EVALUATING AND MODELLING THE

PERFORMANCE OF A PORTABLE X-RAY

IMAGING SYSTEM

Thesis submitted for the degree of

Master of Philosophy

at the University of Leicester

by

Prodromos Chatzispyroglou

Department of Physics and Astronomy

University of Leicester

2016

ABSTRACT

The current study was carried out at the premises of the University of Leicester and 3DX-Ray

Ltd. The analysis was done on a portable X-ray system that is destined for security

applications and consists of an X-ray source, a digital panel and a laptop. Given several

constraints related to the modern needs of security applications and to the commercial aspect

of the product, not only the overall performance of the system has been evaluated but also a

series of factors that can reduce the image quality, in terms of resolution and contrast, has

been analysed.

To achieve this, two models that estimate the absorption and the scattering signal have been

developed. The absorption model alone failed to predict the transmitted intensity that reaches

the screen when low contrast, low density materials are exposed. A qualitative analysis on the

scattering signal showed that scattering plays an important role, hence, another model has

been developed to simulate the scattering process. During model development various

physical parameters, that were required for the correct projection, have been quantified.

Although the detector panel has not been studied thoroughly, the sum of the two models

resulted in a very good approximation of the exposure as it was verified by the comparison of

the calculations against the experimental data. Throughout calculations, a semi-empirical

discrete energy spectrum was used to simulate the spectrum of the generated X-ray beam, as

there was no spectral analysis done on the source. In addition to the model development, a

method that estimates the dimensions of one of the fundamental limits of system’s resolution,

the focal spot, has been devised.

Future work includes the unification of the two models and the thorough investigation of the

detector.

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to the University of Leicester and 3DX-Ray Ltd,

not only for giving me the opportunity to fulfill my dream of the present MPhil title but also

for funding my studies.

I would like to thank my supervisors, Prof. Richard Willingale, for his patience and his

perpetual guidance throughout this project and Dr John Lees for his accurate suggestions. To

the staff of 3D-Xray Ltd, thank you – especially Dr. John Anglesea for accommodating my

visits and helping me with the conduction of the experiments.

I also record my sincere thanks to Teresa Smith, IRSA Project Manager, for her unceasing

support.

Dedicated to the sorrow moments of my life…

“Our greatest glory is, not in never falling, but in rising

every time we fall”

INDEX

CHAPTER 1 – INTRODUCTION & X-RAY PHYSICS

1.1. Scientific Background 1

1.2. Scope of the Study

1.3. X-ray Physics

1.3.1. Bremsstrahlung

1.3.2. Heel Effect

1.3.3. Absorption

1.3.4. Compton Scattering

1.3.5. Characteristic Lines & X-ray Fluorescence

1.3.6. X-ray Detection

2

2

2

3

3

4

6

8

CHAPTER 2 – EQUIPMENT AND METHODS

2.1. Measurements 10

2.1.1. X-ray Generator 10

2.1.2. X-ray Detector 13

2.1.3. Purpose of Experiments 17

2.1.4. Test Pieces

2.1.5. Experimental Configurations

18

20

2.2. Calculations 26

2.2.1. R Software 26

2.2.2. Absorption Model 26

2.2.3. Compton Scattering Model 33

CHAPTER 3 – RESULTS AND DISCUSSION

3.1. Experimental Results 39

3.2. Absorption Model Development 45

3.2.1. First Calculations of Absorption Model 45

3.2.2. Determination of Reference Pixel 47

3.2.3. Position of the Focal Spot and Detector Diodes 51

3.2.4. Focal Spot Size 54

3.3. Offset Interpretation 59

3.4. Observation of Scattering 64

3.5. Scattering Model Development 71

3.6. Sum of Models 72

CHAPTER 4 – GENERAL DISCUSSION AND CONCLUSIONS

4.1. Limitations 77

4.2. Summary - Performance of Kit 78

4.3. Future Work 80

BIBLIOGRAPHY

82

1

CHAPTER 1 - INTRODUCTION & X-RAY PHYSICS

1.1 Scientific Background

3DX-Ray Ltd is a global market and technology leader in line-scan X-ray imaging systems

for the security and industrial inspection markets. The company offers portable, in-place X-

ray screening systems for the X-ray examination of suspicious objects, which fulfil the need

for fast, accurate and trustworthy security measures.

The FlatScan2 TPXi X-ray system was used in the present study. FlatScan2 TPXi is a

portable, lightweight X-ray system providing real time high resolution digital images. The

system is designed for outdoor use for accurate identification of threat and non-threat items.

3DX-Ray Ltd assembles and releases the product in the market. The system is ideal for use in

security, military, police and customs applications where bag, package, vehicle inspection

and EOD evaluation is demanded.

Several constraints must be taken into account during the design and the development of a

new X-ray system. First of all, the security market demands ergonomic X-ray systems that

have high detecting efficiency but small dimensions and easy deployment. This is because the

suspicious objects are usually placed in spots that do not attract people’s attention or in

inaccessible places, like the trunk of a car or in close proximity to practically immobile

objects, like walls. However, it is well-known that X-rays are detected when they deposit

their whole energy in the detecting system, which means that the detecting efficiency of the

system is related to the dimensions of the detector. Secondly, security applications demand

fast decision making, which consequently means less scan time. However, fast scans lead to

poor quality images. Thirdly, the system is destined for commercial use. This means that the

fine balance must be found between the manufacturing cost and the final price of the product.

The high cost of the detector modules prevents the development of large detecting surfaces,

thus, FlatScan2 TPXi uses a one dimensional array of photodiodes. During the exposure a

motor moves the sensor arm along the line of scanning, which is perpendicular to the detector

array, so that the whole active surface is scanned. This is challenging for 3DX-Ray because,

regardless the low manufacturing cost, high quality images try to be captured by a small

detecting system in a short time span in order the system to be competitive among other X-

ray screening systems. To achieve this, fast read out electronics, oversampling and

sophisticated smoothing functions are used to improve the quality of signal that is detected by

a small number of diodes.

A measure of the performance of the system should be no other than the quality of the

captured image. Although, it is more a matter of the observer’s subjective judgement, the

basis of the image quality is the ability of the imaging system to detect differences and show

fine details of the irradiated object. Thus, the terms of spatial resolution and contrast can be

used as a measure of quality between images. Several factors will degrade the image quality,

some of which are due to inherent properties of the imaging device, such as the size of the

detector photodiodes or the size of the generator’s focal spot. Others are due to the initial

2

parameters of the exposure, such as the scan time and the voltage – current combination, the

arrangement of the equipment and the material of the irradiated objects. Objects under

investigation may vary in size, shape, density and chemical composition. This results in

dissimilar projected shadows on the detector plane, because of the different attenuation the

incident radiation encounters. Given the primary energy, the X-rays interact with matter

through the absorption and the scattering process. The unwanted scattering signal goes on top

of the absorption signal and obstructs the distinction between the object shadows. Electric

noise is another factor that affects image quality. The major source of noise is the random

distribution of photons per picture element. Although noise cannot be eliminated, the signal

to noise ratio can be optimised by increasing scan time or by selecting the optimum initial

parameters for voltage and current leading to images of better resolution and contrast.

1.2 Scope of the Study

The scope of this study is the detection efficiency characterisation of FlatScan2 TPXi X-ray

system. For this reason, a model was developed in R software including all the important

factors that determine and limit the performance. The model simulates the absorption and the

scattering processes that take place during an X-ray exposure. Additionally, an evaluation of

the current performance of the portable X-ray imaging system and a qualitative and

quantitative analysis of the most significant parameters affecting the quality of the captured

image will take place.

1.3 X-Ray Physics

The basic physical interactions that dominate during an X-ray exposure are the interactions of

electrons and photons with matter. X-rays are generated as a result of Bremsstrahlung and are

detected when they deposit their whole energy in the scintillator, which converts them into

visible light that is then detected by the photodiodes. Only a fraction of the incident X-ray

intensity passes through materials, as the beam interacts with matter and gets absorbed, via

photoelectric effect, coherent and incoherent scattering. X-ray exposures often lead to

secondary X-ray photon emissions, such as the X-ray fluorescence which strongly depends

on the material.

1.3.1 Bremsstrahlung

Bremsstrahlung is the German term for braking radiation. When a charged particle (e.g.

electron) travels in an electric field, it emits Bremsstrahlung radiation. As an electron

approaches an atom, it interacts with the orbiting electrons. This interaction causes the

electron to change kinetic state, decelerate and change direction and is followed by

simultaneous emission of photons. The interaction with the nucleus is also possible. The

strong positive charge of the nucleus may stop the incident electron. The result of the

3

complete stop of the electron is the emission of a photon at the maximum energy, which is

equal to the kinetic energy of the incident photon.

1.3.2 Heel Effect

The Heel effect describes the effect of the anode on the intensity during the production of the

primary X-ray beam. X-rays generated at a certain depth in the anode leave its surface at

different angles and have to cover different distances within the anode material. This results

in different attenuations, as well as hardening, of the beam. The resulting inhomogeneity in

the intensity of the primary beam explains the non-uniformity in the detected radiation at the

detector plane (Hietschold, 2012). The beam is unevenly hardened, which means that spectral

variations along the two dimensions of the panel could occur.

1.3.3 Absorption

A narrow beam of monoenergetic photons with incident intensity I0, penetrating a layer of

material with mass thickness x, attenuation coefficient μ, and density ρ, emerges with

intensity I given by the exponential attenuation law

𝐼 = 𝐼0𝑒−(

𝜇

𝜌𝑥)

. (eq. 1.1)

Equation (1.1) can be rewritten as

𝜇

𝜌=

𝑙𝑛(𝐼0

𝐼⁄ )

𝑥 , (eq. 1.2)

from which μ/ρ can be obtained from measured values of I0, I and x.

Note that the mass thickness is defined as the mass per unit area and is obtained by

multiplying the thickness t by the density ρ, i.e., x = ρt.

Present tabulations of μ/ρ rely heavily on theoretical values for the total cross section per

atom, σtot, which is related to μ/ρ according to

𝜇

𝜌=

𝜎𝑡𝑜𝑡

𝑢𝐴 . (eq. 1.3)

In (eq. 1.3), u (= 1.6605402 × 10-24

g) is the atomic mass unit (1/12 of the mass of an atom of

the nuclide 12

C), A is the relative atomic mass of the target element, and σtot is the total cross

section for an interaction by the photon, frequently given in units of b/atom (barns/atom),

where b = 10-24

cm2.

4

The attenuation coefficient, photon interaction cross sections and related quantities are

functions of the photon energy. Explicit indication of this functional dependence has been

omitted to improve readability.

The total cross section can be written as the sum over contributions from the principal photon

interactions,

𝜎𝑡𝑜𝑡 = 𝜎𝑝𝑒 + 𝜎𝑐𝑜ℎ + 𝜎𝑖𝑛𝑐𝑜ℎ + 𝜎𝑝𝑎𝑖𝑟 + 𝜎𝑡𝑟𝑖𝑝 + 𝜎𝑝ℎ.𝑛 , (eq. 1.4)

where σpe is the atomic photoeffect cross section, σcoh and σincoh are the coherent (Rayleigh)

and the incoherent (Compton) scattering cross sections, respectively, σpair and σtrip are the

cross sections for electron-positron production in the fields of the nucleus and of the atomic

electrons, respectively, and σph.n. is the photonuclear cross section.

In X-ray generators, the energy of the generated X-ray beam cannot be greater than the

energy of the accelerated electron beam. The X-ray generator, that was used in the present

study is capable to produce photons with energies between 40 keV and 120 keV. The

dominant photon interactions in the energy band up to 120 keV are the photoelectric

absorption, the coherent and the incoherent scattering.

The equations 1.1 - 1.4 were found at the website of the National Institute of Standards and

Technology (see reference National Institute of Standards and Technology). The tables of X-

Ray mass attenuation coefficients are based on the work of Seltzer and Hubbell (1995).

1.3.4 Compton Scattering

The result of a Compton scattering interaction is the creation of a recoil electron and a

scattered gamma-ray photon, with the division of energy between the two dependent on the

scattering angle (Compton, 1924). A sketch of the interaction is given in Figure 1.1.

Figure 1.1: Compton scattering. The incident photon interacts with the electron in rest and

gets scattered in an angle θ with respect to its initial direction (This image is available at

https://universe-review.ca/R15-12-QFT10.htm)

5

The energy of the scattered gamma ray hv' in terms of its scattering angle θ is given by

ℎ𝑣′ =ℎ𝑣

1+(ℎ𝑣/𝑚0𝑐2)(1−𝑐𝑜𝑠𝜃) , (eq. 1.5)

where m0c2 is the rest mass energy of the electron (0.511 MeV). The kinetic energy of the

recoil electron is therefore

𝐸𝑒 = ℎ𝑣 − ℎ𝑣′ = ℎ𝑣 ((ℎ𝑣/𝑚0𝑐2)(1−𝑐𝑜𝑠𝜃)

1+(ℎ𝑣/𝑚0𝑐2)(1−𝑐𝑜𝑠𝜃)) . (eq. 1.6)

The probability of Compton scattering per atom of the absorber depends on the number of

electrons available as scattering targets and therefore increases linearly with Z. The angular

distribution of scattered X-rays is predicted by the Klein – Nishina formula for the

differential scattering cross section dσ/dΩ:

𝑑𝜎

𝑑𝛺= 𝛧𝑟0

2 (1

1+𝑎(1−𝑐𝑜𝑠𝜃))2

(1+𝑐𝑜𝑠2𝜃

2) (1 +

𝛼2(1−𝑐𝑜𝑠𝜃)2

(1+𝑐𝑜𝑠2𝜃)[1+𝛼(1−𝑐𝑜𝑠𝜃)]) , (eq. 1.7)

where 𝑎 = ℎ𝑣𝑚0𝑐2⁄ and r0 is the classical electron radius (Knoll, 2000).

The cross section of the angular distribution is shown in Figure 1.2. The strong tendency for

forward scattering increases for higher incident X-ray energies.

The likelihood of photon interaction with matter depends on the material the beam passes

through. Although it’s not unusual for a photon to have no interaction with the matter,

photons can either be photoelectrically absorbed, Rayleigh scattered or Compton scattered. In

case of scattering, the scattered photon is still in play and can interact again with the atoms of

the material. The energy of the primary beam defines the energy and the preferred angles of

the scattered photons. Notice that both the first and the higher order scattered photons are

subjected to further absorption and scattering.

6

Figure 1.2: Polar plot of the angular distribution of the scattered gamma rays as calculated by

the Klein-Nishina formula. Given a random initial energy (here is 120 keV) the solid red line

shows the number of photons (incident from the left) Compton scattered into a unit solid

angle at the scattering angle θ. The red dashed line shows the angle of the scattered photon,

while the blue dashed line shows the angle of the recoiled electron (Blinder, 2009).

1.3.5 Characteristic Lines & X-Ray Fluorescence

Under normal circumstances an atom is neutral. If the orbital electrons are disrupted from

their normal configuration by some excitation process, the atom may exist in an excited state

for a short period of time. There is a natural tendency for the electrons to rearrange

themselves to return the atom to its lowest energy or ground state within a time that is

characteristically a nanosecond or less in a solid material. The energy liberated in the

transition from the excited to the ground state takes the form of a characteristic X-ray photon,

whose energy is given by the energy difference between the initial and final states. As it can

be seen in Figure 1.3, if the vacancy is temporarily created in the K shell of an atom, then a

characteristic K X-ray is liberated when that vacancy is subsequently filled. If that electron

comes from the L shell, then a Kα, photon is produced whose energy is equal to the

difference in binding energies between the K and L shells. If the filling electron is originated

in the M shell instead, then a Kβ photon is produced with slightly larger energy, and so on.

The maximum K-series photon is produced when the vacancy is filled by a free or unbound

electron, and the corresponding photon energy is then simply given by the K shell binding

0

15 °

30 °

45 °

60 °

75 °90 °

105 °

120 °

135 °

150 °

165 °

180 °

195 °

210 °

225 °

240 °

255 °270 °

285 °

300 °

315 °

330 °

345 °

0.

0.2

0.4

0.6

0.8

1.d

d0.819 re

2T 5.935 re

2

e 71.5° KEe 0.007 m c2

7

energy. Vacancies created in outer shells by the filling of a K shell vacancy are subsequently

filled with the emission of L-, M-, . . . series characteristic X-rays. Because their energy is

greatest, the K-series X-rays are generally of most practical significance. Their energy

increases regularly with atomic number of the element and is, for example, about 1 keV for

sodium with Z = 11, 10 keV for gallium with Z = 31, and 100 keV for radium with Z = 88.

The L series X-rays do not reach 1 keV until Z = 28 and 10 keV at Z = 74. Because the

energy of the characteristic X-rays is unique to each individual element, they are often used

in the elemental analysis of unknown samples. For an atom in an excited state, the ejection of

an Auger electron is a competitive process to the emission of characteristic X-rays. The

fluorescent yield is defined as the fraction of all cases in which the excited atom emits a

characteristic X-ray photon in its de-excitation. A large number of different physical

processes can lead to the population of excited atomic states from which characteristic X-rays

originate. In general, the relative yields of the K, L, and subsequent series will depend on the

excitation method, but the energy of the characteristic photons is fixed by the basic atomic

binding energies (Knoll, 2000).

Figure 1.3: Characteristic Kα and Kβ X-rays occur when electrons of the L and M shell

respectively, fill the vacancies in the K shell (This image is available at

http://www.amptek.com/xrf/)

This means that the test objects, the materials of the chamber and the materials of the

equipment such as the hard case of the detector, may have components that introduce new

characteristic lines to the spectrum of the primary beam. Figure 1.4 shows the X-ray

fluorescence of the ABS plastic that the detector’s case is made of. This means that the shape

of the X-ray spectrum changes when the X-rays pass through objects, not only because the

lower energies of the beam are filtered out but also because the characteristic lines of the

materials, that the objects are made of, are added to the spectrum.

8

Figure 1.4: Spectra for measurements of four samples with Cr, Pb, Br, Cd: ABS at about

1000 ppm of each impurity (solid red), ABS at about 500 ppm (dashed red), PVC at about

1000 ppm (solid blue), and PVC at about 500 ppm (dashed blue). The incident X-ray energy

is 33 keV (Lee et al., 2006)

1.3.6 X-ray Detection

The previously mentioned natural mechanisms take place during the X-ray detection. The

basic components of the X-ray detection system that was used in the present study, are the

scintillator and the silicon photodiodes. The scintillator is placed in front of the photodiodes

in order to convert the X-rays into visible light. The incident X-rays excite or ionise the

atoms of the scintillator, leading its atoms to a higher energy state. The atoms return to their

normal state by doing electron rearrangements so that the gap of the missing electron is filled.

De-excitation is followed by simultaneous emission of photons, which have wavelengths

within the visible spectrum. The scintillator used in the detector modules of this detection

system is made of Gd2O2S:Tb (Gadolinium oxysulfide, Terbium activated), which is a

commonly used scintillator in radiography. The wavelength of the primary emission peak of

the scintillator is approximately at 540 nm (Figure 1.5), which designates green light. X-rays

are only detected when they deposit their whole energy on the detection system. Gadolinium

oxysulfide is a widely used luminescent host material, because of its high density

(7.32 g/cm3) and high effective atomic number of Gd, which results in adequate stopping

power for X-ray radiation.

9

Figure 1.5: Room temperature luminescent spectra for scintillators used for radiography. The

operating voltage was set at 60 kV and the spectra were normalised to their peak output. The

strong peak of gadolinium oxysulfide at 540 nm, can be clearly seen. (Duclos, 1998)

10

CHAPTER 2 – EQUIPMENT AND METHODS

2.1 Measurements

The experimental equipment used in the present study is developed and assembled by 3DX-

Ray Ltd. Among other security systems 3DX-Ray launches Flatscan2-TPXi, which is a

portable, lightweight system that provides real-time digital X-ray screening with high quality

images. Powerful image processing tools are also provided to enable the operator to acquire

and interpret X-ray images quickly and simply. The system consists of an X-ray generator, an

X-ray detector panel and a laptop along with the preinstalled ThreatSpect software (see

reference 3DX-Ray Ltd). The Flatscan2-TPXi system is designed for outdoor use. Figure 2.1

(a) demonstrates the proper use of the equipment. The detector panel is placed behind the

“suspicious object” and the generator is placed across the detector panel. All the exposures of

the present study took place in a lead shielded chamber for radiation safety reasons, as it is

illustrated in Figure 2.1 (b).

(a) (b)

Figure 2.1: (a) Explosive ordnance evaluation of a suspicious box (This image is available at

http://www.3dx-ray.com/security/explosive-ordnance-disposal). (b) Configuration during a

test exposure at the 3DX-Ray premises.

2.1.1 X-ray Generator

X-rays can be generated by instruments such as the electron synchrotron and the linear

accelerator, but in this case are produced by a small electron accelerator called X-ray tube

(XRT) (Coolidge, 1915). The primary X-ray beam of this study was generated by the

commercially available X-ray generator CP120. The generator’s output voltage range is from

40 kV to 120 kV, while the tube current reaches up to 1.5 mA. The nominal dimensions of

the focal spot are 0.8 mm width by 0.5 mm height and the maximum useful angle of the X-

ray beam is 50o both in the horizontal and the vertical axis.

11

The basics of its operation are described in Figure 2.2. During thermionic emission the

thermal energy given to electrons overcomes the binding potential of the copper cathode,

allowing the electrons to escape the atom bond. High potential difference between the copper

cathode and the tungsten anode drives the accelerated electrons to the positive charged

tungsten target, where they deposit their energy. A focusing cup is used to concentrate the

electron beam in a very small area called the focal spot (Coolidge, 1938). This is where the

X-rays are generated via Bremsstrahlung. During the collisions, electrons are decelerated

causing electromagnetic emissions in the X-ray energy band. This process has very low

energy conversion efficiency as most of the electron energy deposited on the anode is

converted to heat with less than 1% actually producing X-rays. For this reason special

consideration is taken for the management of the excessive heat in order to keep the generator

within the operating temperature range, which is below 50 oC. Not only the anode is made of

large chunks of high heat capacity materials, in this generator tungsten, to dump heat but also

a gas cooling system is used as an extra measure to prevent wear after long time use.

Figure 2.2: Overview of the X-ray generation process in the X-ray tube. After the thermionic

emission, electrons are accelerated to the anode. The collision with the anode target leads to

X-ray production. (This image is available at http://www.arpansa.gov.au/RadiationProte-

ction/basics/xrays.cfm).

The fraction of the electron energy converted into Bremsstrahlung increases with increasing

electron energy and is largest for absorbing materials of high atomic number. Figure 2.3

clarifies the X-ray generation process. High speed incident electrons may interact with the

nucleus and/or the electrons of tungsten. For monoenergetic electrons that slow down and

stop in a given material, the Bremsstrahlung energy spectrum is a continuum with photon

energies that extend as high as the electron energy itself. Soft X-rays occur due to distant

interactions with the nucleus, while hard ones are due to close interactions or even direct

impact with the nucleus. Finally, interactions between the incident electrons and the atomic

electrons are also possible, resulting in the emission of characteristic X-rays.

The angle of the anode target affects the intensity of the generated X-rays. Due to the Heel

effect, X-rays produced in the anode cover different distances within the tungsten. The

different attenuation leads to the production of a non-uniform primary X-ray beam. In the

system of the present study, although the equipment is properly aligned, the left hand side of

the panel is illuminated more than the right hand side.

12

Figure 2.3 The four different interactions of the incident electron beam with the atoms of the

tungsten anode. (1) and (2) show the generation of soft and medium X-rays respectively, due

to Bremsstrahlung following interactions with the nucleus (3) The incident electron deposits

its whole energy on the tungsten atom after a direct hit with the nucleus, generating an X-ray

with maximum energy, equal to the energy of the incident electron. (4) The incident electron

interacts with a bound electron of the inner shells of the atom, causing ionisation. The hole is

filled by another electron coming from the outer shells, resulting in the emission of a

characteristic X-ray (Seibert, 2004)

The shape of a typical spectrum produced by the monoenergetic electron beam is shown in

Figure 2.4. The emission of low-energy photons predominates, and the average photon

energy is a small fraction of the incident electron energy. The maximum energy is equal to

the operating voltage of the generator. Kα and Kβ characteristic X-rays of tungsten are also

present in the spectrum.

The shape of the energy spectrum from an X-ray tube can be beneficially altered by filtration

or passage through appropriate absorber materials. CP120 has 3.5 mm thick Al filtration.

Through this filter that preferentially removes the lower-energy photons, a peaked spectrum

can be produced that, although far from monoenergetic, can be useful in the energy

calibration of detectors whose response changes only gradually with energy. (Knoll, 2000).

Throughout this study, the CP120 generator is operated at 120 kV, which means that the

maximum achievable energy, although having a small fraction of the spectrum, is 120 keV.

As far as the minimum X-ray energy is concerned, this is mostly defined by the window

filtration. For a given primary intensity I0, the transmitted intensity Ι through a material of

thickness x and linear attenuation coefficient μ, is given by the equation:

𝐼 = 𝐼0𝑒−𝜇𝑥 . (eq 2.1)

Given the 3.5 mm Al window of CP120 the transmitted intensity for a primary beam with

energy 30 keV and 20 keV, respectively, is calculated. At 30 keV, 66% of the incident

radiation is attenuated as it can be seen in (eq 2.2) .

13

𝐼 = 𝐼0𝑒−𝜇𝑥 = 𝐼0𝑒

−3.0456 𝑐𝑚−1⋅0.35𝑐𝑚 = 0.34𝐼0 = 34% 𝐼0 . (eq. 2.2)

Equation 2.3 shows that the Al filtration is sufficient to attenuate completely the radiation

having energy 20 keV as only 4% of the incident radiation was transmitted,

𝐼 = 𝐼0𝑒−𝜇𝑥 = 𝐼0𝑒

−9.2907 𝑐𝑚−1⋅0.35𝑐𝑚 = 0.04𝐼0 = 4% 𝐼0 . (eq. 2.3)

Therefore the generator’s window defines the minimum energy of the produced spectrum at

20 keV. Regardless the attenuation of the window, both 120 keV and 20 keV energies have

very small weight factors in the energy spectrum as it is generated by the Bremsstrahlung

process.

Figure 2.4: The shape of the X-ray energy spectrum generated by an XRT is shown. Lower

energies are filtered by the generator’s window. The maximum energy is equal to the energy

of the incident electrons, in this example 100 keV, while CP120 can reach up to 120 keV.

Characteristic X-rays of tungsten are also present. The 60 kV spectrum is seen in comparison

to be of much lower intensity and to have insufficient energy to generate any K-Characteristic

Radiation in the tungsten atoms. (The image is available at

http://upload.wikimedia.org/wikipedia/commons/thumb/3/35/XrtSpectrum.jpg/320px-

XrtSpectrum.jpg)

2.1.2 X-Ray Detector

A photodiode array suitable for X-ray detection is the basic component of the detector

module. The S8865-128G Hamamatsu module is a photodiode array with an amplifier and a

phosphor sheet made of Gd2O2S:Tb attached to the photosensitive area for X-ray detection

(Figure 2.5 (a)). Each module is formed by 128 elements of 0.4 mm pitch. The signal

processing circuit chip is formed by CMOS process and incorporates a timing generator, shift

register, charge amplifier array, clamp circuit and hold circuit, making the external circuit

14

configuration simple. The detectable energy range is from 30 keV to 100 keV. (see

Hamamatsu datasheet reference).

In FlatScan2-TPXi, two groups of four photodiode arrays are used to form a single pixel

width column that detects the incident radiation (Figure 2.5 (b)). During the exposure, a

motor moves the diodes along the line of scanning creating an active surface where the X-

rays can be detected.

(a) (b)

Figure 2.5: (a) S8865-128G photodiode array manufactured by Hamamatsu. The diodes are

placed under the Gd2O2S:Tb sheet (white stripe), which is used to convert X-rays to visible

light that can be detected by the photodiodes (b) A group of four photodiode arrays.

Sheets of lead and aluminium foil are wrapped around the scintillator to prevent the detection

of scattered X-rays and of visible light respectively (Figure 2.6 (a),(b)). Specifically, stripes

of lead cover both the region between the connectors and the scintillator on the front side of

the module and the whole surface of the module on the back side. Special care is given to the

placement of the lead stripes so that the X-ray path to the scintillators remains unobstructed.

Finally, a stripe of aluminium foil is placed over the scintillators. Throughout this study, the

detecting system was used as delivered.

A hard case made of Acrylonitrile Butadiene Styrene (ABS) provides protection for the

outdoor use of the equipment. The active area of the detecting system is 53.5 cm and 41.2 cm

for the horizontal and the vertical dimension respectively. Although the height of the active

surface corresponds directly to the number of the physical diodes that are used in the detector

array, this doesn’t stand for the width. During the exposure, a motor moves the diodes along

the line of scanning creating an active surface where the X-rays can be detected. Thus, the

pixels of an image are the result of a complex process that includes oversampling, fast

readout and precise data processing during the image reconstruction. A fine balance between

the motor speed, the integration period during the readout, the distance covered by the sensor

arm and the scan time is achieved so that the pixels of the captured image are approximately

square. The captured images are formed by 1536 x 1024 pixels. In (eq. 2.4) and (eq. 2.5) the

pixel size for both dimensions is calculated.

𝑃𝑖𝑥𝑒𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 =𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑐𝑡𝑖𝑣𝑒 𝑎𝑟𝑒𝑎 (𝑚𝑚)

𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑚𝑎𝑔𝑒 (𝑝𝑖𝑥𝑒𝑙𝑠)=

412 (𝑚𝑚)

1024 (𝑝𝑖𝑥𝑒𝑙𝑠)= 0.40 𝑚𝑚 . (eq. 2.4)

𝑃𝑖𝑥𝑒𝑙 𝑤𝑖𝑑𝑡ℎ = 535 (𝑚𝑚)

1536 (𝑝𝑖𝑥𝑒𝑙𝑠)= 0.35 𝑚𝑚 . (eq. 2.5)

15

(a) (b)

(c)

Picture 2.6: (a) Lead foil is wrapped around the phosphor sheet. (b) Aluminium foil used over

the phosphor sheet. (c) Inside view of the detector panel. The diodes are mounted on the

sensor arm in such a way so that the line of motion is perpendicular to the array of the diodes.

A laptop is connected wirelessly to both the X-ray generator and detector. Pre-installed

ThreatSpect software not only allows full operation of the system but also provides image

processing tools for the full understanding of the output (Figure 2.7). Through ThreatSpect

the operator sets the values of the important variables of the system, such as the operating

voltage (from 40 to 120 kV), the current (from 0.1 to 1.5 mA), the integration period (from

2.43 to 9.77 ms) and the time of scan (from 10 to 120 s). The software comes along with

several tools, such as the DeepFocus, which optimises the contrast for each area of the image

independently revealing potential hidden information, the Colour modes, which allows the

display of the image in mono, inverted and false colours and the 3D Emboss which gives a

3D effect to the image. However, the most widely used tool in this project is the Histogram as

it can be seen on the left side of Figure 2.7, which allows the operator to look in detail at

different density levels of the target and to analyse image data acquired by the system which

the human eye cannot see (see ThreatSpect datasheet reference).

16

Figure 2.7: View of the Threatspect software. The image processing tools are shown in the

left hand side of the picture.

The Histogram tool is a mapping from raw signal to contrast. The incident X-rays create

charge before this is converted to an analogue voltage signal between 0 and 5 V. The charge

is proportional to the energy of the incident X-ray. An analogue to digital converter is used to

convert the signal to digital. The signal is stored in 12 bit digital values, which range from 0

to 4095, before being normalised to the “global brightfield” value, as it will be explained

next. Hence, histogram is a representation of the signal in 0 – 1 values. Before each exposure,

the software reads the signal coming from the detectors without the X-rays being present. The

weak signal measured is due to the background and the electronics dark current and is called

“darkfield”. The 0 value is assigned to “darkfield” while the 1 value is assigned to

“brightfield”. ThreatSpect software can display the image in the desired sub-region of the

dynamic range, as it allows the user to set the minimum and the maximum value of the

display. This helps the operator to focus on different regions of the dynamic range, which in

turn means that the effect of X-rays of a specific energy band, can be examined. Table 2.1

summarises the range of the initial parameters.

Table 2.1: The range of the most important initial parameters of the system

Parameter Range

Voltage (kV) 40 - 120

Current (mA) 0.1 – 1.5

Integration period (ms) 2.43 – 9.77

Scan time (s) 10 – 120

Raw data (12-bit) 0 - 4095

In Figure 2.8 the response of a single detector diode in relation to the X-ray energy can be

seen. Even when there is no X-ray flux, a weak signal is read from the diode due to the

17

electronic noise (darkfield). The response of each diode is higher for higher incident X-ray

energy until the threshold of saturation. After the point of saturation, further increase in the

incident energy doesn’t affect the response. Although, the exact relation between the response

and the incident energy is unknown, a linear approximation of the actual response from 0 keV

to 120 keV results in high quality images.

This approximation is a part of the gain/offset calibration process that must be done at the

beginning of each experiment. The system is calibrated during the image reconstruction of an

open exposure. The calibration determines the diode gains for the current configuration and

ensures that the intensity received is independent of each diode’s unique sensitivity. Due to

differences in sensitivity, each one of the diodes has its own “brightfield” value, however,

every image has a “global brightfield” value. The software uses the “darkfield” value and the

“global brightfield” value for a two point calibration in every single diode. The slope between

these two points determines the diode gain. During calibration each pixel is multiplied by the

diode gain in order to reach the global “brightfield” value. As a result, the inherent

characteristic of the detection efficiency drop at the tiling edges of the modules, is corrected.

Figure 2.8: This plot shows the normalised response of a single diode versus the generated

charge which is proportional to the incident X-ray energy. The minimum value of the curve is

determined by the “darkfield”. The upper limit of response is defined by the saturation point.

A “global brightfield” value is wisely chosen so that the response of each diode is in the

linear region.

2.1.3. Purpose of Experiments

A series of experiments was devised both to measure significant system parameters and to

facilitate the model development. The acquired data is used in several ways. Firstly,

exposures are used to provide information required for the development of the model, such as

the intensity of the unobstructed primary beam that reaches the detector. Given the primary

intensity, the model can calculate the transmitting intensity by simulating the attenuation

Energy

Normalised

Diode Response

Darkfield

Brightfield

18

caused by the objects the primary beam encounters. Secondly, exposures are used as a test

point for the correct development of the model. Several test pieces placed in various positions

are used to ensure that the predicted projection is correct and in accordance with the

experiment. Thirdly, the experimental data can be compared against the model in order to

extract information of significant physical meaning. For example, a prediction regarding the

dominant energies in the spectrum of the primary beam can be done. Looking forward,

similar comparisons led to the development of the scattering model as it was proven that the

absorption model alone is not sufficient to simulate the exposure successfully. Finally, the

experiments allow the measurement of important physical parameters of the system, such as

the location and the size of the generator’s focal spot that is measured in this study.

2.1.4 Test Pieces

During object irradiation, absorption and Compton scattering are the two main processes that

take place. X-ray fluorescence could also play a role, as it changes the energy spectrum of the

primary radiation by adding the characteristic lines of each material that X-rays pass through.

Although every object is subjected to both absorption and scattering, the tradeoff between the

number of electrons in the material and its absorption capability will define whether the

object acts as a scatterer or as an absorber. Wood, wax, some types of plastic and in general

low density, low contrast materials are considered to be scatterers, while high density, high

contrast materials such as lead, steel and aluminium are absorbers.

The objects that were used in the present study are summarised in Figure 2.9 (a)-(i) (p. 19). In

this figure the dimensions and the chemical composition of the test objects can be seen. The

exact chemical composition of the test pieces is unknown, hence, it is considered that the

objects are made of the dominant of their components, ignoring the contribution of minor

components. For example, the aluminium wedge is considered to be made of pure Al

regardless that its stiffness indicates that it is probably made of an aluminium alloy.

Consequently, the steel wedge is considered to be made of Fe and the wooden block to be

made of cellulose ((C6H10O5)n).

19

(a) Aluminium wedge (b) Steel wedge (c) Wooden block

Aluminium (Al) Iron (Fe) Cellulose (C6H10O5)n

(d) Polyethylene terephthalate

cylinder

(e) Lead brick

Lead (Pb)

(f) Steel sheet with holes

Iron (Fe)

Ethylene terephthalate (C10H8O4)

(g) Candle (h) Candle (i) Steel plate

Paraffin wax (C25H52) Paraffin wax (C25H52) Iron (Fe)

Figure 2.9: (a) – (i) The test objects that were used in the exposures of this study.

30

cm

Hole

15

cm

4.5

cm

15

cm

15

.1 c

m

8.2 cm

12

cm

10

cm

15

cm

7 cm

7.5

cm

6.8 cm

3.5

cm

0.025 cm

20

2.1.5 Experimental Configurations

In this part the experimental configurations that were used in the study are presented. The X-

ray tube was placed at the bottom of the chamber. The elevation difference between the

generator and the panel is partially compensated by rotating the tube so that the height of the

window was elevated at 8.8 cm (Figure 2.10). The direction of the window guided the exiting

X-ray beam well on the active surface of the panel. The source-to-panel distance was

measured from the window to the panel and was set at 80 cm. This was the preferable setup

for a number of reasons. First of all, the risk of detector saturation is reduced. Taking into

account that the module is formed by large diodes (0.4 mm element pitch) saturation can be

easily reached when the system is operated at full power and the source is close to the

detector. It was verified that this setup doesn’t saturate the detector. Secondly, this

arrangement not only accommodates the placement of the test objects in various positions in

between the X-ray equipment but also allows the conduction of several experiments, where a

varying source-to-object distance is required. Thirdly, given that the exiting angle of the

primary beam is 50o in both the horizontal and the vertical axis, the generator must be placed

at approximately 65 cm in order to illuminate the 53.5 cm wide active surface of the panel.

The 80 cm distance allows the cone shaped primary beam to slightly overlap the rectangular

active surface, enabling the use of the whole active area for data collection.

Figure 2.10: The red sticker designates the generator’s window. The cross sign helps the

operator to align the equipment, as it indicates the centre of the exiting X-ray beam. The X-

ray tube is free to rotate. Its position was set so that the centre of the cross is 8.8 cm over the

bottom surface of the chamber. The grip is not shown for demonstration purposes.

The detector panel was perpendicularly oriented to the normal line between the generator and

the detector. It was ensured that the plane of the active surface was in the right angle with

respect to the bottom surface of the chamber (Figure 2.11). The white marks on the detector

surface and the cross mark on the generator’s window enabled the alignment of the

instruments.

z

y

x

h=8.8 cm

21

Figure 2.11: The FlatScan detector panel. The active surface is the one in between the white

marks.

Through TreatSpect software the initial parameters of the scan are set. The operating voltage

and current combination affects the quality of the exiting X-ray beam while the integration

period and scan time combination affects the readout. As it was mentioned earlier, both the

X-ray generation and the X-ray detection processes are complicated, hence, even a small

difference in the initial parameters could change the detecting signal dramatically. For

example, different initial operating voltage results in different X-ray energy spectra, which

become even more different if the spectral variations due to the Heel effect are taken into

account. Therefore, the initial parameters should be kept constant throughout this study in

order to achieve consistent and comparable results. Table 2.2 summarises the initial

parameters as they have been set in ThreatSpect software.

Table 2.2: Initial parameters set in Threatspect software throughout the study, unless

mentioned otherwise.

Voltage (kV) 120

Current (mA) 1

Integration period (ms) 2.43

Scan time (s) 15

In Figures 2.12 – 2.17 the experimental configurations that were used in the present study are

summarised. The origin of the Cartesian system is at the generator’s window as it was shown

in Figure 2.10.

Middle of the

active width

Right angle

22

Figure 2.12: An aluminium wedge was placed on top of a wooden block. The dimensions of

the objects are shown in Figure 2.9 (a) and (c) (p. 19). Both the wooden block and the

aluminium wedge were aligned with respect to the line between the centre of the generator’s

window and the middle of the detector’s active surface. Data was collated for placing the

objects in different distances away from the generator, from 10 cm to 70 cm. The distance

between the generator and the detector was fixed at 80 cm. The operating voltage was set at

120 kV and the current at 1 mA.

Figure 2.13: An aluminium wedge was placed on top of a wooden block. The dimensions of

the objects are shown in Figure 2.9 (a) and (c) (p. 19). The objects were placed at 18.5 cm

along the x-axis and at 70 cm along the z-axis, while the distance between the generator and

the detector was fixed at 80 cm. The operating voltage was set at 120 kV and the current at 1

mA.

y

x

z

y

z

x

23

Figure 2.14: An aluminium wedge was placed on top of a wooden block. The dimensions of

the objects are shown in Figure 2.9 (a) and (c) (p. 19). There was a 12.1 cm offset to the right

with respect to the line between the centre of the generator’s window and the middle of the

detector’s active surface. The objects were placed at 70 cm while the distance between the

generator and the detector was fixed at 80 cm. The operating voltage was set at 120 kV and

the current at 1 mA.

Figure 2.15: A steel wedge was placed over a wooden block. The dimensions of the objects

are shown in Figure 2.9 (b) and (c) (p. 19). There was a 12.1 cm offset to the right with

relation to the line between the centre of the generator’s window and the middle of the

detector’s active surface. The objects were placed at 70 cm while the distance between the

generator and the detector was fixed at 80 cm. The operating voltage was set at 120 kV and

the current at 1 mA.

y

z

x

12.1 cm

24

Figure 2.16: A steel block containing holes both in the horizontal and the vertical direction

was placed between the generator and the detector. Its dimensions are shown in Figure 2.9 (f)

(p. 19). Two shots were taken for the block placed initially at 14 cm and then at 24 cm, while

the detector was placed at 80 cm away from the generator. The operating voltage was set at

120 kV and the current at 1 mA.

Figure 2.17: A polyethylene terephalate (black) cylinder was placed 54 cm away from the

generator. Its dimensions are shown in Figure 2.9 (d) (p. 19). The generator was rotated 34o

clockwise. A 3 cm thick lead obstacle was placed 23 cm away from the generator resting on

two lead bricks in order to prevent direct X-rays from reaching the detector. Another lead

brick was in contact with both the active surface of the detector and the cylinder. Its

dimensions are shown in Figure 2.9 (e) (p. 19).

y

z

x

25

Figure 2.18: A steel sheet and two candles were placed over a wooden block. The dimensions

of the objects are shown in Figure 2.9 (c), (g), (h) and (i) (p. 19). The sheet was aligned with

respect to the line between the centre of the generator’s window and the middle of the

detector’s active surface and two candles were placed on both sides. The wooden block was

placed at 70 cm. The steel plate and the centre of the candles were located at 73.5 cm, while

the distance between the generator and the detector was fixed at 80 cm. The operating voltage

was set at 120 kV and the current at 1 mA.

Figure 2.19: A steel square tile was placed on top of a piece of wood. The square tile is the

same shown in Figure 2.9 (f) (p. 19) but before being drilled. The dimensions of the wooden

block are shown in Figure 2.9 (c) (p. 19). Both objects were aligned with respect to the line

between the centre of the generator’s window and the middle of the detector’s active. The

objects were placed at 70 cm while the distance between the generator and the detector was

fixed at 80 cm. The operating voltage was set at 120 kV and the current at 1 mA.

y

z

x

80 c

m

26

2.2 Calculations

A laptop with a 64-bit Windows 7 Professional SP1 operating system was used. The system

consists of an Intel(R) Core(TM) i3-3120M processor operating at 2.50 GHz, a 4.00 GB

installed memory (RAM) and 500 GB storage.

2.2.1 R Software

The models used in this study were developed by using the R software. R is a language and

environment for statistical computing and graphics. It is a GNU project which is similar to

the S language and environment which was developed at Bell Laboratories (formerly AT&T,

now Lucent Technologies) by John Chambers and colleagues. R can be considered as a

different implementation of S. There are some important differences, but much code written

for S runs unaltered under R.

R provides a wide variety of statistical and graphical techniques, and is highly extensible. The

S language is often the vehicle of choice for research in statistical methodology, and R

provides an Open Source route to participation in that activity. R can be extended (easily)

via packages. There are about eight packages supplied with the R distribution and many more

are available through the CRAN family of Internet sites covering a very wide range of

modern statistics (see R Core Team reference).

R is available as Free Software under the terms of the Free Software Foundation’s GNU

General Public License in source code form. It compiles and runs on a wide variety of UNIX

platforms and similar systems (including FreeBSD and Linux), Windows and MacOS.

2.2.2 Absorption Model

Absorption is the dominant phenomenon in the X-ray exposures that were used in the present

study. Thus, an absorption model was developed to simulate this process. The outcome of the

absorption model will be a data matrix similar to the data matrix of a real exposure. The

images that are captured in digital radiography are in fact images that show the intensity

profile of the active surface of the panel which means that the image corresponds to a data

matrix with dimensions equal to the number of pixels in width times the number of pixels in

height. The essential purpose of the absorption model is to estimate the X-ray intensity that

passes through objects. The transmitted intensity, I, is calculated by the equation

𝐼 = 𝐼0𝑒−𝜇𝑥 , (eq. 2.6)

where I0 is the intensity of the unobstructed beam, μ is the linear attenuation coefficient and x

is the thickness of the material. The input intensity for the model is given by the open

exposures. In case of elements, the linear attenuation coefficient is given by the tables of

National Institute of Standards and Technology (Seltzer and Hubbell, 1995), while in case of

compounds the linear attenuation coefficient is calculated by the XCOM ver. 1.5 web

27

database (Berger et al, 2010). After taking into account the material of the test object and the

energy of the incident radiation the suitable linear attenuation coefficient value is replaced in

(eq. 2.6.). The estimation of thickness of the material that the X-rays pass through, is the most

complicated part of the absorption model because of the divergence of the X-ray photons. For

this reason, the test objects of Figure 2.9 (p. 19) are modelled using a series of pixellated

planes that correspond to a series of data matrices. The dimensions of these matrices are finite

and equal to the image dimensions measured in pixels.. Thus, the matrices could have no

other dimensions than the 1024x1536 pixels, which is the standard outcome of the X-ray

system. Each matrix describes the thickness and the shape of an object slab. Therefore, each

cell can have either a zero value, which means that there is no slab and subsequently the

thickness at that position is zero, or the value dz, which means that there is a slab of thickness

dz at that position. Essentially, the complete objects are formed by the sum of the desired

number of parallel slabs. The overall depth of the object equals the number of slabs times dz,

as it can be seen in Figure 2.20.

(a)

(b)

Figure 2.20: (a) A wedge and (b) a cylinder sliced in 16 pieces and 11 pieces respectively, as

they considered in the model. The thickness of the object is quantised by dz. A random

incident X-ray penetrates different number of slabs with the overall thickness varying from

zero to the maximum object depth. The spacing between the slabs is for demonstration

reasons only.

X-r

ays

dz

dz

X-rays

y

z

x

y

z x

28

Although, the generated X-ray beam is not parallel in real exposures, the absorption model

considers that X-rays enter the surface of each one of the slabs with the right angle. This

means that each X-ray passes through a quantised fraction of the object’s depth, which is a

multiple of the quantum dz as the path that the X-ray traverses inside the slab is equal to the

thickness of the slab. This is not true in actual exposures as X-rays follow random paths with

respect to the position of the generator and of the test object. The effect of this acceptance

will be discussed later.

During an actual exposure the object that is placed between the X-ray generator and the

detector panel is subjected to magnification due to the divergence of the generatetd X-ray

beam, that comes from a practically infinitely small area. The model takes into account the

magnification by introducing a magnification factor that is applied to each one of the slabs. If

SOD is the source to object distance and SDD is the source to detector distance, the

magnification M is given by the equation

𝑀 =𝑆𝐷𝐷

𝑆𝑂𝐷 . (eq. 2.7)

The magnification occurs around the reference pixel, which is the detector pixel that has the

shortest distance from the generator. A robust method for the determination of this pixel is

proposed in chapter 3.2.2. Given, the x and y position of the reference pixel, xref , yref , the

relation between the position of the pixels on the object plane, xobj, yobj, and the position of

the pixels on the detector plane, xdet, ydet, is given by the equations

𝑥𝑑𝑒𝑡 = 𝑀 · (𝑥𝑜𝑏𝑗 − 𝑥𝑟𝑒𝑓) , (eq. 2.8)

𝑦𝑑𝑒𝑡 = 𝑀 · (𝑦𝑜𝑏𝑗 − 𝑦𝑟𝑒𝑓) . (eq. 2.9)

According to these equations each object pixel is projected onto the detector plane with

respect to its original distance from the reference pixel. Consequently, each one of the slabs is

projected on the detector plane. Notice that their projections are different due to the different

magnification factor as the SOD distance varies. The sum of the overlapping projections on

the detector plane is a matrix with regions of varying thickness that is quantized by dz. This

matrix of thickness corresponds to the path that the X-rays travel inside the object and is the

input for the (eq. 2.6), which calculates the transmitted intensity.

The determination of the reference pixel is a very important parameter for the correct

magnification. In particular, the relative position of the object with respect to the normal line

should be taken into account so that its projection on the detector plane is correct. Figure 2.21

illustrates the mechanism of magnification. A cylindrical object made of three slabs is

projected on the panel. Firstly, notice that each slab has a different projection on the screen as

it was mentioned earlier. Secondly, notice the position of the shadows. The shadows are

concentric because the centre of the object was initially placed on the normal line. In cases

where the centre is off the normal line the slabs’ shadows are eccentric.

29

Figure 2.21: The projection of a cylinder (simply made of three slabs) onto the detector panel

is shown. Each slab is magnified by a different magnification factor as the source-to-object

distance varies. Even though the red and the cyan slabs are identical, their projection on the

detector plane is different due to the difference in their magnification factors. The sum of the

slabs’ shadows results in the final outcome. The dashed line indicates the normal line

between the point source and the panel.

Although this results in a good approximation of the shadows’ position, the maximum

attenuation cannot be larger than the attenuation caused by the maximum thickness of the

object regardless the path the X-ray travelled. At this point the significance of this acceptance

is examined. In reality, X-rays exiting the generator’s window travel in random paths and

enter object surfaces in random angles with respect to the geometry of the configuration. This

means that the path the X-rays travel within the object may be larger than the thickness of the

object at the entering point. Given the positions of the generator and the panel, the maximum

deviation in the entering angle occurs for the X-rays that their trajectory meets the top left or

the top right corner of the panel. The active surface of the panel is 53.5 cm by 41.5 cm. The

generator’s window was pointing the middle of the panel with respect to the horizontal axis

and was located 8.8 cm above the ground. The distance between the focal spot and the diodes

Object

Point

Source

Detector panel

y

z x

30

was roughly 87 cm. Using the Pythagorean theorem and simple trigonometrical equations the

entering angle can be measured. The entering angle differs approximately 26o from the right

angle, which means that the path can be up to 11% longer than the thickness of the object at

that point. For example, for an object of constant thickness 5.5 cm, the path that the X-ray

traverses could be up to 6.1 cm.

This was not taken into account in the absorption model for a number of reasons. Firstly, the

difference becomes important only when the test piece is placed close to the corners of the

panel. These regions are usually unimportant because in security applications the operators

opt to place the suspicious objects at the centre. This is preferable because a) the Heel effect

is less significant b) the position of the object and its projection are concentric and c) the

thickness of the panel case is almost constant which otherwise would be larger towards the

corners, given the position of the generator. Thus, the goal is to develop a model which gives

good predictions at the areas close to the normal line. Secondly, the difference is significant

for a small fraction of the active surface and diminishes towards the centre of the panel. At

the arrangements of the present study, the path becomes 11% longer only for the X-rays that

meet the furthermost diodes of the detector, which are the top right and the top left diodes of

the active surface. The difference is only 4% at the bottom left and bottom right corners of

the active surface. Thirdly, the error in the transmitted intensity, δΙ, due to the error in the

thickness, δx, can be calculated through the error propagation and is equal to

𝛿𝛪 = 𝜇 · 𝛪0 · 𝑒−𝜇·𝑥 · 𝛿𝑥 , (eq.2.10)

where I, is the transmitted intensity and μ is the linear attenuation coefficient. Given that the

maximum error in the thickness is 11%, δx can be replaced in (eq. 2.10). Hence,

𝛿𝛪 = 𝜇 · 𝛪0 · 𝑒−𝜇·𝑥 · (0.11 · 𝑥) => 𝛿𝛪 = 0.11 · 𝛪0 · 𝜇 · 𝑥 · 𝑒−𝜇·𝑥 . (eq. 2.11)

As it can be seen, the error in the transmitted intensity depends on the primary intensity, the

linear attenuation coefficient and the thickness of the object. For a known material and given

that the dominant energy of the primary X-ray beam should be between 40 and 60 keV, the

effect of the model acceptance regarding the thickness of the objects can be quantified.

Figure 2.22 shows the error in the transmitted intensity versus the object thickness.

The I0 value that was used in the calculations was that of the diode in the top left corner of the

panel. It can be clearly seen that an 11 % increase in the thickness of the object results in

maximum 0.0041 maximum intensity error for an object made of aluminium. The error

becomes maximum at thickness 1.8 cm and then drops exponentially to zero. The intensity

error follows the same trend for objects made of iron but the maximum occurs at 0.7 cm. For

light, low atomic number objects the maximum occurs in larger object thickness. The

divergence of the X-rays doesn’t lead to significant miscalculations. It can be seen later in

this study that this error is not comparable to the calculated intensities of the model and hence

angular terms can be omitted in the absorption model.

31

Figure 2.22: Error in the transmitted intensity versus the object thickness for aluminium

(blue) and steel (Fe) (red). A monochromatic beam at 50 keV was used in the computations.

Fourthly, the acceptance that the X-rays enter the objects perpendicularly reduces the

complexity of the calculations. Otherwise a different entry angle should have been calculated

for every pixel of every object slab. Given that the objects are formed by hundreds of slabs,

this would increase the time of calculations.

The core of absorption model’s code is demonstrated and explained next.

1. l=list()

2. length(l)=number_of_slices

3. jj=(1:number_of_slices)-1

4. zeta=jj*dz+source_to_object_distance

5. for (j in 1:number_of_slices)

6. l[[j]]=outer(xd, yd, blockslab, block_parameters, zeta[j])

----------------------------------------------------------------------------------------------------------

7. blockslab= function(xx,yy,param,zeta){

a. nn= length(yy)

b. out= double(length=nn)

c. xxx=xx*(zeta/source_to_object_distance)-x_offset

d. yyy=yy*(zeta/source_to_object_distance)-y_offset

e. for (i in 1:nn){

f. out[i]=blockfun(xxx[i],yyy[i],param,zeta)

g. }

h. return(out)

i. }

32

----------------------------------------------------------------------------------------------------------

8. blockfun= function(x,y,param,zeta){

a. if(abs(x)< half_object_width & abs(y)< half_object_height){

b. a=dz

c. }

d. else {

e. a=0

f. }

g. return(a)

}

---------------------------------------------------------------------------------------------------------

9. sumofblocklayers=Reduce('+',l)

---------------------------------------------------------------------------------------------------------

10. I=I0*exp(-mass_attenuation_coefficient*density*sumofblocklayers)

---------------------------------------------------------------------------------------------------------

1. Creates a list named “l”. Each one of the list elements contains one pixelated plane-

slab, of thickness dz, where dz is equal to the object’s depth divided by the number of

the desired slices.

2. List’s length is equal to the number of the desired slabs.

3. (see line 4)

4. zeta is the variable that defines the distance between the front face of each slab and

the source.

5. A for loop is used to enable the iterative process between the slabs.

6. xd and yd are the horizontal and vertical dimension of the detector area respectively.

Notice that these numbers are defined by the size of the image of the open exposure.

yd is a vector from 1 to 1024, where 1024 are the physical diodes (pixels) of the

detector. xd is a result of oversampling along the line of scan. Although, the width of

the image is varying, it is normally between 1500 and 1536 pixels. block_parameters

is a vector that contains the basic parameters of the object, such as the height, the

width, the density and the mass attenuation coefficient. The basic function of the code

is the outer function. The outer function has 3 main arguments. Two vector arguments

(xd and yd) and a function argument (blockslab). The basic operation of the outer

function is to apply the blockslab function to every combination of the xd and yd

33

vectors. So the j-th element of the list “l” contains the projected shadow of j-th slab of

the object. The blockslab function does the magnification for the projected slab.

7. The important part of this function is found in lines 7c, 7d and 7f. In lines 7c and 7b

the magnification factor zeta/source_to_object_distance is applied to the horizontal

and vertical direction, while an offset is also taken into account. In line 7f the

blockfun function is called.

8. The blockfun function contains an if loop that checks whether the xd, yd combination

is in or out of the objects’ shadow. In case the pixel is in, a dz value is assigned to this

pixel.

9. Reduce function is used to sum the all the different elements of the l list. Thus,

sumofblocklayer is a pixelated plane that contains the object.

10. sumofblocklayers is used as an argument in the formula of the transmitted intensity.

2.2.3 Compton Scattering Model

Compton scattering is, after absorption, the dominant phenomenon in X-ray screening.

Scattering is a more complicated phenomenon than absorption. Firstly, it can occur in every

single atom of the medium and secondly the scattered photon can land to any pixel of the

active surface. In fact, photons can be scattered to any direction, even go out of bounds of the

active surface and avoid being detected.

More specifically, every atom of the irradiated object is able to scatter the incident X-ray

everywhere in space. Even if we focus on the active surface of the detector, a single pixel

receives scattered photons from any atom of the object, which in turn means that for every

detector pixel, every object pixel of every object slab deflects photons towards this pixel. A

primary photon that gets scattered can scatter again and again. Notice that both the primary

and the scattered photons are subjected to absorption This results in a very complicated

process which contains a vast number of photon histories and demands Monte Carlo

calculations and adequate computer power in order to have a good prediction.

In the present study a simplified scattering model was developed to describe Compton

scattering. Rayleigh (coherent) scattering was not taken into account. Given a specific pixel

on the detector plane the model generates 3D-arrays representing the incident and scattered

X-rays. The scattering cross section is given by the Klein-Nishina formula and depends on

the energy of the primary beam and the solid angle between the incident and the scattered

photon. The model was based on the following acceptances:

The objects are compressed to a very thin layer, so that the electrons are spread in a

surface equal to the object’s width times the object’s height. The position of this layer

is set at the middle of the object’s depth (Figure 2.22).

34

Figure 2.22: This is how scattering model handles objects. Objects are compressed to a thin,

infinitely small layer that contains all the electrons of the object and is placed in the middle of

the original object’s depth.

As far as the attenuation is concerned the path that an X-ray traverses inside the object

is equal to the mean depth of the actual object regardless of the entrance and the

scattering angles. Thus, in case of a rectangular block the path is equal to its depth,

while in case of a cylinder the path is equal to its radius.

Although, every detector pixel receives scattered photons from every pixel of the

object’s surface, the calculations are performed for single detector pixels.

Open exposures are used to provide the initial intensity of the uninterrupted beam.

However, in case of scattering, the initial trajectory of the primary X-rays could meet

the detector plane out of the bounds of the active surface. The X-rays that escape the

detector are not measured, so the I0 value of these X-rays is unknown. To overcome

this obstacle the model assigns the I0 value of the border to every primary X-ray that

misses the detector’s surface (Figure 2.23).

Source to Object distance

Source to Detector distance

Source

Detector

Object Compressed Object

X-rays

Depth

35

Figure 2.23: The initial direction of an X-ray could meet the detector plane outside the

bounds of the active surface (red dashed line). This is more likely when the object is closer to

the detector. The present model overcomes this problem by setting the I0 values of the

primary beam that escape the detector area equal to the I0 values of the border.

As it was previously mentioned, the scattered photon is still in play inside the objects.

Secondary and upper orders of scattering may occur resulting in very complicated

calculations. The present model includes first order Compton scattering only.

The main equations that are used in the scattering model are explained next. The angular

distribution for the differential scattering cross-section due to an atom is given by the Klein –

Nishina formula

𝑑𝜎

𝑑𝛺= 𝛧𝑟0

2 (1

1+ℎ𝑣

𝑚0𝑐2(1−𝑐𝑜𝑠𝜃)

)

2

(1+𝑐𝑜𝑠2𝜃

2)(1 +

(ℎ𝑣

𝑚0𝑐2)2

(1−𝑐𝑜𝑠𝜃)2

(1+𝑐𝑜𝑠2𝜃)[1+ℎ𝑣

𝑚0𝑐2(1−𝑐𝑜𝑠𝜃)]

) , (eq. 2.12)

where Z is the atomic number, hv the energy of the incident photon, θ the scattering angle, r0

the classical electron radius, m0 the electron rest mass. In this formula Z, provides the number

of electrons that participate in scattering, however, given the acceptance that the scattering

model considers the objects to be compressed to a very thin layer, the total number of

electrons per object area must be calculated. Given the mass of the object the total number of

electrons is calculated from the equation

𝑛𝑢𝑚𝑏𝑒𝑟_𝑜𝑓_𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 =𝑚·𝑁𝐴𝑣𝑜𝑔𝑎𝑑𝑟𝑜·𝑍

𝑀𝑟 , (eq. 2.13)

Source to Object distance

Source to Detector distance

Source

Detector

Compressed Object

Unknown I0

I0

36

where m is the mass of the test piece, N is the Avogadro’s number and Z is atomic number.

The number of electrons is spread over the surface of the layer uniformly. Taking into

account that the surface is quantized by the pixel size, the number of electrons in each pixel is

given by

𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠_𝑝𝑒𝑟_𝑝𝑖𝑥𝑒𝑙 =𝑛𝑢𝑚𝑏𝑒𝑟_𝑜𝑓_𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠

𝑎𝑟𝑒𝑎_𝑜𝑓_𝑜𝑏𝑗𝑒𝑐𝑡 , (eq. 2.14)

where the area_of_object is equal to the product of the object width times the object height,

both measured in pixels. To determine the scattering angle θ, the trajectories of the incident

and the scattered photons are represented by vectors given the position of the source, the

position of the object pixel that participates in scattering and the position of the detector pixel

that the total scattering signal is calculated. Thus, the angle is calculated from the dot product

formula between the incident and the scattered vector:

𝜃 = 𝑐𝑜𝑠−1 (𝑣𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ · 𝑣𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑒𝑑⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗

‖𝑣𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ‖·‖𝑣𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑒𝑑⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ‖) , (eq. 2.15)

The scattered x-rays are subjected to absorption as well. Following the acceptance of the

model the absorption can be calculated using equation 2.6 but for a distance that is equal to

the mean depth of the object.

For the correct determination of the scattering process the calculation of the solid angle is

also important. By definition, solid angle is the angle that, seen from the centre of a sphere,

includes an area on the surface of that sphere. The value of the solid angle is numerically equal to

the area divided by the square of the radius of the sphere. In this case the solid angle is given by the

ratio of the pixel area as it seen by the object pixel over norm of the scattered vector. Hence,

𝛥𝛺 =𝑑𝑒𝑡𝑒𝑐𝑜𝑟_𝑝𝑖𝑥𝑒𝑙_𝑎𝑟𝑒𝑎

‖𝑣𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑒𝑑⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ⃗⃗ ‖ . (eq. 2.16)

Although, the model returns the intensity received by single detector pixels at a given

position, the contribution of every object pixel is taken into account. The outcome is given by

the equation

𝑜𝑢𝑡𝑐𝑜𝑚𝑒 =𝐼0·𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠_𝑝𝑒𝑟_𝑝𝑖𝑥𝑒𝑙·

𝑑𝜎

𝑑𝛺·𝛥𝛺·𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛

𝑝𝑖𝑥𝑒𝑙_𝑎𝑟𝑒𝑎 , (eq. 2.17)

The core of code that describes the scattering model is demonstrated and explained next. For

a given detector pixel, “for” loops are used to scan the object’s surface. During the iterative

process the important parameters of the model are calculated. The basic functions that were

used are shown:

37

1. angle_fun <- function(x,y){

a. dot.prod <- x%*%y

b. norm.x <- norm(x,type="2")

c. norm.y <- norm(y,type="2")

d. theta <- acos(dot.prod / (norm.x * norm.y))

e. as.numeric(theta)

f. }

---------------------------------------------------------------------------------------------------------

2. number_of_e <- function(grams,atom_num,mol_weight){

a. grams/mol_weight*Avogadro*atom_num

b. }

---------------------------------------------------------------------------------------------------------

3. electrons_per_pixel=electrons(grams,atomic_number,molar

weight)/(obj's_width_in_pixels*obj's_height_in_pixels)

--------------------------------------------------------------------------------------------------------

4. absorption <- function(dens,mass_atten_coef,path){

a. exp(-dens*mass_atten_coef*path)

b. }

--------------------------------------------------------------------------------------------------------

5. dSigma_dOmega=function(energy,sc_angle){

a. 0.5*re^2*((1/(1+energy*(1-cos(sc_angle))))^3+(1/(1+energy*(1-

cos(sc_angle))))-(1/(1+energy*(1-cos(sc_angle))))^2*sin(sc_angle)^2)

b. }

--------------------------------------------------------------------------------------------------------

6. delta_omega[i,j]=(xpix*cos_theta_x[i]*ypix*cos_theta_y[j])/norm(scattered,type="2"

)

--------------------------------------------------------------------------------------------------------

7. outcome[i,j]=I0[[x_u_i,y_u_i]]*electrons_per_pixel*dSigma_dOmega(energy,scatteri

ng_angle)/(xpix*ypix)*delta_omega[i,j]*absorption(dens,mass_atten_coef,path)

-------------------------------------------------------------------------------------------------------

38

1. This function computes the angle between two vectors and is called to calculate the

angle between the incident and the scattered photon.

2. This function computes the number of electrons located in a given substance, based

on the molecular weight of the substance.

3. This function computes the number of electrons per object pixel. Given the fact that

the object is compressed to an infinitely thin layer, the object’s electrons are spread

uniformly in this surface.

4. This function calculates the X-rays absorption factor. Density, mass attenuation

coefficient and the mean path an X-ray traverses are the arguments for this

calculation.

5. The Klein-Nishina formula that returns the Compton scattering cross section, which

depends on the energy of the primary X-ray and the scattering angle.

6. delta_omega is the area of the object pixel as it is seen by the detector pixel.

7. Given a detector pixel, this is the intensity that comes from the individual object

pixels to the chosen detector pixel. The sum of all these contributions results in the

scattering signal that the object sends to the detector pixel.

39

CHAPTER 3 – RESULTS AND DISCUSSION

The experimental configurations and the code described in Chapter 2 were used to produce

the results shown in Chapter 3. The results are presented using R GUI and ThreatSpect image

capture tool.

3.1 Experimental Results

An open exposure is the simplest form of radiography. Apart from simplicity the open

exposures provide qualitative and quantitative information that can be used in system

checking and system calibration. The intensity that reaches the detector panel after an

ordinary blank shot is shown in Figure 3.1 (a). Figure 3.1 (b) illustrates the same image after

activating the heat colours option in ThreatSpect, which allows a quantitative analysis on the

captured images. There is a very bright area (purple) which gradually fades. The X-rays’

intensity follows the inverse square law, which means that it is inversely proportional to the

square of the distance between the generator and the source. After making adjustments on the

histogram of the image, the rings of varying intensity become visible. The centre of the beam

is off the center of the active surface of the detector because the window of the generator is

standing at 8.8 cm over the bottom of the chamber. Figure 3.1 (c) shows the surface intensity

plot of the open exposure. The intensity peaks at 0.168 and drops towards the sides of the

panel due to the effect of the inverse square law.

The intensity and the shape of the image depend on the distance between the focal spot and

the detector diodes, the operating voltage and current and the angular distribution of the

beam. The window of the detector acts as high pass filter which hardens the beam. The hard

case of the panel plays role as well. Notice that, although the thickness of the hard case is the

same throughout the active surface, the attenuation becomes higher away from the normal

line. This becomes significant only when the system is operated close to its minimum power.

40

(a) (b)

(c)

Figure 3.1: (a) Open exposure as it is seen in ThreatSpect software. There is a wide white

region in the centre of the image while darker areas are visible mostly in the four corners. (b)

Open exposure with heat colours option enabled in ThreatSpect. (c) Surface intensity plot of

the open exposure.

A simple way to demonstrate the results is by looking at the horizontal or the vertical

intensity profile of the data matrix that creates the image. R commands are used to create the

plots shown in the following figures. In Figure 3.2 the intensity along a row and a column

versus the horizontal and vertical position, respectively, is illustrated. The term “intensity” is

used in these plots but is often referred as “response” of the detecting system in other plots. In

fact, the output can be interpreted in various ways. This is because the detecting process

consists of several different stages. The detector returns signal each time it is exposed to X-

rays, thus the term “intensity” can be used to interpret the measurement, as it is defined as

energy per unit area, per unit time [Joule/m2∙s]. Nevertheless, it is not as simple as this

because according to the physics of radiation detection, the X-rays are being converted into

visible light before they are detected by the photodiodes. The detected visible light creates a

Inte

nsi

ty

41

charge which is then collected. This means that the term “charge” [Coulombs] or “current”

[Amperes] could be used equivalently to the term “intensity”. The charge is then converted to

analogue voltage, thus the term “voltage” [Volts] is also correct. Taking into account that

harder X-rays create more visible photons during their conversion by the scintillator, which in

turn, create more charge in the photodiodes, the measured signal is proportional to the energy

of the incident X-rays. Hence, the term “energy” [Joule] could be used to describe the

outcome. It is worth mentioning that the incident energy depends on the operating voltage

and current combination of the XRT, therefore the signal is proportional to these values as

well. The more generalized term of “response” of the detection system can also be used given

the initial voltage and current. Although different, these terms could be used to describe the

output equivalently. Besides, the values of the measured signal could be reproduced if the

correct conversion rates between the different stages of the previously mentioned process

were known. In the present study the term “intensity” and the term “response” of the system

are used in the demonstration of the plots.

(a) (b)

Figure 3.2: This plot shows the intensity (a) along the 238th

row out of 1024 (b) along the

757th

column out of 1536. Both data are fitted with a fourth order polynomial fit (red line).

As it can be seen in Figure 3.2 the intensity of an open exposure peaks at approximately the

757th

column and 238th

row respectively and then drops following the inverse square law.

Notice that the left part of the image receives more intensity than the right hand side, which

means that the exiting X-ray beam is not uniform. Data was collated for several open

exposures resulting that the X-ray beam is not uniformly distributed along the active surface

of the detector panel. This is due to the Heel effect that was described in chapter 1.3.2.

According to the effect the surface of the tungsten anode target forms an angle with the

direction of the high speed electrons causing the photons to travel in selective way.

Although, an internal intervention on the XRT was not possible to verify that, a non-invasive

way was selected to prove that more photons could reach the left hand side of the panel. This

was to capture an image of the CP120 generator by another generator of the same type in

42

order to perform an internal examination of the XRT. For safety reasons, XRTs use heavy

radiation shielding in the housing of the instrument in order to prevent X-rays to escape from

surfaces other than the window. Thus, X-rays generated by another CP120 cannot penetrate

the shield adequately. Operating the generator at full power and taking advantage of the

absence of heavy radiation shielding in the area of the window allows the visual examination

of the instrument. Figure 3.3 (a) shows an X-ray image of the CP120 generator as it can be

seen through ThreatSpect software. The experimental arrangement is shown in Figure 3.3 (b).

Due to the absorption caused by the shielding, only a small fraction of the X-rays could

penetrate the instrument, thus the image has very small dynamic range. The image processing

tools of the ThreatSpect software allow the operator to adjust the histogram and create an

image by using the high energy X-rays alone. However, this reflects in the image quality, as

the image seems to fade. Despite the poor contrast the focusing cup and the tungsten anode of

the XRT are visible. It can be clearly seen that the angle of the anode is such that the

distribution is affected in favor of the left hand side of the panel, which comes in accordance

with the outcome of Figure 3.2 (a).

(a) (b)

Figure 3.3: (a) The picture shows the irradiation of the X-ray generator focused on the more

penetrating X-rays. The operating voltage and current was set at 120 kV and 1.5 mA,

respectively. Notice that the shape of the anode is the one showed in Figure 2.2, which means

that the angular distribution of the generated X-rays is affected. (b) Arrangement as viewing

from above. The generator under examination was placed with its window facing the detector

panel.

In both plots of Figure 3.2, fluctuations can be seen on top of the signal. This is the result of

electric noise coming from the printed circuit board (PCB) and the electronic parts of the

detection system. Noise is caused by small current and voltage fluctuations inside the circuit

and is practically inevitable. As we are going to see later, electric noise creates a signal even

when the X-rays are off. Therefore, it sets the lower limit for the detectable signal. In

Focusing cup

Tungsten anode New CP120 generator

Anode Window

CP120

generator under

examination

Detector panel

43

addition, X-ray generation and detection are processes that are driven by statistics. This is

another factor that causes fluctuations on top of the detecting signal, as photons not only they

are distributed randomly but also they deposit their energy randomly on the detector.

To facilitate the quantification of the fluctuations on top of the detected signal, the effect of

the inverse square law and the Heel effect must be compensated. Firstly, the data is fitted

with a fourth order polynomial curve, which as it will be seen later fits best on the data and

secondly the signal is flattened to the maximum detected signal. Figure 3.4 (a) and (b) shows

the flattened data of Figure 3.2 (a) and (b) respectively.

Figure 3.4: (a) Flattened intensity profile at the 238th

row. (b) Flattened intensity profile at the

757th

column.

The mean intensity of the unobstructed beam is found to be approximately 0.163 for both the

horizontal and the vertical dimension. Table 3.1 summarises the main characteristics of the

flattened unobstructed intensity signal. Although there are fluctuations on top of the signal,

the detected signal of each individual diode doesn’t differ significantly from the mean, as it

can be seen in the small value of the standard deviation. This is also reflected on the small

value of the signal range, which is the difference between the maximum and the minimum

value of the signal.

Table 3.1: Characteristics of the flattened open exposure signal

238th

row 757th

column

Mean 0.1629 0.1636

Standard deviation 0.0013 0.0013

Range 0.0091 0.0082

X-ray systems that are used in security applications often deal with bags or luggages that

contain a large number of items with varying physical characteristics and different

radiological aspects. Adequate security measures demand X-ray systems that help the

44

operator to discriminate between threat and non-threat items. Absorption plays a very

important role in material discrimination, as high atomic number, high density materials

attenuate the X-ray beam more. Figure 3.5, shows a close ranged irradiation of a bag

containing a laptop and a grenade replica. The contrast variation that is noticed is mostly due

to absorption, hence the first approach to simulate the exposure is the development of an

absorption model.

Figure 3.5: Close ranged irradiation of a bag containing, among other objects, a laptop and a

grenade replica which is designated by the blue dashed line.

Overlapping shadows are a perpetual constraint for the object discrimination. A commonly

used technique, is the dual irradiation of the suspicious object with a high and a low energy

X-ray beam. Software like ThreatSpect cross examines the two images and uses sophisticated

functions to colour the image, so that the operator can distinguish between organic, mixtures

and inorganic compositions. However, the full understanding of the absorption demands the

study of simple objects first. Therefore, the experiments that were conducted in this study are

based on the irradiation of simple objects of known dimensions and chemical composition.

Figure 3.6 shows the exposure of an aluminium wedge placed on top of a wooden block. The

experimental arrangement is the one described in Figure 2.12 (p. 22). The operating voltage

and current was set at 120 kV and 1 mA, while the objects were placed at 70 cm away from

the generator’s window. Notice that the dynamic range of system is very good as it is capable

to distinguish the shadow of a knot inside the wooden block. Looking at the intensity profile

of Figure 3.6 (b), the intensity drops significantly at the regions of the aluminium wedge due

to absorption. In Figure 3.6 (c), from top to bottom, the intensity increases due to the inverse

square law until the region of the aluminium wedge, where it drops exponentially because of

the increasing thickness of the wedge. The transmitted intensity at the wooden block region is

practically constant and stands at higher level, compared to the thicker parts of the aluminium

wedge, because X-rays penetrate easier low density, low atomic number materials.

45

(a)

(b) (c)

Figure 3.6: (a) Irradiation of an aluminium wedge placed on top of a wooden block. (b)

Horizontal intensity profile of the image at the 250th

row. (c) Vertical intensity profile of the

image at the 768th

column.

3.2 Absorption Model Development

3.2.1 First Calculations of Absorption Model

The model was used to reproduce the experimental shots. Figure 3.7 shows the reproduction

of the exposure where an aluminium wedge is placed on top of a wooden block using the

configuration shown in Figure 2.12 (p. 22).

250th

row

768th

column

46

(a)

(b) (c)

Figure 3.7: (a) Reproduction of the exposure of an aluminium wedge placed on top of a

wooden block. The model objects were placed at 70 cm. (b) Horizontal profile of the

intensity matrix at the 250th

row. (c) Vertical profile of the intensity matrix at the 768th

column.

A comparison between the Figures 3.6 (a) and 3.7 (a) can be done. At first sight, the

projection of the objects seems to be correct and the intensity contrast of the image seems to

be similar to the actual radiography. However, the proper comparison between the

experimental data and the model will be done through the intensity profiles of rows and

columns.

768th

column

250th

row

47

Despite the fact that the predicted image has many similarities with the actual radiography,

the dimensions of the estimated shadow of the object seem to be different. The difference is

due to the aspect ratio used in ThreatSpect software. Although the aspect ratio of the output

image is 1536:1024, ThreatSpect software corrects the ratio to 4:3, which is the popular

format that was initially developed to match the size of the first digital displays. The

correction in the aspect ratio is for the image display only and doesn’t affect the data matrix.

Fluctuations in the prediction can be seen both in the vertical and in the horizontal intensity

profile regardless the fact that the absorption model does not take into account the noise

factor. However, as it was mentioned in the description of the absorption model in chapter

2.2.2, an open exposure is used to provide the input intensity of the beam and this is how the

noise signal is introduced in the model predictions.

Before the in detail comparison between the experimental data and the calculations, various

physical offsets were determined. The shortest path between the generator and the detector

and the actual position of the focal spot inside the X-ray tube are two parameters important

for the development of the model. Even a very small difference in these parameters could

result in misalignments and wrong projections. Taking into account that the size of the

projected shadows is measured in pixels on the detector plane, misalignments as small as the

pixel pitch, that is approximately 0.04 cm, could occur. For example, an 8 mm difference

between the actual and the estimated shadow is equal to 20 pixels difference that can ruin the

comparison.

3.2.2 Determination of Reference Pixel

The absorption model development demanded the determination of a single detector pixel

that is the centre of the projection. The reference pixel corresponds to the shortest path

between the generator and the detector and is a requirement for the correct projection. In

other words, this is the pixel that receives the maximum intensity. However, the individual

sensitivity of each photodiode along with the electric noise and with the photon statistics

impedes the determination of the reference pixel. Despite the fact that the equipment

remained unchanged, the pixel that received the maximum intensity was different, even

among consecutive blank shots. For this reason a robust way to determine the exact position

of this pixel has been developed. Three different ways of estimating the reference pixel were

compared in a sample of 12 consecutive open exposures.

In the beginning, the reference pixel was considered to be the one with the maximum

received intensity, that is the brightest pixel of the screen. The results among the 12 shots are

summarized in the following Table.

48

Table 3.2: Coordinates (in pixels) of the maximum according to the data matrices.

The standard deviation of the mean x and y position is 60.54 and 22.67 pixels respectively,

which means that the reference pixel is not well defined. In the previous method, the

coordinates of the maximum were calculated by one row and one column of each one of the

12 consecutive blank shots. The outcome could be a result of poor statistics due to the small

sample.

It would be preferable to determine the position of the maximum by summing the total

number of rows and columns, respectively, of a single open exposure. The sum results in a

distribution along the horizontal and the vertical axis respectively. Although the value of sum

doesn’t provide valuable information, the peak of the distribution is defined better.

Essentially, this method takes into account all the available rows and columns and finds the

maximum of the distribution along the horizontal and vertical direction, respectively, which

gives the position of the centre of projection. This is repeated for each one of the 12 open

exposures. The results are shown in Table 3.3.

Table 3.3: Coordinates (in pixels) of the maximum according to the data matrices.

x-position

(in pixels)

y-position

(in pixels)

1. 649 257

2. 668 257

3. 766 267

4. 745 257

5. 705 206

6. 557 257

7. 650 257

8. 752 257

9. 683 193

10. 757 258

11. 765 257

12. 724 228

x-position

(in pixels)

y-position

(in pixels)

1. 764 267

2. 785 267

3. 726 267

4. 731 257

5. 790 258

6. 720 267

7. 720 257

8. 736 257

9. 728 257

10. 762 257

11. 715 255

12. 740 257

�̅� = ∑𝑥𝑖

𝑛

𝑛=12

𝑖=1

= 701.75

�̅� = 245.92

𝜎�̅� = √ ∑(𝑥𝑖 − �̅�)2

𝑛

𝑛=12

𝑖=1

= 60.54

𝜎�̅� = 22.67

�̅� = 743.08

�̅� = 260.25

𝜎�̅� = 24.72

𝜎�̅� = 4.82

49

Although the standard deviation is improved for both directions, the reference pixel is far

from stabilized, despite the fact that the shots were taken under the same conditions. As it

was mentioned earlier, noise signal is added to the intensity signal. Hence, a weaker intensity

signal coupled with these fluctuations may result in a maximum overall signal regardless that

the primary intensity signal was not the maximum.

To overcome these fluctuations, the points of the distribution were fitted by a polynomial

curve. The position of the maximum is now defined by the peak of the fit curve. Figure 3.8

(a) and (b) shows that a 4th

order polynomial fits best the experimental points. Lower order

polynomials result in poor fits while higher order polynomials result in no smoother curves as

it is seen in the R2 values of the polynomials used (Table 3.4).

Table 3.4: R2 values of the polynomials used to fit the data.

Polynomial R2

1st order 0.0734

2nd

order 0.9906

3rd

order 0.9990

4th

order 0.9992

5th

order 0.9992

6th

order 0.9992

The position of the brightest pixel is the one predicted by the position of the peak of the 4th

order polynomial fit. The method is applied to the 12 open exposures. Table 3.4 summarises

the results.

Table 3.4: Coordinates of the maximum of the fourth order polynomial fit.

x-position

(in pixels)

y-position

(in pixels)

1. 755 242

2. 751 242

3. 755 242

4. 752 242

5. 750 242

6. 754 242

7. 755 242

8. 752 242

9. 751 242

10. 751 242

11. 753 242

12. 754 242

�̅� = 752.75

�̅� = 242

𝜎�̅� = 1.74

𝜎�̅� = 0

50

(a)

(b)

Figure 3.8 (a),(b): Comparison between polynomial fits on the experimental data. 1st order

polynomial (purple), 2nd

order polynomial (green), 3rd

order polynomial (red), 4th

order

polynomial (yellow), 5th

order polynomial (cyan), 6th

order polynomial (orange). Polynomial

curves higher than 4th

order are not visible because they match the curve of the 4th

order fit.

● Experimental data

ꟷ 1st

order polyfit

ꟷ 2nd

order polyfit

ꟷ 3rd

order polyfit

ꟷ 4th

order polyfit

ꟷ 5th

order polyfit

ꟷ 6th

order polyfit

● Experimental data

ꟷ 1st

order polyfit

ꟷ 2nd

order polyfit

ꟷ 3rd

order polyfit

ꟷ 4th

order polyfit

ꟷ 5th

order polyfit

ꟷ 6th

order polyfit

51

The coordinates of the brightest pixel are 753 and 242. There is a zero standard deviation on

the vertical position and a very small standard deviation on the horizontal position. The

determination of maximum’s x-position, which is along the line of scanning, was expected to

be more difficult because the measured signal is a combination of oversampling and sensor

arm movement. On the contrast, the maximum’s y-position is well defined because it

corresponds directly to the physical diodes of the system.

3.2.3 Position of the Focal Spot and Detector Diodes

So far, all the distances of the experimental configuration were measured with respect to the

generator’s window. However, the X-rays are generated in the focal spot, which is located

inside the X-ray tube, but its exact position is unknown. Similarly, the detector diodes are

located somewhere inside the case of the panel. The white marks on the panel are used to

indicate the dimensions of the active surface for the proper alignment of the equipment but do

not provide details for the exact position of the diodes inside the panel. Although it is easy to

measure the position of the photodiodes inside the hard case beforehand, other factors such as

the tilting of the detector panel can slightly affect this position during the exposure. For this

reason it was ensured that the panel was standing perpendicular to the ground before each

exposure. Nevertheless, the most important configuration parameter that affects the exposure

is the relative position of the photodiodes with respect to the focal spot. The determination of

this parameter ensures the correct projections, which in turn allows the comparison between

the experimental data and the calculations.

The distance between the outer surface of the hard case and the diodes was measured to be

1.2 cm. Unfortunately, the distance between the X-ray window and the focal spot cannot be

measured as no intervention in the XRT is allowed. To estimate this parameter, the

magnification factor was used. Data was collated for placing an aluminium wedge in different

distances between the panel and the generator. A scaling factor was used in the calculated

data in order to match the dimensions between the actual and the predicted shadow. A 5.5 cm

increase in both the source-to-object and the source-to-detector distance corrects the

magnification factor of the calculations. This is a plausible interpretation, as the focal spot is

expected to be somewhere in the middle of the X-ray tube which has diameter 12.4 cm.

After adjusting the magnification factor, the alignment between the generator and the detector

followed. Through data processing, a difference in the height of the predicted shadow

compared to the actual shadow was noticed. This was due to a wrong estimation of the actual

height of the source. Figure 3.9 illustrates the effect of the source height on the projection.

The panel is placed at known distance SDD from the generator. Suppose the red object is

placed at position SOD and the green at position SOD’ away from two identical X-ray

sources S and S’, where the S’ source is located lower than the S source. Points A and A’ are

two points on top of the red and green object respectively. The projection of points A and A’

goes to point O when the objects are lit up by the S source. On the contrary, the projection of

points A and A’ goes to points B and B’, respectively, when the objects are lit up by the S’

source. For a given source height difference, OB is greater than OB’ which means that

52

objects’ shadows become greater when SOD is smaller than SOD’. Another thing to notice,

regarding the correct projection, is that the actual height of either the photodiodes or the X-

ray source is not as important as the relative difference between the two of them.

Figure 3.9: Effect of the source’s height on the object’s projection.

An experiment was conducted to provide a correction in the position of the source between

the experimental configuration and the model. Data was captured and compared against the

model after placing an aluminium wedge at varying co-axial distance between the generator

and the panel. Figure 3.10 shows the difference between the predicted and the actual height

of the shadow of an aluminium wedge that was placed at 30, 40, 50, 60 and 70 cm away from

the generator’s window. As it was mentioned earlier, the actual distance between the focus

and the object is 5.5 cm longer. The different data sets indicate the varying relative source

height of the model between 0 and 2 cm.

SOD

Source to Detector distance

S

Detector

A

S’

SOD’

A’

B

B’

O

y

z

53

Figure 3.10: (a) Difference between the estimated and the measured height of the object’s

shadow. The plot shows that the current relative source height is wrong (red), as the shadow’s

height isn’t constant for different source-to-object distances. The reduction in the relative

height by 0.5 cm (blue), by 1.0 cm (yellow), by 1.5 cm (green) and by 1.8 (purple) gradually

diminishes the difference, while the reduction by 2.0 cm (black) has the opposite result.

Given the geometry of the experimental arrangement, triangles ΔSAS’ and ΔABO are

similar, which means that the sets of the corresponding sides are in proportion. Thus, SS′

OB=

SA

AO

which becomes 𝑂𝐵 =SDD·SS′

SOD− 𝑆𝑆′ after replacing SA with SOD and AO with SDD – SOD.

Given that SS’ and SDD are constant, the difference, y, between the predicted and the actual

height of the shadow is related to the source-to-object distance, x, by the equation

𝑦 = 𝑃1

𝑥+ 𝑃2 , (eq. 3.1)

where P1 and P2 are constants. Therefore, a 1/x function is used to fit the data.

As the Figure 3.9 illustrates, a reduction by 1.8 cm (purple) in the height of the model’s

source results in a constant relative difference regardless the position of the test piece. The

slope of this curve at every SOD can be seen in Table 3.5 . Firstly, the coefficients P1 and P2

of the fit curve are retrieved by the R software and secondly the slope of the curve is

calculated for every SOD.

For P1 = 1.9534283 and P2 = 0.7977783, (eq. 3.1) becomes

𝑦𝑝𝑢𝑟𝑝𝑙𝑒 = 1.9534283

𝑥− 0.7977783 , (eq. 3.2)

which is the equation of the purple fit curve. The slope is given by the first derivative

𝑑𝑦𝑝𝑢𝑟𝑝𝑙𝑒

𝑑𝑥= −

1.9534283

𝑥2 . (eq. 3.3)

54

The slope can be calculated by replacing x with the SOD values. The gradient of the curve is

practically zero throughout the SOD points. Hence, the calculations after the reduction by 1.8

cm of the model’s source height match the experimental results. The same analysis performed

in the horizontal direction but there was no relative offset.

Table 3.5: Gradient of the purple fit line at SOD points

SOD (cm) 𝒅𝒚𝒑𝒖𝒓𝒑𝒍𝒆

𝒅𝒙

35.5 -0.0015509060

45.5 -0.0009439861

55.5 -0.0006344071

65.5 -0.0004554571

75.5 -0.0003427825

3.2.4 Focal Spot Size

Throughout this study the focal spot is considered to be infinitely small. In other words, the

X-rays come from the same point of the tungsten anode. However, this is not true as the

electron beam deposits its energy in a small but finite area. This means that electrons coming

from different starting points of the focal spot area create different shadows of the object on

the detector plane. The different viewing angles of photons result in the “penumbra” effect

which blurs the image. This effect is illustrated in Figure 3.11.

Figure 3.11: Penumbra effect caused by the focal spot size. As it is clearly seen the edges of

the object’s shadow are not well defined due to the overlapping shadows. Notice that the

penumbra is larger for larger spot size. (This image is available at

http://www.embedded.com/print/4382009).

Small

spot size

Object Detector Source

Large

spot size

55

The pixel pitch is the main factor that limits the resolution of the output image, because the

X-rays that reach the screen deposit their energy to a specific pixel or to a pixel in close

proximity to the first. The blurring effect is another fundamental limit of resolution, as it

makes the distinction between the neighboring pixels harder. For example, it is difficult to

define the borderline of an object because of the overlapping shadows caused by the focal

spot size. The actual size of the focal spot, compared to the size of the pixels, will determine

the best resolution achievable by the system.

The actual dimensions of many focal spots are usually larger than the nominal sizes quoted

by the manufacturers (Kemp and Nichols, 1958). For this reason an investigation regarding

the size of the focal spot must take place. Several techniques have been developed for the

accurate measurement of the focal spot size. One of them is the “knife edge method”

(Crooks, 1973) which determines the dimension of the focal spot from the penumbra in the

image of a very sharp object. Another, is the “resolution method” (Friedman and Greenspan,

1969), (Rao, 1971), (Spiegler and Breckenridge, 1972) which determines the focal spot

dimensions after the exposure of a spatially varying test pattern. More modern methods

(Russo and Mettivier, 2011) suggest the use of a coded aperture mask, which essentially is a

radiation collimator consisting of numerous apertures that are disposed in a predetermined

arrangement, for the accurate measurement of the focal spot dimensions out of a single shot.

However, the oldest and the most widely used technique that allows the focal spot size

measurement is the “pinhole method”. The size of the focal spot is determined by measuring

the size of the bright dot which appears on the panel after the x-ray beam passes through a

circular aperture. According to this technique, a pinhole in a sheet of an absorbing material,

usually lead, is placed at the centre of the beam as it exits the X-ray tube. The result is a

magnified image of the focal spot which can be measured. However, for an accurate

measurement, the condition between the size of the focal spot and the size of the hole

(1 +1

𝑚) 𝑑 ≤ 0.1𝑓 , (eq. 3.4)

that Kuntke (1957) suggested must be fulfilled, where m is the ratio pinhole to panel distance

over focus to pinhole distance, d is the diameter of the pinhole and f is the size of the focal

spot in one axis. Otherwise, the measurement of the focal spot size will be susceptible to the

blurriness due to the penumbra effect caused by the pinhole.

The length of the pinhole plays an important role as well. When the length is greater that the

diameter of the hole, the intensity drops, as the angle of the incident X-ray beam increases. If

n is the length over diameter ratio and α the angle of the incident radiation, the intensity that

passes through becomes zero when the condition

𝑛 · 𝑡𝑎𝑛𝛼 = 1 , (eq. 3.5)

is fulfilled. The useful field of the pinhole is the field where the intensity is not less than 75%

of the maximum at the edges. Therefore the above condition becomes

𝑛 · 𝑡𝑎𝑛𝛼 = 0.2 . (eq. 3.6)

56

Robertson and Watson (1958) showed that the ratio n should not be greater than 5.

Another significant factor for the accurate measurement of the focal spot size is the material

that the sheet is made of. The sheet must absorb a large fraction of the incident radiation so

that the bright dot on the panel is easily distinguishable. Apart from high absorption, the

material should have adequate mechanical strength to allow holes to be made and retain their

shape and size, such as tantalum or gold (Robertson and Watson, 1958), (Law, 1993). Kuntke

(1957), suggested an alloy made of 90% gold and 10% platinum.

According to Robertson and Watson (1958), in order to measure a focal spot with nominal

dimension between 0.3 mm and 1 mm, a sheet made of tantalum that contains a 0.025 mm

diameter hole should be used. The diaphragm should not be thicker than five times the

pinhole diameter. By solving the equations of the above conditions, an estimation regarding

the dimensions of the hole needed to measure the focal spot size of the CP120 XRT can be

done. Given the dimensions of the chamber the minimum m ratio is achieved if the pinhole

sheet is placed against the window of the generator. This is:

𝑚 = 𝑝𝑖𝑛ℎ𝑜𝑙𝑒 𝑡𝑜 𝑑𝑖𝑜𝑑𝑒𝑠 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑓𝑜𝑐𝑎𝑙 𝑠𝑝𝑜𝑡 𝑡𝑜 𝑝𝑖𝑛ℎ𝑜𝑙𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒=

81.2 𝑐𝑚

5.5 𝑐𝑚= 14.76 . (eq. 3.7)

Notice that the focal spot-to-window and the hard case-to-diodes distances were taken into

account. Given that the nominal height of the focal spot is 0.5 mm, the ideal hole should have

diameter approximately 0.05 mm, as it can be seen in (eq. 3.8)

𝑑 =0.1𝑓

(1+1

𝑚)≃ 0.05 𝑚𝑚 . (eq. 3.8)

Even though this threshold seems to be the theoretical threshold for good measuring

conditions, it suggests that the size of the hole should be a fraction of the size of the focal

spot. This subsequently means that the diaphragm should be no thicker than 0.25 mm.

Given the requirements and the equipment at the 3DX-ray premises, on the one hand

materials, similar to the ones used in standard pinhole experiments, such as tantalum, gold or

gold alloys were not available and on the other hand the production of pinholes as small as

0.05 mm diameter was impossible.

An experiment has been devised that allows the estimation of the focal spot size without

buying a new custom made diaphragm. Similar to the pinhole experiments, a 0.08 cm thick

steel sheet containing 0.15 cm diameter holes, 2 cm apart (Figure 2.9 (f) (p. 19)) was placed

initially at 14 cm and then at 24 cm away from the generator’s window. Instead of the direct

measurement of the size of the focal spot, data is compared between the actual intensity that

reaches the screen and the predicted intensity as it is calculated by the absorption model,

described in chapter 2.2.2. The steel sheet shown in Figure 2.9 (f) (p. 19) is modelled using a

series of pixelated planes, the magnification is taken into account and the absorption is

calculated using the (eq. 2.6), where the input intensity was given by the open exposure. A

table drill was used to create the holes in both the horizontal and vertical dimension of the 0.8

mm thick sheet. Although, the use of a lead sheet would be preferable as far as the absorption

57

of the beam around the hole is concerned, its malleability and flexibility doesn’t allow the

production of accurate pinholes. Lead seems unsuitable due to its poor mechanical strength,

hence, stainless steel was preferred.

When photons pass through circular apertures, in this case holes in the steel sheet, diffraction

occurs. Instead of a bright dot, a diffuse circular disc with concentric circles of constructive

and destructive interference could appear on the panel. However, this only occurs when the

diameter of the hole is comparable to wavelength of the incident light. The wavelengths of

the exiting energy spectrum can be calculated. As it was shown in (eq. 2.3) the 3.5 mm Al

window of the CP120 blocks 96 % of the incident radiation with energy 20 keV. This

practically sets the minimum of the energy spectrum. The maximum is 120 keV and is equal

to the energy generated by the complete stop of the incident electron beam when the

operating voltage is set at 120 kV. The wavelengths of the incident radiation are between

0.01 nm and 0.06 nm, which is 108 times smaller than the diameter of the hole in the steel

sheet. Therefore, the X-ray diffraction is insignificant and is not affecting the comparison.

Given that the model predicts the transmitted intensity as if the X-rays were generated by an

infinitely small source, an estimation of the focal spot size can be done by comparing the two

intensities at the region of the pinholes. Figure 3.12 shows the exposure of the object placed

at 24 cm and Figure 3.13 shows the method that is used in the comparison between the

experimental data and the calculations.

Figure 3.12: Exposure of the steel sheet placed at 24 cm as it is seen via ThreatSpect

software, with the operating voltage and current at 120 kV and 1 mA respectively.

The comparison takes place between single holes of the steel sheet, where a difference in the

curves of the measured intensity (green curve) and of the calculated intensity (red curve) is

noticed. Actually, the red curve shows what the intensity shape should look like if the X-rays

were generated by a point source. The fact that data forms a bell shaped curve is due to the

larger focal spot. Given the difference between the curves, a function could be convolved

with the predicted intensity to compensate for the different starting points of the X-rays

within the focal sport area. In other words, a function could be used to make smoother the

58

estimated curve and give it a bell shape similar to the experimental curve simulating the focal

spot area. The best match is achieved when the predicted curve (red) is convolved with a

Gaussian function (orange). Their convolution (black) matches the experimental curve

(green) after wisely choosing the width of the Gaussian by changing its standard deviation.

Figure 3.13: Convolution between the estimated intensity and the chosen Gaussian curve in

order to achieve match with the experimental data. This hole is used to examine the vertical

size of the focal spot. Its coordinates are 757 and 106 pixels for the horizontal and the vertical

direction respectively, after the projection on the detector plane. The vertical axis of the plot

is used to provide an indicator for the width of the curves. It has no other practical

importance.

Although, the intensity per focal spot area is unknown, a Gaussian intensity profile is a

reasonable approximation given that the electron beam flux is driven by statistics and that a

focusing cap is used to narrow the beam.

Data was collated for every single hole located in the central row and column of two different

exposures. Figure 3.14 (a) and (b) shows the focal spot size for a series of holes along the

horizontal and the vertical position. The focal spot is measured to be 0.092 cm by 0.080 cm.

There are two main conclusions coming out of this experiment. Firstly, the size of the focal

spot is submillimeter which comes in accordance with the nominal value of the XRT

manufacturer. Secondly, the focal spot is not symmetric, as there is size difference between

the horizontal and the vertical direction.

y-p

osi

tio

n (

in p

ixel

s)

Intensity

ꟷ Experimental data

ꟷ Calculations

ꟷ Gaussian function

ꟷ Convolution

59

(a) (b)

Figure 3.14: (a) Horizontal focal spot size as it is estimated from a series of holes along the

horizontal position for two different exposures, one for placing the object at 14 cm (red

points) and one for placing the object at 24 cm (blue points). The mean predicted width of the

focal spot is 0.092 cm. (b) Estimation of the vertical focal spot size after following the same

technique. The mean predicted height of the focal spot is 0.080 cm.

3.3 Offset Interpretation

The determination of the various physical offsets of the experiment led to the correct

projection enabling the data comparison. Figures 3.15 and 3.16 show the comparison of the

vertical intensity profile between the calculations and the experimental data. The

experimental configuration that was used is shown in Figures 2.12 (p. 22) and 2.14 (p. 23).

(a) (b)

Figure 3.15: (a) Radiography as it is seen in ThreatSpect software. (b) Vertical intensity

profile at the 768th

column. Comparison between the calculated (red curve) and the measured

(green curve) intensity.

0.092 cm

0.080 cm

○ SOD = 14 cm

○ SOD = 24 cm

○ SOD = 14 cm

○ SOD = 24 cm

768th

column

ꟷ Experimental data

ꟷ Calculations

60

(a) (b)

Figure 3.16: (a) Radiography as it is seen in ThreatSpect software. (b) Vertical intensity

profile at the 1118th

column. Comparison between the calculated (red curve) and the

measured (green curve) intensity.

In both configurations the aluminium wedge was placed on top the wooden block. The

differences between them is the initial position of the test pieces and the orientation of the

wooden block. In Figure 3.15 the test pieces were placed in the centre of the panel while in

Figure 3.16 there was a 12 cm offset towards the right side. In the former, the aluminium

wedge was resting on top of the large area of the block while in the latter, the block was

rotated by 90o with respect to the x axis. Moving from top to bottom, the intensity of the

unobstructed beam can be seen, followed by the declining intensity in the aluminium wedge’s

region. The calculated intensity matches the experimentally measured intensity not only in

the unobstructed path of the primary beam but also in the thinner regions of the wedge.

However, there is an obvious mismatch at the bottom of the wedge in both images. A similar

mismatch can be seen at the region of the wooden block. The predicted intensity is practically

zero when the thickness of the wedge reaches its maximum value. This does not come in

accordance with the minimum measured intensity, which stands at 0.017 and 0.020 at Figures

3.15 (b) and 3.16 (b) respectively.

Another remark is that the shape of the two curves differs at the bottom of the wedge. This

difference cannot be explained by the spectrum variation used in the calculations because the

different spectra can only change the overall steepness of the calculated curve in the region of

the wedge. It is clear that there is a shift at the location of the minimum measured intensity,

as it is not in the place it was expected to be, that is where the thickness of the wedge

becomes maximum. Moreover, instead of a sharp edge at the boundary between the two

objects a round edge is noticed leading to greater intensities at the bottom of the wedge and

1118th

column

ꟷ Experimental data

ꟷ Calculations

61

pushing the minimum in the thinner regions of the aluminium wedge. This is indicated by the

black dashed circles.

The noticeable difference is essentially independent of the initial position of the test pieces,

therefore, a first approach to interpret this difference is through the effect of the electronic

noise, which is also known as “dark current”. Electronic noise is present even when the X-

rays are off. Its effect was not taken into account during the absorption model development

and could explain the difference seen previously. In this case the values of the “dark current”

should be either added to the calculated intensity or subtracted from the measured intensity.

However, the X-ray detection system is programmed to measure the background signal

before every exposure. When the operator commands the system to scan, the motor moves

the sensor arm in the centre of the active surface of the detector and reads the signal of the

diodes before the X-ray generation A typical readout of the background, as it was captured

before an open exposure, can be seen in Figure 3.17 .

Figure 3.17: Background signal of the detector diodes.

It can be seen that the average background signal of the 1024 photodiodes stands at

approximately 0.0605 . Notice that the borders between the 8 detector modules, that form the

detector array, are distinguishable due to reductions in sensitivity. Although, the sensitivity at

the tiling edges decreases due to the inherent characteristics of the detector module, it is still

high enough to be corrected by the software during calibration. Table 3.6 shows the mean, the

standard deviation and the range of the fluctuations of the “dark current” in each module.

Although each diode has its own “dark current” sensitivity, the mean dark current value can

be calculated for each module. In this calculation the sensitivity reduction at the edge is

neglected by not taking into account the three first pixels at the top of each module. It can be

seen that electronics on each detector module produce similar background signals. After the

image is captured the background signal is subtracted from the total signal which is the first

step of the calibration process. Then the diode gains are applied in order to scale the image to

the global “brightfield” value and create a high quality image. Therefore, it is obvious that the

62

effect of the “dark current” is compensated and the result is the original transmitted intensity

of the exposure.

Table 3.6: Mean, standard deviation and range of fluctuations on top of the “dark current” for

each one of the eight detector modules.

Detector

module Mean

Standard

deviation Range

1 0.06139 0.0001512 0.0008547

2 0.06038 0.0001556 0.0007326

3 0.06133 0.0001722 0.0008547

4 0.06068 0.0001644 0.0008547

5 0.06044 0.0001757 0.0007937

6 0.06039 0.0001556 0.0007937

7 0.05989 0.0001669 0.0010380

8 0.05971 0.0001525 0.0008547

The second approach that could explain the offset at the bottom of the wedge is the contrast.

The detector’s software assigns a value between 0, which designates “darkfield” and 1, which

designates “brightfield”, to every pixel of the image according to the received intensity. It is

known that the software reads the value of the brightest pixel in order to define “brightfield”.

Supposing that, not only the “brightfield” but also the “darkfield” is read when the X-rays are

on, when the darkest part of the image is higher than the actual “darkfield” value, the

software should force the contrast to compress in order to produce a high quality image.

A new experiment has been devised to test what the software does. The previous exposures

were repeated but this time a thick lead block shown in Figure 2.9 (e) (p. 19) was added. The

object was placed at 70 cm, in a way so that the back surface of the brick is in touch with the

hard case of the detector (Figure 3.18). The high atomic number of lead coupled with its high

density and thickness makes sure that no X-rays can pass through it, even for the higher

energies of the spectrum. Given the maximum output energy of generator, which is 120 keV,

the amount of lead needed to absorb the X-ray photons is calculated. The half value layer

(HVL) given in (eq. 3.9) is the thickness of the material required to absorb half of the

intensity of the incident radiation.

𝐻𝑉𝐿120𝑘𝑒𝑉,𝐿𝑒𝑎𝑑 =𝑙𝑛2

𝜇= 0.015 𝑐𝑚 , (eq 3.9)

where μ is the linear attenuation coefficient of lead for 120 keV photon energy. It can be

clearly seen that the 10 cm lead brick that was used equals to 667 HVLs which means that the

incident radiation is fully absorbed. Hence, the shadow of the lead brick will determine the

“darkfield” value and this value cannot be other than the actual “darkfield” value. In this case

the software is forced to stretch the contrast from the actual “darkfield” up to the

“brightfield”.

63

Figure 3.18: A lead block is added close to the detector panel for the actual “darkfield”

measurement. The lead bricks that are present on the right hand of the image are not

radiologically important, as they are located outside the active surface of the panel, which is

designated by the white marks. The purpose of their use is to improve the stability of the

panel.

In Figure 3.19 a comparison of the intensity profile between the experimental (green) and the

calculated (red) curve can be seen. Again, there is a 0.017 difference in the minima between

the calculated and the measured intensity, similar to the one shown in Figure 3.15 (p. 59).

This proves that the “darkfield” is read from the photodiodes when the X-rays are off. And

the software stretches the contrast from actual “darkfield” to “brightfield”, regardless the

image contrast.

(a) (b)

Figure 3.19: (a) Exposure of an aluminium wedge placed over a wooden block. A thick lead

block is also added to the bottom left corner of the panel. Its shadow helps in the

determination of “darkfield”. (b) Vertical intensity profile at the 768th

column.

768th

column

ꟷ Experimental data

ꟷ Calculations

64

3.4 Observation of Scattering

Both the “dark current” and the image contrast hypothesis failed to interpret the offset

between the predicted and the measured intensity. Although it is widely known that scattering

plays an important role in X-rays interaction with matter and will definitely be present in the

current exposures, it is still unknown whether its magnitude could explain the difference

noticed earlier. Scattering was firstly observed in the exposure of the lead brick that was

placed on top a wooden block (Figure 3.20 (a)).

(a) (b)

(c) (d)

Figure 3.20: (a) This is the image of a lead brick placed on top of a piece of wood. The

operating voltage and current was set at 120 kV and 1mA, respectively. (b) Heat coloured

image, focused on specific region of the contrast. A yellowish region is noticed at the border

between the two objects. (c) This is the image of a lead brick, two wooden blocks and an

aluminium wedge. The operating voltage and current was set at 120 kV and 1 mA. (d) Again,

a yellowish region is noticed at the border between the pieces of wood and the other objects.

Notice that no similar region is apparent between the lead block and the aluminium wedge.

Taking advantage of the ability of the ThreatSpect software to focus on specific regions of

the contrast histogram a qualitative analysis can be done. Figure 3.20 (b) shows the same

image in heat colours after setting the “brightfield” to be less than the transmitted intensity in

65

the region of the wooden block. This is the reason the wooden block cannot be seen. This

setting increases the contrast sensitivity at the dark regions of the image, which allows a more

detailed examination. A look at the border between lead and wood enhances the argument

that the scattering factor interferes strongly with the overall signal. A bright region (yellow)

at the bottom of the lead brick is noticed, indicating that there are photons that deposit their

energy at the bottom of the shadow of the lead block. However, as it was shown earlier, the

lead brick can absorb the incident beam completely. Given that the lead object used in the

exposures is very thick, even for the harder X-rays, to penetrate the only plausible

explanation is that scattered X-rays from the wooden block deposit their energy at the shadow

of the lead brick. Behind the lead brick, in the absence of direct X-ray light, the diodes can

detect scattered X-ray photons coming from other materials inside the chamber as well. The

experiment was repeated after adding an aluminium wedge and another wooden block

(Figure 3.20 (c)). In Figure 3.20 (d) the yellowish surface is apparent at the borders between

lead and wood and aluminium and wood but not between lead and aluminium, which means

that different materials have a different radiological behavior.

During object irradiation both absorption and scattering occur, however, the tradeoff between

the number of electrons in the material and its absorption capability distinguishes scatterers

from absorbers. Wood acts as a scatterer due to its low density, while lead or aluminium act

as absorbers.

Wood scatters X-rays in all directions. However, the scattering signal is detected nowhere but

in the shadow of thick absorbers. The reason is that the scattering signal is very faint and thus

hard to distinguish in bright regions. A quantification of the scattering signal with respect to

the absorption signal, the “brightfield” and the “darkfield” is necessary.

Another experiment has been devised, where the generator and a polyethylene terephthalate

cylinder are placed in a proper way so that the scattered signal can be isolated and measured.

The experimental configuration and the radiography are illustrated in Figure 2.17 (p. 24) and

Figure 3.21 respectively. A thick lead wall prevents the direct X-rays from reaching the

panel, allowing the measurement of the scattering signal that comes from the cylinder and

deposits its energy at the shadow of the lead wall. A lead brick is also placed behind the

scatterer in close proximity to the detector panel. Its use ensures that no X-rays pass through,

so that the “darkfield” can be measured. The height of the cylinder is higher than the height

of the lead brick, which allows the measurement of the absorption signal.

66

(a)

(b) (c)

Figure 3.21: (a) This exposure associates scattering signal with “darkfield”, absorption signal

and “brightfield”. (b) The same image heat coloured and zoomed in at the region of the

scattering signal. (c) This is a heat coloured image taken after a shot under the same

configuration but with the cylindrical scatterer absent. A faint scattering signal is observed

coming from the right. It is probably due to the materials at the side of the chamber.

In this exposure, the maximum intensity of the scattering signal was measured to be 0.01,

which is 5% and 10% of the “brightfield” value and of the mean absorption signal

respectively. This indicates that the contribution of the scattering signal to the overall

measured signal can be significant. Some qualitative characteristics are also visible in the

previous figure. The shape of the scattering signal proves that scattering is a wide

phenomenon compared to absorption. Hence, it is not highly affected by the physical

characteristics of the object, such as the exact shape or the exact position of the scatterer.

Thus, the sharp edges of the cylindrical object are not visible in the shadow. All it can be seen

x-position (in pixels) x-position (in pixels)

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is a region of maximum intensity which fades while moving further on the screen. The shape

of the scattering signal is not expected to change dramatically by using different scatterers.

Another important remark in the previous experiment is that scattering signal comes from

sources of scattering, other than the object itself. Figure 3.21 (c) shows that scattering signal

comes from the right side of the chamber, because the left edge of the lead brick that was

present in the shot can be clearly seen. This means that all the materials of the chamber

contribute to the signal measured by the diodes. Moreover, the materials that the chamber is

made of and any other materials that are exposed to X-rays may fluoresce and emit

characteristic X-rays.

Another experiment was conducted to prove that the difference between the experimental

data and the calculations, shown in Figure 3.15 (p. 19), is due to the scattering components of

the exposure. Data was collated after filtering out one by one the scatterers that were present

in the exposure. Figures 3.22 (a) and (b) show the preparation and (c) shows the final

configuration of the experiment.

(a) (b)

(c)

Figure 3.22: (a) Lead foil is used to cover the wooden surface that the bottom of the chamber

is made of. (b) Lead foil is also wrapped around the wooden block. (c) This is the final

experimental configuration of the exposure of an aluminium wedge placed on top of a lead

covered wooden block.

y

x

z

68

Lead is used to prevent X-rays from reaching the scatterers, thus the scattering signal is

eliminated. The contribution of each one of the scattering signals to the overall signal is

illustrated in Figure 3.23, which shows a comparison between the predicted (red curve) and

the experimental (green, orange and blue curve) intensity profile at the 768th

column of the

data matrix. The green curve represents the response of the detector when the scatterers

(bottom surface of the chamber and piece of wood under the wedge) are not lead-shielded.

Orange curve represents detector’s response after laying lead foil on the bottom of the

chamber, in order to diminish the scattering signal that comes from this surface. Blue curve

represents the response when both the bottom surface and the piece of wood are covered with

lead. The red curve is the predicted response as it was calculated by the absorption model.

Although the model describes the absorption process adequately, it doesn’t take into account

the scattering effect.

Figure 3.23 Vertical intensity profile at the 768th

column. As the scatterers are being filtered

out the experimental curves tend to match the calculated curve as it is predicted by the

absorption model.

Although the curves do not differ significantly along the aluminium wedge, there is a

mismatch at the bottom of the object. For this reason, the minimum intensity at the wedge

region can be used to quantify the difference between the curves. The relative difference of

the minimum intensity between the experimental data curve (green) and the other curves

(orange, blue, red) at the region of the wedge is calculated by the (eq. 3.9). The results are

presented on Table 3.7 .

𝑅𝑒𝑙. 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =𝑚𝑖𝑛−𝑚𝑖𝑛0

𝑚𝑖𝑛0 , (eq. 3.9)

ꟷ Experimental data

ꟷ Experimental data

(lead foil on the

bottom of the

chamber)

ꟷ Experimental data

(lead foil on the

bottom of the

chamber and

around the

wooden block)

ꟷ Absorption model

69

where min is the minimum intensity at the region of the wedge for the orange, the blue and

the red curve and min0 is the minimum intensity at the region of the wedge for the green

curve.

Table 3.7: Relative difference of the minima of the curves with respect to the green curve

Minimum at the

wedge region

Relative difference

from green

Green 0.0170 0%

Orange 0.0147 -13.5%

Blue 0.0052 -69.4%

Red 0.0000 -100%

It can be seen that, as the scattering factors are being filtered out, the experimental curves

tend to match the predicted curve as it was calculated by the absorption model, which means

that the observed difference is due to scattering. The elimination of the scattering signal that

comes from the bottom surface of the chamber resulted in a 13.5 % reduction of the

minimum of the transmitted intensity. However, the main scatterer is the wooden block.

When lead was wrapped around the block the minimum at the wedge region was reduced by

approximately 70 % . The materials located in the surrounding environment of the panel also

contribute to the overall signal. This explains the remaining difference shown between the

minimum of the blue and the red curve. Another thing to notice, is that the border between

the aluminium wedge and the wooden block is sharper for the blue curve compared to the

green and the orange curves, which means that the shift of minimum that is noticed both on

the orange and green curves is related to scattering signal. The difference in the steepness of

the red curve is due to a wrong estimation of the wedge’s attenuation factors, which have to

do with the unknown energy spectrum of the initial beam.

Similar conclusions are extracted from the exposures with the configurations shown in Figure

3.24 (a) and (b). In this arrangement, which was carefully chosen so that the scattering signal

is highlighted, a steel plate and two candles are placed on top of a wooden block. The plot

shown in Figure 3.24 (c) shows the comparison between i) a thin steel plate placed on top of

a wooden block (blue curve) ii) a steel plate placed between two candles, all on top of a

wooden block (orange curve) and iii) a steel plate placed between two candles covered by

lead, all above a piece of wood (green curve).

70

(a) (b)

(c)

Figure 3.24: (a), (b) Experimental arrangement. (c) Horizontal intensity profile at the 150th

row. The transmitted intensity from the wooden block is not visible in this plot because the

150th

row is over the wooden block’s region.

Scatterers shed light all over the active surface of the detector panel. The effect of scattering

sums and becomes more significant at the region of the steel plate as it can be seen by the

comparison of the orange and the blue curve. The absorption signal coupled with the

scattering signal from the two candles and the wooden block stands higher than the

absorption signal coupled with the scattering signal coming from the wooden block only.

Also, the regions of the unobstructed beam that are close to the candles stand higher due to

the scattered X-rays. The experiment proves that scattering signals sum and the

discrimination between the objects is limited. Another useful conclusion coming out of this

plot is that there is another signal coming from other scattering surfaces of the chamber. The

flux in the shadow of the steel sheet is smaller when lead is wrapped around the candles

ꟷ Steel plate

ꟷ Steel plate and candles

ꟷ Steel plate and lead covered candles

71

compared to the previous configurations. This means that lead prevents an amount of

unwanted X-rays that were scattered in the surrounding materials of the panel from

depositing their energy at the shadow of the steel plate.

An experiment that leads to the quantification of the scattering signal that is shown in the

previous plot was devised. The concept was to add an increasing number of thin sheets of

paper, right in front of the steel plate in the configuration described in Figure 2.18. The

attenuation due to the stacked pieces of papers would lead to a match between the orange and

the blue curve in the region of the steel plate. This would quantify the scattering signal in

terms of number of papers. Although, the number of stacked papers reached up to 50, no

significant drop in the intensity was noticed and the quantification wasn’t possible. A new

series of shots using a larger stack is necessary.

3.5 Scattering Model Development

After the detailed examination of the scattering phenomenon, it is clear that light materials,

such as wood, produce the majority of the scattering signal that was measured with the

FlatScan TPXi X-ray system. A simple model, described in chapter 2.2.3, was developed in

order to predict the effect of this process. Figures 3.25 (a) and (b) show a comparison

between the absorption and the scattering signal produced by the wooden block, shown in

Figure 2.9 (c) (p. 19), along a single row and column of the image.

(a) (b)

Figure 3.25: (a) Vertical intensity profile at the 768th

column. The red and orange curves

show the predictions of the absorption and of the scattering model respectively. The shape of

the scattering model is the one expected according to the measurements. The curve has a

maximum at the middle of the height of the object and then fades. No sharp edges are visible

as scattering is a wider phenomenon than absorption. (b) Horizontal intensity profile at the

40th

row. There are similar conclusions to the previous plot.

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Response

ꟷ Absorption model

ꟷ Experimental data

Res

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ꟷ Absorption model

ꟷ Experimental data

x-position (in pixels)

72

The scattering model calculates the intensity received by single detector pixels. The

scattering signal was calculated for nine different detector pixels for both the horizontal and

the vertical direction. The orange curves that are shown in Figures 3.25 (a) and (b), show an

interpolation between these points, which gives the final shape of the scattering signal in both

directions. The detector pixels that are used in the interpolation must be wisely chosen so that

they include the pixels with the minimum and the maximum expected intensity. Otherwise,

the risk of missing the extremities due to the interpolation is entailed.

Although there is no experimental reference for the magnitude of the scattering signal, the

shape of the predicted curve is correct. The signal peaks in the middle of each dimension and

then fades towards the sides of the panel. Hence, the predicted scattering signal has many

similarities with the measured scattering signal shown in Figure 3.21 (b). No specific shape

can be noticed in contrast with the well-defined shape of the absorption signal.

3.6 Sum of Models

In this chapter the sum of the two models is compared to the experimental data. Figure 3.26

shows the irradiation of an aluminium wedge placed on top of a wooden block. The

configuration used is the one shown in the embedded picture. The red curve represents the

prediction for the absorption model while the orange curve represents the estimated scattering

signal coming from the chunk of wood. The purple curve is the sum of the absorption and the

scattering predicted signal and is compared to the green curve, which represents the

experimental data.

Figure 3.26: Vertical intensity profile of the comparison between the sum of the absorption

and the scattering model with the experimental data.

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ꟷ Experimental data

ꟷ Absorption model

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ꟷ Sum of models

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Before highlighting the main conclusions of this comparison, a few points regarding the setup

of the calculations should be clarified. The first point has to do with the energy and the

density used in the calculations. Although, the actual X-ray beam consists of a continuous

energy spectrum, the absorption model uses a discrete energy spectrum and the scattering

model uses a monoenergetic beam. This isn’t a poor estimation, as the dominant energy of

each phenomenon may vary. The energy and the density are the main arguments that are used

in the absorption simulation of the primary and the scattered X-rays. A discrete energy

spectrum containing 40, 50 and 60 keV X-rays with weight factors 10%, 20% and 70%

respectively, was used in the absorption model, while a single energy at 20 keV was used in

the scattering model. Although the density of the aluminium and steel wedges can be

determined easily, the same cannot happen for unknown and not uniform compounds, such as

the wooden block. The piece of wood that was used in the exposures contains a knot, which

means that the density varies throughout the object. The measured density is 0.5 g/cm3, but

the density used as a parameter in the absorption and scattering model is 0.7 g/cm3.

The second point is that the two models run separately and the scattering signal is added to

the absorption signal. Thus, there is no interaction between the two predicted signals. This

contradicts the actual exposure where both the attenuated and the scattered X-rays are

subjected in further attenuations due to other materials that block their path to the screen.

Finally, a criterion that defines the good match between the curves should be determined. The

model is still in early stage, as a result, several parameters that strongly affect the estimated

curve, such as the spectrum of the X-ray beam or the effect of the detection system, have not

been thoroughly studied. The judgement is based on noise fluctuations. Given the

quantification of noise fluctuations shown in Table 3.1 (p. 43), the criterion of good match is

set as the half of the range of noise fluctuations. Hence, two curves match when they differ

less than 0.005 and 0.004 for the horizontal and the vertical direction respectively.

As far as the comparison between the sum of the models and the data is concerned, it is clear

that there is an overestimation in the magnitude of the scattering signal. The overestimation is

visible in the thicker region of the wedge. However, the shape of the scattering signal coupled

with the absorption signal in the wedge’s region explains the shift of the minimum that was

noticed earlier in Figures 3.15 (p. 59) and 3.16 (p. 60), as it pushes the minimum transmitted

intensity higher. In general, the predicted curve has a good match with the data. The drop of

the experimental curve in the region of the wooden block is due to the local increase of

wood’s density. This is where the knot is located.

The same spectrum and density of the wood was used in the plots that follow. The

comparison between different experiments under the same circumstances was done for two

reasons. Firstly, taking into account that the generator is operated at a given voltage and

current, a constant X-ray spectrum is produced. Although, no spectral analysis was performed

in the X-ray beam, the semi-empirical recipe that was described earlier makes the model

more realistic. Secondly, a model should have the ability to estimate the transmitted intensity

for various objects placed in different positions between the detector panel and the generator.

74

By keeping the same initial parameters the accuracy and the consistency of the model in a

wide range of objects is tested.

Figure 3.27 shows the irradiation of a steel wedge placed on top of a wooden block. The

configuration used is the one shown in the embedded image.

Figure 3.27: Vertical intensity profile at the 1125th

column of the comparison between the

sum of the absorption and the scattering model with the experimental data.

Again, a small overestimation in the scattering signal is shown at the bottom of the wedge.

Overall, there is a good match between the prediction and the experimental data. Notice that

the model does a good prediction despite the fact that the test object was different. The

radiological effects of the discrete spectrum used in the model seem to match the radiological

effects of the continuous spectrum of the actual source.

In Figure 3.28 the result of a similar experiment is illustrated. An aluminium wedge was

placed on top of a wooden block with the configuration shown in the embedded image. An

offset is seen between the calculations (red curve) and the experimental data (green curve).

The absorption model coupled with the scattering model (purple curve) is compared with the

experimental data. Although the shape of the purple and green curve is very similar, there is

an offset that extends along the vertical cut, which is larger than the match criterion.

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ꟷ Experimental data

ꟷ Absorption model

ꟷ Scattering model

ꟷ Sum of models

75

Figure 3.28: Vertical intensity profile at the 150th

column of the comparison between the sum

of the absorption and the scattering model with the experimental data.

A comparison between experimental data and calculations is illustrated in Figure 3.29 . The

arrangement can be seen in the embedded image. A mismatch between the predictions and

the data is noticed at the thicker region of the wedge and the region of the piece of wood. The

difference is larger than the match criterion for both regions.

Figure 3.29 Vertical intensity profile at the 768th

column of the comparison between the sum

of the absorption and the scattering model with the experimental data.

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ꟷ Experimental data

ꟷ Absorption model

ꟷ Scattering model

ꟷ Sum of models

ꟷ Experimental data

ꟷ Absorption model

ꟷ Scattering model

ꟷ Sum of models

76

This may be due to the simplicity of the scattering model and due to the effect of the wooden

surface of the chamber. Despite the fact that the scattering model predicts with ease the

scattering signal coming out of thin objects, it seems that the scattering approximation in one

plane fails to predict the scattering signal of the thicker scatterers, such as the 9.8 cm thick

wooden block. In this configuration, the objects are closer to the bottom of the chamber

which means that the scattering signal coming from the wooden bottom is more significant

compared to the previous plots.

The interaction between the absorption and the scattering signal that was mentioned earlier

illustrated in Figure 3.30. The steel square sheet shown in Figure 2.9 (f) (p. 19) was used in

another exposure before being drilled. The configuration of this exposure is shown in the

embedded image. There is a very good match between the predicted and the calculated curve

with respect to the match criterion. Notice that a large fraction of the scattering signal that is

produced by the piece of wood is blocked by the steel tile before reaching the screen. The

purple curve shows the sum of the scattering and the absorption signal. In reality, the

scattering signal is further attenuated by the steel sheet. However, the secondary interactions

were not taken into account in the model. This explains the higher predicted intensity at the

bottom of the steel sheet. A mismatch in the region of the wooden block is noticed again.

Figure 3.30: Vertical intensity profile at the 768th

column of the comparison between the sum

of the absorption and the scattering model with the experimental data.

ꟷ Experimental data

ꟷ Absorption model

ꟷ Scattering model

ꟷ Sum of models

77

CHAPTER 4 – GENERAL DISCUSSION AND CONCLUSIONS

4.1 Limitations

There are limitations due to the characteristics of the specific parts of the equipment. These

limitations may reduce or even define the maximum performance of the screening system. As

it was mentioned earlier the system is designed to withstand hard outdoor use. For this reason

a hard but flexible case made of acrylonitrile butadiene styrene is used. However, as every

other material that is placed between the generator and the detector, it participates in

absorption, scattering and fluorescence processes. Ideally, the beam should not be obstructed

by materials other than the ones that are being inspected and the ones that participate in the

detection, such as the scintillator. But in case of FlatScan detector, a case made of light

materials is used, which definitely changes the intensity and the spectrum of the incident X-

ray beam.

The size of the diodes limits the image resolution. The smaller the diode size the better the

resolution is. The nominal dimensions of the diodes in FlatScan’s detector modules are

submillimeter, which means that the active surface of a single diode is less than a square

millimeter. The diode’s width and height are the quanta of distance for both the horizontal

and the vertical direction because the information that reaches the photodiode is allocated

either to this diode or to one of its neighbors. Another fundamental limit of resolution is the

focal spot size. The finite dimensions of the focal spot blur the image, leading to low

discrimination especially when looking at the sharp edges of an object. The resolution of the

system is defined either by the diode dimensions or by the focal spot size, depending on the

larger value between the two of them.

The electronic noise plays some role as well. The noise fluctuations are a result of variations

in the voltage and current within the sensor and photon statistics. Noise goes on top of the

signal reducing the quality of the image. It appears as a random variation of brightness which

looks like a grainy layer on top of the image. Both the contrast and the resolution are affected

by noise.

The quality of the image is also affected by the objects under inspection. Scattering adds a

wide unwanted signal to the absorption signal. This reduces the distinction between the

objects’ shadows. Low density and low contrast materials will definitely add more unwanted

signal on top of the absorption signal. The same thing will happen when the system is

operated close to scattering surfaces. Scattered signal from the surrounding environment will

be added to the main signal.

The shape of the primary beam depends on the shape of the focal spot and the angle formed

by the trajectory of the incident electrons and the top surface of the anode. This affects the

angular distribution and the uniformity of the beam. Given that a part of the beam passes

through several amounts of the anode material, the beam is partially hardened. This

introduces spectral variation on the exiting beam.

78

The material and the thickness of the generator’s window is a factor that affects the energy

spectrum of the beam. The window hardens the primary beam by absorbing the lowest

energies of the spectrum. Although far from monochromatic the window could narrow the

energy spectrum down to a small energy region. However, a thick window could reduce the

intensity and the flux of the generated X-rays.

4.2 Summary - Performance of Kit

In this part the main achievements of the present study are summarised followed by an

evaluation regarding the performance of FlatScanTPXi equipment.

Several physical offsets that are related to the arrangement of the equipment have been

determined. The most important of them is the exact position of the focal spot. It was found

that the X-rays are generated 5.5 cm behind the window. Thus, the source-to-object distance

that is measured from the generator’s window should be increased by 5.5 cm so that the

actual position of the focal spot is taken into account. In addition, the relative difference

between the position of the photodiodes and the position of the focal spot (as it is measured

by the cross mark) in the vertical dimension is furtherly reduced by 1.8 cm regardless the

relative difference in height between the panel and the generator.

The range of noise along a flattened vertical and a flattened horizontal intensity profile was

measured to be 0.0091 and 0.008 respectively. This defines the match criterion between two

curves. It is considered that two curves match when they differ less than 0.005 and 0.004 for

the horizontal and the vertical direction respectively.

A method that makes a safe estimation about the diode that receives the maximum intensity

regardless the noise fluctuations has been developed. According to the inverse square law,

that diode is associated with the shortest distance between the generator and the detector.

Given that the standard output is a data matrix with dimensions 1024 rows by 1536 columns,

the maximum intensity for the arrangement of this study is received by the diode located at

the 242nd

row and the 753rd

column. The determination of the reference pixel not only allows

the user to align the equipment correctly but also plays an important role in the development

of the model.

The system uses a commercially available source. The operating voltage can be set between

40 kV and 120 kV. Although an energy spectrum is produced, the dominant X-ray energy is

approximately between the half and the third of the operating voltage measured in keV units.

The production of higher energies demands larger generators that dump heat better. It is

known that only a very small fraction of the incident electron beam is converted to X-rays

and the majority of the energy deposited on the target just heats the anode. The energy

produced by the FlatScan generator is sufficient to fulfill the needs of a vast number of

security applications. The X-rays generated with a 120 kV voltage typically penetrate 29 mm

of steel, which is more than enough for X-ray inspection. The 3.5 mm thick aluminium

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window cuts off photons below 20 keV, which are anyway not useful in X-ray screening. In

general, the generator had a very good performance.

The dimensions of the focal spot were estimated to be 0.092 cm by 0.080 cm for the

horizontal and the vertical dimension respectively. The estimation was based on the

assumption that the number of generated photons per focal spot area is given by a Gaussian

function which seemed to match data better. The finite size of the focus is responsible for the

penumbra regions at the edges of the objects. In terms of resolution the system is close to its

maximum potential. The dimensions of the pixel are 0.080 cm by 0.052 cm and are

comparable to the dimensions of the focal spot, which means that neither the former nor the

latter limits the other

A qualitative analysis of the scattering signal was done. Scattering affects the X-ray system

more than expected. In fact, the real purpose of the use of the wooden block was for elevating

the other test objects rather than studying its radiological effects. However, the piece of wood

introduced a strong scattering signal that affected the outcome significantly. The absorption

model alone cannot simulate adequately the radiography process as its predictions failed

when thick objects were placed next to scattering surfaces. There was a 0.017 and 0.020

difference between the calculations and the experimental data in two arrangements that could

not be explained, as it was larger than the match criterion. That difference was eliminated

when the scattering surfaces of the arrangements were covered by lead. The main

characteristic of the scattering signal is that it is very broad without providing details about

the shape or the actual size of the scatterer. It was found that not only the scatterers that block

the path of the X-ray beam to the screen, but also scattering surfaces that are well off the

active surface of the panel shed scattering light on the screen. The excess signal can reduce

the distinction between objects. Another important parameter is the positioning of the objects.

Given the geometry of the arrangement, scattered X-rays are subjected to further attenuation

by other objects that block their way to the screen.

As far as the dynamic range is concerned, the system performs well. The data is stored in 12-

bit values, which means that the digitation extends from 0 up to 4095. The bit depth allows

the system to distinguish low contrast regions such as a knot inside a chunk of wood.

Material discrimination is another aspect the security industry is interested in. Material

discrimination works up to a point. Beyond this point scattering limits the equipment and the

distinction between the objects becomes impossible, especially when there is a number of

scatterers that shed cumulative light in a region of the screen.

The deliverable of this study is the development of an absorption and a scattering model. The

absorption model gets the input intensity from an open exposure and calculates the

attenuation of known materials by using a discrete energy spectrum. It considers objects as

pixelated planes and predicts the correct projection on the screen given the position of the

screen, the generator and the objects. The model can be used in absorption estimations of

objects of various physical characteristics, such as shape, size and chemical composition. A

simplified scattering model has also been developed. The scattering model is based on the

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assumptions a) that objects are infinitely thin, which means that scattered photons are

generated from the same plane b) the path that the X-rays follow inside the object is always

equal to the actual thickness of the object regardless the path followed in reality and c) the

primary beam is monochromatic. Again, scattering can be estimated for objects of various

physical characteristics.

The sum of the two models results in a good estimation of the irradiation process. The best

match, among experiments involving objects with different physical aspects, is achieved

when a discrete energy spectrum that contains 40, 50 and 60 keV X-rays with weight factors

10%, 20% and 70% respectively, is used in the estimations of the absorption model and a

monochromatic X-ray beam at 20 keV in the estimations of the scattering model. Although

the spectrum of the absorption model is plausible, the 20 keV beam that is used as an

argument in the scattering model doesn’t seem to have a physical interpretation, as the

aluminium window of the generator cuts off the photons of this energy. However, this doesn’t

mean that the model is wrong. It means that this recipe produces the same radiological results

with the actual radiography regardless the physical phenomena that take place in reality. A

slight overestimation in of the scattering signal was also noticed. This can be explained by the

fact that the models do not interact. In reality, the scattered signal is subjected to further

attenuation given the geometry of the arrangement.

The investigation that took place in this study allows the suggestion of changes that can

improve the performance of the system. Although the study does not include the investigation

of the detection system, which definitely plays significant role in the performance, a few safe

conclusions can be extracted.

A smaller focal spot size would improve the resolution. The improvement will be noticeable

only if the pixel size is equal to or smaller than the focal spot. Similar improvement in

resolution can occur the other way around, by replacing the current diodes with diodes of

smaller pixel pitch. Again the effect of the new diodes will be noticeable only if the size of

the focal spot is less than or equal to the size of the pixel.

Regarding the noise fluctuations on top of the signal, the electronic noise is always present

and practically inevitable. Nevertheless, improving the signal to noise ratio could diminish its

effect. The ratio can be improved by detecting more X-rays, thus it depends on the operating

voltage and current combination, the time of scan and the readout capability of the detector.

Finally, the operator should choose a suitable, if possible, place to deploy the equipment

because the surrounding materials introduce new signals that interfere with the original. For

example, the bottom and the sides of the chamber added scattering signal on top of the

primary signal.

4.3 Future Work

Future work includes the unification of the two separate models in order to achieve better

match between the data and the calculations. So far, in the absorption model the objects are

81

divided in several parallel planes each one projecting on the detector plane. At the same time

the objects are considered to be infinitely thin in the scattering model. The next step is to

unify the two models by modifying the code so that every slab of the object produces both an

absorption and a scattering signal.

Further investigation is required on the detection system. An X-ray that reaches the screen

has to pass through the hard case, the aluminium foil and the scintillator before being

detected by the photodiodes. This complicated process was neither examined nor included in

the model. Although, the open exposure is used to provide the primary intensity it is

unknown whether the same physical phenomena occur between an open exposure and an

exposure where objects are irradiated. The use of the lead shield in close proximity to the

scintillator, in order to block scattered X-rays from the materials of the sensor arm, may

interfere with the scintillator. Not only electrons could jump off lead depositing energy in the

detector, but also X-rays that were not detected in the first place could backscatter and be

detected afterwards.

Finally, a study on the optimal conditions between the scan time, the operating voltage and

current and the integration period could be done.

82

BIBLIOGRAPHY

3DX-Ray Ltd, 2014: 3DX-Ray ThreatSpect software, Build version: 2.0.1.0, manufactured in

England.

Berger et al. 2010: XCOM: Photon Cross Section Database (version 1.5). National Institute

of Standards and Technology, Gaithersburg. Accessed 23/6/2014

http://physics.nist.gov/xcom

Blinder S. M. 2009: Klein-Nishina Formula for Compton Effect. Wolfram Demonstration

Project. Accessed 10/12/2014

http://demonstrations.wolfram.com/KleinNishinaFormulaForComptonEffect/

Compton, A.H. 1924: The scattering of X-rays. Journal of the Franklin Institute, 198 (1), pp.

57-72.

Coolidge, W.D. 1915: Hard X-rays. Journal of the Franklin Institute, 180 (4), pp. 492-493.

Coolidge, W.D. 1938: The production X-Rays of very short wave length. Radiology, 30 (5),

pp. 537-543.

Crooks, H. E. 1973: Some aspects of radiographic quality with special reference to image

sharpness. Radiography, 39, pp. 317-327.

Duclos S. J. 1998: Scintillator Phosphors for Medical Imaging, The Electrochemical Society

Interface, 7 (2), pp. 34-38.

Friedman, P. J. and Greenspan, R. H. 1969: Observations on magnification-radiography;

visualisations of small blood vessels and determination of focal spot size. Radiology, 92, pp.

549-577.

Hamamatsu datasheet (2/2014) Photodiode arrays with amplifier. Accessed 10/6/2014

http://www.hamamatsu.com/jp/en/product/category/3100/4005/4126/S8865-128G/index.html

Hietschold, V. 2012: X-Ray imaging. In R. Salzer (ed.), Biomedical imaging: principles and

applications. New Jersey: John Wiley & Sons, pp. 63-96.

Kemp, F. H. and Nichols, A. F. 1958: Focal spot sizes. British Journal of Radiology, 31, pp.

486-488.

Knoll, F.G. 2000: Radiation Detection and Measurements. USA: John Wiley & Sons, Inc.

Kuntke A. H. G. 1957: On the determination of roentgen tube focal spot sizes by pin-hole

camera roentgenography. Acta Radiologica, 47 (1), pp. 55-64.

83

Law, J. L. 1993: Measurement of focal spot size in mammography X-ray tubes. British

Journal of Radiology, 66, pp. 44-50.

Lee et al. 2006: X-ray physics in plastics: Low absorption keeps photon in play. Denver X-

ray Conference (DXC) on Applications of X-ray Analysis, International Centre for

Diffraction Data, Denver.

National Institute of Standards and Technology (17/9/2009) X-ray mass attenuation

coefficients. Accessed 1/4/2014

http://physics.nist.gov/PhysRefData/XrayMassCoef/chap2.html

R Core Team, 2013: R: A language and environment for statistical computing. R Foundation

for Statistical Computing, Vienna. Accessed 8/4/2014 http://www.R-project.org/

Rao, G. U. V. 1971: A new method to determine the focal spot size of X-ray tubes. American

Journal of Roentgenology, 111 (3), pp. 628-633.

Robertson, C. W. 1958: Precise Measurements of Focal Areas in Diagnostic X-ray Tubes and

Their Applications in Tube Development. British journal of radiology, 31, pp. 489-491.

Russo P. and Mettivier G. 2011: Method for measuring the focal spot size of an x-ray tube

using a coded aperture mask and a digital detector. Med Phys, 38 (4), pp. 2099-2115.

Seibert, J. A. 2004: X-Ray Imaging Physics for Nuclear Medicine Technologists, Part 1:

Basic Principles of X-Ray Production. Journal of Nuclear Medicine Technology, 32 (3), pp.

139-147.

Seltzer, S.M. and Hubbell, J.H. 1995 (14-16 April): 45 Years (1950-1995) with X-Ray

Interactions and Applications. 51st National Meeting of the Japanese Society of Radiological

Technology, Nagoya, Japan.

Spiegler, P. and Breckenridge, W. C. 1972: Imaging of focal spots by means of the star test

pattern. Radiology, 102, pp. 679-684.

Threatspect datasheet Advanced software for x-ray inspection. Accessed 23/6/2014

http://www.3dx-ray.com/products/software-products/threatspect