Nuclear Instruments and Methods in Physics Research A 471 (2001) 276–280

Collimatorless imaging of gamma rays with helpof gamma-ray tracking

J. van der Marel*, B. Cederwall

Physics Department Frescati, Royal Institute of Technology, Frescativ .aagen 24, S-104 05 Stockholm, Sweden

Abstract

In many gamma-ray detector systems that are built for imaging purposes Compton scattered photons are suppressedas much as possible. However, the information from photons that scattered inside a detector system can be used toreconstruct the tracks of the photons with help of gamma-ray tracking. Estimates of the incident directions of the

photons can be made and an image can be created. Examples of potential applications for this technique are the use as agamma-camera in medical imaging (e.g. SPECT) or as a detector for PET. Due to the omission of collimators, muchhigher detection efficiencies can be achieved, reducing the doses required for an image. A gamma-ray tracking method,called backtracking, has been developed for nuclear spectroscopy. The method tracks gamma-rays originating from a

point source in the center of a spherical detector system consisting of position-sensitive germanium detectors. Thismethod can also be used as a tracking technique for imaging of an unknown source distribution. With help of MonteCarlo simulations the method has been investigated for simple test cases with one or two planar detectors and one or

two point sources. The results show that the sources can be located accurately in three dimensions. r 2001 ElsevierScience B.V. All rights reserved.

PACS: 29.40.Gx; 07.85.Yk

Keywords: Tracking; Gamma-ray imaging; Compton imaging; Backtracking

1. Introduction

In nuclear spectroscopy a new concept for thedetection of g-rays is under development: g-raytracking [1]. In the future shells of highlysegmented detectors in which the individual inter-actions of g-rays (Compton scattering, photo-absorption, pair production) are detected, together

with g-ray tracking to reconstruct the scattered g-rays, may provide detector systems that are manytimes more powerful than existing germaniumdetector arrays. When applying g-ray tracking tonuclear spectroscopy one normally assumes thatthe g-rays are emitted from a known point in space(usually the target). The primary goal is to be ableto accurately determine the individual energies of alarge number of g-rays simultaneously interactingwith the detector system.However, the g-ray tracking technique can also

be applied in a different way. If the positions of theemission points of the g-rays are unknown one can

*Corresponding author. Present address: Nederlands Mect-

instituut, P.O. Box 80000, 3508 TA Utrecht, The Netherlands.

Tel.: +31-30-2539098.

E-mail address: hvdmarel@nmi.nl (J. van der Marel).

0168-9002/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 0 0 7 - 5

apply the technique to determine the distributionof the source. From the g-ray tracking procedureone gets information about the initial directions ofthe photons and this can be used to reconstruct animage of the source. The tracking is independentof the initial direction of the photons, therebyeliminating the need for a collimator. This canincrease the efficiency of the detector systemconsiderably. In contrast with previously proposedCompton cameras [2,3] the gamma-ray trackingtechnique is able to track g-rays that scattered overlarge angles or short distances, thus improving theefficiency. Due to the ability to correctly trackmultiple coincident g-rays this technique is alsosuitable for high count rate environments or slowread-out schemes. Germanium as the detectormaterial provides a very good energy resolution,allowing the rejection of g-rays that scatteredoutside the detector system. The high efficiencythat can be obtained with an imaging device basedon g-ray tracking and a germanium detectormakes it very promising for application in e.g.nuclear medicine ðPET; SPECTÞ, where the radia-tion dose should be as low as possible.

2. The c-ray tracking principle

In the nuclear physics community two methodshave been developed to perform g-ray tracking:the clustering method [4] and the backtrackingmethod [5]. Both methods rely on the Comptonscatter formula. For a shell-like geometry ofgermanium detectors as it is often used in nuclearspectroscopy the (simulated) performance of bothmethods is similar. In this paper the backtrackingmethod is used.In the backtracking method one tries to find the

last (photoelectric) interaction of a scattered g-ray.It appears that the energies deposited by theseinteractions are in a rather well-defined range (seeRef. [5]). Starting from this last interaction thepath of the g-ray is tracked backwards to theemission point with help of the Compton scatterformula and the Compton and photoelectricabsorption cross-sections. To every track a figureof merit is given, which reflects the probability thatthe g-ray is properly tracked. The tracks with the

highest figures of merit are selected as ‘good’ g-rays. For an extensive description of this methodthe reader is referred to Ref. [5]. The backtrackingmethod has also been studied in a simulation witha planar detector (see Ref. [6]).

3. Image reconstruction

Monte Carlo simulations using the GEANT [7]code were used to investigate the image recon-struction properties of the backtracking method.In the simulations one or more g-ray emissionpoints are created and the interactions of the g-rays in the germanium detectors are calculated.This is used as input for the backtrackingprogram. The program tracks the g-rays andstores the coordinates of the first interaction, thedirection of the vector between the second and thefirst interaction and the scattering angle yc ascalculated with help of the Compton scatterformula (see Fig. 1). This information is used asinput to the image reconstruction program.In the image reconstruction it is assumed that no

information about the direction of the photoelec-tron or Compton electron is available. Therefore,for every tracked g-ray a cone is created using theinformation from the tracking program. This coneis backprojected on a grid in the volume outside

Fig. 1. The track of a g-ray in a piece of germanium with the

different interactions. Also indicated is the scattering angle y forthe first interaction.

J. van der Marel, B. Cederwall / Nuclear Instruments and Methods in Physics Research A 471 (2001) 276–280 277

the detector. By applying this for many g-rays thedensity of crossing points between different coneswill reflect the density of the source distribution.

4. Results

The above outlined image reconstruction meth-od has been tested in a simulation with theconfiguration shown in Fig. 2. Either one or twogermanium detectors of a size of 20� 20 cm2 anda thickness of 2 cm were employed. If twodetectors were used the distance between thedetectors was 20 cm. To make the simulationsmore realistic, the detectors have a limited positionand energy resolution. For the position resolutionit is assumed that interactions closer together than1 mm cannot be separated and they are combined.The resulting energy is the sum of the interactionenergies and the position is the weighted averageof the positions. Apart from that the interactionsare given a random displacement according to aGaussian distribution with a standard deviationspos ¼ 0:2 mm. The interaction energies are sub-ject to an energy-dependent statistical noise withsstat ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFwGe Eint

p, in which F ¼ 0:05 is the Fano

factor of germanium, wGe ¼ 2:96 eV is the energyrequired to create an electron–hole pair in

germanium and Eint is the energy deposited byan interaction. A constant electronic noise withsel ¼ 0:5 keV is added to each interaction energy.For the reconstructions in the space betweendetectors 1 and 2 a grid is built with 100� 100�100 elements (the pitch is 2 mm in all directions),also if only detector 1 is being used. In thesimulations the source (one or two points) emits106 photons of 511 keV.The projections on the xy-, xz- and yz-plane of

the reconstruction of a single point source areshown in the cases that only detector 1 (Fig. 3) orthat both detectors (Fig. 4) are used. In theprojections the highest values in the columnsperpendicular to the planes are plotted. For bothcases the positions of the sources are correctlyreconstructed. When one detector is employed,there is a background between the source and thedetector, which is greatly suppressed if twodetectors are applied.In the Figs. 5 and 6, the projections are shown

for the case that there are two point sourcesbetween the detectors. The two point sources areclearly resolved. In the case of one detector there isa significant background between the sources andthe detector. With two detectors this backgroundis suppressed, but it is still visible. For more pointsources the results are similar.

Fig. 2. The configuration of the detectors in the simulation.

Detector 2 is not used in all calculations.

Fig. 3. Projections on the three planes of a reconstruction with

detector 1. The source is positioned at x ¼ 10 cm, y ¼ 10 cm,

z ¼ 10 cm.

J. van der Marel, B. Cederwall / Nuclear Instruments and Methods in Physics Research A 471 (2001) 276–280278

5. Conclusions

It has been demonstrated by means of simula-tions that gamma-ray tracking can be used forimaging purposes. Because collimators can beomitted, an imaging device based on the gamma-ray tracking technique can be very efficient.With the aid of Monte Carlo simulations tests

have been performed with one or two detectorsand one or two point sources. In all cases the

position of the sources could be determinedaccurately and the reconstructed sources are reallypoint-like. The results for two detectors look evenbetter than with one detector, due to the suppres-sion of the background between the source and thedetector. It is expected that the application ofmore detectors in a circular geometry can furtherenhance the image.In order to successfully apply gamma-ray

tracking for imaging, a good energy resolutionand a good intrinsic 3D position sensitivity arerequired. An other important requirement for thedetector material is that for the g-ray energy ofinterest the Compton cross-section is sufficientlylarge. In this example germanium was used for thedetection of 511 keV g-rays. An application forthis combination can be in nuclear medicine whenpositron emitters are used. The technique can alsobe applied successfully with germanium detectorsand 141 keV g-rays, an energy that is often used inSPECT. Since collimators are not required amuch higher efficiency than in conventionalSPECT can be obtained. One can also think ofapplications for computed transmission tomogra-phy with g-rays.The preliminary results shown in this paper for

imaging with help of gamma-ray tracking are veryencouraging. Because of the wide field of applica-tions and their importance this g-ray imagingapproach deserves further investigation.

Fig. 4. Projections on the three planes of a reconstruction with

detector 1 and 2. The source is positioned at x ¼ 10 cm,

y ¼ 10 cm, z ¼ 10 cm.

Fig. 5. Projections on the three planes of a reconstruction with

detector 1. The two sources are positioned at x ¼ 5 cm,

y ¼ 10 cm, z ¼ 10 cm and x ¼ 15 cm, y ¼ 10 cm, z ¼ 10 cm.

Fig. 6. Projections on the three planes of a reconstruction with

detector 1 and 2. The two sources are positioned at x ¼ 5 cm,

y ¼ 10 cm, z ¼ 10 cm and x ¼ 15 cm, y ¼ 10 cm, z ¼ 10 cm.

J. van der Marel, B. Cederwall / Nuclear Instruments and Methods in Physics Research A 471 (2001) 276–280 279

Acknowledgements

This work was supported by the Commission ofthe European Communities within the TMRprogramme under contract No. ERBFMRXCT97-0123.

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J. van der Marel, B. Cederwall / Nuclear Instruments and Methods in Physics Research A 471 (2001) 276–280280