tomography with medipix2 semiconductor pixel detector

Tomography with Medipix2Semiconductor Pixel Detector

by

Carlos Felipe Roa Garcıa

A thesis submitted in partial fulfillment for theDegree of Physicist

Director

Dr. Bernardo Gomez Moreno

Universidad de los AndesFacultad de Ciencias

Departamento de FısicaBogota D.C., Colombia

January 2009

“A man is not old unitl regrets take place of dreams”

John Barrymore

UNIVERSIDAD DE LOS ANDES

AbstractFacultad de Ciencias

Departamento de Fısica

Tomography with Medipix2 Semiconductor Pixel Detector

by Carlos Felipe Roa Garcıa

The Medipix2 pixel presents features that make it interesting for medical applications

that demand high resolution imaging. An overview of biomedical imaging is presented

with a discussion on current developments, including the Medipix2 detector. The mea-

surements done to characterize and calibrate the Medipix2 are presented. The energy

calibration of the detector and its capability of setting an energy window are used to

take radiographies at different energies. A set of projections is obtained for two phan-

toms and an object to perform their tomographical reconstruction. Some slices of the

reconstructed samples are shown along with a surface render of each object.

Acknowledgements

Agradezco a todas las personas que contribuyeron de alguna manera a la realizacion de

este proyecto. A mis padres y hermanos por el apoyo incondicional y por estar junto a

mı siempre y en especial cuando mas los he necesitado. Al Profesor Bernardo Gomez

Moreno por su colaboracion y su sabidurıa. Muchas gracias por sus ensenanzas y por

darme la oportunidad de trabajar en este tema. A los Profesores Carlos Avila y Juan

Carlos Sanabria por estar pendientes del avance del proyecto y por sus ideas valiosas a lo

largo del proceso. Al Ing. Marco Antonio Gonzalez y a Luis Carlos Gomez por su valiosa

ayuda en la construccion del montaje. A la gente de fısica por los momentos compartidos.

Agradezco tambien a todo aquel que lea esto y crea que deba ser mencionado.

I would like to acknowledge the following organizations that have contributed to the

development of this project:

• The Medipix Collaboration, specially Dr. Michael Campbell, Dr. Xavier Llopart

and Dr. Lukas Tlustos.

• The Institute of Experimental and Applied Physics (IEAP) of the Czech Technical

University in Prague. In particular, Dr. Carlos Granja.

• The School of Science of The Universidad de los Andes.

• The Department of Physics of The Universidad de los Andes.

• The High Energy Physics Group of The Universidad de los Andes.

• The High Energy Physics Latinamerican-European Network (HELEN).

• The Colombian Institute for the Development of Science and Technology (COL-

CIENCIAS).

I gratefully acknowledge the developers of the Octopus tomography reconstruction pack-

age, from the Ghent University, who made available a fully-functional version of the Oc-

topus software for this project. In particular, I would like to thank Dr. Manuel Dierick

for his support during the realization of this project.

iii

Contents

Abstract ii

Acknowledgements iii

List of Figures vi

List of Tables viii

1 Introduction to Biomedical Imaging 11.1 Principles of Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 X-ray Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Measurement of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Detection of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.1 Scintillation Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 81.4.2 Charge-Coupled Devices . . . . . . . . . . . . . . . . . . . . . . . . 81.4.3 Fast CT Scanners . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4.4 Energy-Resolving Methods . . . . . . . . . . . . . . . . . . . . . . 101.4.5 Single-Photon Detection . . . . . . . . . . . . . . . . . . . . . . . . 10

2 The Medipix2 Detector 122.1 The Medipix2 Chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.1 The Analog Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.2 The Digital Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1.3 The Chip Periphery . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 The Mpix2MXR20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 The USB Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4 The Pixelman Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Preliminary Measurements and Energy Calibration 213.1 Threshold Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 DACs Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 Validation of Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4 Radiographical Imaging with Medipix2 31

iv

Contents v

4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 Flat Field Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2.1 Foils Phantom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2.2 Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Radiographies at Different Energies . . . . . . . . . . . . . . . . . . . . . . 354.4 Beam Hardening Correction . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.4.1 Foils Phantom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.4.2 Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Methods for Tomographical Reconstruction 415.1 The Filtered Back Projection Method . . . . . . . . . . . . . . . . . . . . 41

5.1.1 The Projection of an Object . . . . . . . . . . . . . . . . . . . . . . 415.1.2 The Fourier Slice Theorem . . . . . . . . . . . . . . . . . . . . . . 425.1.3 The Filtered Back Projection . . . . . . . . . . . . . . . . . . . . . 44

5.2 Iterative Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6 Tomographical Imaging with Medipix2 476.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.2 Tomographical Reconstruction with Octopus 8.3 . . . . . . . . . . . . . . 48

6.2.1 Three Objects Phantom . . . . . . . . . . . . . . . . . . . . . . . . 496.2.2 Helicoidal Wire Phantom . . . . . . . . . . . . . . . . . . . . . . . 506.2.3 Cone Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7 Final Discussion 54

A Specifications of Step Motor and Driver 55

B External Control of the Step Motor Driver 58

C The PHYWE X-ray Unit 60

D The Medipix2 Support and the Sample Holder 62

E Comments on Octopus 8.3 64

Bibliography 65

List of Figures

1.1 Radiography of Ms. Rontgen’s Hand . . . . . . . . . . . . . . . . . . . . . 21.2 PET Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 X-ray Tube Schematic and Spectrum . . . . . . . . . . . . . . . . . . . . . 51.4 Schematic of a CCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5 Largest Commercial CCD . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6 Example of an ERM for Radiographic Imaging . . . . . . . . . . . . . . . 10

2.1 Medipix2 Chip Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Medipix2 Pixel Schematic and Layout . . . . . . . . . . . . . . . . . . . . 142.3 Mpix2MXR20 Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 The USB Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5 The Pixelman Principal Window . . . . . . . . . . . . . . . . . . . . . . . 192.6 The Pixelman Preview Window . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1 THL Equalization Distribution . . . . . . . . . . . . . . . . . . . . . . . . 223.2 THH Equalization Distribution . . . . . . . . . . . . . . . . . . . . . . . . 233.3 THL DAC Scan with Test Pulses . . . . . . . . . . . . . . . . . . . . . . . 243.4 Copper and Molybdenum X-ray Tube Spectra . . . . . . . . . . . . . . . . 263.5 Derivative of the THL DAC Scan for Cu and Mo Tubes . . . . . . . . . . 273.6 Cross Sections for Ni, Cu and Zn . . . . . . . . . . . . . . . . . . . . . . . 283.7 Derivative of the THL DAC Scan for Ni, Cu and Zn Foils . . . . . . . . . 293.8 Energy Calibration and Validation . . . . . . . . . . . . . . . . . . . . . . 30

4.1 Medipix2 Inside the PHYWE X-ray Unit . . . . . . . . . . . . . . . . . . 324.2 Comparison of Raw and FF Corrected Image of Foils Phantom . . . . . . 334.3 Photograph of Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Comparison of Raw and FF Corrected Image of Capacitor . . . . . . . . . 354.5 Radiography of the Capacitor at Different Energies . . . . . . . . . . . . . 364.6 Comparison of Raw and STC-Corrected Image of Foils Phantom . . . . . 384.7 Comparison of Raw and STC-Corrected Image of Capacitor . . . . . . . . 39

5.1 Geometry Definition for Tomographical Reconstruction . . . . . . . . . . 425.2 Comparison Between FBP and OSEM Reconstructions . . . . . . . . . . . 46

6.1 Sinogram Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.2 Photograph and Projection of the Three Objects Phantom . . . . . . . . . 496.3 Reconstructed Slice and Multi-surface Render of Three Objects Phantom 506.4 Photograph and Projection of the Helicoidal Wire Phantom . . . . . . . . 506.5 Reconstructed Slice and Multi-surface Render of Helicoidal Wire Phantom 51

vi

List of Figures vii

6.6 Photograph and Projections of the Cone Shell . . . . . . . . . . . . . . . . 526.7 Reconstructed Slices and Multi-surface Renders of Cone Shell . . . . . . . 53

A.1 Photograph of the Step Motor of Sample Holder . . . . . . . . . . . . . . 55A.2 Dimensions of Step Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . 56A.3 Dimensions of Step Motor Driver . . . . . . . . . . . . . . . . . . . . . . . 57

B.1 Interface of the LabVIEW Program . . . . . . . . . . . . . . . . . . . . . . 58B.2 LabVIEW Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

C.1 PHYWE X-ray Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

D.1 Medipix2 Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62D.2 Sample Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63D.3 Experimental Setup For Tomography Imaging . . . . . . . . . . . . . . . . 63

List of Tables

1.1 Weighting Factors for Different Tissues . . . . . . . . . . . . . . . . . . . . 7

3.1 Characteristic Lines for Cu and Mo X-ray Tubes . . . . . . . . . . . . . . 253.2 Values from Energy Calibration with Cu and Mo X-ray Tubes . . . . . . . 283.3 Values from Energy Calibration with Ni, Cu and Zn Foils . . . . . . . . . 29

viii

Dedicated to my parents and siblings

ix

Chapter 1

Introduction to Biomedical

Imaging

The subject of Biomedical Imaging arises from the requirement of studying the internal

body organs and tissues with non-destructive techniques that provide accurate informa-

tion of the condition of a patient. Since the early ages of medicine until the twentieth

century, there were no means of having a clear image of internal organs without looking

directly at them. The development of instruments capable of taking such images was

based on rather simple physical concepts and improved with the power of computer

technology. Today, it is possible to obtain very accurate images of the bones, organs,

vessels and even very small regions of interest, to help in the diagnosis and treatment of

diseases.

In 1895, Wilhelm Conrad Rontgen, discovered, almost by accident, a new kind of ra-

diation that could penetrate solid objects and caused the darkening of a photographic

plate. With his discovery, which he called X-rays, on December 22, 1895, he was able to

take a radiography of his wife’s hand, in which the bones could be easily identified (see

Figure 1.1).[1] Rontgen’s discovery soon became one of the most important advances in

Medicine, providing it allowed to study the body without opening it.

Another important advance by Allan Mcleod Cormack and Godfrey Newbold Hounsfield

complemented the discovery of X-rays and revolutionized the medical practice. In 1963,

Cormack demonstrated mathematically that it is possible to reconstruct a slice of an

image by its projections.[2, 3] Some years after, Hounsfield invented a machine that

could produce digital axial images with medical application. Cormack and Hounsfield

were awarded, in 1979, the Nobel prize in Medicine for their work.[4]

1

Chapter 1. Introduction to Biomedical Imaging 2

Figure 1.1: The first radiography taken by W. K. Rontgen of his wife’s hand.[1]

The field of Biomedical Imaging has been an interdisciplinary collaboration between

Physics and Medicine. It is founded on the principle of existence and characteristics

of X-rays and has been extended to other types of radiation, such as gamma rays and

positrons. It is possible to obtain images of the body of a patient by (1) the emission

of radiation from a source inside the body and (2) the measurement of the radiation

that passes through the body. In the first mechanism, a radioactive source or tracer

is administered to the patient and its radiation is measured. This gives metabolical

and anatomical information, because the tracer is carried by a substance that some

organs use and the measurement of radiation can give information on the position of

the source. The second mechanism is based on the absorption of radiation by different

tissues, leading to the visualization of the anatomy of the body, in a similar way a

shadow created by an object gives information of its geometry. Both approaches have

required mutual cooperation between physiologists and physicists. The extension of

Rontgen’s discovery and the advances of Cormack and Hounsfield to other types of

radiation required Becquerel’s, and Marie and Pierre Curie’s knowledge of radioactivity,

as well as the work of J. J. Thomson, Rutherford and Bohr on the atomic model.

Engineers have been important contributors to this field, because it was important to get

knowledge in computer technology and data processing techniques, in order to produce

commercial machines that could take useful images of the body.[4]


1.1 Principles of Radioactivity

Radioactivity is the phenomenon ocurring inside an atomic nucleus, in which, an atom

that has become unstable releases some of its energy by emitting a particle or electro-

magnetic wave. This causes the nucleus to suffer a transformation into a more stable

form or to continue emitting particles until it becomes stable. The most common proc-

cesses by which the emission of particles takes place are the alpha, beta and gamma

decays.

• Alpha Decay. An alpha particle, composed by two protons and two neutrons,

which resemble a helium nucleus is produced (42He). It happens in the atoms

of uranium and radium and is sometimes accompanied by a gamma decay. An

example of this reaction is:

23892 U →234

90 Th + α (1.1)

The number of protons and neutrons must be conserved, so the difference in atomic

number between the original and the produced atom must equal to two.

• Beta Decay. Involves the production of electrons (β−) or positrons (β+) in the

nucleus of an atom. Despite the nucleus has protons and neutrons, it can produce

an electron by the transformation of a neutron into a proton1. An example of a

reaction in which beta decay takes place is:

146 C →14

7 N + e− + ν (1.2)

The atomic number increases as a neutron is transformed into a proton, but the

overall number of nuleons remains constant. The reverse reaction is also possible,

but in this case, the decay produces a positron and a neutrino (the antiparticles2

of the electron and the antineutrino, respectively).

127 N →12

6 C + e+ + ν (1.3)

The atomic number decreases as a proton is transformed into a neutron, leaving

the total number of nucleons constant.[4]1In the process, an antineutrino (ν) is also produced. The existence of the antineutrino was inferred

by the fact that the electron did not come out always with the same energy. There had to be anotherparticle responsible for this discrepancy but left no footprint, so it had to be neutral.[5]

2An antiparticle is a particle with the same mass but the opposite quantum numbers (electric charge,lepton number, etc.).[5]


• Gamma Decay. This decay produces electromagnetic radiation in the frequency of

gamma rays. The difference with other types of electromagnetic waves is the energy

and thus the frequency of the photons. It always comes alongside with another

type of decay. Because of their high energies, gamma rays penetrate large amounts

of matter before they are completely absorbed, which makes them interesting for

medical applications as diagnosis and treatment. When a positron encounters an

electron, they annihilate and produce a pair of photons of 0.511 MeV.

e+ + e− → γ + γ (1.4)

This process is used in Positron Emission Tomography (PET) for the diagnosis of

diseases by tracing the metabolical activity in certain parts of the body (Figure

1.2).

Figure 1.2: PET of a physiologically normal patient compared with that of a patientsuffering Alzheimer’s disease.[6]

These types of radiation are often referred to as ionizing radiation because all of them can

change the electrical charge of an atom, which may be the cause of damage to biological

tissues. This process is used to measure the presence of radiation with a Geiger counter.

Alpha particles are blocked by a sheet of paper, while beta and gamma radiation pass

through a paper barrier. Beta radiation is blocked with a thin piece of aluminum and

gamma rays can be attenuated with thick pieces of lead. Alpha decay has the shortest

range and can be easily stopped by skin.[7]

1.2 X-ray Production

X-ray radiation is the most widely used type of radiation for medical diagnosis. X-rays

are electromagnetic waves, with energies between 120 eV and 120 keV. In an X-ray tube,

electrons are thermally emitted from a filament (cathode) and are accelerated towards


the anode by a high voltage (of the order of 50 kV). When the electrons reach the target

in the anode, the Coulomb interaction with the nucleus of the atoms in the material

causes a continuum spectrum of electromagnetic radiation, called bremsstrahlung. The

maximum energy of the emitted X-rays is proportional to the voltage of the tube and

the spectrum covers energies up to this value, as an electron can interact with many

atoms in the target, until all its kinetic energy is converted into photons (the energy

that the target gains during the interactions can be neglected).

The difference in the kinetic energy of the electron before and after the interaction should

be equal to the energy of the emitted photon.

hν =hcλ

= K −K ′ (1.5)

The maximum energy that can be converted equals the energy gained by the electron

when it is accelerated by the voltage V (K − K ′ = eV ), from which the minimum

wavelength of the photons can be obtained.

λmin =hceV

(1.6)

� �

�

��

��

��

��

��

��

Figure 1.3: (a) Schematic drawing of an X-ray tube in which the electrons are accel-erated by the voltage V, from the cathode C towards the anode A. (b) X-ray spectrum

showing bremsstrahlung and characteristic lines Kα and Kβ .[8]

The energetic electrons can excite the atoms of the anode target and when they return

to the ground state, a photon is emitted. The energy of this photon depends on the

difference of energies between the initial and final state of the electron and it falls in


the range of X-rays. The characterisitc lines of the material of the anode arise from the

fact that the intensity of X-rays is considerably larger than the bremsstrahlung at these

energies (see Figure 1.3b).[8]

1.3 Measurement of Radiation

Measurement of radiation can be a challenging task as we are not able to detect its

presence without specialized instruments. Different types of radiation usually come

together and are difficult to distinguish from each other. In that way, it is possible to

measure (1) the number of disintegrations per unit time in a sample, (2) the electric

effect this radiation has on atoms or ions, (3) the energy deposited to a sample and (4)

the biological effects that a dose has on a tissue.

The activity, or number of disintegrations that occur per unit time, regardless of the

source, is measured in Becquerel (Bq) or in Curie (Ci). One Becquerel (S.I. unit) equals

to one disintegration per second. However, this unit is not very convenient, so the Curie

is introduced. One Curie equals 3.7× 1010 Bq.

The exposure is related to the capability of ionizing certain material. The interaction

of radiation with atoms can cause a change in the net charge of the atoms and the

measurement of this charge can indicate how energetic the radiation is. The unit is

the Rontgen (R), which equals the amount of radiation needed to create a charge of

2.58× 10−4 C per kg of air.

The absorbed dose is a direct measure of the amount of energy delivered to a sample

by any kind of radiation. It can be measured in rad or Grays (Gy, S.I. unit). One rad

equals to 0.01 joule absorbed by one kg of material. One gray equals 100 rads, or 1 joule

absorbed per kg.[4]

The measurement of dose equivalent takes into account the effects of radiation in biolog-

ical tissues. This effect varies among the different types of radiation, even if they have

the same energy. This is expressed by the following equation:

DE = AD ×WR (1.7)

where AD is absorbed dose. If AD is in Gy, the unit of DE is the Sievert (Sv, S.I. unit).

If AD is in rad, the unit of DE is the Rontgen equivalent man (rem). It can be easily

seen that one Sv equals 100 rems. The weighting factor WR depends on the type of

radiation. For X-rays, gamma rays and beta particles it is equal to one and for alpha

particles to 10.


The biological effect of radiation depends also on the tissue that is affected. The effective

dose takes account of the affection to different organs:

ED = AD ×WT (1.8)

The effective dose (ED) is given in Gy, as the AD. The weighting factor WT is different

for each organ, defining the factor for the total body as equal to one. Table 1.1 lists the

weighting factors for different tissues.[9]

Tissue WT

Gonads 0.25Breast 0.15

Red Bone Marrow 0.12Lung 0.12

Thyroid 0.03Bone Surface 0.03Remainder* 0.03Total Body 1

Table 1.1: Weighting factors for different tissues. *For the remaining organs, a factorof 0.06 is used for each of the five organs receiving the highest dose.[10]

1.4 Detection of Radiation

The detection of radiation is a very important issue in the field of biomedical imaging

and is the one that presents the most difficulties. It must be clear that the detection of

radiation is based on its effect, as the darkening of a photographic film, the ionization of

a gas and the further measurement of produced charge, the production of luminiscence

in a crystal, or the production of charge carriers in a semiconductor. The first one, which

Rontgen used to give evidence of his discovery, is still used in some applications that

do not require the post-processing of images. The detection of radiation by ionization

is used in a Geiger counter, in which the ionization of a gas in a tube causes a current

to flow between the tube and a filament that goes trough the center of the tube. The

measurement of this electric current is an indirect measurement of radiation, as its

magnitude is proportional to the amount of incident radiation. The last mechanism is

the most widely used for medical imaging applications.

The next section presents a discussion of some instruments used to detect radiation with

imaging purposes. It is not intended to be a complete review of all of them, but a brief

description of some devices that have influenced the development of this field.


1.4.1 Scintillation Detectors

Scintillation detectors, which can be used with all types of radiation, use the production

of light in some crystals, such as zinc sulfide or sodium iodine, upon the deposition of

the energy carried by the incoming particles. The amount of light emitted in the crystal

is proportional to the energy of the particle that caused it. The scintillation crystal

can be placed next to an electronic device called a photomultiplier, that converts the

photons to electric pulses. The height of the pulses will be proportional to the energy

of the incident particle. These pulses can then be amplified, analized and stored, thus

giving information of the amount of radiation and its nature. The pulses have to be

amplified, as they are low voltage pulses at the end of the photomultiplier. This can

cause the background effects to affect the quality of the detection. The analysis of the

signal gives the possibility to distinguish radiation comming from different radionuclides,

an important issue in some medical applications. The user can program the electronic

device to show only the measurements that correspond to certain energies.[4]

In imaging devices, the signal of the photomultiplier is used to determine spatially the

origin of the radioactive source. In spite of the distortion that can affect the signal, due

to the fact that the light source lies in a three dimensional array and not bidimensional

as in other detectors, the introduction of scintillation devices resulted in an increase

of sensitivity and thus in the quality of the images. However, on recent years several

devices that give more spatial resolution than scintillators have been developed.

1.4.2 Charge-Coupled Devices

Charge-coupled devices (CCD) use a scintillator crystal or a semiconductor material

to convert the incident ray into a charge pulse that can be then measured in the shift

register, or the CCD. The detector is divided in small pixels that work indepedently to

collect and measure charge. In a one-dimensional row of pixels, each of them is divided

into three parts (i.e. φ1, φ2 and φ3) as shown in Figure 1.4. The applied voltage on each

division of one pixel is changed during the process of detection to move the accumulated

charge towards the end of the pixel line. During the first step, the voltage in φ1 and φ3

is kept high, while the voltage in φ2 is low. The accumulated charge in the high voltage

bins moves and is collected in the potential well defined by the voltage of φ2. After that,

the voltage of φ3 is lowered, and the charge in the potential well distributes in the bins

φ2 and φ3. Next, the voltage in φ2 is raised, causing all the charge to move to the φ3

bin. The voltage in φ1 is kept high to avoid the difussion of charge carriers from pixel

to pixel. This process is repeated and the charge that gets to the end of the pixel line

is measured and recorded.[11]


��

��

��

��

��

�

�

�

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�

Figure 1.4: Schematic diagram of a CCD detector. Each pixel is divided in threeparts in which the absorbed charge moves to be measured.[11]

A two-dimensional array of pixels can be created by tiling several one-dimensional arrays,

working independently as described above. In this way, a two-dimensional image is

generated and can then be analyzed, processed and stored.

The advantage of CCD devices is the high resolution that can be achieved. The pixels

can have a size of the order of tens of microns, making this kind of detector suitable for

sensitive applications. The largest commercial CCD detector is 4K × 7K pixels, each

one measuring 12 µm × 12 µm (see Figure 1.5).

Figure 1.5: Largest commercial CCD with a sensitive area of 86 mm × 49 mm.[1]

1.4.3 Fast CT Scanners

The combination of high quality scintillator crystals and silicon photodiodes with a fast

gantry results in a fast Computed Tomography (CT) scanner, in which an image of the

whole body can be taken in about 25 seconds. The detector is able to take 64 slices per


revolution and the X-ray generator makes one complete rotation in 0.33 seconds. Besides

that, the X-ray tube has an advanced cooling system that uses oil in direct contact with

the anode, which allows to scan for prolonged periods (i.e. 25 s). The speed of this

system gives the possibility to reconstruct a beating heart, a difficult task due to the

fast movements of the imaged specimen.[1]

1.4.4 Energy-Resolving Methods

Radiography is based on the difference of absorption of X-rays in different tissues. The

amount of radiation that is absorbed by one material depends on its energy. For one

spectrum it is possible to have equal absorption with different materials, but this is no

longer true with another spectrum. The dependence of absorption with the incident

energy can be used to discriminate among different kinds of tissue. It is also possible to

enhance the contrast of an image by using this method.

An example of an Energy-Resolving Method (ERM) is shown in Figure 1.6. The addition

of images taken with X-rays of different energies, weighted by the appropriate factors,

makes it possible to obtain an image of the soft tissues. In a similar way, an image of the

bones can be obtained. The ERMs have the power of resolving very small malformations

or calcifications that are surrounded by different tissues, such as breast cancer.[1] This

task would be difficult to accomplish by any other method.

Figure 1.6: Radiographies taken with low (a) and high (b) energy spectra. An algo-rithm that uses both radiographies allows to visualize soft tissues (c) or bones (d) in

one image.[1]

1.4.5 Single-Photon Detection

In the common detectors it is required to integrate the signal and perform an analog-to-

digital conversion to handle information at a later point. However, quantum detectors

count single events, which results in a higher detective quantum efficiency (DQE), a

measurement of the quality of the resulting image. Single counting detectors work almost


without noise signal, because they are able to discriminate among different signals and

thus work over the noise level. Another advantage is the possibility of counting single

photons of different energies. There is one limitation that has to be considered with this

type of detectors. The amplifiers, discriminators and counters must be small enough to

fit in a detector containing a vast amount of pixels. The frequency at which the detector

counts is a limiting factor, as well.

Recent investigations of a chip that combines energy-resolving capabilities with single

photon counting, directed towards medical applications have given promising results.

The Medipix2 chip, developed at CERN, is a read-out matrix that, coupled to a semi-

conductor, allows the detection of charged particles and photons. It has a small effective

area of 14 mm × 14 mm, which, combined with its high resolution, makes it perfect

for the production of micro-radiographies, but it is also possible to tile several chips for

larger applications.[1]

Chapter 2

The Medipix2 Detector

The Medipix2 is based on the design of the Medipix1, the first approach to single photon

detection by the CERN Collaboration. The images taken with a Medipix1 showed

very good contrast and were free of noise, an advantage over other types of detectors.

However, it had some limitations that were overcome by the Medipix2. Among these

limitations was the size of the pixel (170 µm × 170 µm), that affected the spatial

resolution of the detector. The new detector had to have smaller pixels to increase the

granularity of the images. Another limitation was the lack of sensitivity to negative

impulses, thus the bias voltage had to be set to accumulate holes in the chip. The

compensation for leakage current was done in each column and for better results it had

to be done in each pixel. The dead area around the detector had to be decreased, to open

the possibility of tiling chips to have a detector with a larger sensitive area. To avoid

noise, the analog biasing had to be done in each pixel instead of being done externally.

The Medipix1 had only one discriminator, so it was not possible to set an energy window

for the detected particles. This had to be improved by adding another discriminator to

allow the setting of an energy window.

These improvements were implemented in the Medipix2, a 16120 µm × 14111 µm chip,

in an array of 256 × 256 pixels, each one of 55 µm × 55 µm, with a total sensitive area

of 1.982 cm2 (see Figure 2.1). The non sensitive area of the chip measures 2040 µm ×

14111 µm and has the wire-bonding pads, biasing Digital to Analog Converters (DACs)

and control logic.[13]

2.1 The Medipix2 Chip

When a charged particle or a photon incides on the semiconductor detector, an electron

hole pair is created. The bias voltage creates a high electric field in the material that

12

Chapter 2. The Medipix2 Detector 13

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separates the electron from the hole, drifting one of them towards the counting chip.

The charge is accumulated and amplified and it is translated into a voltage. This voltage

is compared with two thresholds and if it falls between the two thresholds, a counter in

incremented. This is done in every pixel of the matrix, giving rise to a quanta-counting

detector with an energy-resolving property.

2.1.1 The Analog Part

The analog part of the pixel (in red in Figure 2.2a) has a test capacitance, the Charge

Sensitive Amplifier (CSA) and the two discriminators. The input is the current pulse

that comes from the semiconductor detector upon the interaction of a photon or a

charged particle with the crystal.

The test capacitance is used to input a known amount of charge to the pixel to test the

settings. The CSA integrates the input charge and shapes it. It also has a compensation

for positive or negative leakage currents. The two discriminators are equal, but the

threshold voltage on each of them can be set individually. The high and low thresholds

are set by an 8-bit DAC for all the pixels of the matrix. A 3-bit DAC is used in each

discriminator branch of each pixel to minimize the threshold variation due to differences


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Figure 2.2: (a) Schematic of one Medipix2 pixel showing the analog (red) and dig-ital (blue) parts. (b) Pixel layout showing dimensions and the bump bond (green) inwhich the chip is connected to the semiconductor detector. (1) Preamplifier; (2) HighThreshold Discriminator; (3) Low Threshold Discriminator; (4) 8-bit Pixel Configura-

tion Register; (5) DDL; (6) SR/C (13-bit shift register and logic).[12]


in the transistors and power consumption. This DAC controls the amount of current

that is added to the output of the discriminator and is unique for each threshold and

each pixel. At the end of each discriminator there is a mask bit that allows to discard

the information from noisy or defective pixels.[13]

2.1.2 The Digital Part

The digital part of the pixel (in blue in Figure 2.2a) has the Double Discriminator Logic

(DDL), the Shift Register Counter (SR/C) and the Pixel Configuration Register (PCR).

The DDL uses the output of each discriminator branch and its output is used as a clock

to increment the counter of the SR/C. A global clock is used to shift the data from

pixel to pixel, to set the 8 configuration bits or to read the 13 pixel counts bits with the

Shutter and Conf signal controls.

The DDL compares the output of each discriminator and depending on the configuration

of the thresholds it uses a clock to count bits. The detector can be set in a single threshold

mode, by setting the high threshold (THH) lower than the low threshold (THL). In this

setting, the pulses with a voltage higher than THL are counted. On the window mode,

an energy window is set with the THL and THH voltages. The pulses with a voltage

higher than THL and lower than THH are counted. The rest of the pulses are discarded.

If the Shutter and Conf are low, the SR/C counts each clock impulse comming from

the DDL, up to 8001 counts. If the Shutter is high, a global clock shifts the data from

pixel to pixel. In this mode, if Conf is low, the information of the counts of each pixel

is read out. On the contrary, if the Conf is high, the PCR sets the configuration of the

pixel.[12]

The PRC is an 8-bit memory that stores the configuration of the pixel. The configuration

it stores is the THL (3 bits), THH (3 bits), one test bit and one mask bit.

Figure 2.2b shows the pixel layout. The bump bonding aperture, shaded in green, has

a diameter of 20 µm. It lies upon the analog part of the pixel and communicates the

semiconductor detector with the chip. The detector is assembled to the chip using an

eutectic tin-lead solder process.[13]

2.1.3 The Chip Periphery

The periphery is the non-sensitive area of the chip, which provides the analog biasing

and the digital controls of the matrix. It has the width of the matrix and the height

provides enough clearance for the wire bonding process.


The analog part of the periphery has 13 8-bit Digital to Analog Converters (DACs),

which provide bias voltages and currents to each of the pixels of the matrix. The DACs

are set with an 8-bit code that can be set in different ranges of values for each of the

controlled parameters. The principal DACs are the FBK (set to 128), the Ikrum (set to

20) and the THL and THH. The FBK and the Ikrum are parameters of the CSA that

control the amplification (FBK voltage) and leakage current effects (Ikrum current).

The effect of rising the FBK is to lower the voltage equivalent to a charge impulse,

affecting also the noise level. This DAC is important when working with paticles that

deposit a large amount of energy that saturates the pulse. The Ikrum controls the rise

time of the pulse. A higher Ikrum gives a shorter time, thus a higher voltage pulse.[14]

The test pulse is also controlled by the analog periphery of the chip. It sets the amount

of charge that will be injected to each pixel, the number of pulses and the rise and fall

time of the input voltage.

The digital part of the periphery does the reading and writing of the pixel matrix and

the loading of the DAC digital codes. The Low Voltage Differential Signaling (LVDS)

is the pathway to data transmission to and from the chip.[13]

2.2 The Mpix2MXR20

The Mpix2MXR20 is the redesign of the Medipix2 that adresses the correction of some

limitations of the Medipix2. The Medipix2 solved the problems that the Medipix1 had by

using 0.25 µm CMOS technology. It had very small power consumption, fast operation

and tiling of several chips was possible. However, there were still some problems that

limited the practical applications of the chip.

The most important limitations of the Medipix2 were the following:

• The voltage DACs had a high temperature dependence and a lack of linearity.

• There were variations in the analog buffers from pixel to pixel, limiting the func-

tionality of the test pulse.

• The counter was reinitialized when it reached 8001 counts and there were no means

to know if this happened, which generated a loss of information.

• The radiation hardness (i.e. 10 krad) was not as high as expected with the tech-

nology used. This means that the integrated dose that caused a clear variation in

the THL equalization mask was an order of magnitude lower than expected.


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Figure 2.3: Schematic of one Mpix2MXR20 pixel showing the analog (red) and digital(blue) parts.[13]

Besides solving the previous limitations, the redesign of the Medipix2 modified some

parts of the pixel and periphery electronics. The dimensions of the chip and pixel cell

and the readout architectrure were not modified to use the same sensor materials and

readout systems designed for the Medipix2. At a pixel level, NMOS enclosed layout

transistors were used in the sensitive nodes to eliminate the effect of parasitic currents

due to radiation. A local mirror was added to generate the Ikrum/2 used for leakage

current compensation. In this way, the dispersion of the threshold was improved. The

discriminator block was simplified and the mask bit was changed to the digital side

(see Figure 2.3). In the digital side, an overflow bit was added and the SR/C was

slightly changed. The counter was changed to have a dynamic range of 11810 counts

in acquisition mode (Shutter low). If this number is reached during an acquisition, the

overflow bit is modified and the logic changes the pixel from acquisition to read-out

mode (Shutter high).

The periphery was modified to improve the DACs temperature dependence, linearity, use

of test pulses and readout speed. The dimensions of the periphery were not changed.

The most important modification in the chip periphery was the improvement of the

DACs stability and temperature dependence by the implementation of a circuit that

delivers a temperature independent current. The periphery of the Mpix2MXR20 has 11

8-bit current and voltage DACs to control the analog and digital parts of each pixel. It

also has two 14-bit voltage DACs to set the thresholds in a more precise way. Each of

them has a linear 10-bit DAC to set the fine threshold and a 4-bit DAC to set the coarse

threshold.[13] With this two DACs, the low and high threshold can be set in a wide

range of values with the THL coarse and THH coarse and then tuned more precisely

with the THL and THH. The latter present high linearity with the voltage, which is

useful to detect particles or photons with a good energy resolution.


The Mpix2MXR20 is the chip that was used for all the measurements. From now on

the Mpix2MXR20 will be referred to as Medipix2.

2.3 The USB Interface

The USB Interface, developed at the Institute of Experimental and Applied Physics

(IEAP) of the Czech Technical University in Prague is needed to connect the Medipix2

to a PC. It is an alternative to the MUROS2 interface, developed at the National Insti-

tute for Nuclear Physics and High Energy Physics (NIKHEF) in the Netherlands. The

USB Interface allows to readout the pixel matrix and to control the acquisition and its

parameters.

The USB Interface has an internal source of variable bias voltage with leakage current

monitor that allows to set voltages from 5 to 100 V. This is the voltage along the

semiconductor sensor that separates the electron hole pair for the detection of one of

them. Besdies the independence of an external power source, the USB Interface is more

portable than the MUROS2, an advantage for some applications. The firmware can be

flashed directly via USB and it has a PCB module for additional applications.[15]

Figure 2.4: The USB Interface (a) in the box and (b) out of the box.[15]

2.4 The Pixelman Software

The Pixelman software, developed at the IEAP controls the acquisition of Medipix2 via

the USB Interface or the MUROS2. It is an alternative to the Medisoft4 sotware, de-

veloped at the University of Napoli. The plugins allow to perform operations additional

to the acquisition, such as coincidence control, beam hardening correction and more

complex measurements.


Figure 2.5: The Pixelman principal window in which the parameters of the acquisitioncan be controlled.[15]

The principal window has the acquisition options. The acquisition type, time of ac-

quisition, number of acquisitions, and Spacing can be set before the acquisition begins.

The Spacing is an important parameter of the acquisition. It controls the number of

pixels that are active during the acquisiton to avoid coupling effects among neighboring

pixels. The number of Spacing corresponds to the number of inactive pixels between

the ones that are counting. The type of output and the file extension can be changed in

this window. This window also provides access to the Preview window, Settings, DACs

control panel and DACs Scan.

Figure 2.6: The Pixelman Preview window in which the acquired data is displayed.[15]


The Preview window displays the data that is read from the Medipix2 in a matrix

with different color schemes. It also presents a histogram that gives the information of

number of pixels with a certain count and statistical data of the displayed values. The

equalization masks, test bits and mask bits can be visualized in the Preview window.

The software allows to save the data in image or text files.

The user can control the settings of the Medipix2 in the Settings window. The polarity

of the device can be selected to collect holes (Positive) or electrons (Negative) and the

Bias Voltage can be set up to 100 V. A digital test can be performed to know the number

of good and bad pixels. The program writes and reads a random matrix and compares

the data to know how many pixels are working. The DACs can be controlled in this

window, as well as in the DACs Control Panel, which can be accessed from the principal

window.

The Tools menu in the principal window gives access to the DACs Scan, the DACs

Control Panel, the Threshold Equalization and the Beam Hardening Module.

Chapter 3

Preliminary Measurements and

Energy Calibration

This chapter describes the measurements done with the Medipix2 detector prior to the

acquisition of radiographies. The first procedure was the threshold equalization, in which

the two thresholds of each pixel are corrected with a 3-bit DAC. This allows to have

a more unified threshold throughout the matrix. After that, a DAC scan of the THL

was done. From this scan some propierties of the detector can be obtained, such as the

effective threshold and the pixel linearity.

The next part presents the energy calibration of the detector using the procedure de-

scribed in [14, 16]. The objective of this calibration is to find the correspondence between

DAC threshold value and actual energy. This is an important procedure to take advan-

tage of the energy window feature of the Medipix2.

3.1 Threshold Equalization

In the analog part of each pixel there are two discriminators in which the incoming

pulse is compared with two voltages that constitute the energy window. Each branch

has a 3-bit DAC used to control the amount of current that is injected to the output of

the discriminator in order to minimize the threshold variation due to differences in the

transistors and power consumption. This 3-bit DAC is different for each branch and for

each pixel.

The threshold equalization is the procedure by which the 3-bit DAC value is set for the

THL and THH branch for each pixel. The first is the low threshold equalization, that

uses the noise floor to determine the vaule of THL DAC at which a pixel stops counting.

21

Chapter 3. Preliminary Measurements and Energy Calibration 22

This is done once with the 3-bit current DAC set to 000 (red distribution in Figure 3.1)

and then set to 111 (blue distribution in Figure 3.1). As the behavior of the threshold is

linear, an interpolation can be done to determine the 3-bit current DAC that minimizes

the dispersion (black distribution in Figure 3.1).

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Figure 3.1: Distribution for the low threshold equalization with 000 correction (red),111 correction (blue) and after the equalization (black).

In this case, the standard deviation was 10.38 and 9.50 (in DAC units) for 000 and 111

correction, respectively. After the THL equalization, the standard deviation was 2.43.

The result of this procedure is a 256×256 matrix with values between 0 and 7, that

represent the 3-bit current DAC that corrects each pixel’s low threshold.

After the THL is equalized, the high threshold equalization has to be done if an energy

window is to be set. This was done following the procedure described in [17]. The

Double Discriminator Logic of the Medipix2 is such that if the THH is below the THL,

the detector works in a single threshold mode and all the pulses with voltage larger than

the THL are counted. In the double threshold mode the THL is below the THH and

the pulses that lie in the energy window are counted. The equalization of the THH uses

this transition from single to dual energy mode, setting the THL above the noise level

and pulses with voltage higher than the THL. The THH was scanned in the vicinity of

the THL such that when it was below the THL, the pulses were counted and when it

was above the THL, and worked in double threshold mode, the pixel stopped counting

the pulses.


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Figure 3.2: Distribution for the high threshold equalization with 000 correction (red),111 correction (blue) and after the equalization (black).

This THH scan was done with the 3-bit current DAC set to 000 (red distribution in Fig-

ure 3.2) and then set to 111 (blue distribution in Figure 3.2). The same interpolation

technique was used to get the narrower distribution of the corrected pixels (black distri-

bution in Figure 3.2). The standard deviation was 15.14 and 12.88 (in DAC units) for

000 and 111 correction, respectively. After the THH equalization, the standard deviation

was 3.82.

The equalization procedure has the possibility of masking the pixels that are far from

the average. The user can set the number of standard deviations from which the pixels

begin to be masked. In this equalization, the pixels lying three standard deviations

from the mean were masked. After the THL and THH equalizations, the total number

of masked pixels was 647.

3.2 DACs Scan

The DACs Scan is a useful plugin to perform a scan of any DAC value. The electrical

characterization of the pixel was done with this utility, following the procedure described

in [13]. The test pulse was used to inject pulses to eight pixels along the matrix (while

the rest was masked). The THL was scanned over values ranging from above the pulse

voltage to below the noise level. The THH was set at half the distance between the

pulse height and the noise level. The graph obtained is shown in Figure 3.3.


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Figure 3.3: THL DAC scan with 4000 test pulses of 0.1 V.

The first information that can be obtained from the graph is that a larger THL DAC

corresponds to a smaller voltage value. This is the reason for the noise level to be at

a larger DAC value than the pulse level. The first rise occurs when the THL crosses

the test pulse height, going towards the noise level. The number of counts in the active

pixels rises up to the number of pulses injected in each pixel. In this region the Medipix2

works in single threshold mode. Thus, the Counts value remains constant until the THL

crosses the THH. In this moment the detector passes to a double threshold mode, giving

no counts, as the pulse height is above the energy window. The next rise comes when

the THL crosses the noise level.

This graph also gives information of the effective threshold, linearity, gain and noise.

The effective threshold can be extracted using the s-curve method, that states that the

effective threshold is at 50% of the rising or falling edge of the curve.[13] The gain is

the distance between the effective threshold and the noise floor. If this scan is done

for different voltages of the test pulse, an effective threshold can be found for each one.

The linearity of the threshold with the voltage can be measured with these values. The

measurement of gain and noise can be done for different values of the Preamp and Ikrum

DACs. A Preamp of 128 and Ikrum of 20 is found to give an optimal combination of

gain and noise.[13]

All these measurements were done with an active matrix of eight pixels to avoid coupling

among pixels. The Pixelman software has a utility that controls the number of active

pixels during an acquisition. The Spacing is the number of masked pixels between active


pixels during a subacquisition. This is used to minimize the coupling effects from pixel

to pixel. The number of subacquisitions is equal to 2S where S is the Spacing. A

Spacing of 4 has a good balance between pixel coupling and time required to complete

the acquisition.[15]

3.3 Energy Calibration

The next step was the energy calibration, for which the procedure described in [14, 17]

was used. The Medipix2 is illuminated with a known X-ray or gamma ray spectrum and

a THL DAC scan is performed. The points at which the rate of change of the Counts

has peaks are the points at which the characteristic lines of the source lie.

Before calibrating the Medipix2, the spectrum of each tube was measured with the

PHYWE X-ray unit (see Appendix C). Bragg’s Law states that maximum intensities of

light inciding at an angle θ to a crystal of lattice constant d occur at integral number n

of wavelengths λ,[18] such that:

2d sin θ = nλ (3.1)

An expression that relates the energy of the reflected light with the angle of reflection

can be found from Bragg’s Law:

E =nhc

2d sin θ(3.2)

The PHYWE X-ray unit was used to measure the intensity of X-rays at angles ranging

from 3◦ to 30◦, covering the first order of diffraction (i.e. n = 1), for both tubes with a

voltage of 35 kV and current of 1 mA. Figure 3.4 has the results of the measurement of

the spectrum of the Cu and Mo X-ray tubes. The characteristic lines, found with (3.2),

are:

Element/Line λ [pm] Energy [keV]Cu Kα 154.794 8.009Cu Kβ 139.746 8.872Mo Kα 71.330 17.382Mo Kβ 63.012 19.676

Table 3.1: Characteristic lines for Cu and Mo X-ray tubes.

The Medipix2 was illuminated with each tube and a THL DAC scan was performed. The

THL was scanned towards the noise level with a step of 3 DAC values. The scan with

the Cu tube shows only one peak (see Figure 3.5a), corresponding to an energy between


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Figure 3.5: Derivative of the flux found with the THL DAC scan with Cu (a) andMo (b) X-ray tube.


the Kα and Kβ lines. The scan with the Mo tube shows two peaks that correspond to

the two characteristic lines (see Figure 3.5b). This gives rise to three values of energy

with their corresponding THL value.

THL DAC Energy [keV]317 8.44256 17.382250 19.676

Table 3.2: Values obtained from energy calibration with Cu and Mo X-ray tubes.

3.4 Validation of Calibration

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Figure 3.6: Cross sections for Ni (blue), Cu (black) and Zn (red) showing the K lineat 8.333, 8.979 and 9.659 keV, respectively.[19]

The calibration obtained with the characteristic lines of the Cu and Mo X-ray tubes

was compared with THL DAC values obtained from the K lines of three elements.[19]

Nickel, copper and zinc foils were used as absorbers in the Mo X-ray tube aperture, with

a voltage of 17 kV and current of 1 mA, using the bremsstrahlung of the tube. The

cross section of these materials shows the K line at energies below 10 keV. The rise in

the cross section at these energies should be visible if the element is illuminated with

X-rays, as suggested by Figure 3.6.

Figure 3.7 shows the derivative of the flux obtained from the THL DAC scan. The peaks

of each material can be related with the respective K line energy (see Table 3.3).


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Figure 3.7: Derivative of the flux found from the THL DAC scan with Ni (blue), Cu(black) and Zn (red) foils, illuminated with the bremsstrahlung from a Mo X-ray tube

at 17 kV.

THL DAC Energy [keV]318 8.333314 8.979310 9.659

Table 3.3: Values obtained from THL DAC scan with Ni, Cu and Zn foils.

A linear fit was done with the values of THL DAC and corresponding energies, as shown

in Figure 3.8. The linearity of the energy of the inciding photons with the Medipix2

threshold is evident from the fit.

E = 58.81574± 5.002− 0.15911± 0.01812× THL

R2 = 0.98720 (3.3)


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Figure 3.8: Energy calibration with Cu and Mo X-ray tubes (�) and validation withNi, Cu and Zn foils illuminated with X-rays (N).

Chapter 4

Radiographical Imaging with

Medipix2

When passing through a sample, the intensity of an X-ray beam is attenuated. Different

materials attenuate an X-ray beam in different amounts. These differences in attenuation

can be used to evaluate the internal structure of a sample, without having to look directly

at it.

This chapter describes the procedures done to obtain radiographies with Medipix2 semi-

conductor pixel detector. The first section decribes the experimental setup used to ob-

tain radiographical images with the PHYWE X-ray unit and the Medipix2. After that,

the flat field correction is presented with an example showing its possible contribution

to the quality of the radiographies. Then, the energy window feature of the Medipix2

is exploited to take radiographies at different energies, from which the need of beam

hardening correction arises. The beam hardening correction is then presented and some

examples that display a noticeable difference with raw and flat field-corrected images

are shown.

4.1 Experimental Setup

The Medipix2 was placed inside the PHYWE X-ray unit using the Medipix2 support

designed and constructed at UniAndes (see Appendix D for details). Figure 4.1 shows the

Medipix2 on the support, inside the PHYWE X-ray unit. For the following radiographies

the Mo tube with a voltage of 35 kV and current of 1 mA was used. The detector was

placed in front of the 5 mm collimator at a distance of 390 mm. An exposure time of

31

Chapter 4. Radiographical Imaging with Medipix2 32

Figure 4.1: Experimental setup used for radiographical imaging with Medipix2. Thefigure shows the PHYWE X-ray unit with a Mo tube and the Medipix2 on the support

designed and constructed at UniAndes.

2.5 seconds, divided in 5 acquisitions of 0.5 seconds each, was used to avoid the pixel

counter overflow and to have images with good statistics.

The sample was placed next to the detector. For this section, a sample support was not

used due to the dimensions of the sample. The active area of the Medipix2 of 14 mm

× 14 mm was not suitable to take a complete image of the sample if it was not placed

next to the detector’s window.

4.2 Flat Field Correction

The flat field correction is used to eliminate the distorition of the image due to the differ-

ence in efficiency among pixels. This correction can also compensate the negative effects

of a non-uniform radiation field. After correcting with flat field, a radiography displays

details of the sample with higher contrast and the statistical variation throughout the

image is reduced. The regions with little or no attenuation show the best results after

the flat field correction with an open beam image.

To correct an image with this method,[20] the raw image has to be multiplied by a

matrix C containing the correction factor for each pixel. These factors can be found

by illuminating the detector with the same parameters of the acquisition, but without

the sample in between. The correction factor for the i,j th pixel is given by cij = f/fij ,

where f is the mean value of all pixels and fij is the value of counts in the i,j th pixel


of the open beam image. The corrected image, represented by a matrix V is given by

vij = cijrij , where rij is the value of counts in the i,j th pixel of the raw image R.

4.2.1 Foils Phantom

The foils phantom was constructed with aluminum foils with a thickness of 1.58 mm

each. The phantom had a part without foils (lowermost), one foil, two foils and three

foils (uppermost). The radiography was taken with an energy window from 8 to 35 keV.

Figure 4.2a shows the raw image and the respective histogram of pixel counts of the foils

phantom. Figure 4.2b shows the image and the respective histogram of pixel counts of

the foils phantom after the flat field correction with open beam.

��

Figure 4.2: Comparison of raw (a) and flat field-corrected (b) image of foils phantomwith their respective histograms of pixel counts. The black points in both images are

masked pixels.

The first difference between the raw and corrected image is the visibility of the non-

uniform radiation field in the first one. On the other hand, the corrected image shows

little or no effect due to the non-uniform X-ray beam. The uniformity of the colors is

better in the corrected image, especially in the parts with less absorption (two lower


regions). This is due to the fact that the correction was done with an open beam image.

If it were done with a flat field image of two or three aluminum foils, the two upper

regions would display better uniformity than the lower ones.[20]

The histograms of pixel counts of both images show three peaks that correspond to the

first three regions (from top to bottom) of the phantom. It is evident that the histogram

of the first image has a wider distribution for the three peaks than the second. The flat

field correction causes the distributions to be narrower, another sign of better uniformity

after the correction.

4.2.2 Capacitor

Figure 4.3: Photograph of capacitor.

The next radiographies were taken to the capacitor shown in Figure 4.3. The raw image

of the capacitor (Figure 4.4a) has a visible non-uniformity, which fades away after the

flat field correction with an open beam image. The color variation in the internal part

of the capacitor is better in the corrected (Figure 4.4b) than in the raw image. The

effect of the correction on the histogram is more evident in this case than in the foils

phantom. The two distributions appear more separated and with less deviation in the

second image, which translates into a more uniform image.

It is therefore clear that the flat field correction has to be taken into account to get the

best resolution and quality from the pixel detector. However, as will be shown in the next

sections, it is only part of the whole correction needed to obtain actual radiographies.


��

Figure 4.4: Comparison of raw (a) and flat field-corrected (b) image of capacitor withtheir respective histograms of pixel counts. The black points in both images are masked

pixels.

4.3 Radiographies at Different Energies

The absorption of radiation depends on the material through which it passes and also on

the energy of the inciding photons. Radiation of low energy is stopped in a higher amount

than that of higher energy. Therefore, if the detector has the possibility of counting only

the radiation with certain energy, it is possible to visualize different information with

different parts of the spectrum of a polychromatic X-ray tube (see Figure 1.6).

The energy window feature of the Medipix2 was used to take radiographies of the same

capacitor of last section (see Figure 4.3). The Mo X-ray tube was used with a voltage

of 35 kV and current of 1 mA. Each radiography is corrected with an open beam flat

field taken with the same parameters as the raw image.

The radiographies taken with 5 to 10 keV and 10 to 15 keV X-rays (Figures 4.5a and

4.5b) show very little contrast inside the capacitor. This is due to the high absorption of

the photons of low energies. It is not possible to distinguish among the different materials


��

��

Figure 4.5: Radiographies with flat field correction of the capacitor of Figure 4.3 at(a) 5 to 10 keV, (b) 10 to 15 keV, (c) 15 to 20 keV, (d) 20 to 25 keV, (e) 25 to 30 keV

and (f) 30 to 35 keV.

with these spectra. Figures 4.5c and 4.5d, taken with 15 to 20 keV and 20 to 25 keV

X-rays, respectively, display better contrast among materials of different densities. In

Figures 4.5e and 4.5f, taken at 25 to 30 keV and 30 to 35 keV, respctively, the statistical

nature of radiation is evident. This effect is due to the low quantity of photons at these

energies. Even though the images are corrected with an open beam flat field, the last

two display high non-uniformity.

Taking radiographies at different energies gave complementary information of the studied

sample. Spectra of low energies can show differences among materials of low density.

The high quantity of low-energy photons gives images with very good statistics, which

drops at high energies. Higher energies are able to show differences among more dense

materials, but the low quantity of photons affects que quality of the radiographies. This

has to be compensated with higher exposure times. Despite the advantages that bring

an energy-resolving detector and the flat field correction, the radiographies obtained so

far present variations and are not suitable for tomographical purposes.


4.4 Beam Hardening Correction

The attenuation of X-rays depends on the beam energy, as shown in the last section. In a

pixel detector used for transmission radiography the spectrum in each pixel is unique and

depends on the composition of the sample it passed through. The energy dependance

of the absorption causes the spectrum to be harder in the thicker parts. As each pixel

has a unique efficiency, a correction method has to be implemented in order to address

for the beam hardening issue.

The Signal to Thickness Calibration (STC) is based on the assumption that the sample is

composed of one material with different denisty from point to point.[20] The calibration

is done with flat absorbers of various thicknesses. An open beam image is taken with each

absorber, until the thickness of the sample is covered. The absorbers can be aluminum

or plastic foils. A set of values of count rates yk and thicknesses xk for each pixel is

used to find the equivalent thickness of a certain count rate by interpolation. If the raw

image has counts rij , the corrected image will have counts bij = h(rij), where h is the

calibration function. It is assumed that each point can be modeled by an exponential

function with offset.

y = h−1(x) = Akeakx + Ok (4.1)

The parameters of the exponential fit, Ak, ak and Ok are found for each pixel using the

set of measurements with absorbers. The value y is corrected by interpolation between

the two nearest calibration points, such that yk > y > yk+1. This value is given by:

h(y) =y − yk+1

ak(yk − yk+1)ln

y −Ok

Ak+

yk − yak+1(yk − yk+1)

lny −Ok+1

Ak+1(4.2)

The Pixelman software has a Beam Hardening plugin that computes the exponential fit

for every pixel from a stack of flat field images, taken with a set of absorbers of different

thickness. This configuration can be saved to perform the correction of the raw images

at a later time. The parameters of the acquisition and the experimental setup have to

be the same for the calibration and the acquisition of the raw images. The plugin has

an algorithm for correcting defective pixels by nearest-neighbor weighted average.[15]

Aluminum foils of 0.02 mm to 0.3 mm in 0.02 mm increments and 1.58 mm to 14.22

mm in 1.58 mm increments were used for the following corrections. Each foil or stack of

foils was placed in front of the X-ray tube aperture with the same parameters as before.


4.4.1 Foils Phantom

The first difference between the raw image of the foils phantom (Figure 4.6a) and the

STC-corrected image (Figure 4.6b) is the change in uniformity in the lowermost part

(region with no foils and one foil). The other two regions do not show the same level of

correction, but this is due to the low amount of counts in these parts. The histogram

gives evidence of this correction by narrowing the deviation of the peaks. Moreover, the

distance between peaks becomes constant after the correction. In the first histogram

only three out of four peaks are visible (the small peak at zero counts corresponds to

masked pixels). In the histogram of the corrected image the four peaks, corresponding

to the four regions, are visible.

��

Figure 4.6: Comparison of raw (a) and STC-corrected (b) image of foils phantomwith their respective histograms of pixel counts.

It is also noticeable that the corrected image presents no noisy or masked pixels. The

algorithm included in the beam hardening correction compensates very well this problem

by detecting pixels with zero counts (masked) and pixels with bad fitting curves (noisy).


4.4.2 Capacitor

In the case of the capacitor, the STC-corrected image (Figure 4.7b) is clearly more

uniform than the raw image (Figure 4.7a). The difference beween the wall of the cylinder

and the internal material is clearly defined in the second image as well as the distinction

among the materials in the interface between the two wires and the capacitor. It is

possible to distinguish the wires from a round plastic part and the metal plates in the

interior of the capacitor.

The histogram of the raw image has a high frequency at the first and last bins. The

correction, besides inverting the histogram, decreases the separation between the two

peaks. The peak at the high pixel counts in the first histogram corresponds to the

narrow distribution around zero in the second histogram. This is a clear sign of better

uniformity, which is also visible in the open part of the corrected radiography.

��

Figure 4.7: Comparison of raw (a) and STC-corrected (b) image of capacitor withtheir respective histograms of pixel counts.

In this chapter it was shown that, despite the raw radiographies give information of

the internal structure of an object, as long as the radiation is absorbed in a convenient


way (not totally absorbed or totally unaffected), the images have to be corrected to

have an optimal quality. The flat field correction eliminates the differences in efficiency

of the pixels and is enough for monochromatic radiaton. However, the availability of

a monochromatic radiation source in practical applications of radiography is unusual.

The beam hardening correction has proved to eliminate the negative effects of a poly-

chromatic source of radiation. The energy window feature of the Medipix2 was used to

show the difference in absorption of different parts of the spectrum by the same sample,

although this is not the only application of this capability (see Chapter 1).

Chapter 5

Methods for Tomographical

Reconstruction

This chapter presents two approaches to the problem of reconstructing the cross section

of an object from its projections. The first approach is the mathematical formulation of

the problem by Allan Mcleod Cormack.[2, 3] It is based on the Fourier Slice Theorem

and is implemented with the use of the Fast Fourier Transform. The second approach

is an iterative algorithm that has proved to be useful when the number of projections is

low. Finally, a short comparison between the two methods is presented.

5.1 The Filtered Back Projection Method

The Filtered Back Projection (FBP) method is an analytic algorithm to solve the prob-

lem of reconstructing the slice of an object from its projections. The combination of line

integrals gives rise to the projection of an object. This definition is used to derive the

Fourier Slice Theorem which leads to the possiblility of reconstructing the cross section

of the object with the FBP algorithm, as presented in [21].

5.1.1 The Projection of an Object

The projection of an object arises from the evaluation of a parameter of the object along

a line. In this case, the parameter is the attenuation of X-rays as they pass though a

material.

41

Chapter 5. Methods for Tomographical Reconstruction 42

�

�

��

��

Figure 5.1: Geometry definition for tomographical reconstruction. The functionf(x, y) represents the object and P (θ, t) its projection.

Figure 5.1 shows an object with attenuation coefficient given by the function f(x, y) and

(θ, t) the two parameters that define the line integral given by:

P (θ, t) =∫

(θ,t)f(x, y)ds (5.1)

The function P (θ, t) is the Radon transform of the function f(x, y). The Radon trans-

form is related to the coefficient of transmission by:

P (θ, t) = − ln(

IIo

)

(5.2)

The projection is the combination of several line integrals, from which the object can be

reconstructed.

5.1.2 The Fourier Slice Theorem

The Fourier transform of the object function is given by:

F (u, v) =∫ ∞

−∞

∫ ∞

−∞

f(x, y)e−2πi(ux+vy)dxdy (5.3)


The Fourier transform of the projection at an angle θ is given by:

S(θ, w) =∫ ∞

−∞

P (θ, t)e−2πiwtdt (5.4)

If the case θ = 0 is considered, setting v = 0 in (5.3) gives:

F (u, 0) =∫ ∞

−∞

[∫ ∞

−∞

f(x, y)dy]

e−2πiuxdx (5.5)

F (u, 0) =∫ ∞

−∞

P (θ = 0, x)e−2πiuxdx (5.6)

The integrals can be splitted and the term in square brackets is equal to the projection

at an angle θ = 0. The result is that the Fourier transform of the object function equals

the Fourier transform of the projection:

F (u, 0) = S(θ = 0, u) (5.7)

This particular result can be generalized to all (θ, t) leading to the Fourier Slice Theorem[21],

that reads:

The Fourier transform of a parallel projection of an image f(x, y) taken at

an angle θ gives a slice of the two-dimensional transform, F (u, v), subtending

an angle θ with the u-axis.

The result of (5.7) can be generalized by considering the (t, s) coordinate system obtained

by rotating the (x, y) coordinate system an angle θ, such that:

[

t

s

]

=

[

cos θ sin θ

− sin θ cos θ

] [

x

y

]

(5.8)

The projection along a line of constant t is:

P (θ, t) =∫ ∞

−∞

f(t, s)ds (5.9)

And its Fourier transform is:

S(θ, w) =∫ ∞

−∞

∫ ∞

−∞

P (θ, t)e−2πiwtdsdt (5.10)

A transformation to the original (x, y) coordinate system, using (5.8), yields:

S(θ, w) =∫ ∞

−∞

∫ ∞

−∞

f(x, y)e2πiw(x cos θ+y sin θ)dxdy (5.11)


S(θ, w) = F (w, θ) = F (w cos θ, w sin θ) (5.12)

This gives the equality between the Fourier transform of the object function and the

Fourier transform of the projection. The result is that if the F (u, v) function is known

by taking projections at angles θ1, θ2, ..., θk, the function f(x, y) can be reconstructed

by using the inverse Fourier transform.

f(x, y) =∫ ∞

−∞

∫ ∞

−∞

F (u, v)e2πi(ux+vy)dudv (5.13)

However, in practice it is impossible to have an infinite number of projections and thus,

only a finite number of Fourier components will be known. The object function will be,

for −A/2 < x < A/2 and −A/2 < y < A/2:

f(x, y) ≈1

A2

N/2∑

m=−N/2

N/2∑

n=−N/2

F(m

A,nA

)

e2πi((m/A)x+(n/A)y) (5.14)

As it is impossible to have an infinite number of projections, the function F (u, v) is

known only in radial lines. An interpolation is necessary to reconstruct the object

function, but this does not always lead to stable solutions. It would be better to find

this function by a nearest-neighbor scheme, but radial lines get sparser as the radius

increases, which introduces errors that compromise the quality of the reconstruction.

5.1.3 The Filtered Back Projection

The FBP algorithm is an alternative approach to find the object function, without

direclty performing an inverse Fourier transform on the Fourier components. The idea

is to measure the projections, find their Fourier transform, multiply it by a weighting

function and sum the inverse Fourier transforms of the filtered projections.

The object function of (5.13) can be rewritten using a change of coordinates from the

rectangular (u, v) system to the polar coordinate system (w, θ).

f(x, y) =∫ 2π

0

∫ ∞

0F (w, θ)e2πiw(x cos θ+y sin θ)wdwdθ (5.15)

By splitting the integral over θ in 0 to π and π to 2π, writing t = x cos θ + y sin θ and

using the property F (w, θ + π) = F (−w, θ), the object function may be wirtten as:

f(x, y) =∫ π

0

[∫ ∞

−∞

F (w, θ)|w|e2πiwtdw]

dθ (5.16)


By the Fourier Slice Theorem, this is equal to:

f(x, y) =∫ π

0

[∫ ∞

−∞

S(θ, w)|w|e2πiwtdw]

dθ (5.17)

Which can be written as:

f(x, y) =∫ π

0Q(θ, x cos θ + y sin θ)dθ (5.18)

with

Q(θ, t) =∫ ∞

−∞

S(θ, w)|w|e2πiwtdw (5.19)

The Q(θ, t) is the filtered projection in which the filtering is given by |w|. The object

function is obtained by summing the filtered projection at different angles. This process

is often referred to as back projecting the filtered function Q(θ, t).

The integration over frequency in (5.19) has to be done over all frequencies. However,

the contribution to the function over a certain frquency is negligible. If W is a frequency

higher than the highest frequency in a projection and the projection is sampled at

intervals of 1/2W , the approximate Fourier transform of the projection is given by:

S(θ, w) ≈ S(

m2WN

)

=1

2W

N/2−1∑

k=−N/2

P(

θ,k

2W

)

e−2πi(mk/N) (5.20)

with N the number of samples of the projection. In that way, the filtered projection for

a discrete number of projections is given by:

Q(

θ,k

2W

)

≈2WN

N/2∑

m=−N/2

S(

θ, m2WN

)∣

∣

∣

∣

m2WN

∣

∣

∣

∣

e2πi(mk/N) (5.21)

for k = −N/2, ...,−1, 0, 1, ..., N/2. The filtered projection can be multiplied by a func-

tion (e.g. Hamming window) to reduce the noise in the reconstructed images. The

convolution theorem can be used to write (5.21) as:

Q(

θ,k

2W

)

≈2WN

P(

θ,k

2W

)

∗ φ(

k2W

)

(5.22)

where φ (k/2W ) is the inverse discrete Fourier transform of the multiplication of the

function used to reduce the noise and |m(2W/N)|, with m = −N/2, ...,−1, 0, 1, ..., N/2.

Finally, the filtered projection can be back projected to obtain the object function:

f(x, y) =πK

K∑

i=1

Q(θi, x cos θi + y sin θi) (5.23)


where K is the number of projections.

It is important to say that this process is only valid for parallel beam geometry. In

practical applications this beam profile is not very common. The calculations have to

be modified to give the correct results with other geometries. This can be done for fan

and cone beam profiles. For more complex geometries it is not possible to modify the

algorithm and other reconstruction metods must be used.

5.2 Iterative Algorithms

Another approach to reconstructing an object from its projections is based on iterative

methods. The Expectation Maximization (EM) is an algorithm that begins with a trial

object and computes its projections. It then compares them with the real projections.

The trial object is modified in such way that the new projections are more similar to

the real ones. This is done until the two projections perfectly match.

The EM algorithm is very demanding in terms of computational resources. In the

mayority of the cases it is faster to use the FBP algorithm. However, a technique

of Ordered Subsets (OS) can help to speed up the process. The OSEM divides each

iteration in subitarations that use a small amount of projections (as low as 3 or 4).[20]

The iterative algorithms are useful when the number of projections is low, the projections

are noisy or the geometry is complex (see Figure 5.2).

��

Figure 5.2: Comparison between FBP reconstruction showing artifacts due to thesmall number of projections (a) and OSEM3 reconstruction (b).[20]

Chapter 6

Tomographical Imaging with

Medipix2

The process of tomographical reconstruction with Medipix2 is discussed in this chapter.

The first section describes the experimental setup used to take the projections of the

sample at different angles. The next section describes the process of reconstruction of

the sample from the projections. Finally, some examples of reconstructed images are

shown along with a discussion of the results.

6.1 Experimental Setup

The setup used for this part of the project was the same as the one used for radiographical

imaging (see Figure 4.1). The only difference was that a sample holder attached to a

step motor was included, as shown in Figure D.2. The step motor provided the precise

rotation of the sample to take radiographies at different angles.

The Mo tube was set to 35 kV and 1 mA, as before. The distance between the 5 mm

collimator and the Medipix2 was 390 mm. The sample was placed at 355 mm from

the collimator. An exposure time of 2.5 seconds was used for the projections as well

as for the calibration of the beam hardening correction. The sample was rotated, via

a LabVIEW program (see Appendix B), after each projection was taken. It took from

five to ten minutes to acquire 200 projections in 360◦.

47

Chapter 6. Tomographical Imaging with Medipix2 48

6.2 Tomographical Reconstruction with Octopus 8.3

The reconstruction of the sample from the projections was done with Octopus 8.3, a

commercial tomography reconstruction package for CT, developed at the Centre for X-

ray Tomography of the Ghent University. A time-limited full version of the Octopus

8.3 and Octopus 3D Viewer was made available for this project by its developers. The

Octopus 8.3 combines high performance algorithms with a user-friendly interface for

parallel, fan, cone and spiral CT.

The Octopus 8.3 receives the projections in 8-bit (or 16-bit) TIFF images. It has a

module for converting RAW images or images in other formats (i.e. BMP, JPEG or

PNG) to the correct format (see Appendix E). The images are then imported and pro-

cessed. They can be cropped to the desired region of interest, spot filtered, normalized

and ring filtered before producing the sinograms. The spot filter and ring filter correct

detector-based defects and the normalization is the same flat field correction with an

open beam image.[22] After the projections are ready, they are reorganized into sino-

grams (see Figure 6.1). A sinogram is the image that results after a Radon transform.

It is the collection of the projections at different angles of one row of pixels.

Figure 6.1: Example of a sinogram from the cone shell.

Once the sinograms are ready, the slices can be reconstructed. The parameters of the

reconstruction can be modified and individual slices can be reconstructed to test them.

When the settings produce the desired results, the whole volume can be reconstructed.

The reconstruction of the total volume took less than 30 seconds, because of the small

size of the images (256 × 256 pixels) The scaling of the visualization can be changed to

keep the relevant information and the stack of slices is saved as TIFF images. The slices

can be visualized and rendered with the Octopus 3D Viewer.


6.2.1 Three Objects Phantom

The three objects phantom had a wood stick, a wire from a resistance and a piece of

cable embedded in clay (see Figure 6.2a). The phantom was thought to determine if

it was possible to distinguish among the different materials (i.e. wood, metal, plastic

and clay) in a rather simple geometry. The reconstruction was done assuming a parallel

beam profile from 100 projections (see Figure 6.2b for an example of a projection) in

180◦.

��

Figure 6.2: Photograph (a) and STC-corrected projection (b) of the three objectsphantom. The phantom had a wood stick, a piece of cable and the wire of a resistance.The region of interest was the central part of the phantom at a height between 1 and

2 cm.

The reconstructed slice of the three objects phantom (see Figure 6.3a) is from a height

of about 1.5 cm in Figure 6.2a. The two metal wires appear clear in the slice as well

as in the multi-surface render in Figure 6.3b. The wood stick is barely noticeable in

both figures. This is due to the similarity in absorption of wood and clay. The plastic

cover of the cable is impossible to distinguish because of the same reason. Both images

present artifacts from the reconstruction, due to the small amount of projections (i.e.

100 projections) and due to the fact that the sample was only rotated 180◦. The artifacts

also come from the assumption that the beam profile was parallel, when it was actually

conic, as it came from an X-ray tube. These are the reasons of the black lines between

the two wires, that appear in the render as a plane passing through both wires.


��

Figure 6.3: Reconstructed slice (a) and multi-surface render (b) of the three objectsphantom.

6.2.2 Helicoidal Wire Phantom

The next phantom was a helicoidal wire embedded in wax, as shown in Figure 6.4a.

The objective of this phantom was to test the cone beam reconstruction with a sample

presenting a more complex geometry than the three objects phantom. Therefore, the

reconstruction was done assuming a point source of radiation, using 200 projections (see

Figure 6.4b for an example of a projection) in 360◦.

��

Figure 6.4: Photograph (a) and STC-corrected projection (b) of the helicoidal wirephantom.


��

Figure 6.5: Reconstructed slice (a) and multi-surface render (b) of the helicoidal wirephantom.

The reconstructed slice (see Figure 6.5a) shows the wire and a less dense material sur-

rounding it. It is inferred that this corresponds to the plastic cover of the wire. A clear

difference in absorption among these two materials and wax is noticeable in the slice,

as well as in the multi-surface render in Figure 6.5b. The green surface in the render

corresponds to the metal wire, while the blue regions indicate where the absorption is

less than that of metal but higher than wax. The helix is perfectly rendered and the

slice is almost artifact-free, which results in a considerable difference with the former

reconstruction. This can be accounted to the double number of projections and to the

geometry used for the reconstruction (cone beam geometry needs projections in 360◦ and

some additional parameters as source-detector distance and source-object distance).

6.2.3 Cone Shell

The cone shell in Figure 6.6a was reconstructed with the same parameters and number

of projections used for the helicoidal wire phantom. The projection acquisition had to

be divided in two, one for the lower part (see Figure 6.6b) and another for the upper part

(see Figure 6.6c), because of the dimensions of the shell. It was important to reconstruct

the whole volume, as it has an interesting internal structure from top to bottom.

The reconstructed slices in Figure 6.7a and 6.7c show a clear distinction of the material

of the shell. However, some artifacts can be seen in both slices. It is known[20] that

analytic reconstruction algorithms are fully correct when noise levels are low and an

infinite number of projections is available. The Octopus software is based on analytic


algorithms that give rise to these kind of artifacts, which can be reduced with a greater

amount of projections. Despite the artifacts, the multi-surface renders of the lower

(see Figure 6.7b) and upper parts (see Figure 6.7d) of the shell show an almost-perfect

representation of the internal structure of the shell.

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Figure 6.6: Photograph (a), STC-corrected projection of lower part (b) and STC-corrected projection of upper part (c) of the cone shell.

Two phantoms and one object were reconstructed from their projections at different

angles. Different geometries and compositions were used to test the parameters of the

reconstruction with Octopus 8.3. It was shown that, even though the geometry of the

three objects phantom was rather simple, the low amount of projections (i.e. 100 in

180◦) and the parallel beam profile assumption resulted in a low-quality reconstruction

with artifacts that distorted the slices and surface render. On the other hand, the

reconstruction of the helicoidal wire and the cone shell gave better results, because of

the greater amount of projections (i.e. 200 in 360◦) and the cone reconstruction profile


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Figure 6.7: Reconstructed slice of lower part (a), multi-surface render of lower part(b), reconstructed slice of upper part (c) and multi-surface render of upper part (d) of

the cone shell.

assumption. The combination of the PHYWE X-ray unit, the Medipix2 detector and the

Octopus 8.3 was optimal for tomographical reconstruction of objects with a resolution

close to 1 mm. For better resoultions it is essential to raise the source-detector distance

or to have an X-ray tube with a smaller focus (i.e. micro or nano-focus).

Chapter 7

Final Discussion

The main objective of this project was to obtain tomographical reconstructions of two

phantoms and an object from projections at different angles, taken with Medipix2. A

review on biomedical imaging was presented and the Medipix2 pixel detector was briefly

described, emphasizing the features that make it interesting. After performing an energy

calibration of the detector, the energy window feature of the Medipix2 was used to take

radiographies of a phantom and an image, at different energies. The flat field and beam

hardening correction were implemented to the radiographies and it was shown that the

beam hardening correction is necessary to produce high-quality images.

The Octopus 8.3 software was used to do the reconstruction process in two phantoms

and an object. The size of the focus of the X-ray tube (∼ 1 mm) and the low intensity

of the beam were not a limitation for the quality of the reconstructed images. However,

if higher resolution is needed, it is essential to change the distance between the source

and the detector, or to use an X-ray tube with a smaller focus.

To improve the experimental setup it is important to construct an automated positioning

device for the sample holder. This upgrade is nedded to take radiographies at a large

scale. It is also useful to automate the beam hardening correction and the acquisition of

projections to reduce the exposure time. This project sets the basis for the construction

of a Computed Tomography facility at UniAndes with the Medipix2 pixel detector.

54

Appendix A

Specifications of Step Motor and

Driver

The step motor used for the sample holder was an Applied Motion Products NEMA 14

5014-820.1 This motor has a step angle of 1.8◦, weight of 0.33 lbs, voltage of 3.2 V and

current of 0.35 A. The dimensions of the motor are shown in Figure A.2.

Figure A.1: Photograph of step motor in which the sample holder was mounted.

The motor was controlled with the PDO-2035 driver from Applied Motion Products

(Figure A.3). This controller has to be connected to a 120 V AC outlet. The step motor

is connected to the output of the driver. The input of the driver controls the direction

and steps of the motor. These parameters are controlled via an external source of 5 V.

The Enable input is to control if there is current or not in the motor. The Direction

input controls the direction of rotation of the motor with a logical 0 or 1. The Step

input uses the rise edge of the 5 V pulse to move the motor one step in the direction

indicated by Direction.1All the information about the step motor and driver was taken from the Applied Motion Products

Website http://www.applied-motion.com/products/stepper/index.php

55

Appendix A. Specifications of Step Motor and Driver 56

Figure A.2: Dimensions of step motor.

Appendix A. Specifications of Step Motor and Driver 57

Besides these controls, the current that passes through the motor has to be selected

with the DIP switches. The current that was selected for the whole project was 0.25

A/phase. The torque requirements were not very demanding due to the small weight of

the samples. However, this has to be re-evaluated for larger samples to prevent undesired

rotations or vibration of the specimen. It is also possible to select between full step (1.8◦

with this motor) or half step (0.9◦ with this motor).

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Figure A.3: Dimensions of step motor driver.

Appendix B

External Control of the Step

Motor Driver

Figure B.1: Interface of the LabVIEW program used to control the step motor.

The inputs of the step motor driver were controlled via a National Instruments PCI-

6053 NI-DAQmx connected to a CB-50 I/O Connector Block. A LabVIEW program was

created (see Figure B.2), with the help of Ing. Marco Antonio Gonzalez (UniAndes),

to control the step motor from the same PC in which the Medipix2 acquisition was

controlled. Figure B.1 shows the interface of the program, in which the current in the

motor can be enabled or disabled and the direction and the number of steps can be

selected. The OK button performs the number of steps selected. The Done display

shows the number of steps the motor has rotated in each cycle. It is reinitialized the

next time the OK button is pressed. The program can be modified to count steps until

a dedicated button is pressed to reinitialize the counter.

58

Appendix B. External Control of the Step Motor Driver 59

Figure B.2: LabVIEW program used to control the step motor.

Appendix C

The PHYWE X-ray Unit

The PHYWE X-ray unit (see Figure C.1) was used to perform all the measurements

and image acquisitions in the project1. The X-ray tube is inside a shielded box with a

safety mechanism that prevents opening the unit while the tube is operating. The unit

has the unique feature of three different tubes with anodes made of Cu, Mo and Fe (only

the Cu and Mo tubes were available). It has a goniometer controlled with a step motor

where a diffracting crystal is placed between the tube aperture and the Geiger counter

holder. The goniometer and the tube are controlled with a microprocessor. The unit

can also be controlled remotely from a PC.

Figure C.1: PHYWE X-ray unit showing the possibility of changing the X-ray tube.

1All the information about the PHYWE X-ray unit was taken from the PHYWE Websitehttp://www.phywe.de

60

Appendix C. The PHYWE X-ray Unit 61

The tube voltage can be set between 0 and 35 kV in 0.1 V increments. The current in

the tube can be set between 0 and 1 mA in 0.1 mA increments. The counting time of

the device can be set between 0.5 and 100 seconds in 0.1 seconds increments.

The goniometer was removed from the unit to place the Medipix2 and the sample holder

inside the radiation field, as shown in Figure D.3.

Appendix D

The Medipix2 Support and the

Sample Holder

The Support for the Medipix2 (see Figure D.1) was designed and constructed at UniAn-

des by Luis Carlos Gomez. It was designed to fit in the PHYWE X-ray unit and to

position the Medipix2 in front of the X-ray tube aperture. Four magnets at the bottom

of the support fix it to the floor of the PHYWE X-ray unit. The Medipix2 is secured to

the support with four screws. It has two screws to move the support horizontally and

vertically to place the detector in the correct position with respect to the beam.

Figure D.1: Medipix2 and support inside the PHYWE X-ray unit.

The sample holder (see Figure D.2) was constructed using a precision slider. The step

motor described in Appendix A was attached to the slider. The additional parts were

designed and constructed by Luis Carlos Gomez. The height of the sample holder can

be varied with the screw of the slider. Two magnets at the bottom of the sample holder

fix it to the floor of the PHYWE X-ray unit. The sample holder has to be positioned

62

Appendix D. The Medipix2 Support and the Sample Holder 63

manually in front of the Medipix2, as well as its height to have the sample in the field

of view of the detector.

Figure D.2: Sample holder inside the PHYWE X-ray unit.

Figure D.3 shows the Medipix2 on the support and the sample holder inside the PHYWE

X-ray unit. The Medipix2 and the sample holder are aligned with the X-ray beam.

Figure D.3: Experimental setup for tomography imaging, inside the PHYWE X-rayunit.

Appendix E

Comments on Octopus 8.3

A full version of Octopus 8.3 and the Octopus 3D Viewer was made available for this

project, by it developers. Without this contribution from the Octopus team, the task of

reconstructing the slices from the projections would have been more difficult due to the

time limitations. The support of Dr. Manuel Dierick from the Ghent University was

valuable throughout the project. All the information about the Octopus software can

be found in the website XRayLAB.com

Comment on Input Images

The radiographies taken with Medipix2 and STC-corrected in Pixelman were saved as

text matrices of 256 × 256. This information was imported to Mathematica 6.0 and

exported as 8-bit TIFF files that were used as the input of Octopus 8.3. This method

allowed to set the same contrast level in the stack of projections and to export them in

an automated way.

64

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