- Email: [email protected]
A scintillating GEM for 2D-dosimetry in radiation therapy
Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
A scintillating GEM for 2D-dosimetry in radiation therapy J.H. Timmera, T.L. van Vuureb, V. Bomb, C.W. van Eijkb, J. de Haasb, J.M. Schippersa,* b
a Kernfysisch Versneller Instituut, Zernikelaan 25, 9747 AA Groningen, Netherlands Interfacultair Reactor Instituut, TU Delft, Mekelweg 15, 2629 JB Delft, Netherlands
Abstract The first results of a study on the properties of a gaseous scintillation detector based on a Gas Electron Multiplier (GEM) are reported. The detector is designed for use in position-sensitive dosimetry applications in radiation therapy. A double GEM system, operating in a 90–10% Ar–CO2 gas mixture at a gas amplification factor of B3000, emits a sufficient amount of detectable light to perform measurements of B1 Gy doses in two dimensions. The light yield does not suffer from quenching processes when particles with high stopping power are detected. This operation mode of GEMs offers the dosimetric advantages of a gas-filled detector and the 2D read-out can be performed with a CCD camera. Compared to the existing dosimeters, this system is relatively simple and no complex multi-electrode read-out is necessary. r 2002 Elsevier Science B.V. All rights reserved. PACS: 87.66.a; 87.58.Mj; 87.58.Sp; 29.40.Cs; 29.40.Gx; 29.40.Mc Keywords: Dosimetry; Gaseous detectors; Gas electron multiplier; Gas scintillation
1. Introduction Accurate 2D position-sensitive dosimetry equipment is becoming increasingly important in modern radiation treatments of cancer. The extremely high fluences in a radiation-therapy beam do not allow single event detection methods, but integration of the signal over some time interval is used instead. Since the electric currents in these systems (e.g. ion chambers) have to be read out whilst the radiation is administered, dynamic irradiation techniques require a pixel *Corresponding author. Tel.: +41-56-3104229; Fax: +4156-3103383. Present address: Paul Scherrer Institut; CH-5232 Villigen-PSI, Switzerland. E-mail address: [email protected] (J.M. Schippers).
type of read-out for 2D dosimetry. For the scanning-beam irradiation-technique used in proton therapy [1], a system based on a scintillating screen [2] has been developed. In the screen, the deposited dose is converted into a light spot, which is observed by a CCD camera. It has been shown [2,3] that the observed light pattern is a very good measure of the dose distribution at the screen position. The signal read-out by means of a CCD has proven to be a reliable, as well as accurate and standard read-out methods can be used. A fundamental drawback of a scintillating screen, however, is that the light yield does not scale with dose in the last part of the proton track, where the stopping power reaches a maximum (the Bragg peak). A quenching of the signal by up to 20% has been observed for proton beams of
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 7 1 8 - 1
J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
clinical relevance [2]. The quenching is caused by an integration (blurring) of the signal over the thickness of the screen and/or a different excitation energy of the phosphor with respect to water (the reference medium for dosimetry) and/or by a temporal unavailability of scintillation centers. This problem could be solved by using a gaseous detector. In order to take advantage of the CCD read-out, we employed the gas scintillation process to extract the signal from the detector. We have thus replaced the screen by a thin layer of gas and we use a Gas Electron Multiplier (GEM) [4] system to initiate a charge amplification followed by gas scintillation.
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Here, ne equals the number of created electrons in the detection region. L is assumed to be in the order of 5 102 [5]. The detector has been tested in the beam line normally used for radiobiology experiments at the AGOR cyclotron in the KVI in Groningen [6]. The tests were performed in realistic proton-therapy conditions with well-calibrated proton beams of different energies (130–190 MeV), beam crosssections (o8 cm diameter) and dose rates (up to 20 Gy/min; 1 Gy/minB104–106 protons/mm2/s ).
3. Results 3.1. Gas amplification
2. Experimental setup The GEM-based scintillation detector has been tested with a gas mixture of 90–10% Ar–CO2 (Fig. 1). Between a cathode foil and the first GEM, a layer of 3.5 mm gas serves as the detection region. The electrons, which have drifted towards the first GEM, are amplified and they cross a 3 mm drift region towards the second GEM. In the second GEM, again, a charge amplification occurs and the electrons are collected at its exit face. The electric currents to the GEMs were measured and by relating these to the beam-intensity monitors, the gas amplification M was calculated. In the gas-amplification process, the electrons also excite atomic levels, which decay by light emission. The light is detected by a CCD camera [2] with quantum efficiency ZE0:3 at 1.2 m from the GEMs (solid angle O) which are mounted in a gas-tight box. The GEM foils, having an active area of 10 10 cm2 with 80 mm holes at a pitch of 140 mm, have been kindly supplied by F. Sauli, CERN. When L photons are emitted per accelerated electron in the second GEM, the number of electrons per CCD pixel I; can been estimated as
3.2. Light yield
I ¼ ne MLOZ ¼ 104 2102
Gas amplification measurements in single and double GEM systems have been performed in a proton beam with beam intensity Ibeam ; which resulted in a count-rate of 5 104 Hz/mm2. Since most electrons are collected on the last GEM’s electrode surface, the total effective M can then be derived from IGEM2 =Ibeam : As can be seen in Fig. 2a, the total amplification Mdouble is not equal 2 to M 2 ; but rather to Mdouble ¼ 0:3 Msingle due to the loss of charges. For larger count rates, a quenching of the gas amplification seemed to occur (see Fig. 2b). This, however, was due to an artifact in our setup. For beam sizes of several cm2, the overall count rate is so large that this resulted in a current of several mA in the resistors in the voltage-division chain connected to the HV-power supply. At the second GEM, this caused a decrease of DVGEM ¼ 10250 V, so that its gas amplification factor decreased by a factor of 1.5–4. However, when the curves are corrected from ‘‘set-voltage’’ to ‘‘actual voltage’’, as calculated from IGEM2 ; the upper curves in Fig. 2b are obtained. This shows that the gas amplification does not depend on the count-rate until a few times, 105 Hz/mm2.
ðCCD-electrons= proton crossing the GEMÞ:
ð1Þ
Measurements of the light yield were performed at typical therapy conditions: proton doses of 0.1–2 Gy and count-rates of 6.104–4.106 Hz/mm2.
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J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
incident beam
--HV
cathode foil
-HV
ne primary electrons
cascaded GEMs
gas amplification: M light emission L transparent foil
IGEM2 +HV
CCD camera quantum eff. η Ω
mirror
Fig. 1. The setup of a scintillating GEM detector together with the connections to the power supply as used in the test experiments.
Compared with the scintillating screen, the total amount of detected light from a scintillating double GEM system was typically a factor of 10 less when operating at ME3000: Using Eq. (1), the number of photons per proton has been measured as a function of M (see Fig. 3). L can be derived from the signal in the CCD and IGEM2 (see Fig. 4). We found that L does not depend on the proton count-rate. We also found that LðMÞ does not change with the number of available electrons after a gas amplification process. This is very important, since the electrons created in a single avalanche are more susceptible to recombination and space-charge effects compared to those from different particle tracks. This means that the
scintillation process itself does not suffer from quenching due to a saturation effect. The observed value of LE8 103 ; is smaller than the values reported by Fraga [5]. This might be due to slight differences in gas composition and absorption in the gas layer between GEM2 and the exit foil of the detector box. 3.3. Image quality In Fig. 5, a light-image of a + ¼ 30 mm proton beam is shown. As can be seen, the image shows intensity variations of up to 10%. These variations are fixed to the detector and they are reproducible. They are caused by GEM-hole variations and a non-flat GEM surface due to a limited amount of
101
J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
Vgem(V) 10000 Double GEM
(a)
Single GEM
1000
Total gas-amplification factor
100
10000 2.2e4Hz /mm2 6.6e4Hz /mm2 3.3e5Hz /mm2 1.0e6Hz /mm2 2.2e4 c orrec ted 6.6e4 c orrec ted 3.3e5 c orrec ted 1.0e6 c orrec ted
1000
(b)
100 260
280
300
320
340
360
380
Set Vgem2 or Actual Vgem 2 (V) Fig. 2. (a) The measured total gas amplification factor as a function of the GEM voltage at 2.2 104 Hz/mm2; (b) the measured total gas amplification factor for a double GEM at different count-rates (closed symbols). After a correction from the set voltage to the actual GEM voltage (arrow), the curves with the open symbols are obtained.
Photons/secondary electron
Photons per proton
500 400 300 200 100
Single GEM
0.01 0.008 0.006 0.004 Single GEM Double GEM Double GEM high count rate
0.002
Double GEM
0
0 0
100
200
300 400 500 Gas amplification factor
600
700
Fig. 3. The number of emitted light photons per incident proton as a function of the gas amplification factor.
stretching. This causes a non-uniformity in the thickness of the first gas layer. The images can be corrected for this variation in sensitivity.
0
200
400
600
8000
1000
Gas amplification factor
Fig. 4. The number of emitted light photons per secondary electron as a function of the gas amplification factor.
By comparing the signal fall-off at the edge of the beam with that obtained with a scintillating screen, we found that the spatial resolution was
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J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
CCD signal per pixel (a.u.)
15000
10000
5000 Ionisation chamber Scintillating screen Scintillating GEM Scintillating GEM, corrected 0 0
50
100
150
200
Depth in waterequiv. material (mm)
Fig. 6. The signal as a function of the amount of waterequivalent material in front of the detector, measured with a parallel ionization chamber (proportional to real dose), the scintillating screen (E) and the scintillating GEM (J). The round dots (K) represent the signal of the scintillating GEM after correction for the GEM voltage decrease due to high count-rates. Fig. 5. An image of a circular beam (+ ¼ 30 mm) and a profile, measured with the scintillating GEM. The gray scale has been adjusted to enhance the inhomogeneities.
better than 1 mm, both for a single GEM and a double GEM. 3.4. Measurement of the Bragg peak By varying the amount of material in front of the GEM, we measured a depth-dose curve at a count rate of 3.104 Hz/mm2 and a beam crosssection of + ¼ 30 mm. In Fig. 6, the results are shown, together with the signals from a scintillating screen and an ionization chamber. This last measurement shows the real dose as a function of depth. The signal from the screen is quenched in the Bragg peak. Also the signal of the GEM shows quenching, but this can again be attributed to the reduction of VGEM2 : Since IGEM2 has also been measured, we were able to apply the same correction as the one shown in Fig. 2b. Due to the uncertainties in this correction procedure, no exact matching is obtained but the quenching disappeared to a large extent. 4. Discussion and conclusions The scintillating GEM is a good candidate for a 2D-dosimetry system. In our prototype, the light
yield is still too low, but after modification of the detector box, a change of gas mixture or addition of wavelength shifters, we expect that a factor of 5 can be gained easily. An important observation is that the light yield is proportional to the amount of secondary electrons. This implies that quenching due to the lack of scintillation centers will not occur. In order to investigate the dependence of the light yield on the gas composition in more detail, light emission spectra will be measured. The observed quenching of the gas amplification can be removed by using HV power supplies with stabilized outputs. But saturation in the gasamplification process and recombination of charges remain the most probable causes for quenching in this detection system. Therefore, the trade off between gas amplification and light yield has to be investigated in more detail.
Acknowledgements The authors acknowledge P. van Luijk and H.H. Kiewiet (KVI) for their assistance at the experiments and F. Sauli (CERN) for his advice on the operation of the GEMs. This work was performed as a part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the
J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). References [1] E. Pedroni, et al., Med. Phys. 22 (1995) 37.
[2] [3] [4] [5] [6]
S.N. Boon, et al., Med. Phys. 25 (1998) 464. S.N. Boon, et al., Med. Phys. 27 (2000) 2198. F. Sauli, Nucl. Instr. and Meth. A 386 (1997) 531. M.M. Fraga, et al., IEEE Nucl. Sci. NS-47 (2000) 933. P. van Luijk, et al., KVI Annual Report 1997, p. 73.
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A scintillating GEM for 2D-dosimetry in radiation therapy J.H. Timmera, T.L. van Vuureb, V. Bomb, C.W. van Eijkb, J. de Haasb, J.M. Schippersa,* b
a Kernfysisch Versneller Instituut, Zernikelaan 25, 9747 AA Groningen, Netherlands Interfacultair Reactor Instituut, TU Delft, Mekelweg 15, 2629 JB Delft, Netherlands
Abstract The first results of a study on the properties of a gaseous scintillation detector based on a Gas Electron Multiplier (GEM) are reported. The detector is designed for use in position-sensitive dosimetry applications in radiation therapy. A double GEM system, operating in a 90–10% Ar–CO2 gas mixture at a gas amplification factor of B3000, emits a sufficient amount of detectable light to perform measurements of B1 Gy doses in two dimensions. The light yield does not suffer from quenching processes when particles with high stopping power are detected. This operation mode of GEMs offers the dosimetric advantages of a gas-filled detector and the 2D read-out can be performed with a CCD camera. Compared to the existing dosimeters, this system is relatively simple and no complex multi-electrode read-out is necessary. r 2002 Elsevier Science B.V. All rights reserved. PACS: 87.66.a; 87.58.Mj; 87.58.Sp; 29.40.Cs; 29.40.Gx; 29.40.Mc Keywords: Dosimetry; Gaseous detectors; Gas electron multiplier; Gas scintillation
1. Introduction Accurate 2D position-sensitive dosimetry equipment is becoming increasingly important in modern radiation treatments of cancer. The extremely high fluences in a radiation-therapy beam do not allow single event detection methods, but integration of the signal over some time interval is used instead. Since the electric currents in these systems (e.g. ion chambers) have to be read out whilst the radiation is administered, dynamic irradiation techniques require a pixel *Corresponding author. Tel.: +41-56-3104229; Fax: +4156-3103383. Present address: Paul Scherrer Institut; CH-5232 Villigen-PSI, Switzerland. E-mail address: [email protected] (J.M. Schippers).
type of read-out for 2D dosimetry. For the scanning-beam irradiation-technique used in proton therapy [1], a system based on a scintillating screen [2] has been developed. In the screen, the deposited dose is converted into a light spot, which is observed by a CCD camera. It has been shown [2,3] that the observed light pattern is a very good measure of the dose distribution at the screen position. The signal read-out by means of a CCD has proven to be a reliable, as well as accurate and standard read-out methods can be used. A fundamental drawback of a scintillating screen, however, is that the light yield does not scale with dose in the last part of the proton track, where the stopping power reaches a maximum (the Bragg peak). A quenching of the signal by up to 20% has been observed for proton beams of
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 7 1 8 - 1
J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
clinical relevance [2]. The quenching is caused by an integration (blurring) of the signal over the thickness of the screen and/or a different excitation energy of the phosphor with respect to water (the reference medium for dosimetry) and/or by a temporal unavailability of scintillation centers. This problem could be solved by using a gaseous detector. In order to take advantage of the CCD read-out, we employed the gas scintillation process to extract the signal from the detector. We have thus replaced the screen by a thin layer of gas and we use a Gas Electron Multiplier (GEM) [4] system to initiate a charge amplification followed by gas scintillation.
99
Here, ne equals the number of created electrons in the detection region. L is assumed to be in the order of 5 102 [5]. The detector has been tested in the beam line normally used for radiobiology experiments at the AGOR cyclotron in the KVI in Groningen [6]. The tests were performed in realistic proton-therapy conditions with well-calibrated proton beams of different energies (130–190 MeV), beam crosssections (o8 cm diameter) and dose rates (up to 20 Gy/min; 1 Gy/minB104–106 protons/mm2/s ).
3. Results 3.1. Gas amplification
2. Experimental setup The GEM-based scintillation detector has been tested with a gas mixture of 90–10% Ar–CO2 (Fig. 1). Between a cathode foil and the first GEM, a layer of 3.5 mm gas serves as the detection region. The electrons, which have drifted towards the first GEM, are amplified and they cross a 3 mm drift region towards the second GEM. In the second GEM, again, a charge amplification occurs and the electrons are collected at its exit face. The electric currents to the GEMs were measured and by relating these to the beam-intensity monitors, the gas amplification M was calculated. In the gas-amplification process, the electrons also excite atomic levels, which decay by light emission. The light is detected by a CCD camera [2] with quantum efficiency ZE0:3 at 1.2 m from the GEMs (solid angle O) which are mounted in a gas-tight box. The GEM foils, having an active area of 10 10 cm2 with 80 mm holes at a pitch of 140 mm, have been kindly supplied by F. Sauli, CERN. When L photons are emitted per accelerated electron in the second GEM, the number of electrons per CCD pixel I; can been estimated as
3.2. Light yield
I ¼ ne MLOZ ¼ 104 2102
Gas amplification measurements in single and double GEM systems have been performed in a proton beam with beam intensity Ibeam ; which resulted in a count-rate of 5 104 Hz/mm2. Since most electrons are collected on the last GEM’s electrode surface, the total effective M can then be derived from IGEM2 =Ibeam : As can be seen in Fig. 2a, the total amplification Mdouble is not equal 2 to M 2 ; but rather to Mdouble ¼ 0:3 Msingle due to the loss of charges. For larger count rates, a quenching of the gas amplification seemed to occur (see Fig. 2b). This, however, was due to an artifact in our setup. For beam sizes of several cm2, the overall count rate is so large that this resulted in a current of several mA in the resistors in the voltage-division chain connected to the HV-power supply. At the second GEM, this caused a decrease of DVGEM ¼ 10250 V, so that its gas amplification factor decreased by a factor of 1.5–4. However, when the curves are corrected from ‘‘set-voltage’’ to ‘‘actual voltage’’, as calculated from IGEM2 ; the upper curves in Fig. 2b are obtained. This shows that the gas amplification does not depend on the count-rate until a few times, 105 Hz/mm2.
ðCCD-electrons= proton crossing the GEMÞ:
ð1Þ
Measurements of the light yield were performed at typical therapy conditions: proton doses of 0.1–2 Gy and count-rates of 6.104–4.106 Hz/mm2.
100
J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
incident beam
--HV
cathode foil
-HV
ne primary electrons
cascaded GEMs
gas amplification: M light emission L transparent foil
IGEM2 +HV
CCD camera quantum eff. η Ω
mirror
Fig. 1. The setup of a scintillating GEM detector together with the connections to the power supply as used in the test experiments.
Compared with the scintillating screen, the total amount of detected light from a scintillating double GEM system was typically a factor of 10 less when operating at ME3000: Using Eq. (1), the number of photons per proton has been measured as a function of M (see Fig. 3). L can be derived from the signal in the CCD and IGEM2 (see Fig. 4). We found that L does not depend on the proton count-rate. We also found that LðMÞ does not change with the number of available electrons after a gas amplification process. This is very important, since the electrons created in a single avalanche are more susceptible to recombination and space-charge effects compared to those from different particle tracks. This means that the
scintillation process itself does not suffer from quenching due to a saturation effect. The observed value of LE8 103 ; is smaller than the values reported by Fraga [5]. This might be due to slight differences in gas composition and absorption in the gas layer between GEM2 and the exit foil of the detector box. 3.3. Image quality In Fig. 5, a light-image of a + ¼ 30 mm proton beam is shown. As can be seen, the image shows intensity variations of up to 10%. These variations are fixed to the detector and they are reproducible. They are caused by GEM-hole variations and a non-flat GEM surface due to a limited amount of
101
J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
Vgem(V) 10000 Double GEM
(a)
Single GEM
1000
Total gas-amplification factor
100
10000 2.2e4Hz /mm2 6.6e4Hz /mm2 3.3e5Hz /mm2 1.0e6Hz /mm2 2.2e4 c orrec ted 6.6e4 c orrec ted 3.3e5 c orrec ted 1.0e6 c orrec ted
1000
(b)
100 260
280
300
320
340
360
380
Set Vgem2 or Actual Vgem 2 (V) Fig. 2. (a) The measured total gas amplification factor as a function of the GEM voltage at 2.2 104 Hz/mm2; (b) the measured total gas amplification factor for a double GEM at different count-rates (closed symbols). After a correction from the set voltage to the actual GEM voltage (arrow), the curves with the open symbols are obtained.
Photons/secondary electron
Photons per proton
500 400 300 200 100
Single GEM
0.01 0.008 0.006 0.004 Single GEM Double GEM Double GEM high count rate
0.002
Double GEM
0
0 0
100
200
300 400 500 Gas amplification factor
600
700
Fig. 3. The number of emitted light photons per incident proton as a function of the gas amplification factor.
stretching. This causes a non-uniformity in the thickness of the first gas layer. The images can be corrected for this variation in sensitivity.
0
200
400
600
8000
1000
Gas amplification factor
Fig. 4. The number of emitted light photons per secondary electron as a function of the gas amplification factor.
By comparing the signal fall-off at the edge of the beam with that obtained with a scintillating screen, we found that the spatial resolution was
102
J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
CCD signal per pixel (a.u.)
15000
10000
5000 Ionisation chamber Scintillating screen Scintillating GEM Scintillating GEM, corrected 0 0
50
100
150
200
Depth in waterequiv. material (mm)
Fig. 6. The signal as a function of the amount of waterequivalent material in front of the detector, measured with a parallel ionization chamber (proportional to real dose), the scintillating screen (E) and the scintillating GEM (J). The round dots (K) represent the signal of the scintillating GEM after correction for the GEM voltage decrease due to high count-rates. Fig. 5. An image of a circular beam (+ ¼ 30 mm) and a profile, measured with the scintillating GEM. The gray scale has been adjusted to enhance the inhomogeneities.
better than 1 mm, both for a single GEM and a double GEM. 3.4. Measurement of the Bragg peak By varying the amount of material in front of the GEM, we measured a depth-dose curve at a count rate of 3.104 Hz/mm2 and a beam crosssection of + ¼ 30 mm. In Fig. 6, the results are shown, together with the signals from a scintillating screen and an ionization chamber. This last measurement shows the real dose as a function of depth. The signal from the screen is quenched in the Bragg peak. Also the signal of the GEM shows quenching, but this can again be attributed to the reduction of VGEM2 : Since IGEM2 has also been measured, we were able to apply the same correction as the one shown in Fig. 2b. Due to the uncertainties in this correction procedure, no exact matching is obtained but the quenching disappeared to a large extent. 4. Discussion and conclusions The scintillating GEM is a good candidate for a 2D-dosimetry system. In our prototype, the light
yield is still too low, but after modification of the detector box, a change of gas mixture or addition of wavelength shifters, we expect that a factor of 5 can be gained easily. An important observation is that the light yield is proportional to the amount of secondary electrons. This implies that quenching due to the lack of scintillation centers will not occur. In order to investigate the dependence of the light yield on the gas composition in more detail, light emission spectra will be measured. The observed quenching of the gas amplification can be removed by using HV power supplies with stabilized outputs. But saturation in the gasamplification process and recombination of charges remain the most probable causes for quenching in this detection system. Therefore, the trade off between gas amplification and light yield has to be investigated in more detail.
Acknowledgements The authors acknowledge P. van Luijk and H.H. Kiewiet (KVI) for their assistance at the experiments and F. Sauli (CERN) for his advice on the operation of the GEMs. This work was performed as a part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the
J.H. Timmer et al. / Nuclear Instruments and Methods in Physics Research A 478 (2002) 98–103
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). References [1] E. Pedroni, et al., Med. Phys. 22 (1995) 37.
[2] [3] [4] [5] [6]
S.N. Boon, et al., Med. Phys. 25 (1998) 464. S.N. Boon, et al., Med. Phys. 27 (2000) 2198. F. Sauli, Nucl. Instr. and Meth. A 386 (1997) 531. M.M. Fraga, et al., IEEE Nucl. Sci. NS-47 (2000) 933. P. van Luijk, et al., KVI Annual Report 1997, p. 73.
103