X-Ray Detector Characterization - a comparison of scintillators634109/FULLTEX… · ·...

X-Ray Detector Characterization- a comparison of scintillators

JAKOB LARSSON

Master of Science ThesisBiomedical and X-Ray PhysicsDepartment of Applied Physics

KTH – Royal Institute of TechnologyStockholm, Sweden 2013

TRITA-FYS 2013:40ISSN 0280-316XISRN KTH/FYS/--13:40--SE

Biomedical and X-Ray PhysicsKTH/Albanova

SE-106 09 Stockholm

This Thesis summarizes the Diploma work by Jakob Larsson for the Master ofScience degree in engineering Physics. The work was performed during the springof 2013 under the supervision of Ulf Lundström at Biomedical and X-Ray Physics,KTH – Royal Institute of Technology in Stockholm, Sweden.

© Jakob Larsson, June 25, 2013

Tryck: Universitetsservice US AB

i

Abstract

In this Master thesis work, four different indirect x-ray detector setupshave been compared in terms of resolution, noise and overall performance atdifferent x-ray photon energies; one camera from Photonic Science with a 15µm thick Gadox scintillator and one camera from Princeton Instruments usedtogether with one 48 µm thick Gadox scintillator, one 370 µm thick needlegrown CsI scintillator and one 170 µm thick CsI-based structured scintillatorfrom a company called Scint-X.

Primarily, the modulation-transfer function (MTF), the noise power spec-trum (NPS) and the detective quantum efficiency (DQE) were measured forall detectors. The MTF was measured by imaging a sharp edge, the NPS wasmeasured from flat-field images and the DQE was calculated as a functionof these two quantities. Simulations were also done in order to compare thedetectors at arbitrary energies.

The measurements showed that the detector with a thin Gadox scintilla-tor had both the highest resolution and the best overall performance at lowenergies. At high energies, the CsI-based scintillators performed best and theone from the company Scint-X had highest resolution.

Contents

Abstract i

Contents ii

1 Introduction 1

2 Background 32.1 Indirect x-ray detectors . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Detective Quantum Efficiency (DQE) . . . . . . . . . . . . . . . . . 11

3 Methods 133.1 Setup & equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 DQE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.5 Real detector model . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Results & discussion 254.1 System response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4 DQE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.5 Real detector-model . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Conclusions 35

Acknowledgments 37

Bibliography 39

ii

Chapter 1

Introduction

Ever since Röntgen’s discovery of x-rays in 1895, the field of x-ray imaging has beenunder constant development and today x-ray imaging is widely used in both hos-pitals and in research. Depending on the imaging task, different types of imagingproperties are desired; in medical imaging, large objects such as bones are often ofinterest so the detector’s performance at low frequencies are most important. How-ever, if small objects are of interest a detector with high resolution is needed. Forother imaging methods such as phase-contrast imaging, the detectors performanceover all frequencies needs to be considered.

The imaging properties of an arrangement are often determined by the x-raydetector. Different types of detectors are optimized for different energies and gen-erally provide a trade off between high resolution and low noise, so it is importantto know which one to choose in different situations.

In this thesis, four different indirect x-ray detector setups have been comparedin terms of resolution, noise and overall performance at different energies. Themodulation-transfer function (MTF), the noise power spectrum (NPS) and thedetective quantum efficiency (DQE) were measured for all detectors and simulationswere done in order to compare the detectors at an arbitrary energy.

In Chapter 2, the basic concepts and quantities that are used in this thesis areintroduced. Chapter 3 gives an in depth description of the experimental setup andmethods used for in the measurements. The results are presented and discussed inChapter 4, and a final conclusion is drawn in Chapter 5.

1

Chapter 2

Background

This chapter will introduce the basic concepts that are used further on in this thesis.First, the idea behind an indirect x-ray detector and its components are described.This is followed by a description of resolution and noise in a detector, as wellas different quantities to measure them such as the modulation transfer function(MTF) and noise power spectrum (NPS). Finally, a measure of the systems overallperformance, the detective quantum efficiency (DQE), is described. The materialcovered in this chapter can be found in References [1–5].

2.1 Indirect x-ray detectors

Indirect x-ray detectors use a two-step process to detect x-ray radiation. First,the incident x-ray photons are absorbed by a scintillator and converted into visiblelight. The visible light is then coupled to a charge-coupled device (CCD) via a fiberoptic plate (FOP), where it is collected and converted into a digital signal (Figure2.1a). The main components of such a detector are described in detail below.

Scintillators

The scintillator is one of the three main components in an indirect x-ray detectorand acts as a converter between x-rays and visible light. The x-ray photons areabsorbed in the scintillator and visible light proportional to the x-ray photon’senergy is emitted via the photoelectric effect. It’s often manufactured by combiningsmall particles of a phosphor (e.g. Gd2O2S) with a transparent plastic binder, butother types such as needle grown CsI:Tl are also available.

The scintillator is the component that has the greatest impact on the detector’simaging properties. The converted visible light will be scattered when travelingthrough the scintillator and often spread over several adjacent pixels, limiting theresolution (Figure 2.1b). The amount of diffusion is proportional to the distancethe light has to travel, so a thinner scintillator will give a higher resolution than a

3

4 CHAPTER 2. BACKGROUND

(a) Indirect x-ray detector (b) Effect of scintillator thickness [5].

(c) Unstructured vs structured scintillator [4].

Figure 2.1: a) The three main parts of an indirect x-ray detector; the scintillator,fiber optic plate and CCD. b) Due to spread of the visible light inside the scintillatormaterial, the resolution will decrease with increased scintillator thickness. c) A structuredscintillator guides the visible light in the right direction, leading to less spread inside thescintillator material and higher resolution.

thicker one. However, a thinner scintillator will absorb less of the incident radiationand therefore give a higher relative noise level, thus making the choice of scintillatorthickness a trade off between high resolution or low noise. This problem is reducedin structured scintillators where the visible light is channeled in the right direction,thereby making it possible to increase the thickness without reducing the resolution(Figure 2.1c).

FOP & CCD

The other two main components are the FOP and the CCD. The purpose of theFOP is to protect the CCD from high energy x-ray radiation. It consist of a bundleof optical fibers that blocks the x-rays that were not absorbed in the scintillator,and couples the visible light to the CCD.

The light that reaches the CCD is converted into electrons and collected intoeach pixel. After the exposure, the electrons accumulated in each pixel are shiftedout to an output register where they are read out by external read-out electronicsand converted into a digital signal. The number of electrons required to generate

2.2. RESOLUTION 5

one ADU (analog-to-digital unit) is set by the gain in the read-out electronics andcan often be adjusted in the detector software.

The pixel spacing in the CCD will limit the highest frequency that can beproperly imaged by the detector. According to the sampling theorem, the highestfrequency that can be correctly imaged without any aliasing, is given by the Nyqvistfrequency,

νN = 12∆s

, (2.1)

where ∆s is the pixel spacing in the x and y-direction.

Figure 2.2: A detector’s MTF affects the imaging properties of a system at differentfrequencies. The upper figure shows three objects of frequencies 1 lp/mm, 5 lp/mm and9 lp/mm that are imaged by a detector with the MTF in the center figure, producing theimages in the lower figure.

2.2 Resolution

Resolution is a measure of how well an object can be reproduced in an image.Higher resolution means that finer details in the object can be imaged, somethingthat’s desired in many applications. In a linear translation invariant system, theresolution is perfectly described by the modulation transfer function (MTF). In thissection, the MTF and its impact on a system’s imaging properties will be described.


Figure 2.3: Relationship between the PSF, ESF, LSF and MTF. The PSF can be mea-sured by imaging a pinhole, the ESF by imaging a sharp edge, and the LSF by imaging aslit.

MTFThe contrast in a line pattern can be measured by its degree of modulation, definedas

m = Imax − Imin

Imax + Imin(2.2)

The modulation takes a value between one and zero, where higher modulationcorresponds to higher contrast in the object. At zero modulation no structures arevisible in the image.

The modulation transfer function (MTF) describes how well the modulation ateach spatial frequency in an object is reproduced when imaged. If an object withfrequency fo has a modulation of mo, the modulation in the image, mi, will be

mi = mo MTF(fo). (2.3)

An ideal detector will have an MTF equal to one for all frequencies, thus perfectlyreproducing the modulation in an image. For a real detector, a lot of differentfactors such as scattering inside the scintillator and the pixel size of the CCD willreduce the MTF. Figure 2.2 shows three different objects with frequencies 1 lp/mm(line pair/mm), 5 lp/mm and 9 lp/mm (upper figure) that are imaged by a detectorwith an imperfect MTF (central figure). All the objects have perfect modulation,mo = 1, but when they are imaged the modulation changes according to eq. 2.3,resulting in the images in the lower figure.

Methods for measuring the MTFThe MTF can be measured in several ways. Three of the methods are describedbelow, and the relationship between them are shown in Figure 2.3.

2.3. NOISE 7

PSF: Pinhole measurement The point spread function (PSF) describes howwell a single point in an object is reproduced in an image and can be measuredby imaging a pinhole. The PSF can be used directly as a measure of resolutionby measuring its full width half maximum (FWHM), but it can also be used tocalculate the MTF,

MTF(u, v) = |F {PSF(x,y)}| , (2.4)

where F denotes the Fourier transform.This can be radially binned and normalized to its value at the zero frequency

to get the one-dimensional MTF(f).

ESF: Edge measurement A downside with the PSF measurement is that it’shard to image a small pinhole since very few photons will arrive to the detector.The edge method solves this by first imaging a sharp edge and then calculating theMTF in two steps.

First, a sharp edge is imaged from which the edge spread function (ESF) iscalculated as the line profile perpendicular the edge. From this, the line spreadfunction (LSF) can be calculated as the derivative of the ESF,

LSF(x) = ddx

ESF(x). (2.5)

This can be interpreted as the system’s response to a line stimuli and can bemeasured directly by imaging a slit, but it suffers from the same problems as thepinhole measurements.

Secondly, the LSF can be Fourier transformed to get the MTF,

MTF(f) = |F {LSF(x)}| , (2.6)

which is then normalized to its value at the zero frequency.

MTF(fg): Grating measurement The MTF at a single frequency can be mea-sured directly by imaging a grating and measuring the modulation in the image.If the grating has a modulation of mg and a frequency of fg, and the measuredmodulation in the image is mi, the MTF at that frequency will given by eq. 2.3,i.e.

MTF(fg) = mi

mg. (2.7)

2.3 Noise

Noise is the random variation of intensity over an image. The amount of noise willaffect the visibility of the image; if the noise is large compared to the real signal


the image will be impossible to interpret even if the resolution is high, so it’s oftendesirable to reduce it as much as possible.

This section starts out by describing several different sources of noise, discussingboth their origins and methods to reduce them. This is followed by a descriptionof image correction and its effects on the noise. Finally, the noise power spec-trum (NPS) is described, giving a measure for the noise level at different spatialfrequencies.

Read-out noiseRead-out noise arises due to fluctuations in the output signal. These fluctuationsare caused by thermal effects in the read-out electronics and may be reduced byreducing the read-out speed of data from the sensor.

Dark noiseEven when unexposed, the CCD will always have a small current caused by ther-mally excited electrons. This dark current will build up a dark signal over time,and the random fluctuations in this signal are called dark noise.

The dark signal can be corrected for by making a dark image correction (de-scribed in the section below), but the dark noise cannot. However, since the noiseis caused by thermally excited electrons it can be reduced by cooling the detector.

Static noiseStatic noise - or fixed pattern noise - is caused by defects in the detector’s hardwareand leads to non-uniformities in the acquired image. Typical defects can be damageon the scintillator or the FOP, or a variation of gain between different pixels in theCCD. This noise is static and can be completely removed by making a flat-fieldcorrection (described in the section below).

Photon noisePhoton noise arises due to the quantized nature of light and can be seen as thevariation in the number of photons arriving to the detector. This can be describedby Poission statistics, so the noise will be given by square root of the mean numberof photons,

σph =√

N. (2.8)

Although this noise will increase with exposure time, the relative noise will decrease.Considering only the photon noise, the relative noise becomes

σph,rel =√

N

N= 1√

N. (2.9)

2.3. NOISE 9

Table 2.1: Some common types of noise, their origin and methods to reduce them.

Type of noise Origin Correctable/Reducable

Method

Read-out noise Fluctuations in read-out signal No / Yes Reduce read-out speedDark noise Thermal effects in the CCD No / Yes Cool the CCDStatic noise Imperfections in the hardware Yes / No Flat-field correctionPhoton noise Quantization of light No / Yes† Increase exposure time† The relative noise, i.e. noise/signal, may be reduced by increasing the exposure time.

Total noiseWhen several sources of Gaussian noise are present in a measurement and theirindividual noise levels are known, the total noise level can be calculated as

σtot =

√√√√ n∑i=1

σ2i , (2.10)

where n is the number of sources and σi is the noise level for each individual source.At long exposure times and high enough x-ray flux, the photon noise will become

dominating and other sources of noise may be neglected. At this point, the systemis said to be photon-noise limited and the signal-to-noise ratio becomes

√N , where

N is the mean number of x-ray photons that are absorbed in the scintillator.

Image correctionAn image is often dark-image and flat-field corrected before it’s analyzed. The darkimage correction is made by subtracting a dark image, i.e. an image taken withoutany x-rays, from the real image, thus removing any dark signal and offset addedby the software. This subtraction will increase the noise in the corrected imageaccording to

σcorr =√

σ2 + σ2dark. (2.11)

If the measurement was done in the photon-noise limited region, the noise level σin the real image will be much higher than in the dark image and the increase innoise will be neglectable.

The flat-field correction is made to remove any non-uniformities from the image.This is done by dividing the image with a flat-field image, i.e. an image acquiredunder the same conditions but without any object. Dividing two images gives anincrease in the relative noise (noise/signal) according to

σcorr,rel =√

σ21,rel + σ2

2,rel, (2.12)


and since the two images will have the same relative noise the noise level in thecorrected image will increase by a factor of

√2. This increase in noise has to be

taken into account during the analysis.The increase in noise that is caused by the image correction can be reduced by

using an averaged correction image. Averaging over m images will reduce the noisein the averaged image by

√m, so by choosing a large m the increase in noise can

be made negligible.

NPSThe noise power spectrum (NPS) describes the noise level at different spatial fre-quencies in the image. It can be defined as

NPS(u, v) = limNx,Ny,M→∞

NxNy∆x∆y

M

M∑m=1

∣∣∣DFT{

I(x, y) − I(x, y)}∣∣∣2 , (2.13)

where Nx, Ny are the number of pixels in the x and y direction, ∆x, ∆y are thepixel spacing in the x and y direction, M is the number of sub-regions to averageover, I(x, y) is the intensity in each pixel (x, y), I is the mean intensity in eachsub-region and DFT is the discrete two-dimensional Fourier transform [1].

It is convenient to normalize this expression to that of an ideal detector, i.e. adetector which absorbs all incident radiation and is only limited by photon noise,

NNPS(u, v) = q2 NPS(u, v)

I(x, y)2 , (2.14)

where I(x, y) is the mean signal over the image and q is the signal-to-noise ratiofor an ideal detector.

This can be radially binned to give the one-dimensional NNPS,

NNPS(f) = q2 NPS(f)

I(x, y)2 , (2.15)

where f =√

u2 + v2.An interesting property of the normalized NPS is that the absorption efficiency

η of the scintillator can be read out directly from its zero frequency,

η = 1NNPS(0)

. (2.16)

Visible light photons per x-ray photonFor a real detector that does not have perfect resolution, the number of visible lightphotons that are generated for each x-ray photon can be calculated directly fromthe NNPS. The value of the NNPS at the zero frequency will have contributions

2.4. DETECTIVE QUANTUM EFFICIENCY (DQE) 11

from both the x-ray photons and the visible light photons, but at frequencies overthe detector’s resolution limit the noise from the x-ray photons cannot be resolvedso only the visible light photons contribute. Therefore, the number of visible lightphotons that are emitted per x-ray photon, Nph,vis, can be calculated according to

Nph,vis = NNPS(0) − NNPS(∞)NNPS(∞)

. (2.17)

2.4 Detective Quantum Efficiency (DQE)

The detective quantum efficiency (DQE) is a measure of how the information at acertain frequency in an object that can be used to form an image. It is defined asthe ratio between the SNR of the incident x-ray photons and the SNR in the imageand can be calculated directly from the MTF and NNPS,

DQE(f) =(

SNRin(f)SNRimg(f)

)2

= MTF2(f)NNPS(f)

. (2.18)

This will give a value between one and zero at each frequency, where one correspondsto an ideal detector with perfect modulation, a perfectly absorbing scintillator andonly photon noise. Since the MTF will always take a value of one at the zerofrequency, the DQE at this point will directly give the absorption efficiency of thescintillator,

DQE(0) = η (2.19)

Integrated DQEA good measure of the overall performance of a detector is given by the area underthe DQE up to its Nyqvist frequency fN,

δ =∫ fN

0DQE(f) df. (2.20)

Chapter 3

Methods

In this chapter the experimental setup and the methods used for characterizing thedetectors will be explained in detail.

3.1 Setup & equipment

The same setup was used in all measurements; the detector was placed 1 m awayfrom the x-ray source and test objects were placed as close as possible to thescintillator. The basic properties of the equipment used are described below.

X-ray sourceA liquid-metal-jet anode x-ray source operating at an electron beam power of 40W with acceleration voltage 50 kVp was used in all experiments. It circulates aGa/In/Sn alloy (68.5% Ga, 21.5% In, 10% Sn) [6], giving an unfiltered emissionspectrum dominated by a peak at 9.25 keV. The spectrum was also hardened with1 mm, 3 mm and 10 mm aluminium, giving emission spectra centered about 25keV, 30 keV and 40 keV respectively (Figure 3.1).

DetectorsTwo indirect x-ray detectors were investigated; PIXIS-XF from Princeton Instru-ments (PI:PIXIS) and FDI-VHR from Photonic Science (PS:FDI). PI:PIXIS iscooled by an air-cooled peltier and has a CCD with a pixel pitch of 13.5 µm whilstPS:FDI is cooled by a water-cooled peltier and has a CCD with a pixel pitch of of9 µm. Both CCDs are coupled 1:1 to a scintillator with a fiber optic plate (FOP).They were operated at -20◦C and -28◦C respectively (Table 3.1). The PS:FDI cam-era uses a 15 µm thick Gadox (Gd2O2S:Tb) scintillator that is fixed to the FOP.The PI:PIXIS camera has an exchangeable scintillator, and three different oneswere used in the experiments; one 48 µm thick Gadox scintillator on a 50 µm thickaluminium substrate, one 369 µm thick needle grown CsI scintillator on a 2160

13

14 CHAPTER 3. METHODS

(a) 10 keV (No filter)

0

5

10x 1010

Cou

nts/

(s*s

r)(b) 25 keV (1 mm Al)

0

1

2x 109

0 10 20 30 40 500

2

4

6x 108

Energy (keV)

Cou

nts/

(s*s

r)

(c) 30 keV (3 mm Al)

0 10 20 30 40 500

2.5

5

x 107

Energy (keV)

(d) 40 keV (10 mm Al)

Figure 3.1: Emission spectra recorded at 40 W with acceleration voltage 50 kVp. Theunfiltered spectrum in (a) is centered around the Ga Kα peak at 9.25 keV. This peak iscompletely absorbed in 1 mm Al (b), whose spectrum is instead centered around the InKα peak at 24.2 keV. This peak is significantly reduced when filtering with 3 mm Al (c)and almost completely absorbed in 10 mm Al (d).

Figure 3.2: Flat-field images of the scintillators. The leftmost three are used togetherwith the camera from Princeton Instrument and the rightmost are used with the camerafrom Photonic Science. From the left: Gadox, Scint-X, CsI and Gadox.

µm thick substrate of graphite, and one structured scintillator from the companyScint-X which consists of CsI-filled hexagon shaped wells that are etched into a 500µm thick silicon substrate. The wells are approximately 170 µm deep with a pitchof 30.8 µm and a wall thickness of 3.9 µm (Table 3.2).

Flat-field images acquired with the different detector setups are shown in Figure3.2.

3.1. SETUP & EQUIPMENT 15

Table 3.1: List of the cameras that were used in the experiments and their basic prop-erties.

Name FOP ratio CCD size [pixels] Pixel size [µm]

Princeton Instruments: Pixis-XF 1:1 2048 × 2048 13.5 × 13.5Photonic Science: FDI-VHR 1:1 4008 × 2670 9 × 9

Table 3.2: List of the scintillators and their properties. The densities were calculatedfrom the scintillators absorption spectra and the fill factors were measured from the images.

Scintillator SubstrateCamera Material ρA

[mg/cm2]Thickness

[µm]Material ρA

[mg/cm2]Thickness

[µm]Size[mm2]

PI:Pixis Gd2O2S:Tb 18.1 48 Al 13.5 50 27.6×27.6Scint-X† 77.2 171 Si 117 329 27.6×26.3CsI 166 369 C 464 2160 16×14

PS:FDI Gd2O2S:Tb 5.00 15 - - - 36×24† Hexagonal holes are etched into the silicon substrate and filled with CsI. The holes havea pitch of 30.8 µm and a wall thickness of 3.9 µm.

0 25 500

0.5

1

Energy (keV)

Tra

nsm

ittan

ce

PI:Gadox

MeasuredFitted

0 25 500

0.2

0.4

0.6

Energy (keV)

PI:Scint−X

MeasuredFitted

0 25 500

0.1

0.2

0.3

Energy (keV)

PI:CsI

MeasuredFitted

Figure 3.3: Absorption spectra for the scintillators used together with the PI:PIXIScamera. The measured data were fitted to the theoretical absorption spectra in order todetermine the thickness and density of the scintillators.

Absorption spectraThe scintillators’ surface densities in Table 3.2 were measured from their absorptionspectra by making a fit of the theoretical spectrum for different scintillator- andsubstrate thicknesses and densities to the measured data. The thickness was alsomeasured by hand, and showed good agreement with the fitted parameters. Themeasurements could only be made for the exchangeable scintillators, but the datafor the PS:FDI scintillator was specified in its manual.


(a) Edge placement (b) Fit of the edge position (c) Fit of the edge angle

Figure 3.4: a) The sharp edge device placed at a small angle in front of the detector. Amirror is fixed to device in order to align it with an alignment laser. b) The fit made ineq. 3.2 for one row, i. The central position of the edge, C3,i is stored in the new array,Ei which is then used to determine the edge angle by making the fit in eq. 3.4 (c).

3.2 Resolution

The resolution was measured using two methods. In the first method the modula-tion transfer function (MTF) was calculated by measuring the edge spread function(ESF) from an edge device, giving a complete description of the systems modula-tion transfer over all spatial frequencies. In the second method the modulation ata set of frequencies were measured from periodic gratings in order to verify theresults from the edge measurement. The basic theory and concepts for this methodis described in Chapter 2.2 and the methods used are consistent with previouslypublished articles (References [7] and [8]).

MTF: Edge method

The system’s MTF was determined in several steps using an edge method. Theidea behind this method is to calculate the MTF from the system’s ESF, which canbe measured by imaging a sharp edge. A detailed description of the experimentalprocedure follows below.

i) System setup The detector was placed 1 m from the source and an edge deviceconsisting of a 1.2 mm thick tungsten plate with polished edge was placed directlyin front of the camera (approximately 6 mm in front of the scintillator). The edgewas placed in a small angle relative the CCD sampling array and aligned perpen-dicular to the optical axis with an alignment laser (Figure 3.4a).

ii) Image pre-processing Three images were taken in each measurement; oneedge image (Ie), one flat-field image (If) and one dark image (Id). First, the darkimage was subtracted from both the edge image and flat-field image in order toremove any dark signal, and to remove the baseline offset added in the software.Next, the edge image was divided by the flat-field image in order to remove any

3.2. RESOLUTION 17

non-uniformities that may be present in the CCD, scintillator, FOP or x-ray beam,giving the pre-processed image as

Iij = Ie,ij − Id,ij

If,ij − Id,ij. (3.1)

for each pixel ij.

iii) Edge angle The calculation of the edge angle was made in two steps. First,the position (x coordinate) of the edge relative the sampling matrix was determinedby making a least square fit of the error function to each row of the image,

f(x) = C1 + C2 · erf(

x − C3

C4

), (3.2)

where the error function is defined as

erf(x) = 2√π

∫ x

0e−t2

dt. (3.3)

The fitting parameters C1 and C2 corresponds to the lower value of the edge andthe edge contrast, whilst C3 and C4 corresponds to the edge position and standarddeviation. The mean position for each row, C3,i, was stored in a new array, Ei =C3,i (Figure 3.4b).

Secondly, a first order polynomial fit of the edge position array E was made(Figure 3.4c),

p(x) = p1x + p2 (3.4)

giving the center of the edge as p2 and the edge angle as

θ = tan(p1). (3.5)

iv) Projection and binning Having calculated the edge angle, all pixel valuesin the image were projected along the edge and binned into a sub-pixel spaced one-dimensional array perpendicular to the edge (Figure 3.5a). The bin size, ∆u, waschosen to be 10% of the pixel size, p, in accordance with previous publications [7].The value of the edge spread function (ESF) in each bin k was calculated as

ESFk = 1nk

∑ij

Iijrect(

p(i cos θ − j sin θ) − k∆u

∆u

), (3.6)

where nk is the number of pixels projected into bin k, Iij is the intensity in pixelij, and rect is the rectangular function defined as

rect(x) =

{1, − 1

2 ≤ x ≤ 12

0, otherwise(3.7)


(a) Projection and binning [7] (b) ESF

−10 −5 0 5 100

0.5

1

Distance from edge [mm]

(c) LSF

−10 −5 0 5 100

0.5

1

Distance from edge [mm]

(d) MTF

0 20 40 600

0.5

1

Spatial frequency [mm−1

]

Figure 3.5: In (a), the the two-dimensional image data are projected along the edge andbinned into a one-dimensional array, giving the edge spread function (b). Differentiatingthis gives the line spread function (c), whose Fourier transform is the modulation transferfunction (d).

When sufficiently long exposure times were used, no smoothing of the ESF wasneeded.

v) Calculating the LSF The line spread function (LSF) was calculated by nu-merically differentiating the ESF using a finite difference approximation,

LSFk = ESFk+1 − ESFk

∆u. (3.8)

vi) Calculating the MTF The MTF was calculated by taking the discrete Fouriertransform (DFT) of the LSF,

MTF(f) = DFT {LSF(x)} (3.9)

3.3. NOISE 19

and normalizing it to its value at the zero frequency.

vii) Fitting In order to implement the results in simulations and to get an es-timate of the point spread function (PSF), a fit was made to the MTF. This wasdone by fitting the ESF to a sum of error functions (eq. 3.3),

g(x) = C +N∑

i=1Ai erf

(x − m

σi

)(3.10)

and from which the LSF and MTF could be calculated analytically.

Grating measurements

The grating measurements were done with a test object containing line patternswith frequencies between 33 mm−1 and 100 mm−1 and a Siemens star. The testobject was imaged with several different magnifications in order to get informationfor a larger span of frequencies.

The image analysis was very similar to that of finding the ESF in the edgemeasurements. First, the grating images were dark- and flat-field corrected,

Iij = Ig,ij − Id,ij

If,ij − Id,ij. (3.11)

Secondly, the grating angle was found by making a first order polynomial fit ofthe grating’s edge positions. The pixel values were projected along the grating andbinned into a sub-pixel sized one-dimensional array, giving an averaged line profileof the grating. The intensity peaks and valleys in the line profile were located andstored, and the degree of modulation was calculated as

m = Ipeaks − Ivalleys

Ipeaks + Ivalleys, (3.12)

where the over-line represents the mean value.

3.3 Noise

Three different sources of noise were investigated; read-out noise, dark noise andphoton noise. The first two are directly related to effects on the CCD and weremeasured from dark images, i.e. images acquired without x-rays. The photonnoise was characterized by measuring the system’s noise power spectrum (NPS)which gives the photon noise as function of spatial frequency. The basic theory andconcepts for this method is described in Chapter 2.3


Read-out noiseThe read-out noise was calculated as

σread-out = 1N

N∑i=1

std (Ib,i − Imb) , (3.13)

where Ib is a bias image (zero exposure time) and Imb is a master bias image definedas

Imb = 1M

M∑j=1

Ib,j . (3.14)

The master bias image was calculated from 100 bias images (M=100) and all ofthese were used to calculate the average read-out noise (N=100).

Dark signalThe dark signal, Ndark, was measured as the mean of a very long dark image. Beforethe analysis was made, the mean of a master bias image was subtracted from theimage in order to remove any offset added by the software and to remove any signalarising from read-out noise,

Ndark = Id − Imb. (3.15)

The dark noise will increase proportionally to the exposure time, so a time inde-pendent quantity was also defined,

Ndark = Ndark

t. (3.16)

NPSThe noise power spectrum (NPS) was calculated for four different emission spectra(Figure 3.1). The analysis was done in several steps, including image pre-processing,numerical calculation of the NPS, and normalization to an ideal detector. Themethods used for calculating the NPS are consistent with previous publications(References [9–11]).

i) Setup and system check The detector was placed 1 m in front of the sourceand aligned to optical axis with an alignment laser. Before the NPS measurementswere started, the system response was confirmed to be linear and the exposure timewas chosen long enough for the system to be photon noise limited.

ii) Image pre-processing Two flat-field images (Iaf and Ib

f ) and one dark im-age (Id) were taken for each measurement. One of the flat-field images was dark-

3.3. NOISE 21

and flat-field corrected in order to remove any non-uniformities from the image andthe mean value of the flat-field image was then multiplied to the corrected imagein order to get the same mean as in the original image,

Iij =Iaf,ij − Id,ij

Ibf,ij − Id,ij

Iaf . (3.17)

iii) Calculating the NPS The pre-processed image was split up in several non-overlapping sub-regions of 256x256 pixels, and the two-dimensional NPS was cal-culated as

NPS(u, v) = NxNy∆x∆y

2M

M∑m=1

∣∣DFT{

Im(x, y) − Im

}∣∣2 , (3.18)

where Nx, Ny are the number of pixels in the x- and y direction, ∆x, ∆y are the pixelspacing in the x- and y direction, M is the number of sub-regions the calculation ismade over, Im(x, y) is the intensity in each pixel (x, y) and Im is the mean intensityin each sub-region [1]. The factor 2 in the denominator compensates for the increasein noise that’s introduced by the image pre-processing.

The one-dimensional NPS was then calculated by radially binning the frequen-cies in the two-dimensional NPS

NPSk = 1nk

∑u,v

NPSu,v rect(

u2 + v2 − k∆r

∆r

), (3.19)

where nk is the number of pixels in bin k, ∆r is the radal frequency bin size, andrect is the rectangular function defined in eq. 3.7.

Since the calculation was made over a finite area and not over infinity as for-mally required (eq. 2.13), the value of the NNPS at the zero frequency could notbe calculated directly and was instead found by extrapolating the data in MATLAB.

iv) Normalization to ideal detector The normalized NPS was calculated ac-cording to eq. 2.15,

NNPS(f) = q2 NPS(f)

I(x, y)2 . (3.20)

The signal-to-noise ratio for the ideal detector, q, was calculated from the sourceemission spectrum as

q2 =(∫

n(E)E dE)2∫

n(E)E2 dE, (3.21)

where n(E) is the number of photons with energy E (keV) that’s incident to onepixel on the detector.


Visible light photons per x-ray photonThe number of visible photons that were generated per x-ray photon was calculatedfrom the NNPS as,

Nph,vis = NNPS(0) − NNPS(fmax)NNPS(fmax)

. (3.22)

3.4 DQE

The DQE was calculated from the MTF (eq. 3.9) and the normalized NPS (eq.3.20) as

DQE(f) = MTF(f)2

NNPS(f). (3.23)

The integrated DQE, δ, was calculated by numerically integrating the measuredDQE up to its Nyqvist frequency,

δ =Nny∑k=1

DQEk∆f, (3.24)

where Nny is the number of bins up to the Nyqvist frequency and ∆f is the fre-quency bin size.

3.5 Real detector model

The expected noise level for an image can be simulated from the emission spectrumof the source, the exposure time and the scintillator parameters. The simulation isdone by modeling the attenuation of the x-rays from the source to the scintillatorand calculating the noise as the variation in the number of photons absorbed bythe scintillator.

Given an arbitrary emission spectrum with Φ(E) photons at each energy E, theamount of the photons that reaches the scintillator is given by Beer-Lambert’s law

Φ′(E) = Φ(E) exp

(−∑

i

(µ(E)/ρ)i ρA,i

), (3.25)

where (µ(E)/ρ)i is the energy dependent mass attenuation coefficient and ρA,i isthe surface density for each material in front of the scintillator. The amount ofphotons absorbed in the scintillator for each energy can then be calculated as

Φabs(E)Φ′(E)

= 1 − e−(µ(E)/ρ)scint ρA,scint . (3.26)

3.5. REAL DETECTOR MODEL 23

from which the signal-to-noise ratio can be determined

q2real(Φ) =

(∫Φabs(E)E dE

)2∫Φabs(E)E2 dE

. (3.27)

Normalizing this to the noise level of an ideal detector gives the NNPS at the zerofrequency,

NNPS0,real(Φ) =(

q(Φ)qreal(Φ)

)2

. (3.28)

Real detector model: DQE0(Φ)Since this model doesn’t give any information about the MTF and the NPS is onlyknown at the zero frequency, it’s not possible to calculate the full DQE. However,since the MTF is always equal to one at the zero frequency, the DQE at this pointcan be calculated as

DQE0,real(Φ) = 1NNPS0,real(Φ)

. (3.29)

Real detector model: δ(Φ)Completing the model with experimental data and assuming that the shape of theMTF and NPS doesn’t change with energy, the model can be extended to calculatethe integrated DQE, δ, for an arbitrary spectrum.

First, the NPS from a measurement is normalized and multiplied with the sim-ulated NPS in order to get a the correct shape and amplitude,

NNPSreal(f, Φ) = NNPS(f)NNPS(0)

NNPSreal(Φ). (3.30)

This is used together with the experimentally measured MTF to calculate the DQE,

DQEreal(f, Φ) = MTF(f)2

NNPSreal(f, Φ), (3.31)

which can then be integrated to give δ(Φ)

δ(Φ) =∫ fN

0DQEreal(f, Φ) df. (3.32)

Chapter 4

Results & discussion

In this chapter the results from the measurements are presented, and a comparisonof the four different detectors systems is made. The validity of the real detector-model is investigated by comparing simulations to real data, and simulations ofDQE0 and the integrated DQE, δ, are shown.

The system response and resolution measurements were only done for the unfil-tered spectrum (10 keV) but the NNPS measurements were done for four differentspectra, here denoted by their approximate center energies; 10 keV (unfiltered),20 keV (hardened with 1 mm Al), 25 keV (hardened with 3 mm Al) and 40 keV(hardened with 10 mm Al).

4.1 System response

All four detector setups showed a linear response. The exposure times needed toreach the photon-noise limited region are shown in Table 4.1. The photon flux isproportional to the electron beam power and inversely proportional to the distancesquared, so the measured exposure times are normalized to these parameters inorder to easily get an estimate of the minimum exposure time that’s needed for ameasurement made under different conditions.

As the data in the table shows, PI:Gadox and PI:CsI reaches this region tentimes faster than PI:Scint-X and 300 times faster than PS:Gadox.

Table 4.1: Minimum exposure time needed for the detectors to reach the photon-noiselimited region. The times are normalized to the electron beam power and measurementdistance.

PI:Gadox PI:Scint-X PI:CsI PS:Gadox

2.5 25 2.5 750 [ms W−1 m−2]

25

26 CHAPTER 4. RESULTS & DISCUSSION

0 10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

1

Spatial frequency [mm−1]

MT

F

PI:Gadox MTFPI:Gadox GratingPI:Scint−X MTFPI:Scint−X GratingPI:CsI MTFPI:CsI GratingPS:Gadox MTFPS:Gadox GratingPI:PIXIS Nyqvist frequencyPS:FDI Nyqvist frequency

Figure 4.1: Comparison of the MTF for the different scintillators.

4.2. RESOLUTION 27

4.2 Resolution

MTF

The results from the edge measurements, together with data from grating measure-ments are shown in Figure 4.1. As can be seen in the figure, PS:Gadox has thehighest MTF at all spatial frequencies, and it also has a higher Nyqvist frequencythan the PI:PIXIS-based detectors since its CCD has smaller pixels. As for thescintillators used together with the PI:PIXIS camera, PI:Scint-X has the highestresolution although PI:Gadox gets slightly better MTF at low frequencies. PI:CsIhas the worst resolution and its MTF drops to zero already at half its Nyqvistfrequency.

These results agree well with theory; both reducing the scintillator thicknessand using a structured scintillator will increase the resolution due to less spread ofthe visible light inside the scintillator. Comparing PI:Gadox and PI:Scint-X givesan idea of the impact of using a structured scintillator; although PI:Scint-X is morethan three times thicker than PI:Gadox, it still have higher resolution.

Gratings measurements

The data from the grating measurements are in general slightly lower than thedata from the edge measurements, but seems to follow the same shape. This ismost likely caused by the fact that the source has a finite size that is in the sameorder of magnitude as the line width of the gratings. This will case a reduction inthe measured modulation that will increase the closer the object is to the source.Another possible reason is that the grating is not perfectly absorbing, which willalso reduce the modulation in the image. The three rightmost data points forPS:Gadox were done for a magnification of one and have a higher value than themeasured MTF. A possible reason for this lies in the difference in the the methods.The images acquired with PS:Gadox have hexagonal distortions caused by the FOP.The edge method uses the whole image during the analysis, causing a reduction inthe MTF from these distortions. The grating measurements, however, do not takethese distortions into account and should therefore result in a higher value.

PSF and Siemens star

The resolution was also measured as the FWHM of the LSF, and the results arepresented in Table 4.2. The same conclusions can be draw from this data as fromthe MTF; PS:Gadox has the highest resolution, followed by PI:Scint-X, PI:Gadoxand PI:CsI.

A Siemens star was imaged for all detectors and the results are shown in Figure4.2. The lines in the Siemens star correspond to frequencies of 100 lp/mm, 40lp/mm, 20 lp/mm, 10 lp/mm and 5 lp/mm, seen from the inside out. The resolutionis clearly best for PS:Gadox where lines over 40 lp/mm are visible, but the hexagonal


Table 4.2: The FWHM of the PSF for the different scintillators.

PI:Gadox PI:Scint-X PI:CsI PS:Gadox

58 µm 46 µm 150 µm 27 µm

Figure 4.2: A Siemens star imaged with the different scintillators. Seen from the centerof the star, the lines corresponds to frequencies of 100 lp/mm, 40 lp/mm, 20 lp/mm, 10lp/mm and 5 lp/mm.

distortions caused by the FOP can also be seen clearly. For PI:Scint-X, frequenciesup to 20 lp/mm are imaged correctly but at higher frequencies a Moiré patterncaused by the hexagonal holes in the scintillator is visible. PI:Gadox and PI:CsIshow no defects and can resolve lines up to 20 lp/mm and 10 lp/mm, respectively.These results are in good agreement with the measured MTFs.

MTF for different positions and filterings

For PI:Gadox, the MTF at different positions of the detector was investigated bychanging the position of the edge relative to the CCD (Figure 4.3a). As can beseen in the figure, the MTF was identical at the measured positions.

The effect of spectrum filtering on the MTF was investigated for PI:Scint-Xby doing the edge measurement for three different spectra (Figure 4.3b). Whenincreasing the spectrum energy, the MTF was reduced as much as 40% at very lowfrequencies but was unaffected at higher frequencies. This is most likely causedby Compton scattering, whose effect increases at higher energies. In the figure it

4.3. NOISE 29

(a) MTF for different x-positions on thedetector

0 20 40 600

0.2

0.4

0.6

0.8

1


MT

F

Leftmost

Rightmost

(b) MTF for different spectra

0 20 40 600

0.2

0.4

0.6

0.8

1


MT

F

10 keV30 keV40 keVHexagons FDHexagons PD

Figure 4.3: a) The MTF for PI:Gadox measured at different x-positions on the detector.b) The MTF for PI:Scint-X measured for different spectra and the MTF of the hexagonalwells in the scintillator. FD and PD corresponds to the orientation of the hexagons andstands for flat side down and pointy side down respectively.

can also be seen that the measured MTFs are much lower than the MTF of thehexagonal wells in the scintillator. This reduction is most likely caused by thespread of light inside the scintillator and the FOP, but it might also be caused bythe fact that the scintillator is not in perfect contact with the FOP.

4.3 Noise

Read-out noise and dark signalThe read-out noise and dark signal for both cameras are listed in Table 4.3. Thevalues are listed in ADU (analog-to-digital units) which are dependent on the gain,so the two cameras cannot be compared with each other. Looking at the PI:PIXIS-XF camera, we can see that the read-out noise gets more then three times largerwhen increasing the read-out rate. The dark signal is independent of the read-outtime and is therefore the same in both cases. As for the PS:FDI-VHR camera, thedark signal was very low compared to the read-out noise.

The measurements in this report were done with a typical signal of 40 000 ADUand 4000 ADU respectively, so the noise is very small in comparison.

Table 4.3: Read-out noise and dark noise for the two cameras.

Camera Read-out noise Dark signal

PI:PIXIS-XF (100 kHz) 9.69 ADU 4.0 ADU/minPI:PIXIS-XF (2 MHz) 30.3 ADU 4.0 ADU/minPS:FDI-VHR 2.59 ADU 0.071 ADU/min



0

2

4

6

NN

PS

PI:GadoxPI:Scint−XPI:CsIPS:Gadox

(b) 25 keV (1 mm Al)

0

5

10

15


0 10 20 300

5

10

15

20


NN

PS



0 10 20 300

10

20

30

40



(d) 40 keV (10 mm Al)

Figure 4.4: Comparison of the NNPS for the different scintillators.

4.3. NOISE 31

NNPSA comparison of the NNPS for the scintillators at different spectrum energies areshown in Figure 4.4. PI:CsI has the best absorption efficiency at all energies, closelyfollowed by PI:Scint-X at higher energies. At 10 keV both unstructured scintillatorsabsorbs slightly more than PI:Scint-X, but they both get worse at higher energiesand at 40 keV PS:Gadox only absorbs one in every thirty x-ray photons.

These results are in good agreement with theory; the Gadox-based scintillatorsshould have high absorption at low energies but gradually get worse at higherenergies. The amount of absorption is also greatly dependent on the scintillatorthickness, which is why the very thin PS:Gadox always has worse absorption thanPI:Gadox. PI:CsI and PI:Scint-X are both very thick and use CsI as scintillatormaterial so they should absorb close to all incident radiation at all energies. Thereason for the reduced absorption at lower energies is that their substrate materialsare highly absorbing in that region, thus reducing the amount of x-ray photons thatreaches the scintillator. For PI:Scint-X, the CsI-filled hexagonal holes don’t coverthe full area of the scintillator, but have a fill factor of about 76%. This will seta limit for the highest possible absorption and its NNPS will be limited to a valueof 1.3. The peaks that occur close to the zero frequency at 10 keV and 25 keV arelikely caused by some non-uniformity that was left after the image pre-processing.This don’t affect the result so no further investigation was done.

Detected visible light photons per x-ray photonThe number of detected visible light photons per x-ray photon was calculated fromthe NNPS data and the result are shown in Table 4.4. The amount of emittedvisible light is proportional to the energy of the x-ray photon, so the measuredvalues correspond well with theory.

Table 4.4: Detected visible light photons per x-ray photon.

10 keV 25 keV 30 keV 40 keV

PI:Gadox 180 293 335 427PI:Scint-X 48.0 49.9 60.5 56.6PI:CsI 325 411 473 482PS:Gadox 15.5 23.5 29.1 31.0



0

0.2

0.4

0.6

0.8

1

DQ

E


(b) 25 keV (1 mm Al)


0 10 20 300

0.2

0.4

0.6

0.8

1


DQ

E



0 10 20 30Spatial frequency [mm−1]


(d) 40 keV (10 mm Al)

Figure 4.5: Comparison of the DQE at different energies.

4.4 DQE

The DQE for each detector setup is shown in Figure 4.5 and the integrated DQEs,δ, are listed in Table 4.5. At 10 keV, PS:Gadox has both the highest resolutionand largest area, although PI:Gadox and PI:CsI have slightly higher DQE at lowfrequencies. At higher energies, both Gadox-based scintillators quickly gets worsedue the reduced absorption, and both CsI-based scintillators gets better. Here,PI:Scint-X has the highest resolution but PI:CsI has higher absorption efficiency,making it slightly better when looking at the integrated DQE. Looking at value ofthe DQE, we can notice that PI:CsI has the highest value up to a frequency of 8.25mm−1, after which PI:Scint-X gets better.

Table 4.5: The integrated DQE, δ [mm−1], for the scintillators at different energies.

10 keV 25 keV 30 keV 40 keV

PI:Gadox 4.90 2.74 2.08 1.33PI:Scint-X 2.59 4.30 4.56 4.91PI:CsI 3.25 5.03 5.23 5.68PS:Gadox 7.48 1.71 1.19 0.73

4.5. REAL DETECTOR-MODEL 33

(a) Comparison of measured and simulateddata.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

DQ

E0


10 25 30 400

2

4

6

8

10

Spectrum energy [keV]

δ [m

m−

1 ]

(b) Simulations of DQE0(E) and δ(E).

0

0.2

0.4

0.6

0.8

1

DQ

E0


0 20 40 60 80 1000

5

10

15

Energy [keV]

δ [m

m−

1 ]

Figure 4.6: a) The measured DQE0 and δ(Φ) (markers) together with simulations donefrom the source emission spectrum (solid lines). b) Simulations of DQE0 and δ(Φ) donefor single energies.

4.5 Real detector-model

A comparison of the simulated and measured values for DQE0(Φ) and δ(Φ) areshown in Figure 4.6a. The simulations are in good agreement with the measureddata for all scintillators, but δ(Φ) is slightly higher than the measured values forPS:Gadox and slightly lower for PI:CsI at higher energies.

There are several possible explanations for the difference between the measuredand simulated data. First of all, the model is very sensitive to the thicknessesand densities of the scintillators and their substrates. These value were fitted fromthe scintillators absorption spectra, but this was not possible for PS:Gadox so theapproximative values stated in the the manual were used. Secondly, the shapesof both the MTF and NNPS were assumed to be independent of energy in thesimulations of DQE0. Referring to Figure 4.3b, it can be seen that the MTF isslightly reduced with increased energy, but it should not be enough to affect thefinal result. Looking at Figure 4.4, the general shape of the NNPS also seem to bethe same for different energies.

Seeing that the simulations agreed well with the measured data, they werealso done for single energies from 10 keV to 100 keV (Figures 4.6b). Referring tothe previous discussion, δ(E) should be slightly lower for PS:Gadox and slightly


higher for PI:CsI, but this does not affect the outcome; PS:Gadox has the bestoverall performance at low energies and PI:CsI at high energies, closely followedby PI:Scint-X. It it also worth to notice that although PI:CsI has better overallperformance at higher energies, PI:Scint-X has much better resolution.

Chapter 5

Conclusions

The choice of detector greatly depends on the imaging task and on the spectrumenergy. In absorption imaging the frequency region of interest depends on the sizeof the object being imaged. For large objects the lower frequencies are of interestso PI:CsI would be the best choice for all energies. For small objects the higherfrequencies are most important, making PS:Gadox best at 10 keV and PI:Scint-Xbest at higher energies.

In phase contrast imaging the overall performance is important, making δ theimportant factor. This makes PS:Gadox best at 10 keV and PI:CsI best at higherenergies.

Table 5.1: Summary of the conclusions.

High resolution Overall performance

Low energies PS:Gadox PS:GadoxHigh energies PI:Scint-X PI:CsI

35

Acknowledgments

In the end, I would like to to express my deepest gratitude to all the people thathave supported me and made this project possible.

First to my supervisor Ulf Lundström for all your guidance all through thisproject. I have learned a lot from you and this project would not have been possiblewithout you.

To all the members of the BioX group; to Prof. Hans Hertz for introducingme to this project, to my examiner Ulrich Vogt for always guiding me in the rightdirection, to Daniel Larsson and Tunhe Zhou for helping me out in the lab and toeveryone else for all interesting discussions and for making BioX to what it is.

To the company Scint-X and the medical imaging group at KTH for providingme with scintillators.

Finally, to my mother Elisabeth, my father Christer and my sister Josefine fortheir love and everlasting support.

37

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[2] K. Carlsson, Imaging Physics. Applied Physcis Department, KTH, 2009.

[3] S. Smith, The scientist and engineer’s guide to digital signal processing. Cali-fornia Technical Publishing, 1997.

[4] H. G. Chotas, J. T. Dobbins, and C. E. Ravin, “Principles of digital radiogra-phy with large-area, electronically readable detectors: A review of the basics,”Radiology, vol. 210, no. 3, pp. 595–599, 1999.

[5] M. J. Yaffe and J. A. Rowlands, “X-ray detectors for digital radiography,”Physics in Medicine and Biology, vol. 42, no. 1, p. 1, 1997.

[6] D. H. Larsson, P. A. C. Takman, U. Lundstrom, A. Burvall, and H. M. Hertz,“A 24 kev liquid-metal-jet x-ray source for biomedical applications,” Reviewof Scientific Instruments, vol. 82, no. 12, p. 123701, 2011.

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[8] P. B. Greer and T. van Doorn, “Evaluation of an algorithm for the assessmentof the mtf using an edge method,” Medical Physics, vol. 27, no. 9, pp. 2048–2059, 2000.

[9] K. A. Fetterly and N. J. Hangiandreou, “Effects of x-ray spectra on the dqe ofa computed radiography system,” Medical Physics, vol. 28, no. 2, pp. 241–249,2001.

[10] J. T. Dobbins, III, E. Samei, N. T. Ranger, and Y. Chen, “Intercomparison ofmethods for image quality characterization. ii. noise power spectrum,” MedicalPhysics, vol. 33, no. 5, pp. 1466–1475, 2006.

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