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Aspects that govern the timing

resolution of scintillation detectors

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben; voorzitter van het College voor Promoties,

in het openbaar te verdedigen op woensdag 30 september 2015 om 10:00 uur

door

David Nicolaas TER WEELE Natuurkundig Ingenieur Technische Universiteit Delft

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TO MY PARENTS

This dissertation has been approved by the promotor: Prof. dr. P. Dorenbos

copromotor: Dr. ir. D.R. Schaart

Composition of the doctoral committee: Rector Magnificus chairman

Prof. dr. P. Dorenbos Delft University of Technology Dr. ir. D.R. Schaart Delft University of Technology Independent members:

Dr. H. Wieczorek Philips Research Prof. dr. P. Fischer University of Heidelberg Prof. dr. ir. H. van der Graaf Delft University of Technology Prof. dr. L.D.A. Siebbeles Delft University of Technology Prof. dr. ir. P. Kruit Delft University of Technology

The research presented in this thesis was carried out at the Luminescence Materials Research Group that was first part of the section Radiation Detection and Medical Imaging and later of the section Fundamental Aspects of Materials and Energy, both within the department of Radiation Science and Technology of the Faculty of Applied Sciences of Delft University of Technology.                            

Cover design: Proefschriftmaken.nl || Uitgeverij BOXPress Printed by: Proefschriftmaken.nl || Uitgeverij BOXPress Published by: Uitgeverij BOXPress, ’s-Hertogenbosch

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TO MY PARENTS

This dissertation has been approved by the promotor: Prof. dr. P. Dorenbos

copromotor: Dr. ir. D.R. Schaart

Composition of the doctoral committee: Rector Magnificus chairman

Prof. dr. P. Dorenbos Delft University of Technology Dr. ir. D.R. Schaart Delft University of Technology Independent members:

Dr. H. Wieczorek Philips Research Prof. dr. P. Fischer University of Heidelberg Prof. dr. ir. H. van der Graaf Delft University of Technology Prof. dr. L.D.A. Siebbeles Delft University of Technology Prof. dr. ir. P. Kruit Delft University of Technology

The research presented in this thesis was carried out at the Luminescence Materials Research Group that was first part of the section Radiation Detection and Medical Imaging and later of the section Fundamental Aspects of Materials and Energy, both within the department of Radiation Science and Technology of the Faculty of Applied Sciences of Delft University of Technology.                            

Cover design: Proefschriftmaken.nl || Uitgeverij BOXPress Printed by: Proefschriftmaken.nl || Uitgeverij BOXPress Published by: Uitgeverij BOXPress, ’s-Hertogenbosch

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Table of

Contents

1. Introduction . . . . 1 1.1 Time-of-flight positron emission tomography . . . . 1 1.2 Aspects that govern the timing resolution of scintillation detectors . . . . 3 1.3 Thesis research objectives . . . . 6 1.4 Set-ups and ray tracing software . . . . 7 1.5 Thesis outline . . . . 14

2. The effect of self-absorption on the scintillation properties of Ce3+ activated LaBr3 and CeBr3 . . . . 17

2.1 Introduction . . . . 17

2.2 Experimental methods . . . . 18

2.3 Results . . . . 20

2.4 Discussion . . . . 25

2.5 Conclusions . . . . 30

3. Intrinsic scintillation pulse shape measurements by means of picosecond x-ray excitation for fast timing applications . . . . 35

3.1 Introduction . . . . 35 3.2 Experimental methods . . . . 36 3.2.1 The set-up . . . . 36 3.2.2 Measurements . . . . 38 3.3 Results . . . . 40 3.4 Discussion . . . . 45 3.5 Summary and conclusions . . . . 49

4. Comparative study of co-doped and non co-doped LSO:Ce and LYSO:Ce scintillators for TOF-PET . . . . 51

4.1 Introduction . . . . 51

4.2 Experimental methods . . . . 52

4.3 Results . . . . 54

4.4 Discussion . . . . 57

4.5 Summary and conclusions . . . . 63

5. Picosecond time resolved studies of photon transport inside scintillators . . . 67

5.1 Introduction . . . . 68

5.2 Materials and methods . . . . 69

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Aspects that govern the timing resolution of scintillation detectors

Chapter 1

Introduction

1.1 Time-of-flight positron emission tomography

Positron emission tomography (PET) is a nuclear medicine technique which is used to image the three-dimensional distribution of a radioactive isotope in an object. A typical PET image of living animals or persons provides information on functional processes rather than the anatomy. A clinical application of PET is as a diagnostic tool in oncology where PET scans are routinely employed to detect and/or localize tumors and metastases. PET is, however, a very versatile technique and therefore used in many other fields such as neurology, e.g. diagnostics of dysfunctional brain diseases, and cardiology, e.g. evaluation of heart tissue viability [1-3].

PET is based on the emission of positrons. Before a patient undergoes a scan, a short lived radioactive isotope is injected into the body. It is chemically incorporated

into biological active molecules, called tracers. 18F-fluoro-deoxy-glucose (18F-FDG) is

the most prominent tracer in PET. The targeting mechanism of the tracer is that its chemical structure is very similar to the structure of glucose. As a result, the tracer will accumulate within regions with high glucose uptake, such as cancer cells.

Fig. 1.1. The detection of two γ-photons by PET-detectors, resulting in a line of response (LOR). LOR 5.2.2 Optical transit time-spread . . . . 70 5.2.3 Teflon time-spread . . . . 72 5.2.4 Surface profiler . . . . 73 5.2.5 Ray tracing software . . . . 73 5.3 Results and discussion: Experiments . . . . 75 5.3.1 Optical transit time-spread: Experiments . . . . 75 5.3.2 Teflon time-spread . . . . 82 5.3.3 Surface profile . . . . 85 5.4 Results and discussion: Ray tracing software . . . . 88 5.4.1 Factors determining λ . . . . 88 5.4.2 Study of reflections on the crystal surfaces . . . . 91 5.4.3 Analytical determination of λ . . . . 93 5.4.4 Effect of Teflon and crystal dimensions on λ . . . . 94 5.5 Summary and conclusions . . . . 95

6. Scintillation detector timing resolution; a study by ray tracing software . . . 99

6.1 Introduction . . . . 100 6.2 Methods . . . . 101 6.2.1 Timing resolution . . . . 101 6.2.2 Ray tracing software . . . . 103 6.2.3 Simulations . . . . 107 6.3 Results and discussion . . . . 108 6.3.1 Intrinsic timing resolution . . . . 108 6.3.2 Polished versus etched crystals . . . . 109 6.3.3 Influence of the refractive index of the photon detector . . . . 115 6.3.4 Co-doped and non co-doped LYSO:Ce and LSO:Ce . . . . 117 6.3.5 Influence of intrinsic scintillation properties . . . . 118 6.3.6 The effect of Teflon reflector dwell time on the timing resolution 120 6.4 Summary and conclusions . . . . 121 Summary . . . . 125 Samenvatting . . . . 129 Acknowledgements . . . . 133 Curriculum Vitae . . . . 135 List of Publications . . . . 137

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Chapter 1

Introduction

1.1 Time-of-flight positron emission tomography

Positron emission tomography (PET) is a nuclear medicine technique which is used to image the three-dimensional distribution of a radioactive isotope in an object. A typical PET image of living animals or persons provides information on functional processes rather than the anatomy. A clinical application of PET is as a diagnostic tool in oncology where PET scans are routinely employed to detect and/or localize tumors and metastases. PET is, however, a very versatile technique and therefore used in many other fields such as neurology, e.g. diagnostics of dysfunctional brain diseases, and cardiology, e.g. evaluation of heart tissue viability [1-3].

PET is based on the emission of positrons. Before a patient undergoes a scan, a short lived radioactive isotope is injected into the body. It is chemically incorporated

into biological active molecules, called tracers. 18F-fluoro-deoxy-glucose (18F-FDG) is

the most prominent tracer in PET. The targeting mechanism of the tracer is that its chemical structure is very similar to the structure of glucose. As a result, the tracer will accumulate within regions with high glucose uptake, such as cancer cells.

Fig. 1.1. The detection of two γ-photons by PET-detectors, resulting in a line of response (LOR).

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Aspects that govern the timing resolution of scintillation detectors

Fig. 1.2 Schematic view of the estimation of the position of annihilation along the line-of-response in case of conventional PET and TOF-PET.

In conventional PET there is no information where on the LOR the annihilation event took place. Using TOF-information the point of annihilation along the LOR can be

determined with an accuracy , which is given by , where c is the speed

of light. As a result, all counting noise in the reconstructed image reduces. The time difference between the detection of the two γ-photons in coincidence is less than a few hundred picoseconds up to a few nanoseconds. This requires detectors with excellent timing resolution.

1.2 Aspects that govern the timing resolution of scintillation detectors In addition to (TOF-)PET there are other applications that requires high timing resolution. For instance, in high energy physics high timing resolution is needed to observe rare particles against a large background of other event [10]. For the detection of γ-photons scintillation detectors are used. Scintillators are materials that convert the energy of ionizing radiation into a flash of light, which can be detected by a photon detector, resulting in an output signal. Fig. 1.3 shows a cuboid shaped scintillation crystal coupled to a photon detector.

Aspects that govern the timing resolution of scintillation detectors

 

Figure 1.1 shows a patient positioned within a ring of detectors. An emitted positron travels no more than a few millimeters in a random direction inside the tissue of interest, slowing down until it annihilates with an electron. This results in the emission of two annihilation photons (-photons) traveling in approximately opposite directions. Each -photons carries the energy equivalent to the electron and positron rest mass, viz. 511 keV. Although most of the -photons will not be detected, some will remain in the plane of the detector ring and hit a detector. Two -photons are considered to form an annihilation pair if they are detected within a small time window, denoted as a coincidence event. The path in between the two detectors is referred to as the line of response (LOR). After the collection of a large number of lines-of-responses the activity concentration in the body can be plotted as a function of position by a reconstruction algorithm [4],[5]. Due to a finite number of LORs there is statistical noise that is inherent to conventional PET image reconstruction. In addition, there are other phenomena that contribute to the noise level of the reconstructed image. -photons can undergo Compton scattering before being detected. This is associated with a change in traveling direction and may lead to an incorrect LOR. When photons scatter they lose a part of their energy which increases with the scattering angle. A good energy resolution is essential for PET detectors to discriminate scattered -photons. If two detected unscattered -photons originate from the same annihilation event it is called a true event. If they originate from a different annihilation event it is called a random event. Reducing the number of random events improves the signal-to-noise level of the reconstructed image. A small time window is therefore required, but it is limited by the accuracy with which the time difference between two -photons can be measured, often expressed as the coincidence resolving time (CRT). The time window is furthermore limited by the maximum time difference between the detection of two -photons, which is determined by the position and dimensions of the imaged object. A smaller time window reduces the number of true events as well as random events and is therefore not beneficial.

Additional benefits can be obtained if the CRT is smaller than ~1 ns by making use of time-of-flight information (TOF) [6-9]. By measuring the difference in detection time between the two detected -photons one can estimate the position of annihilation along the LOR. Figure 1.2 shows the probability density function to estimate the position of the annihilation event on the LOR.

Aspects that govern the timing resolution of scintillation detectors

 

Fig. 1.2 Schematic view of the estimation of the position of annihilation along the line-of-response in case of conventional PET and TOF-PET.

In conventional PET there is no information where on the LOR the annihilation event took place. Using TOF-information the point of annihilation along the LOR can be

determined with an accuracy , which is given by , where c is the speed

of light. As a result, all counting noise in the reconstructed image reduces. The time difference between the detection of the two -photons in coincidence is less than a few hundred picoseconds up to a few nanoseconds. This requires detectors with excellent timing resolution.

1.2 Aspects that govern the timing resolution of scintillation detectors

In addition to (TOF-)PET there are other applications that requires high timing resolution. For instance, in high energy physics high timing resolution is needed to observe rare particles against a large background of other event [10]. For the detection of -photons scintillation detectors are used. Scintillators are materials that convert the energy of ionizing radiation into a flash of light, which can be detected by a photon detector, resulting in an output signal. Fig. 1.3 shows a cuboid shaped scintillation crystal coupled to a photon detector.

LOR

activity

Conventional PET Time-of-flight PET

Introduction

3 Aspects that govern the timing resolution of scintillation detectors

Figure 1.1 shows a patient positioned within a ring of detectors. An emitted positron travels no more than a few millimeters in a random direction inside the tissue of interest, slowing down until it annihilates with an electron. This results in the emission of two annihilation photons (γ-photons) traveling in approximately opposite directions. Each γ-photons carries the energy equivalent to the electron and positron rest mass, viz. 511 keV. Although most of the γ-photons will not be detected, some will remain in the plane of the detector ring and hit a detector. Two γ-photons are considered to form an annihilation pair if they are detected within a small time window, denoted as a coincidence event. The path in between the two detectors is referred to as the line of response (LOR). After the collection of a large number of lines-of-responses the activity concentration in the body can be plotted as a function of position by a reconstruction algorithm [4],[5]. Due to a finite number of LORs there is statistical noise that is inherent to conventional PET image reconstruction. In addition, there are other phenomena that contribute to the noise level of the reconstructed image. γ-photons can undergo Compton scattering before being detected. This is associated with a change in traveling direction and may lead to an incorrect LOR. When photons scatter they lose a part of their energy which increases with the scattering angle. A good energy resolution is essential for PET detectors to discriminate scattered γ-photons. If two detected unscattered γ-photons originate from the same annihilation event it is called a true event. If they originate from a different annihilation event it is called a random event. Reducing the number of random events improves the signal-to-noise level of the reconstructed image. A small time window is therefore required, but it is limited by the accuracy with which the time difference between two γ-photons can be measured, often expressed as the coincidence resolving time (CRT). The time window is furthermore limited by the maximum time difference between the detection of two γ-photons, which is determined by the position and dimensions of the imaged object. A smaller time window reduces the number of true events as well as random events and is therefore not beneficial.

Additional benefits can be obtained if the CRT is smaller than ~1 ns by making use of time-of-flight information (TOF) [6-9]. By measuring the difference in detection time between the two detected γ-photons one can estimate the position of annihilation along the LOR. Figure 1.2 shows the probability density function to estimate the position of the annihilation event on the LOR.

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Fig. 1.2 Schematic view of the estimation of the position of annihilation along the line-of-response in case of conventional PET and TOF-PET.

In conventional PET there is no information where on the LOR the annihilation event took place. Using TOF-information the point of annihilation along the LOR can be

determined with an accuracy , which is given by , where c is the speed

of light. As a result, all counting noise in the reconstructed image reduces. The time difference between the detection of the two γ-photons in coincidence is less than a few hundred picoseconds up to a few nanoseconds. This requires detectors with excellent timing resolution.

1.2 Aspects that govern the timing resolution of scintillation detectors In addition to (TOF-)PET there are other applications that requires high timing resolution. For instance, in high energy physics high timing resolution is needed to observe rare particles against a large background of other event [10]. For the detection of γ-photons scintillation detectors are used. Scintillators are materials that convert the energy of ionizing radiation into a flash of light, which can be detected by a photon detector, resulting in an output signal. Fig. 1.3 shows a cuboid shaped scintillation crystal coupled to a photon detector.

 

Figure 1.1 shows a patient positioned within a ring of detectors. An emitted positron travels no more than a few millimeters in a random direction inside the tissue of interest, slowing down until it annihilates with an electron. This results in the emission of two annihilation photons (-photons) traveling in approximately opposite directions. Each -photons carries the energy equivalent to the electron and positron rest mass, viz. 511 keV. Although most of the -photons will not be detected, some will remain in the plane of the detector ring and hit a detector. Two -photons are considered to form an annihilation pair if they are detected within a small time window, denoted as a coincidence event. The path in between the two detectors is referred to as the line of response (LOR). After the collection of a large number of lines-of-responses the activity concentration in the body can be plotted as a function of position by a reconstruction algorithm [4],[5]. Due to a finite number of LORs there is statistical noise that is inherent to conventional PET image reconstruction. In addition, there are other phenomena that contribute to the noise level of the reconstructed image. -photons can undergo Compton scattering before being detected. This is associated with a change in traveling direction and may lead to an incorrect LOR. When photons scatter they lose a part of their energy which increases with the scattering angle. A good energy resolution is essential for PET detectors to discriminate scattered -photons. If two detected unscattered -photons originate from the same annihilation event it is called a true event. If they originate from a different annihilation event it is called a random event. Reducing the number of random events improves the signal-to-noise level of the reconstructed image. A small time window is therefore required, but it is limited by the accuracy with which the time difference between two -photons can be measured, often expressed as the coincidence resolving time (CRT). The time window is furthermore limited by the maximum time difference between the detection of two -photons, which is determined by the position and dimensions of the imaged object. A smaller time window reduces the number of true events as well as random events and is therefore not beneficial.

Additional benefits can be obtained if the CRT is smaller than ~1 ns by making use of time-of-flight information (TOF) [6-9]. By measuring the difference in detection time between the two detected -photons one can estimate the position of annihilation along the LOR. Figure 1.2 shows the probability density function to estimate the position of the annihilation event on the LOR.

 

Fig. 1.2 Schematic view of the estimation of the position of annihilation along the line-of-response in case of conventional PET and TOF-PET.

In conventional PET there is no information where on the LOR the annihilation event took place. Using TOF-information the point of annihilation along the LOR can be

determined with an accuracy , which is given by , where c is the speed

of light. As a result, all counting noise in the reconstructed image reduces. The time difference between the detection of the two -photons in coincidence is less than a few hundred picoseconds up to a few nanoseconds. This requires detectors with excellent timing resolution.

1.2 Aspects that govern the timing resolution of scintillation detectors

In addition to (TOF-)PET there are other applications that requires high timing resolution. For instance, in high energy physics high timing resolution is needed to observe rare particles against a large background of other event [10]. For the detection of -photons scintillation detectors are used. Scintillators are materials that convert the energy of ionizing radiation into a flash of light, which can be detected by a photon detector, resulting in an output signal. Fig. 1.3 shows a cuboid shaped scintillation crystal coupled to a photon detector.

LOR

activity

Conventional PET Time-of-flight PET

3 Figure 1.1 shows a patient positioned within a ring of detectors. An emitted positron

travels no more than a few millimeters in a random direction inside the tissue of interest, slowing down until it annihilates with an electron. This results in the emission of two annihilation photons (γ-photons) traveling in approximately opposite directions. Each γ-photons carries the energy equivalent to the electron and positron rest mass, viz. 511 keV. Although most of the γ-photons will not be detected, some will remain in the plane of the detector ring and hit a detector. Two γ-photons are considered to form an annihilation pair if they are detected within a small time window, denoted as a coincidence event. The path in between the two detectors is referred to as the line of response (LOR). After the collection of a large number of lines-of-responses the activity concentration in the body can be plotted as a function of position by a reconstruction algorithm [4],[5]. Due to a finite number of LORs there is statistical noise that is inherent to conventional PET image reconstruction. In addition, there are other phenomena that contribute to the noise level of the reconstructed image. γ-photons can undergo Compton scattering before being detected. This is associated with a change in traveling direction and may lead to an incorrect LOR. When photons scatter they lose a part of their energy which increases with the scattering angle. A good energy resolution is essential for PET detectors to discriminate scattered γ-photons. If two detected unscattered γ-photons originate from the same annihilation event it is called a true event. If they originate from a different annihilation event it is called a random event. Reducing the number of random events improves the signal-to-noise level of the reconstructed image. A small time window is therefore required, but it is limited by the accuracy with which the time difference between two γ-photons can be measured, often expressed as the coincidence resolving time (CRT). The time window is furthermore limited by the maximum time difference between the detection of two γ-photons, which is determined by the position and dimensions of the imaged object. A smaller time window reduces the number of true events as well as random events and is therefore not beneficial.

Additional benefits can be obtained if the CRT is smaller than ~1 ns by making use of time-of-flight information (TOF) [6-9]. By measuring the difference in detection time between the two detected γ-photons one can estimate the position of annihilation along the LOR. Figure 1.2 shows the probability density function to estimate the position of the annihilation event on the LOR.

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Aspects that govern the timing resolution of scintillation detectors

electrons are liberated and accelerated to the next dynode. This multiplication process repeats several times resulting in the release of millions of electrons which are then read out by electronics. Other types of photon detectors are the avalanche photodiode (APD) and the silicon photomultiplier (SiPM). In the detection process of these solid state photon detectors photoelectrons are attracted to a depletion layer where they

trigger a so called avalanche, resulting in 102 to 107 electron-hole pairs. Regardless of

the type of photon detector, there is always a time-spread in the detection process,

expressed in terms of the single-photon detector transit time-spread , which is

often described by a Gaussian distribution.

In this thesis we will mainly focus on the scintillator and therefore we consider an idealized photon detector that creates a time stamp for every detected scintillation photon in the remainder of this work. The scintillation photon time stamp distribution

is referred to as the observed scintillation pulse shape and equals the

convolution between , , and . It was shown in [11] and [12] that the

timing resolution is proportional to the square root of the steepness of the rising edge

of the observed scintillation pulse .

The scintillator must offer a high light yield, a short decay time constant, and a short scintillation rise time, which are all determined by scintillation mechanisms at a fundamental level, such as the creation of electron-hole pairs, energy transfer from the ionization track to luminescence centres, and radiative and non-radiative decay of luminesce centres.

As the timing resolution of a scintillation detector is determined by the slope the light collection efficiency of scintillation photons traveling from the ionization track to the photon detector is just as important as the light yield. Scintillators are therefore often packed on 5 of their surfaces in a material with a high reflection coefficient and attached to the photon detector with a coupling material having a refractive index in between the refractive index of the scintillator and photon

detector. For high timing resolution, and are desired to be small.

is expected to broaden with the dimensions of the crystal and it depends on the properties of the packaging material, such as the reflection coefficient. Lastly, the detection efficiency of the photon detector, referred to as the photodetection efficiency (pde) is another important property that determines the timing resolution of a scintillation detector.

Aspects that govern the timing resolution of scintillation detectors

Fig 1.3. The schematic view of a scintillation detector.

An incoming γ-photon enters the crystal and creates an ionization track inside the bulk of the crystal. During this process, electron-hole pairs are created, which subsequently migrate through the crystal and excite luminescence centres. Excited luminescence centres can decay either radiative, under the emission of a photon, or non-radiative,

under the emission of a phonon. The intrinsic scintillation pulse shape , defined

as the intensity of the emitted light created by the ionization track per unit time as a function of time, can often be described by Eq. (1.1).

(1.1) where c1 is a constant determined by the light yield of the crystal. The latter is defined as the number of emitted scintillation photons per unit absorbed energy. is the decay time constant and equals the average life time of an excited luminescence centre, and is the average migration time of an electron-hole pair from the ionization track to a luminescence centre, in this work referred to as the scintillation rise time. Since the scintillation pulse is emitted isotopically the scintillation photon traveling path from the ionization track to the photon detector varies significantly from photon to photon. This results in a time-spread distribution, in this thesis defined

as the optical transit time-spread . The detected scintillation photons create

photoelectrons inside the photon detector. Nowadays, the most widely used photon detector in PET is the photomultiplier tube (PMT). In the detection process of a PMT photoelectrons are accelerated to a dynode by a potential difference where multiple

Fig 1.3. The schematic view of a scintillation detector. (-)Source Emitted Particle (-Photon) Scintillation Crystal Photon detector Emission Absorption Signal Readout electronics Time stamp Chapter 1

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electrons are liberated and accelerated to the next dynode. This multiplication process repeats several times resulting in the release of millions of electrons which are then read out by electronics. Other types of photon detectors are the avalanche photodiode (APD) and the silicon photomultiplier (SiPM). In the detection process of these solid state photon detectors photoelectrons are attracted to a depletion layer where they

trigger a so called avalanche, resulting in 102 to 107 electron-hole pairs. Regardless of

the type of photon detector, there is always a time-spread in the detection process,

expressed in terms of the single-photon detector transit time-spread , which is

often described by a Gaussian distribution.

In this thesis we will mainly focus on the scintillator and therefore we consider an idealized photon detector that creates a time stamp for every detected scintillation photon in the remainder of this work. The scintillation photon time stamp distribution

is referred to as the observed scintillation pulse shape and equals the

convolution between , , and . It was shown in [11] and [12] that the

timing resolution is proportional to the square root of the steepness of the rising edge

of the observed scintillation pulse .

The scintillator must offer a high light yield, a short decay time constant, and a short scintillation rise time, which are all determined by scintillation mechanisms at a fundamental level, such as the creation of electron-hole pairs, energy transfer from the ionization track to luminescence centres, and radiative and non-radiative decay of luminesce centres.

As the timing resolution of a scintillation detector is determined by the slope the light collection efficiency of scintillation photons traveling from the ionization track to the photon detector is just as important as the light yield. Scintillators are therefore often packed on 5 of their surfaces in a material with a high reflection coefficient and attached to the photon detector with a coupling material having a refractive index in between the refractive index of the scintillator and photon

detector. For high timing resolution, and are desired to be small.

is expected to broaden with the dimensions of the crystal and it depends on the properties of the packaging material, such as the reflection coefficient. Lastly, the detection efficiency of the photon detector, referred to as the photodetection efficiency (pde) is another important property that determines the timing resolution of a scintillation detector.

Fig 1.3. The schematic view of a scintillation detector.

An incoming γ-photon enters the crystal and creates an ionization track inside the bulk of the crystal. During this process, electron-hole pairs are created, which subsequently migrate through the crystal and excite luminescence centres. Excited luminescence centres can decay either radiative, under the emission of a photon, or non-radiative,

under the emission of a phonon. The intrinsic scintillation pulse shape , defined

as the intensity of the emitted light created by the ionization track per unit time as a function of time, can often be described by Eq. (1.1).

(1.1) where c1 is a constant determined by the light yield of the crystal. The latter is defined as the number of emitted scintillation photons per unit absorbed energy. is the decay time constant and equals the average life time of an excited luminescence centre, and is the average migration time of an electron-hole pair from the ionization track to a luminescence centre, in this work referred to as the scintillation rise time. Since the scintillation pulse is emitted isotopically the scintillation photon traveling path from the ionization track to the photon detector varies significantly from photon to photon. This results in a time-spread distribution, in this thesis defined

as the optical transit time-spread . The detected scintillation photons create

photoelectrons inside the photon detector. Nowadays, the most widely used photon detector in PET is the photomultiplier tube (PMT). In the detection process of a PMT photoelectrons are accelerated to a dynode by a potential difference where multiple

Fig 1.3. The schematic view of a scintillation detector. (-)Source Emitted Particle (-Photon) Scintillation Crystal Photon detector Emission Absorption Signal Readout electronics Time stamp

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Aspects that govern the timing resolution of scintillation detectors

1.4 Set-ups and ray tracing software

This section introduces two set-ups that were built and ray tracing software that was developed during this research. The timing resolution of a scintillator with negligible optical transit time-spread Iotts (t) is primarily determined by the steepness of the rising

edge of the scintillation pulse. For the fast scintillator materials LaBr3:5%Ce, LSO:Ce,

and LYSO:Ce the rising part of the scintillator pulse is shorter than 1 ns. For the accurate measurements of the scintillation pulse in the first nanosecond time range after the absorption of the gamma photon a laser driven x-ray tube that produces 100 ps (FWHM) x-ray pulses was used. The measurements are based on the principle of time-correlated single photon counting (TCSPC). Optical photons (~440 nm) emitted by the pulsed diode laser liberate photoelectrons in the cathode of the x-ray tube. The photoelectrons are subsequently accelerated to the anode to an energy of 40 keV. X-rays hit the crystal under study mounted in a sample chamber, possibly connected to a cryostat, which allows measurements under vacuum and can be used for hygroscopic scintillator and temperature-dependent studies. From the opposite site of the sample an ID Quantique single-photon detector that has a detection area of 50 µm in diameter is positioned at 4 cm distance. At this distance and with such small detection area, the number of scintillation photons incident on the detector per x-ray pulse essentially never exceeds 1. The laser output is connected to the start input of a time-to-amplitude convertor, whereas the detector output is connected to the stop input. The measured time-differences are then digitized by an amplitude-to-digital convertor. The created histogram of all measured time differences represents the scintillation pulse shape. By wrapping the sample on all of its surfaces (except the surface that faces the photon detector) in a material with a low reflection coefficient, Iotts (t) can be made negligibly small. In this way, one obtains the intrinsic scintillation pulse shape Isci (t), from which intrinsic scintillation rise times can be derived. The set-up will be explained in more detail in chapter 3. In addition, Isci gives information about scintillation mechanisms at a fundamental level, such as energy transfer and quenching mechanisms, and can be used to calculate intrinsic timing resolutions.

As scintillators are often wrapped in a material with a high reflection coefficient for

high light collection efficiency, Iotts (t) is non-negligible. A set-up was built to

determine the relation between Iotts and the crystal dimensions, the surface conditions, and the reflector properties. A femtosecond pulsed diode laser illuminates a cuboid shaped crystal from the side (without exciting the crystal) that is wrapped, apart from 1 surface, in Teflon tape. A fast imaging streak camera can measure the intensity of the light that emanates from the uncovered crystal surface with 2 ps (FWHM) accuracy. The obtained Iotts (t) can be used to calculate its contribution to the timing resolution, Aspects that govern the timing resolution of scintillation detectors

1.3 Thesis research objectives

The diagnostic value of a (TOF-)PET image depends on the image quality, which is determined by both the sensitivity of the scanner and the (average) information per detected γ-photon. The simultaneous maximization of both of them has proven to be a challenging task as it leads to competing requirements for many scanner characteristics. For instance, thick crystals are required for efficient detection of γ-photons, but they show a worse timing (and energy) resolution compared so small crystals. Trade-offs have to be made in the design of a PET detector.

For the design of (TOF-)PET detectors and for the development of new scintillation materials it is important to have a full understanding what the timing resolution is

determined by and how the slope can be maximized. TOF-PET improves the

signal-to-noise ratio compared to conventional PET, but it requires excellent timing resolution (< ~500 ps CRT). A promising scintillation material that fulfils this

requirement is LaBr3:5%Ce, discovered at TU Delft in 2001. It was shown before that

emitted scintillation photons can be absorbed by luminescence centres before they escape the crystal [13]. This phenomenon is known as self-absorption. One of the objectives of this thesis is to study self-absorption, as a function of temperature and

dopant concentration, and map how it affects the timing resolution. LaBr3:5%Ce has

the disadvantages that it is expensive and hygroscopic. Commonly used (and

non-hygroscopic) scintillation materials in conventional PET systems are Lu2SiO5:Ce

(LSO:Ce) and (LuY)2SiO5:Ce (LYSO:Ce) and it has been shown that Ca co-doped

LSO:Ce and LYSO:Ce show even better scintillation properties. It this thesis we intended to find the best scintillation material among several doped and non co-doped LSO:Ce and LYSO:Ce crystals.

The traveling path of scintillation photons from the ionization track to the photon detector varies from photon to photon. To our knowledge, this optical transit time-spread has never been determined experimentally, while it can have a great influence on the timing resolution of a scintillation detector. We have built a set-up to actually measure this time-spread with a few picoseconds timing resolution. The results can be compared to the results obtained by means of ray tracing software, from which new insight into photon traveling paths inside the crystal can be gained. All experimental results can be used as an input for ray tracing software that subsequently can be used to study the detector timing resolution.

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1.4 Set-ups and ray tracing software

This section introduces two set-ups that were built and ray tracing software that was developed during this research. The timing resolution of a scintillator with negligible optical transit time-spread Iotts (t) is primarily determined by the steepness of the rising

edge of the scintillation pulse. For the fast scintillator materials LaBr3:5%Ce, LSO:Ce,

and LYSO:Ce the rising part of the scintillator pulse is shorter than 1 ns. For the accurate measurements of the scintillation pulse in the first nanosecond time range after the absorption of the gamma photon a laser driven x-ray tube that produces 100 ps (FWHM) x-ray pulses was used. The measurements are based on the principle of time-correlated single photon counting (TCSPC). Optical photons (~440 nm) emitted by the pulsed diode laser liberate photoelectrons in the cathode of the x-ray tube. The photoelectrons are subsequently accelerated to the anode to an energy of 40 keV. X-rays hit the crystal under study mounted in a sample chamber, possibly connected to a cryostat, which allows measurements under vacuum and can be used for hygroscopic scintillator and temperature-dependent studies. From the opposite site of the sample an ID Quantique single-photon detector that has a detection area of 50 µm in diameter is positioned at 4 cm distance. At this distance and with such small detection area, the number of scintillation photons incident on the detector per x-ray pulse essentially never exceeds 1. The laser output is connected to the start input of a time-to-amplitude convertor, whereas the detector output is connected to the stop input. The measured time-differences are then digitized by an amplitude-to-digital convertor. The created histogram of all measured time differences represents the scintillation pulse shape. By wrapping the sample on all of its surfaces (except the surface that faces the photon detector) in a material with a low reflection coefficient, Iotts (t) can be made negligibly small. In this way, one obtains the intrinsic scintillation pulse shape Isci (t), from which intrinsic scintillation rise times can be derived. The set-up will be explained in more detail in chapter 3. In addition, Isci gives information about scintillation mechanisms at a fundamental level, such as energy transfer and quenching mechanisms, and can be used to calculate intrinsic timing resolutions.

As scintillators are often wrapped in a material with a high reflection coefficient for

high light collection efficiency, Iotts (t) is non-negligible. A set-up was built to

determine the relation between Iotts and the crystal dimensions, the surface conditions, and the reflector properties. A femtosecond pulsed diode laser illuminates a cuboid shaped crystal from the side (without exciting the crystal) that is wrapped, apart from 1 surface, in Teflon tape. A fast imaging streak camera can measure the intensity of the light that emanates from the uncovered crystal surface with 2 ps (FWHM) accuracy. The obtained Iotts (t) can be used to calculate its contribution to the timing resolution, 1.3 Thesis research objectives

The diagnostic value of a (TOF-)PET image depends on the image quality, which is determined by both the sensitivity of the scanner and the (average) information per detected γ-photon. The simultaneous maximization of both of them has proven to be a challenging task as it leads to competing requirements for many scanner characteristics. For instance, thick crystals are required for efficient detection of γ-photons, but they show a worse timing (and energy) resolution compared so small crystals. Trade-offs have to be made in the design of a PET detector.

For the design of (TOF-)PET detectors and for the development of new scintillation materials it is important to have a full understanding what the timing resolution is

determined by and how the slope can be maximized. TOF-PET improves the

signal-to-noise ratio compared to conventional PET, but it requires excellent timing resolution (< ~500 ps CRT). A promising scintillation material that fulfils this

requirement is LaBr3:5%Ce, discovered at TU Delft in 2001. It was shown before that

emitted scintillation photons can be absorbed by luminescence centres before they escape the crystal [13]. This phenomenon is known as self-absorption. One of the objectives of this thesis is to study self-absorption, as a function of temperature and

dopant concentration, and map how it affects the timing resolution. LaBr3:5%Ce has

the disadvantages that it is expensive and hygroscopic. Commonly used (and

non-hygroscopic) scintillation materials in conventional PET systems are Lu2SiO5:Ce

(LSO:Ce) and (LuY)2SiO5:Ce (LYSO:Ce) and it has been shown that Ca co-doped

LSO:Ce and LYSO:Ce show even better scintillation properties. It this thesis we intended to find the best scintillation material among several doped and non co-doped LSO:Ce and LYSO:Ce crystals.

The traveling path of scintillation photons from the ionization track to the photon detector varies from photon to photon. To our knowledge, this optical transit time-spread has never been determined experimentally, while it can have a great influence on the timing resolution of a scintillation detector. We have built a set-up to actually measure this time-spread with a few picoseconds timing resolution. The results can be compared to the results obtained by means of ray tracing software, from which new insight into photon traveling paths inside the crystal can be gained. All experimental results can be used as an input for ray tracing software that subsequently can be used to study the detector timing resolution.

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Aspects that govern the timing resolution of scintillation detectors

of the nth detected photon is determined for n = 1 till n = 100. The settings of the

software will be explained the remainder of this section, which can be used as a manual for future users. The input parameters are given below.

x0, L, z0 The dimensions of the crystal in the x, y, and z direction, respectively, see Fig. 1.4

n1 The refractive index of the scintillator

n2 The refractive index of the photon detector

l The attenuation coefficient of the scintillator for gamma detection

Isci (t) The intrinsic scintillation pulse shape

The total number of simulated gamma events

Nsci The total number of emitted scintillation photons per gamma event

pabs The absorption probability, defined as the probability of losing a photon

when it hits one of the 5 packed crystal surfaces.

dwell time The dwell time is the time a photon dwells inside the reflector during the

reflection process. The dwell time is added to the total traveling time each time a photon reflects at the crystal reflector interface.

Idtts (t) The detector transit time-spread function, in this work considered to be

Gaussian distributed. The remaining parameters are as follows:

The nth traced γ-photon

nsci The nth traced scintillation photon for a given γ-photon

nph The nth traced optical photon, emitted by the laser

The traveling time of the gamma photon inside the crystal

tem The time between the absorption of the gamma photon and the emission of the scintillation photon

tott The traveling time of the scintillation photon inside the crystal

trefl The total traveling time of photon inside the reflector, i.e. the dwell time times the total number of reflections at the crystal reflector interface

tdtt The detector transit time, i.e. time between the creation of a photoelectron in the photon detector and the time stamp

Iotts (t) The optical transit time-spread

Iobs (t) The observed scintillation pulse, i.e. the time stamp distribution obtained from a single gamma event.

Δt (n) The FWHM of the distribution in the Nγ time stamps of the nth detected

scintillation photon Aspects that govern the timing resolution of scintillation detectors

e.g. with the timing model described in [14]. This set-up can furthermore be used to measure how long photons dwell inside reflectors. For instance, it was shown in [15] that a delta light pulse is spread out in time while transmitting through Teflon tape. When photons dwell inside the reflector medium for some time Iotts (t) is expected to broaden. The photon dwell time can be used as an input for ray tracing software to study its effect on the timing resolution. The set-up is described in more detail in chapter 5.

Ray tracing software is a powerful tool to attain information about optical transit time-spread. Codes such as GATE, GEANT4, and Litrani [16-19] are often used to study Iotts (t) and its contribution to the timing resolution [20-26]. Using these software packages it cannot be studied how the dwell time of photons during the reflection process affects Iotts (t) and the timing resolution. In this research a new Monte Carlo-based ray tracing software package was developed that takes into account the photon dwell time inside the reflector medium. Two software codes were written, one to obtain the detector timing resolution and one to obtain Iotts (t). The former, which is used in chapter 6, will be explained first.

Timing resolution

Figure 1.4 shows a cuboid shaped crystal with a refractive index n1 coupled to a

photon detector with a refractive index n2. The crystal is wrapped on 5 of its surface by

a reflector material. The remaining surface, known as the exit surface, is polished and attached to the photon detector without a coupling substance.

Fig 1.4. A cuboid shaped crystal with dimensions xo, L, and zo, as used by the ray

tracing software. Gamma photons enter the crystal from the left-hand side, whereas the right-hand side is coupled to a photon detector.

During the simulation Nγ gamma events are traced, each one resulting in the

emission of Nsci scintillation photons. Thus, for each gamma event the path of Nsci

photons are traced. Each detected scintillation photon creates a time stamp. The time stamps are subsequently ordered in time. The time variation (FWHM) in the detection Chapter 1

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of the nth detected photon is determined for n = 1 till n = 100. The settings of the

software will be explained the remainder of this section, which can be used as a manual for future users. The input parameters are given below.

x0, L, z0 The dimensions of the crystal in the x, y, and z direction, respectively, see Fig. 1.4

n1 The refractive index of the scintillator

n2 The refractive index of the photon detector

l The attenuation coefficient of the scintillator for gamma detection

Isci (t) The intrinsic scintillation pulse shape

The total number of simulated gamma events

Nsci The total number of emitted scintillation photons per gamma event

pabs The absorption probability, defined as the probability of losing a photon

when it hits one of the 5 packed crystal surfaces.

dwell time The dwell time is the time a photon dwells inside the reflector during the

reflection process. The dwell time is added to the total traveling time each time a photon reflects at the crystal reflector interface.

Idtts (t) The detector transit time-spread function, in this work considered to be

Gaussian distributed. The remaining parameters are as follows:

The nth traced γ-photon

nsci The nth traced scintillation photon for a given γ-photon

nph The nth traced optical photon, emitted by the laser

The traveling time of the gamma photon inside the crystal

tem The time between the absorption of the gamma photon and the emission of the scintillation photon

tott The traveling time of the scintillation photon inside the crystal

trefl The total traveling time of photon inside the reflector, i.e. the dwell time times the total number of reflections at the crystal reflector interface

tdtt The detector transit time, i.e. time between the creation of a photoelectron in the photon detector and the time stamp

Iotts (t) The optical transit time-spread

Iobs (t) The observed scintillation pulse, i.e. the time stamp distribution obtained from a single gamma event.

Δt (n) The FWHM of the distribution in the Nγ time stamps of the nth detected

scintillation photon e.g. with the timing model described in [14]. This set-up can furthermore be used to

measure how long photons dwell inside reflectors. For instance, it was shown in [15] that a delta light pulse is spread out in time while transmitting through Teflon tape. When photons dwell inside the reflector medium for some time Iotts (t) is expected to broaden. The photon dwell time can be used as an input for ray tracing software to study its effect on the timing resolution. The set-up is described in more detail in chapter 5.

Ray tracing software is a powerful tool to attain information about optical transit time-spread. Codes such as GATE, GEANT4, and Litrani [16-19] are often used to study Iotts (t) and its contribution to the timing resolution [20-26]. Using these software packages it cannot be studied how the dwell time of photons during the reflection process affects Iotts (t) and the timing resolution. In this research a new Monte Carlo-based ray tracing software package was developed that takes into account the photon dwell time inside the reflector medium. Two software codes were written, one to obtain the detector timing resolution and one to obtain Iotts (t). The former, which is used in chapter 6, will be explained first.

Timing resolution

Figure 1.4 shows a cuboid shaped crystal with a refractive index n1 coupled to a

photon detector with a refractive index n2. The crystal is wrapped on 5 of its surface by

a reflector material. The remaining surface, known as the exit surface, is polished and attached to the photon detector without a coupling substance.

Fig 1.4. A cuboid shaped crystal with dimensions xo, L, and zo, as used by the ray

tracing software. Gamma photons enter the crystal from the left-hand side, whereas the right-hand side is coupled to a photon detector.

During the simulation Nγ gamma events are traced, each one resulting in the

emission of Nsci scintillation photons. Thus, for each gamma event the path of Nsci

photons are traced. Each detected scintillation photon creates a time stamp. The time stamps are subsequently ordered in time. The time variation (FWHM) in the detection

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Aspects that govern the timing resolution of scintillation detectors

Optical transit time-spread

In chapter 5 Iotts (t) will be determined by means of experiment using the set-up

introduced earlier in this section. In chapters 5 and 6 our ray tracing software will be

used to obtain Iotts (t) by means of simulation. The block diagram of this software

package is given in Fig. 1.6. A delta light pulse enters the crystal through a given position on the (y,z)-plane at x = x0 at t = 0. In the experiment the crystal is packed on 5 of its surface leaving the crystal surface at y = L unwrapped. This wrapped surface faces the streak camera which measures the intensity of the light that escapes the crystal. In the simulations Nph are emitted from a given position on the crystal surface

at x = x0. All scintillation photons are emitted at t = 0. A typical value for Nph to obtain

good statistics is 200,000. The direction the scintillation photon is emitted to is determined the same way as when the photon hits the crystal surface from the inside assuming Lambertian-Beer reflection. Since there is an air gap in between the crystal and streak camera, n2 was chosen 1.0. For each reflection at the crystal reflector interface there is a probability pabs of losing the photons. If the photon eventually escapes the exit surface it instantly creates a time stamp, due to the excellent timing performance of the streak camera. The time stamp is calculated by totts + trefl. When the number of traced photons nph equals Nph a histogram is created from all time stamps with a bin width of 1 ps. An example is added to Fig. 1.6.

Aspects that govern the timing resolution of scintillation detectors

Δtbest The smallest Δt (n). It provides a measure, or figure of merit, for the obtainable timing resolution.

ttimestamp The time stamp created for each detected photon

Since it is a Monte Carlo-based code the traces of single emitted scintillation photons are simulated. The block diagram in Fig. 1.5 will be explained step by step. When running the software it defines nγ = 0, since no gamma events have been traced so far. A 511 keV photon

enters the crystal through the (x,z)-plane at y = 0 and t = 0 at a random position. Since a gamma photon is absorbed, nγ is raised by 1, i.e. nγ = nγ +1. The depth (y-coordinate) at which

the gamma photon creates an ionization track is determined from the probability density function (pdf) given by . tγ is calculated by dividing the depth of interaction by the

speed of light in vacuum. The ionization track is considered to be infinitely short.

Since no scintillation photons have been traced yet, the software defines nsci = 0. From the

ionization track one scintillation photon is emitted in a random direction. Since a scintillation photon is emitted nsci is raised by 1, i.e. nsci = nsci + 1. tem is determined from the pdf given by

Isci (t). The scintillation photon either hits 1 of the 5 packed crystals surfaces or it hits the

crystal exit surface. If it hits a packed crystal surface there is a probability pabs of losing the

photon. If the photon is absorbed and nsci < Nsci the next scintillation photon is emitted and

therefore nsci = nsci + 1. If the photon is not absorbed at the crystal reflector interface it either

undergoes Labertian-Beer or specular reflection, determined by the user. Again, the photon either hits 1 of the 5 packed crystal surfaces or the exit surface. If the photons hits the exit surface it reflects specularly if the angle of incidence is larger than the critical angle , where = arcsin . If < there is a probability R that it reflects specularly and a probability 1 - R that it enters the photon detector and creates a time stamp, where

R = .

The time stamp ttimestamp is calculated by tγ + tem + totts + trefl + tdtts, where totts is calculated

by the total traveling path divided by the speed of light in vacuum and multiplied by n1. trefl

equals the total number of reflections times the dwell time. tdtts is determined from the pdf Idtts

(t). If nsci < Nsci the next scintillation photon is emitted and nsci = nsci +1. If nsci = Nsci all time

stamps are ordered in time and stored as one time stamp distribution. If nγ < Nγ the next

γ-photon enters the crystal. If nγ = Nγ, the FWHM of the distribution in the Nγ time stamps of the

nth detected photon is defined as Δt (n). The software subsequently plots Δt (n) for n = 1 till n

= 100 in steps of 1. An example is added to Fig 1.5. Chapter 1

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Optical transit time-spread

In chapter 5 Iotts (t) will be determined by means of experiment using the set-up

introduced earlier in this section. In chapters 5 and 6 our ray tracing software will be used to obtain Iotts (t) by means of simulation. The block diagram of this software package is given in Fig. 1.6. A delta light pulse enters the crystal through a given position on the (y,z)-plane at x = x0 at t = 0. In the experiment the crystal is packed on 5 of its surface leaving the crystal surface at y = L unwrapped. This wrapped surface faces the streak camera which measures the intensity of the light that escapes the crystal. In the simulations Nph are emitted from a given position on the crystal surface

at x = x0. All scintillation photons are emitted at t = 0. A typical value for Nph to obtain

good statistics is 200,000. The direction the scintillation photon is emitted to is determined the same way as when the photon hits the crystal surface from the inside assuming Lambertian-Beer reflection. Since there is an air gap in between the crystal and streak camera, n2 was chosen 1.0. For each reflection at the crystal reflector interface there is a probability pabs of losing the photons. If the photon eventually escapes the exit surface it instantly creates a time stamp, due to the excellent timing performance of the streak camera. The time stamp is calculated by totts + trefl. When the number of traced photons nph equals Nph a histogram is created from all time stamps with a bin width of 1 ps. An example is added to Fig. 1.6.

Δtbest The smallest Δt (n). It provides a measure, or figure of merit, for the obtainable timing resolution.

ttimestamp The time stamp created for each detected photon

Since it is a Monte Carlo-based code the traces of single emitted scintillation photons are simulated. The block diagram in Fig. 1.5 will be explained step by step. When running the software it defines nγ = 0, since no gamma events have been traced so far. A 511 keV photon

enters the crystal through the (x,z)-plane at y = 0 and t = 0 at a random position. Since a gamma photon is absorbed, nγ is raised by 1, i.e. nγ = nγ +1. The depth (y-coordinate) at which

the gamma photon creates an ionization track is determined from the probability density function (pdf) given by . tγ is calculated by dividing the depth of interaction by the

speed of light in vacuum. The ionization track is considered to be infinitely short.

Since no scintillation photons have been traced yet, the software defines nsci = 0. From the

ionization track one scintillation photon is emitted in a random direction. Since a scintillation photon is emitted nsci is raised by 1, i.e. nsci = nsci + 1. tem is determined from the pdf given by

Isci (t). The scintillation photon either hits 1 of the 5 packed crystals surfaces or it hits the

crystal exit surface. If it hits a packed crystal surface there is a probability pabs of losing the

photon. If the photon is absorbed and nsci < Nsci the next scintillation photon is emitted and

therefore nsci = nsci + 1. If the photon is not absorbed at the crystal reflector interface it either

undergoes Labertian-Beer or specular reflection, determined by the user. Again, the photon either hits 1 of the 5 packed crystal surfaces or the exit surface. If the photons hits the exit surface it reflects specularly if the angle of incidence is larger than the critical angle , where = arcsin . If < there is a probability R that it reflects specularly and a probability 1 - R that it enters the photon detector and creates a time stamp, where

R = .

The time stamp ttimestamp is calculated by tγ + tem + totts + trefl + tdtts, where totts is calculated

by the total traveling path divided by the speed of light in vacuum and multiplied by n1. trefl

equals the total number of reflections times the dwell time. tdtts is determined from the pdf Idtts

(t). If nsci < Nsci the next scintillation photon is emitted and nsci = nsci +1. If nsci = Nsci all time

stamps are ordered in time and stored as one time stamp distribution. If nγ < Nγ the next

γ-photon enters the crystal. If nγ = Nγ, the FWHM of the distribution in the Nγ time stamps of the

nth detected photon is defined as Δt (n). The software subsequently plots Δt (n) for n = 1 till n

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Aspects that govern the timing resolution of scintillation detectors

Fig 1.6. A block diagram of the ray tracing software used to obtain the optical transit time-spread of a scintillation detector.

start

from the position where the laser enters the crystal a scintillation photon is emitted. Its direction is

determined the same as if the photon hits the crystal reflection

interface from the inside, assuming Lambertian-Beer

reflection.

photon hits 1 of the 5

wrapped crystal surfaces photon hits exit surface

nph = 0

nph = nph +1

pab

s

photon reflects at the crystal reflector interface: - Lambertian-Beer - specular 1 - pabs specular reflection if θi > θ c detection of photon time stamp = totts+tref +tdtts if θi < θ c R 1 - R if nph < Nph a histogram is created from all time stamps

with a bin width of 1 ps if nph =

Nph

optical transit time-spread is plotted if nph < Nph

if nph =

Nph

Aspects that govern the timing resolution of scintillation detectors

Fig 1.5. A block diagram of the ray tracing software used to obtain the timing resolution of a scintillation detector.

511 keV photon enters the crystal through the (x,z)-plane at y = 0 and t = 0.

start

depth of interaction is determined from an exponential decay

ecay with an attenuation coefficient of 1.14 cm for LSO:Ce

A new scintillation photon is emitted in a random direction (isotropic emission). The time of emission is determined from

the pdf given by Isci(t).

photon hits 1 of the 5 wrapped crystal

surfaces

photon hits exit surface nγ = 0 nsci = 0 nsci = nsci +1 pabs

photon reflects at the crystal reflector interface:

- Lambertian-Beer - specular

1 -

pabs reflection specular

if θi > θ c detection of photon time stamp = tγ+tem+totts+tref +tdtts if θi < θ c R 1 - R if nsci < Nsci

all time stamps are ordered in time and stored as one time stamp distribution if nsci = Nsci if nγ < Nγ nγ = nγ +1

From all time stamp distributions the time variation

of the nth detected photon is calculated, where n varies from 1 to 100 is steps of 1.

timing curve is plotted if nγ = Nγ if nsci < Nsci

if nsci =

Nsci

(19)

Fig 1.6. A block diagram of the ray tracing software used to obtain the optical transit time-spread of a scintillation detector.

start

from the position where the laser enters the crystal a scintillation photon is emitted. Its direction is

determined the same as if the photon hits the crystal reflection

interface from the inside, assuming Lambertian-Beer

reflection.

photon hits 1 of the 5

wrapped crystal surfaces photon hits exit surface

nph = 0

nph = nph +1

pab

s

photon reflects at the crystal reflector interface: - Lambertian-Beer - specular 1 - pabs specular reflection if θi > θ c detection of photon time stamp = totts+tref +tdtts if θi < θ c R 1 - R if nph < Nph a histogram is created from all time stamps

with a bin width of 1 ps if nph =

Nph

optical transit time-spread is plotted if nph < Nph

if nph =

Nph

Fig 1.5. A block diagram of the ray tracing software used to obtain the timing resolution of a scintillation detector.

511 keV photon enters the crystal through the (x,z)-plane at y = 0 and t = 0.

start

depth of interaction is determined from an exponential decay

ecay with an attenuation coefficient of 1.14 cm for LSO:Ce

A new scintillation photon is emitted in a random direction (isotropic emission). The time of emission is determined from

the pdf given by Isci(t).

photon hits 1 of the 5 wrapped crystal

surfaces

photon hits exit surface nγ = 0 nsci = 0 nsci = nsci +1 pabs

photon reflects at the crystal reflector interface:

- Lambertian-Beer - specular

1 -

pabs reflection specular

if θi > θ c detection of photon time stamp = tγ+tem+totts+tref +tdtts if θi < θ c R 1 - R if nsci < Nsci

all time stamps are ordered in time and stored as one time stamp distribution if nsci = Nsci if nγ < Nγ nγ = nγ +1

From all time stamp distributions the time variation

of the nth detected photon is calculated, where n varies from 1 to 100 is steps of 1.

timing curve is plotted if nγ = Nγ if nsci < Nsci

if nsci =

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