- Email: [email protected]
Comparison of simulated and measured spectra from an X-ray tube for the energies between 20 and 35 keV
Nuclear Instruments and Methods in Physics Research A 799 (2015) 50–53
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Comparison of simulated and measured spectra from an X-ray tube for the energies between 20 and 35 keV M. Yücel, E. Emirhan, A. Bayrak, C.S. Ozben, E. Barlas Yücel n Istanbul Technical University, Faculty of Science and Letters, Department of Physics Engineering, 34469 Maslak Sarıyer, Istanbul, Turkey
art ic l e i nf o
a b s t r a c t
Article history: Received 25 May 2015 Received in revised form 22 July 2015 Accepted 27 July 2015 Available online 5 August 2015
Design and production of a simple and low cost X-ray imaging system that can be used for light industrial applications was targeted in the Nuclear Physics Laboratory of Istanbul Technical University. In this study, production, transmission and detection of X-rays were simulated for the proposed imaging device. OX/70-P dental tube was used and X-ray spectra simulated by Geant4 were validated by comparison with X-ray spectra measured between 20 and 35 keV. Relative detection efficiency of the detector was also determined to confirm the physics processes used in the simulations. Various time optimization tools were performed to reduce the simulation time. & 2015 Elsevier B.V. All rights reserved.
Keywords: Geant4 X-ray spectrum Monte Carlo simulation X-ray tube Detector
1. Introduction Applications using X-ray imaging techniques have been widely used in industry. As is known, use of advanced medical X-ray techniques is undoubtedly very common in our daily lives. Additionally, X-ray radiography is commonly used for non-destructive inspection of wide range of industrial samples. Inspecting nonmagnetic impurities in food is a good example to the use of X-ray radiography. Hence, design and production of low cost X-ray imaging systems have always been a point of interest. We have planned to produce an X-ray imaging system based on a dental Xray tube, custom-made high voltage power supply and silicon pin photo diode based detector array. Obviously, simulations are useful tools to reduce R&D costs for prototypes. Geant4 simulations are used to minimize the effort of having a better imaging system. In that sense, it is crucial to know the photon spectrum produced by the X-ray tube as accurately as possible to optimize the X-ray imaging system. The validation of the present work is checked by the comparison of measured and simulated spectra. Monte Carlo (MC) simulations are one of the most accurate tools to predict the behavior of particles in matter. Studies based on Monte Carlo simulations help designing new experiments. Design costs and time are reduced dramatically with the help of MC tools. Recent studies showed that MC simulations are capable
n
Corresponding author. Tel.: þ 90 212 285 7384; fax: þ90 212 285 6386. E-mail address: [email protected] (E.B. Yücel).
http://dx.doi.org/10.1016/j.nima.2015.07.055 0168-9002/& 2015 Elsevier B.V. All rights reserved.
of generating good results for determining experimental parameters [1,2]. We have used Geant4 (Geometry and Tracking) simulation package in this work [3]. Electrons with given energy and momentum distributions are driven to the tungsten anode and production of X-rays are fully simulated by MC simulations. Many similar studies using Geant4 simulation package showed good agreement for various target materials in different experimental setups [4–6]. For this study, the geometry of the OX/70-P dental tube [7] was constructed and X-ray beams were produced for different accelerating voltages. Simulations were compared with the experimental results. Experimental X-ray spectra were measured with Amptek X123 X-ray spectrometer [8]. Active part of Amptek spectrometer is a Si-PIN detector and it is also included into the Geant4 simulations. As a result, we have shown that experimental and simulation results are in excellent agreement and characterization of any Xray tube can be obtained by modifying the tube parameters used in the simulation code.
2. Experimental setup In our experiments as an X-ray source, OX/70-P model dental tube with 191 tungsten anode angle was used. High voltages between 20 and 35 kV were applied to the tube to drive the electrons emitted from the heated filament towards the anode. The electrons hitting the anode produce X-rays via Bremsstrahlung process and characteristic X-rays of tungsten were also generated. X-ray spectra of the tube were measured with Amptek X-123 X-ray
M. Yücel et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 50–53
Table 1 X-ray lines of the radioisotopes used for the energy calibration. Radioisotope
3.1. Simulation setup As described in the experimental setup section, the geometries of the tube and the detector seen in Fig. 2 were defined in the Geant4 code. The visualization of the system was performed with OpenGL Stored Qt (OGLSQt) driver, enabling users to have full control over the scene using intuitive graphical user interface. Overlapping geometries and tracks or hits of particles can be seen easily with OGLSQt in situ. Inside the X-ray tube, electrons across the filament were directed towards the tungsten anode. 0.5 keV RMS value for the energy distribution of the electrons was used in MC simulations due to the fluctuations in the tube voltage and current. An equivalent absorber of 0.5 mm thick aluminum (an inherent filter) was used instead of original glass bulb of the tube. Geometry of Amptek XR-100CR [14] detector which is embedded in Amptek X-123 spectrometer was not included into the simulations completely. Only the Si-PIN section with 25 μm thick beryllium window was taken into account. Intrinsic full energy detection efficiency for the detector was simulated and good agreement between the simulations and the efficiency curve given by the manufacturer [8] was obtained and it is shown in Fig. 3. Photons reaching the detector window and deposit all their
Cd
0.112 0.358 0.852
1.4 1.2 1 0.8
L
L
0.6
6 9 .0 ke V
5 7 .9 ke V
1.6
5 9 .3 ke V
0.133
12.61 74.97 22.10
1.8
Counts (A.U.)
Geant4 is a toolkit which enables detailed simulations of interactions of particles with matter in the presence of electromagnetic field [3]. It has the ability to handle complex geometries and including the physics interactions. Geant4 uses a set of class libraries: CLHEP (Computing Library for High Energy Physics) includes different kinds of random number generators, physics vectors, geometry, unit definitions and linear algebra [11]. We used Geant4.10.01 version with CLHEP.2.0.4.2 in this study. Geant4 has many electromagnetic physics list options for different purposes. We have used Emstandard_opt3 [12] electromagnetic physics list in this study, since it has been claimed to be the most appropriate physics list to demonstrate Bremsstrahlung events. With this recent physics list, Monte Carlo generation with high statistics was established and CPU time for the simulations was reduced significantly. Elastic scattering, ionization and Bremsstrahlung physics processes were defined in the simulations for the electrons. Rayleigh scattering, photoelectric effect, Compton scattering and pair production were defined for photons. G4KleinNishinaModel was used to simulate atomic deexcitation including the production of fluorescence photons and Auger electrons. We also used energy cuts for the electrons and photons to reduce the CPU time. Result of the physics used in the simulations was cross checked with the literature [13]. In the simulations, electrons were driven to the tungsten anode with 100 keV energy and then produced Xrays were filtered with 1 mm thick aluminum. Characteristic Xrays of tungsten were obtained successfully in addition to Bremsstrahlung continuum as seen in Fig. 1. The characteristic photo peaks below 10 keV are not seen due to the aluminum absorber.
0.254
10.55
K
109
3. Geant4 simulations
5.90
Bi
Fe
207
Intensity
6 7 .2 ke V
55
Energy (keV)
K
spectrometer. We have used aluminum blocks with various thicknesses to reduce the dead time of the detector during the data taking. Detector source distance was taken as 30 cm and aluminum blocks were positioned between the source and the detector. Energy calibration of the spectra was performed with 55Fe, 207Bi and 109Cd calibrated standard sources [9] by using the photo peaks with energies [10] given in Table 1. Some energies in the table were calculated from the weighted mean for close X-ray lines due to the insufficient energy resolution.
51
0.4 0.2 0 10
20
30
40
50
60
70
80
90
100
Energy (keV) Fig. 1. Simulation result of X-ray spectrum (filtered with 1 mm thick Al absorber) obtained from 100 keV electron beam in tungsten target.
Fig. 2. Setup of Geant4 simulation geometry.
energies in silicon material were counted for efficiency calculations in the simulations. 3.2. CPU time optimization While it is relatively quick to take a spectrum using the experimental setup, it takes considerable amount of time to simulate the same amount of events. X-ray production efficiency increases with energy of electrons hitting the anode. When the angular distribution of X-rays and layers of absorbers in front of the detector are taken into account, number of X-rays reaching the detector becomes quite small due to the attenuation. In order to obtain reasonable statistics, billions of electrons have to be generated in the filament. As a nature of particle tracking, both electrons and generated X-rays have to be tracked in the medium one by one in Geant4. Hence, several optimization steps were required to shorten the simulation time. The experiments were performed with aluminum absorbers in order to reduce the dead time of the detector. For direct comparison of the simulation results and the experimental measurements, the
52
M. Yücel et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 50–53
0.16 Amptek XR-100CR EmStandard-Opt3
0.14
Simulation without the absorber
0.12
Simulation with the absorber
Penelope
0.8 Counts (A.U.)
Intrinsic Full Energy Efficiency
1
0.6 0.4
0.1 0.08 0.06 0.04
0.2 0.02
0
0 0
1
10
5
10
15
102
20
25
30
35
40
Energy(keV)
Energy(keV) Fig. 3. Monte Carlo results of energy dependence of the detector obtained from counting the photons deposit all of their energies in the detector material. Dots represent the results from Penelope physics and open squares show the results from EmStandard-Opt3 physics. The intrinsic full energy detection efficiency curve from the manufacturer is given as solid line.
Fig. 4. Comparison of simulation results with absorber (open squares) and without absorber (dots). The simulation without absorber includes Beer–Lambert's law correction.
Measurement (20 keV) Simulation (20 keV)
2
IðEÞ ¼ I 0 e μðEÞρl
ð1Þ
where, I0 is the initial and I(E) is the final beam intensities, μðEÞ is the mass attenuation coefficient, ρ is the density and l is the thickness of the absorber. NIST database [15] provides photon attenuation coefficients for various energies. Interpolation was made on this data set to obtain the mass attenuation coefficients for energies of interest. One of the great advantages of this procedure is having the statistical power of the photons when there is no absorber. Absorbers reduce the number of photons reaching the detector dramatically, resulting large statistical fluctuations in count rate. In order to justify the procedure, full simulation including the absorber at 35 keV was generated and compared with the simulation including Beer–Lambert's correction as mentioned above. Fig. 4 shows that both methods give similar results. On the other hand, full simulation including an absorber has to be run nearly thousand times longer in order to have similar statistical power. Hence, we prefer to run the simulations without absorbers and apply corrections to the data after that. Analysis of the simulated spectra shows that very few number of photons with energies lower than 10 keV reach the detector after the corrections based on Beer–Lambert's law. For that reason, we had 10 keV low energy cut for the production of energy spectra in our simulations to get rid of the time consuming unnecessary tracks. This procedure helps us reducing the CPU time.
4. Results and discussion 4.1. Efficiency simulations of Amptek XR-100CR detector Amptek XR-100CR detector is embedded in Amptek X-123 spectrometer. This detector has 500 μm thick silicon, 13 mm2 cross-sectional area and 25 μm thick Be window. In order to determine detector response to photons, a simulation was performed for obtaining intrinsic full energy efficiency of the detector.
Measurement (25 keV) Simulation (25 keV) Measurement (30keV)
Counts (A.U.)
simulations should be performed with the same geometry as the experiments. This requires including the mentioned absorbers into the simulations. However, instead of running the simulations with various absorber materials and thicknesses, one can obtain the simulation data without the absorbers and apply corrections later. For this reason, we have decided to remove the aluminum absorbers from the simulation geometry and corrected the data based on well known Beer–Lambert law:
Simulation (30 keV)
1.5
Measurement (35 keV) Simulation (35 keV)
1
0.5
0 0
5
10
15
20
25
30
35
40
Energy(keV)
Fig. 5. Comparison of measured and simulated spectra for various energies.
X-rays between 1 and 100 keV were directed to the detector and photons with full energy deposition were registered in the simulations. Fig. 3 shows the comparison between the simulation result and the efficiency curve provided by the manufacturer [8]. These simulations were made with both standard and Penelope physics list [16]. Penelope physics is included into the MC simulations because it is known to provide better results for escape peaks [17]. It can be seen that the simulation results based on Penelope physics is in good agreement below 2 keV and the standard physics list used in this study provides better results for the energies above 2 keV which is our main region of interest. 4.2. Comparison of simulated and measured spectra Fig. 5 shows the comparison of the simulated and experimental spectra for energies of 20 keV, 25 keV, 30 keV and 35 keV. Since operation voltage of the tube was lower than 35 keV, no characteristic X-ray peaks of tungsten are seen in the figure. However, experimental spectra include small peaks between 3 keV and 14 keV. They are originated from the shielding materials (mostly lead) used in the experimental setup. Since the shielding blocks were not included in the simulation geometry, they are not visible in the MC results. Additionally, the simulations have 10 keV low energy cut for reducing the CPU time. All of the measurements were taken using aluminum absorbers with different thicknesses for reducing dead time of the detector. This procedure resulted in different statistics for the measured spectra. For that reason, each measured spectrum was scaled to be able to make visual comparison between the spectra taken with
M. Yücel et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 50–53
various X-ray energies. The same procedure was applied to the simulated spectrum for each energy (20 keV, 25 keV, 30 keV and 35 keV). Fig. 5 shows an excellent agreement between the simulated and experimental spectra. The validation of the code was also checked by generating the characteristic X-ray lines of the target material as well as the Bremsstrahlung continuum in the simulations. This was successfully performed and shown in Fig. 1 in the present work. 5. Conclusions OX/70-P dental tube with relatively low operating voltage was used to validate our simulations based on Geant4. A complete simulation including the production, transportation and detection of X-rays was successfully conducted. An important result of this study is that X-ray spectra of different kinds of X-ray tubes can be obtained accurately with the written code in Geant4 simulations. When the parameters such as tube operation voltage (including its statistical fluctuations), type of target material, thickness of glass bulb and geometry of target are given as inputs, all that is needed is to run the code with reasonable number of events. Using the spectra produced from the simulation, one can design a prototype imaging system without doing actual measurements. This procedure obviously reduces R&D cost and time dramatically. Acknowledgments We would like to thank the Scientific and Technological Council of Turkey (TUBITAK) for supporting this work (113F104).
53
References [1] J. Giersch, J. Durst, Nuclear Instruments and Methods in Physics Research Section A 591 (2008) 300. [2] A. Sofiienko, C. Jarvis, A. Voll, Physics Research International (2014) 847651. [3] S. Agostinelli, et al., Nuclear Instruments and Methods in Physics Research Section A 506 (2003) 250. [4] A. Miceli, et al., Nuclear Instruments and Methods in Physics Research Section A 580 (2007) 123. [5] A. Miceli, et al., Nuclear Instruments and Methods in Physics Research Section A 583 (2007) 313. [6] M. Guthoff, et al., Nuclear Instruments and Methods in Physics Research Section A 675 (2012) 118. [7] OX/70-P Dental Tubes Technical Data, Retrieved from: 〈http://www.ceixray. com/ox70-p-2/〉, (24 April 2015). [8] X-123 Complete X-ray Spectrometer with Si-PIN Detector, Retrieved from: 〈http://www.amptek.com/products/x-123-complete-x-ray-spectrometer-wthsi-pin-detector/〉, (1 July 2015). [9] Gamma Standard Sources Set, Ritverc Isotope Products, (Production Date 2007), Retrieved from: 〈http://www.ritverc.com/products/detail.phpID=1702〉, (24 April 2015). [10] R.B. Firestone, L.P. Ekstrom, Database Version 2.1, 2004, Retrieved from: 〈http://ie.lbl.gov/toi/perchart.htm〉, (24 April 2015). [11] L. Lönnblad, Computer Physics Communications 84 (1994) 307. [12] J. Allison, et al., Geant4 electromagnetic physics for high statistic simulation of LHC experiments, Journal of Physics: Conference Series 396 (2013) 022013. [13] F.M. Khan, The Physics of Radiation Therapy, fourth ed., Lippincott Williams & Wilkins, Philadelphia, PA, 2010 (Page 32). [14] XR-100CR Si-PIN X-Ray Detector, Retrieved from: 〈http://www.amptek.com/ products/xr-100cr-si-pin-x-ray-detector/〉, (1 July 2015). [15] J.H. Hubbell, S.M. Seltzer (2004), Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients, National Institute of Standards and Technology, Gaithersburg, MD. Originally published as NISTIR 5632, National Institute of Standards and Technology, Gaithersburg, MD, Retrieved from: 〈http://physics.nist.gov/xaamdi〉, 1995 (accessed 30.03.15). [16] L. Pandola, C. Andenna, B. Caccia, Nuclear Instruments and Methods in Physics Research Section B 350 (2015) 41. [17] A.I. Skrypnyk, A.A. Zakharchenko, M.A. Khazhmuradov, Problems in Atomic Science and Technology 5 (2011) 93.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Comparison of simulated and measured spectra from an X-ray tube for the energies between 20 and 35 keV M. Yücel, E. Emirhan, A. Bayrak, C.S. Ozben, E. Barlas Yücel n Istanbul Technical University, Faculty of Science and Letters, Department of Physics Engineering, 34469 Maslak Sarıyer, Istanbul, Turkey
art ic l e i nf o
a b s t r a c t
Article history: Received 25 May 2015 Received in revised form 22 July 2015 Accepted 27 July 2015 Available online 5 August 2015
Design and production of a simple and low cost X-ray imaging system that can be used for light industrial applications was targeted in the Nuclear Physics Laboratory of Istanbul Technical University. In this study, production, transmission and detection of X-rays were simulated for the proposed imaging device. OX/70-P dental tube was used and X-ray spectra simulated by Geant4 were validated by comparison with X-ray spectra measured between 20 and 35 keV. Relative detection efficiency of the detector was also determined to confirm the physics processes used in the simulations. Various time optimization tools were performed to reduce the simulation time. & 2015 Elsevier B.V. All rights reserved.
Keywords: Geant4 X-ray spectrum Monte Carlo simulation X-ray tube Detector
1. Introduction Applications using X-ray imaging techniques have been widely used in industry. As is known, use of advanced medical X-ray techniques is undoubtedly very common in our daily lives. Additionally, X-ray radiography is commonly used for non-destructive inspection of wide range of industrial samples. Inspecting nonmagnetic impurities in food is a good example to the use of X-ray radiography. Hence, design and production of low cost X-ray imaging systems have always been a point of interest. We have planned to produce an X-ray imaging system based on a dental Xray tube, custom-made high voltage power supply and silicon pin photo diode based detector array. Obviously, simulations are useful tools to reduce R&D costs for prototypes. Geant4 simulations are used to minimize the effort of having a better imaging system. In that sense, it is crucial to know the photon spectrum produced by the X-ray tube as accurately as possible to optimize the X-ray imaging system. The validation of the present work is checked by the comparison of measured and simulated spectra. Monte Carlo (MC) simulations are one of the most accurate tools to predict the behavior of particles in matter. Studies based on Monte Carlo simulations help designing new experiments. Design costs and time are reduced dramatically with the help of MC tools. Recent studies showed that MC simulations are capable
n
Corresponding author. Tel.: þ 90 212 285 7384; fax: þ90 212 285 6386. E-mail address: [email protected] (E.B. Yücel).
http://dx.doi.org/10.1016/j.nima.2015.07.055 0168-9002/& 2015 Elsevier B.V. All rights reserved.
of generating good results for determining experimental parameters [1,2]. We have used Geant4 (Geometry and Tracking) simulation package in this work [3]. Electrons with given energy and momentum distributions are driven to the tungsten anode and production of X-rays are fully simulated by MC simulations. Many similar studies using Geant4 simulation package showed good agreement for various target materials in different experimental setups [4–6]. For this study, the geometry of the OX/70-P dental tube [7] was constructed and X-ray beams were produced for different accelerating voltages. Simulations were compared with the experimental results. Experimental X-ray spectra were measured with Amptek X123 X-ray spectrometer [8]. Active part of Amptek spectrometer is a Si-PIN detector and it is also included into the Geant4 simulations. As a result, we have shown that experimental and simulation results are in excellent agreement and characterization of any Xray tube can be obtained by modifying the tube parameters used in the simulation code.
2. Experimental setup In our experiments as an X-ray source, OX/70-P model dental tube with 191 tungsten anode angle was used. High voltages between 20 and 35 kV were applied to the tube to drive the electrons emitted from the heated filament towards the anode. The electrons hitting the anode produce X-rays via Bremsstrahlung process and characteristic X-rays of tungsten were also generated. X-ray spectra of the tube were measured with Amptek X-123 X-ray
M. Yücel et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 50–53
Table 1 X-ray lines of the radioisotopes used for the energy calibration. Radioisotope
3.1. Simulation setup As described in the experimental setup section, the geometries of the tube and the detector seen in Fig. 2 were defined in the Geant4 code. The visualization of the system was performed with OpenGL Stored Qt (OGLSQt) driver, enabling users to have full control over the scene using intuitive graphical user interface. Overlapping geometries and tracks or hits of particles can be seen easily with OGLSQt in situ. Inside the X-ray tube, electrons across the filament were directed towards the tungsten anode. 0.5 keV RMS value for the energy distribution of the electrons was used in MC simulations due to the fluctuations in the tube voltage and current. An equivalent absorber of 0.5 mm thick aluminum (an inherent filter) was used instead of original glass bulb of the tube. Geometry of Amptek XR-100CR [14] detector which is embedded in Amptek X-123 spectrometer was not included into the simulations completely. Only the Si-PIN section with 25 μm thick beryllium window was taken into account. Intrinsic full energy detection efficiency for the detector was simulated and good agreement between the simulations and the efficiency curve given by the manufacturer [8] was obtained and it is shown in Fig. 3. Photons reaching the detector window and deposit all their
Cd
0.112 0.358 0.852
1.4 1.2 1 0.8
L
L
0.6
6 9 .0 ke V
5 7 .9 ke V
1.6
5 9 .3 ke V
0.133
12.61 74.97 22.10
1.8
Counts (A.U.)
Geant4 is a toolkit which enables detailed simulations of interactions of particles with matter in the presence of electromagnetic field [3]. It has the ability to handle complex geometries and including the physics interactions. Geant4 uses a set of class libraries: CLHEP (Computing Library for High Energy Physics) includes different kinds of random number generators, physics vectors, geometry, unit definitions and linear algebra [11]. We used Geant4.10.01 version with CLHEP.2.0.4.2 in this study. Geant4 has many electromagnetic physics list options for different purposes. We have used Emstandard_opt3 [12] electromagnetic physics list in this study, since it has been claimed to be the most appropriate physics list to demonstrate Bremsstrahlung events. With this recent physics list, Monte Carlo generation with high statistics was established and CPU time for the simulations was reduced significantly. Elastic scattering, ionization and Bremsstrahlung physics processes were defined in the simulations for the electrons. Rayleigh scattering, photoelectric effect, Compton scattering and pair production were defined for photons. G4KleinNishinaModel was used to simulate atomic deexcitation including the production of fluorescence photons and Auger electrons. We also used energy cuts for the electrons and photons to reduce the CPU time. Result of the physics used in the simulations was cross checked with the literature [13]. In the simulations, electrons were driven to the tungsten anode with 100 keV energy and then produced Xrays were filtered with 1 mm thick aluminum. Characteristic Xrays of tungsten were obtained successfully in addition to Bremsstrahlung continuum as seen in Fig. 1. The characteristic photo peaks below 10 keV are not seen due to the aluminum absorber.
0.254
10.55
K
109
3. Geant4 simulations
5.90
Bi
Fe
207
Intensity
6 7 .2 ke V
55
Energy (keV)
K
spectrometer. We have used aluminum blocks with various thicknesses to reduce the dead time of the detector during the data taking. Detector source distance was taken as 30 cm and aluminum blocks were positioned between the source and the detector. Energy calibration of the spectra was performed with 55Fe, 207Bi and 109Cd calibrated standard sources [9] by using the photo peaks with energies [10] given in Table 1. Some energies in the table were calculated from the weighted mean for close X-ray lines due to the insufficient energy resolution.
51
0.4 0.2 0 10
20
30
40
50
60
70
80
90
100
Energy (keV) Fig. 1. Simulation result of X-ray spectrum (filtered with 1 mm thick Al absorber) obtained from 100 keV electron beam in tungsten target.
Fig. 2. Setup of Geant4 simulation geometry.
energies in silicon material were counted for efficiency calculations in the simulations. 3.2. CPU time optimization While it is relatively quick to take a spectrum using the experimental setup, it takes considerable amount of time to simulate the same amount of events. X-ray production efficiency increases with energy of electrons hitting the anode. When the angular distribution of X-rays and layers of absorbers in front of the detector are taken into account, number of X-rays reaching the detector becomes quite small due to the attenuation. In order to obtain reasonable statistics, billions of electrons have to be generated in the filament. As a nature of particle tracking, both electrons and generated X-rays have to be tracked in the medium one by one in Geant4. Hence, several optimization steps were required to shorten the simulation time. The experiments were performed with aluminum absorbers in order to reduce the dead time of the detector. For direct comparison of the simulation results and the experimental measurements, the
52
M. Yücel et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 50–53
0.16 Amptek XR-100CR EmStandard-Opt3
0.14
Simulation without the absorber
0.12
Simulation with the absorber
Penelope
0.8 Counts (A.U.)
Intrinsic Full Energy Efficiency
1
0.6 0.4
0.1 0.08 0.06 0.04
0.2 0.02
0
0 0
1
10
5
10
15
102
20
25
30
35
40
Energy(keV)
Energy(keV) Fig. 3. Monte Carlo results of energy dependence of the detector obtained from counting the photons deposit all of their energies in the detector material. Dots represent the results from Penelope physics and open squares show the results from EmStandard-Opt3 physics. The intrinsic full energy detection efficiency curve from the manufacturer is given as solid line.
Fig. 4. Comparison of simulation results with absorber (open squares) and without absorber (dots). The simulation without absorber includes Beer–Lambert's law correction.
Measurement (20 keV) Simulation (20 keV)
2
IðEÞ ¼ I 0 e μðEÞρl
ð1Þ
where, I0 is the initial and I(E) is the final beam intensities, μðEÞ is the mass attenuation coefficient, ρ is the density and l is the thickness of the absorber. NIST database [15] provides photon attenuation coefficients for various energies. Interpolation was made on this data set to obtain the mass attenuation coefficients for energies of interest. One of the great advantages of this procedure is having the statistical power of the photons when there is no absorber. Absorbers reduce the number of photons reaching the detector dramatically, resulting large statistical fluctuations in count rate. In order to justify the procedure, full simulation including the absorber at 35 keV was generated and compared with the simulation including Beer–Lambert's correction as mentioned above. Fig. 4 shows that both methods give similar results. On the other hand, full simulation including an absorber has to be run nearly thousand times longer in order to have similar statistical power. Hence, we prefer to run the simulations without absorbers and apply corrections to the data after that. Analysis of the simulated spectra shows that very few number of photons with energies lower than 10 keV reach the detector after the corrections based on Beer–Lambert's law. For that reason, we had 10 keV low energy cut for the production of energy spectra in our simulations to get rid of the time consuming unnecessary tracks. This procedure helps us reducing the CPU time.
4. Results and discussion 4.1. Efficiency simulations of Amptek XR-100CR detector Amptek XR-100CR detector is embedded in Amptek X-123 spectrometer. This detector has 500 μm thick silicon, 13 mm2 cross-sectional area and 25 μm thick Be window. In order to determine detector response to photons, a simulation was performed for obtaining intrinsic full energy efficiency of the detector.
Measurement (25 keV) Simulation (25 keV) Measurement (30keV)
Counts (A.U.)
simulations should be performed with the same geometry as the experiments. This requires including the mentioned absorbers into the simulations. However, instead of running the simulations with various absorber materials and thicknesses, one can obtain the simulation data without the absorbers and apply corrections later. For this reason, we have decided to remove the aluminum absorbers from the simulation geometry and corrected the data based on well known Beer–Lambert law:
Simulation (30 keV)
1.5
Measurement (35 keV) Simulation (35 keV)
1
0.5
0 0
5
10
15
20
25
30
35
40
Energy(keV)
Fig. 5. Comparison of measured and simulated spectra for various energies.
X-rays between 1 and 100 keV were directed to the detector and photons with full energy deposition were registered in the simulations. Fig. 3 shows the comparison between the simulation result and the efficiency curve provided by the manufacturer [8]. These simulations were made with both standard and Penelope physics list [16]. Penelope physics is included into the MC simulations because it is known to provide better results for escape peaks [17]. It can be seen that the simulation results based on Penelope physics is in good agreement below 2 keV and the standard physics list used in this study provides better results for the energies above 2 keV which is our main region of interest. 4.2. Comparison of simulated and measured spectra Fig. 5 shows the comparison of the simulated and experimental spectra for energies of 20 keV, 25 keV, 30 keV and 35 keV. Since operation voltage of the tube was lower than 35 keV, no characteristic X-ray peaks of tungsten are seen in the figure. However, experimental spectra include small peaks between 3 keV and 14 keV. They are originated from the shielding materials (mostly lead) used in the experimental setup. Since the shielding blocks were not included in the simulation geometry, they are not visible in the MC results. Additionally, the simulations have 10 keV low energy cut for reducing the CPU time. All of the measurements were taken using aluminum absorbers with different thicknesses for reducing dead time of the detector. This procedure resulted in different statistics for the measured spectra. For that reason, each measured spectrum was scaled to be able to make visual comparison between the spectra taken with
M. Yücel et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 50–53
various X-ray energies. The same procedure was applied to the simulated spectrum for each energy (20 keV, 25 keV, 30 keV and 35 keV). Fig. 5 shows an excellent agreement between the simulated and experimental spectra. The validation of the code was also checked by generating the characteristic X-ray lines of the target material as well as the Bremsstrahlung continuum in the simulations. This was successfully performed and shown in Fig. 1 in the present work. 5. Conclusions OX/70-P dental tube with relatively low operating voltage was used to validate our simulations based on Geant4. A complete simulation including the production, transportation and detection of X-rays was successfully conducted. An important result of this study is that X-ray spectra of different kinds of X-ray tubes can be obtained accurately with the written code in Geant4 simulations. When the parameters such as tube operation voltage (including its statistical fluctuations), type of target material, thickness of glass bulb and geometry of target are given as inputs, all that is needed is to run the code with reasonable number of events. Using the spectra produced from the simulation, one can design a prototype imaging system without doing actual measurements. This procedure obviously reduces R&D cost and time dramatically. Acknowledgments We would like to thank the Scientific and Technological Council of Turkey (TUBITAK) for supporting this work (113F104).
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References [1] J. Giersch, J. Durst, Nuclear Instruments and Methods in Physics Research Section A 591 (2008) 300. [2] A. Sofiienko, C. Jarvis, A. Voll, Physics Research International (2014) 847651. [3] S. Agostinelli, et al., Nuclear Instruments and Methods in Physics Research Section A 506 (2003) 250. [4] A. Miceli, et al., Nuclear Instruments and Methods in Physics Research Section A 580 (2007) 123. [5] A. Miceli, et al., Nuclear Instruments and Methods in Physics Research Section A 583 (2007) 313. [6] M. Guthoff, et al., Nuclear Instruments and Methods in Physics Research Section A 675 (2012) 118. [7] OX/70-P Dental Tubes Technical Data, Retrieved from: 〈http://www.ceixray. com/ox70-p-2/〉, (24 April 2015). [8] X-123 Complete X-ray Spectrometer with Si-PIN Detector, Retrieved from: 〈http://www.amptek.com/products/x-123-complete-x-ray-spectrometer-wthsi-pin-detector/〉, (1 July 2015). [9] Gamma Standard Sources Set, Ritverc Isotope Products, (Production Date 2007), Retrieved from: 〈http://www.ritverc.com/products/detail.phpID=1702〉, (24 April 2015). [10] R.B. Firestone, L.P. Ekstrom, Database Version 2.1, 2004, Retrieved from: 〈http://ie.lbl.gov/toi/perchart.htm〉, (24 April 2015). [11] L. Lönnblad, Computer Physics Communications 84 (1994) 307. [12] J. Allison, et al., Geant4 electromagnetic physics for high statistic simulation of LHC experiments, Journal of Physics: Conference Series 396 (2013) 022013. [13] F.M. Khan, The Physics of Radiation Therapy, fourth ed., Lippincott Williams & Wilkins, Philadelphia, PA, 2010 (Page 32). [14] XR-100CR Si-PIN X-Ray Detector, Retrieved from: 〈http://www.amptek.com/ products/xr-100cr-si-pin-x-ray-detector/〉, (1 July 2015). [15] J.H. Hubbell, S.M. Seltzer (2004), Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients, National Institute of Standards and Technology, Gaithersburg, MD. Originally published as NISTIR 5632, National Institute of Standards and Technology, Gaithersburg, MD, Retrieved from: 〈http://physics.nist.gov/xaamdi〉, 1995 (accessed 30.03.15). [16] L. Pandola, C. Andenna, B. Caccia, Nuclear Instruments and Methods in Physics Research Section B 350 (2015) 41. [17] A.I. Skrypnyk, A.A. Zakharchenko, M.A. Khazhmuradov, Problems in Atomic Science and Technology 5 (2011) 93.