Pfeiffer Dr

Evaluation of the Medipix Detectors forMedical X-Ray Imaging, with SpecialConsideration of Mammography

Den Naturwissenschaftlichen Fakultatender Friedrich-Alexander-Universitat Erlangen-Nurnbergzur Erlangung des Doktorgrades

vorgelegt vonKarl-Friedrich G. Pfeifferaus Ndoungue

Als Dissertation genehmigt von den Naturwissenschaftlichen Fakultatender Universitat Erlangen-Nurnberg

Tag der mundlichen Prufung:

15.12.2004

Vorsitzender derPromotionskommission:

Prof. Dr. D.-P. Hader

Erstberichterstatter:

Prof. Dr. G. Anton

Zweitberichterstatter:

Prof. Dr. E. Steffens

Contents1 Introduction

1

2 Photon Counting Detectors2.1 Basic Types of Imaging Detectors2.2 Advantages of Photon Counting .2.3 The Medipix1 Detector . . . . .2.4 The Medipix2 Detector . . . . .

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3 Basic Quality Definitions3.1 Definitions . . . . . . . . . . . . .3.2 Determination of MTF and DQE3.2.1 Measuring the MTF . . .3.2.2 Calculating the DQE . . .

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4 Experimental Setup and ROSI4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . .4.1.1 Equipment and Accessories . . . . . . . . . . . . . .4.1.2 Calibration of the X-ray Source . . . . . . . . . . . .4.2 The Simulation Tool ROSI . . . . . . . . . . . . . . . . . .4.3 Reasons for Using ROSI . . . . . . . . . . . . . . . . . . . .4.3.1 Comparison Between Ideal and Non-Ideal Detectors4.3.2 The Influence of Scattered Radiation . . . . . . . . .4.3.3 Test of the Image Assembling Routines . . . . . . .

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151515161819192123

5 Detector Characterisation5.1 The Medipix1 Detector . . . . . . . . . . . . . . . . .5.1.1 Effects of the Detector Bias . . . . . . . . . . .5.1.2 Threshold Tuning . . . . . . . . . . . . . . . .5.1.3 Threshold Calibration . . . . . . . . . . . . . .5.1.4 Fixed-Pattern Correction and Quantum Noise .5.1.5 MTF, NPS and DQE . . . . . . . . . . . . . .5.1.6 Charge Sharing . . . . . . . . . . . . . . . . . .5.2 The Medipix2 Detector . . . . . . . . . . . . . . . . .5.2.1 Effects of the Detector Bias . . . . . . . . . . .5.2.2 Threshold Tuning and Calibration . . . . . . .5.2.3 Quantum Noise and Fixed-Pattern Correction .5.2.4 MTF, NPS and DQE . . . . . . . . . . . . . .5.2.5 Charge Sharing . . . . . . . . . . . . . . . . . .

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ii

CONTENTS5.3

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44444649495353

6 Large-Scale Images6.1 Basic Ideas and Concepts . . . . . . . . . . . . . . . . . .6.1.1 Move & Tile . . . . . . . . . . . . . . . . . . . .6.1.2 Tile & Move . . . . . . . . . . . . . . . . . . . .6.1.3 Comparison Between Both Methods . . . . . . . .6.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . .6.3 Image Acquisition and Composition . . . . . . . . . . . .6.3.1 Image Acquisition . . . . . . . . . . . . . . . . . .6.3.2 Data Processing and Image Composition . . . . . .6.4 Examples of Large-Scale Images . . . . . . . . . . . . . . .6.4.1 Move & Tile . . . . . . . . . . . . . . . . . . . . .6.4.2 Tile & Move . . . . . . . . . . . . . . . . . . . . .6.5 Further Ideas for Automated Image Assembly . . . . . . .6.5.1 Image Difference Method . . . . . . . . . . . . . .6.5.2 Autocorrelation Methods and Similar Approaches

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5.4

Phantoms for Characterisation & Comparison . . . .5.3.1 Phantoms used for the Basic Characterisation5.3.2 Mammographic Phantoms . . . . . . . . . . .Direct Detector Comparison . . . . . . . . . . . . . .5.4.1 Images of the WMRP 152A . . . . . . . . . .5.4.2 The CDMAM Phantom: Visual Comparison5.4.3 The CDMAM Phantom: Measured values . .

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7 Summary and Outlook

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8 Zusammenfassung und Ausblick

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A PhantomsA.1 Simple Phantoms . . . . . . . . . . . . . . . . . . . . . . .A.1.1 Siemensstar . . . . . . . . . . . . . . . . . . . . . .A.1.2 Huttner grid . . . . . . . . . . . . . . . . . . . . .A.1.3 Contrast-Detail Mammographic Phantom . . . . .A.1.4 Wisconsin Mammographic Random Phantom 152A

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838383838485

B Technical Specifications of the EquipmentB.1 The Mammomat B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B.2 Translation Stages and Motion Controller . . . . . . . . . . . . . . . . . .B.3 Dose Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87878788

C Programs and ScriptsC.1 Server/Client Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . .C.2 MATLAB Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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D Glossary

91

List of Figures

92

Bibliography

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Chapter 1

IntroductionSemiconductor sensors and detectors have been introduced over 60 years ago [E.H03] andare by now widely in use. The applications of semiconductor detectors range from thedetection of infrared radiation (e. g. for telecommunication purposes) over X-ray imaging(e. g. detectors for medical imaging using amorphous silicon) and gamma-ray detectors(e. g. EPIC on XMM-Newton) up to high energy physics and particle detectors (e.g. ATLAS at CERN).The work presented here studies two generations of a new kind of semiconductor pixeldetectors which were developed for X-ray imaging in the photon counting regime. Theyconsist of two layers which are connected via so-called bump bonds: a semiconductor layerto convert the X-ray photons directly to electron-hole pairs and another layer containingsophisticated electronics to count the absorbed photons in every pixel separately. Adetailed description of the detectors can be found in chapters 2.3 and 2.4.Figure 1.1 shows the first good image taken with a Medipix1 detector at the beginningof this work. One can see a blown fuse1 : the gap in the wire coil can be seen in theupper right part of the coil. The metal which evaporated there condensed at the glasshousing (encircled spot) and even the fibre bundle supporting the wire coil is visible. Aphotograph of this fuse is shown in figure 1.2: one can see the encircled metal droplet justbelow the wire coil.This image is also an example for one of the main advantages of the concept of photoncounting detectors (cf. chapter 2.2), namely the very large dynamic range.

1 This

fuse was actually from the X-ray machine used to take all the images (see chapter 4.1.1).

1

2

CHAPTER 1. INTRODUCTION

50004500104000

30003025002000

40

counts / pixel

3500

20

150050

1000500

6010

20

30

40

50

60

0

Figure 1.1: The first good image taken with the Medipix1 detector at the beginning of thiswork. It shows a blown fuse ( 5 mm): the encircled spot is metal which evaporated from thewire coil when the fuse was blown and condensed at the colder glass housing. The gap in thewire coil is also clearly visible. The grey value encodes the number of photons counted in therespective pixel. The spread white points are noisy pixels set to zero.

Figure 1.2: Photograph of the blown fuse shown in figure 1.1. One can see the metal dropletencircled in the X-ray image just below the wire coil. By comparing the X-ray image with thephotograph one can also try to find the second metal droplet, which could have been a noisypixel just as well (the apparent lateral distance to the coil depends on the angle of rotation ofthe fuse!).

Chapter 2

Photon Counting Detectors2.1

Basic Types of Imaging Detectors

Requirements for MammographyIn the field of medical imaging there are so many different and sometimes conflictingrequirements for the detector that it is very hard to find a single detector that can fulfilthem all. It is therefore probably most promising to optimise a new detector for a morelimited task such as for example angiography or mammography.Since one probable field for the Medipix detectors is mammography, the particularrequirements are given in more detail: For mammography there are two factors which areespecially important for the diagnostic value of an imaging system: on the one hand thespatial resolution should be of the order of 50 m (i. e. 10 lp/mm 1 ) or better to resolvethe shape of microcalcifications, since their shape is an indicator for the probability of afinding to be malignant [YAMY04, FLGB+ 02]. On the other hand the Signal-to-NoiseRatio (SNR) of the imaging system must be very high since the contrast caused by differenttypes of soft tissue is quite low. Additional requirements are high sensitivity for the X-rayspectra used to keep the patient dose as low as possible2 and a large dynamic range tominimise the risk of under- or overexposed images.Imaging Systems and Comparative ValuesThere are a number of different parameters which can be taken into account for thecomparison of different imaging systems. Often the maximum resolution of a detectorand the image SNR for a certain object and X-ray dose are given, both of which canbe determined rather easily. Especially for medical imaging another figure of merit isfrequently used although it cannot be determined directly from a single image: the socalled Detective Quantum Efficiency (DQE), which describes the overall efficiency of adetector as a function of spatial frequency. The DQE and how it can be measured will bedescribed in detail in chapters 3.1 and 3.2.2.Simple photographic films offer a very high spatial resolution, but their sensitivityis very low and there is always the problem of the limited dynamic range, which can1 line

pairs / mm, a commonly used unit for spatial frequencies.main argument against routine screening mammography in Germany is the high X-ray doseneeded for good image quality using commercially available systems and the therewith associated risk ofradiation induced disease.2 The

3

4

CHAPTER 2. PHOTON COUNTING DETECTORS

easily lead to under- or overexposed images of little or no diagnostic value. Today thesimple photographic films have been nearly completely replaced by film-screen systemswhich have an increased sensitivity due to the added X-ray sensitive scintillating layer(or layers), but have also a slightly lower spatial resolution due to the spread and thescattering of the scintillation photons.Image plates accumulate photon-generated electrons in meta stable trapping levelswhen exposed to X-rays.3 These charges can be read out in a dedicated system by scanningthe plate with a laser which stimulates an optical transition of the trapped electrons. Theintensity of this stimulated emission is proportional to the number of the X-ray photonswhich were absorbed and thus carries the image information. Image plates are reusableand the data is available faster than with film screen systems. Since the image informationis extracted by scanning and therefore already digitised, it can be easily processed andcan be archived digitally. The spatial resolution is limited by the grain size and thicknessof the sensitive material and by the resolution of the read-out scanner. The detectionefficiency for typical X-ray spectra for mammography can be as high as 50%.Another type of detectors are gaseous detectors using avalanche amplification of thesignals. The incoming X-ray photons interact with the gas (e. g. Krypton) of the detectorproducing photoelectrons, which are accelerated in an electric field towards the anode. Ifthe field strength is sufficiently high, each primary photoelectron can undergo avalancheamplification creating a large number of secondary electrons. This electron cloud canthen in turn be detected with the (segmented) anode, which gives the wanted spatialinformation. Since the effects involved in generating the image are all fast processes, thistype of detectors can work in photon counting mode even for a rather high photon flux.One detector of this type is described in detail in [FEE+ 01]. Depending on the thicknessof the detector and the gas pressure the quantum efficiency and the spatial resolution varystrongly between different detectors. One detector4 designed for medical applications hasfor example a spatial resolution of 10 lp/mm.Solid state detectors or flat panel detectors are up to now mainly based on the combination of a scintillator layer which converts the incident X-ray photons into visible lightand an array of photodiodes which detect the light emitted by the scintillator. In everypixel there is a capacitor which integrates the photogenerated charge over the acquisitiontime. The spatial resolution is limited by the size of the photodiodes and by the thicknessand structure of the scintillator layer.The fact that scintillation photons are emitted isotropically and that there is a limitingangle under which the photons can leave the scintillator due to internal total reflection,every X-ray photon creates effectively a cone of scintillation photons which are detected bythe photodiodes. The further away from the photodiodes the X-ray photon is absorbed,the larger is the resulting light cone, which can decrease the spatial resolution drastically.It is therefore necessary to keep the scintillator as thin as possible, which decreases theabsorption efficiency, or to structure the scintillating layer somehow to achieve high spatialresolution independent from the interaction depth of the conversion process. Fortunatelyit is possible to grow some scintillating materials in needle-like structures (e. g. CsI):scintillation photons generated inside one of these needles are guided inside it down to thephotodiode beneath.The main sources of noise in this type of detector are the dark current of the photodiodes and the analogue-to-digital conversion of the accumulated charges. In additionthere is the problem of the scintillator afterglow, read-out errors can occur and there are3 The4 The

here.

dynamic range depends on the density of the trapping levels and can be fairly high.XCounter ; see http://www.xcounter.se/. Unfortunately no efficiency or DQE values are given

5

2.2. ADVANTAGES OF PHOTON COUNTING

further effects like cross-talk between adjacent pixels and blooming. A good overview offlat panel detectors, their technology, their characteristics, and their fields of applicationis given by J.A. Rowlands and J. Yorkston in [BKM00a].The Medipix detectors, which are the subject of this work, belong to a new type of solidstate detectors which utilises a physically or electrically structured semiconductorlayer for the direct conversion of X-ray photons into electron-hole pairs and a separateelectronics chip or layer for the signal processing, to which the charge generated in thepixels of the conversion layer is transferred. In the case of the Medipix detectors both thesensor and the electronics layer have pixels of the same size and are connected one-to-onevia so-called bump bonds (see figure 2.3). Thus photons impinging on one pixel of thesensor can be counted within the corresponding pixel of the electronics chip. Thereforethis type of detector is called a hybrid photon counting pixel detector.Table 2.1 gives an overview over the spatial resolution and DQE values of the differentbasic concepts, for a more detailed comparison between the Medipix1 and Medipix2 detectors see table 2.2. Since the DQE values depend strongly on the X-ray spectrum used theyshould be treated as approximate values as long as no X-ray spectrum is specified. Thenumbers given here are for common medical spectra5 and therefore only an indicationof the limits of the detector type.The next section will describe the basic concepts and advantages of photon countingdetectors per se, followed by a more detailed description of the Medipix1 and Medipix2detectors, respectively.ConceptFilm-screen systemImage plateGas detectorsFlat panel detectorsMedipix1Medipix2

Spatial resolution in lp/mm

max. DQE

up to 20

0.30

510up to 1058 4.5

12.5

0.45n.a.

0.80

0.11ab

Table 2.1: Overview over existing imaging systems and their maximum spatial resolution; allnumbers are approximate values only. The DQE values are given for zero line pairs/mm (lp/mm),the resolution of the Medipix detectors was determined from measurements (see chapter 5.1.5).a preliminaryb not

value; 35 kV tube voltage, Mo anode, 2 mm Al filteringreliable data yet

2.2

Fundamental Concepts and Advantages ofPhoton Counting

Due to the fact that the X-ray flux itself is already quantised, it seems most adequate todetect and process each photon individually. Doing so is the best way to convert theinformation contained in the X-ray field into an image and this method is called (single)photon counting for apparent reasons. There are several advantages to this approach:5 Tube

voltages in the range of 4080 kV, various anode materials and filters.

6

CHAPTER 2. PHOTON COUNTING DETECTORS1. The information is digitised as soon as possible, only the number of photons detected by each pixel is stored and read out. Therefore typical CCD-effects likeblooming, cross-talk between adjacent pixels or read-out errors due to incompletecharge transfer cannot occur.2. By applying a threshold to the charge signal coming from the sensor layer darkcurrent can be discerned from actual signals and therefore discarded.3. If more than one threshold and counter are implemented in every pixel, spectroscopicdata can be gained which can improve image quality. In the best case the energy ofevery single photon is recorded, giving the maximum information extractable.64. The maximum contrast achievable within a single image is only limited by theavailable counter depth in each pixel. Thus over-exposed bright regions in an overallrather dark image and vice versa pose no longer an insolvable problem.5. The detector shows a completely linear response over the whole exposure range.

Figure 2.1 shows a sample image taken with the Medipix1 detector, illustrating the advantages of a photon counting detector. The different grey levels represent different countsper pixel, the lighter the grey the lower the counts (just as for X-ray films). In this imagethree distinct areas can be seen: the darkest one is only air, the medium grey level is theshadow of an aluminium sheet (2 mm thick) and the lightest one is the area underneath2 mm of lead. The histogram (number of pixels vs. counts per pixel) of the image is shownon the right. Figure 2.2 shows the profile along column 32 of figure 2.1; one can see thatthe edges are very sharp because there is no crosstalk between neighbouring pixels andno blooming effects.

aluminium10

lead

250

20number of pixels

200

30

air40

aluminium150

air100

50

50

60

lead10

20

0

30

40

50

60

0

100 200 300 400 500 600 700 800 900 1000counts / pixel

Figure 2.1: Sample image with three different materials between the X-ray source and thedetector (just air, 2 mm aluminium, 2 mm lead). The graph on the right shows the histogram ofthe image on the left; the three areas can be distinguished very well.

6 For

some modalities a kind of time stamp or other time information about each photon could possiblyyield extra information, therefore the term maximum information might be debatable.

7

2.3. THE MEDIPIX1 DETECTOR1000

counts

800600

aluminium

lead

air

4002000

10

20

30

40

50

60

pixel

Figure 2.2: Profile along column 32 of the image shown in figure 2.1. One should note thesharp edges, especially between the areas air and lead, where the counts drop from over 900to almost 0 from one pixel to the next.

2.3

The Medipix1 Detector

Hybrid pixel detectors have evolved rapidly mainly in the field of high energy particlephysics. Especially the RD19 collaboration at CERN has developed several generations ofsilicon pixel detectors, one of the most recent ones being the LHC1/Omega3 chip. Basedon this chip the Medipix Collaboration7 developed the first so-called Photon CountingChip (PCC). It has 64 64 square pixels with 170 m side length and can be read outeither serially or in parallel. Using this PCC and connecting it via so-called bump bondsto a semiconductor sensor layer the first Medipix1 detector was manufactured.A schematic view of the Medipix1 detector can be seen in figure 2.3, showing the sensorlayer, the connecting bump bonds and the ASIC (PCC) on the bottom. Figure 2.4 showsa schematic view of the pixel cell layout of a single Medipix1 pixel (after [CEM+ 98]). Themost important components for photon counting are the discriminator and the counter inevery pixel cell.

Figure 2.3: Schematic view of a Medipix detector, consisting of the sensor layer, the bumpbonding, and the ASIC (the drawing is not to scale and only a few pixels are shown for clarity).

When a photon is absorbed in the sensor layer, the generated charge is transferred viathe respective bump bond to the corresponding pixel on the ASIC. After a preamplifier thecharge is fed into a discriminator which compares the signal to a previously set threshold.If the signal is higher than the threshold, the counter of this pixel is increased by one; this7 http://medipix.web.cern.ch/MEDIPIX/

8


from previous pixel3 bitThresholdAdjust

Shutter

MUX

MaskbitVth

Preamp

InputBump bond

Disc

MUX

15 bitCounter/ShiftRegister

Clock extC testTestbit

to next pixel

Test InputAnalogue Part

Digital Part

Figure 2.4: The simplified pixel cell layout of a single Medipix1 pixel (after [CEM+ 98]). Thecounter / shift register acts as the counter of the pixel during image acquisition and as shiftregister during read-out.

is done in each pixel independently. When the acquisition is complete, the counters of allpixels are read out to obtain the image. Between the discriminator and the counter thereis also a switch which is set via a mask bit: if a pixel is known to be defective or noisy, itcan be switched off using the mask bit.The setting of a threshold for the discriminator allows to suppress signals generatedby electronic noise or dark current of the sensor layer, leading to a background-free image. The threshold is set globally for all pixels, but there is an additional individual 3bit threshold adjustment to correct for inhomogeneities due to fabrication variations (seechapter 5.1.2 for details). Because the global threshold can be set within a wide rangeit can also be utilised to discard low energy X-ray photons which may reduce the image contrast in some cases. Dynamic range and image contrast are only limited by thecounter depth, which is 15 bit (corresponding to a maximum of 32767 counts per pixeland acquisition) for the Medipix1.8Up to now most Medipix1 detectors were fabricated with 300 m thick sensor layersmade of silicon, but a few with other thicknesses or materials such as gallium arsenide(GaAs) or cadmium (zinc) telluride (Cd(Zn)Te or CZT) were manufactured as well. Butsince the ASIC works only with positive charges, GaAs or Cd(Zn)Te are not as suitable asSi for the sensor layer. Because the hole mobility in these materials is quite low it wouldbe better to collect electrons instead. This problem has been solved in the design of theMedipix2, which can handle electrons as well as holes.The fact that the Medipix detectors are hybrid detectors has an advantage in itself:both main components, the sensor layer and the ASIC, can be developed independently ofeach other. Thus advancements in materials science can improve the sensor layer without8 Although

depth.

it is possible to use a fast readout method which results effectively in a counter with infinite

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2.4. THE MEDIPIX2 DETECTOR

altering the ASIC; new CMOS technology and new designs can further the developmentof the ASIC, leading for example to smaller pixel cells or added features as can be seenwith the Medipix2 detector.

2.4


The Medipix2 detector was developed as the successor for the Medipix1 detector. Sinceit was designed using the 0.25 m CMOS process, it was possible to reduce the pixel cellsize to 55 m 55 m and to add a second discriminator. With this second threshold andthe appropriate additional logic it is possible to use either a single lower energy thresholdor an energy window, counting only photons with an energy lying between the lower andthe upper threshold. Both thresholds can be fine-tuned with a 3 bit threshold adjustseparately, but the counter depth was reduced to 13 bits due to the limited size of thepixel cell. In addition, the input polarity of the ASIC can be switched between positiveand negative. This design feature allows to use GaAs and Cd(Zn)Te sensor layers moreeffectively, since their electron mobility is significantly higher than their hole mobility.The schematic view of a single pixel cell of the Medipix2 (see figure 2.5) was adoptedfrom [LCD+ 02]. The main difference to the Medipix1 is the second discriminator, whichenables the setting of an energy window rather than just a single lower threshold. Asthere is still only one counter implemented in the design, it is unfortunately not possibleto count photons above the lower and the upper threshold separately.from previous pixel

3 bitThresholdAdjust

Shutter

Maskbit

MUX

Vth HighDisc HDoubleDiscLogic

Preamp

InputBump bond

MUX

Disc LVth Low

C test

Clock ext

13 bitCounter/ShiftRegister

Testbitto next pixelTest InputAnalogue Part

Digital Part

Figure 2.5: The simplified pixel cell layout of a single Medipix2 pixel (after [LCD+ 02]). Compared to the Medipix1 pixel cell (see figure 2.4) one can see the additional discriminator andthe following double discriminator logic which makes it possible to use an energy window. Thecounter / shift register acts as the counter of the pixel during image acquisition and as shiftregister during read-out.

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Feature

Medipix1

Medipix2

Pixel size

170 m 170 m

55 m 55 m

Number of pixelsSensitive area

64 64

1.18 cm

2

256 2561.98 cm2

Number of thresholds

1

2

Number of counters

1

1

Counter depth

15 bit

13 bit

Input polarity

pos.

pos. / neg.

CMOS process

1 m

0.25 m

Table 2.2: Technical parameters of the Medipix1 and Medipix2 detectors.

Chapter 3

Basic Quality Definitions3.1

Definitions

In order to compare different sensors or imaging methods it is essential to agree on a setof parameters to describe the image quality. In the following a few definitions are givenfor parameters commonly used in imaging theory as well as in medical imaging.The modulation transfer function (MTF) characterises the spatial frequency responseof an imaging system and basically just describes how well the object contrast is transmitted through the imaging chain for a given spatial frequency.It is defined as the ratio between the modulation of a sinusoidal test pattern Min at aspatial frequency f and the modulation of the obtained image, Mout .MTF (f ) =

Mout (f )Min (f )

(3.1)

By definition it ranges between zero and 1 for all frequencies and can be described byanalytical functions or a convolution of functions in simple cases. Assuming for examplesquare pixels (as it is the case for both Medipix detectors) with lateral dimension l and auniform sensitivity over the whole pixel area, the theoretical limit for the MTF is givenbysin(f l)=: sinc(f l)(3.2)MTF sq =(f l)where f denotes the spatial frequency. Comparisons between this theoretical limit andactual values for the Medipix detectors will be shown in chapters 5.1 and 5.2, respectively.Whereas the MTF describes only one aspect of the imaging process, the detectivequantum efficiency (DQE) encompasses more than one aspect and is therefore a keyparameter when describing the properties of an imaging system, especially for medicalequipment. The DQE includes the MTF, but it also accounts for the quantum efficiencyand the noise characteristics of the system. It can be defined in terms of the Signal-toNoise-Ratios of the incoming X-ray flux (SNRin ) and the image (SNRout ):DQE (f ) =

SNR 2out (f )SNR 2in (f )

(3.3)

Basically, the DQE is a measure for how well the SNR(f ) of the incoming informationis preserved by the imaging system. Unfortunately, only SNR2in is readily available: the

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12

CHAPTER 3. BASIC QUALITY DEFINITIONS

variance of the photon flux isSNR2in as follows:

N for N photons in the X-ray field. Hence one can re-writepSNR 2in = ( Nin )2 = Nin

(3.4)

This leads to a modified equation for the DQE:DQE (f ) =

SNR 2out (f )Nin

(3.5)

This still leaves the problem of obtaining SNR2out , which will be addressed in section 3.2.2.The concepts of MTF and DQE have been explained in detail by I. Cunningham[BKM00b] and are now widely used for describing and comparing the performance ofdifferent detectors and systems. It should be kept in mind that the DQE of a detectordepends on the X-ray spectrum used; thus only evaluations made with the same spectrumcan be compared directly.

3.2

Determination of MTF and DQE

Since it is not possible to determine the DQE of an imaging system using the basicdefinition given in equation (3.3), it is necessary to measure the MTF of the system and afew other parameters to obtain its DQE experimentally. The next part will describe twomethods to determine the MTF of a system, followed by a description of how to measurethe values needed to compute the DQE.

3.2.1

Measuring the MTF

There are basically two methods for measuring the MTF of a given system: either byusing a phantom with known modulation at different spatial frequencies or especiallyfor digital systems or pixel detectors by using a sharp edge and the so-called edgemethod after Fujita [FTI+ 92]. The latter one is a derivative of the slit method which usesa fine slit instead of a sharp edge.Edge MethodThe edge method is a relatively fast and easy method to derive the MTF of a digital imaging system from a single, maybe even rather small, image. This is especially convenientwhen working with small detectors and at an early development stage. For this method aprecision edge made from e.g. tungsten is placed slightly tilted to the pixel rows over thedetector and an image is acquired. By projecting the image data along the direction ofthe edge, a one-dimensional oversampled1 dataset is obtained from which the edge spreadfunction is determined and numerically differentiated, leading to the line spread function(LSF) perpendicular to the edge. Calculating the modulus of the Fourier transform of theLSF results in the desired MTF, also perpendicular to the edge.Slit MethodThe slit method uses a fine slit instead of the edge employed when using the edge method.The advantage of the slit method when compared to the edge method is the fact that theprojection of the image data along the slit axis leads directly to the LSF without the need1 For

a small tilt angle and a pixel size d the sample length s is given by: s = d tan .

3.2. DETERMINATION OF MTF AND DQE

13

to calculate the derivative of the edge spread function. But it has also disadvantages: thefabrication of a fine, accurate slit is more difficult than that of an edge and the lowestfrequency components are not readily available in the image because only a very narrowstrip of the detector is illuminated. To evaluate the measurement the low frequencycomponents of the LSF must be extrapolated. Last but not least the positioning of theslit can be seen as rather difficult because only a nearly perfect alignment produces asatisfactory slit image; the side walls of the slit must be oriented exactly perpendicularto the detector plane for the slit to be seen at all. On the other hand it is not easy toachieve a very good alignment when using a single edge since the edge image does notshow misalignments so clearly.Square Wave MethodSince it is very difficult to fabricate a phantom which modulates the X-ray attenuationsinusoidally2 with high precision, it is more convenient to achieve a square wave modulation of the X-ray fluence and to analyse the constituent sinus waves which make upthe square wave by superposition independently. It is thus not a direct measurementof the MTF as it is defined and one must convert the measured square wave response ofthe system to a sinusoidal response first. Equation (3.6) shows the Fourier expansion ofa square wave f (x) with wavelength 2L and amplitude a:f (x) =

(2n 1)x4a X 1sin n=1 2n 1L

(3.6)

Using this equation one can extract thus the desired information from the measuredvalues. The bar pattern grid is positioned slightly tilted with respect to the pixel rows toavoid sampling artifacts. To evaluate the MTF at a certain frequency the modulation ofthe part of the image with this fundamental frequency is read out by projecting the imagedata on a line perpendicular to the bar pattern. This projection reduces the influence ofstatistical fluctuations. The result is an oversampled one-dimensional dataset of the squarewave response which can be easily analysed. In most cases it would pose no problem hereto derive modulation values even for frequencies beyond the Nyquist limit, thus gettingthe pre-sampled MTF.But by evaluating only the modulation of the fundamental frequency of the respectivepart of the bar pattern one can minimise the influence of numerical errors and noise,finally getting a set of MTF values for certain spatial frequencies. These can be comparedto theoretical values or an otherwise determined MTF.There are, however, drawbacks to this method: for good results the bar pattern has tobe manufactured with high precision, the data analysis is quite complex, and when usingsmall detectors one can need several images3 . In contrast to the edge method it is alsoimpossible to extract the zero-frequency component of the MTF.

3.2.2

Calculating the DQE

Since the definition of the DQE given by equation 3.3 contains parameters which cannotbe measured directly, another formulation must be found which contains parameters thatcan be acquired from measurements. One quantity which can be derived from measuredimages is the noise power spectrum or NPS. The NPS is the variance of the signal for2 As

it was assumed for the definition given in equation 3.1.on the size of the bar patterns and the number of frequencies to be evaluated.

3 Depending

14

CHAPTER 3. BASIC QUALITY DEFINITIONS

different spatial frequencies or simply put the noise content of each spatial frequency.It can be obtained by calculating the modulus-squared two-dimensional Fourier transformof a homogeneously exposed image. Using the NNPS (Normalised NPS) one can writethe SNR2out of the image as:SNR 2out (f ) =

MTF 2 (f )NNPS (f )

(3.7)

Using equations (3.4) and (3.7), equation (3.3) can be reformulated:DQE (f ) =

MTF 2 (f )SNR 2out (f )=2NNPS (f ) NinSNR in (f )

(3.8)

The number of photons can be calculated from the tube spectrum and the dose used. Toget reliable results for the NNPS one normally averages over a large set of overlappingregions of interest, e. g. 256 256 pixels in size. In most cases only one-dimensional subsetsof the full two-dimensional NPS diagonal to the pixel columns or rows are considered forcalculating the DQE as the MTF is also evaluated for these directions. Results of DQEcalculations can be found in chapter 5.1.5 for the Medipix1 detector and in chapter 5.2.4for the Medipix2.For more details on special properties and problems of MTF and DQE for digitalsystems see for example [BKM00c].

Chapter 4

Experimental Setup and ROSI4.14.1.1

Experimental SetupEquipment and Accessories

Data Acquisition Hardware and SoftwareSeveral hardware parts and dedicated software were used for the acquisition of data withthe Medipix detectors. Since the requirements were different for both detector generations,two separate data acquisition systems were used.Medipix1: For the Medipix1 the data acquisition system includes a dedicated, custombuild interface board MUROS11 ., two computer boards and the software Medisoft 3; thecomputer boards are plugged into a standard PC running Microsoftr Windows NTr .The MUROS1 board was developed by NIKHEF, Amsterdam, and has three functions:it supplies the voltages needed by the Medipix1 chip, it converts signal levels betweenthe levels the Medipix1 ASIC is using and the standard levels used by the PC, and itaccommodates a pulse generator which can be used for detector testing and calibrating.The chipboard hosting the Medipix1 detector is connected directly to the MUROS1. It ispossible to use a connecting cable for more flexibility but the standard setup is the directconnection.The two computer boards plugged into the PC are a digital input/output PCI board(NI PCI-6533) and an analogue output ISA board (NI AT-AO-10), both manufacturedby National Instruments2 . These boards handle the communication and data transferbetween the MUROS1 and the PC and supply the voltages needed by the MUROS1. But thesetup has proven to be more stable and to produce better results when an external powersource is used for the 3 V supply instead using one of the boards.The Medisoft 3 software was developed by the University of Napoli INFN-group(Italy). It has been written using the LabWindows/CVI programming environment3 andcontrols all data handling and communication between the PC and the Medipix1 detectorvia the NI boards and the MUROS1. For details of the data acquisition system see [BBA+ 00].1 Medipix1

reUsable Read-Out System

2 http://www.ni.com3 Software

by National Instuments.

15

16

CHAPTER 4. EXPERIMENTAL SETUP AND ROSI

Medipix2: The data acquisition system for the Medipix2 is quite similar to the oneused for the Medipix1: it consists of a custom build interface board (MUROS2, also byNIKHEF), only one PCI computer board (NI PCI-6533 by National Instruments), andthe software Medisoft 4 (by the University of Napoli INFN-group).In contrast to the MUROS1 the MUROS2 is able to handle not only a single-detectorchipboard as was used for the work presented here but also a chipboard hosting up toeight Medipix2 chips which was not yet available during this thesis. The main componentof the MUROS2 board is a field-programmable gate array (FPGA), thus a large part ofthe system can be updated electronically without the need to alter the hardware. Thedetector chip board is connected to the MUROS2 using a commercially available SCSI cablewhich makes the setup more flexible, since there is no need to move the whole MUROS2board.Details of the software can be found in [CMM+ 03], details of the MUROS2 in [BvBJ+ 03].X-ray Source and Mechanical SetupThe X-ray source for all imaging experiments was a Siemens Mammomat B. It has aMolybdenum anode and four tube voltage settings (25 kV, 30 kV, 35 kV, 40 kV). A radiation proof housing shielded with 1.4 mm lead was used within which the X-ray tube andthe detectors were placed (see figure 4.1). For a more detailed description see [Gie02].The functional scheme of the experimental setup is shown in figure 4.2. The tubeheight can be varied but was set to 65 cm for most of the images. The Medipix detectorswere mounted on a x-y translation stage which could be remote-controlled. An additionalrotating unit was also implemented for a CT-like setup, where the phantom / objectcould be rotated instead of moving the X-ray source and the detector as it is done inconventional CT setups. Since large field imaging had to be simulated by moving thedetector in the x-y-plane and patching the single images afterwards, a small server / clientprogram4 was implemented which allowed for scripted image acquisition. It controls thetranslation stages (via a suitable motion controller), a rotation unit, data acquisition(which is handled by the aforementioned PC hosting the NI boards), and the X-ray tube.This program runs under UNIX on a standard PC; the connections to all parts of the setupare made through serial ports. For dose measurements the dosimeters PTW DIADOS 5and later the Solidose 400 6 were used; both are equipped with solid state detectors. Thetechnical specifications of the hardware can be found in B.1 - B.3.

4.1.2

Calibration of the X-ray Source

To ensure the comparability of different measurements it was necessary to calibrate theX-ray field generated by the tube.The homogeneity of the field was measured using a scintillating film coated withGd2 O2 S and a CCD camera [Gie02]. Figure 4.3 shows the spatial distribution of theX-ray fluence with a pronounced heel effect [HS91]. This is a desired feature of systemsused for mammography since the absorption near the chest wall is higher due to the highertissue thickness and thus a better uniformity of the exposure over the whole image canbe achieved.The proportionality between the settings of the X-ray generator (anode charge in mAs)and the dose delivered at a fixed distance was tested using a dose meter. Figure 4.4 shows4 Written

by Ch. Bert and D. Niederlohner, see also appendix C.1.PTW-Freiburg GmbH, Germany.6 By RTI Electronics AB, Sweden.5 By

17

4.1. EXPERIMENTAL SETUP

Figure 4.1: The shielded housing of the X-ray tube and detectors (large black box). The casingof the generator and controlling panel can be seen on the left (the covering has been removed formaintenance).Xray tubeswitching: on/off

*adjustabledistance

Computer server / client(UNIX)programComputer(Windows)

phantom / objectto be imaged

data acqisition

MotionController

position controlDetector onxy translation stage

Figure 4.2: The functional schema of the experimental setup. The shielding and the generatorof the X-ray source are not shown for clarity.

18


intensity(a.u.)

frontright side

depthlateralpositionmiddle

back

Figure 4.3: The X-ray field of the Mammomat B. The edge with highest intensity correspondsto the front side of the field; since it is nearly laterally symmetrical, only one half of the field isshown here for clarity.

the very linear behaviour of the measured dose versus the mAs setting of the Mammomatusing the high dose range, which was also seen for all settings in the low dose range.7

4.2

The Simulation Tool ROSI

Monte Carlo simulations are widely used tools in many fields of research and can also bevery useful for the development of new X-ray imaging systems. On the one hand theycan help to understand experimental data, on the other hand they allow to construct andevaluate virtual imaging systems. The information gained from virtual setups can leadto new ideas and a better understanding of the experiment. The X-ray simulation toolROSI8 has been developed by J. Giersch [GWA03].9ROSI is mostly based on the object-oriented C++ simulation library LSCAT-GISMO[ABB+ 93], the interaction algorithms are based on the established EGS4-code and itscurrent LSCAT extension. Therefore it gives valid results down to a photon energy ofa few keV. Modelling stochastic physical parameters such as the energy and direction ofphotons emitted by the X-ray tube is possible by using random variables; they have beenimplemented and put in a separate class-library (RAVAR10 ), which can also be used byitself.The simulation has a simple user interface: all necessary data for the modelling ofthe setup is put into a single file using C++ code. For the description of more complexgeometries a phantom library with predefined geometric objects has been implementedand is under constant further development. This facilitates the modelling of realistic7 The

different settings switch between two anode currents and spot sizes, respectively.is derived from the German words Roentgen Si mulation.9 It has also been made available in the internet: www.pi4.physik.uni-erlangen.de/Giersch/ROSI/10 www.pi4.physik.uni-erlangen.de/Giersch/RAVAR/8 ROSI

19

4.3. REASONS FOR USING ROSI140

30 kV35 kV40 kV

measured dose / mGy

1201008060402000

100

200

300

400

500

mAs settingFigure 4.4: The linear behaviour of the dose delivered at a fixed distance versus the mAs setting(high dose range) of the Mammomat. This kind of measurement was taken with all availablecombinations of mAs values and tube voltages. The sets shown here are only an example.

setups and the comparison between simulated and measured results. Another importantpart for the simulation of real-life-problems is a broad database of materials, both fordetectors and tissues, following the ICRU reports 44 and 46 [oRUM89, oRUM92].Figure 4.5 shows a simple black-box model of the simulation ROSI illustrating inputand output data (after [GWA03]).

4.3

Reasons for Using ROSI

There are several reasons why the tool ROSI has been employed in the scope of this work.It was used to compare the measurements taken with the real detectors to what one wouldexpect from an ideal one; it allowed to estimate the influence of scattered radiation andit provided simple image data to test and improve the routines used to assemble largerimages from small detector-sized ones.

4.3.1

Comparison Between Ideal and Non-Ideal Detectors

The tool ROSI was used to simulate the imaging process with an idealised version ofthe Medipix detectors: The detectors implemented for the simulations shown in thiswork are perfect in the sense that they do not show any charge sharing effects and noimperfections of the sensor layer. Instead, the simulation was used to track each photonand to determine whether it is absorbed in the simulated detector or not. In the first casethe lateral position (x- and y-coordinates) of the interaction with the detector is storedand the photon is detected, in the latter case the photon either passed through thedetector without interaction or was scattered into some other direction by an object infront of the detector.Because only the first interaction of a photon with the detector is stored and writteninto a two-dimensional histogram representing the appropriately sized pixels, no charge-

20

CHAPTER 4. EXPERIMENTAL SETUP AND ROSIList of networkcomputers

Socket address forrequest of statusinformation

Description of thephysical world

Photon parameters alongthe photon trajectory

Xray source dataMaterial dataGeometrical data

EnergyMomentumInteraction points

ROSI

Number ofphotonsUser input

Program output

Figure 4.5: A simple black-box model of the simulation tool ROSI

sharing or other image-degrading effects are simulated. When comparing the thus simulated images with the real ones, one can estimate the influence of detector imperfectionson the image quality.

Measurement

Simulation50

50

100

100

150

150

200

200

250

25050 100 150 200 250

50 100 150 200 250column 159

column 128

2000

0

50

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pixel number

200

0250

5000counts / pixel

counts / pixel

4000

300010000

50

100

150

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0250

pixel number

Figure 4.6: Comparison between a simulated and a measured image of a Siemensstar. It can beseen that the differences between the simulated (ideal) and the real detector for this high-contrastobject are rather small. The plots below the images are intensity profiles along columns at a fixedrelative position close to the centre of the star.

21

4.3. REASONS FOR USING ROSI

4.3.2

The Influence of Scattered Radiation

It is possible to assess the influence of scattered radiation on the image quality usingROSI. For every photon emitted by the source one can store the angle of emission. Bycomparing this angle to the angle of incidence when the photon hits the detector, onecan distinguish between scattered and unscattered photons, thus simulating anti-scattergrids with various angular acceptance. That way one can compare images simulated witha different degree of scattered radiation background, which is known to degrade imagestaken with conventional detectors significantly.For the comparison shown here a setup was chosen which should produce a highpercentage of scattered radiation: an aluminium disc (diameter 1 mm, thickness 500 m)was embedded in the middle of a large PMMA block (20 cm 20 cm, thickness 4 cm). Thedetector consisted of 40 40 square pixels (size 55 m), using 300 m silicon for the sensorlayer. It was placed at a distance of 1 cm behind the centre of the PMMA block and theX-rays irradiate the complete PMMA block to give a large amount of scattered photons.For the first image all photons that hit the detector were accepted, which is equivalentto no anti-scatter grid at all. For two further images the angle of emission from the sourcewas recorded for all photons and when a photon hit the detector, the angle of incidencewas compared to the angle of emission. The photon was counted if the difference ofthese angles was less than 10 or 0.01 , respectively. Thus an anti-scatter grid with anangular acceptance of 10 and a (nearly) perfect grid were simulated. By comparing thehistograms the image quality was evaluated in terms of contrast and SNR.All three simulated images are shown in figure 4.7: between no scattered photonsand 10 acceptance there is nearly no visible difference, only the mean photon count perpixel is slightly higher in the latter one. The grey scales were set for similar appearanceno scattered photons

10 acceptance

all photons

10

10

10

20

20

20

30

30

30

10

20

20

40

30

10

60

20

20

40

30

60

10

40

60

20

30

80

100

Figure 4.7: The images with no scattered photons, 10 acceptance and all photons, respectively.The grey scales were set for similar appearance of both images.

of all images, but one can see that there is a higher degree of noise in the image with allphotons (which is equivalent to no anti-scatter grid). Figure 4.8 shows the histograms ofall three simulated images.All numerical values (the intensities of the background Iback and the disc Idisc as wellas the standard deviations RM Sback and RM Sdisc ; all in counts per pixel) were takenfrom Gaussian fits to the data. They are given in table 4.1 and were defined as follows:Cdiff

= Iback Idisc

22


350

all photons10o acceptanceno scattered photons

number of pixels

3002502001501005000

20

40

60

80

100

counts / pixelFigure 4.8: The histograms of three simulated images: only the angle of acceptance was variedand thus different anti-scatter grids were simulated. As was already seen in figure 4.7, thedifferences between no scattered photons and 10 acceptance are rather small.

Cnorm

=

SNR

=

Iback IdiscIbackIback Idiscp22RM Sback+ RM Sdisc

Grid

Cdiff

Cnorm

SNR

no grid

28.5

0.37

2.53

10 acceptance

28.5

0.55

3.12

perfect grid

29.0

0.61

3.41

Table 4.1: Comparison of contrast and SNR values between no anti-scatter grid, a perfect gridand an intermediate situation. All values were taken from Gaussian fits to the simulated data.

For systems with a limited dynamical range (and probably a non-linear response)such as the film-screen system the normalised contrast Cnorm is important because anadditional background intensity limits the useable dynamical range of the image. Forcounting detectors with a large linear dynamical range (and for a constant X-ray dose)the simple contrast Cdiff can be used as well, since an additional background can betreated as a simple offset which does not limit the useable dynamical range and is thusnot very important for the image quality, as can be seen in this example. But because ofthe lower SNR it might be advisable to use an anti-scatter grid, especially for low-contrastobjects such as soft tissues.One has to keep in mind, though, that any real anti-scatter grid not only absorbsscattered radiation but also part of the primary radiation and thus reduces the SNR incomparison to an ideal anti-scatter grid. The transmission of primary radiation ranges

4.3. REASONS FOR USING ROSI

23

from about 64% for high resolution grids to about 75% for mammographic grids;11 thisloss of primary radiation leads to a reduced SNR. Taking the SNR of the perfect grid inthe example above, the resulting values would lie between 2.73 (65% transmission) and2.95 (75% transmission), which is still better than the SNR without a scatter grid. Thisexample shows that the necessity of an anti-scatter grid should be examined closely forevery setup.Since no anti-scatter grid was available for the measurements made during the workfor this thesis it was important to gain some insight into how scattered radiation affectsimage quality (contrast, SNR) to be able to compare the performance of the Medipixdetectors with existing systems employing anti-scatter grids.

4.3.3

Test of the Image Assembling Routines

Simulated images are also a good method to test the routines which were written forscripted image assembling. Since it is possible to simulate a wide variety of phantoms,the simulations were also quite useful to test new ideas for automated image assemblyin the case of an unknown overlap between the images, which would likely occur whencheaper and less precise translation stages12 are used instead of the high-precision onesused for the experiments for this work. The assembly routine presented in chapter 6.5.1(pages 71ff.) was at first tested on very simple simulated images and then with actualmeasurements.

11 These12 I.e.

numbers are given by SIEMENS for some of their grids.translation stages with a precision of the order of the detector pixel size.

24


Chapter 5

Characterisation of theMedipix Detectors5.1


5.1.1

Effects of the Detector Bias

One of the most simple tests that can be done with a Medipix detector is to examine thedependence of counted photons for a fixed dose on the bias voltage of the sensor layer.For increasing bias the fraction of the sensor layer which has a non-zero electric fieldincreases up to the point where the depletion depth is equal to the layer thickness. Afurther increase of the bias increases the field strength in the sensor until the breakdownfield strength of the material is reached.These effects can be seen when taking images at different sensor biases while keepingthe dose constant. Since the conversion of the X-ray photons into electron-hole pairs isdistributed over the whole thickness of the sensor layer1 , but the separation of these carriers happens only in the presence of an electric field, one can expect to collect a differentpercentage of the photogenerated carriers at the electrodes for different thicknesses of thedepleted region. Thus the number of photons counted is proportional to the depletiondepth of the sensor layer. In figure 5.1 the average number of counts per unit dose appliedis shown versus the bias voltage of the sensor layer. As long as the sensor is not fullydepleted, the number of counts rises linearly with increasing bias. As soon as the sensor isfully depleted, the curve shows a plateau. For even higher voltages the number of countedphotons would finally rise again due to avalanche effects until the breakdown field strengthof the sensor is reached. The fit to the measured data was done using the error function,assuming that the depletion thickness increases proportional to the applied voltage andthat the photon absorption occurs evenly distributed throughout the whole thickness ofthe sensor layer.Another effect of the partial depletion of the sensor layer can be seen in images taken atlow electric field strengths. Due to inhomogeneities of the sensor layer (mainly caused bynon-uniformities in the doping) the depletion depth differs over the detector area. Thesedifferences can be seen in the images as patterns with low spatial frequency which arenot correlated to the X-ray field because they lead to a variation of the counts per pixel.1 This

can be assumed for the 300 m Si layers and the X-ray energies used for this work.

25

26

CHAPTER 5. DETECTOR CHARACTERISATION

35000

mean counts / Gy

3000025000200001500010000mean counts / Gyfit

50000

10

20

3040detector bias / V

50

60

70

Figure 5.1: The number of counts/Gy averaged over the whole detector increases up to a plateauvalue when the bias of the sensor layer is increased. The plateau shows that full depletion isreached and all absorbed photons are counted. The fit was done using the error function.

bias voltage: 10 V

bias voltage: 20 V

10

10

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30

40

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60

6010

20

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Figure 5.2: Two flat-field images (raw data) taken with different bias voltages of the sensor.The grey scales were set differently so that the images look similar despite the different meancounts (cf. figure 5.1).


27

They change slightly with increasing bias and vanish quite suddenly when the sensor isfully depleted. This effect has been studied in detail by [TDC+ 03].Figure 5.2 shows two images taken with different bias voltages (10 V and 20 V). Theyshow basically the same pattern caused by the inhomogeneous dopant distribution. Thegrey scales were set differently so that the overall brightness of both images is comparable.The following chapters show that there are also fixed patterns with rather high spatialfrequencies; these do not originate from the sensor layer but from the electronics layerand can be accounted for using an adjustment possibility built into the pixel electronicsand data post-processing.

5.1.2

Threshold Tuning

Threshold AdjustmentAs shown in the description of the pixel cell of the Medipix1 detector in chapter 2.3(page 7), there is a built-in 3-bit threshold adjustment to correct for inhomogeneities ofthe single pixel cells due to variances of the ASIC fabrication. The 3-bit adjustment valuesare written into a mask file (the so-called threshold adjust mask) which can be loaded ontothe chip. But since this is a digital correction with limited range and only 8 distinctivelevels it cannot remove all differences between the pixels. For greater variability the rangeof this adjustment is tuneable via a voltage setting (threshold adjust voltage Vtha ): ifa detector shows stronger inhomogeneities the spread of the adjustment levels can beincreased with the disadvantage of larger steps between the different levels.Creating the Threshold Adjust MaskTo find the right correction setting for each pixel, there is a pulse generator with tuneablepulse height built into the MUROS1 board which is controlled via the software Medisoft3. This pulse generator can be connected to the test input of each pixel (cf. figure 2.4,page 8) to simulate photogenerated charges coming from the sensor layer. The higherthe pulse is, the higher is the energy of the thus simulated photon. The procedure isas follows: for a fixed global setting of the threshold voltage (Vth ) and with the 3-bitthreshold adjust set to 0 (lowest setting), the height of the pulses fed to the test input isvaried. This simulates photons of different energies and for each pixel the 50% value ofthe resulting S-curve2 of counts vs. pulse height is recorded as its individual threshold.The distribution of these individual thresholds over the whole detector can be visualisedas a histogram with the pulse height as the abscissa. This is repeated with the thresholdadjust set to 7 (highest setting) and the histograms of both measurements are compared.They should have an overlap of 1/8th of their width corresponding to the eight settingsof the threshold adjust. The overlap depends on the range of the threshold adjust, whichis determined by the threshold adjust voltage Vtha as mentioned above.Once the best adjustment range is found, the pulse height is varied for each setting ofthe threshold adjust (settings 0-7), so that for each pixel a complete dataset is recordedwhich contains the threshold pulse height3 for each threshold adjust setting. Using thisdata a threshold adjust mask can be generated which minimises the influence of the pixelinhomogeneities on the threshold behaviour of the detector. Figure 5.3 shows the uncorrected histograms with the threshold adjust set to 0 and 7, respectively, and the histogram2 The response of the pixels should ideally be a step function, but mainly due to electronic noise it isrounded to an S-shaped curve or S-curve for short.3 The test pulse height for which the 50% value of the S-curve is reached.

28


of the adjusted distribution. The widths of the histograms before the adjustment (as givenby a Gaussian fit to the data) are broader than the adjusted distribution by a factor of3.81.4000

setting 0setting 7final distribution

number of pixels counting

35003000250020001500100050000

10

203040threshold pulse height / mV

50

60

Figure 5.3: Histograms of the counting threshold of each pixel. The leftmost distributioncorresponds to the adjust bit setting of 0 and the rightmost to the setting 7, both before thethreshold adjust mask is generated. The narrow distribution in the middle is the result of thefine tuning. Its width would be ideally 1/8th of the uncorrected width, but in this example it is1/4th .

As a side remark it should be noted that the response function of each pixel (S-curve)can be taken as a measure of the quality of the pixel: the steeper the curve the better isthis individual pixel.Since the image is already quite flat after doing the threshold adjustment it may notbe necessary to do any further data processing in some cases. But in order to work closeto the minimum noise level given by the quantum noise of the X-ray field itself one hasto apply an additional fixed-pattern correction as described in chapter 5.1.4 (page 31).

5.1.3

Threshold Calibration

One big advantage of the Medipix1 detector when compared to integrating detectors isthe tunable threshold which determines whether a photon is counted or not and whichsuppresses signals coming from electronics noise and the dark current of the sensor. Tofully use the potential of this threshold one has to know the relation between the thresholdvoltage Vth and the corresponding minimum energy for a photon to be counted. Unfortunately this relation is no simple linear proportionality for the Medipix14 : measurementsusing synchrotron radiation have shown that the correlation between photon energy andVth can be best approximated with an exponential relation:Ephoton = a 10Vth /b

(5.1)

where a and b are parameters which can differ between different detectors. The procedureused to calibrate the threshold in terms of photon energy is as follows:4 The

desirable linearity has been achieved with the Medipix2.

29


1. Using a suitable and if possible monoenergetic source (e.g. 109 Cd) a number ofimages is taken with increasing threshold voltage. When plotting the number ofcounts versus the threshold voltage for a single pixel or a group of pixels one getsa curve as shown in figure 5.4 (open squares): as soon as the threshold exceeds thephoton energy, the number of counted photons drops to zero. The steepness of thecurve is a measure of the quality of the pixel: the steeper the better5 . Ideally itwould be a step function. The inflexion point can be identified with the voltagecorresponding to the photon energy of the source. The (numerical) derivative ofthe curve shows the shape of the emission line(s) as seen with the detector and cantherefore be used to check the energy resolution of the detector.2. This process of pairing up threshold voltage with photon energy is repeated withseveral known photon energies. The more energies are available, the better will bethe calibration. Using synchrotron radiation is the most accurate way to gauge thedetector.3. The data gathered from several emission lines is finally fitted using equation (5.1),resulting in a parametric calibration curve for the detector.When looking at the numerical derivative in figure 5.4, one can see a small shoulder inthe right hand flank of the peak. It shows that the detector can see that the 109 Cd sourceused here has a double line with photon energies 22.1 keV and 25 keV; the 25 keV line has1/5th of the intensity of the 22.1 keV line and causes the small shoulder.

counts || diff. counts

10000

1000

100measured countsnum. derivative (x40)fit to num. derivative1.5

1.55

1.6

1.65Vth / V

1.7

1.75

1.8

Figure 5.4: Measured counts vs. threshold voltage Vth and numerical derivative. The countswere fitted with an error function and the numerical derivative was fitted with the sum of twoGaussian peaks, because the 109 Cd source which was used here has a double line.

An example of a parametric calibration curve obtained in this way is shown in figure 5.5. Using the data gathered with a 109 Cd source (main photon energies 22.1 keV5 The

imperfections showing here are mainly threshold noise and charge sharing effects (cf. chapter 5.1.6).

30


and 25 keV) and another mixed nuclide source containing 210 Pb (main photon energy46.54 keV) it has been possible to fit equation (5.1) to obtain the parameters a = 0.73 andb = 1.09 for the detector under examination. Since it is difficult to find suitable radioactive sources with emission lines in the range of 10 keV60 keV, the exposure times arequite long due to the low activity of the sources available and since the absorption probability of the silicon sensor for photons of higher energy is very low, only three data pointshave been used. For the purpose of a basic calibration, however, this has been sufficient.The thus generated parametric curve can now be used to calculate the threshold voltageneeded to cut off the incoming X-ray spectrum at a given photon energy.50

peak datafit

photon energy / keV

4540353025201.6

1.65

1.7

1.75

1.8 1.85Vth / V

1.9

1.95

2

Figure 5.5: Threshold calibration of a Medipix1 detector. The fit was made using equation (5.1).

The parameters of this calibration are fixed for one detector but are different fordifferent detectors. Thus it would be necessary to perform this calibration for everydetector for best results when using the threshold to cut into the incoming X-ray spectrum.Possible applications of the threshold set to certain energies include: Suppression of Compton scattered photons for increased SNR instead of using ananti-scatter grid.6 Increasing image contrast by using only part of the spectrum: e.g. by making imageswith the threshold set below and above an absorption edge (cf. [NBG+ 03]). Autoradiography: rejection of unwanted emission lines or suppression of backgroundradiation.Threshold Variations and Threshold NoiseThe above-mentioned applications of the tunable threshold have one key problem in common: the usability of the threshold for image improvement depends on the pixel-to-pixelvariation of the threshold and on the threshold noise. The first one can be (at least partially) corrected using the threshold adjustment mask, the latter is the sum of electronic6 Simulations

have shown that this helps only for rather large objects, where the ration of Raleighscattering to Compton scattering is sufficiently low [Gie02].


31

noise and the statistics of charge generation and transport in the sensor layer. Both thepixel-to-pixel variation and the noise are the more critical the higher the spectral intensityat the threshold is, since the difference between the counts of two pixels is given by theintegral over the spectrum from the lower to the higher pixel threshold.

5.1.4

Fixed-Pattern Correction and Quantum Noise

In order to determine whether the detector works close to the Poisson limit, i.e. whetherthe detector adds any noise to the basic noise already present in the X-ray flux, one canhave a closer look at flat-field images. From the histograms of the images the width ofthe distribution of counts per pixel can be determined, which should be the square rootof the mean counts per pixel ( N ) for a purely Gaussian distribution and no additionalnoise.Figure 5.6 shows a flat-field image before (left) and after (right) a so-called fixedpattern correction was applied. This was done by scaling the counts of every pixel with anappropriate gain factor. The fixed-pattern correction eliminates residual inhomogeneitiesof the image due to non-perfect threshold adjustment and inhomogeneities of the sensorlayer.The respective histograms of the flat-field images can be seen in figure 5.7: thecorrected data is quite close to the Poisson limit, the width of the distribution is 1.12 N .This shows that the detector works very close to the quantum noise limit.Since the noise in every image is a superposition of the fixed-pattern noise and therandom fluctuations of the quantised X-ray flux itself, it is necessary to average a largenumber of flat-field images to calculate the fixed-pattern correction image. The thusgenerated correction image shows only the deviations from a truly flat image caused bythe detector and it can therefore be used to improve the image quality without introducingany artifacts or throwing away any actual data. For the example shown here 40 flat-fieldimages were used to calculate the fixed-pattern correction image.7 Since this correctionimage represents the different gain factors of the individual pixels it is also called a gainmap and the fixed-pattern correction is also called a gain-map correction.

5.1.5

MTF, NPS and DQE

The MTF of the Medipix1 detector has been measured using the edge method as wellas using the square wave method (cf. chapter 3.2.1, page 12). Figure 5.8 shows theresults of the edge method for both the Medipix1 and the Medipix2 detector.8 Theindicated Nyquist frequencies9 were calculated using the physical pixel size (170 m and55 m, respectively). Measurements using the square wave method however indicate thatthe effective pixel size of the Medipix1 is somewhat smaller than 170 m. This can beseen in figure 5.9, where the MTF values derived from measurements using the squarewave method10 are compared to two theoretical curves given by the sinc-function (cf.equation 3.2, page 11) and the indicated pixel sizes.The NPS, which is needed to determine the DQE later on, was calculated using 20flat-field images. Figure 5.10 shows a cut of the two-dimensional NPS of the Medipix1 at45 degrees to the axes. The average value was drawn as a horizontal linear fit, it showsthat the NPS is very flat for all but the lowest spatial frequencies. This is equivalent to7 These

images had in sum about 12 105 counts per pixel.Matlab scripts used for the calculation were kindly provided by L. Tlustos, CERN.9 For a definition of the Nyquist frequency see the glossary, page 92.10 This and all further calculations in this chapter were performed by Dr. M. Hoheisel, Siemens.8 The

32


10

10

20

20

30

30

40

40

50

50

60

6010

20

30

40

50

60

10

20

30

40

50

60

Figure 5.6: The left image shows the raw data, the right one the data after a fixed-patterncorrection (using 40 flat-field images) was applied. Mean counts per pixel and grey scales are thesame for both.

raw datacorr. data

number of pixels

1000800600400200020000

21000

2200023000counts/pixel

24000

Figure 5.7: Histograms of the raw data and of the fixed-pattern corrected data of a flat-fieldimage. The solid lines are Gaussian fits to the data; the width of the corrected distributionis 1.12 N .

33


1

Medipix1, f

Nyq.

= 2.94 lp/mm

Medipix2, f

Nyq.

0.8

= 9.09 lp/mm

Medipix1presampling resolution 4.63 lp/mm

MTF

0.6

Medipix2presampling resolution 12.45 lp/mm

0.40.200

5

10

15

20

25

30

35

40

lp/mm

Figure 5.8: The MTF curves for both the Medipix1 and Medipix2 detectors as obtained viathe edge method. For the presampling resolution a MTF value of 0.3 is used. The Nyquistfrequencies are calculated using the physical pixel size; the effective pixel size can be smaller (e.g.due to charge sharing effects in the sensor layer).

measured MTF160 m pixel size170 m pixel size

1

MTF

0.80.60.40.200

1

2

3lp/mm

4

5

6

Figure 5.9: The result for the MTF of the Medipix1 calculated using the square wave methodfrom measurements with a bar pattern phantom. The two theoretical curves were calculated forthe indicated pixel sizes.

34


white noise or in other words: the detector does not add any spatial noise components,as could already be seen from the corrected flat-field images themselves. Thus one canspeak of the Medipix1 detector as working at the quantum noise limit.NPS (meas. data)average

NPS / mm2

10000

1000

0

0.5

1

1.5

22.5lp/mm

3

3.5

4

Figure 5.10: The plot shows a cut of the two-dimensional NPS of the Medipix1 detector at 45degrees to the axes. The line of average NPS demonstrates the very flat behaviour for reasonablyhigh spatial frequencies which shows that the detector noise is quantum limited.

From the data shown in figures 5.9 and 5.10 the DQE of this detector has been calculated, which can be seen in figure 5.11. The overall shape of the DQE curve is quitepromising, but the maximum value of only 10% is surprisingly low. One reason for thelow DQE is that the silicon sensor layer of the detector has a low integral absorptionprobability of only 23.8% for the X-ray spectrum used. Taking this absorption probability into account one can estimate the peak DQE to be approximately 42% for a perfectabsorption layer, which is still quite low.To clarify the reasons for this, some calculations using flat-field images with preciselyknown applied dose were carried out which show that only 19.4% of the incoming Xray quanta were detected. This discrepancy to the theoretical value of 23.8% can beattributed to a charge collection efficiency of less than 100% and the effect of charge sharingbetween neighbouring pixels, which can in conjunction with the threshold energy set to10 keV lead to a loss of photons. For details of the charge sharing effect see the nextchapter (5.1.6) and [CM01]. Since the X-ray fluence was sufficiently low, there should beno loss of photons due to the limitations of the count rate of the detector.Further investigations of the effects leading to the rather low DQE are still necessary.

5.1.6

Charge Sharing

The effect of charge sharing occurs in the sensor layer of the detector. Free carriers ina semiconductor move by drift and diffusion, where the drift is caused by electric fieldswhile the diffusion is driven by a slope in the carrier concentration and for high carrierconcentrations the Coulomb repulsion between them. While the drift is needed for thesignal generation at the contacts, the diffusion can decrease the spatial resolution andeven the overall sensitiveness of the detector: when a photon is absorbed near the borderbetween two pixels, the generated charge clouds move towards the contacts with their

35


measured data

10

DQE / %

7.5

5

2.5

00

0.5

1

1.5

2lp/mm

2.5

3

3.5

4

Figure 5.11: The DQE of one Medipix1 detector as calculated using the data from figures 5.9and 5.10.

drift velocity. At the same time the clouds spread perpendicular to the drift direction dueto diffusion. Since the sensor layer is not physically segmented and the pixels are onlydefined by the contacts it can happen that the charge generated by a single photon ispartially detected by both neighbouring pixels. Depending on the photon energy this canlead to three basic cases:1. The charge detected in one pixel is higher than the threshold and passes the discriminator, thus the photon is counted in this pixel. Meanwhile the charge detected inthe second pixel is too small to pass the discriminator and the photon is not countedin the second pixel.2. The charge detected in both pixels is too small to pass the discriminator, so thatthe photon is not counted at all.3. For high energy photons the amount of charge generated can be so large that itexceeds the threshold in both pixels, thus leading to a double count of this photon.This can only happen if the photon energy is higher than twice the threshold energy.Of these possibilities, the first one does not change the image noticeably. The secondone leads to a reduced sensitivity of the detector at the pixel edges: it can be eitherdescribed as a reduced pixel sensitivity or as a reduced active pixel area. But it can alsobe seen as an increase of the spatial resolution at the expense of sensitivity, especially if arather low-energy X-ray spectrum is used (e.g. for mammography). The third possibilityleads to a slight decrease of the spatial resolution or blurring of the image as the photonis detected in two adjacent pixels. This effect will be stronger if the fraction of photonswith at least twice the threshold energy gets larger, i.e. when the tube voltage is increasedwhile keeping the detection threshold at the same level. The reverse can be seen also:when the photon energy is kept constant the number of counts will depend on the energythreshold. As soon as the threshold is higher than the photon energy, the counts willdrop to zero (as it was already described in chapter 5.1.3). But when the threshold isbelow the photon energy one can see effects of charge sharing: the lower the threshold is

36


the more photons are counted due to double counts and due to the fact that a decreasingfraction of the generated carriers is sufficient for the photon to be counted. Additionallysome Compton-scattered photons might contribute. This is shown in figure 5.12, where athreshold scan using a 109 Cd11 source is plotted together with a theoretical curve.The same basic reasoning holds true when the photon hits the detector close to a pixelcorner, where the charge can be split between four pixels. Of course the photon energyneeds to be rather high for a triple or quadruple count.

meas. av. countsno charge sharing

35003000

av. counts

250020001500100050001.35

1.4

1.45

1.5

1.55 1.6Vthr

1.65

1.7

1.75

1.8

Figure 5.12: Counts vs. threshold voltage using a 109 Cd source. The slope of the measuredcurve (average counts/pixel) for voltages below 1.6 volts is at least partly due to charge sharingeffects. The dashed line shows what would be expected without charge sharing.

Lateral Charge DiffusionThe spread of the charge clouds can be estimated using some very simple formulas [SH85,HGMB04]. The diffusion length x perpendicular to the drift direction can be calculatedas:x = 2Dt(5.2)where D is the diffusion coefficient of the carriers and t is the respective drift time. Sincethe diffusion coefficient is proportional to the mobility of the carriers, whereas the drifttime is inversely proportional to it, the diffusion length can be expressed in terms of driftlength and electric field:rrrddkB T[m](5.3)x = 100 2= 23eEEwhere kB is the Boltzmann constant, T the temperature, e the elementary charge, d thedrift length in m, and E the electric field in units of V/cm. The scaling factor 100is due to the different length units of d and E. The resulting factor of 23 (for roomtemperature) does thus not depend on the material or carrier type (electrons or holes).A few calculations are shown in table 5.1. A drift length of 300 m corresponds to an11 Main

photon energies 22.1 keV and 25 keV.

37


absorption of the photon near the top of the sensor layer, whereas a drift length of 150 moccurs when the photon is absorbed about halfway between top and bottom contact.The bias voltages used for the measurements were in the range of 3560 V. One shoulddrift length

detector bias

lateral diffusion length

300 m

50 V

9.76 m

300 m

100 V

6.90 m

150 m

50 V

6.90 m

150 m

100 V

4.88 m

Table 5.1: Diffusion lengths for different setups: the drift length of 300 m is the worst casescenario, but even with only 150 m drift the diffusion length is considerable.

keep in mind, though, that also the initial size of the charge cloud can vary significantly(dependent on the primary X-ray photon energy and sensor material), mainly due to thegeneration of fluorescence photons [HGMB04].Since the diffusion length depends only on detector thickness and bias voltage, theeffects of charge sharing should decrease with increasing detector bias. This can be seenin figure 5.13, where the average counts per pixel vs. the detector bias are shown. Thedelivered X-ray dose is kept constant, but the counts/pixel decrease slightly instead ofstaying level. This is mainly due to the fact that less photons are counted twice inadjacent pixels. For smaller pixels the charge sharing effects increase (see chapter 5.2.5)because the ratio of diffusion length to pixel size gets larger.

12000

average counts / pixel

10000800060004000av. countsfit with lin. detrending

20000

10

20

304050detector bias / V

60

70

80

Figure 5.13: Average counts vs. bias voltage: due to the decreasing charge sharing for highervoltages, the number of double counts decreases.

The effects of charge sharing on the performance of the Medipix1 have been studiedin detail in [CM01].

38


5.2


5.2.1

Effects of the Detector Bias

The effects of the detector bias are basically the same as they are for the Medipix1 detector(cf. chapter 5.1.1), but because of the smaller pixel size it is better to apply a higher voltageto minimise the effect of charge sharing (see also chapter 5.2.5) between adjoining pixels.In the scope of this work there have been no further studies concerning the detector biasand the effects of a partially depleted sensor, but since the low-frequency patterns seenwith the Medipix1 detector in underdepletion were caused by the sensor layer, one canexpect to see the same effect with the Medipix2, too.

5.2.2

Threshold Tuning and Calibration

In contrast to the Medipix1 the Medipix2 detector has two discriminators and thereforetwo adjustable thresholds. These two thresholds allow for two different image acquisitionmodes: one using only the lower threshold (effectively just like the Medipix1) and oneusing both thresholds for energy windowing, i.e. only photons with an energy betweenboth thresholds are counted.Creating the threshold adjust mask works very similar to the method described forthe Medipix1 (cf. chapter 5.1.2) with two simplifications. Since the Medipix2 shows goodlinearity for the threshold adjustment settings, only the lowest and the highest setting forthe 3-bit adjust are measured using test pulses, all intermediate values are interpolated.In addition it is also possible to use the electronic noise of the preamplifier of the pixelinstead of an external pulser to test the threshold characteristics of each pixel, which isthe faster method to create a threshold mask. Detailed measurements which show thegood performance of the detector have been carried out by [LC03].The threshold calibration works exactly like it was described in chapter 5.1.3 for theMedipix1 detector. A sample threshold scan using the 109 Cd source is shown in figure 5.14.As already mentioned in the description of the Medipix2 detector in chapter 2.4, it hasbeen shown that the relation between the threshold voltage and the photon energy islinear (in contrast to the Medipix1) as can be seen exemplarily in figure 5.15.

5.2.3

Quantum Noise and Fixed-Pattern Correction

Just as described for the Medipix1 detector in chapter 5.1.4, the Medipix2 detector shows acertain residual fixed-pattern noise which cannot be corrected completely by simply usingthe built-in 3-bit threshold adjustment. But after correcting for this fixed-pattern noise12the histogram of a flat field image shows that the Medipix2 can also work very close to thequantum noise limit. Figure 5.16 demonstrates this effect, the respective histograms areshown in figure 5.17. Gaussian fits were applied to theraw data and the corrected data,giving a width of the corrected distribution of 1.04 N . The fixed-pattern correctionimage used here was calculated by averaging 58 flat-field images.13

5.2.4

MTF, NPS and DQE

The MTF of the Medipix2 was determined using the edge method (see figure 5.8) andalso by evaluating an image of a bar pattern phantom (Huttner grid) using the square12 As

it was described in chapter 5.1.4.images had in sum about 110000 counts per pixel.

13 These

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av. counts || diff. counts

1000

measured countsnum. derivative

100

10

1165

170

175

180

185

190

THLFigure 5.14: Threshold scan of a Medipix2 detector using the 109 Cd source (22.1 keV and25 keV). The abscissa shows the setting of the THL DAC which corresponds to a certain energythreshold. The numerical derivative shows the two lines of the source quite clearly (cf. figure 5.4).The energy calibration shown in figure 5.15 is taken from this measurement and another one usingan 241 Am (59.54 keV) source.

60

photon energy / keV

55504540353025200.02

measured pointslinear fit0.04

0.06

0.08

0.1

0.12

0.14

0.16

threshold setting / a.u.Figure 5.15: The relation between threshold voltage and photon energy for a Medipix2 detector,showing the linearity.

wave method.14 Figure 5.18 shows the measured data together with the sinc-function (cf.equation 3.2, page 11) calculated for pixel sizes of 55 m and 65 m, respectively. TheMTF of both the Medipix1 and Medipix2 detectors can be seen in figure 5.19 in directcomparison. Here it can be seen that in contrast to the Medipix1 the measured values forthe

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