Signal to Noise Optimization in Front-End
Electronics for X-ray Imaging
CHRISTEL SUNDBERG
Master of Science Thesis
ISSN 0280-316X ISRN KTH/FYS/–17:47—SE
KTH Department of Physics SE-100 44 Stockholm
Sweden
Supervisor: Mats Danielsson
©Christel Sundberg
iii
Abstract
X-ray imaging is one of the most important tools in medical diagnostics and involves non-invasive methods that utilize x-rays to create images of the human interior. In computed tomography (CT), 3D images are formed from x-ray pro- jections taken at different angles of the patient. CT images enable diagnosis, treatment planning and treatment verification, however, as x-rays are ionizing, methods to reduce the radiation dose are desired.
In recent years, photon-counting detectors for spectral CT have been reported.
One such detector is the silicon strip detector developed by the Physics of Med- ical Imaging group at KTH. The performance of a silicon strip detector system is affected by electronic noise which decreases the dose efficiency. In this work, a detector system including a silicon strip detector and an application specific integrated circuit (ASIC) is simulated. The work is focused on the relation between the peak time of the ASIC filter and the number of registered photons.
Based on the modeled detector system, it is shown that increasing the peak time reduces the noise. At low photon fluxes, high peak times can be used to increase the number of registered counts and thereby increase the dose ef- ficiency. By utilizing two parallel filters of peak times 40 and 100 ns, it is estimated that the dose efficiency increases in the order of 5% compared to a single filter with either of the two peak times.
Sammanfattning
Medicinsk röntgendiagnostik utgörs av icke-invasiva metoder där bilder av pa- tientens inre skapas med hjälp av röntgenstrålning. Med datortomografi (CT) skapas 3D-bilder utifrån röntgenprojektionsbilder tagna vid olika vinklar av patienten. CT är en viktig medicinsk teknik som möjliggör diagnos, behand- lingsplanering samt utvärdering av den givna behandlingen. Dock anses strål- dosen som associeras med CT-undersökningar hög och metoder som möjliggör en lägre stråldos eftersträvas.
Under de senaste åren har fotonräknande detektorer för spektral CT presen- terats. En sådan detektor är kiselstrippdetektorn utvecklad av gruppen inom medicinsk bildfysik på KTH. I en kiselstrippdetektor påverkar elektroniskt brus systemets totala doseffektivitet. I detta arbete har ett detektorsystem med en kiselstrippdetektor och en applikationsspecifik integrerad krets (ASIC) simule- rats. Arbetet syftar till att undersöka relationen mellan ASIC-filtrets peaking- tid och antalet registrerade fotoner.
Resultaten utifrån det modellerade detektorsystemet visar att en ökning av pe- akingtiden resulterar i mindre brus. Vid låga fotonflöden kan en hög peakingtid användas för att öka antalet registrerade fotoner och därmed öka doseffektivi- teten. Med två parallella filter med peakingtider 40 och 100 ns i samma kanal estimeras doseffektiviteten öka i storleksordningen 5% i jämförelse med enbart ett filter med någon av de två peakingtiderna.
v
Acknowledgements
I would like to thank my supervisor Professor Mats Danielsson at KTH, for his guidance during this work. I would also like to thank Professor Emeritus Christer Svensson for help with modeling the ASIC.
Further, I would like to thank Dr. Cheng Xu for helping me with Penelope and GATE. The GATE geometry was modeled by Dr. Mats Persson and I owe him a debt of gratitude for always being helpful and patient. I would also like to thank Dr. Jacob Wikner for guiding me through the analog front-end electron- ics and constantly providing excellent answers to all of my questions. Finally, I would like to thank Dr. Martin Sjölin and Fredrik Grönberg for providing ideas and giving helpful advice.
Contents vi
1 Introduction 1
1.1 Computed Tomography . . . 1
1.2 Radiation Dose and Image Quality . . . 1
1.3 Noise in a Semiconductor Detector System . . . 2
1.4 Objectives . . . 3
2 Theoretical Background 5 2.1 X-rays in Computed Tomography . . . 5
2.1.1 Interactions between X-rays and Matter . . . 6
2.2 CT Detectors . . . 11
2.2.1 Silicon Strip Detector . . . 11
2.3 ASIC . . . 13
2.3.1 Analog Channel Description . . . 13
2.3.2 Circuit Noise . . . 16
2.3.3 Filters, Peak Time and Noise . . . 17
3 Simulation Methods 19 3.1 Simulation of the Signal . . . 19
3.1.1 Deposited Energy Spectrum . . . 19
3.1.2 Pulse Shape Simulation . . . 20
3.2 ASIC Model . . . 21
3.2.1 Modeled Circuit Noise . . . 21
3.3 Photon-Counting and Energy Classification . . . 22
3.4 Evaluation of Parallel Filters . . . 22
3.4.1 Noise Size and DAC0 . . . 22
3.4.2 Dead Time . . . 23
3.4.3 Filter Performance . . . 23
4 Results 25 4.1 Signal . . . 26
4.2 Pulse Length and Dead Time . . . 27
4.3 DAC0 and Deposited Energy Spectrum . . . 30 vi
CONTENTS vii
4.4 Modeled Output Noise . . . 33
4.5 Filter Performance . . . 35
4.5.1 Low Flux . . . 36
4.5.2 Medium Flux . . . 39
4.5.3 High Flux . . . 42
5 Discussion 45 5.1 ASIC Model . . . 45
5.2 Optimal DAC0 . . . 46
5.3 Dead Time . . . 46
5.4 Simulation Results . . . 47
5.4.1 Performance of Parallel Filters . . . 48
5.5 Baseline Holder . . . 48
5.6 Further Work . . . 49
Bibliography 51
Chapter 1
Introduction
1.1 Computed Tomography
In projection radiography, an x-ray beam is transmitted through the human body and the x-rays are, to some degree, absorbed. The amount of absorption is tissue dependent and therefore varies according to the internal structures of the body.
The remaining x-ray pattern is detected and an x-ray image is created. The im- age is a superimposition of each structure between the x-ray source and the detector.
To obtain 3D images, information about where x-ray attenuation occurs is needed.
In 1979, Allan M. Cormack and Godfrey N. Hounsfield were awarded the Nobel Prize in Physiology or Medicine for the development of computed tomography (CT) [1].
In CT, the x-ray source and detector are rotated around the patient, gathering x- ray images from many different angles. From the different projections, it is possible to computationally reconstruct the imaged section of the patient, resulting in a 3D image.
Computed tomography is today one of the most common medical examinations throughout the world. In the US, approximately 82 million CT exams were per- formed in 2016 [2]. A major advantage of CT is the rapid acquisition of images that contain clear and accurate information. From a medical perspective, obtaining information about internal structures enables diagnosis, treatment planning, and treatment evaluation. CT images provide a geometrically correct representation of the human body, and are therefore commonly used in radiation treatment planning.
1.2 Radiation Dose and Image Quality
Despite the advantages and popularity of CT imaging, the x-ray dose during a CT examination is considered high. X-rays are ionizing and cause biologic damage, which can lead to cancer induction [3]. CT scanning contributes to the total cancer risk [4], but for many applications, CT is for performance and practical reasons
1
Figure 1.1. CT image of a human skull phantom.
the method of choice. It is therefore of great importance to reduce the imaging radiation dose.
To enable correct assessment and diagnosis from a CT image, sufficient image qual- ity is required. Noise is closely related to radiation dose, i.e. for low radiation doses, image noise increases. Noise limits the ability to perceive contrast and thereby re- duces image quality [5]. Decreasing the radiation dose is therefore performed at the expense of image quality.
Recently, with the advent of iterative reconstruction and improved imaging proto- cols, the radiation dose in CT has been reduced, and the associated risk thereby decreased. New technology, like photon-counting detectors, is expected to decrease the dose further.
1.3 Noise in a Semiconductor Detector System
CT systems using semiconductor detectors have received considerable attention in recent years [6]. In a semiconductor detector, photons that interact with the detec- tor create electron-hole pairs. The electrons and holes are transported in an applied electric field, inducing a current. An application specific integrated circuit (ASIC) amplifies and converts the current to voltage and the number of interacting photons and their energies can be registered.
1.4. OBJECTIVES 3
Noise from the detector and the ASIC is added to the signal. For sufficient image quality, only a certain level of registered noise is allowed. Therefore, a threshold is applied, below which, no signal is registered, see Figure 1.2.
0 20 40 60 80 100
Time [7s]
-15 -10 -5 0 5 10 15
Voltage [mV]
Figure 1.2. Noise voltage and an exemplified threshold.
The threshold effectively prevents noise from registering as photon signals. However, it also prevents registration of low energy signals, decreasing the total dose efficiency.
1.4 Objectives
One of the ASIC components is a low-pass filter with peak time τp. Peak time is defined as the time at which the output pulse from the filter has its maximum voltage when the input pulse is a delta function at time t = 0. The filter reduces the noise, and more so for larger values of τp since it effectively reduces the frequency bandwidth of the filter.
A large value of τp reduces the noise but also decreases the speed of the detection process. At high photon fluxes, that causes some photon signals, (that in many cases would be detectable with a smaller τp) to go unnoticed or become incorrectly registered, so called pile-up.
The main aim of this work is to simulate how peak time affects the number of de- tected photons and thereby the dose efficiency. The objectives include simulating an ASIC input signal, developing an ASIC model, and, from the output voltage provided by the modeled ASIC, registering photon signals and their energies. By assessing the performance of the simulated system at different peak times and pho- ton fluxes, the concept of having two parallel filters with different peak times is evaluated.
Chapter 2
Theoretical Background
2.1 X-rays in Computed Tomography
In medical CT, the x-ray energy ranges between 30-140 keV. In an x-ray tube, x-rays are produced when accelerated electrons hit a target material. When the electrons interact with the target material, x-rays arise from bremsstrahlung and character- istic radiation.
The acceleration of the electrons is performed by an electric potential which is applied across the x-ray tube. An x-ray tube operating at e.g. 100 kVp has an applied potential of 100 kV which results in a maximum photon energy of 100 keV.
0 20 40 60 80 100 120 140
Energy [keV]
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Probability density [0.1 keV-1 ]
Figure 2.1. Energy spectrum of an x-ray source.
In Figure 2.1, a typical x-ray energy spectrum of an x-ray source can be seen. The spectrum shows the energies that are emitted by the x-ray source and their rela- tive intensities. Photons of low energies are filtered out by the x-ray tube and are
5
therefore not present in the spectrum.
The main part of the energy spectrum is created by bremsstrahlung. Bremsstrahlung occurs when high-speed electrons are decelerated by nuclei of the target material.
The sharp peaks in the energy spectrum originate from characteristic radiation:
when a high-speed electron releases an inner shell electron from an atom in the target material, x-rays of specific energies are produced [6].
2.1.1 Interactions between X-rays and Matter
When an object is located between the x-ray source and the detector, the incident energy spectrum at the detector becomes different compared to the x-ray source spectrum. This is due to interactions between the x-ray photons and the atoms of the object. For the photon energies in medical CT, three different types of interac- tions can occur:
• The photoelectric effect: an incident x-ray photon uses its entire energy to liber- ate an electron from a deep shell of an atom. The vacancy left by the electron is filled by another electron from an outer shell and characteristic radiation is emitted.
• Compton scattering: an incident x-ray photon strikes and frees an electron of an atom. The photon is deflected and loses some of its initial energy.
• Rayleigh scattering: a photon beam is an electromagnetic wave with an oscillat- ing electric field. The oscillating electric field sets the electrons in the atoms of the object into vibration and radiation of the same wavelength as the incident photon beam is emitted.
The interactions of the x-rays with the detector results in the deposited energy spec- trum, showing the energies that are deposited in the detector by incident photons.
A typical deposited energy spectrum with 30 cm soft tissue between the x-ray source and the detector can be seen in Figure 2.2. No signals are generated by Rayleigh scattering.
The maximum voltage of each output pulse from the ASIC corresponds to the energy deposited by the photon. The threshold, as in Figure 1.2, can therefore be translated to an energy. To evaluate the effect of a certain threshold in terms of the amount of signals below the threshold, the threshold can directly be applied in the deposited energy spectrum.
2.1. X-RAYS IN COMPUTED TOMOGRAPHY 7
0 20 40 60 80 100 120 140
Energy [keV]
0 1 2 3 4 5 6 7
Probability density [0.1 keV-1 ]
#10-3
Figure 2.2. Spectrum of the deposited energies in a detector.
Compton Scattering
At low energies, the deposited energy spectrum is created by Compton scattered electrons. Compared to the photoelectric effect, where the electron obtains the en- tire energy of the photon, Compton scattering is quite different.
When Compton scattering occurs, the energy of the scattered photon, Es, depends on the scattering angle θ and the incident photon energy, Ei, according to the Compton formula
1 Es − 1
Ei = 1
mec2(1 − cos θ) , (2.1)
with me as the electron mass and c as the speed of light. In Figure 2.3, Compton scattering is illustrated.
Ei θ
Es
Figure 2.3. Compton scattering caused by an incident photon of energy Ei.
The detected energy, the energy of the electron, Ee, is related to the incident photon energy and the scattered photon energy according to
Ee= Ei− Es . (2.2)
Combining (2.1) and (2.2), it is clear that Compton scattering can result in electrons of many different energies based on the incident energy and the scattering angle of the photon. Figure 2.4 shows how the scattering angle θ is related to the electron energy.
0 0.5 1 1.5
Ee [keV]
0 10 20 30 40 50 60
3 [° ]
40 keV 60 keV 80 keV
Figure 2.4. Scattering angles and resulting electron energies for three different incident energies.
Klein Nishina
In the Compton scattering formula, equation (2.1), the probability of scattering is not the same for all scattering angles. The angular dependence of scattering can be found using the Klein-Nishina formula:
dσ dΩ = re2
2
1 + cos2θ
(1 + (1 − cos θ))2 1 + 2(1 − cos θ)2
(1 + cos2θ)(1 + (1 − cos θ))
!
, (2.3)
where = mEi
ec2 and re is the classical electron radius. Ω is the solid angle and the solid angle element dΩ is defined as
dΩ = 2π sin θdθ . (2.4)
2.1. X-RAYS IN COMPUTED TOMOGRAPHY 9
The Klein Nishina formula describes the differential cross-section, dΩdσ, as a function of the incident photon energy Ei, assuming that the electron is initially free and at rest. Therefore, the formula only acts as an approximation in this work.
To obtain the probability of a certain scattering angle, equations (2.3) and (2.4) are first combined;
dσ = r2e 2
1 + cos2θ
(1 + (1 − cos θ))2 1 + 2(1 − cos θ)2
(1 + cos2θ)(1 + (1 − cos θ))
!
2π sin θdθ . (2.5) Using equation (2.5), the probability of scattering within [θ −dθ2, θ +dθ2 ) for a certain Ei, P(θ,Ei), can then be written as:
P (θ, Ei) = dσ(θ, Ei) Rπ
0 dσ(θ, Ei) . (2.6)
In Figure 2.5, the Klein Nishina differential size of the cross-section is presented and Figure 2.6 shows P (θ, Ei).
Probability of scattering below the noise floor
From Klein Nishina, it is possible to approximate the probability of primary Comp- ton interactions that result in Ee≤ Ethreshold.
The Compton scattering formula, equation (2.1), gives that with a constant Ei, a decrement of θ results in an increment of Es. From equation (2.2) it is also clear that increasing Es decreases Ee. With Ee = Ethreshold, a corresponding θthreshold can be calculated. Energies below Ethreshold will then occur for angles smaller than θthreshold.
Given Ei, the probability of Ee≤ Ethreshold is P (Ee≤ Ethreshold|Ei) =
Z θthreshold
0
dσ(θ, Ei) (2.7)
From the energy spectrum that interacts with the detector, the probability of each Ei, P(Ei)dEi, is given. The total probability of Ee≤ Ethreshold for all Ei can then be calculated according to
P (Ee≤ Ethreshold) = Z Emaxi
Eimin
Z θthreshold 0
dσ(θ, Ei)P (Ei)dEi (2.8) Table 2.1 shows P (Ee ≤ Ethreshold) for different values of Ethreshold. The calcula- tions were based on an x-ray source operated at 120 kVp with an object of 30 cm soft tissue located between the source and the detector.
It is important to note that the probabilities in Table 2.1 are under the assumption that a Compton interaction has occurred - the probability of a Compton interaction occurring has not been included.
0 50 100 150 200 3 [°]
0 0.5 1 1.5 2 2.5 3
d< [m2 ]
#10-29
40 keV 60 keV 80 keV
Figure 2.5. Klein Nishina differential size of the cross-section.
0 50 100 150 200
3 [°] 0
0.002 0.004 0.006 0.008 0.01
Probability density [1/degree]
40 keV 60 keV 80 keV
Figure 2.6. Klein Nishina probability of scattering at a certain dθ.
Table 2.1. Probability of primary Compton interactions resulting in Ee≤ Ethreshold.
Ethreshold[keV] P (Ee≤ Ethreshold) [%]
2 13.7
3 19.6
4 25.2
5 30.6
2.2. CT DETECTORS 11
2.2 CT Detectors
Commercial CT systems today use scintillation detectors. Scintillation detectors contain scintillating material coupled to photodiodes or photomultipliers. An inci- dent x-ray photon interacts with the scintillating material, creating a photoelectron.
The photoelectron induce emission of visible light, which in turn is detected by a photodiode.
All commercially available detectors today are energy integrating detectors, inte- grating the energy deposited by a multitude of x-rays over a certain exposure time.
One drawback with energy integration is that the energy information in the incident x-rays is lost. Since the x-ray attenuation in a material is dependent on the x-ray energy, x-ray photons of higher energies generally carry less contrast information [7].
In an energy integrating detector, that is not taken into consideration, instead, the generated signal is proportional to the energy [8]. Electronic noise is also integrated, resulting in poor image quality for low radiation doses.
An emerging detector type in CT is the semiconductor detector. In a semiconductor detector, the energy information of each incident photon can be detected. It enables photon-counting spectral CT, in which the spectral information of the x-rays can be utilized to improve image quality.
2.2.1 Silicon Strip Detector
In recent years, the performance of silicon strip detectors has been evaluated by the Physics of Medical Imaging group at KTH [9–15].
The energy required to create one electron-hole pair in a silicon detector is
3.6 eV [16]. For a photon that deposits the energy Edeposited, N electron-hole pairs are created according to
N = Edeposited
3.6 eV . (2.9)
Under the influence of an electric field, the electrons move to the backside of the detector and the holes to the front (Fig. 2.7 b). During the transport, a current is induced in the detector electrode (Fig 2.7 a) which can be detected in an ASIC.
In this work, the simulated detector is a silicon strip detector with an edge-on ge- ometry as presented by Cheng Xu et. al [17].
Using silicon strip detectors, a full CT detector is obtained by first arranging the silicon strips in linear arrays, forming detector modules. The detector modules are then stacked together. In Figure 2.8, an example of a silicon strip detector module can be seen.
a.)
A B
0 V
300 V C
D E
F
A: Front side of detector B: Electrode
C: Pixel D: Sensor E: X-rays
F: Backside of detector
b.)
0 V 300 V
A B
C D
E
A: Hole B: Electron C: X-ray photon D: Front side of detector E: Backside of detector
Figure 2.7. a.) Array of silicon strip detectors. b.) Cross-section of a silicon strip detector.
Figure 2.8. Photograph of a detector module with 9 depth segments. X-rays enter from the top.
2.3. ASIC 13
2.3 ASIC
One of the key components in the silicon strip detector system is the ASIC. It is a mixed-signal circuit which performs the readout from the detector; photon-counting and energy classification. For CT, the main requirements of the ASIC involve a high count rate and a low threshold for minimum detectable energy.
2.3.1 Analog Channel Description
Cf
Detector CSA Differentiator
Cdet
Rf
Cs
Rs
Cpz
Rpz
PZC Circuit
Digital block 8 comparators
Vref0
Vref1
Vref7
Clk Globally distributed programmable thresholds
Gm-C Filter
Figure 2.9. Block diagram of the ASIC analog front-end, i.e., the interface to the detector diode.
In this work, the simulation of the analog electronics is based on the ASIC presented by Mikael Gustavsson et al. in [18]. It is a high-rate energy-resolving photon- counting ASIC aimed for spectral CT with an average gain of 2.10 mV/keV.
The ASIC consists of 160 channels. Figure 2.9 shows an overview of the analog interfacing circuits in each channel. The first component is the charge sensitive amplifier (CSA). For every photon that interacts with the detector, a current of total charge Q is produced according to
Q = Edeposited 3.6 eV · e =
Z
Idt , (2.10)
with Edeposited as the deposited energy, e = 1.60217662 · 10−19 C, I as the current, and t as the time.
In the CSA, the current is integrated, resulting in an output voltage. The
transimpedance, Z, i.e., the current-to-voltage gain of the CSA, can be expressed by Ohm’s law: the voltage across the CSA is given by the feedback impedance multiplied with the current:
(Vout− Vin)
Z = Iin , (2.11)
where Vinand Vout are the input and output voltages to and from the CSA respec- tively and Iin is the input current. Assuming Vin= 0 gives
Vout= ZIin . (2.12)
Under the assumption of an infinite feedback resistance Rf, the transimpedance of the CSA can be expressed from the block diagram in Figure 2.9 using the formalism in [19]
Z(s) = − 1
sCf , (2.13)
where Cf is the feedback capacitance.
The CSA is followed by a pole zero cancellation (PZC) circuit and a differentiator.
The PZC circuit eliminates undershoot due to the decay time of the CSA feedback loop. The gain of the PZC circuit and the differentiator is
Av(s) = − sCpzRs 1 + sRsCs
, (2.14)
where Cpz is the capacitance of the PZC circuit and Rs and Cs are the resistance and the capacitance of the differentiator respectively.
The filter block is implemented using two cascaded lossy transconductance-C (Gm-C) integrator stages. The two stages effectively form one pole each and com- bined act as a second order filter with peak time τp. For a second order filter with identical integrators, the time constant for each Gm-C integrator, τ0, can be expressed as τ0 = τp/2. The gain of one Gm-C integrator is
Avf(s) = 2 1 + Gms
C
, (2.15)
where C is the filter capacitance and Gm is the transconductance of the filter.
In Figure 2.10, the frequency response of the second order filter with a peak time of 40 ns is presented. Increasing the filter order gives a higher roll-off frequency for higher frequencies. For each additional pole, the attenuation further increases by 20 dB/decade.
Combining equations (2.13), (2.14), (2.15) and setting τ0 = RsCs = C/Gm, the total output voltage can be written as
vout = ZtAvAnvfiin= 1 Cf
Cpz
Cs τ0
1 + sτ0
2
1 + sτ0
n
iin , (2.16) where n is the filter order and iin is the input current.
2.3. ASIC 15
10-2 100 102 104
Frequency [MHz]
-100 -80 -60 -40 -20 0 20
Gain [dB]
Figure 2.10. Frequency response of the filter block.
Comparators
The photon-counting and energy classification is enabled by comparators. The com- parators are located at the output of the analog circuit. Each comparator compares the analog voltage to a level set by a digital-to-analog converter (DAC). There are eight different DAC levels of which DAC0 is the lowest, representing the lowest energy threshold. DAC0 is the previously discussed threshold, set to remove noise.
Each comparator receives the output voltage, vout, as input and whenever the volt- age is above DAC0, a count is registered.
The energy of each count is determined during a fixed measuring period, the dead time, which is triggered when the voltage exceeds the DAC0 level. The dead time consists of a number of clock cycles. At each clock cycle, the voltage is compared to the DAC of each comparator. At the end of the dead time, the energy is determined from the highest DAC level exceeded by the voltage.
During each dead time, only one count is registered. This limits the count rate since, for a set measurement time, there can only be a certain number of dead times. At high photon fluxes, pulses created by different photons might lie within the same dead time, causing pile-up. Pile-up describes the phenomenon when two or more photon pulses occur within the same dead time and become registered as one photon with an incorrect energy. The phenomenon also includes pulses that occur close in time and become correctly counted but assigned incorrect energies.
Pile-up results in count loss and spectral distortion. To reduce pile-up, a short dead time is desired.
2.3.2 Circuit Noise
The ASIC output noise power is defined as the variance of the output voltage for a zero input current. In the ASIC read-out chain, two of the major noise sources are the thermal noise in the CSA and the active components in the filter. The thermal noise has a time average of zero and is uncorrelated in time. Pink noise, 1/f-noise, also originates from the CSA, but can be designed to be low compared to the thermal noise [18].
With an input current of zero, the relation between the output noise and the noise from the noise sources is
σoutput2 = σCSA2 + σFilter2 , (2.17)
where σoutput is the standard deviation of the output noise and σCSA and σfilter are the individual standard deviations of the output noise originating from the CSA and the filter block respectively.
Depending on where noise occurs within the ASIC, the noise transfer functions are different. In this work, the CSA noise is modeled as an input current before the CSA block while the filter noise is represented as an input voltage before the filter block.
CSA noise
The transimpedance for the noise from the CSA is vnoise,CSA= 1
G Cdet
Cf Cpz
Cs sτ0
1 + sτ0
2
1 + sτ0
n
iin , (2.18)
where G is the DC gain of the stage and Cdet is the detector capacitance. Since the equivalent input noise current of the CSA is multiplied by the detector capacitance, the function is different than the one presented in equation (2.16).
Filter noise
The transfer function of the noise from the filter block is Z(s)noise,filter = 2
1 + sτ0
n
. (2.19)
With, τ0 = C/Gm, the filter noise and the signal have the same transfer function through the filter block, see equation (2.14).
2.3. ASIC 17
2.3.3 Filters, Peak Time and Noise
The filter block performs pulse shaping. By limiting the bandwidth of the trans- mitted signal, the pulse shape of the output signal is altered. Filters with a small bandwidth have a low transmission of signal noise. For CT purposes, a small band- width is therefore desired, giving a low noise floor and thereby a low DAC0 level.
From equation (2.14), with τ0 = C/Gm, the second order filter is described by Avf(s) = 2
1 + sτ0
2
. (2.20)
The time constant τ0 depends on the peak time. With a long peak time, τ0 increases and the bandwidth of the filter decreases; less noise is transmitted. However, the noise reduction is performed at the expense of the count rate. With a long peak time, the pulse maximum occurs later than with a short peak time; the resulting pulse becomes longer. To avoid registering two or more counts from one pulse, the dead time must be adjusted according to the peak time. As the dead time is in- creased, the count rate decreases.
It is possible to include two parallel filter blocks of different peak times and separate comparators within the same channel. In this work, the performance of the detector system using one fast filter with a short peak time and one slow filter with a longer peak time is evaluated. A fast filter is in general well adapted for high photon fluxes but results in a high noise level. With a slow filter, pile-up arises at high photon fluxes but the output noise level is lower compared to that of the fast filter.
With separate comparators connected to each filter, parallel count registration is enabled. Due to the lower noise level, the slow filter enables a lower DAC0. The idea is to utilize the DAC0 of the slow filter as an extra threshold at low photon fluxes.
Allowing the two filters to complement each other, more counts of low energies are included without increasing the pile-up. The trade-off between a high count rate and a low noise level can thereby be mitigated.
ASICs with two parallel filters, operating at a fast and slow peak time, have previ- ously been reported for other detector types and purposes [20–22]. However, within those systems, the fast filter only provides information about the arrival time of the pulse. The energy classification is therefore solely based on the slow filter output.
Chapter 3
Simulation Methods
3.1 Simulation of the Signal
The input current is modeled by a number of pulses of different energies, distributed over a certain frame time. Each such realization is referred to as a pulse train. In this work, each pulse train has a fixed frame time of 100 µs.
According to photon statistics, the number of pulses in each pulse train is Poisson distributed [23]. The energy of each pulse is determined from the deposited en- ergy spectrum. Pulse trains are created for three different incident photon fluxes:
5 · 104, 4 · 105, and 3 · 106 counts per second (cps). The unit cps is in this work used to describe the number of photons that have deposited energies in the detector.
The pulse shapes are created by simulating the current induction in the detector electrode including the specific detector geometry.
3.1.1 Deposited Energy Spectrum
The deposited energy spectrum shows the energies that are deposited in the de- tector by incident photons. In this work, it is used to determine the pulse train energies and to evaluate how a certain DAC0 affects the number of detected pho- tons. Depending on the geometry of the detector, the spectrum differs. For correct pulse train generation and analysis, a detector specific deposited energy spectrum is therefore required.
The deposited energy spectrum is obtained by combining two separate simulations:
• Detector response to monoenergetic photon fluxes.
• Incident energy spectrum from the x-ray source including object filtration.
19
Monte Carlo simulation of the detector response
The detector response describes the energies that are deposited in the detector by an incident photon flux which is independent of the incident energy spectrum. The detector response for the specific detector geometry is obtained by Monte Carlo simulating the detector in GATE [24].
Separate simulations are performed with monoenergetic photon fluxes between 1 and 160 keV in steps of 0.1 keV. In each separate simulation 100 000 photons are simulated using a monoenergetic x-ray gun, aimed at one pixel. No phantom or specific x-ray source are included.
The GATE simulations only simulate the deposited energies and not the resulting currents. Therefore, the diffusion process of charge sharing is not included in any GATE simulation in this work.
Incident spectrum
The incident spectrum is obtained by filtering the energy spectrum of an x-ray source with tungsten as the target material at an 8◦ target angle through 0.8 mm beryllium and 8.38 mm aluminum. To include a simple phantom, the x-ray spectrum is attenuated by soft tissue. Three different peak voltages of the x-ray source are used in combination with three different tissue thicknesses. These are found in Table 3.1.
Table 3.1. X-ray source voltage and tissue thickness.
X-ray source voltage [kVp] Soft tissue thickness [cm]
80 20
120 30
140 40
Total deposited energy spectrum
For each monoenergetic photon flux, the relative intensity of that specific energy is found in the incident energy spectrum. To obtain the deposited energy spec- trum, the detector response of each monoenergetic photon flux is therefore weighed according to the incident energy spectrum.
3.1.2 Pulse Shape Simulation
The pulse shapes are simulated using the Monte Carlo simulation code system Pene- lope [25]. Separate simulations are performed at 9 equidistant interaction positions of the detector thickness for photon-deposited energies of 30, 60, and 90 keV. The interaction positions are presented in Table 3.2.
3.2. ASIC MODEL 21
Table 3.2. Simulated interaction positions. The positions are measured from the front side of the detector.
Pulse ID Position [mm]
1 0.0625
2 0.1250
3 0.1875
4 0.2500
5 0.3125
6 0.3750
7 0.4375
8 0.5000
9 0.5625
3.2 ASIC Model
The ASIC is simulated in Matlab [26]. It is based on equations (2.13), (2.14) and (2.15) with s = jω and Cf = 200 fF, Cpz = 1600 fF, and Cs = 200 fF. Every input pulse train, P , is Fourier transformed into frequency domain using Matlab’s fft.
Without noise, the output voltage is according to equation (2.16):
vout = 1 Cf
Cpz
Cs τ0
1 + sτ0
2
1 + sτ0
2
· fft(P ) . (3.1)
Since the objective is to evaluate the number of counts for different peak times and resulting DAC0s, only one comparator is included (DAC0). It operates at a clock cycle of 10 ns.
Based on [18], a peak time of 40 ns is used as the initial peak time value. The corresponding dead time is set to 120 ns.
3.2.1 Modeled Circuit Noise
CSA, PZC, Differentiator Filter DAC0
Input signal
CSA noise Filter noise
Figure 3.1. Overview of noise sources within the ASIC.
The noise is modeled as Gaussian white noise in both the CSA and the filter [27]. In Figure 3.1, a schematic overview of the ASIC and noise sources as modeled in this work can be seen. The corresponding transfer functions are described by equations (2.18) and (2.19).
As an approximation, the noise is divided as 2/3 from the CSA noise source and 1/3 from the filter. From equation (2.17), this results in
σCSA= r2
3σoutput , σFilter= r1
3σoutput . (3.2)
3.3 Photon-Counting and Energy Classification
Based on the system parameters, a certain gain factor in mV/keV of the simulated ASIC is obtained. Using the gain factor, the output voltage from the filter block can be translated into energy. In this work, for simplicity, all voltages are translated directly into energies.
The photon-counting is modeled according to the same principle as in the real ASIC:
a count is registered whenever the output voltage exceeds the DAC0. It is followed by a dead time during which, no new counts can be registered.
Since only DAC0 is included, the spectral information, as provided by the compara- tors, is lost. To include an indication of spectral distortion, the maximum energy of each count is however sampled. In the real ASIC, at the end of each dead time, there is a reset time. During the reset time, no energy information of the count is registered. In this work, a reset time of 20 ns is included.
3.4 Evaluation of Parallel Filters
As the two filters in this work are parallel and connected to separate comparators, they can be simulated independently of each other. To evaluate the performance of one filter at a certain peak time, three parameter values are required: the noise size, the DAC0 value, and the dead time.
3.4.1 Noise Size and DAC0
With a peak time of 40 ns, the standard deviation of the output noise, σoutput, is assumed to be 1.5 keV (similar to the noise reported by Cheng Xu et. al. [11]). For other peak times, the input noise from the noise sources is held constant.
To obtain the relation between the peak time and the output noise size, the input current is set to zero. The output voltage is thereby solely created by noise from the two noise sources. The noise size is evaluated by measuring the standard deviation of the output signal during each frame time and then averaging over all simulated frame times.
An optimal DAC0 value is based on the number of noise counts relative to the total number of counts. Depending on the photon flux, the allowed number of noise
3.4. EVALUATION OF PARALLEL FILTERS 23
counts per frame time changes. In this work, the DAC0 is set to remove all noise counts independently of the incident photon flux. Zero noise counts is approximated as allowing 0.0005 noise counts during one frame time.
3.4.2 Dead Time
Using a conventional approach, the dead time is determined from the pulse length.
With a 40 ns peak time, the 120 ns dead time corresponds to the length of a specific pulse at a certain energy threshold. Using the same input pulse and energy thresh- old, the dead time can be found for other peak times by measuring the resulting pulse length.
In [11], a linear relation between the dead time and the peak time was presented.
3.4.3 Filter Performance
A first evaluation of filter performance is based on count characterization. From an input pulse train, the registered counts can be classified according to
• True counts: counts that originate from real photons.
• Double counts: single photon signals being counted multiple times.
• Noise counts: counts that do not originate from photons.
In this work, noise counts are eliminated by the DAC0.
In every generated pulse train, the total number of pulses and their arrival times are known. Identification of double counts is thereby possible by comparing the time stamp of each count to the arrival time of each pulse. If two registered counts occur from one photon signal, the second count is labelled as a double count.
At low photon fluxes, assuming no pile-up or noise, it is possible to calculate the percentage of true counts, ptrue, according to
ptrue= Ncounts− Ndouble
Npulses , (3.3)
with Ncountsas the total number of counts, Ndouble as the number of double counts, and Npulses as the total number of input pulses.
For each peak time and corresponding DAC0, an indication of the filter performance is obtained by comparing ptrue to the amount of the spectrum that lies above the DAC0 level, pdetectable.
To evaluate the effect of the dead time value, the ratio between the total number of double counts and the total number of counts, pdouble is also calculated:
pdouble= Ndouble Ncounts
. (3.4)
A small pdoubleis desired as the double counts incorrectly increase the total number of counts and provide erroneous spectral information.
At higher photon fluxes, double counts become difficult to identify since many photons have similar arrival times. Pile-up also increases and must be taken into consideration. Based on the energy classification of each count, it is possible to compare the deposited energy spectrum to the energy spectrum of the registered counts. This comparison enables identification and evaluation of spectral effects.
Peak times of 20, 40, 100, 200, 500, and 1000 ns are evaluated at the three previously discussed photon fluxes.
Chapter 4
Results
With the described simulation methods, pulse trains are first created. Using single pulses and entire pulse trains as input signals, the modeled read-out chain is ana- lyzed based on the output voltage. From the output pulse lengths, a dead time is determined for each peak time. The output noise is also evaluated and DAC0 values are set, enabling count registration. For pulse trains of different fluxes, counts are then registered and identified. The resulting counts are presented and compared to energy spectra describing the input pulses.
25
4.1 Signal
Figure 4.1. Example of simulated pulse trains at different photon fluxes.
In Figure 4.1, three different pulse trains are presented. The energies are based on the deposited energy spectrum of a 120 kVp x-ray source filtered by 30 cm soft tissue. The deposited energy spectra from x-ray sources of 80, 120, and 140 kVp are presented in Figure 4.2.
The pulses in each pulse train are given a randomly selected pulse shape from the pulses presented in Figure 4.3. Each pulse in Figure 4.3 shows the induced current, created from both holes and electrons. As the electrode is located at the front side of the detector, interaction positions close to the front side result in narrower pulses.
Independently of pulse shape, pulses of equal energy have equal charge.
4.2. PULSE LENGTH AND DEAD TIME 27
0 50 100 150
Energy [keV]
0 0.002 0.004 0.006 0.008 0.01 0.012
Probability density [a.u.]
80 kVp
0 50 100 150
Energy [keV]
0 0.005 0.01 0.015
Probability density [a.u.]
120 kVp
0 50 100 150
Energy [keV]
0 0.005 0.01 0.015
Probability density [a.u.]
140 kVp
Figure 4.2. Deposited energy spectra from an x-ray source operating at a.) 80 kVp, 20 cm soft tissue included. b.) 120 kVp, 30 cm soft tissue included. c.) 140 kVp, 40 cm soft tissue included.
In Figure 4.4, input pulses of different deposited energies are presented. The rela- tion between pulse height and deposited energy is linear. The pulses of each pulse train are scaled accordingly.
4.2 Pulse Length and Dead Time
Based on the output pulses resulting from the input pulses in Figure 4.3, the average gain of the simulated system at a peak time of 40 ns is ∼1.9 mV/keV. Output pulses at different peak times are presented in Figure 4.5. With a peak time of 20 ns, the gain is slightly lower than 1.9 mV/keV while for higher peak times, the gain is higher.
Ideally, the gain should reflect the input energies correctly, however, changing the gain according to peak time also alters the noise size. To maintain the noise size, a constant gain of 1.9 mV/keV is used throughout.
0 50 100 150 200 250 Time [ns]
0 0.2 0.4 0.6 0.8 1 1.2
Current [A]
#10-6
Figure 4.3. Simulated pulse shapes of a 60 keV pulse. From left to right, pulses 1-9.
0 5 10 15 20 25 30 35 40
Time [ns]
0 0.2 0.4 0.6 0.8 1
Current [A]
#10-6
30 keV 60 keV 90 keV
Figure 4.4. Pulse 5 at different deposited energies.
Output pulse length as a function of peak time is presented in Figure 4.6. As the pulse length increases linearly with peak time, the relation between dead time and peak time also becomes linear, see Figure 4.7. The relation between dead time and peak time can be approximated as τdead time = 2.97τp.
In Table 4.1, the peak times used in this work are listed with their corresponding dead time values.
4.2. PULSE LENGTH AND DEAD TIME 29
5 5.02 5.04 5.06 5.08 5.1
Time [ns] #104
-10 0 10 20 30 40 50 60 70
Energy [keV]
20 ns 40 ns 100 ns 200 ns
Figure 4.5. Output of a 60 keV pulse for different peak times. No noise is included.
0 200 400 600 800 1000
Peak time [ns]
0 1000 2000 3000 4000
Pulse length [ns] 120 keV
90 keV 60 keV 30 keV
Figure 4.6. Output pulse length at DAC = 5 keV for pulses of energies 30-120 keV.
Table 4.1. Peak times and corresponding dead time values.
Peak time [ns] Dead time [ns]
20 62.3
40 120.0
100 297.7
200 594.6
500 1485.9
1000 2971.5
0 200 400 600 800 1000 Peak time [ns]
0 500 1000 1500 2000 2500 3000
Dead time [ns]
Figure 4.7. Approximated dead time values based on a peak time of 40 ns and a corresponding dead time of 120 ns.
4.3 DAC0 and Deposited Energy Spectrum
Without considering count rate or noise, the effect of a certain DAC0 value, regard- ing the amount of detectable counts, is obtained from the deposited energy spectra in Figure 4.2.
Including noise, photon signals that originally lie below the noise threshold can be boosted above the threshold. Since such counts originate from true photons, they are not considered as noise counts. According to the same principle, counts can also be lost due to noise counteracting the photon signal.
The spectra in Figure 4.2 exhibit a negative slope at low energies. With a DAC0 value between 0 and ∼25 keV, it is therefore more likely that signals become boosted above the threshold than lost below it. To account for this effect, each deposited energy spectrum is convolved with a Gaussian of σ = σoutput. Three convolved spectra can be seen in Figure 4.8.
Based on the three convolved spectra, the effect of different DAC0 values can be seen in Figure 4.9, where pdetectable describes the percentage of the spectrum located above the threshold. Since the deposited energy spectrum consists of positive ener- gies, the convolution causes some counts to be lost. At DAC0 = 0 keV, pdetectable is therefore less than 100%.
4.3. DAC0 AND DEPOSITED ENERGY SPECTRUM 31
0 50 100 150
Energy [keV]
0 1 2 3 4 5
Probability density [a.u.]
#10-3 80 kVp
0 50 100 150
Energy [keV]
0 1 2 3 4 5
Probability density [a.u.]
#10-3 120 kVp
0 50 100 150
Energy [keV]
0 1 2 3 4
Probability density [a.u.]
#10-3 140 kVp
Figure 4.8. Deposited energy spectra convolved with a Gaussian of σ = 1.5 keV.
0 5 10 15
DAC0 [keV]
40 50 60 70 80 90 100
p detectable [%]
80 kVp 120 kVp 140 kVp
Figure 4.9. Detectable signals at different DAC0 values.
The effect of different σ values can be seen in Figure 4.10. For DAC0 values ranging from 5 to 15 keV, the effect of the noise amplitude on pdetectable is small. However, since σ represents the noise, a different value of σ results in a new DAC0 level. I.e.
with more noise, the DAC0 level is forced up, resulting in a smaller pdetectable.
0 5 10 15
DAC0 [keV]
50 60 70 80 90 100
pdetectable [%]
80 kVp
< = 1.0 keV
< = 1.5 keV
< = 2.0 keV
0 5 10 15
DAC0 [keV]
40 50 60 70 80 90 100
pdetectable [%]
120 kVp
< = 1.0 keV
< = 1.5 keV
< = 2.0 keV
0 5 10 15
DAC0 [keV]
50 60 70 80 90 100
pdetectable [%]
140 kVp
< = 1.0 keV
< = 1.5 keV
< = 2.0 keV
Figure 4.10. pdetectable at different σ and DAC0 values.
4.4. MODELED OUTPUT NOISE 33
4.4 Modeled Output Noise
0 20 40 60 80 100
Time [7s]
-20 0 20 40 60 80 100
Energy [keV]
Figure 4.11. Output voltage from an input pulse train of 5 · 104 cps. Peak time of 40 ns, σoutput= 1.5 keV.
In Figure 4.11, an example of an output voltage is presented. At a peak time of 40 ns, with a zero input current, the number of noise counts is affected by σoutput according to Figure 4.12.
-5 0 5 10
DAC0 [keV]
0 200 400 600 800 1000
Counts
1.0 keV 1.5 keV 2.0 keV
Figure 4.12. Noise counts at a peak time of 40 ns peak time and a dead time of 120 ns for three different values of σoutput.
Table 4.2. σoutput at different peak times.
Peak time [ns] σoutput [keV]
20 2.12
40 1.50
100 0.95
200 0.67
500 0.42
1000 0.30
Table 4.2 shows the standard deviation of the output noise at different peak times.
The highest σoutput is obtained with the lowest peak time. Similarly, the lowest σoutput arises from the highest peak time. In Figure 4.13, noise counts as a function of DAC value are presented for different peak times. All peak times were equipped with a dead time of 120 ns, making the count rate constant and thereby giving all peak times the same value of noise counts at -5 keV. Noise counts were registered for the four peak times during 10 000 runs and averaged into one frame time. A lower peak time results in a higher σoutput, and therefore, a more flat noise curve.
-5 0 5 10
DAC [keV]
0 200 400 600 800 1000
Counts
20 ns 40 ns 100 ns 200 ns
Figure 4.13. Noise counts at different peak times.
Using the dead time values from Table 4.1 and a zero input current, noise counts are registered for each peak time. Each DAC0 value is set based on the average number of noise counts from 1000 different pulse trains. Figure 4.14 presents the resulting DAC0 values including an exponential fit.
4.5. FILTER PERFORMANCE 35
More precise values, based on 10 000 pulse trains for each peak time, are presented in Table 4.3. The presented standard deviation σDAC0was obtained by first splitting the 10 000 pulse trains into sets of 1000. In each set, a DAC0 value was determined.
From the ten DAC0 values, the standard deviation was then calculated.
0 200 400 600 800 1000
Peak time [ns]
0 2 4 6 8 10 12
DAC0 [keV]
Simulated threshold Exponential fit
Figure 4.14. DAC0 as a function of peak time, including an exponential fit. The error bars represent one standard deviation.
Table 4.3. DAC0 at approximately zero noise counts for each peak time, including the standard deviation, σDAC0, of each presented DAC0 value.
DAC0 [keV] σDAC0 [keV] Peak time [ns]
11.3 0.32 20
8.1 0.29 40
4.9 0.15 100
3.4 0.13 200
2.1 0.12 500
1.5 0.07 1000
4.5 Filter Performance
Every peak time is evaluated with its corresponding dead time value from Table 4.1. The results in each section below are based on the counts and their energies for 10 000 different pulse trains. The energy spectrum comparisons are made solely for x-ray sources at 120 kVp with 30 cm soft tissue included.
4.5.1 Low Flux
A first indication of filter performance is obtained from Figure 4.15. It presents the input pulse train and the output signal from filters with peak times of 40 and 1000 ns. At a flux of 5 · 104 cps, the number of pulses during one frame time is low. The output signal from the 40 ns peak time filter shows narrow peaks that are well separated in time. However, the signal suffers from a visibly high noise level and one input pulse is therefore lost. The output signal from the 1000 ns peak time filter has substantially less noise and the previously lost pulse can be de- tected. The output pulses are long but there appears to be no problem with pile-up.
0 20 40 60 80 100
Time [7s]
0 10 20 30 40 50 60
Energy [keV]
a.)
0 20 40 60 80 100
Time [7s]
-10 0 10 20 30 40 50 60
Energy [keV]
b.)
0 20 40 60 80 100
Time [7s]
-10 0 10 20 30 40 50 60
Energy [keV]
c.)
Figure 4.15. a.) Input pulse train at 5 · 104 cps, x-ray source at 120 kVp, 30 cm soft tissue included. b.) Output signal with a peak time of 40 ns, 120 ns dead time.
c.) Output signal with a peak time of 1000 ns, 2971.5 ns dead time.
The performance regarding true counts and double counts is presented in Tables 4.4, 4.5, and 4.6. pdetectable is also included.
