A Compton Spectrometer for 30-150 keV photons

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A Compton Spectrometer for 30-150 keV photons

Coen Pijpker

Department of Physics University of Groningen

A thesis submitted for the degree of

Bachelor of Science

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Acknowledgements

And I would like to acknowledge:

Dr. Marc-Jan van Goethem and prof. dr. Sytze Brandenburg for their guidance.

Ir. Roel Kierkels for his patience and time during the measurements at UMCG.

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Abstract

This report describes the building of a Compton spectrometer in order to measure the energy spectrum of a diagnostic radiographic device.

High photon fluxes in CT scanners are the biggest problem in de- termining the spectrum shape. By building a spectrometer based on the Compton scattering principle it is possible to measure the spectra by attenuating the photon flux. The spectrum measured must be reconstructed by algorithms given in this report. Other applica- tions include measuring of the influence of biological materials on the measured spectrum.

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List of Figures

2.1 Naming conventions in atomic transitions, which produce characteristic x-rays. The big letter describes the shell which is empty, the Greek letter describes from which shell the electron came which fills the hole and the number describes the different angular momentum states. . . 5 2.2 Schematic of a typical x-ray tube. The K stands for the cathode,

the A for anode, the C for cooling liquid, U_h is the heating voltage and U_a is the accelerating voltage . . . 6 2.3 Image showing the normal bremsstrahlung curve and the final curve

which arises from beam hardening. The final spectrum also contains a characteristic x-ray in this image. . . 7 2.4 Absorption of 2mm Aluminum as a function of energy . . . 7 2.5 A photon Compton scattering of a particle, changing direction and

losing a bit of energy to the recoiling electron. . . 8 3.1 Horizontal cross section of the apparatus (not to scale), the black

blocks are lead collimators and shielding material, the light yellow is PVC tube, the orange is a cylindrical PVC block in which a cavity is milled out for the detector. The blue represents the detector and the red represent the active part of the detector. The grey bar at the left of the figure represents the scatterer. . . 10 3.2 Thickness of lead required to attenuate the flux by a factor 10⁻⁴ . 12

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LIST OF FIGURES

3.3 Set-up at UMCG showing the orthovolt x-ray tube positioned above the collimator hole in the apparatus. The yellow square is the apparatus with the detector inside. The red square shows the field collimator limiting the irradiation area. The green square is the x-ray tube of the orthovolt machine and the blue square shows the robotic positioning arm. . . 15 3.4 Overview of the set-up at UMCG showing the apparatus (yellow

square) totally wrapped in a lead coat and the multi channel analyzer (purple square) in the front of the photo. The x-ray tube is at the location of the green square, the red block is where the field collimator is and the blue square is where the robotic positioning arm is located. . . 16 5.1 Calibration spectra for different target materials showing two char-

acteristic peaks which have specific energies. . . 21 5.2 Graphs showing the two calibration curves for different days. The

difference between the two plots is very small. . . 22 5.3 Graph showing the original, Compton scattered and zeroth-order

reconstructed spectrum as simulated with ROOT . . . 24 5.4 Graph showing the original, zeroth-order and first-order reconstructed

spectrum as simulated with ROOT. The first-order reconstructed shows a better agreement between the original and reconstructed spectrum. . . 25 5.5 Graphs showing the difference in signal strength between a piece of

lead placed on the floor directly under the x-ray tube and no piece of lead under the x-ray tube. The reduce in background radiation is apparent. . . 26 5.6 Graph showing the spectrum with lead shielding (purple line) and

without shielding (red line). The resulting attenuation of the background signal is very large. . . 27 5.7 Graph showing the original direct characteristic peaks of lead pro-

duced in the second collimator . . . 28

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LIST OF FIGURES

5.8 Result of the first Compton scattered bremsstrahlung measurement, produced with one collimator and with two millimeter pinholes, measured for ten minutes. . . 30 5.9 Result of the second Compton scattered bremsstrahlung measure-

ment, produced with one collimator and with enlarged pinholes, measured for ten minutes. . . 31 5.10 Graph showing figure 5.8(b) rebinned. The content of four bins is

put together into one bin, thus reducing the statistical noise . . . . 32 5.11 Graph showing figure 5.9(b) rebinned. The content of four bins is

put together into one bin, thus reducing the statistical noise . . . . 32 5.12 Graph showing the reconstructed spectrum starting from the spec-

trum in figure 5.8(b) using the modified zeroth-order reconstruction algorithm as mentioned in the text. . . 34 5.13 Graph showing the reconstructed spectrum starting from the spec-

trum in figure 5.8(b) using the first-order reconstruction algorithm as discussed in 4.2 . . . 34 5.14 Graph showing the reconstructed spectrum starting from the spec-

trum in figure 5.9(b) using the modified zeroth-order reconstruction algorithm as mentioned in the text. . . 35 5.15 Graph showing the reconstructed spectrum starting from the spec-

trum in figure 5.9(b) using the first-order reconstruction algorithm as discussed in 4.2 . . . 35 A.1 SP001: 100 kV accelerating voltage without the scatterer inside

the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter and the x-ray tube was positioned above the apparatus. The measurement was aborted before five minutes were done. . . 38 A.2 SP002: 100 kV accelerating voltage without the scatterer inside

the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter in combination with a filter consisting of 0.35 mm Al and 1.5 mm Cu. The x-ray tube was positioned above the apparatus. . . 39

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LIST OF FIGURES

A.3 SP004: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. A slab of lead in front of the first collimator and the x-ray tube positioned 1 meter away from the apparatus. . . 40 A.4 SP005: 100 kV accelerating voltage without the scatterer inside the

apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. A slab of lead in front of the first collimator and the x-ray tube positioned 1 meter away from the apparatus. A slab of lead was also placed on a chair right beneath the x-ray tube. . . 40 A.5 SP006: 100 kV accelerating voltage without the scatterer inside the

apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. A slab of lead in front of the first collimator and the x-ray tube positioned 1 meter away from the apparatus. Two slabs of lead were placed: one on the chair and one directly under the chair. Both are directly underneath the x-ray tube. . . 41 A.6 SP007: 100 kV accelerating voltage without the scatterer inside the

apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. A slab of lead in front of the first collimator and the x-ray tube positioned 1 meter away from the apparatus. A slab of lead was also placed on the floor directly under the x-ray tube. . 41 A.7 SP010: 100 kV accelerating voltage without the scatterer inside the

apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 1.5 mm thick lead and the x-ray tube was 1 meter moved away from the apparatus. . . 42 A.8 SP011: 100 kV accelerating voltage without the scatterer inside

the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 1.5 mm thick lead except for the entry collimator. The x-ray tube was positioned directly above the entry collimator. . . 43

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LIST OF FIGURES

A.9 SP013: 100 kV accelerating voltage with the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus is wrapped in a coat of lead except for the entry collimator and is placed directly underneath the x-ray tube. . . 43 A.10 SP014: 100 kV accelerating voltage without the scatterer inside

the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 1.5 mm thick lead except for the entry collimator. The x-ray tube was positioned directly above the entry collimator. Instead of three collimators between the scatterer and the detector only one was used and placed directly in front of the detector. . . 44 A.11 SP017:See SP016 . . . 44 A.12 SP018: 100 kV accelerating voltage with the scatterer inside the

apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 1.5 mm thick lead except for the entry collimator. The x-ray tube was positioned directly above the entry collimator. Instead of three collimators between the scatterer and the detector only one was used and placed directly in front of the detector. Both of the collimators were drilled out to enlarge the pinhole. The measurement was aborted after two and a half minute. . . 45 A.13 SP021: 100 kV accelerating voltage without the scatterer inside

the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 4.5 mm thick lead except for the entry collimator. The x-ray tube was positioned directly above the entry collimator. The collimator that was inside the tube was moved away from the scatterer towards the detector. . . 46 A.14 SP022: The same set-up as measurement SP021 only with the scat-

terer inside the apparatus. . . 46

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List of Symbols

µ Linear attenuation coefficient

µ_s(E_γ) Linear attenuation coefficient of the incident photon in the scatterer µ_s(E_γ⁰) Linear attenuation coefficient of the scattered photon in the scatterer Ω Solid angle

∆Ω Solid angle integrated over the photon energy Φ The angular-component in cylindrical coordinates

φ_{0, E} The zeroth-order approximation of the photon flux at the position of the scatterer

φ_{1, E} First-order approximation of the photon flux at the position of the scatterer φ_E(E_γ) Photon flux of the x-ray tube at the place of the scatterer

ρ The radial-component in cylindrical coordinates σ Compton scattering cross section

θ Angle between incident photon and scattered photon θ_max Maximal scattering angle able to reach the detector θ_min Minimal scattering angle able to reach the detector

A(E_γ, E_γ⁰) Attenuation of the incident and scattered photon in the air and in the scatterer

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LIST OF FIGURES

c Speed of light

E_γ Incident photon energy

I Intensity of the x-ray beam after passing through an object of thickness x I₀ Intensity of the x-ray beam before passing through an object

l Half the effective length of the scatterer m_e Electron rest mass

n Electron density in the scatterer

N_e Amount of electrons inside the scatterer

NE(E_γ⁰) Amount of compton scattered photons with energy E_γ⁰ P (E_γ, θ) Incident photon energy divided by scattered photon energy r The scatterer radius

r_e Classical electron radius = 2.8179402894 ∗ 10⁻¹³cm² T Mean kinetic energy of the scatterer electrons

X Distance traveled inside the scatterer before scattering by a photon x distance traveled through a material

X_c Distance traveled by a scattered photon inside the scatterer z The z-component in cylindrical coordinates

∆G(E_γ⁰) Maximal geometrical peak broadening given in keV E_γ⁰ Scattered photon energy

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Chapter 1 Introduction

The Universitair Medisch Centrum Groningen (UMCG) requested a method to determine the shape of the x-ray spectrum of their CT-scanners because one of their CT-scanners did not show a good quality image. One possibility was that the x-ray tube that is used in the CT-scanner now irradiated a slightly different spectrum which messed up the imaging. By measuring the incident spectrum, it is possible to see if the x-ray tube is operating properly and if the spectrum does not change over time. Besides quality control also the influence of biological material on CT spectra can be measured. In regular CT-scanners the intensity over all energies is added into one value which describes the total attenuation by the material between the source and the detector. When using a spectrometer, a more detailed analysis can be made over all different energies, which allows greater detail.

In the 1980’s and 1990’s scientists were searching for an easy and compact solution to measure the photon energy spectrum of an x-ray tube. There is however a problem with the x-ray tubes in diagnostic x-ray machines; they had a very high photon flux, which a detector cannot handle. This means that the only way to measure these x-ray spectra was by either increasing the distance between the detector and the source or by lowering the voltage or current. In CT-scanners the distance between the patient table and the x-ray source is not large enough to sufficiently attenuate the photon flux. The x-ray tubes have to be removed and tested elsewhere, which is a difficult and time-consuming job. Decreasing the operating voltage or current distorts the shape of the spectrum and thus

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does not give a good representation of the spectrum at diagnostic conditions. In 1976 Yaffe et al. developed a new method of spectroscopy by means of Compton scattering. They placed a thin Lucite disk at an angle of 45 degrees to the x-ray beam and placed a detector under 90 degrees with respect to the x-ray source. They measured the spectrum and reconstructed the incoming spectrum using the Klein-Nishina differential cross section, which describes the Compton scattering process. The problem with this method is the fact that peaks tended to broaden. In 1982 Carlsson et al. analyzed the broadening by means of a so- called Compton profile, which is a way to describe the velocity distribution of the electrons in the scattering material. Matscheko & Ribberfors (1987) utilized the theory of Carlsson to write an advanced deconvolution algorithm which improved the resolution around characteristic peaks.

The goal of this research project is to produce an apparatus which implements Compton scattering to measure Compton scattered spectra of an x-ray tube. The spectra that are measured need to be reconstructed to find the relative flux of the x-ray tube. It is not important at the moment to measure the absolute flux, but to have a good representation of the overall shape of the spectrum.

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Chapter 2 Theory

2.1 X-Rays

X-rays were discovered by W.C. R¨ontgen in the late 19th century. He observed an until then unknown type of radiation which penetrated materials opaque to visible light. The radiation he saw was produced when an electron beam was shot on a metal or alloy target. The new form of radiation named x-rays is produced by interactions with electrons and can have any energies.

R¨ontgen discovered the penetrating ability when he saw a photographic plate which changed shades. After this discovery he took the first x-ray of his wife showing the bones in her hands and the rings she wore. This discovery quickly led to the production of the first diagnostic x-ray machine which was made in 1896. Within half a century diagnostic radiography skyrocketed and multiple devices were developed. A few examples of these diagnostic devices are: projection radiography devices, fluoroscopy devices and computed tomography. In this section the different x-ray production methods are explained, followed by the section describing a basic lay-out of an x-ray tube and finally the interactions of x-rays with matter are given in the last section of this chapter.

2.1.1 Bremsstrahlung

Bremsstrahlung is composed of the German words bremms and strahlung, one meaning break and the other radiation. So bremsstrahlung is radiation which is

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2.1 X-Rays

produced by deceleration or acceleration of a charged particle.

When an electron enters the vicinity of a nucleus it can be deflected by the nucleus it’s electric field or by a collision. The electron loses energy due to this deceleration and a bremsstrahlung photon is emitted. Because the electron is not bound, a continuous spectrum of photons can be emitted. The bremsstrahlung probability has a _E¹ dependence and the maximum bremsstrahlung photon energy is limited by the kinetic energy of the electron.

The shape of the bremsstrahlung spectrum as described above is valid for the scattering of monochromatic electrons of one nucleus. To describe bremsstrahlung produced in a material we can assume it consists of layers of one atom thick sheets of material. Each one of these sheets can be treated as the aforementioned case of one electron and one atom. For the first sheet the incoming electrons have a kinetic energy E. For the second sheet however the electrons have traveled through one sheet of atoms and the electrons have lost energy. The energy lost of electrons in a material is mostly due to process other than bremsstrahlung. In the case of medical x-ray tubes only one percent of the energy transferred is emitted as bremsstrahlung. The energy loss in the first sheet means that the second sheet of atoms has the same distribution as the first sheet, but is compressed toward lower energies. If we now add all these probability distributions of the consecutive sheets, we obtain the total bremsstrahlung distribution. The resulting distribution has a slope which drops much faster than the one atom case.

2.1.2 Characteristic X-Ray lines

When fast electrons hit a material there is a possibility that electrons in the target nuclei are ejected from the K,L or M shell. An electron in a higher energy state will spontaneously decay to the empty lower energy state where the electron was ejected from. The energy that is released by this electron moving to a lower energy state can be used to produce a photon with this specific energy, named a characteristic x-ray. In figure (a)¹ & figure 2.1(b)² can be seen how the names

1Figure 2.1(a): http://www.mwit.ac.th/ physicslab/hbase/quantum/imgqua/xterm.gif

2Figure 2.1(b): http://en.wikipedia.org/wiki/File:Copper K Rontgen.png

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2.2 X-ray tubes and spectra

of the characteristic transitions are derived. If the electron decays to the K- shell it is called a K x-ray. If the electron moves from the L-shell to the K-shell it’s called a Kα transition and if it decays from the M-shell to the K-shell it is called a Kβ transition. The Kα and Kβ peaks are also split depending on the spin-orbit interaction states. For this report however only the K_α and K_β are interesting, the L peaks do not have enough energy to fall into our region of interest. The probability of the transitions from each higher energy state to the empty shell is fixed. This means that the relative intensities of the characteristic peaks will always have a fixed ratio. This relative intensity can however differ when measuring due to the difference in absorption cross section for the different photon energies.

(a) Different characteristic transitions in an atom

(b) Characteristic Kαand Kβ lines in Copper

Figure 2.1: Naming conventions in atomic transitions, which produce characteristic x-rays. The big letter describes the shell which is empty, the Greek letter describes from which shell the electron came which fills the hole and the number describes the different angular momentum states.

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2.2 X-ray tubes and spectra

Figure 2.2: Schematic of a typical x-ray tube. The K stands for the cathode, the A for anode, the C for cooling liquid, Uh is the heating voltage and Ua is the accelerating voltage

2.2 X-ray tubes and spectra

In figure 2.2¹ a schematic overview of a typical x-ray tube is shown. The x-ray tube consists of an anode and a cathode in a vacuum chamber. The cathode is heated to high temperatures, which allows electrons to be emitted easier. A voltage difference is applied between the anode and cathode to accelerate the emitted electrons from the cathode toward the anode. The electrons acquire a kinetic energy equal to the acceleration voltage. The anode usually consists of a metal or an alloy, which for medical uses is mostly tungsten or molybdenum. The target usually has a high Z value in order to create more photons than possible with a low Z material. When the electrons hit the plate of metal a spectrum is produced consisting of bremsstrahlung x-rays and characteristic x-rays. The produced x-rays are emitted through a beryllium window which absorbs the low energy end of the spectrum more than the higher end of the spectrum. In medical uses there is often a filter applied to attenuate the lower end of the spectrum even more. In figure 2.4 the absorption of a 2mm aluminum filter is shown, the low energetic x-rays are absorbed more than the higher energetic photons. This effect, as can be seen in figure 2.3², is called spectrum hardening and is widely used in diagnostic and therapeutic radiography because the low energetic photons can’t penetrate very far in the tissue. This means that the quality of the treatment will

1Figure 2.2: http://en.wikipedia.org/wiki/File:Roentgen-Roehre.svg

2Figure 2.3: http://www.e-radiography.net/radsafety/rad physics7.gif

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2.3 X-ray Interactions

not be affected by taking these low energetic photons away, while the acquired dose is decreased.

Figure 2.3: Image showing the normal bremsstrahlung curve and the final curve which arises from beam hardening. The final spectrum also contains a characteristic x-ray in this image.

Figure 2.4: Absorption of 2mm Aluminum as a function of energy

2.3 X-ray Interactions

Scattering is one of the interactions which x-rays can have with matter. The pro- cesses can be ranked according to the photon energy at which the most important:

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Figure 2.5: A photon Compton scattering of a particle, changing direction and losing a bit of energy to the recoiling electron.

photo-electric effect, Compton scattering and pair production. The photo-electric effect describes the process of an atom absorbing a photon to get in the excited state. Pair production can occur in the neighborhood of an atom when the incoming photon has an energy larger than 1,022 MeV in which case an electron and a positron are produced. The main process however is Compton scattering, therefore we will treat it in a little more detail. In figure 2.5¹ can be seen how a photon and an electron interact and an amount of energy is transferred from the photon to the electron. The photon’s direction is changed and the electron recoils under another angle to conserve momentum. Considering the conservation of energy and momentum one can derive the shift in energy between the incoming and the scattered photon to be the following,

E_γ⁰ = Eγ× P (Eγ, θ) = Eγ

1 + _m^E^γ

ec² (1 − cos(θ)) (2.1) where E_γ is the incoming X-ray energy, E⁰_γ is the scattered x-ray energy and θ is the angle between the incoming and scattered photon.

The differential Klein-Nishina cross section describes the probability that an incoming photon is scattered over a certain angle,

dσ dΩ = 1

2r_e²(P (E_γ, θ))² P (E_γ, θ) + P (E_γ, θ)⁻¹− 1 + cos²(θ)

(2.2)

1Figure 2.5: http://hyperphysics.phy-astr.gsu.edu/HBASE/quantum/imgqua/compton.gif

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where _dΩ^dσ is the Klein-Nishina differential cross section in ^cm_sr². Equation 2.1 shows that for lower photon energies the Compton shift is less than at higher photon energies. This means that we can here assume that the incoming photon energy is almost equivalent to the outgoing energy, resulting in a coherent contribution to the spectrum. Matscheko & Ribberfors (1989) provides a reconstruction algorithm for lower photon energies, however the difference between the first-order and second-order is negligible if you are measuring relative photon distributions. The energy for which the coherent contribution becomes important is said to be below 20 keV according to Matscheko & Ribberfors (1989).

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Chapter 3 Design and Set-up

3.1 Apparatus

Figure 3.1: Horizontal cross section of the apparatus (not to scale), the black blocks are lead collimators and shielding material, the light yellow is PVC tube, the orange is a cylindrical PVC block in which a cavity is milled out for the detector. The blue represents the detector and the red represent the active part of the detector. The grey bar at the left of the figure represents the scatterer.

In figure 3.1 the schematic of the apparatus is shown. The schematic shows a few important components: shielding, collimators, scatterer and detector. The

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3.1 Apparatus

shielding and the scatterer will be discussed in the subsections below. The collimators consist of a 5mm thick lead circle with a 2mm pinhole in the center.

There are two reasons for this: firstly by narrowing the solid angle the photon count in the detector will be attenuated, secondly the uncertainty in the angle θ will be less. The first collimator is directly above the scatterer in 3.1 and selects a narrow part of the x-ray tube flux to hit the scatterer. The x-rays that reach the scatterer are scattered over all solid angles, therefore a second, third and fourth collimator are placed. The collimators select only the photons scattered under a ninety degree angle with respect to the incoming beam. It is however never possible to select purely the ninety degree angle, since the collimators have a finite pinhole size. The finite size of the pinhole creates a broadening in the characteristic peaks. This is due to the fact that the energy shift of the scattered photon is different for angles other than ninety degree. The broadening caused by this so called geometrical broadening can be described by the following formula:

∆G(E_γ⁰) = E_γ 1

1 + _m^E^γ

ec² (1 − cos(θ_min))− 1 1 + _m^E^γ

ec² (1 − cos(θ_max))

!

(3.1)

where θ_min is the minimal scattering angle which can reach the detector and θ_max is the maximal scattering angle able to reach the detector and ∆G(E_γ⁰) is the maximum energy broadening due to the apparatus design. This is one of the sources of peak broadening, the other sources are respectively: the Compton profile and the detector itself. The Compton broadening describes the energy broadening due to the distribution of the velocities, often represented by the Compton profile, of the electrons in combination with the Doppler shift due to these velocities. The detector energy broadening is due to the energy resolution of the detector.

The detector is placed inside a cylindrical PVC block which fits just in the outer tube in which a square cavity is milled out. In this cavity the detector is placed to keep it stable and centered to simplify aligning. The detector is placed at a certain distance, this also is due to geometrical broadening and the expected count rate.

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3.1 Apparatus

Figure 3.2: Thickness of lead required to attenuate the flux by a factor 10⁻⁴

3.1.1 Shielding

The detector consists of a highly sensitive cadmium-tellurium semiconductor crys- tal. Because the x-rays that hit the scatterer are scattered over all angles, shielding is required to keep the background signal as low as possible and to select a small solid angle at a scattering angle of ninety degrees. The best way to do this is by placing a material between the detector and the source of the x-rays which has a high density and a high Z value. The transmittance of a material is characterized by its linear attenuation coefficient. The ratio of intensity after attenuation and before is given by the following expression:

I

I₀ = e^−µx (3.2)

where I is the intensity after passing through the material, I0 is the intensity before going through the material, µ is the linear attenuation coefficient and x is the thickness of the material through which the x-rays passed. Because photon per second yields in the order of 10⁴ are expected, attenuation of a factor 10⁻⁴ is sufficient. A good candidate material for this shielding is lead, because it’s easy obtainable and is one of the best shielding materials due to its high density and Z value of eighty-two. From figure 3.2 we can deduce the thickness of material needed to reduce the intensity to about one count per second.

One problem of shielding with lead however is the characteristic x-rays produced

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3.1 Apparatus

when high energy x-rays hit the lead. If the x-ray incident on the lead has an energy higher than 88 keV, which is the K-edge of lead, the electron in the K-shell will be ejected. An electron in a higher energy state will decay to this empty state and produce a characteristic x-ray. The characteristic x-rays that are produced are produced in the first few layers of the lead in all directions. This means that these characteristic x-rays will also have to travel through the rest of the lead, before reaching the detector. By traveling through the remaining thickness of lead, the intensity will be sufficiently attenuated. Some x-rays will be produced at the edges of the collimator pinholes, which can reach the detector. However this background signal can be suppressed by placing multiple collimators.

3.1.2 Scatterer Material

The scatterer has a few parameters which are important for the application which is described in this report. First of is the cross section for the photo-electric effect, which determines the absorption of the material. For low Z materials this cross section is much lower than for higher Z materials, for which it is the dominating photon interaction. Besides a low cross section for the photo-electric effect, also the cross section of coherent scattering decreases with decreasing Z. This is because the coherent differential cross section depends quadratically on the atomic form factor which is lower for lower Z materials. The incoherent cross section however increases with lower Z material. This means that Compton scattering will mostly dominate the shape of the spectrum especially for higher energy x-rays.

Finally the choice of the scatterer with a low Z means that the mean velocity of the electrons is lower than with a high Z material, thus narrowing the Compton profile which in turn reduces the peak broadening. So in choosing a scatterer material plastics are a good choice due to the combination of carbon, oxygen and hydrogen atoms which all have low Z values. Lucite in particular is very suitable because it can be produced very cheaply and has a higher purity level than most other plastics.

The dimensions of the scatterer determine the photon flux and the angular uncertainty of the scatterer. For our application the length of the scatterer is irrelevant, because only a small section of it is irradiated by the incoming beam and only a

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3.2 Experimental Set-Up at UMCG

small part is ‘looked’ at by the detector. This means that the most obvious way to increase photon flux and at the same time decrease resolution is by increasing the scatterer radius.

3.2 Experimental Set-Up at UMCG

In figure 3.3 the set up at UMCG is showed, where you can see the orthovolt x-ray tube above the apparatus. The orthovolt x-ray tube is used for irradiations of surface tumors and has a higher intensity than a CT scanner does, however it is not used as often as a CT-scanner and therefore more convenient to start measurements. Figure3.4shows the overview of the set-up. The detector is inside the tube and is connected to a multi-channel analyzer (MCA) which counts x- rays and sorts them by their energy. This MCA is connected to a laptop which is inside the irradiation area and is controlled by a laptop in the control room using a remote desktop connection.

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Figure 3.3: Set-up at UMCG showing the orthovolt x-ray tube positioned above the collimator hole in the apparatus. The yellow square is the apparatus with the detector inside. The red square shows the field collimator limiting the irradiation area. The green square is the x-ray tube of the orthovolt machine and the blue square shows the robotic positioning arm.

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Figure 3.4: Overview of the set-up at UMCG showing the apparatus (yellow square) totally wrapped in a lead coat and the multi channel analyzer (purple square) in the front of the photo. The x-ray tube is at the location of the green square, the red block is where the field collimator is and the blue square is where the robotic positioning arm is located.

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Chapter 4 Reconstruction and Deconvolution

4.1 Zeroth-order reconstruction

Matscheko & Ribberfors (1987) derived a formula for the reconstruction of the incoming spectrum which will be treated in short detail below. If we want to calculate how the spectrum of the x-ray tube looks like at the place of the scatterer, we first need to know how many photons are scattered and in what fashion.

This means we first assume we know the incoming flux φ and then reverse the equation to find out φ. The amount of photons that arrive at the detector with energy E_γ⁰ in an energy interval d(E_γ⁰) is given by:

N_E(E_γ⁰) d(E_γ⁰) = φ_E(E_γ) d(E_γ) n dσ dΩ

Z +l

−l

dz Z r

0

ρ dρ

× Z 2π

0

dΦ e^(−µ^s^(E^γ^)X−µ^s^(E^γ⁰^)X^c⁾∆Ω

(4.1)

where N_E(E_γ⁰) is the amount of Compton scattered x-rays with energy E_γ⁰ reaching the detector in an energy interval d(E_γ⁰). φ_E(E_γ) is the flux of photons with energy E_γ in a energy interval d(E_γ), n is the electron density of the scatterer and _dΩ^dσ is the Klein-Nishina differential cross section. l is half the effective of the scatterer, r is the radius of the scatterer, Φ is the angle over which the photon is scattered inside the scatterer, ρ the radius and z the length in

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4.2 First-order reconstruction

cylindrical coordinates. X and X_care the lengths traversed by the x-ray through the medium before and after scattering, which are multiplied by µ_s(E_γ) and µs(E_γ⁰) respectively which are the attenuation coefficients in Lucite. Lastly ∆Ω is the solid angle of the detector to the scatterer. The integral describes the overlap between the incident beam and the scatterer, which multiplied by the electron density will give the total amount of scattering electrons. After filling all the information and making some assumptions we arrive at the following expression for the flux of the beam before scattering:

φ_{0, E} = N_E(E_γ⁰) N_e ¹₂ r_e²A(E_γ, E_γ⁰)_E0

γ

Eγ + ^E_E^γ0

γ − sin²(θ)

∆Ω

(4.2)

where φ_{0, E} is the zeroth order approximation of the x-ray flux of the incoming x- rays before hitting the scatterer, r_e is the classical electron radius and A(E_γ, E_γ⁰) is the attenuation function which describes the attenuation of the x-ray before and after scattering in the Lucite rod and the air. For a detailed derivation of this formula see (Matscheko & Ribberfors, 1987, Appendix 1 & 2).

4.2 First-order reconstruction

In the derivation of equation4.2the assumption has been made that the variation in flux for different energies is relatively small. This is however incorrect around characteristic peaks where the energy derivative of the flux is quite large. Around these peaks we cannot assume that the flux is constant and thus it cannot be taken out the integral over all electron momenta. When all these factors are taken into account we arrive at the following equation for the first-order approximation of the photon flux:

φ_{1, E}(E_γ) = φ_{0, E}(E_γ) − T 3m_ec²(E_γ

E_γ⁰)²× d²φ_{0, E}

d(E_γ)² (E_γ)²+ (E_γ⁰)²− 2E_γE_γ⁰cos(θ) +2dφ_{0, E}

d(E_γ)(E_γ− E_γ⁰cos(θ))

(4.3) where φ_{1, E}(E_γ) is the first-order approximation for the incident photon flux before hitting the scatterer and T is the mean kinetic energy per electron of the

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4.2 First-order reconstruction

scatterer. This deconvolution algorithm should be used only at an area where characteristic peaks are present and only deconvolutes the broadening due to the Doppler shift of the electrons. The geometrical broadening is much smaller and thus can be neglected compared to Compton broadening. The fact that the algorithm mentioned above can only be used around characteristic peaks is because this algorithm requires a fast changing photon flux, which is only around characteristic peaks. Usage outside these intervals would lead to the amplification of the statistical noise on the spectrum, since these derivatives are usually far greater than the derivative of the spectrum. To see the full derivation of this first order approximation see (Matscheko & Ribberfors, 1987, Appendix 3).

The two reconstructions mentioned above are however not exactly accurate at lower photon energies. If the photon energy is lower than about 20 keV, according to Matscheko & Ribberfors (1989), the coherent contribution becomes more important. However the graphs in the article show that effects due to the coherent contribution on the reconstructed spectrum are small.

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Chapter 5 Results

5.1 Calibration

For the calibration of our detector we used a variable x-ray source powered by Am- 241. The Americium source shoots alpha particles at one of the 6 targets, which in turn produces characteristic x-rays (see 2.1.2). Because we know at which energies these characteristic x-rays are emitted we can find a linear equation which relates the bin numbers of the detector to the energy in keV. The 6 targets are copper, rubidium, molybdenum, silver, barium and terbium. All of these elements have K_α and K_β lines which gives us twelve peaks to calibrate with.

Figure 5.1 shows the calibration spectra of silver and terbium. In both spectra the largest peaks are the characteristic K_α,1 and K_α,2 peaks. The other peaks in the spectrum are produced either by the other metal targets or by impurities in the target material.

The variable x-ray source was however not available at UMCG. So to calibrate Day Parameter a Parameter b Correlation coefficient r

Day one 8.096 × 10⁻² 0.9277 0.9999245 Day Two 8.076 × 10⁻² 1.1804 0.999925 Difference 2.0 × 10⁻⁴ 0.2527

Table 5.1: Calibration Parameters for data measured on two different days. The parameters a en b come from the function y = a × x + b

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5.1 Calibration

(a) Silver

(b) Terbium

Figure 5.1: Calibration spectra for different target materials showing two characteristic peaks which have specific energies.

the equipment either the characteristic peaks in the spectrum must be used or an early defined calibration must be used. In order to judge if the calibration of the detector is stable enough to allow use without recalibration at the hospital a calibration was made with one day’s difference. Below in table 5.2 the results of the two measurements is given. You can clearly see a difference between the two days of about two bins. Table 5.1 and figure 5.2 show the two calibration curves and data, which show a very tiny difference except for a 0.25 keV offset in

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5.1 Calibration

the b parameter. This means that the calibration can be used on the next day without too much problem. This means that you can calibrate by using just one or two characteristic peaks and finding the difference in parameter b between the calibration done at the KVI and the UMCG.

Accuracy in the calibration can also decrease if the detector is operated at room

Figure 5.2: Graphs showing the two calibration curves for different days. The difference between the two plots is very small.

temperature. By cooling the detector to around 220 K the dark current is lowered and the resolution of the detector is increased. When operating the Peltier unit which cools the detector, the detector will reach the target temperature after about ten to twenty seconds. Besides the detector being sensitive to temperature difference, also the electronics react to temperature.

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5.2 Simulation and Reconstruction of artificial spectrum

Element Peak energy Bin centroid day 1 Bin centroid day 2

Rb K_α 13.37 156.53 153.57

Rb K_β 14.97 175.55 173.07

Mo K_α 17.44 203.65 201.02

Mo K_α 19.63 230.18 227.63

Ag K_α 22.10 259.35 256.88

Ag K_α 24.99 295.03 292.74

Ba K_α 32.06 382.97 381.00

Ba K_α 36.55 438.90 436.53

Tb K_α 44.23 537.76 535.80

Tb K_α 50.65 614.38 613.00

Table 5.2: Characteristic peak energies and bin centroids measured on two different days

5.2 Simulation and Reconstruction of artificial spectrum

To test the reconstruction and deconvolution algorithms given in chapter 4, a series of simulations has been made. A GEANT-4 simulation of the scattering of a monochromatic beam with energy of 100 keV was performed. A simplified down version of the apparatus was recreated in this simulation to see how the peak broadened with this set-up. The value for the FWHM (Full Width at Half Maximum) was used to partly account for the geometrical broadening and effects due to electron velocities.

First a bremsstrahlung spectrum was made with characteristic peaks superim- posed on the spectrum, the heights of these peaks were determined by their emission probability ratios. The spectrum was Compton scattered by shifting the energies using formula2.1 and after that the characteristic peaks were broadened using a Gaussian peak profile with the FWHM from the simulation. The Compton scattered spectrum was then reconstructed using the zeroth-order reconstruction 4.2 with some details let out which are the following: The amount

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5.2 Simulation and Reconstruction of artificial spectrum

of electrons in the scatterer, the attenuation in the scatterer and the air, the solid angle of the detector and the detector response function. These details do affect the spectrum, however they also were not used in the simulation. To create a better simulation these parameters must be taken into account. Figure 5.3shows that the zeroth-order reconstruction works and has exactly the same shape as the original spectrum has, with the exception of lower and broadened peaks.

To increase this resolution around the characteristic peaks the deconvolution algorithm or first-order reconstruction algorithm discussed in section 4.2 must be used. This reconstruction algorithm has no parameters that are neglected and assumes a mean kinetic energy of 0.111 keV for Lucite as given by Matscheko &

Ribberfors (1987). Figure 5.4 shows a better resolution around the K_α and K_β peaks. It is possible to discern the difference between the K_α1 and K_α2 peaks.

The Kβ peaks however are too close together to discern, this is because there is geometrical broadening.

Figure 5.3: Graph showing the original, Compton scattered and zeroth-order reconstructed spectrum as simulated with ROOT

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5.3 Measurements performed at UMCG

Figure 5.4: Graph showing the original, zeroth-order and first-order reconstructed spectrum as simulated with ROOT. The first-order reconstructed shows a better agreement between the original and reconstructed spectrum.

5.3 Measurements performed at UMCG

The measurements at the UMCG showed a large amount of background radiation at first (5.3.1). After resolving the issues with this background signal, which was due to insufficient shielding around the detector, a couple of spectra were detected which were identified as Compton scattered bremsstrahlung spectra presented in section 5.4. These measurements were made with only one collimator, because the alignment of the collimators was not good due to the shifting of the collimators with respect to the inner tube on which they were mounted. Because the count rate was not sufficient—see subsection (5.3.2)—the collimator pinholes were drilled out to allow a greater solid angle to reach the detector. The collimator was also placed closer to the scatterer to increase the count rate and better align the scatterer and collimator, this produced characteristic lines in the collimator which showed up in the spectrum(5.3.3). The measurements which were important for making the apparatus work are all given below, for all graphs see appendixA. All measurements were performed with the orthovolt x-ray machine, which had an accelerating voltage of 100 kV , and lasted for 500 MU or 5 min-

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utes unless indicated otherwise. Between the x-ray tube and the apparatus a 2.4 millimeter thick aluminum filter was placed.

5.3.1 Ground scattering and extra shielding

Figure 5.5: Graphs showing the difference in signal strength between a piece of lead placed on the floor directly under the x-ray tube and no piece of lead under the x-ray tube. The reduce in background radiation is apparent.

The first measurements indicated a large amount of background radiation reaching the detector. To see where this background originated from the x-ray tube was moved one meter away from the apparatus. Figure 5.5 shows that placing a lead slab on the ground directly under the the x-ray tube seriously attenuated the background radiation. This proved that the detector was not shielded of properly. The apparatus was wrapped entirely in a coat of lead, as can be seen in figure (picture lead coat), except for the small area where the first collimator was located. Figure5.6 shows a severe reduction in background signal when the x-ray tube was placed above the apparatus again. One extra layer of shielding proved sufficient to reduce the background radiation enough to allow the detection of the bremsstrahlung spectra.

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Figure 5.6: Graph showing the spectrum with lead shielding (purple line) and without shielding (red line). The resulting attenuation of the background signal is very large.

5.3.2 Alignment and count rate

When the apparatus was sufficiently shielded measurements were made with the scatterer in place to detect a spectrum. However no spectrum could be measured due to problems with the alignment of the collimators between the scatterer and detector. The lead collimators are glued on a piece of PVC tube, which is placed inside the larger PVC tube. Because the glue did not attach very well to the small PVC tube, the lead collimators sunk down to one side and were not properly aligned anymore. Besides this hanging effect, the inner PVC tube also has a smaller outer radius than the inner radius of the big PVC tube. This means that they don’t fit neatly together, but have a gap of about two millimeter around. Therefore by putting tape around the inner tube, you can not exactly position these inner tubes and there will always be some difference.

The measurements performed later with only one collimator between the detector and the scatterer showed count rate of about ten counts per second. This means that to achieve enough counts to have a low relative statistical error and a lower

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measurement time, the count rate must increase. In this experiment we used the orthovolt irradiation tube, which can irradiate for about ten minutes at a time.

A CT-scanner x-ray tube however cannot operate for this long, hence we need a higher count rate, or several measurements in succession.

5.3.3 Collimator K

_α

and K

_β

lines

Figure 5.7: Graph showing the original direct characteristic peaks of lead produced in the second collimator

In an attempt to increase the count rate for reasons mentioned above, the pinholes of the remaining collimators were drilled out. This increased the amount of scatterer which was irradiated and the solid angle subtended by the detector.

For the same reason the collimator between the scatterer and the detector was moved very close to the collimator. This however introduced characteristic x-rays in the spectrum. Figure 5.7 shows that the characteristic K peaks were not produced after scattering, but were directly produced inside the collimator. Because the second collimator was so close to the scatterer, characteristic x-rays could be produced from radiation directly from the x-ray tube. These characteristic x-rays now produced in the collimator would normally not reach the detector due to the

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5.4 X-Ray spectrum and background

presence of the third and fourth collimator. By moving the collimator further away from the scatterer out of the radiation field and under the extra shielding, the characteristic x-rays disappeared.

5.4 X-Ray spectrum and background

In the experiments at UMCG two spectra containing the characteristic x-rays and bremsstrahlung profile were measured. The first spectrum was measured with one collimator in the tube and the initial pinhole size (two millimeters diameter) and the measurement took place for ten minutes. Also a measurement without the scatterer in place was made with the same conditions as the measurement with scatterer. Figure 5.8(a) shows the first bremsstrahlung spectrum and the corresponding background signal and figure 5.8(b) shows the spectrum when the background signal is subtracted from the first measured bremsstrahlung spectrum. A second measurement was made where the pinholes in both remaining collimators were drilled larger and all other parameters were the same as mentioned above, however the count rate did not increase noticeable. Figure 5.9(a) shows the second measured bremsstrahlung spectrum with its corresponding background spectrum and figure 5.9(b) shows these signals subtracted from one another. The statistical noise on these signals is significant due to the low count rate. By rebinning these spectra, adding data from four bins into one bin, the statistical noise reduces but the resolution also reduces. The statistical noise is reduced by a factor 2. However the resolution of the histogram is lower than the decrease in resolution introduced by this rebinning. Figure 5.10 and figure 5.11 show these rebinned spectra for measurement one and two respectively.

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(a) Signal and background spectra

(b) Spectrum of background subtracted from signal

Figure 5.8: Result of the first Compton scattered bremsstrahlung measurement, produced with one collimator and with two millimeter pinholes, measured for ten minutes.

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(a) Signal and background spectra

(b) Spectrum of background subtracted from signal

Figure 5.9: Result of the second Compton scattered bremsstrahlung measurement, produced with one collimator and with enlarged pinholes, measured for ten minutes.

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Figure 5.10: Graph showing figure 5.8(b) rebinned. The content of four bins is put together into one bin, thus reducing the statistical noise

Figure 5.11: Graph showing figure 5.9(b) rebinned. The content of four bins is put together into one bin, thus reducing the statistical noise

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5.4.1 Reconstruction

The spectra that are rebinned above were reconstructed using the same reconstruction algorithm as used in the simulations. Due to lack of time the full reconstruction algorithm could not be implemented in the computer code. Figure 5.12 and 5.13 show the zeroth-order and first-order reconstructed spectra respectively for the first measurement as mentioned above.

The first-order approximation is good enough to show the combined K_α and K_β peaks. This is exactly as anticipated from the simulations performed in section 5.2. The first-order reconstruction shows a better resolution around the Kα peaks and it is possible to discern the two different peaks. The Kβ peaks are very hard to distinguish separately and the first-order reconstruction is not very good here.

Figure 5.14 and 5.15 show the zeroth-order and first-order reconstructed spectra for the second measurement. The zeroth-order approximation shows much detail around the K_α peaks and it is possible to discern the two different tungsten peaks. The K_β peaks however are very hard to discern and only by knowing the x-ray tube target material do we know the peaks are present. The first-order approximation shows the different K_β peaks, however some K_β peaks are too close together to discern them with the detector resolution. The K_α peaks show a little dent in between the two peaks, this is due to statistical uncertainties which influence the first order reconstruction heavily.

The reason why the second set of spectra will not reach zero intensity is probably due to characteristic L lines of lead with energies ranging from 9 to 15 keV which are created inside the second collimator and overlap with the point where the bremsstrahlung spectra should reach zero intensity. These L lines probably are created because the collimator hole was not drilled out properly. Because the drilling was done with a pen and a skewer, the diameter of the pinhole was not the same for the collimator and the pinhole is tapered. This could explain why the first set of spectra does not have this problem, while the second set of spectra does.

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Figure 5.12: Graph showing the reconstructed spectrum starting from the spectrum in figure 5.8(b) using the modified zeroth-order reconstruction algorithm as mentioned in the text.

Figure 5.13: Graph showing the reconstructed spectrum starting from the spectrum in figure 5.8(b) using the first-order reconstruction algorithm as discussed in 4.2

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Figure 5.14: Graph showing the reconstructed spectrum starting from the spectrum in figure 5.9(b) using the modified zeroth-order reconstruction algorithm as mentioned in the text.

Figure 5.15: Graph showing the reconstructed spectrum starting from the spectrum in figure 5.9(b) using the first-order reconstruction algorithm as discussed in 4.2

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Chapter 6 Conclusions, discussion and Recommendations

6.1 Conclusion

Figure 5.13 and 5.15 show two bremsstrahlung spectra that are reconstructed and deconvoluted, thus showing that it is possible to measure the general spectrum shape and reconstruct this. The general technique works which means it’s possible to measure a CT scanner spectrum by a few changes to the apparatus..

There are however a few problems which still need to be solved in order for this apparatus to function properly. The most vital problems are the alignment of the collimators with the scatterer and detector, which proved tedious in the construction. The lead collimators were now mounted on a piece of PVC tube using glue, which was not strong enough to support the weight of the lead. Glue was also applied to the different lead slabs of which the collimator was made of. To improve this alignment the lead collimators must be screwed onto the PVC tube to make sure it will not budge and the alignment is durable. Besides the mounting of the collimators to the PVC tube, the alignment of these inner tube collimators with respect to the outer tube must be considered. In this experiment the inner tubes were positioned in the outer tube using tape, this however makes it difficult to move them inside the tube, because they have to fit perfectly. An easy solution for this problem is to drill holes in the outer tubing and use screws to position the inner tube, this also decreases the ability of the collimators to wobble on the

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6.1 Conclusion

places where tape was applied.

The alignment of the collimators should increase the count rate slightly, however not sufficient for the measurement of a CT spectrum, because when one collimator was placed inside the tube, the count rate was not yet sufficient. Because the photon flux of the x-ray tubes was not really known the choice was made for very small pinholes to make sure the detector was not flooded. To increase the count rate, the pinholes in the collimators must be increased to at least three millimeters for the collimators between the scatterer and detector. The pinhole in the collimator between the x-ray source and the scatterer should be increased so the entire scatterer is irradiated by the source. This increases the count rate dramatically and simplifies the calculations for the reconstruction. By increasing the count rate in this manner the geometrical broadening increases, but it is possible to measure a CT spectrum. A higher count rate also decreases the relative statistical error in the measured spectrum, thus giving a greater accuracy when using the first-order reconstruction.

The first order reconstruction works but can be improved, because a few aspects were neglected which affect the shape of the spectrum. The first aspect that must be considered is the detector response function. The detection efficiency depends on the photo-electric cross section of the detector material, which is not equal for different energies. The higher the photon energy is, the lower the efficiency of the detector is. When reconstructing the spectrum, this response function must be applied before the zeroth-order reconstruction. The second aspect that must be taken into account is the attenuation of the x-rays in the scatterer and in the air. This effect is also not the same for different photon energies, which distorts the shape of the spectrum. Finally a calculation must be made to determine the value of ∆Ω, which also depends on the photon energy, thus distorting the spectrum.

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Appendix A

All measurements at UMCG

This appendix gives all measurements in UMCG with corresponding details. All measurements that are used inside the report will be referenced to in this appendix and not given for the second time. The measurements are named SP001 to SP024 respectively, these names will also be used here. All measurements were performed for 5 minutes unless indicated otherwise.

Figure A.1: SP001: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter and the x-ray tube was positioned above the apparatus. The measurement was aborted before five minutes were done.

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Figure A.2: SP002: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter in combination with a filter consisting of 0.35 mm Al and 1.5 mm Cu. The x-ray tube was positioned above the apparatus.

SP003: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator with a 2.4mm aluminum filter and the x-ray tube positioned above the apparatus. A slab of lead was placed between the tube and the apparatus. See the red curve in 5.6.

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Figure A.3: SP004: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. A slab of lead in front of the first collimator and the x-ray tube positioned 1 meter away from the apparatus.

Figure A.4: SP005: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. A slab of lead in front of the first collimator and the x-ray tube positioned 1 meter away from the apparatus. A slab of lead was also placed on a chair right beneath the x-ray tube.

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Figure A.5: SP006: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. A slab of lead in front of the first collimator and the x-ray tube positioned 1 meter away from the apparatus. Two slabs of lead were placed: one on the chair and one directly under the chair. Both are directly underneath the x-ray tube.

Figure A.6: SP007: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. A slab of lead in front of the first collimator and the x-ray tube positioned 1 meter away from the apparatus. A slab of lead was also placed on the floor directly under the x-ray tube.

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SP008: The same set-up was used as with measurement SP004, see 5.5 the red curve for the graph of this measurement.

SP009: The same set-up as in measurement SP007 was used, see 5.5 the purple curve for the graph of this measurement.

Figure A.7: SP010: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 1.5 mm thick lead and the x-ray tube was 1 meter moved away from the apparatus.

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Figure A.8: SP011: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 1.5 mm thick lead except for the entry collimator. The x-ray tube was positioned directly above the entry collimator.

SP012: The same measurement as SP011 except for the fact that a lead slab was placed in front of the entry collimator. See 5.6 the purple curve is this measurement.

Figure A.9: SP013: 100 kV accelerating voltage with the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus is wrapped in a coat of lead except for the entry collimator and is placed directly underneath the x-ray tube.

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Figure A.10: SP014: 100 kV accelerating voltage without the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 1.5 mm thick lead except for the entry collimator. The x-ray tube was positioned directly above the entry collimator. Instead of three collimators between the scatterer and the detector only one was used and placed directly in front of the detector.

SP015: The same measurement set-up as SP014 only the measurement lasted ten minutes instead of 5 minutes. See 5.8(a) the green curve is this measurements.

SP016: The same measurement as SP015, only this time with the scatterer positioned inside the apparatus. See 5.8(a) the blue curve is this measurement.

Figure A.11: SP017:See SP016

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Figure A.12: SP018: 100 kV accelerating voltage with the scatterer inside the apparatus, a 10x10 cm field collimator was used with a 2.4mm thick aluminum filter. The apparatus was wrapped in a coat of 1.5 mm thick lead except for the entry collimator. The x-ray tube was positioned directly above the entry collimator. Instead of three collimators between the scatterer and the detector only one was used and placed directly in front of the detector. Both of the collimators were drilled out to enlarge the pinhole. The measurement was aborted after two and a half minute.

SP019: 100 kV accelerating voltage with the scatterer, two collimators with drilled out holes placed between the detector and the scatterer. A 2.4 mm aluminum filter was used. The collimator was placed very close to the scatterer and the measurement was aborted. See 5.7 the black curve is this measurement.

SP020: The same set-up as SP019 only without the scatterer inside the apparatus.

See 5.7 the red curve is this measurement.

A Compton Spectrometer for 30-150 keV photons