- Email: [email protected]
Discriminator threshold dependency of the zero-frequency DQE of photon-counting pixel detectors
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 576 (2007) 235–238 www.elsevier.com/locate/nima
Discriminator threshold dependency of the zero-frequency DQE of photon-counting pixel detectors Ju¨rgen Durst, Gisela Anton, Thilo Michel Physikalisches Institut, Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnberg, Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany Available online 6 February 2007
Abstract In this paper, we apply the method of calculating the zero-frequency DQE using the concept of an average multiplicity to the Medipix2 detector. This photon counting pixel detector sets a discriminator threshold for the minimum energy needed to trigger a count. The average multiplicity of counts per detected photon and the detection efficiency depend on the threshold setting. Therefore, the DQE depends on this setting. We investigated the impact of physical effects on the DQE and present the according results generated with the Monte Carlo simulation ROSI for monoenergetic and for spectral X-ray sources. An optimum threshold setting can be derived. r 2007 Elsevier B.V. All rights reserved. PACS: 87.59.e; 87.57.s; 07.85.Fv; 42.50.Ar Keywords: X-ray imaging; Photon-counting detector; Signal-to-noise ratio, SNR; Detective quantum efficiency, DQE; Multiplicity of counts; Medipix; Pixel detector
1. Introduction Using counting X-ray detectors, it can happen that one X-ray photon triggers several pixels to count. We call this number of counts the multiplicity of an event. Even clusters with diagonal neighbouring pixels showing a count are possible. For example, first a compton scattering event occurs and in a second step, the scattered photon is absorbed by photo-absorption. The resulting Compton electron and the photo-electron deposit their energy resulting in two charge clouds. If the charge cloud related to the photo-electron is near the boundary between two pixels, both pixels will count due to charge sharing. The resulting event has a signature like the cluster shown in Fig. 1. For photon counting detectors multiple counts have a large impact on image quality. For a given number Nin of incoming photons the number Ntrue, i.e. the number of photons generating at least one count, determines the detection efficiency e ¼ Ntrue/Nin. The number of clusters Ni for each cluster size i can be Corresponding author. Tel.: +49 9131 85 27153; fax: +49 9131 15249.
E-mail address: [email protected] (J. Durst). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.01.158
measured using cluster analysis. With these values one can calculate the average multiplicity per detected photon: 1 P
hmi ¼
i¼1 1 P
iN i ¼ Ni
N meas N true
(1)
i¼1
and the average quadratic multiplicity 1 P
i2 N i
hm2 i ¼ i¼1 1 P
Ni
1 P
i2 N i
¼ i¼1 N true
(2)
i¼1
Nmeas is the number of counts produced by Ntrue detected X-ray photons. The zero-frequency DQE for photon-counting pixel detectors (for derivation see [1]) is given by DQE ¼
hmi2 hm2 i
(3)
with the detection efficiency e, the average multiplicity of counts per event /mS and the average quadratic multi-
ARTICLE IN PRESS J. Durst et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 235–238
236
plicity /m2S. The factor /mS2//m2S is called the multiplicity factor. In this work, we investigated the dependency of these quantities on the discriminator threshold setting.
55 mm 55 mm. The simulation includes diffusion effects at a sensor voltage of 250 V for both sensors (see Refs. [4,5]). We achieved the values of the Ni for varying discriminator threshold settings without taking discriminator threshold noise into account. Using these values we can calculate the discriminator threshold dependency of e, /mS, /m2S and the zero-frequency DQE.
2. Influence of the discriminator threshold The following results are calculated with the Monte Carlo simulation package ROSI [2,3]. The setup comprises a silicon sensor of 700 mm thickness or a GaAs sensor of 300 mm, both modelled including the Medipix2 ASIC and bump bonds. This detector has a pixel size of
2.1. Silicon sensor For a monoenergetic beam of X-ray photons with an energy of 100 keV the results are shown in Fig. 2. We have chosen this energy to show the impact of compton scattering on multiplicity. The average multiplicity (Fig. 2(a)) equals 1 for threshold values larger than half of the impinging X-ray energy. For lower thresholds the average multiplicity has higher values due to multiple counting. It is important to take
Fig. 1. Cluster of a sample event with three triggered counts.
1.2
neglecting diffusion with diffusion
2.4
1
22/
multiplicity
2.2
neglecting diffusion with diffusion
1.8 1.6
0.8 0.6 0.4
1.4 0.2
1.2 1
0 0
10
20 30 40 50 discriminator threshold energy [keV]
60
70
0
0.05
10
70
0.05 neglecting diffusion with diffusion
neglecting diffusion with diffusion
0.04
0.04
0.03
0.03 DQE
efficiency ε
20 30 40 50 60 discriminator threshold energy [keV]
0.02
0.02
0.01
0.01
0
0 0
10
20
30
40
50
discriminator threshold energy [keV]
60
70
0
10
20 30 40 50 60 discriminator threshold energy [keV]
70
Fig. 2. Discriminator threshold dependency of (a) average multiplicity (b) multiplicity factor decreasing the DQE (c) the efficiency and (d) the zero-frequency DQE simulated with the Medipix chip with a 700 mm silicon sensor and sensor voltage 250 V for monoenergetic irradiation with a 100 keV X-ray beam.
ARTICLE IN PRESS J. Durst et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 235–238
2.2. GaAs sensor For the simulation with the GaAs sensor an electron lifetime of infinity is assumed in order to investigate the influence of fluorescence effects on the multiplicity and DQE. Because fluorescence photons are mainly caused by photoeffect we have chosen an energy of 40 keV where photoeffect is the dominant X-ray absorption process. The K-edge of gallium and arsenide are found at energies 10.37 and 11.87 keV, respectively [6]. The results are shown in Fig. 5. If diffusion is neglected the average multiplicity,
intensity
diffusion into account because diffusion affects the multiplicity strongly for low thresholds. The local maximum near 28 keV for the case neglecting diffusion is due to compton scattering. Fig. 2(b) shows the relative decrease of the DQE due to multiplicity effects. For small thresholds a drop of about 20% can be observed. The efficiency to detect an event at least in one pixel is shown in Fig. 2(c). Due to the high primary energy of 100 keV and the low cross-section of silicon for this energy the efficiency reaches values of only a few percent. Therefore, the DQE (Fig. 2(d)) is dominated by the efficiency at this energy. Fig. 3 shows the multiplicity factor for a range of monoenergetic X-ray beams. For thresholds above half the X-ray energy a value of one is reached. For low thresholds due to the multiplicity factor the DQE is decreased by about 20% almost independent of X-ray energy. For most medical applications a spectrum from an X-ray tube is used, i.e. different photon energies contribute to the resulting quantities like efficiency, multiplicity and DQE. These quantities are presented in Fig. 4 for a 35 kV molybdenum spectrum. There is a broad optimum for the threshold setting between 5 and 10 keV. The threshold should be adjusted in this region in order to get an optimum DQE value.
237
0
5
10
15 20 x-ray energy [keV]
25
30
35
12/ efficiency ε DQE
0.8
0.6
0.4
0.2
0 0
5 10 15 20 discriminator threshold energy [keV]
25
Fig. 4. For a filtered 35 kV Mo spectrum (top) detection efficiency, multiplicity factor and zero-frequency DQE are shown (bottom).
efficiency and DQE change significantly at discriminator threshold energies near the K-edges of the contributing elements. For the efficiency and the DQE edges at the energy of the impinging X-ray photon minus the energy of the Ka fluorescence of gallium and arsenide are visible in Fig. 5. 3. Conclusion
Fig. 3. Dependency of the multiplicity factor on discriminator threshold and X-ray energy.
For silicon the zero-frequency DQE mainly depends on the detection efficiency. For spectra like the spectrum shown in Fig. 4 the detection efficiency is approximately constant for low thresholds. The multiplicity factor decreases the DQE up to 25% for low thresholds. The generation of fluorescence photons in the sensor material causes structures in the DQE. If charge carrier diffusion plays an important role, e.g. for small pixel size, these structures are blurred. The multiplicity framework is an adequate tool to investigate the dependence of discriminator threshold energy on the imaging properties of the detector expressed as the DQE.
ARTICLE IN PRESS J. Durst et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 235–238
238
2.2
1
2
0.82/
multiplicity
1.2
neglecting diffusion with diffusion
2.4
1.8 1.6
neglecting diffusion with diffusion 1
0.6 0.4
1.4 0.2
1.2 1
0 0
10
20
30
40
50
0
discriminator threshold energy [keV]
10
20
1
40
50
1 neglecting diffusion with diffusion
neglecting diffusion with diffusion
0.8
0.8
0.6
0.6 DQE
efficiency ε
30
discriminator threshold energy [keV]
0.4
0.4
0.2
0.2
0
0 0
10
20
30
40
50
discriminator threshold energy [keV]
0
10
20
30
40
50
discriminator threshold energy [keV]
Fig. 5. Discriminator threshold dependency of (a) average multiplicity (b) the multiplicity factor decreasing DQE, (c) efficiency and (d) zero-frequency DQE simulated with the Medipix chip with a 300 mm GaAs sensor and sensor voltage 250 V for monoenergetic irradiation with a 40 keV X-ray beam.
References [1] T. Michel, G. Anton, M. Bo¨hnel, J. Durst, M. Firsching, A. Korn, B. Kreisler, A. Loehr, F. Nachtrab, D. Niederlo¨hner, F. Sukowski, P. Takoukam Talla, Nucl. Instr. and Meth. A 568 (2006) 799. [2] J. Giersch, A. Weidemann, G. Anton, Nucl. Instr. and Meth. A 509 (2003) 151.
[3] Download address of the Monte Carlo package ROSI: /http:// www.pi4.physik.uni-erlangen.de/Giersch/ROSIS. [4] A. Korn, et al., Nucl. Instr. and Meth. A, doi:10.1016/j.nima. 2007.01.159. [5] H.G. Spieler, E.E. Haller, IEEE Trans. Nucl. Sci. NS-32 (1) (1985) 419. [6] R.B. Firestone, V.S. Shirley (Eds.), Table of Isotopes, eighth ed, Wiley, 1996.
Nuclear Instruments and Methods in Physics Research A 576 (2007) 235–238 www.elsevier.com/locate/nima
Discriminator threshold dependency of the zero-frequency DQE of photon-counting pixel detectors Ju¨rgen Durst, Gisela Anton, Thilo Michel Physikalisches Institut, Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnberg, Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany Available online 6 February 2007
Abstract In this paper, we apply the method of calculating the zero-frequency DQE using the concept of an average multiplicity to the Medipix2 detector. This photon counting pixel detector sets a discriminator threshold for the minimum energy needed to trigger a count. The average multiplicity of counts per detected photon and the detection efficiency depend on the threshold setting. Therefore, the DQE depends on this setting. We investigated the impact of physical effects on the DQE and present the according results generated with the Monte Carlo simulation ROSI for monoenergetic and for spectral X-ray sources. An optimum threshold setting can be derived. r 2007 Elsevier B.V. All rights reserved. PACS: 87.59.e; 87.57.s; 07.85.Fv; 42.50.Ar Keywords: X-ray imaging; Photon-counting detector; Signal-to-noise ratio, SNR; Detective quantum efficiency, DQE; Multiplicity of counts; Medipix; Pixel detector
1. Introduction Using counting X-ray detectors, it can happen that one X-ray photon triggers several pixels to count. We call this number of counts the multiplicity of an event. Even clusters with diagonal neighbouring pixels showing a count are possible. For example, first a compton scattering event occurs and in a second step, the scattered photon is absorbed by photo-absorption. The resulting Compton electron and the photo-electron deposit their energy resulting in two charge clouds. If the charge cloud related to the photo-electron is near the boundary between two pixels, both pixels will count due to charge sharing. The resulting event has a signature like the cluster shown in Fig. 1. For photon counting detectors multiple counts have a large impact on image quality. For a given number Nin of incoming photons the number Ntrue, i.e. the number of photons generating at least one count, determines the detection efficiency e ¼ Ntrue/Nin. The number of clusters Ni for each cluster size i can be Corresponding author. Tel.: +49 9131 85 27153; fax: +49 9131 15249.
E-mail address: [email protected] (J. Durst). 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.01.158
measured using cluster analysis. With these values one can calculate the average multiplicity per detected photon: 1 P
hmi ¼
i¼1 1 P
iN i ¼ Ni
N meas N true
(1)
i¼1
and the average quadratic multiplicity 1 P
i2 N i
hm2 i ¼ i¼1 1 P
Ni
1 P
i2 N i
¼ i¼1 N true
(2)
i¼1
Nmeas is the number of counts produced by Ntrue detected X-ray photons. The zero-frequency DQE for photon-counting pixel detectors (for derivation see [1]) is given by DQE ¼
hmi2 hm2 i
(3)
with the detection efficiency e, the average multiplicity of counts per event /mS and the average quadratic multi-
ARTICLE IN PRESS J. Durst et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 235–238
236
plicity /m2S. The factor /mS2//m2S is called the multiplicity factor. In this work, we investigated the dependency of these quantities on the discriminator threshold setting.
55 mm 55 mm. The simulation includes diffusion effects at a sensor voltage of 250 V for both sensors (see Refs. [4,5]). We achieved the values of the Ni for varying discriminator threshold settings without taking discriminator threshold noise into account. Using these values we can calculate the discriminator threshold dependency of e, /mS, /m2S and the zero-frequency DQE.
2. Influence of the discriminator threshold The following results are calculated with the Monte Carlo simulation package ROSI [2,3]. The setup comprises a silicon sensor of 700 mm thickness or a GaAs sensor of 300 mm, both modelled including the Medipix2 ASIC and bump bonds. This detector has a pixel size of
2.1. Silicon sensor For a monoenergetic beam of X-ray photons with an energy of 100 keV the results are shown in Fig. 2. We have chosen this energy to show the impact of compton scattering on multiplicity. The average multiplicity (Fig. 2(a)) equals 1 for threshold values larger than half of the impinging X-ray energy. For lower thresholds the average multiplicity has higher values due to multiple counting. It is important to take
Fig. 1. Cluster of a sample event with three triggered counts.
1.2
neglecting diffusion with diffusion
2.4
1
2
multiplicity
2.2
neglecting diffusion with diffusion
1.8 1.6
0.8 0.6 0.4
1.4 0.2
1.2 1
0 0
10
20 30 40 50 discriminator threshold energy [keV]
60
70
0
0.05
10
70
0.05 neglecting diffusion with diffusion
neglecting diffusion with diffusion
0.04
0.04
0.03
0.03 DQE
efficiency ε
20 30 40 50 60 discriminator threshold energy [keV]
0.02
0.02
0.01
0.01
0
0 0
10
20
30
40
50
discriminator threshold energy [keV]
60
70
0
10
20 30 40 50 60 discriminator threshold energy [keV]
70
Fig. 2. Discriminator threshold dependency of (a) average multiplicity (b) multiplicity factor decreasing the DQE (c) the efficiency and (d) the zero-frequency DQE simulated with the Medipix chip with a 700 mm silicon sensor and sensor voltage 250 V for monoenergetic irradiation with a 100 keV X-ray beam.
ARTICLE IN PRESS J. Durst et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 235–238
2.2. GaAs sensor For the simulation with the GaAs sensor an electron lifetime of infinity is assumed in order to investigate the influence of fluorescence effects on the multiplicity and DQE. Because fluorescence photons are mainly caused by photoeffect we have chosen an energy of 40 keV where photoeffect is the dominant X-ray absorption process. The K-edge of gallium and arsenide are found at energies 10.37 and 11.87 keV, respectively [6]. The results are shown in Fig. 5. If diffusion is neglected the average multiplicity,
intensity
diffusion into account because diffusion affects the multiplicity strongly for low thresholds. The local maximum near 28 keV for the case neglecting diffusion is due to compton scattering. Fig. 2(b) shows the relative decrease of the DQE due to multiplicity effects. For small thresholds a drop of about 20% can be observed. The efficiency to detect an event at least in one pixel is shown in Fig. 2(c). Due to the high primary energy of 100 keV and the low cross-section of silicon for this energy the efficiency reaches values of only a few percent. Therefore, the DQE (Fig. 2(d)) is dominated by the efficiency at this energy. Fig. 3 shows the multiplicity factor for a range of monoenergetic X-ray beams. For thresholds above half the X-ray energy a value of one is reached. For low thresholds due to the multiplicity factor the DQE is decreased by about 20% almost independent of X-ray energy. For most medical applications a spectrum from an X-ray tube is used, i.e. different photon energies contribute to the resulting quantities like efficiency, multiplicity and DQE. These quantities are presented in Fig. 4 for a 35 kV molybdenum spectrum. There is a broad optimum for the threshold setting between 5 and 10 keV. The threshold should be adjusted in this region in order to get an optimum DQE value.
237
0
5
10
15 20 x-ray energy [keV]
25
30
35
1
0.8
0.6
0.4
0.2
0 0
5 10 15 20 discriminator threshold energy [keV]
25
Fig. 4. For a filtered 35 kV Mo spectrum (top) detection efficiency, multiplicity factor and zero-frequency DQE are shown (bottom).
efficiency and DQE change significantly at discriminator threshold energies near the K-edges of the contributing elements. For the efficiency and the DQE edges at the energy of the impinging X-ray photon minus the energy of the Ka fluorescence of gallium and arsenide are visible in Fig. 5. 3. Conclusion
Fig. 3. Dependency of the multiplicity factor on discriminator threshold and X-ray energy.
For silicon the zero-frequency DQE mainly depends on the detection efficiency. For spectra like the spectrum shown in Fig. 4 the detection efficiency is approximately constant for low thresholds. The multiplicity factor decreases the DQE up to 25% for low thresholds. The generation of fluorescence photons in the sensor material causes structures in the DQE. If charge carrier diffusion plays an important role, e.g. for small pixel size, these structures are blurred. The multiplicity framework is an adequate tool to investigate the dependence of discriminator threshold energy on the imaging properties of the detector expressed as the DQE.
ARTICLE IN PRESS J. Durst et al. / Nuclear Instruments and Methods in Physics Research A 576 (2007) 235–238
238
2.2
1
2
0.8
multiplicity
1.2
neglecting diffusion with diffusion
2.4
1.8 1.6
neglecting diffusion with diffusion 1
0.6 0.4
1.4 0.2
1.2 1
0 0
10
20
30
40
50
0
discriminator threshold energy [keV]
10
20
1
40
50
1 neglecting diffusion with diffusion
neglecting diffusion with diffusion
0.8
0.8
0.6
0.6 DQE
efficiency ε
30
discriminator threshold energy [keV]
0.4
0.4
0.2
0.2
0
0 0
10
20
30
40
50
discriminator threshold energy [keV]
0
10
20
30
40
50
discriminator threshold energy [keV]
Fig. 5. Discriminator threshold dependency of (a) average multiplicity (b) the multiplicity factor decreasing DQE, (c) efficiency and (d) zero-frequency DQE simulated with the Medipix chip with a 300 mm GaAs sensor and sensor voltage 250 V for monoenergetic irradiation with a 40 keV X-ray beam.
References [1] T. Michel, G. Anton, M. Bo¨hnel, J. Durst, M. Firsching, A. Korn, B. Kreisler, A. Loehr, F. Nachtrab, D. Niederlo¨hner, F. Sukowski, P. Takoukam Talla, Nucl. Instr. and Meth. A 568 (2006) 799. [2] J. Giersch, A. Weidemann, G. Anton, Nucl. Instr. and Meth. A 509 (2003) 151.
[3] Download address of the Monte Carlo package ROSI: /http:// www.pi4.physik.uni-erlangen.de/Giersch/ROSIS. [4] A. Korn, et al., Nucl. Instr. and Meth. A, doi:10.1016/j.nima. 2007.01.159. [5] H.G. Spieler, E.E. Haller, IEEE Trans. Nucl. Sci. NS-32 (1) (1985) 419. [6] R.B. Firestone, V.S. Shirley (Eds.), Table of Isotopes, eighth ed, Wiley, 1996.