EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN PH–EP/2004–05019 August 2004

Novel Geometrical Concept of a High Performance Brain PET Scanner -

Principle, Design and Performance Estimates

J. Seguinota,b, A. Braemb, E. Chesib, C. Joramb∗, S. Mathotb, P. Weilhammerb, M. Chamizo Llatasc,J.G. Correiad, M. Ribeiro da Silvae, F. Garibaldif , R. De Leog, E. Nappig, F. cOrsih, A. Dragoneh,F. Schoenahli and H. Zaidii

aCollege de France, Paris, France

bCERN, PH Department, Geneva, Switzerland

cUniversity of Geneva, Department of Corpuscular and Nuclear Physics, Geneva, Switzerland

dInstituto Tecnolgico e Nuclear, Sacavem, Portugal

eCentro di Fisica Nuclear da Universidade de Lisboa, Portugal

fInstituto Superiore di Sanita, Roma, Italy

gINFN, Sezione di Bari, Italy

hDEE, Politecnico di Bari, Bari, Italy

iDivision of Nuclear Medicine, Geneva University Hospital, Geneva, Switzerland

We present the principle, a possible implementation and performance estimates of a novel geometrical concept

for a high resolution positron emission tomograph. The concept, which can for example be implemented in a

brain PET device, promisses to lead to an essentially parallax free 3D image reconstruction with excellent spatial

resolution and constrast, uniform over the complete field of view. The key components are matrices of long axially

oriented scintillator crystals which are read out at both extremities by segmented Hybrid Photon Detectors. We

discuss the relevant design considerations for a 3D axial PET camera module, motivate parameter and material

choices, and estimate its performance in terms of spatial and energy resolution. We support these estimates by

Monte Carlo simulations and in some cases by first experimental results. From the performance of a camera

module, we extrapolate to the reconstruction resolution of a 3D axial PET scanner in a semi-analytical way and

compare it to an existing state-of-the art brain PET device. We finally describe a dedicated data acquisition

system, capable to fully exploit the advantages of the proposed concept. We conclude that the proposed 3D Axial

concept and the discussed implementation is a competitive approach for high resolution brain PET. Excellent

energy resolution and Compton enhanced sensitivity are expected to lead to high quality reconstruction and

reduced scanning times.

Keywords: Positron Emission Tomograph; PET; Hybrid Photon Detector; HPD; Scintillator.

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1. Introduction

We propose a novel geometrical concept2 of apositron emission tomograph (PET) which aimsat an optimized performance in terms of sensitiv-ity, spatial resolution and image constrast. Thegoal is to maximize the detection efficiency for an-nihilation photons and, at the same time, to pushthe spatial resolution towards the physical limitsinherent to the annihilation process. Those aredetermined by the positron range in the organictissue and the non-collinearity of the 511 keV an-nihilation photons. A further goal is to achievean optimized ratio of signal to noise, which finallytranslates into image contrast.

Our proposal is motivated by the demand of themedical imaging community, expecting compre-hensive and high quality information for a moreprecise and certain assessment of malign tumoursor major neurodegenerative diseases, combinedwith an improved comfort for the patient dur-ing the examination. This implies a significantshortening of the scanning time, or in some casesa reduced injected radiotracer dose.

PET is widely recognized as the best availablemolecular non-invasive diagnosis technique sensi-tive to tracer concentrations on the picomole level[1–5]. It provides access to metabolic and kineticparameters of a particular molecular process andhence not only allows the detection of major de-seases but also the follow-up of their treatment.

In recent years there has been significantprogress in PET instrumentation, data quan-tification and image reconstruction [6–8]. PETinstrumenation is benefitting of the ongoing de-velopment of new particle physics detector com-ponents like inorganic scintillators of high den-sity, atomic number and light yield as well asphotodetectors like MAPMT, APD and HPD3.A similar impact have come through advances inmicroelectronics, which led to highly integratedCMOS front-end circuits, fast data acquisitionprocessors and ultra rapid FPGAs (Field Pro-

∗Corresponding author, Christian.Joram@cern.ch2Patent application filed under PCT/EP02/07967, inter-national publication number WO 2004/008177 A1.3MAPMT = Multi Anode Photomultiplier Tube, APD =Avalanche Photodiode, HPD = Hybrid Photon Detector.

grammable Gate Arrays).

State of the art in PET instrumentationOne of the most recent and powerful PET

devices [9,11] is the so-called High ResolutionResearch Tomograph (ECAT-HRRT) [10,12,13],developed by CPS-Innovations4, which we con-sider as reference for the new generation of PETscanners. Its performance approaches the phys-ical limits which are intrinsic to a design con-cept based on the radial arrangement of scintilla-tors blocks, read out with PMTs. The centroidmethod (Anger logic) and the phoswich techniqueare used to reconstruct the interaction point ofthe annihilation photons in the crystal [14]. TheECAT-HRRT consists of octagonal arrangements(42.4 cm face-to-face) of phoswich scintillatorblock detectors, made of two layers of 64 smallLSO crystals (each 2.1 × 2.1 × 7.5 mm3) with 2different decay times (∆τ ≈ 7 ns). The total ac-tive length is therefore 15 mm. The crystals areoriented normal to the octagon sides, hence essen-tially pointing in radial direction. Each block isreadout by an arrangement of 4 standard PMTs(diameter 19.6 mm), which are optically coupledto the block by means of a light guide whichspreads the light from the individual crystals overall 4 PMTs. The centroid corresponds to the trueinteraction point of the annihilation photon, incase of conversion by photoelectric effect, or tothe energy averaged mean position of the interac-tion in case Compton scattering in the detectoris involved.

The phoswich technique is able to roughlyhalve the uncertainty of the depth of interaction(DOI) and hence significantly reduces the par-allax error. However, the phoswich approach isstill only a compromise between the maximumcrystal length, which can be tolerated for paral-lax error reasons, and the minimum length whichis required to achieve high detection efficiency.Moreover the phoswhich approach demands a del-icate pulse shape discrimination of the analoguesignal delivered by the PMTs in order to iden-tify the hit crystal layer. The readout electronicsbecomes unavoidably more complex and possibly

4CPS Innvoations, Knoxville, TN, USA

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limits the data acquisition rate.The centroid method is intrinsically precise,

but the granularity of the Anger logic readoutremains relatively poor. It is therefore impossi-ble to track annihilation photons which undergoone or two Compton scatterings in the same de-tector block. They can not be rejected as Comp-ton events if the total deposited energy falls in-side the energy acceptance window, and hence de-grade the spatial resolution. In the case of theHRRT, about 40% of all events fall in this cate-gory. A large fraction of these Compton eventscreate energy deposition in both phoswich layersand can in principle be rejected by a careful pulseshape and energy discrimination.

We conclude that a substantial improvementof the PET imaging technique requires a differentconcept which is able to increase at the same timesensitivity, spatial resolution and background dis-crimination. The ultimate performance requiresa thick and finely segmented array of high densityand high Z scintillating crystals, individually readout. Precise 3D reconstruction of the photon in-teractions in such a crystal matrix allows to trackannihilation photons which undergo photoelectricor Compton scattering. Compton events, if un-ambiguously reconstructed, are able to enhancethe sensitivity without degrading image qualityor contrast. Finally it is the patient who profitsfrom this in form of a lower injected radioactivedose or a reduced scanning time which not onlyimproves the patient’s comfort but also lowers therisk of patient movements during the scan.

Co-registration of the metabolic activity byPET with a precise imaging of the anatomicstructure using gamma or X-ray computed to-mography (CT) is a proven way of improvingthe diagnostic potential. This multimodality ap-proach allows, by means of image fusion, for anaccurate localisation of the detected radiotraceremission pattern. In addition the CT informationcan be used to correct for the gamma ray atten-uation in the tissue, an effect which still leads tofalse estimation of the source intensity and henceprevents a precise quantification of PET informa-tion.

Several developments projects in PET instru-mentation have been proposed or are currently

under design or test. To our knowledge, most ofthem rely on the classical radial scintillator ar-rangement.

In this article we describe in detail a conceptfor a brain PET scanner based on long scintillat-ing crystals which are axially oriented. This con-cept allows to achieve the maximum detection ef-ficiency and at the same time provides precise 3Dand parallax free reconstruction of photoelectricand Compton events over the full field of view(FOV). The spatial resolution in the transaxialplane does not depend on the source position andmatches the intrinsic physical limitations due tothe range of the positron in the organic tissue andthe non-collinearity of the 511 keV annihilationphoton pair.

The axial arrangement of the scintillating crys-tals is a natural and straightforward idea to sup-press the parallax error which is inherent to all ra-dial geometries. As we discovered only recently,essential parts of the concept described in thisarticle, were already proposed in 1988 [15], how-ever the proposal seemed pre-mature given thestate-of-the-art of scintillating crystals and pho-todetectors at that time. Matrices of BGO crys-tals (3 × 5 mm2) of 50 mm length were intendedto be read out on both ends by position sensi-tive PM tubes with crossed wire anodes. Such areadout does not permit to track photon interac-tions in the crystal matrix and therefore leads toreconstruction ambiguities for Compton interac-tions. In addition the modest light yield of BGOcrystals compromised the achievable reconstruc-tion resolution in the axial direction. The authorshave not pursued this development much further,which probably also explains why it is not men-tioned in recent review articles.

The paper is organized as follows: In Section 2we describe the geometrical concept of a 3D Ax-ial PET camera and its principle of operation.We discuss the key components, i.e. the longscintillators and the segmented Hybrid PhotonDetectors. Section 3 is devoted to performanceestimates in terms of spatial and energy resolu-tion, based on analytical and Monte Carlo calcu-lations. We also derive an estimate of the achiev-able image reconstruction resolution and compareit with the HRRT as an existing state-of-the-art

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device. It is followed by a detailed discussion ofthe achievable sensitivity and its enhancement byexploiting events which involve Compton scatter-ing in the crystal matrix (Section 4). In Section 5we define a specific factor of merit, allowing anoverall characterisation and benchmarking of theconcept and its implementation. We finally (Sec-tion 6) present a conceptual study of a dedicateddata acquisition system, which is able to exploitthe advantages of the 3D Axial concept and itssegmented photon detectors.

2. The 3D Axial geometry with HPD read-out – A novel concept

In the following we describe in detail the prin-ciple and a possible implementation of a 3D AxialPET concept using HPDs for the readout of thescintillation light. The basic features of the con-cept have already been described briefly in recentpublications [16–18].

2.1. Geometry and principle of operationWe propose detector modules which, for a brain

PET scanner (Fig.1), could be arranged in aring5 of 35 cm inner free diameter. The distancebetween opposite crystals is in this case about38 cm. A detector module (Fig. 2) consists ofan array of long (15 to 25 cm depending on thescintillating material) optically polished crystalsof small cross section (3.2×3.2 mm2), axially ori-ented and separated by 0.8 mm. Each array of16 × 13 crystal bars is optically coupled at bothends to proximity focused Hybrid Photon Detec-tors made with a thin sapphire entrance windowand a bi-alkali photocathode. The HPDs featurea Si sensor with a readout granularity of 4×4 mm2

to accurately match the matrix configuration.A large fraction of the scintillation light is

trapped in the crystal bar and propagates by totalinternal reflection to the opposite extremities. Inthe transaxial (x, y) plane the highly segmentedgeometry provides, from the readout of the crys-tal bar address, accurate x,y coordinates with anexcellent and uniform resolution (see Sect. 3), to-tally independent of the detector thickness. The

5a second concentric ring with larger diameter can beadded for full azimutal coverage.

line of record (LOR) reconstructed from a de-tected 511 keV annihilation photon pair is con-

Figure 1. Schematic representation of a PETscanner based on 3D axial detector modules.

Figure 2. Drawing of a 3D axial detector moduleconsisting of a matrix of 150 mm long crystals,read out by two HPDs.

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sequently free of the parallax error intrinsic tothe classic radial detector geometry. It resultsthat the detector thickness can be increased upto 3 attenuation lengths which roughly double thesensitivity to photoelectric interactions comparedto conventional detectors.

The fine segmentation in the transaxial planeallows the tracking of single or multiple Comp-ton scatterings in the matrix. Their reconstruc-tion, with a measurement of the total energy lostprovides, unambiguously, an enhancement of thedetection efficiency of 511 keV photons (Sect.4.1).

The measurement of the asymmetry of theamounts of light detected at the two crystal endsprovides, with good accuracy, the determinationof the axial coordinate z (see Sect. 3.1). The to-tal deposited photon energy can be derived withgood precision from the sum of the signals atthe two ends, as the light attenuation during thepropagation through the crystals can be correctedfor.

As the critical angle for reflection at the inter-face with the sapphire window is higher than themaximum incident angle for LSO or LaBr3 crys-tals, the number of photons transmitted onto thephotocathode is only determined by the fractionof light trapped inside the bar and its attenuationin the crystal bulk. Because of the good matchof the refractive indices at the wavelength of thescintillation light 6, the loss of photons by reflec-tivity at the interface crystal window is negligi-ble.

The robustness of sapphire permits the use ofa very thin (1.8 mm) window in order to limit thelight spreading on the adjacent readout channels.Figure 3 is an illustration of a detector module de-signed for the demonstration of the concept withtwo round 5-in. HPDs. The gap of 0.8 mm be-tween crystal bars is defined by means of nylonstrings stretched at both ends on accurate frameswithout screening between bars to absorb the re-fracted light coming out of the crystal at the scin-tillation emission point.

6nsapphire = 1.798 at 350 nm for LaBr3 (n = 1.88);

nsapphire = 1.780 at 420 nm for LSO (n = 1.82)

2.2. The scintillator matrix: Fast Ce dopedinorganic crystals

Table 1 summarizes the physical properties ofCerium doped inorganic fast scintillators alreadyavailable, or still under development, which canbe considered for an advanced PET system [19–29].

On the medium term, Cerium doped LutetiumOxiorthosilicate (LSO: Ce)7, Lutetium YttriumOxyorthosilicate (LYSO:Ce)8 and LanthanumBromide (LaBr3:Ce)9 are the most promisingcandidates. LSO and LYSO have the significantadvantage of a short attenuation length and ahigh photo fraction at 511 keV compared withLaBr3. They are not hygroscopic and can behandled without special precaution contrary toLaBr3. However the performance of LSO is muchworse than the one of LaBr3 in terms of lightyield, energy resolution and linearity of the re-sponse with energy. The peak wavelength of thescintillation light at 358 nm for the LaBr3, com-pared to 420 nm for LSO, leads to a higher de-tection efficiency due to the blue-enhanced sensi-tivity characteristics of standard (bi-alkali) pho-tocathodes (see Sect. 2.3.2).

The use of long crystal bar (15 to 25 cm) inone or two pieces optically coupled, imposes more

7CTI PET system (Knoxville, TN, USA)8Photonic Material (Scotland)9Saint Gobain – Bicron (France)

Figure 3. Prototype of a 3D Axial detector mod-ule for proof of principle measurements. The scin-tillator matrix is composed of already availableYAP crystals of dimensions 3.2× 3.2× 100 mm3.

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Table 1Properties of scintillation crystals used for PET.

Scintillator BGO1) LSO2) LYSO3) GSO4) LuAP5) LaBr6) YAP7)

Density (g/cc) 7.1 7.4 7.1 6.7 8.3 5.3 5.4Light yield (photons/keV) 9 27 32 8 10 61 21

Effective Z 75 66 64∗) 60 65 46.9 31.4Principal decay time (ns) 300 42 48 30-60 18 35 25Peak wavelength (nm) 480 420 420 440 365 358 370Index of refraction 2.15 1.82 ≈ 1.8 1.95 1.95 1.88 1.94Photofraction at 511 keV(%) 41.5 32.5 34.4∗∗) 25 30.6 15 4.5Attenuation length at 511 keV(cm) 1.04 1.15 1.12 1.42 1.05 2.13 2.19Energy resolution∗∗∗) at 662 keV (%) 7.9 8 7.1 6.9 10 2.9 3.8Hygroscopic No No No No No Yes No1)Bi4Ge3O12;

2)Lu2SiO5:Ce; 3)LuYSiO5:Ce; 4)Gd2SiO5:Ce; 5)LuAlO3:Ce; 6)LaBr3:Ce; 7)YAlO3:Ce∗)Calculated; ∗∗)Result of simulation with Geant4; ∗∗∗) ∆E/E FWHM.

constraints for the fabrication (growing, cuttingand polishing) and for the mechanical (robust-ness) and the optical (surface quality) properties.The production of crystals of this length is tech-nically feasible, however it may have an impacton the cost.

The adjustment and the calibration of the lightattenuation in the crystal bars is a key parametersince they determine the reconstruction accuracyof the axial coordinate and the energy resolution.These aspects are discussed in sect. 3 and 4 forLSO and LaBr3 crystals.

Studies with LYSO samples have revealedpromising characteristics. They show an energyresolution comparable to LSO, but, in contrastto LSO, the response scales linearly with energy.Producers claim that a photon yield of 35 · 103

photons/MeV is attainable (LYSO with 31 · 103

photons/MeV is already available from St. Gob-ain). If these performances are confirmed in fu-ture, LYSO would be a very good candidate.

Ce doped LuAP [30] crystals can presently notbe used because of their low light yield (about104 ph/MeV) despite very good physical prop-erties especially their short decay time (18 ns)compared to LSO (42 ns). However new develop-ments have proven that a photon yield of 20 · 103

ph/MeV is possible, opening interesting perspec-tive on a longer time scale.

2.3. The PET HPD - a Hybrid PhotonDetector with enclosed VLSI readoutelectronics

HPDs [31–33] are unique photon detectors formedical imaging applications compared to stan-dards PMTs, MAPMTs and commercially avail-able APDs. An HPD consists of a vacuum en-velope with a transparent entrance window onwhich a semitransparent photocathode is evap-orated. A photoelectron, ejected from the photo-cathode (on potential UC), is accelerated towardsthe segmented silicon anode (ground potential),in which, on impact, a large number of electron-hole pairs and hence a detectable signal is pro-duced. The gain of the HPD is M ≡ Ne−h ≈e · Uc/WSi with WSi = 3.6 eV being the energyneeded to create an electron hole pair in silicon.

HPDs combine the sensitivity to single pho-tons, known from standard vacuum phototubes,with the exceptional spatial and energy resolutionand the great design flexibility (size and geome-try) of silicon sensors. Photon detectors of largesensitive area with a high readout granularity canbe fabricated. The multiplexed VLSI front-endreadout electronic is encapsulated in the detec-tor body. This minimizes the effective capac-itance to a few pF per channel and hence im-proves the signal characteristics (bandwidth andnoise). The number of connecting lines (vacuumfeedthroughs) required for the data acquisition isreduced by about a factor of 5 with respect to the

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number of channels.APDs [34,35] are the most promising competi-

tors to be compared with HPDs. Commerciallyavailable APDs are mostly mono channel photondetector of about 20 mm2 acceptance. They areinsensitive to axial and transversal strong mag-netic fields. Proximity focused HPDs can be op-erated in strong magnetic fields, as long as thefield direction is aligned with the tube axis. Ax-ial magnetic fields have even the beneficial effectof reducing the so-called point spread function,which is a consequence of the angular and en-ergy distribution of the photoelectrons at emis-sion from the photocathode, and therefore leadto an improved spatical resolution.

APD arrays [36–39] of 32 channels (typically2 × 2 mm2/channel) have been developed. Theirgranularity, as for MAPMTs, is usually fixed bythe market. The configuration of the scintillatormatrix has to be adapted to the available read-out granularity, while HPDs can be designed andbuilt to match a crystal array with optimized ge-ometry.

The sensitivity of HPDs is determined by thequantum efficiency of the semi transparent bi-alkali photocathode which, at 400 nm, is about30 to 50% lower than the quantum efficiency ofreverse [40] and high capacitance APDs10, respec-tively.

HPDs operated at a moderate accelerationvoltage of UC = 12 kV have a gain of M ≈3 · 103, well adapted to the performances of mod-ern front-end electronics with an Equivalent NoiseCharge (NEC) of < 2 ·103 electrons. If required,they can be operated up to 20 kV increasing thegain to 5.5·103 without lack of performances. Thegain is achieved in a single stage dissipative pro-cess and is therefore practically free of avalancherelated excess fluctuation. Consequently, the Ex-cess Noise Factor ENF , which enters in the en-ergy resolution of the detection system (see Sec-tion 3.2) is only 1.09 compared to 1.4 ± 0.05 forPMTs. The small excess noise of an HPD iscaused by those ≈20% of photoelectrons whichare back scattered from the silicon sensor and de-posit only partially their kinetic energy.

10cf. data sheets of Hamamatsu APDs

Intrinsic to their principle of operation, thelinearity of the response with the incident light(or energy deposition in the crystal) is excellent.Gain and signal characteristics are unaffected byvariations of the detector temperature.

In principle, APD can achieve gains up to 103,but, in practice, their use is limited to gains of few102 for an acceptable stability (1/M × dM/dV =3.1%/V ) with the operating voltage V . Moreovertheir ENF increases linearly with the gain [41]and usually varies from ENF = 2 or 3 for M = 50to ENF = 9 for M = 103. Therefore, even witha gain of 50, the energy resolution with an APDis 50 to 70% worse compared to a HPD operatedat gains of 3 to 5 × 103.

The temperature dependence (1/M × dM/dT )of APDs is about -2%/K requiring cooling, andtheir dark current at room temperature is of theorder of few nA for M = 50, instead of few tensof pA/pad for HPDs independently of the gain.

The use of APDs at low gain finally requiresvery low noise front-end electronics; a challengingdevelopment if fast response is required with straycapacitances in the 100 pF range.

A last and important advantage of HPDs is thepossibility of reading out the induced signal onthe non-segmented Si sensor back plane (the sideon which the accelerated photoelectrons hit thesensor) providing a fast measurement of the totalenergy deposited in the full Si sensor, i.e. in thetotal crystal matrix coupled to the HPD. Thisunique feature of the HPDs allows for a simpleand fast gamma energy discrimination - withoutneed to readout the individual detector channels.The back plane information can be used to dis-criminate annihilation photons which underwentCompton scattering in the organic tissue of thebody or in the crystal matrix with incompleteenergy deposition. Moreover, the fast back planesignals can be used to find coincident detectormodules with a time resolution of potentially 5 ns(see Section 6).

We believe that HPDs are at the moment thebest performing and flexible position sensitivephoton detectors for our PET concept.

A dedicated plant has been designed and builtat CERN to produce HPDs up to 10 in diame-ter, as well as all the various technologies needed

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to prepare the components [42–45]. The proto-type of a proximity focused HPD for PET ap-plications which we describe below has entirelybeen designed, developed and fabricated in thisframework.

2.3.1. Design of the PET-HPDThe prototype proximity focused HPD devel-

oped at CERN is a round photodetector with a bi-alkali photocathode deposited on a thin (1.8 mm)flat sapphire entrance window of 105 mm diame-ter (see drawing and photograph in Figs. 4 and5). The total length of the HPD is 67 mm. Across section of the HPD is shown in Fig. 6 withthe electron optical configuration simulated usingthe SIMION11 code). The window is sealed to a

Figure 4. Cross-section of the proximity focusedprototype HPD.

metallic ring made of niobium which assures theconnection for the photocathode polarization. Aset of two electrodes in niobium (0.7 mm thick)inserted in between cylindrical alumina spacers(ceramic) guarantee a precise 1:1 electron opti-cal image transfer (i.e. proximity focusing) from

11SIMION 3D, Scientific Instruments Services Inc., Rin-goes, NJ 08551, USA

the photocathode onto the silicon sensor. At thebase of the body a skirt in kovar is welded to astainless steel flange equipped with a gold platedsharp edge knife. The ceramic rings, the sapphirewindow and the metallic components in niobiumand kovar are joint by means of active high tem-perature vacuum brazing. Details on the tubemanufacturing and the indium sealing technol-ogy which is used to seal the tube in-situ afterphotocathode processing are given in [43].

The ceramic hybrid carrier which supportsthe sensor and the readout VATA chips is wirebonded to 40 vacuum feedtroughs of the baseplate to provide the control and data lines con-nections to the data acquisition system.

The sensor consists of a 300 microns thick rect-angular silicon plate with 16 x 13 pads imple-mented as p+n junctions, DC coupled to the frontend electronic. The 208 pads of 3.96× 3.96 mm2

with a gap of 80 microns match precisely the crys-tal matrix configuration. The pad size is largerthan the crystal bar cross section (3.2×3.2 mm2)

Figure 5. Photograph of a proximity focused pro-totype HPD with round silicon sensor and inte-grated front-end electronics.

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to cope with the light spread on the photocath-ode due to the non-zero thickness of the HPDentrance window. This reduces the optical signalsharing with adjacent channels (see sect. 3.1.).

2.3.2. Performance of the prototype HPDThe proximity focused prototype HPD shown

in Fig. 5 has been fabricated with the goal tostudy its electron optical and electrical proper-ties, but also to validate the complete fabrica-tion procedure. The HPD is equipped with around 50 mm diameter Si sensor of 2048 pads of1× 1 mm2 connected to 16 standard readout VAprime chips. This high granularity Si sensor al-lows to map out with high precision the electronoptical properties. Fig. 7 shows the quantumefficiency of the photocathode of this first prox-imity focused prototype HPD. Once the cath-ode processing parameters are optimized, we ex-pect a 10-15% higher sensitivity, similar to otherHPDs, which we have fabricated. The windowwas scanned along diameters with a fine light spot(≈0.5 mm RMS) generated by a self triggered H2

Figure 6. Cross-section of the proximity fo-cused HPD as used in SIMION simulations. Left:Equipotentials and individual electron trajecto-ries. Right: Bundle of electron trajectories froma point source allowing to determine the pointspread function.

Figure 7. Measured quantum efficiency of the firstprototype HPD.

flash lamp. The resulting correlation between theradial position of the light spot and the centre ofgravity of the charge distribution measured withthe Si sensor exhibits, as shown in Fig. 8, a per-fect 1:1 linear imaging within 1% deviation. Thepoint spread function which describes the chargedistribution for a point source is of the order of0.3 mm (RMS). Fig. 11 shows for a fixed spot po-sition the variation of the total charge measuredin the image spot with the acceleration voltage.Above 10 kV, the variation is strictly linear. Be-low this value, i.e. at photoelectron energies be-low 10 keV, the energy loss in the dead n+ layerimplanted on the entrance bias side of the waferincreases and favours a minimum operating volt-age of 12 kV.

2.4. The VLSI auto-triggering front-endelectronic: the VATA–GP5

The Front end electronic is an important com-ponent of the PET concept designed to cope withhigh counting rates (up to 2 Mhz per module of208 channels) and to be operated in a self trig-gering mode with a sparse readout of the data inorder to optimize the data taking rate.

The VATA-GP5 chip is an optimized ASIC ver-sion of the existing VATA–GP3 and was devel-

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Figure 8. Measured relation between the photoncoordinate at the photocathode and the photo-electron hit on the silicon sensor.

oped for the PAD HPD by IDEAS12 in collabo-ration with CERN. For cost reasons the first pro-totype version was produced in 0.6 micron CMOStechnology in order to validate the PET concept.In the future the chip should be implemented indeep submicron technology to increase the band-width and thus lead to optimal performance interms of response speed, as require by a full PETsystem.

The VATA chips comprise 128 channels and isequiped with three readout modes: serial, sparseand sparse with adjacent channels.

Fig. 10 shows a block diagram of the VATA–GP5. The charge amplifier is optimized for a totaldetector capacitance of 5 to 7 pF and an inputdynamic range of 1.2 pC for positive polarity.

12Ideas ASA, Norway

Figure 9. Pulse height (a.u.) versus cathode volt-age (kV).

The analogue chain is a classical arrangement,where a Sample and Hold (S/H) signal is appliedat the peaking time (150 ns) of the ’slow’ shaperwhen a coincidence between a pair of modules isdetected by an external logic (see Sect. 6). Thehold signal stores the amplitude proportional tothe input charge, to be later readout. The ex-cellent linearity of the amplifier/shaper circuitis demonstrated in Fig. 11, where signals in therange from 0.06 to 1.25 pC were injected. Above1 pC saturation effects become noticable, whichare however due to the limited dynamic range ofthe ADC. The signal from the ’fast’ shaper, of 40ns peaking time, goes to a discriminator. A com-mon threshold is applied to all channels. Indi-vidual channels can be trimmed by 4 bit DACs.Fig. 12 shows for two gain settings the excellentlinearity of the discriminator in the range 0 to120 fC. A timewalk compensation circuit is imple-mented at the input of each discriminator to sup-press timewalk due to different signal amplitudes.The effect of the time walk compensation is shownin Fig. 13. Signals in the range from 60 to 160 fCare compensated within ±5 ns. The outputs ofall the 128 discriminators are then ORed togetherproviding a Fast Or signal (FOR) able to detectcoincidences with an expected timing resolutionof less than 10 ns. The VATA chip provides in

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Figure 10. Schematic and simplified block dia-gram of the VATA-GP5 circuit.

addition a FOR signal with an amplitude pro-portional to the multiplicity of hit channels.

When a discriminator output is activated, thecorresponding address of the channel is stored ina register. In sparse readout mode, if a FOR isdetected, a veto signal blocks the generation offurther ORs and only the analogue values of thehits channels with their address will be readout.

In normal PET operation the coincidence be-tween two annihilation photons is established ex-ternally (see section 7) on the basis of the siliconbackplane signals. On the contrary, if no coin-cidence is found, a reset signal is applied to theregister in a minimum time delay (< 12 ns) inorder to reduce the probability of having acci-dentals recorded when applying the common S/Hsignal. In addition, each discriminator output canbe masked in case of malfunctioning of a channel.

The data acquisition speed is determined bythe readout clock frequency which is currentlylimited to 20 MHz. The readout time is propor-tional to the number of hit channels plus threeclocks per chip which are needed before to reachthe first stored data.

If the sparse readout mode is an essential fea-

Figure 11. Response of the VATA-GP5 ampli-fier/shaper circuit to injected input charges from0.06 to 1.25 pC .

ture to maximize the data acquisition rate, the se-rial readout is needed to test the correct function-ing of all the channels by injecting a calibratedpulse into each input, and register the pedestalsfor subtraction.

The lowest threshold of the fast discriminatorranges from 4 to 6 fC including the thresholdspread after tuning with the channel trim DAC. Itcorresponds to about 5 sigmas of the shaper noise.With an HPD operated at 12 kV (M = 3 · 103)a threshold setting of 5 fC would select annihila-tion photons (or recoil electrons) of energy higherthan 10 to 12 keV for a scintillator matrix withLSO crystals. For LaBr3 scintillators, the samethreshold would provide a factor of about 1/3 onthe minimum energy.

The equivalent noise charge (ENC) of the slowshaper is of about 2 · 103 electrons, a negligiblecontribution to the energy resolution (< 0.1%) at511 keV.

2.5. Configuration of a PET scannerFig. 14 shows a possible arrangement of 12

modules in a ring of 350 mm free inner diame-ter with rectangular HPDs. Those could be fab-ricated with a moderate upgrade of the toolingand production facilities. A full azimuthal cov-

12

Figure 12. Characterization of the VATA-GP5fast discriminator circuit with injected inputcharges from 0 to 120 fC.

erage would require a second concentric ring atlarger radius.

3. Spatial reconstruction and energy de-termination

In the following we discuss the spatial and en-ergy resolution which can be achieved with theaxial concept. We also perform a direct compar-ison of certain characteristics between the axialand a conventional radial geometry.

3.1. Number of detected photoelectronsThe number of scintillations photons Nph gen-

erated by a 511 keV photon is 13.8 · 103 and31.2 · 103 in LSO and LaBr3, respectively. Ig-noring initially the light absorption in the crystalbulk, the total light trapping and transport effi-ciency εTT has been determined by means of a mi-croscopic photon transport Monte Carlo code (seebelow). As the light propagates by total internalreflections, almost perfect reflectivity (99.9% ateach bounce) has been assumed. For square crys-tals of 3.2 × 3.2 mm2, εTT has been found to be0.614 (LSO) and 0.60 (LaBr3). The small differ-ence is due to the small difference in refractiveindex of the two materials.

Figure 13. Characterization of the VATA-GP5time walk compensation in the input charge range10 to 160 fC.

Figure 14. Possible arrangement of 3D Axialmodules to a ring scanner.

13

With εQ being the quantum efficiency of thebialkali photocathode at the wavelength of thescintillation peak emission (εQ = 0.18 for LSOand 0.25 for LaBr3), the total number of photonsdetected (≡ Np.e.) at the two ends of the crystalis

Np.e.(z) = N1(z)+N2(z) =No

2·[e−z/λ+e−(LC−z)/λ](1)

with

N0 = Nph · εQ · εTT =

1525± 39 (LSO)4681± 68 (LaBr3)

(2)

and z being the axial coordinate of the interactionof the annihilation photon, with origin at one endof the crystal bar of length LC .

The effective light absorption lenght λ is dif-ferent from the bulk absorption length λb as itaccounts for the real path length of the photons,which is increased due to the multiple bounces:λ = k · λb. The geometrical parameter k =z/〈path length〉 depends on the refractive indexof the scintillator and has been determined forLSO and LaBr3 in the M.C. code as ≈ 0.7.

The spatial distribution of the photoelectronsover the segmented silicon sensor is shown in Fig.15. About 70% of the photoelectrons of a hitcrystal bar are detected by the associated sensorpad, while the rest is spread over the closest ad-jacent pads in a well defined pattern. Expressedin terms of energy, a 511 keV photon will depositon an adjacent pad not more than the equivalentof about 30 keV.

3.2. Energy resolutionThe energy resolution R = ∆E

E (FWHM), withwhich the photon energy can be measured, is thequadratic convolution of three contributions:

R = Rsci ⊕ Rstat ⊕ Rnoise (3)

The intrinsic resolution of the scintillator Rsci dueto material inhomogenities, impurities etc. wasderived from ref. [22] by deconvoluting the statis-tical fluctuation term as Rsci = 6.2% and 1.2% forLSO and LaBr3, respectively (see table 1). Rstat

accounts for the statistical fluctuation involved inthe light generation, transport and detection pro-

Figure 15. Simulated distribution of the hit mapon the silicon sensor for the readout of a scintil-lator crystal centred over the cental Si pad.

cess

Rstat(FWHM) = 2.35

√

1.09

Np.e.(4)

and includes the Excess Noise Factor of the HPDENF = 1.09.

The contribution due to noise in the electronicdetection chain including the photodetector (am-plifier, shaper, ADC, ...) is negligible for HPDs.With an Equivalent Noise Charge (ENC) of about103 e−, the noise term becomes

Rnoise(FWHM) =2.35 · 103

Np.e. · M≈ 10−3 (5)

where M ≈ 103 is the gain of the HPD at UC =12 kV.

The full energy resolution (acc. to eqn.3) atE = 511 keV is therefore 9% and 3.2% (FWHM)for LSO and LaBr3, respectively.

3.3. Reconstruction of the interactionpoint of the annihilation photon

The coordinates of the photon interaction pointin the transaxial (x, y) plane are derived from the

14

address of the hit crystal bars forming the scin-tillator matrix. The resolution σx (σy) is deter-mined by the cross section of the bar

σx = σy =s√12

(6)

where s = 3.2 mm is the width of the squarecrystals. The x and y coordinates of the photoninteraction points can thus be localized with aprecision of 2.2 mm (FWHM). Consequently thespatial resolution of the reconstructed positronannihilation point is in first order given by

σrec.x = σrec.

y =s√24

≈ s

2(FWHM) (7)

This approximation is strictly valid for a sourcecentred in the transverse field of view, indepen-dent of the axial coordinate.

The axial coordinate z of the photon interac-tion is derived from the measurement of the num-ber of photoelectrons (N1, N2), detected at thetwo ends of the crystal bars.

z =1

2[λ · ln(

N1

N2) + LC ] (8)

Error propagation w.r.t. the fluctuations of N1

and N2 (ignoring again the very small influence ofelectronics noise) leads to the measurement pre-cision13

σz =λ√2N0

[ez/λ + e(Lc−z)/λ]1

2 (9)

and σrecz ≈ σz/

√2.

3.4. Monte Carlo simulations of the lighttransport

The above mentioned Monte Carlo code allowsto track scintillation photons individually fromcreation to detection. The code takes into ac-count refraction and reflection at all optical in-terfaces (crystal/air, crystal/photodetector win-dow), reflection and absorption losses as well asphotodetector characteristics like quantum effi-ciency, point spread function and segmentation.

13eq. 9 ignores the contribution of pathlength fluctuations.Those are however accounted for by the M.C. calculationsdescribed in the next section.

The code allows to assess spatial and energy res-olution and their variation with material and ge-ometrical parameters and also provides an inde-pendent cross-check of the above derived analyt-ical expressions.

3.4.1. The influence of the bulk absorptionlength λb

The axial geometry with long scintillator crys-tals requires to choose the crystal bulk absorptionlength λb in relation to the length of the crystalLC , in order to define an optimal compromise be-tween achievable energy and z-resolution.

Figure 16. Variation of the number of detectedphotons with the bulk absorption length of thescintillator crystal.

Figures 16, 17 and 18 show simulation resultsfor LSO (LC = 150 mm) and LaBr3 crystals(LC = 150 and 250 mm), with λb as free pa-rameter. For every configuration light emissionat zem = 10 mm and zem = Lc/2 has been sim-ulated, while xem and yem were varied uniformly0 ≤ x, y ≤ 3.2 mm. As good compromise ap-pear 150 mm long crystals (LSO or LaBr3) withλb ≈ 100 mm. For 250 mm long LaBr3 crystalsλb values around 140 mm give the best overall re-sults. The lower light yield of LSO would lead topoor resolutions for 250 mm long crystals. Thisconfiguration was therefore discarded.

15

Figure 17. Dependence of the statistical term ofthe energy resolution (Eγ = 511 keV) on the bulkabsorption length of the scintillator crystal.

With these λb parameters the achievable energyand spatial resolution has been investigated asfunction of the axial emission point zem.

Fig. 19 shows the number of photoelectrons,detected by the two HPDs as a function of theemission point z. For comparison the results ofthe analytical calculation (dashed lines, acc. toequation 1) are shown together with the M.C.data, revealing a small but systematic discrep-ancy. The analytical calculations are made witha constant value of εTT , while in reality εTT de-pends slightly on the emission position. This is apure geometrical effect and is due to the increas-ing fraction of scintillation photons which can di-rectly hit the photodetector without prior reflec-tion from the crystal side faces. The maximumdifference is about 5%. The number of detectedphotons and the z coordinate depend strongly onthe effectice light absorption length λ (see equa-tions 1 and 8). For an accurate reconstruction ofthe energy and interaction point of the annihila-tion photon, the effective light absorption lengthλ of all crystal bars needs to be determined ex-perimentally, in order to cope with productionrelated variations. In the annex we describe asimple procedure to measure λ with a precisionon the percent level. The statistical term of theenergy resolution (σEstat/E) and the spatial ax-

Figure 18. Dependence of the expected axial (z)resolution for single photons (Eγ = 511 keV) onthe bulk absorption length of the scintillator crys-tal.

ial resolution σz are plotted in Figs. 20 and 21,again as function of the emission point z. Forthe LaBr3 crystals the simulations predict excel-lent values in both respects. An energy resolu-tion acc. to eq. 3 of about 6-6.5% (FWHM)seems to be achievable. The axial spatial resolu-tion σz is of the order 2 mm (150 mm) and 3 mm(250 mm long crystals), predicting an axial res-olution of the positron annihilation point of 3.3and 5 mm (FWHM), respectively. The statisticalterm of the LSO energy resolution is somewhatworse, however still matches the intrinsic resolu-tion. The axial spatial resolution is also inferiorcompared to LaBr3.

3.5. Spatial reconstruction resolution –Comparison with a conventional radialPET geometry

Basic M.C simulations have been performedto assess the achievable reconstruction resolution.We compare the spatial (volumetric) reconstruc-tion resolution of the proposed axial concept withpublished HRRT data and simulation results ofa classic (HRRT-like) radial scintillator arrange-ment.

For a simple and clear interpretation of theresults, the simulations only consider photoelec-

16

Figure 19. Variation of the detected number ofphotoelectrons (Eγ = 511 keV) with the detec-tion point along the crystal z-axis. Note that inFigs. 19 to 21 the distance is measured from thecrystal centre and not from the crystal end.

tric interactions of 511 keV photons disregardingCompton scatterings in the organic tissue and inthe scintillator matrices. The contribution of thescatter events to the HRRT performance is diffi-cult to be interpreted because of the lack of de-tailed information on the data processing fromthe readout of the phoswich layers. However, asit will be shown, even in these conditions, thecomparison between the simulations and the pub-lished HRRT experimental data allows a good un-derstanding of the responses.

The M.C. code starts off with a pattern of small1 × 1 × 1 mm3, i.e. quasi point–like, positronsources. The range of the positrons in the or-ganic tissue (a Gaussian distribution of 0.5 mm(FWHM) for the 18F radiotracer) and the non-collinearity of the 511 keV annihilation photons(180 ± 0.25) are accounted for. Both the pathof the positron and the emission direction of theannihilation photons follow an isotropic distribu-tion. A scanner based on the axial geometry witha free inner diameter of 320 mm was simulated us-ing crystals of 3.2 × 3.2mm2 width and 150 mm(LSO) and 250 mm (LaBr3) length. For the z-resolution the crystals were assumed to have a

Figure 20. Dependence of the single gammaenergy resolution (only statistic term, Eγ =511 keV) on the z-coordinate.

Figure 21. Dependence of the axial spatial res-olution (single photons, Eγ = 511 keV) on thez-coordinate. The dashed lines correspond to theanalytical formula (eq. 9 multiplied by an empir-ical factor 1.13. The correction factor is requiredto account for the pathlength fluctuations whichare not included in the analytical expression.

bulk light attenuation length of 100 mm and 140mm, respectively.

17

The scanner based on a radial geometry con-sists of a circular (Øint. = 46.8 cm) arrangementof LSO crystals of 2.1 × 2.1 × 30 mm3 size. Thisgeometry differs of the octagonal shape of theHRRT but should not alter too much the inter-pretation of the results. The photon conversionpoint in a hit crystal is assumed at half the crystallength.

The trajectories of the annihilation photons areextrapolated from the source to the sensitive vol-ume. The detection points are determined ac-cording to the attenuation length and the seg-mentation of the sensitive volume. The line ofrecord (LoR) is then drawn between the two de-tection points.

To avoid the complication of a real tomographicreconstruction, the resolution is obtained by cal-culating analytically the shortest distance be-tween the line of record and the original positronemission point. The projections of this distancein the x–y (transaxial) and z (axial) direction areaccumulated in histograms and fitted by Gaussiancurves. Their width corresponds to the resolutionsearched for.

An empirical multiplication factor of 1.25 [48]is applied to the results in the transaxial plane toaccount for the additional uncertainty which thetomographic reconstruction procedure would in-troduce. As the proposed axial geometry uses in-dividual crystal readout, a block decoding scheme(Anger logic), which would lead to further reso-lution degradation (≈ 2.2mm (FWHM) added inquadrature [48]), is not necessary.

Small sources of 1 × 1 × 1 mm3 were sim-ulated at coordinates equidistantly distributed(xi, yi = 0, 2, 4, 6, 8, 10 cm) over the transverseFOV. Figures 22 and 23 show examples of theoriginal and reconstructed distributions in thetransaxial plane for z=0.

Figures 25 and 26 show the results of the sim-ulations with the published data of the HRRT[12,13], see also Table 2. The resolutions are de-rived from Gaussian fits to the distributions ofthe x-y - in the transaxial plane – and z projec-tions of the shortest calculated distance betweenthe reconstructed LOR and the true positron an-nihilation point.

For illustration purposes the same source con-

Figure 22. Distribution of the pointlike sources(1 × 1 × 1 mm3) in the transaxial (x–y) plane atz=0.

figuration has been simulated and reconstructedfor a HRRT-like radial geometry with crystals of30 mm length (see Fig. 24). At 10 cm from thecentre of the FOV, and without DOI measure-ment (Phoswich technique not employed), theparallax error in the transaxial plane is sizableand gives rise to a clear astigmatism.

The comparison of the HRRT experimental res-olutions with the simulations is more difficult toanalyze in absence of detailed informations onthe data processing. In the transaxial plane, atcentre of the FOV there is a difference of about35% between the data and the simulations whichcan be explained by the contribution of Comp-ton interactions in the scintillator blocks. At10 cm off centre, the agreement is good becausethe dominant contribution to the resolution isthe parallax error well accounted by the simu-lation. For the axial z coordinate, the conclusionof the comparison is inverted. At centre of theFOV the agreement is good within the errors. At

18

Table 2Comparison of reconstruction resolution (FWHM values): HRRT data vs. HPD–PET simulation. In thesimulations a crystal length of 150 mm was assumed. All values correspond to the central plane (z=0).

Transaxial resolution Axial resolution Mean volumetric reso-lution

Rx(= Ry) (mm) Rz (mm) RV = Rx × Ry × Rz

(mm3)x=0;y=0

x=100;y=0

x=0;y=0

x=100;y=0

HRRT data, span 9 2.35 2.75 2.5 3.6 20HRRT data, span 3 2.35 2.75 2.5 2.8 18HPD-PET LSO 1.85 2.35 5.78 6.33 26HPD-PET LaBr3 1.59 2.13 3.43 3.57 11.8

10 cm off centre the deviation strongly dependson the esoteric axial data compression, character-ized by span and ring difference which determinethe maximum angular acceptance.

As the Compton events are clearly recon-structed with the axial PET concept, one mustcompare the M.C simulations with the experi-mental data of the HRRT. At centre of the FOV(x = 0), the resolution has the expected value,independently of the crystal choice, but degradesby about 40% at x = 10 cm because of the asym-metry of the LOR with respect of the emissionpoint. As previously stressed, the high photonyield of LaBr3 crystals significantly improves theaxial resolution.

With 15 cm long LaBr3 crystals a mean vol-umetric reconstruction resolution of 11.8 mm3

is attainable, hence about 40% better than theHRRT measured one. For 15 cm long LSO crys-tals the expected resolution is about 14% worsethan the HRRT results. This last performancewould obviously improve by a factor 0.86 if LSOwould be replaced by LYSO crystals with a pho-ton yield of 35 ph/keV in addition by a factor0.85 by increasing the photocathode quantum ef-ficiency from 18 to 25%.

4. Detection efficiency for true PET events

In this paragraph we discuss, from a physicspoint of view, the detection efficiency of True (T)events for photon incidence normal to the scintil-lator array. The values thus obtained are char-

acteristic of the matrix configuration and of thescintillating material, independently of the scan-ner geometry.

A True event is defined as the detection of twoannihilation quanta of 511 keV energy emitted inopposite directions and which undergo either aphotoelectric conversion or a Compton scatteringin the matrix of scintillators which, unambigu-ously, can be reconstructed.

The results which are given in table 3 are de-rived from analytic calculations and suffer of in-evitable approximations. Their validity, however,was tested for a matrix of LSO crystals with aM.C simulation using GEANT 4 code. Agree-ment was found within about +-10% error. Thedetection efficiencies are rather underestimated,but allow a coherent comparison of the expectedperformances with those of the HRRT-PET scan-ner.

The values of photon cross-sections, attenua-tion and absorption lengths for 511 keV photonsare listed in table 1, and were derived by inter-polation from the Hubbel tables of the NationalBureau of Standards.

4.1. Compton scattering : Reconstructionand limitations

In order to unambiguously distinguish the co-ordinates of the primary Compton interaction ofthose of the secondary interactions (photoelec-tric conversion or Compton scattering) the recon-struction program restricted to events in whichthe photon of the primary Compton scattering is

19

Figure 23. Reconstruction of the source distribu-tion in the transaxial (x–y) plane at z=0.

emitted in the forward direction.We have used as selection criteria, the Klein-

Nishima formulation which describes the kine-matics and the cross section dependence with theincident photon energy and scattering angle θC

(see Figs. 27 and 28).A detailed analysis shows that the scattering

angle in the forward hemisphere must be re-stricted to 0 < θC < 60 if the energy of therecoil electron in the primary interaction is be-low 170 keV for 511 keV photons. About 60%of all scatter events fall in this category. How-ever, for reconstructing with an acceptable preci-sion the z axial coordinate a minimum recoil elec-tron energy of 50 keV is required, a limit whichconceptually is not needed for the reconstructionin the transaxial plane. Finally, the acceptancein energy between 340 and 460 keV of the scat-tered photon reduces to about 25% the fractionof scatter events which unambiguously can be re-constructed.

Figure 24. As Fig. 23, however for a radial ar-rangement of 30 mm long crystal.

4.2. Estimation of the detection efficiencyIf λatt is the attenuation length of incident

511 keV photons, the probability of interactionin a scintillator of thickness t is 1− exp(−t/λatt)and the mean depth of interaction 〈DOI〉 =λatt − t/(exp(t/λatt) − 1). Therefore, the resid-ual mean path for a photon emitted in theforward direction is simply 〈tres〉 = [t/(1 −exp(−t/λatt) − λatt]/cos(θC). Hence the proba-bility of a 2nd interaction (photoelectric or Comp-ton int.) in 〈tres〉 is 1 − exp(−〈tres〉/λatt(EC)),and the probility of a full absorption 1 −exp(−〈tres〉/λabs(EC)).

The results shown in Table 3 have been ob-tained assuming a mean photon energy in the pri-mary Compton interaction of 400 keV.

In Table 3 two selection criteria of unambigu-ously reconstructed Compton events are given.For the first criteria a scatter event is selectedas T if the scattered photon undergoes a sec-ondary photoelectric conversion, whilst for thesecond criteria an event is taken as T if the totalenergy is lost in the scintillator matrix.

20

Figure 25. Resolution of spatial reconstruction inthe transaxial (x–y) plane. The simulation resultsare for LaBr3 crystals of 150 mm length. TheHRRT data has been extracted from ref. [12].

A sensitivity of 4.4 cps/kBq has been mea-sured for the HRRT [10] with a phantom of20 cm in diameter and 20 cm in length, in confor-mity with the standard NEMA-NU2 test proto-col. However, according to M.C simulations of theHRRT (see next par.) one expects a sensitivityof 2.9 cps/kBq for the detection of two coincidentphotons that underwent a photoelectric effect.The difference can be understood by the detec-tion of Compton scattered events which developin a single scintillator block and, for part, are notrejected by their detection in both phoswich lay-ers. This scatter events enhance the detectionefficiency for two coincident annihilation photonsfrom 4.6 to 6.9% (see table 3).

Note that for the axial PET-HPD we assumea total scintillator thickness of 41.2 mm for LSOcrystal bars, hence 13 layers of 3.2 mm accordingto the design discussed in sect. 2.1, and 51.2 mm(16 × 3.2 mm) for LaBr3 coresponding to a 90

rotation of the previous matrix configuration.Using LSO (LYSO) scintillators the intrinsic

detection efficiency of the PET-HPD matrix is afactor about 2.5 higher than the one of the HRRT.

Because the photofraction of LaBr3 is a factor

Figure 26. Resolution of spatial reconstructionin the axial (z) plane. The simulation resultsare again for LaBr3 crystals of 150 mm length.The grey shaded area corresponds to HRRT data(ref.[12]) obtained in different operation and re-construction modes.

twice lower than the one of LSO the Compton en-hancement is dominant but, as it can be seen, thedetection efficiency is lower. As the attenuationlength of LaBr3 crystal is long compared to LSO,their use requires a larger matrix volume hence asignificant increase of the cost.

4.3. PET sensitivity and NEMA-NU2 pro-tocol of characterization

The sensitivity, i.e. the True event rate Tper activity (cps/kBq), and the scatter fraction(SF = S/(S + T )) have been estimated in theconditions of the NEMA-NU2 test protocol usinga phantom of 20 cm in diameter et 20 cm longfilled with a dilution of 18F in water. S denotesthe event rate involving photons which underwentCompton scattering in the patient (or phantom).

If concentrations up to 1 or 1.5 µCi/ml are usu-ally used to measure the dependence of the NoiseEquivalent Count rate NEC = T 2/(T + S + R)with the electronic dead time, we assume for thepresent estimates a low radioactivity. Here R de-scribes the rate of random coincideces.

M.C simulations of the NEMA experimental

21

Table 3Comparison of detection efficiencies: HRRT vs. PET-HPD (at normal incidence)

LSO:Ce LaBr3:Cedetector HRRT 3D Axial 3D Axial -detector depth 15 mm 41.2 mm 51.2 mm ∞single photon efficienciesa) photoelectric 21.4% 30% 13.8% 15%b) C → pe 4.8% 5.7% 3.4%c) C → C → pe 4.8% 4% 2.6%d) C → absorption 12.6% 12.3% ∼ 21%i) a+b+c 26.2% 39.7% 19.8%ii) a+d → absorption 42.6% 26.1% ∼36%photon pair efficienciesi) a+b+c 6.9%1) 15.7% 3.9%ii) a+d 18.1% 6.8% ∼ 13%ratio HPD-PET / HRRTi) a+b+c 2.3 0.6ii) a+d 2.6 1Compton enhancement ∼2.0 ∼2.51) HRRT data. For pure photoelectric events a photon pair efficiency of 4.6% would beexpected. We conclude that the HRRT events contain a substantial fraction of eventswith Compton interactions.

test configuration have been performed for thePET-HPD and the HRRT scanners to deter-mine the respective solid angle for detection ofT events. The mean value of the acceptance(∆Ω/4π) thus estimated is 0.165 for the axialPET design with 150 mm long crystals and 0.344for the HRRT respectively.

The photon mean free path calculated fromthe distribution of the path lengths inside thephantom for detected photons is 8.55 cm. There-fore, for a photon attenuation length of 10.3 cmin water (µatt(511 keV)= 0.097cm−1) the prob-ability of a True event to escape the phantom isexp(−17.1/10.3) = 0.19.

Taking the detection efficiencies listed in ta-ble 3 one can estimate a PET-HPD sensitivity of2.7 and 5.5 cps/kBq without and with Comptonenhancement respectively.

For the HRRT, as already quoted, a sensitivityof 4.4 cps/kBq is estimated from a measurementof S + T events, by assuming according to theauthors a SF of 0.4, which suggests the detectionof Compton events but with a limited degradationof the spatial resolution.

5. Figure of merit: Estimate and compar-ison

We define a figure of merit as,

FoM = εdet ·∆Ω

4π· QF (10)

where εdet is the detection efficiency for Tevents and ∆Ω/4π describes the acceptance ofthe scanner. We introduce the quality factorQF = (∆E

E · RV )−1 as a combination of energyand spatial resolution, which to a certain extentcharacterizes the achievable image contrast. Thequantity FoM can therefore serve for a globalcharacterization of the overall technical perfor-

mance. The impact of the running conditionson the image contrast through the detection ofscatter events (S) in the organic tissues and ofrandom coincidences (R) is obviously ignored inthis simple approach. While the S rate dependson the discrimination in energy of the detectedphotons, the R rate is determined by the widthof the coincidence time window. This aspect isdiscussed in the next section devoted to data ac-quisition (DAQ) system.

22

Table 4Performance summary and comparison

HRRT PET–HPDscintillator LSO:Ce LSO:Ce LaBr3:CeAFOV (mm) 250 150 150detector depth (mm) 15 41.2 (13 × 3.2) 51.2 (16 × 3.2)∆Ω/4π 0.344 0.165 0.165

measured PE Compton total PE Compton totalεdet(2 photons) (%) 6.9 8.5 7.2 15.7; 18.1 1.9 4.9 6.8∆E/E (511 keV) (%) 17 10.3(z=0), 12.4(z=L/2) 4.7(z=0), 5.3(z=L/2)∆V (mm3) 20 22 ∼45 ∼33 11 ∼22 ∼18∆E/E · ∆V (%·mm3) 340 250 ∼510 ∼370 55 ∼110 ∼90

FoM1) 0.7 0.6 0.25 0.8 0.6 0.74 1.25Compton enhancement 1.85 2.8sensitivity (cps/kBq) 4.4 2.7 2.8 5.5 0.6 1.0 2.11) Figure of Merit FoM = εdet(2photons) · ∆Ω

4π · (∆EE · RV )−1 (mm−3)

Figure 27. Kinematics of the Compton interac-tion.

The comparative results are shown in Table 4.Because of the low recoil electron energy, the

axial resolution of the reconstructed Comptonevents degrades, worsening the spatial resolutionDV. However, despite an acceptance a factor 2lower than the HRRT, the merit factor of thePET-HPD with LSO scintillators is comparablebut it is about 70% higher with LaBr3.

It must be noticed that the quality factor QFvaries roughly proportionally to the number of de-

Figure 28. Cross-section for Compton interactionas function of scattering angle σC and photon en-ergy.

tected photoelectrons. Therefore, if a light yieldof 35 · 103 photons/MeV (LYSO) is attainableand by improving the photocathode quantum ef-ficiency at 420 nm from 18 to 25% (standard com-mercial value), the figure of merit of the discussed3D Axial PET could be two times larger than theone of the HRRT. A design with 25 cm long LaBr3crystal bars does not allow an improvement of the

23

figure of merit despite the increase of the accep-tance because of the spatial and energy resolutiondegradation.

The intrinsic FoM is, obviously, affected bythe performances of the FE electronic and theDAQ system which determine the image contrastT/(T + S + R) as a function of the operatingenvironment (radioactivity).

6. Data acquisition

6.1. Principle and limitationsThe principle of the data acquisition (DAQ)

system and its particular features are driven bytwo main constraints: (i) the readout architectureof the VATA front-end chip and (ii) the require-ment to detect and analyze photon interactions,which involve Compton scattering in the detector.

The tracking of the latter interactions requiresto run the FE electronic with a relatively lowdetection threshold of about 50 keV/channel inorder to detect and reconstruct the recoil elec-tron of the primary Compton scattering. How-ever, the low threshold prevents the rejection of alarge fraction of photons which underwent Comp-ton scattering in the organic tissue. Such discrim-ination is used in all conventional PET systems,as it allows to drastically decrease the countingrate and thus also reduces the rate of accidentalcoincidences.

In the so-called sparse readout mode, the VATAreadout sequence consists of a multiplexed se-quential readout of only those channels with ahit (see Sect. 2.4). The front-end chip can be op-erated at a clock speed of 20 MHz. This leads to amean readout time of ≈ 1.2µs per event, depend-ing somewhat on the selection criteria applied tothe hit multiplicity. Without a stringent selectionof events, the electronic dead time would paralyzethe readout system already for modest source ac-tivity levels and hence spoil the sensitivity of thePET scanner.

It is a unique and intrinsic property of the HPDphotodetector which allows to resolve this prob-lem. The HPD provides a fast measurement ofthe total energy deposited in the scintillator ma-trix. The total energy information is derived fromthe induced signal on the Si sensor back plane

which, as it covers the full detector area, is pro-portional to the total amount of charge depositedin the Si sensor, and hence to the total energyconverted in the scintillator block. As will be de-tailed below, the large and prompt back plane sig-nal allows to identify and reject low energy pho-tons (from Compton scattering in the patient),without compromising the ability of the FE elec-tronic to detect Compton interactions in the scin-tillator matrix. This is an essential and funda-mental feature of our approach and the proposedDAQ concept.

To better understand the limitations of theDAQ, Table 5 shows the dependence of the trig-ger rates with various event selection criteria, likeenergy threshold for the generation of a Fast OR(FOR signal) and multiplicity of crystal clusters.The numbers were estimated in the conditions ofthe NEMA-NU2 test protocol from M.C simula-tions and analytic calculations, within ±10% er-ror. The rate of accidentals was estimated on thebasis of a Coincidence Time Window (CTW) of10 ns for a phantom radio-tracer concentration of0.35µCi/ml (V = 6310 ml, i.e. total activity =81.4 MBq).

Operating the FE electronic with a detectionthreshold of 50 keV without additional event se-lection would require a huge and technically un-feasible DAQ rate. The conditions improve signif-icantly when applying a cut-off on the hit multi-plicity and, obviously, drastically, if the detectionthreshold is raised to 400 keV (right most col-umn in Table 5), a value which greatly favors thedetection of unscattered photons of 511 keV.

Running with a detection threshold of 50 keV,which enables Compton sensitivity enhancement,and exploiting at the same time the total energyinformation from the Si sensor back plane, leadsto a reduction of the DAQ rate by a factor ofabout 14. However, even in these conditions, areasonably achievable DAQ rate of 0.5 to 0.6 MHzwould result in a poor acquisition efficiency ofabout 50%. Therefore, as described below, theDAQ system is split in several parallel and inde-pendent chains. In the following we discuss a 3DAxial PET scanner comprising 16 modules.

Note that for an activity of 81.4 MBq thecount rate of the FOR signal is of the order 1.9

24

Table 5Trigger selection criteria and DAQ rates

Si sensor back plane readout no yes, Eγ ≥400 keV

energy threshold FOR 50 keV 50 keV 400 keV 50 keVselection: hit multiplicity any m ≤ 2 m = 1 (pho-

topeak)any

phantom ac-tivity

interaction type relative count rate (cps/kBq)

low1) single γ (PE +Compton)

280 115 49 280

low 2 coincident γs (PE+ Compton)

90 ∼ 18 ≤ 3 90

low DAQ rate 90 6-7absolute count rate (cps = Hz)

81.4 MBq2) DAQ rate (8 paral-lel DAQ chains)

7.3 · 106 Hz 5− 6 · 105 Hz

81.4 MBq accidental’s rate(CTW = 10 ns)

∼ 1.2 ·106 Hz ∼ 105 Hz

1) Random count rate is negligible. 2) 81.4 MBq = 0.35 µCi/ml × 6310 ml.

MHz/module but decreases to 0.7 MHz/modulefor a threshold setting of 50 keV.

For Nm = 16 modules covering the azimuthalacceptance, there are Nm · (Nm−1)/2 = 120 pos-sibilities to form module pairs. From the geomet-rical point of view, only roughly half of them willlead to physically meaningful coincidences (T andS events), but all of them will contribute to therandom rate (R). To minimize these accidentalsthe DAQ architecture is designed to accept co-incidences of hit modules only within a limitedangular acceptance, e.g. five or six modules inthe opposite hemisphere (see Fig. 29). The DAQsystem thus searches for coincidences between agiven module and, for example, the 5 or 6 oppo-site modules. This reduces the number of validmodule combinations and consequently the asso-ciated accidentals rate by more than a factor 2.

This selective pair approach allows to structurethe DAQ architecture as 8 coincidence chains,which are defined dynamically and work in par-allel in an independent and asynchronous way. Acoincidence chain consists of a first module and adynamically associated second module from theopposite hemisphere. When a chain detects twomodule pairs in coincidence, all other modules are

unaffected and stay armed for other coincidences.The detection of randoms R is strongly sup-

pressed w.r.t. T and S events by requiring co-incidences of exactly two modules. The randomsrate due to uncorrelated single photons simulat-ing T events decreases by a factor of about tenafter energy discrimination, but still constitutesabout 20% of the acquired data. The estimatedimage contrast T/(T + S + R) is about 0.6, com-pared to 0.4 for the HRRT.

6.2. Energy discriminationThe signal charge, produced in the HPD (UC =

12 kV), following the absorption of a 511 keVphoton in a LSO crystals, ranges from 0.87 to1.23 · 106 electrons (0.14 - 0.2 pC), depending onthe axial coordinate at which the crystal bar ishit. The induced signal on the back plane of thesensor is almost fully due to the holes driftingover the full thickness of the Si sensor (300 µm).The pathlength of the electrons (few µm) does notgive a sizable contribution. Operating the sen-sor above the full depletion voltage (’overbias’),Ubias ∼ 3 ·Udep, the ∼ 106 holes will induce a cur-rent of about 10 µA during the total drift time ofless than 15 ns. A low impedance and large band-

25

Figure 29. Schematic representation of the 16readout modules. For each of the modules a geo-metrical acceptance range is defined in which co-incidences with other modules can be formed.

width amplifier (70 MHz) with a shaping time of5 ns will be able to sense about 1/3 of the to-tal charge, i.e. about 3 · 105e−. Such an ampli-fier has a typical noise of about 2 · 103e− (RMS)even though the backplane capacitance is about300 pF. This means that the back plane signalcan be detected with a very comfortable signal tonoise ratio of about 150.

The signal from the back plane of the sili-con sensor is proportional to the total energydeposited in the crystal matrix. Therefore, itdoes not differentiate between a photoelectricinteraction, where usually only one crystal baris affected, and a detection sequence involvinga Compton interaction, where generally severalcrystal bars are affected.

Summing just the analogue signals AL and AR

of the left and right HPD does not provide anaccurate energy discrimination. Due to the lightabsorption in the crystals, the sum A = AL +AR

varies for the same energy deposit from 0.28 to0.4 pC for interactions occurring at the centreand at the bar end, preventing the applicationof a precise cut for energy discrimination of Sevents. A threshold setting equivalent to 400 keV

at the centre, for example, would correspond toa discrimination threshold of 310 keV at the barend. By using instead the variable (AL + AR) −0.5 · |AL − AR| reduces the maximum dispersionby more than a factor two allowing a threshold of419± 22 keV.

The fast response of the sensor back plane isobviously exploited, as described below, for thesearch of coincidences between modules allowinga time resolution of 5 to 10 ns.

6.3. DAQ architectureTo minimize the DAQ related dead time, only

the module pair detected in coincidence duringthe CTW is read out, while all other modules re-main enabled to accept further coincidences. Thesystem is thus continuously running: some mod-ules can be in the readout state while others areawaiting coincidences.

This implies that the DAQ architecture foreseesone readout card per module, which deals withfour VATA chips (two chips per HPD). With thisconfiguration the DAQ system can read out the16 modules (or potentially more) independentlyin parallel. All the 16 cards are controlled by asingle Process Controller (PC) – implemented asField Programmable Gate Array (FPGA) – thatchecks for the pair of modules in coincidences andenables their readout (see Figs.30 and 31).

The PC receives all the flag signals (FORM)from the discriminator of the analogue signal A ofeach module, and performs, when a coincidence isdetected in the CTW , the combinatorial selectionof meaningful Line Of Records (LOR).

When a module is not in a readout sequence,the VATA chips run in a self reset operationmode: the FOR output of each chip is applied toits reset input after a reset delay of 25 to 30 ns.This delay is driven by the performance of thetime walk compensation circuit, when fed withsignals of different amplitudes (see sect. 2.4 ).

If on the contrary a coincidence is detected,the PC blocks the RESET signal and inhibitsteh VATA chip after a dealy of 50 to 90 ns withrespect to the occurence of true event. The in-hibition, i.e. the vetoing of undesired data inthe VATA output registers, is performed by set-ting the Discard Late Trigger (DLT) Signal of the

26

Figure 30. Components and functionality of theProcess Controller.

VATA chip.In these operational conditions the rate of ran-

dom coincidences for a radiotracer concentrationof 0.35 microCi/ml is only 4.2% for a time resolu-tion of 5 ns if 6 opposite modules are eligible forcoincidences. The probability of two events pilingup in the VATA output registers within the reset

delay (30 ns) is of the same order. However thesepile-up events can be rejected by the offline anal-ysis and only degrade the DAQ efficiency with-out spoling the data quality. The electronic deadtime is thus mainly determined by the readouttime sequence of the VATAs as discussed below.

The DAQ sequence is as follows:When the Process Controller has detected a co-

incidence in the CTW acceptance the FORMsare stored in a register (FORM ), counted and abusy flag (BUSYM ) is generated after a delay of50 ns. The BUSYM signal disables the self resetof the VATAs of all hit modules, and 40 ns laterinhibits the chip operation.

If the FORM counter shows two photons incoincidence, the Process Controller keeps high theBUSYM on the DLT input of the two hit modulesand increases the value of an event counter (EC).If, however, the FORM counter shows less (nocoincidence) or more than 2 (accidental hits), thePC enables the VATA chips of the hit modules

Figure 31. Schematic representation of the sig-nal and data flow. The central box represents adetector module with 2 HPDs.

(BUSYM low) and resets their registers and busyflags.

As an option, the Process Controller can stillcheck the multiplicity of hit crystal bars per mod-ule, which gives a good indication whether thephoton was detected by photoelectric effect ora more complex interaction sequence involvingCompton scattering. For this purpose the VATAchip provides a fast analog signal which is propor-tional to the hit channel multiplicity. After dis-crimination, a flag (REGmul) can be generated.This step ends the first part of the processing.

Assuming a veto time of 12 ns for each gener-ated FOR of the 8 top modules TMi which startthe search for coincidences, the time fraction dur-ing which the FE electronic will be vetoed for aradioactivity of 0.35µCi/ml (or 1.9 Mhz countingrate per module) is about 1.9 · 106 × 12 · 10−9 =0.023. This leads to selection efficiency of εsel =exp(−0.182) ∼ 98%, considering only this firstpart of the acquisition process.

In case of a good event, i.e. if all the abovedescribed criteria are met, the Process Controllerenables the Module Controllers MC (also imple-mented as FPGA’s) of the hit modules to readand save:

(i) the value of the event counter (EC) in theregisters of the MC (header of the event

27

buffer)

(ii) the addresses of the hit modules in coinci-dence registers CR.

As soon as they receive the ENABLE signalfrom the Process Controller, after a delay corre-sponding to the peaking time τs of the shaper inthe analogue chain of the VATA-GP5 the MC’ssend the HOLD signal to the corresponding mod-ules. Then the MC’s start to readout and en-code the data using the sparse readout mode ofthe VATA chips. ADCs with 12 bit resolutionare well suited to the dynamic range. The MCverify for each read module that the hit chan-nels and the multiplicity of the two HPDs cor-respond. In case of LSO crystals a mean valueof 3 hit channels is expected. With a clock fre-quency of 20 Mhz, the mean readout time permodule is (3 + 3) × 50 · 10−9 s = 0.3µs (3 ini-tial clock cycles are needed to address the firstdata). For a total readout rate in the 500 kHzrange, shared between the 8 DAQ chains, and aradiotracer concentration of 0.35µCi/ml, we es-timate a busy fraction of the system of 500 ·103 s−1 /8 × 0.3 · 10−6 s = 0.019, resulting in areadout efficiency of εRO = exp(−0.019) ≈ 98%.The total efficiency of the DAQ system is henceεDAQ = εsel · εRO =96%.

After acquisition, the data (addresses of thehit modules and the digitized signal amplitudes)are stored in a local FIFO memory present ineach MC. Asynchronous data transfer to thecomputer (standard personal computer) is imple-mented via a fast suitable network protocol. Inthe prototype phase USB 2.0 is planned to beused which provides a bandwidth of 3.75 MHzper module. For the full implementation a 10Gbit optical fiber link is a more appropriate op-tion.

7. Conclusions

We described the innovative geometrical con-cept and a possible implementation of a 3D Ax-ial PET scanner and its dedicated data acquisi-tion system. The performance estimates for thereconstruction resolution in both the axial andtransaxial plane and the uniformity of the reso-

lution over the complete field of view make theconcept very competitive in comparison with ex-isting state-of-the-art devices. The possibility tounambiguously reconstruct part of annihilationphotons which underwent Compton scattering inthe crystal matrix is a unique feature of the con-cept and leads to high sensitivity even for limitedsolid angle coverage. The use of recently devel-oped fast high-Z and high density crystals likeLaBr3 leads to excellent energy resolution, whichis expected to facilitate scatter suppression andconsequently will boost image contrast.

The described study is currently still on a con-ceptual level. Several findings require support bymore elaborated and comprehensive simulations,which need to take into account effects linked totomographic data reconstruction. A major mile-stone, the proof of principle in form of a 3D Axialcamera protoype module, is under preparation.Most of the required hardware components havebeen developed and are now available. We willreport about the experimental results in a forth-coming paper.

Appendix

Experimental determination of the lightabsorption length

The determination of the axial z coordinateof the photon conversion point is affected byan error ∆z that strongly depends on the pre-cision with which the effective light absorptionlength λ for the light emitted in the crystal bar,is known. As shown by the equations 8 and9, in order to achieve the required precision of1 mm in z, one must measure λ with a preci-sion ∆λ/λ better than 1.3% and 0.8% for crys-tals of length L of 150 and 250 mm, respectively.The experimental method used to evaluate λ con-sists in measuring the ratio between the pulseheights QR, QL recorded at both ends of thebar as a function of the axial excitation posi-tion. Assuming an optically isotropic crystal, oneexpects a ratio QR/QL = 1 when the scintilla-tion light is emitted at L/2, and an exponentiallydecreasing ratio when the emission point is dis-placed from one bar end (z = 0) to the oppositeone (z = L). The effective attenuation length

28

λ is eventually evaluated from the relationshipQR/QL = exp[(L − 2z)/λ].

Figure 32. Schematic of the experimental set-up.

The schematic of the test bench used for thelight absorption length measurement in shown inFig. 32. Hamamatsu photomultipliers (PMT) H-3165-10 are coupled to each crystal bar with op-tical grease (BC-63014), with a refractive indexn = 1.47 at 400 nm, to reduce photon losses dueto the reflection at the 10 mm diameter photo-multiplier window. No specific reflector materialis used to wrap the crystal bars, thus scintilla-tion light reaches the PMTs either directly orvia total internal reflection from the bar lateralsides. The PMTs, operated at a negative volt-age of 1300 V corresponding to a gain of 106,are equipped with a standard bialkali photocath-ode whose quantum efficiency, peaked at about400 nm, matches the crystal emission wavelength.The crystal is exposed to a finely collimated beamof 511 keV photons from a 10 mCi 22Na source.A linear motion stage allows to study the lightemission as a function of the excitation positionby moving the crystal in nine positions along itsaxis, with an incremental step of 1 cm. Trig-ger signals are provided by the coincidence be-tween the right–left PMT signals and the signal

14Saint – Gobain Group, Bicron

Figure 33. Signal amplitude (ADC counts) mea-sured at the two crystal ends as a function of theaxial emission position.

produced by one of the two back-to-back 22Naannihilation photons into a 28 mm thick BaF2

crystal. Pulse heights and timing information,digitized by means of a LeCroy 2249W charge-sensitive ADC and a CAEN C414 TDC respec-tively, are recorded by a multi-parametric acqui-sition system running under LabView. Measure-ments performed on 100 mm long YAP:Ce crys-tals 15 gave a mean value of the effective lightabsorption length in YAP:Ce of about 190 mm.The bulk absorption length (compare Section 3.1)λb = λ/k = 190/0.7 ∼ 270 mm appears to bealmost double the value reported in [49]. Theoverall precision of 2% on a single measurement iswithin expectations given for 100 mm long crystalbars. Such a long absorption length is unsuitablefor the 3D axial scheme. However, studies on vari-ous reflective coatings have already demonstratedthat the effective absorption length can be tunedto a suitable value (e.g. 100 mm) while the totallight output and hence the energy resolution ismaintained [50].

15The crystals were purchased from Crytur LTD., Czech.Republic.

29

Acknowledgements

We would like to thank the numerous col-leagues who helped in clarifying discussions tocome to a better understanding of the potentialand limitations of the proposed concept. Thanksto Wojtek Dulinski (LEPSI Strasbourg) for themask design of the Silicon sensor. We acknowl-edge the great support of our technical personnelat CERN Francoise Cossey, Claude David, LucKottelat and Ian Mcgill, which was indispensablefor the construction of the photodetector proto-types. We are grateful for the financial supportby the CERN technology transfer service.

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