal attenuated will not be visible.

Signal propagation distance should not exceed 13.24cm before the signal attenuatesbellow -120dB.

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3.3.5 Summary

There are disputes over the actual brain tissue dielectric constant. Most measures foundin the literature are done on corpses. Water content changes in post mortum state thus,the specific relation between dielectrics of the brain matter of a live human and a deadhuman is still under research. Since water content is the main factor for tissue dielectrics,it is legitimate to assume its range rather than a single constant. Therefore matching thedielectric properties of the phantom fluid to actual brain tissue is less relevant as long asthe range known, and have a similar characteristic frequency response. Therefore liquid3, solely dissolved sugar in tap water with a concentration of 0.5g/ml. Since I did notmanage to reduce the loss, the phantom became very lossy.

3.4 Imaging System

In order to construct similar to simulation, I would need to design a device capable tomeasure backscatter from an object. I start to draw a possible design with room foraltering in SolidWorks. SolidWorks is mainly used in mechanical engineering designand manufacturing but would give me the freedom of altering and ability to measurethe dimension needed for the construction. Building material used for the structure wasmainly wood and screws and 3D printed parts for fixtures.

Figure 3.7: Illustration of imaging system setup

Figure 3.7 illustrate the idea of the final construction. It is a large tub containingdielectric with antennas attached to a rotating disk.

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3.4.1 Rotary controller

The rotating disk is utilized to control each antennas position creating a syntheticaperture. The motor used is a AX-12 dynamixel. It is Python compatible servo withfeedback data for rotation speed and position among other functions. In order todetermine the rotating step of degrees I used equation 2.32 to determine the N anglessteps needed to avoid aliasing for maximum frequency present which is 6GHz. Note thatsince the object is submerged in dielectric wavelength changes accordingly

λ =vf=

co√ε′ f

=c0√

60 ∗ 6GHz(3.9)

My calculation is as follows

N =4πR

λ=

4π0.06λ

= 101.157 (3.10)

This means that the complete circular antenna must contain more than 102 elementsequally spaced antennas in order to avoid spatial aliasing. I don’t have 102 antennas orports on the VNA. I solve this by using SAR principles of a moving antenna, thus makingit possible to over-sample. Oversampling the would further increase resolution. I end upusing 180 elements which gives me 2◦ rotation step.

3.4.2 VNA settings

The VNA utilized was a Rhode & Schwarz ZVB20 VNA 10MHz-20GHz calibrated usinga ZV230 kit. 4 ports were utilized in order to do measurements. The main reason behindthe number of ports utilized in this experiments was the reduction of a full rotationaround the imaged domain. With 4 ports limits the rotating range to [0◦, 90◦ − ∆θ],∆θ = 2◦ being the rotating angle step size as found in previous calculation. It wouldfurther reduce the number of sweeps as 4 port scattering parameters measures multiplepropagation paths. A total of 45 frequency sweeps is needed per imaging session. Threelocations where chosen similar to the simulations. One where the object is at center, offcenter and to the side.

Maximizing number of port capability is equivalent with utilizing all the portsavailable on the VNA would maximize the resolution as ports are directly related to thenumber of S-parameter network thus increasing transmission and reflection parameters.The VNA measures the scattering parameters at each rotated angle.

Raw data from the VNA is the scattering parameters, a complex ratio betweenincident and transmitted/reflected signal as a function of frequency. 4 port networkwould give 4x4 S parameters at each rotation of a total of 45 steps. The frequencyresponse is transformed to the time domain with the IFFT operator. T

The Intermediate Frequency bandwidth setting on the VNA lowers the noise floor onthe measurements. VNA measures scattering at one frequency at the time. IF bandwidthis the filter bandwidth at the intermediate frequency. Noise is reduced by lowering thebandwidth of the filter. 1kHz IF to 100Hz IF will get a 10dB lower noise floor in exchangefor increased sweep time by the factor of 10.

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3.4.3 Antenna

The antenna is an ultra-wideband monopole antenna suitable for radiation into dielectricmaterials. The antenna is impedance matched with S11 < -10 dB from 2 GHz to 7GHz,meaning its operating bandwidth. Each of the four antennas uses is fed using a semi-rigid coaxial cable stiff enough to make sure the antennas position is constant relative toa controlled rotating platform. I assume the antenna is omnidirectional, which is a typicalfor monopole and dipole antennas.

Figure 3.8: Monopole Antenna soldiered ona rigid coax

The antenna design specification wheredone by my supervisor which I did notpartake.

3.4.4 Chamber construction

The function of the chamber is to containthe dielectric liquid, a tub of which the an-tennas are submerged.The idea behind thecontainer of large enough size in order tolet the signal attenuate from unwanted re-flection thus not to collude received sig-nal data. Size of the antenna array hasa diameter of 12cm, meaning he maximalpropagation distance is 24 cm. A nearbywall closer than this distance would in-terfere with the reflection from the ob-ject as reflection from the wall will coin-cide. When assuring a wall placed greaterthan 12cm the total roundtrip propaga-tion with a lossy phantom would attenu-ate even more than the signals of interest.Based on this and the available contain-ers, a transparent plastic container, gener-ally used for storage, with the dimensionof 40cm x 48cm x 60cm trapezoid shapedwas the best available regarding the ex-perimental measurements. Some limitingfactors were the volume of phantom liquid needed to be created in order to fill the cham-ber. Theoretical volume capacity is 75L according to the container description. Accordingto the recipe of the 0.5g/ml sugar solution phantom would imply 37.5kg of sugar with75L of water.

3.4.5 Summary

The imaging consists of three parts, chamber, VNA, and rotary controller from a laptop.The chamber is designed in a way that reflected signals outside of the imaging area woulddissipate. The VNA with a frequency sweep of 1GHz-6GHz in order to imitate a UWBsignal. Settings on the VNA would allow a lower noise floor, optimizing the SNR with

39

Figure 3.9: 3d construction

measurement with sweep time prolonged as the tradeoff. The frequency sweep lowerfrequency is outside the antennas impedance matching meaning its the gain at 1GHz -2GHz gain will be somewhat <-10dB. This means reliant data measures of the sweep willlie between 2GHz and 6GHz. A full circular scan around the object requires only 90◦

rotation from the servo since a 4 port network is utilized. For resolution purposes, a stepwas calculated to be 2 degrees to achieve oversampling. It is possible to script the VNA toauto sweep from the controller but to implement VNA commands through python wasmore complicated than I thought, thus made the measuring process repetitive as I had towait for each sweep to finish before I could perform an antenna step.

3.5 Post proscessing rawdata

The signal processing techniques applied has an essential role. There are multiple oper-ations done before the final image reconstruction not intuitive without an explanation.The following subsection are the main operations to consider when applied on the rawdata.

3.5.1 Artefact removal

The general idea behind artefact removal techniques is to subtract scatter data when theobject is present with the scattered data from the background, resulting in scattered datafrom a present object. In reality skin tissue, bone, fat and muscle tissue are all commonartefacts but with different thickness depending on the location of a human body. Othercommon artefacts non-related to the imaged body is the antenna coupling, the directpropagation between neighbouring antennas. Depending on the types of artefactspresent, the prepossessing technique should be adapted accordingly. This means a priori

40

assumption is present. Under the condition of this thesis, an object submerged in ahomogeneous matter with no skin layers present, subtracting the backscattered signalwhere the object is non-present from the signals where the object is present may besufficient [11].

Sobj(t) = S(t)− S0(t) (3.11)

where S0 is backscattered signals with no object presentS is backscattered signals with no object presentSobj is backscattered signals from the object only.

Fig 3.10 show received signal in time domain. The unaltered signals (top plot andmiddle plot) seems identical. The signal measured here signal propagating the shortestpath from the transmitter to the receiver, which is called antenna coupling. Othercommon artefacts can be the reflection from skull, skin, fat layer, i.e., common artefactsregardless of the presence of an object. In the simulated case only antenna coupling is thecommon artefact.

Figure 3.10: Artifact removal on simulated data

Whether artefact removal applies in the time domain or in frequency domain dependson the chosen technique. In my case, where a measurement is done on an empty spaceand a present object in order to subtract it from each other, the domain is trivial and canbe shown with the Fourier equation

F[S(t)− S0(t)] = ∑(S(t)− S0(t))e−jωtδt = ∑ S(t)e−jωtδt−∑ S0(t)e−jωtδt (3.12)

3.5.2 Envelope

Enveloping is a function to simplify the recorded signal wavelet often used to illustrateaudio signal power distribution. It removes the sinusoidal character of the signal as this

41

can collude the data, especially in imaging and ranging. It is not desired that two signalsfrom different sensors, if in opposite phase, cancel each other when performing a delayand sum. Hilbert envelope is utilized before the summation.

Figure 3.11: Enveloped signal

3.5.3 Image reconstruction algorithm

Synthetic focusing to recreate the image is applied to the simulated data S(t). The methodapplied to the data was a standard Delay and Sum.

Algorithm 1: Delay and SumResult: Image reconstruction with DASτtx(x, y); estimated time for signal propagation as a function of distancefor every tx do

for every rx doPFD ← PFD + Stx,rx(τtx)

endend

To prove noise reduction based on adaptive technique, a simple modification canbe made on the standard Delay and sum algorithm. Delay multiply and sum (DMAS)multiplies the signal at each antenna with the received signal from the neighbouringantenna. In theory, this would nullify the contribution when there is a huge mismatchbetween the two signals, and amplify the signal contribution when there is a perfectmatch.

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Algorithm 2: Delay Multiply and SumResult: Image reconstruction with DMASτtx(x, y); estimated time for signal propagation as a function of distancefor every tx do

for every rx doPFD ← PFD + Stx,rx(τtx) ∗ Stx,rx+1(τtx)

endend

The rawdata requires a signal preprocessing in order to do timebased adaptivereconstruction.

Figure 3.12: Signal from different receivers

When observing fig 3.12, it is observable that with a proper delay on each receiverwould maximize output intensity in a conventional DAS. When transceiver position isknown, together with a theoretical velocity of propagating wave, I have what I need tolocate the object.

The image reconstruction process converts the EM intensity at given space to animage space. By defining a high-resolution spatial grid and knowing the signal velocityas a function of dielectrics, I can calculate τ, the time it takes for the propagating waveto take a round-trip to the reflective media location and back, assuming constant velocityin the dielectric material. The time grid contains the specific τ per pixel distance relativeto a transmitter location for each transmitter in all directions. Multiplying it by 2 wouldimply the time for the signal to propagate to the reflector and back. By adding the t0,t0 being the delayed response of the input signal, and the half of the pulse duration t,would time shift the grid according to the reflection theory of a propagating wave. Byinterpolating the time-based data for each τ, I can plot the intensity for any given time. Irepeat this process for each receiver and accumulate to a single grid creating a picture. Isum up the intensity image from each transmitter and normalize the final image. In orderto increase image dynamic range, I scale the final image in dB then normalize showed inthe following equation

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ImdB =| 10log(Im(. . . ) | (3.13)

ImdB,norm = ImdB −max(ImdB) (3.14)

This results in a scale where 0dB is maximum image intensity and cuts of the dynamicrange as it is crucial when comparing the results with a different method.

3.5.4 Summary

The processing of raw data consists of multiple operations in order to transform rawdata into image domain. Enveloping the signal assists interpolation of the receivedsignal when calculating the signal power as a function of time relative to antennaposition. Standard Delay and Sum algorithm and Delay multiply and sum applied whenreconstructing the image.

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Chapter 4

Results

So far I have introduced important stages considered when reconstructing an image ofan object from scattered data, and the choices and assumption made at each stage. In thischapter, I will present the results with multiple approaches and how some of my choicesaffect the reconstructed image. I will introduce the final imaging system. Followingsections shows the image reconstruction from simulated data, while the latter sectioncontains results from measured data.

4.1 Imaging system

The final setup of the imaging system is shown in figure 4.1. The VNA ports areconnected to each antenna, with the direction of rotation set to clockwise. It is not inorientations of my results but is easy to imagine the mirrored results to compensate forthis. My laptop controls the rotation step and speed while recording angle at any giventime. It is not connected to the VNA, however, the VNA is running Window OS systemof its own thus enabling me to transfer the measured data via a USB stick. It is possibleto execute commands to the VNA from an external system. Due to time restrictions,I chose not to overcomplicate trivial improvements and chose to manually start eachsweep and each step. The servomotor is attached to 3D printed plastic parts, which isagain attached to the wood construction. The servo requires its own power supply unitand a USB2Dynamixel converter in order to communicate with the motor. It is importantto fully dissolve the sugar to get the phantom to be as homogeneous as possible equalthe measurements were done on the small sampled phantom.

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Figure 4.1: Final setup

Figure 4.2: Final setup

46

Figure 4.3: Final setup

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4.2 Simulation

4.2.1 Detection and location of an object

The simulated phantom with different location shows it is possible to detect an objectin homogeneous environments while distinguishing the location with 8 transceivers.The standard delay and sum algorithm as seen in figure 4.4. Symmetries arise due toa perfectly centered circular object when referring to figure 4.4a, shadows of where thereis less distribution of EM field is the marked blue. The artifact1 in the image is due tothe DAS algorithm since it a single antenna have to assume that the time of propagationcan come from all angles. It is only when the total sum of all antennas I can point on alocation of a reflecting object. The width of one artefact is directly related to the pulseduration of the excited signal but also the shape of the object. Narrow pulse durationgives a narrow width, making it possible to pinpoint a single object with great accuracy.Figure 4.4b shows the same technique applied where the object is -1cm off center in the x-direction. Artefacts are still present but not as symmetrical. The curvature of the artefactsis more present since the excited with its antenna location as its center. Note that theartefacts to the right of the object are slightly less intense than other artefacts. This is dueto attenuation as a function of signal path length.

(a) (b)

Figure 4.4: (a) center positioned, (b) off center position

Power loss due to the distance between the reflector and transceiver results in thereceiver closest to the reflective substance being most prominent in the results. However,an object close to the center is visible due to similar attenuation across all sensors. Thusable to enhance the dynamic range in the intensity image. This can be a problem if theobject is right next to one antenna. As other signals have experiences more attenuationthan the reflected signal at the nearest antenna, will not contribute as much to the DASalgorithm.

1Artefact in this setting is referring to high intensity in the image at locations other than the object’slocation. It is not the same artefacts described in previous chapters, which are related to mutual coupling,mutual physical object

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4.2.2 Noise reduction

Previous figure showed relatively noisy artifacts in the reconstruct image, spanningacross the total visible area. By increasing number of antennas can reduce the artifacts,referring to the comparison of figure 4.5a and 4.5c. But in reality the arrtifact is stillpresent. The improved visuals is due to summation of the focal point of interests exceedsthe artifact intensity making it weaker relative to the focal point. Additional antennaswould suppress it increase the focal point even more. Figure 4.5d shows further noisereduction in between artifacts, making it more visible but lowers the overall dynamicrange of the image.

(a) (b)

(c) (d)

Figure 4.5: Location off center (a) 8 antenna DAS, (b) 8 Antenna DMAS, (c) 16 AntennaDAS, (d)16 antenna DMAS

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4.2.3 Multiple object detection

The ability to locate multiple targets and the distance of the objects is an importantfeature. In figure 4.6 is the reconstructed images when two circular objects are places 5cmapart using both algorithms and increased number of antennas. In figure 4.6a and 4.6c Ican see that the number of antennas is not enough to separate the two even thou I clearlysee an enlarged area of intensity. Plenty of noise is present in these two figures hence thelow dynamic range of the images. The DMAS algorithm shows a different result. In bothcases irrelevant to number of antennas, figure 4.6b and 4.6d is possible to distinguish twoobjects. The artefact is highly present in figure 4.6b and as described before, the two mostcontributing antennas are the one on the left and right. Only when using more antennastogether with the DMAS algorithm figure 4.6d the artefacts are slightly reduced makingthe two object more visible. The reason why I managed to separate the two objects witha pure noise reduction algorithm is that the high intensity that connects the two objects,making it seem an enlarged single object, is purely noise related.

(a) (b)

(c) (d)

Figure 4.6: 2 objects present 5 cm apart (a) 8 antenna DAS, (b) 8 Antenna DMAS, (c) 16Antenna DAS, (d)16 antenna DMAS

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4.2.4 Summary

Until this point I have presented the results when reconstructing an image on a simulatedphantom, solving the wave equation with a numerical approach using the principles ofFDTD. The principle of a surrounding aperture has been proven to work in order to locatea blood clot in a homogeneous environment. Multiple assumptions have been made asdescribed in the previous chapter. In reality, it is not this simple as will be presented inthe next section.

4.3 Measured data on real phantom

I had three initial positions of an object, center, slightly to the right and close to the rightnear the border. It is worth to note that I was unsuccessful in recreating a good image ofthe location of the object. I will present them regardless as some of it can be explainedcan be explained.

4.3.1 Reflection coefficient based imaging

On inspection of the results when doing a reflection based image reconstruction shownin figure 4.7 I clearly notice a faint inner circle. The inner circle reflection can be dueto the distance to the mounting plate. Measured distance to the mounting plate wasapprox 10cm. If assuming a velocity factor with ε′ = 60, gives a distance of 2x10cmwould indicate a propagation time from the plate and back to be approx 0.5ns. Thetime domain measured signal indicates a presence of a reflector at this point in time.Strongly attenuated due to the distance travelled but enough to be visible in the imagereconstruction.

Figure 4.7c shows somewhat an indication of a reflecting object near the originalposition as it is a lot of activity in intensity on the far right. Comparing with figure4.7a that shows reflection in the same area but more related to the floor reflection as it iswithin the region of what described.

Figure 4.7b show a strong indication of a reflector along forming almost a quarter ofa circle in multiple layers. It is hard to explain this and why this happens. I can onlyspeculate that from the way I sweep across all angles is a 90 degree rotation of 4 antennasperpendicular to one another. This effect comes solely from 1 antenna. The antennasare supposed to be identical and are not present in the other measurements. I can onlyconclude that this is an individual antenna error, possibly due to coax connection.

I also did a tomography based imaging by including the transmission coefficient. Theresults are shown in figure 4.8. The difference is not much compared to the reflected.

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(a) (b)

(c)

Figure 4.7: Reflection based imaging, location at (a) center, (b) off center, (c) side

52

(a) (b)

(c)

Figure 4.8: Tomopgraphy based imaging, location (a) center, (b) off center, (c) side

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4.4 MERIT

This image is generated when using the open source software the scattering parametersmeasured. It uses the same principles of imaging as I did. The idea was the failure ofreconstruction was due to code implementation. But data given to the software was alsounsuccessful. Figure 4.9 indicates a presence of an object in the center when the objectwas placed at the centre. I suspect that they don’t scale according to dB as I did not findany logarithmic functions when inspecting the code.

(a)it

(b)

Figure 4.9: Merit based

This makes me believe that the data of the measurements is not sufficient. Even thouuncertainties arise due to a poor tutorial description, it was worth a try.

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4.5 Discussions

The simulated results were promising as the detection of a present object which showedboth locations and being able to distinguish multiple objects using both transmissioncoefficient and reflection in the time domain.

4.5.1 Possible cause of Error

Apparently, the buoyancy of the nylon plate is increased in sugar water. It did not floatbut became more susceptible for movements with little effort. This resulted in the useof a central mounting hole only in order to distribute weight for support. The locationchange would have me move the hole plate at each imaging making the artefact removalsuboptimal. When compensating for common artefacts in the frequency domain, i.e.,amplitude and phase difference, we are dependant on accurate phase for it to be correct.The wavelength of in the phantom is relatively short compared to the signal in the samefrequency in free space due to change in velocity. I can estimate sensitivity based on onthe wavelength since

λ =vfc

=c0

fc√

ε′=

3 ∗ 108

3.5GHz ∗√

ε′≈ 0.01m (4.1)

Maximum phase error would imply 180◦ phase shift and would give me a maximumerror in phase if the distance of surrounding objects(artefact to be removed) is off byλ2 . This means that in a 1cm wavelength system, a misplacement of 5mm of a commonartefact will give the maximum error. And highly susceptible for human error. Thisrequires a highly stable system to ensure consistent measurements not susceptible formovement.

The nylon plate was 1cm thick, lowering the margin for allowance of the signal toattenuate. The measured distance from the antenna to the nylon mounting pad was 10cm. This is to short for the signal to attenuate more than worst-case distance, which canexplain the inner circle in the measurement based image results.

Rigid coax cables may have been tampered with during measurements. Approxim-ately 8 cm gap between the antennas allowed me to re-position the object, while some ofthe rigid coax connectors were loose as it needed movement in order to rotate. Rotatingthe coaxial connector caused rotation. Thereby changing the relationship between thecalibration data and the actual data.

Antenna distances as coax were not 100% straight which can collude the distance ofpropagation calculated. The radius of the imaging center where assumed to be at 6cm,and equally spaced. Given the margin maximal of error being λ/2, it is difficult to obtainperfect stability with my imaging system.

Error due to oversimplification is present as I assume the propagating velocity solelybased on a single permittivity ε′ value when it is clearly frequency dependent. Notethat I tried various ε′′ within a reasonable range and it had minimal effect. The clearvisible effect would be an enlarged or more focused object since I principle slow downthe wrongly estimate the time of propagation.

55

4.5.2 Improvements

One way to improve the results is by correctly estimating the attenuation in order tocompensate for frequency dependent attenuation. By implementing a FIR filter so thatevery pixel in the image resulting in unity gain. This way weighting stronger reflectionsmore equal to weak reflection.

A better and realistic phantoms in terms of loss could improve the result. The braintissue consists off less water than the sugar solution made as the chosen phantom.Counter-measurements for loss was tried in terms of diluting the phantom with nondipolar, non ionic ethanol was unsuccessful. Oil-based phantoms experience lessattenuation and would be a better liquid of choice.

Other ways to compensate a lossy dielectric is to lower center frequency. I did nothave time to try to lower center frequency by truncating at a lower frequency band. Thiswould again affect resolution, but it would be interesting to see the trade off effect.

Other imaging systems used larger aperture arrays with directional beamwidth andresolution. As the monopole antenna used in this project is isotropic, which is not ideal.

A fine rotation step size of a full circle makes the use of a monopole antennaredundant. A monopole antenna is good to cover a large area with a single antenna,but in this case, a better choice would be a high directional antenna would still cover thewhole are as long as if the step size is fine enough. To coarse rotation, step would leaveshading in the area of interest. Meaning areas not covered by the antenna position, .i.e.,not within the visible region, regardless of all the sampled positions.

Alternative adaptive image reconstructions to improve performance in terms ofresolution and noise can be implemented. And improves array. It uses statisticalproperties of the received signal and assumes all noise are perpendicular to the signal.

4.5.3 Weaknesses

There are critique worthy aspects to this project, other than the failure of creating a goodimaging system. Many aspects of this challenge have been simplified down to the idealproperties. It exists good mathematical representation of EM wave propagation, but theworld is much more complex.

The wave propagation in a heterogeneous environment with dispersion, refractionand loss, has to be taken into account. It is considered non-linear and performing linearmathematical operations will not give an accurate scattering data if one were to trulyexpress the correct scattering field.

Biological tissues in living organisms tend to vary in each individual as permittivity.The algorithm used in this thesis requires a priori information of an empty phantomenvironment, which is not an ideal real case scenario [10][11]. It is possible to do anartefact removal without the prior knowledge of the object absent space.

VNA instrument can simply increase the power transmitted above the regulations setby FCC and ITEAS for human body exposure. This means even if I were to succeed withhigh accuracy, it would still need improvements.

56

4.5.4 Future work

Other than the obvious fact of designing a more stable system, I believe generic algorithmand/or machine learning can be incorporated to classify and identify. With the limitedknowledge in the field, the trend is accelerating and is potentially the future of medicalimaging.

57

58

Part III

Conclusion

59

4.6 Conclusion

This thesis presents the idea behind a circular aperture for 2D slice body imaging formedical applications with UWB technology. In theory, it maps dielectric properties withthe principles of the physical phenomenon of light reflection and transmission.

By simulating how a wave field that propagates through the medium in a finite space,relative to its source position, I predict the scattered data of an object with differentdielectric. I sequentially do multiple simulations to at different source position to forma complete circle, thus simulating a circular aperture. The excited pulse is a Gaussianenveloped sine with a frequency response categorized as UWB signal according to FCCstandards, with a center frequency of 3.2GHz.

Defining a homogeneous matter makes dispersion negligible but in reality, humantissue is highly heterogeneous. Skin penetration and other layers surrounding an objectcomplicate the scattering data if not taken into account, calibration is needed in order tosuppress these common artefacts.

Resolution is investigated with simulation. The ability to measure location in x, y andz-direction and the smallest change possible to detect describe the overall performanceof the imaging system. A comparison between data collected by 8 and 16 antennaelements showed improved performance and image SNR. Comparisons between DASand DMAS image reconstruction technique showed improvements in noise. I designedan imaging system using a 4 port VNA to measure scattering parameters, which operatesin a frequency domain. I sweep the area of interests with a total of 180 different angleswhile collecting transmission and reflection from all ports, thus utilizing SAR principlesmoving the antenna. Hamming window is applied on the frequency bandwidth with acenter frequency of 3.5GHz. A trade-off occurs as higher frequency attenuates by pathloss in free space alone but increases resolution as a single antennas angular resolution isfrequency dependent.

The collected data was under the condition of my own designed lossy dielectricphantom which consisted of 0.5g/ml sugar and water with a permittivity range betweenthe range of ε′ = [62− 40] and ε′′ = [8− 20]. The estimated loss factor was 9.1db/cm.Too high compared to the size of the are of interests. The reconstructed image did not goas expected due to poor stability, making the phase and amplitude difference between anempty and present object too high to get a significant image out of the data. Calibrationtechniques failed as my imaging system was not stable enough and highly susceptible toerror.

4.6.1 Last remark and thoughts

The learning curve was steep during this last year and would attack the problemdifferently if I had more time in hand. This challenge was indeed a large task in hand,as it covers multiple science disciplines. It would be beneficial to improve all aspects bydividing it in smaller challenges, optimizing each stage through the process.

61

62

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[28] M A Martin. Ultra Wideband Preliminaries. eng. Ed. by Boris Lembrikov. 2010.

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[33] Paul Müller, Mirjam Schürmann and Jochen Guck. ‘The Theory of DiffractionTomography’. In: arXiv:1507.00466 [physics, q-bio] (2nd July 2015). arXiv: 1507 .00466.

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[36] K. M. Chew et al. ‘Human Brain Phantom Modeling Based on Relative PermittivityDielectric Properties’. In: 2012 International Conference on Biomedical Engineering andBiotechnology. May 2012, pp. 817–820.

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66

Appendix A

gprMAX

gprMAX .in file

#title: scan 8 element#domain: 0.3 0.3 0.001#dx_dy_dz: 0.0010 0.0010 0.001#time_window: 18e-9#material: 4.1e1 2.4 1 0 mybraintissue#material: 5.7e1 3.25 1 0 myblood#excitation_file: my_pulse.txt#hertzian_dipole: z 0.150 0.225 0 pulse#rx: 0.150 0.225 0#rx: 0.097 0.203 0#rx: 0.075 0.150 0#rx: 0.097 0.097 0#rx: 0.150 0.075 0#rx: 0.203 0.097 0#rx: 0.225 0.150 0#rx: 0.203 0.203 0#box: 0 0 0 0.3 0.3 0.001 mybraintissue#box: 0.1 0.1 0.000 0.116 0.116 0.001 myblood#sphere: 0.100 0.116 0.001 0.008 myblood#sphere: 0.116 0.100 0.001 0.008 myblood

67

#title: scan 8 element#domain: 0.3 0.3 0.001#dx_dy_dz: 0.0010 0.0010 0.001#time_window: 11e-9#material: 4.1e1 2.4 1 0 mybraintissue#material: 5.7e1 3.25 1 0 myblood#excitation_file: my_pulse.txt#hertzian_dipole: z 0.225 0.150 0 pulse#rx: 0.225 0.150 0#rx: 0.219 0.179 0#rx: 0.203 0.203 0#rx: 0.179 0.219 0#rx: 0.150 0.225 0#rx: 0.121 0.219 0#rx: 0.097 0.203 0#rx: 0.081 0.179 0#rx: 0.075 0.150 0#rx: 0.081 0.121 0#rx: 0.097 0.097 0#rx: 0.121 0.081 0#rx: 0.150 0.075 0#rx: 0.179 0.081 0#rx: 0.203 0.097 0#rx: 0.219 0.121 0#box: 0 0 0 0.3 0.3 0.001 mybraintissue#sphere: 0.140 0.150 0.001 0.005 myblood

68

Appendix B

Matlab simulation

Matlab files during simulation

1 clear all;2

3

4 c=299792458;5 timewindow = 18; %nanoseconds6 tetta = linspace (2*pi/4, 9*pi/4,8);7 r= 0.075;8 trxx= r*cos(tetta)+0.15; %[0.150 0.097 0.075 0.097 0.150

0.203 0.225 0.203]; %transmitter and reciver posistions xdirections

9 trxy= 0.075* sin(tetta)+0.15; % [0.225 0.203 0.150 0.097 0.0750.097 0.150 0.203]; %transmitter and reciver posistions ydirections

10 dx = 0.001; dy= 0.001; dz= 0.001; %grid resoluion in gprmax11

12 dt= 1/(c*sqrt (1/dx^2+1/dy^2));13

14 pathname = ’/uio/kant/ifi -student -u03/jjestrad/Master/Circulararray/’;

15 run(strcat(pathname ,’Createtxtpulse.m’))16 want_snapshots = 0; %faster simulation if excluded17 for blood =1:218 for i = 1:819 if blood ==220 fileID = fopen(strcat(’fphantom8_bloodtx ’,num2str(

i),’.in’), ’w’);21 else22 fileID = fopen(strcat(’fphantom8_emptytx ’,num2str(

i),’.in’), ’w’);23

24 end

69

25

26 fprintf(fileID , ’#title: scan 8 element\n’);27 fprintf(fileID , ’#domain: 0.3 0.3 0.001\n’);28 fprintf(fileID , ’#dx_dy_dz: %1.4f %1.4f %1.3f\n’,dx ,

dy ,dz);29

30 fprintf(fileID , ’#time_window: %de -9\n’, timewindow);31 fprintf(fileID ,’#material: 4.1e1 2.4 1 0 mybraintissue

\n’);32

33 if blood ==234 fprintf(fileID , ’#material: 5.7e1 3.25 1 0 myblood

\n’);35 end36

37

38 fprintf(fileID ,’#excitation_file: my_pulse.txt\n’);39 fprintf(fileID ,’#hertzian_dipole: z %1.3f %1.3f 0

pulse\n’,trxx(i), trxy(i));40

41 for ii =1:842 fprintf(fileID , ’#rx: %1.3f %1.3f 0 \n’,trxx(ii),

trxy(ii));43 end44

45 fprintf(fileID ,’#box: 0 0 0 0.3 0.3 0.001mybraintissue\n’);

46

47 if blood ==248 fprintf(fileID , ’#box: 0.1 0.1 0.000 0.116 0.116

0.001 myblood\n’);49 fprintf(fileID , ’#sphere: 0.100 0.116 0.001 0.008

myblood\n’);50 fprintf(fileID , ’#sphere: 0.116 0.100 0.001 0.008

myblood\n’);51

52 end53

54 if (want_snapshots)55 bl = ’nobl’;56 if blood ==257 bl= ’bl’;58 end59 fprintf(fileID ,’#geometry_view: 0 0 0 0.3 0.3

0.001 0.001 0.001 0.001 %s n\n’, strcat(’phantom8 ’,bl ,’tx’,num2str(i)));

70

60 fprintf(fileID , ’#python :\n’)61 fprintf(fileID , ’for i in range(1, 51):\n’)62 fprintf(fileID ,’print(’’#snapshot: 0 0 0 0.3 0.3

0.001 0.001 0.001 0.001 {} snapshot {}’’.format((i/10)*1e-9, i))\n’)

63

64 fprintf(fileID , ’#end_python :\n’)65

66

67

68 end69

70 fclose(fileID);71

72

73

74 end75 end

1 c=299792458;2 dt= 1/(c*sqrt (2/0.001^2));3 fs= 1/dt;4 [time , Pulse] = CreatePulse2 (1/dt, 3.2e9,timewindow *1e-9);5 A = [time; Pulse];6 pathname = ’/uio/kant/ifi -student -u03/jjestrad/miniconda3/

gprMax/mystuff/’;7 s=strcat(pathname , ’my_pulse.txt’);8 fileID = fopen(s,’w’);9 fprintf(fileID ,’%6s %12s\n’,’time’,’pulse’);

10 fprintf(fileID ,’%1.12f %2.4f\n’,A);11 fclose(fileID);

1 function [t, pulse] = CreatePulse2(Fs, fc,timewindow)2

3 % fc = Center frequency [Hz]4 % Fs = Sampling frequency [Hz]5 t0 = 1e-9;6 tau = 327e-12;7 vamp = 1;8 phase = 0.0;9

10 Tp = timewindow; % Pulse duration [s]11 Amp_pulse = 1;12 stdev = 6.3;13

14 %Nt = round(Tp * Fs);

71

15 %t = (1:Nt)/Nt * Tp; % time vector16 %t = linspace(0,Tp,round(Tp*Fs));17 t= 0.5*([0 1:2:2* round(Tp*Fs)])*1/Fs; %gprmax friendly18 % Full width half maximum of pulse19 fwhm_t = (2* sqrt (2*log(2))*tau);20 % Shift center of pulse21 toff = t0+fwhm_t *1.2;22 % Create rectangular window23

24

25 rwin = t>t0 & t<(toff+fwhm_t *1.2);26 %pulse = rwin.*exp(-( ((t - toff).^2) ./ (2*( tau .^2))) ).* cos

(2 * pi * fc .* (t - toff) + (phase)) .* vamp;27 pulse = exp(-( ((t - toff).^2) ./ (2*( tau .^2))) ).* cos(2 * pi

* fc .* (t - toff) + (phase)) .* vamp;28 figure;29 plot(t);30 figure;31 plot(t,pulse);32 end

1 function [ output ] = DAS( data ,time ,ntrx ,rxpos , pulseduration,v,r)

2 %DAS Summary of this function goes here3 % Detailed explanation goes here4 %data signal: data(time:rx:tx)5 % time = simulated time6 %ntrx = number of rx and tx used in simulation. rx=tx7 %rxpos = positions of transrecievers8 %pulseduration fwhm9 %v estimated propagation speed.

10

11 % Creates distance per pixel relative to each transmitter.12

13 %grid containing TAU. time it takes for signal to do a roundtrip to source

14 %and back. t0 = 1ns, input signal delay15 trxx= rxpos (:,1);16 trxy = rxpos (:,2);17 [x y] = meshgrid (0:0.001:0.3);18

19 %flip(y);20 im = [];21 for i=1: ntrx22

23 dxx=trxx(i)-x;

72

24 dyy=trxy(i)-y;25 im(:,:,i)= 2*sqrt(dxx .^2+ dyy .^2)/v;26 end27

28 t0= 1e-9;29 dt = 1/(299792458* sqrt (2/0.001^2));30 timebasedgrid = t0 +im + pulseduration /2;31 ntx = ntrx;32 nrx= ntrx;33 pnormgrid = zeros(size(timebasedgrid));34

35

36 % creating a binary image of object of interest , ’u’ which isthe area within antenna elements. Helps improve calculationspeed.

37

38 [ux uy] = meshgrid ( -0.15:0.001:0.15);39 u = zeros(length(x));40 u((ux.^2+uy.^2)<r.^2) =1;41 u(u==0)=nan;42

43 %DAS algoritm:44 pp = zeros(size(timebasedgrid ,1));45 for i= 1:ntrx46

47 for j = 1:ntrx48 temp2 = zeros(size(timebasedgrid ,1),size(timebasedgrid

,2) );49 pnormgrid (:,:,i) = pnormgrid (:,:,i) + interp1(time ,

data(:,j,i),timebasedgrid (:,:,j).*u,’spline ’);50 end51 pp = pp + pnormgrid (:,:,i);52 i53 end54 output = pp;55 end

1 function [ output ] = DMAS( data ,time ,ntrx ,rxpos ,pulseduration ,v,r)

2 %DAS Summary of this function goes here3 % Detailed explanation goes here4 %data signal: data(time:rx:tx)5 % time = simulated time6 %ntrx = number of rx and tx used in simulation. rx=tx7 %rxpos = positions of transrecievers8 %pulseduration fwhm

73

9 %v estimated propagation speed.10

11 % Creates distance per pixel relative to each transmitter.12

13 %grid containing TAU. time it takes for signal to do a roundtrip to source

14 %and back. t0 = 1ns, input signal delay15 trxx= rxpos (:,1);16 trxy = rxpos (:,2);17 [x y] = meshgrid (0:0.001:0.3);18

19 %flip(y);20 im = [];21 for i=1: ntrx22

23 dxx=trxx(i)-x;24 dyy=trxy(i)-y;25 im(:,:,i)= 2*sqrt(dxx .^2+ dyy .^2)/v;26 end27

28 t0= 1e-9;29 dt = 1/(299792458* sqrt (2/0.001^2));30 %timebasedgrid = 2*t0+ 2*im + pulseduration /2;31 %timebasedgrid = 3*t0+ 2*im;% + pulseduration /2;32 timebasedgrid = t0 + im + pulseduration /2;33 ntx = ntrx;34 nrx= ntrx;35 pnormgrid = zeros(size(timebasedgrid));36

37

38 % creating a binary image of object of interest , ’u’ which isthe area within antenna elements. Helps improve calculationspeed.

39

40 [ux uy] = meshgrid ( -0.15:0.001:0.15);41 u = zeros(length(x));42 u((ux.^2+uy.^2)<r.^2) =1;43 u(u==0)=nan;44

45 %DAS algoritm:46 pp = zeros(size(timebasedgrid ,1));47

48

49 for i= 1:ntrx50 %figure51 % imagesc(timebasedgrid (:,:,i)); colormap(’jet ’)

74

52 for j = 1:(ntrx -1)53 temp = 1;54 temp2 =1;55

56 if (j== 1)57 temp2 = -(ntrx -1);58 end59 if (j == ntrx)60 temp = -(ntrx -1);61 end62 pnormgrid (:,:,i) = pnormgrid (:,:,i) + interp1(time ,

data(:,j,i),timebasedgrid (:,:,j)...63 .*u,’spline ’).* interp1(time ,data(:,j+temp ,i),

timebasedgrid (:,:,j).*u,’spline ’)...64 .* interp1(time ,data(:,j-temp2 ,i),timebasedgrid (:,:,j)

.*u,’spline ’);65

66

67 % for k=j+1: ntrx68 % pnormgrid (:,:,i) = pnormgrid (:,:,i) + interp1(

time ,data(:,j,i),timebasedgrid (:,:,j).*u).* interp1(time ,data(:,k,i),timebasedgrid (:,:,k).*u.* interp1(time ,sqrt(abs(data(:,j,i).*data(:,k,i))),timebasedgrid (:,:,j)));

69 % end70 end71 %figure;72 % imagesc(pnormgrid (:,:,i));73 %pp = pp + pnormgrid (:,:,i)/max(max(pnormgrid (:,:,i)));74 pp = pp + pnormgrid (:,:,i);75 i76 end77 output = pp;78 end

75

76

Appendix C

Matlab Measurements

Matlabfiles during measurements

1 function [ output ,pnormgrid , timebasedgrid] = DAS( data ,time ,nrx ,ntx ,rxpos , pulseduration ,v,r)

2 %DAS Summary of this function goes here3 % Detailed explanation goes here4 %data signal: data(time:rx:tx)5 % time = simulated time6 %ntrx = number of rx and tx used in simulation. rx=tx7 %rxpos = positions of transrecievers8 %pulseduration fwhm9 %v estimated propagation speed.

10

11 % Creates distance per pixel relative to each transmitter.12

13 %grid containing TAU. time it takes for signal to do a roundtrip to source

14 %and back. t0 = 1ns, input signal delay15 trxx= rxpos (:,1);16 trxy = rxpos (:,2);17 [x y] = meshgrid(-r:0.001:r);18

19

20 im = [];21 for i=1:ntx22

23 dxx=trxx(i)-x;24 dyy=trxy(i)-y;25 im(:,:,i)= 2*sqrt(dxx .^2+ dyy .^2)/v; %roundtrip propagation26 end27

28 t0= 1e-9;29 dt = 1/(299792458* sqrt (2/0.001^2));

77

30 %timebasedgrid = 2*t0+ 2*im + pulseduration /2;31 %timebasedgrid = 3*t0+ 2*im;% + pulseduration /2;32 timebasedgrid = im;33

34 pnormgrid = zeros(size(timebasedgrid));35

36

37 % creating a binary image of object of interest , ’u’ which isthe area within antenna elements. Helps improve calculationspeed.

38

39 [ux uy] = meshgrid(-r:0.001:r);40 u = zeros(length(x));41 u((ux.^2+uy.^2)<r.^2) =1;42 u(u==0)=nan;43

44 %DAS algoritm:45 pp = zeros(size(timebasedgrid ,1));46

47

48 for i= 1:ntx49 %figure50 % imagesc(timebasedgrid (:,:,i)); colormap(’jet ’)51

52

53 for j = 1:nrx54 % interpolation. noe skurrer med data og timebasedgrid.55 pnormgrid (:,:,i) = pnormgrid (:,:,i) + interp1(time ,

data(:,j,i),timebasedgrid (:,:,i).*u,’spline ’);56 end57

58 %figure;59 % imagesc(pnormgrid (:,:,i));60 %pp = pp + pnormgrid (:,:,i)/max(max(pnormgrid (:,:,i)));61 pp = pp + pnormgrid (:,:,i);62

63

64 i65 end66 output = pp;67 end

1 function [ output , pnormgrid , timebasedgrid ] = DMAS( data ,time ,nrx ,ntx ,rxpos , pulseduration ,v,r)

2 %DAS Summary of this function goes here3 % Detailed explanation goes here

78

4 %data signal: data(time:rx:tx)5 % time = simulated time6 %ntrx = number of rx and tx used in simulation. rx=tx7 %rxpos = positions of transrecievers8 %pulseduration fwhm9 %v estimated propagation speed.

10

11 % Creates distance per pixel relative to each transmitter.12

13 %grid containing TAU. time it takes for signal to do a roundtrip to source

14 %and back. t0 = 1ns, input signal delay15 trxx= rxpos (:,1);16 trxy = rxpos (:,2);17 [x y] = meshgrid (0:0.001:0.3);18

19

20 im = [];21 for i=1:ntx22

23 dxx=trxx(i)-x;24 dyy=trxy(i)-y;25 im(:,:,i)= 2*sqrt(dxx .^2+ dyy .^2)/v;26 end27

28 timebasedgrid = im;29

30 pnormgrid = zeros(size(timebasedgrid));31

32

33 % creating a binary image of object of interest , ’u’ which isthe area within antenna elements. Helps improve calculationspeed.

34

35 [ux uy] = meshgrid ( -0.15:0.001:0.15);36 u = zeros(length(x));37 u((ux.^2+uy.^2)<r.^2) =1;38 u(u==0)=inf;39

40 %DMAS algoritm:41 pp = zeros(size(timebasedgrid ,1));42

43 for i= 1:ntx -144 %figure45 % imagesc(timebasedgrid (:,:,i)); colormap(’jet ’)46 for j = 1:( ntx)

79

47 temp = 1;48 temp2 =1;49

50 if (j== 1)51 temp2 = -(ntrx -1);52 end53 if (j == ntrx)54 temp =(ntrx -1);55 end56 pnormgrid (:,:,i) = pnormgrid (:,:,i) + interp1(time ,

data(:,j,i),timebasedgrid (:,:,j)...57 .*u,’spline ’).* interp1(time ,data(:,j+temp ,i),

timebasedgrid (:,:,j).*u,’spline ’)...58 .* interp1(time ,data(:,j-temp2 ,i),timebasedgrid (:,:,j)

.*u,’spline ’);59

60

61 %for k=j+1:nrx62 % pnormgrid (:,:,i) = pnormgrid (:,:,i) + interp1(

time ,data(:,1,j),timebasedgrid (:,:,j).*u).* interp1(time ,data(:,1,k),timebasedgrid (:,:,k).*u);

63

64 % end65 end66 %figure;67 % imagesc(pnormgrid (:,:,i));68 %pp = pp + pnormgrid (:,:,i)/max(max(pnormgrid (:,:,i)));69 pp = pp + pnormgrid (:,:,i);70 i71

72 end73 output = pp;74 end

1 clear;2 addpath(’M:\ Master\exptrial_data\’)3 addpath(’M:\ Master\exptrial_data\angels ’)4 empty ={};5 center = {};6 % side ,center ,offcenter7 loc = ’side’;8

9 for i=1:4510 filename= strcat(’empty2_ ’,num2str(i),’.s4p’);11 filename2 = strcat(loc ,num2str(i),’.s4p’);12 empty{i} = sparameters(filename);

80

13 center{i} = sparameters(filename2);14 %data{i} = permute(file{i}.Parameters ,[3 1 2]);15 end16

17 freq= empty {1}. Frequencies;18 new_fs = 1e9;19 freq2 = linspace(min(freq), max(freq) ,500);20 N = size(freq ,1);21 w = window(@hamming ,N);22

23

24 for i=1:4525 empty{i} =rfinterp1(empty{i},freq);26 center{i} = rfinterp1(center{i},freq);27 end28

29 %% read angles30

31 fileid = fopen(strcat(’M:\ Master\exptrial_data\angels\’,loc ,’.txt’),’r’);

32 formatSpec = ’%f’;33 sizeA = [1 inf];34 title = fscanf(fileid ,’%s’ ,[1 2]);35 angles = fscanf(fileid , formatSpec , sizeA);36 fclose(fileid);37

38 angles = [angles angles +90 angles +180 angles +270];39 %% artefact removal40 S = empty;41 for i = 1:4542 S{i}. Parameters=center{i}.Parameters -empty{i}. Parameters;43 end44

45 %% apply window ifft and reformat data to standard vectorizedform , NB channel order according to channel orientationwhen measured.

46 data= zeros(N,4 ,180);47 w=1;48 for i= 1:4549 data(:,:,i) = [ifft(rfparam(S{i},1,1).*w) ifft(rfparam(S{i

},2,1).*w) ifft(rfparam(S{i},3,1).*w) ifft(rfparam(S{i},4,1).*w)].*[1 1 1 1];

50 data (:,:,45+i) = [ifft(rfparam(S{i},1,3).*w) ifft(rfparam(S{i},2,3).*w) ifft(rfparam(S{i},3,3).*w) ifft(rfparam(S{i},4,3).*w)].*[1 1 1 1];

51 data (:,:,90+i) =[ifft(rfparam(S{i},1,2).*w) ifft(rfparam(S

81

{i},2,2).*w) ifft(rfparam(S{i},3,2).*w) ifft(rfparam(S{i},4,2).*w)].*[1 1 1 1];

52 data (:,:,135+i) = [ifft(rfparam(S{i},1,4).*w) ifft(rfparam(S{i},2,4).*w) ifft(rfparam(S{i},3,4).*w) ifft(rfparam(S{i},4,4).*w)].*[1 1 1 1];

53 end54

55

56 %%57

58 close all;59 es = 60;60 us=1;61 c=299792458;62 v = c/sqrt(us*es);63 time = linspace(0,N/(2*5e9),N);64 tau = 327e-12;65 fwhm_t = (2* sqrt (2*log(2))*tau);66

67 r=0.05;68 % rxxpos = r*cos(deg2rad(angles))+0.15;69 % rxypos = r*sin(deg2rad(angles))+0.15;70 rxxpos = r*cos(deg2rad(angles));71 rxypos = r*sin(deg2rad(angles));72 nrx =4;73 ntx= nrx *45;74 [ppdas ,pnormgrid ,TAU] = DAS(data ,time ,nrx ,ntx ,[ rxxpos ; rxypos

]’,fwhm_t , v,r);75

76 figure;77 xi = linspace(-r,r,size(ppdas ,1));78 pp_db= real (20* log10(ppdas));79 pp_db=pp_db -max(pp_db (:));80

81 hold on;82 surf(xi,xi,pp_db); colorbar;83

84 trxx = rxxpos;85 trxy = rxypos;86 for i = 1:ntx87 tmpx = find(round(trxx(i) ,4) == round(xi ,4));88 tmpy = find(round(trxy(i) ,4) == round(xi ,4));89 % surf(tmpx ,tmpy ,’r*’);90 plot3(trxx(i),trxy(i) ,150,’*’,’MarkerEdgeColor ’,’k’)91 end92

82

93 hold off;94

95 view ([0 90]);96 ylim([-r r]); xlim([-r r]);97 shading(’interp ’); colormap(’jet’);98 xlabel(’meters ’); ylabel(’meters ’);99 caxis ([-20 0]); title(’DAS’);

83

84

Appendix D

Servo script

1 import pypot.dynamixel2 import itertools3 import time4 import numpy as np5

6

7

8 N = 49

10 angles = np.linspace (0,90-90/N,N)11

12

13

14 ports = pypot.dynamixel.get_available_ports ()15

16 if not ports:17 raise IOError(’no port found!’)18

19 print(’ports found’, ports)20

21 print(’connecting on the first available port:’, ports [0])22 dxl_io = pypot.dynamixel.DxlIO(ports [0])23

24

25

26 found_ids = dxl_io.scan()27 print(’Found ids:’, found_ids)28

29

30 ids = found_ids31 dxl_io.enable_torque(ids)32

85

33 dxl_io.set_angle_limit ({1: [-150, 150]})34 speed = dict(zip(ids , itertools.repeat (200)))35 dxl_io.set_moving_speed(speed)36 pos = dict(zip(ids , itertools.repeat (0)))37 #dxl_io.set_goal_position(pos)38 print(’Enter filename ’)39 filename = input()40 file = open(("%s.txt" % filename),’w’)41 file.write(’Angular movement\n’)42 for x in range (0, np.size(angles)):43 dxl_io.set_goal_position ({1: (angles[x])})44 time.sleep (2)45 print(dxl_io.get_present_position ((1, )))46 file.write("%f \n" % dxl_io.get_present_position ((1, )))47 input("Do measurements , Press Enter to continue ...")48

49

50 file.close()51 print(’finnished ’)52

53 """54 input("Press Enter to continue ...")55 dxl_io.set_goal_position ({1: 22.5+45})56 input("Press Enter to continue ...")57 dxl_io.set_goal_position ({1: -1000000})58

59 print(pos)60 dxl_io.set_goal_position ({1: 150})61

62 print(dxl_io.get_present_position ((1, )))63 dxl_io.set_goal_position ({1: -150})64 time.sleep (2)65 dxl_io.set_goal_position ({1: 150})66 time.sleep (2)67 print(dxl_io.get_present_position ((1, )))68 dxl_io.set_goal_position ({1: -150})69 time.sleep (2)70 print(dxl_io.get_present_position ((1, )))71 dxl_io.set_goal_position ({1: 150})72 time.sleep (2)73 print(dxl_io.get_present_position ((1, )))74 dxl_io.set_goal_position ({1: -150})75 """

86