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Measurement of effective optical reflectivity using gamma ray spectroscopy method
Optik 163 (2018) 86–90
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Measurement of effective optical reflectivity using gamma ray spectroscopy method Mojtaba Askari, Ali Taheri ∗ , Mohammad Taghan Sasanpour Nuclear Science and Technology Research Institute, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 24 January 2018 Accepted 24 February 2018 Keywords: Optical reflectivity Gamma ray Geant4 simulation Plastic scintillator
a b s t r a c t Reflective materials have an important role in designing the high performance scintillatorbased detectors. The optical reflectivity of these materials has an undeniable effect on the efficiency of these detectors. This parameter is also very important in Monte Carlo simulations of the scintillators. In this work, a new method based on the both gamma-ray spectroscopy and Geant4 simulation is proposed to predict the reflectivity of the reflectors employed in radiation detection setups. © 2018 Elsevier GmbH. All rights reserved.
1. Introduction Optical reflectivity of the materials especially those used as reflectors is an important parameter in simulating the scintillator detectors. Different methods are available to study the surface reflectivity [1] including physical [2–8] and geometrical [9–12] optics modeling and angular distribution measurement. The behavior of the optical photons at the boundaries when the light passes from one medium to another is directly affected by the surface reflectivity. This parameter is very important when a detection setup is designed or simulated [13–19]. The percentage of the reflectivity and its type, namely diffuse or specular can be set as inputs in Monte Carlo softwares i.e. LITRANI [20], GATE [21], DETECT [22], or gean4 [23]. Because of a variety of the materials employed as reflectors, their surface reflectivities are not always known. In this condition, the reflectivity should be measured or ignored in the Monte Carlo simulations which can seriously affect the accuracy of the simulations results. For this reason, doing research on the optical parameters of the reflectors is of particular importance and is favored by academics. In this work, a new method is proposed to determine the effective reflectivity of three reflectors using gamma ray spectroscopy (GRS) and Monte Carlo simulations. The simulations are performed using geant4 simulation toolkit [23]. Furthermore, diffuse reflectance spectroscopy (DRS) is performed to verify the obtained results.
∗ Corresponding author. E-mail address: [email protected] (A. Taheri). https://doi.org/10.1016/j.ijleo.2018.02.093 0030-4026/© 2018 Elsevier GmbH. All rights reserved.
M. Askari et al. / Optik 163 (2018) 86–90
87
Fig. 1. Experimental gamma spectra of 137 Cs; Al-foil wrapped and bare plastic scintillator.
2. Materials and methods 2.1. Gamma ray spectroscopy method 2.1.1. Detection setup Three reflectors, namely Al-Mylar, steel foil and Al-foil were selected to investigate their reflectivity. To do the experiments, we needed a bare scintillator to place the reflectors on. For this reason, a 2 × 2 cylindrical plastic scintillator (BC400) was employed to conduct the experiments. The scintillator was first wrapped in a reflector and then coupled to a 2 PMT (Model CR 169 BEIJING Hamamatsu, China) at one end. The related electronic system consisted of a high voltage supply (CC228 01Y BEIJING Hamamatsu, China), preamplifier (IAP 3001 Iran), amplifier (IAP 3600 Iran), MCA (IAP 4110 Iran). Furthermore, 137 Cs with an activity of 14.6 Ci was used as a gamma-ray source. In the first step, the gamma-ray spectrum of 137 Cs was recorded with the detection setup for each reflector, separately. The gamma spectrum of a bare plastic scintillator with no reflector was also recorded. The recorded gamma-ray spectrum with the Al-foil and that with no reflector are shown in Fig. 1. As illustrated in this figure, the plastic scintillator just show a Compton continuum in its spectral response to 662 keV gamma rays. In other words there is no photopeak in the recorded gamma spectrum of the plastic scintillator for gamma rays with energies more than 100 keV due to the low atomic number and density of the plastics [24]. The channel of the Compton Maxima (CM) in the recorded spectra is directly dependent on the surface reflectance of the employed reflector [25]. With increasing the reflectivity, the CM shifts to the higher MCA channels. The reason is that as the reflectivity is increased, more optical photons, generated by the scintillation, reach the PMT and the signals with greater pulse heights are generated in the PMT anode. 2.1.2. Geant4 simulation The main idea of this work is to simulate the experimentally recorded gamma spectra using geant4. All optical parameters of the detector such as refractive indices, optical absorption, and scattering lengths, scintillation yield etc. are known, except the reflectivity of the employed reflectors. This means that this parameter must be changed until the simulated spectrum is completely identical to the experimental spectrum. The ratio of the channels of CMs for the reflector wrapped to the bare detector (CMrefl /CMbare ) was considered as a measure to find out the agreement level between the simulated and experimentally recorded spectra. In the first step of the simulations, different gamma spectra for different reflectivity values were simulated. Likewise, the spectral response of a bare detector was simulated. Using the results of this step of the simulations, the mathematical relation of the reflectivity value as a function of CMrefl /CMbare was determined. Employing the obtained mathematical equation, the reflectivities related to the recorded experimental gamma spectra were calculated. After calculating the experimental reflectivities, the geant4 simulations were conducted again to verify the results with the experimental gamma spectra. The Monte Carlo simulations were done using geant4 version 10.3 which used G4EMLOW 6.50 data library. The described detector in Section 2.1.1 was simulated using Geant4. Geant4 with an ability to model different aspects of a scintillation detector including the nuclear particle interactions along with the transport of the optical photons inside the materials for different kinds of the boundaries and geometries [15–18] is a powerful tool for our simulations. The scintillation yield, absorption length and refractive index of the plastic are set to 10000, 250 cm and 1.58, respectively [26,27]. All optical properties of the BC400 was considered at its max emission wavelength 423 nm [27]. G4OpBoundaryProcess class using G4OpticalSurface object is responsible for the transport of the optical photon at the optical boundaries. The type of the interfaces was set to dielectric-metal for the selected reflectors and dielectric-dielectric for the bare detector which is actually covered with (encompassed by) air. In the case of a dielectric-metal interface, the optical photons can be absorbed in the metal or be reflected in the dielectric medium. The surfaces of the employed scintil-
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M. Askari et al. / Optik 163 (2018) 86–90
Fig. 2. Experimental gamma spectra of 137 Cs; Al-foil wrapped, Al-Mylar wrapped, steel wrapped and a bare plastic scintillator.
Fig. 3. The geant4 simulated gamma spectra of ranging from 40% to 90%.
137
Cs for a bare plastic scintillator along with the metal wrapped detectors with different reflectivities
lator and the reflectors were completely polished, so the roughness of the surfaces was not considered in the simulations. On the other side, at a dielectric-dielectric interface, the critical angle which is determined by the refractive indices of the two sides ascertains the optical transmission or refraction and there is no reflectivity. 2.2. Diffuse reflection spectroscopy To validate the calculated reflectivity values, necessitated a standard optical reflection spectroscopy. The reflectivity of all three employed reflectors were determined using diffuse reflection spectroscopy (DRS) method. An Avantes Spectrometer (Model Avaspec-2048-TEC) with AvaLamp DH-S Setup was used to carry out the DRS test. The measurements were made in the range of 300–900 nm. 3. Results 3.1. Experimental tests The experimentally recorded gamma spectra of 137 Cs for the plastic scintillator wrapped with the three reflectors mentioned above along with the case without any reflector are shown in Fig. 2. According to the channel of CMs, Al-foil wrapped, Al-Mylar wrapped, steel wrapped, and bare plastic scintillators are ranked from the highest to the lowest output pulse heights. CMrefl /CMbare for Al-foil wrapped, Al-Mylar wrapped, steel wrapped detectors were obtained to be 1.66, 1.55 and 1.12, respectively. This means that we should expect the Al-foil to have the highest and the steel to have the lowest reflectivities. 3.2. Geant4 simulations The aim of this part of the study, was to find the relation between the effective reflectivity and CMrefl /CMbare . For this purpose, the gamma spectra of 137 Cs for a bare plastic scintillator along with the metal wrapped detectors with different reflectivities ranging from 0.4 to 0.9 were simulated. The obtained results are shown in Fig. 3. As it was expected, the channel
M. Askari et al. / Optik 163 (2018) 86–90
89
Fig. 4. The effective reflectivity as a function of CMrefl /CMbare ratio, simulated data and fitting result. Table 1 Effective reflectivities of the selected reflectors obtained using GRS and DRS. Reflector
CMrefl /CMbare
EF-GRS (%)
EF-DRS (%)a
Relative error (%)
Steel Al-Mylar Al-foil
1.12 1.55 1.66
48.9 69.6 73.9
38.2 73.0 74.4
27.9 4.6 0.7
a
423 nm.
Fig. 5. Diffuse reflectivity of the three selected reflectors, DRS method.
of the CM increases, according to the reflectivity of the metal reflectors. Based on the results of the simulations, the bare scintillator is almost equal to a metal wrapped scintillator with an effective reflectivity of 40%. The effective reflectivity as a function of CMrefl /CMbare ratio is plotted in Fig. 4. A second order polynomial was fitted to the calculated data and Eq. 1 was obtained to predict the effective reflectivity as a function of x = CMrefl /CMbare . ER = −0.1743x2 + 0.948x − 0.3545
(1)
Finally, three CMrefl /CMbare derived from the measurements in Subsection 3.1 were replaced in Eq. (1) to obtain their corresponding reflectivities. The obtained results are presented in Table 1. Based on the obtained results the Al-foil and steel showed the highest and lowest reflectivities as expected. 3.3. DRS test The results of the DRS method for the employed reflectors are shown in Fig. 5. The measured reflectivities for Al-foil, Al-Mylar and steel are listed in Table 1. The arrangement of the reflectors in terms of the reflectivity magnitude was the same for both DRS and GRS methods. Considering the results of the DRS as references, the errors related to the GRS results were calculated as reported in Table 1. As shown in this table, the relative errors for Al- foil and Al-Mylar are acceptable, albeit excluding steel. The relative error decreases dramatically as the reflectivity is increased. Considering the reduction of the relative error, we can conclude that this method is likely to show an error of less than 10% in predicting the reflectivities of more than 60%.
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M. Askari et al. / Optik 163 (2018) 86–90
4. Conclusion A new method based on gamma ray spectroscopy (GRS), a combination of the experimental tests and the Geant4 simulations, was proposed to calculate the optical reflectivities of the materials to be used as reflectors in scintillators. Furthermore, the DRS as a standard method was used to validate the obtained results. The calculated reflectivities using GRS method were 48.9%, 69.6% and 73.9% for steel, Al-Mylar and Al-foil, respectively. The corresponding values at 423 nm obtained with the DRS method were 38.2%, 73.0% and 74.4%. The calculated relative errors revealed that the proposed method can be successfully employed to predict the reflectivities more than 60%. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
M. Janecek, W.W. Moses, Optical reflectance measurements for commonly used reflectors, IEEE Trans. Nucl. Sci. 55 (4) (2008). P. Beckmann, A. Spizzichino, The Scattering of Electro-Magnetic Waves from Rough Surfaces, The Macmillan Company, 1963. S.O. Rice, Reflection of electromagnetic waves from slightly rough surfaces, Commun. Pure Appl. Math. 4 (1951) 361–378. H. Davies, The reflection of electromagnetical waves from rough surfaces, Proc. Inst. Electr. Eng. 101 (1954) 209–214. A.K. Fung, Z. Li, K.S. Chen, Backscattering from a randomly rough dielectric surface, IEEE Trans. Geosci. Remote Sens. 30 (2) (1992) 356–369. A.K. Fung, G.W. Pan, A scattering model for perfectly conducting random surfaces I. Model development, Int. J. Remote Sens. 8 (11) (1987) 1579–1593. L. Tsang, J.A. Kong, K.H. Ding, C.O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations, Wiley, 2001. M. Saillard, A. Sentenac, Rigorous solutions for electromagnetic scattering from rough surfaces, Waves Random Media 11 (2001) 103–137. K. Torrance, E. Sparrow, Theory for off-specular reflection from roughened surfaces, J. Opt. Soc. Am. 57 (1967) 1105–1114. T. Whitted, An improved illumination model for shaded display, Commun. ACM 23 (6) (1980) 343–349. B.T. Phong, Illumination for computer generated pictures, Commun. ACM 18 (6) (1975) 311–317. J.F. Blinn, Models of light reflection for computer synthesized pictures, Computer Gr. 11 (2) (1977) 192–198. A. Taheri, R.G. Peyvandi, M.T. Sasanpour, M. Askari, Spectral response evaluation of plastic rod scintillators as position sensitive beta particle detectors, JINST 10 (2015) T12006. A. Taheri, R.G. Peyvandi, The impact of wrapping method and reflector type on the performance of rod plastic scintillators, Measurement 97 (2017) 100. A. Taheri, S. Saramad, S. Setayeshi, ZnO nanowires in polycarbonate membrane as a high resolution X-ray detector (a Geant4 simulation), Nucl. Instrum. Methods A 716 (2013) 15. A. Taheri, S. Saramad, S. Ghalenoi, S. Setayeshi, Fabrication, testing and simulation of a high spatial resolution alpha-particle imager based on ZnO nanowires in a polycarbonate nanoporous membrane, Eur. Phys. J. C 73 (2013) 2649. A. Taheri, M. Sheidaiy, Scintillation and optical behavior of GaN nanowires in the presence of low-energy X-ray photons: a Geant4 simulation, Radiat. Meas. 77 (2015) 5. A. Taheri, M. Sheidaiy, Wurtzite gallium nitride as a scintillator detector for alpha particles (a Geant4 simulation), JINST 10 (2015) T05003. A. Taheri, M. Askari, M. Taghan Sasanpour, Lead foil wrapping of the plastic scintillators for the gamma ray detection: optical reflector or spectrum intensifier? JINST 12 (2017) T08006. F.X. Gentit, Litrani: a general purpose Monte-Carlo program simulating light propagation in isotropic or anisotropic media, Nucl. Instr. Meth. A 486 (June (1–2)) (2002) 35. G. Santin, D. Strul, D. Lazaro, et al., GATE: A Geant4-based simulation platform for PET and SPECT integrating movement and time management, IEEE Trans. Nucl. Sci. 50 (October (5)) (2003) 1516–1521. F. Cayouette, D. Laurendeau, C. Moisan, DETECT2000: An improved Monte-Carlo simulator for the computer aided design of photon sensing devices, in: Proc. SPIE Photonic, North, Quebec, Canada, June, 2002. S. Agostinelli, et al., Geant4 – A simulation toolkit, Nucl. Instr. Meth. A 506 (2003) 250–303. R.G. Peyvandi, A. Taheri, M.A. Lehdarboni, Evaluation of a new position sensitive detector based on the plastic rod scintillators, JINST 10 (2015) T06004. A. Taheri, M.A. Lehdarboni, R. Gholipour, Determination of Gaussian energy broadening parameters for organic scintillators, JINST 11 (2016) P05020. G.F. Knoll, Radiation Detection and Measurement, 4th edition, Wiley, U.S.A., 2010. Saint-Gobain Ceramics and Plastics, BC-400, BC-404, BC-408, BC-412, BC-416 datasheet, URL: http://www.crystals.saint-gobain.com/sites/imdf.crystals.com/files/documents/sgc-bc400-404-408-412-416-data-sheet.pdf.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Measurement of effective optical reflectivity using gamma ray spectroscopy method Mojtaba Askari, Ali Taheri ∗ , Mohammad Taghan Sasanpour Nuclear Science and Technology Research Institute, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 24 January 2018 Accepted 24 February 2018 Keywords: Optical reflectivity Gamma ray Geant4 simulation Plastic scintillator
a b s t r a c t Reflective materials have an important role in designing the high performance scintillatorbased detectors. The optical reflectivity of these materials has an undeniable effect on the efficiency of these detectors. This parameter is also very important in Monte Carlo simulations of the scintillators. In this work, a new method based on the both gamma-ray spectroscopy and Geant4 simulation is proposed to predict the reflectivity of the reflectors employed in radiation detection setups. © 2018 Elsevier GmbH. All rights reserved.
1. Introduction Optical reflectivity of the materials especially those used as reflectors is an important parameter in simulating the scintillator detectors. Different methods are available to study the surface reflectivity [1] including physical [2–8] and geometrical [9–12] optics modeling and angular distribution measurement. The behavior of the optical photons at the boundaries when the light passes from one medium to another is directly affected by the surface reflectivity. This parameter is very important when a detection setup is designed or simulated [13–19]. The percentage of the reflectivity and its type, namely diffuse or specular can be set as inputs in Monte Carlo softwares i.e. LITRANI [20], GATE [21], DETECT [22], or gean4 [23]. Because of a variety of the materials employed as reflectors, their surface reflectivities are not always known. In this condition, the reflectivity should be measured or ignored in the Monte Carlo simulations which can seriously affect the accuracy of the simulations results. For this reason, doing research on the optical parameters of the reflectors is of particular importance and is favored by academics. In this work, a new method is proposed to determine the effective reflectivity of three reflectors using gamma ray spectroscopy (GRS) and Monte Carlo simulations. The simulations are performed using geant4 simulation toolkit [23]. Furthermore, diffuse reflectance spectroscopy (DRS) is performed to verify the obtained results.
∗ Corresponding author. E-mail address: [email protected] (A. Taheri). https://doi.org/10.1016/j.ijleo.2018.02.093 0030-4026/© 2018 Elsevier GmbH. All rights reserved.
M. Askari et al. / Optik 163 (2018) 86–90
87
Fig. 1. Experimental gamma spectra of 137 Cs; Al-foil wrapped and bare plastic scintillator.
2. Materials and methods 2.1. Gamma ray spectroscopy method 2.1.1. Detection setup Three reflectors, namely Al-Mylar, steel foil and Al-foil were selected to investigate their reflectivity. To do the experiments, we needed a bare scintillator to place the reflectors on. For this reason, a 2 × 2 cylindrical plastic scintillator (BC400) was employed to conduct the experiments. The scintillator was first wrapped in a reflector and then coupled to a 2 PMT (Model CR 169 BEIJING Hamamatsu, China) at one end. The related electronic system consisted of a high voltage supply (CC228 01Y BEIJING Hamamatsu, China), preamplifier (IAP 3001 Iran), amplifier (IAP 3600 Iran), MCA (IAP 4110 Iran). Furthermore, 137 Cs with an activity of 14.6 Ci was used as a gamma-ray source. In the first step, the gamma-ray spectrum of 137 Cs was recorded with the detection setup for each reflector, separately. The gamma spectrum of a bare plastic scintillator with no reflector was also recorded. The recorded gamma-ray spectrum with the Al-foil and that with no reflector are shown in Fig. 1. As illustrated in this figure, the plastic scintillator just show a Compton continuum in its spectral response to 662 keV gamma rays. In other words there is no photopeak in the recorded gamma spectrum of the plastic scintillator for gamma rays with energies more than 100 keV due to the low atomic number and density of the plastics [24]. The channel of the Compton Maxima (CM) in the recorded spectra is directly dependent on the surface reflectance of the employed reflector [25]. With increasing the reflectivity, the CM shifts to the higher MCA channels. The reason is that as the reflectivity is increased, more optical photons, generated by the scintillation, reach the PMT and the signals with greater pulse heights are generated in the PMT anode. 2.1.2. Geant4 simulation The main idea of this work is to simulate the experimentally recorded gamma spectra using geant4. All optical parameters of the detector such as refractive indices, optical absorption, and scattering lengths, scintillation yield etc. are known, except the reflectivity of the employed reflectors. This means that this parameter must be changed until the simulated spectrum is completely identical to the experimental spectrum. The ratio of the channels of CMs for the reflector wrapped to the bare detector (CMrefl /CMbare ) was considered as a measure to find out the agreement level between the simulated and experimentally recorded spectra. In the first step of the simulations, different gamma spectra for different reflectivity values were simulated. Likewise, the spectral response of a bare detector was simulated. Using the results of this step of the simulations, the mathematical relation of the reflectivity value as a function of CMrefl /CMbare was determined. Employing the obtained mathematical equation, the reflectivities related to the recorded experimental gamma spectra were calculated. After calculating the experimental reflectivities, the geant4 simulations were conducted again to verify the results with the experimental gamma spectra. The Monte Carlo simulations were done using geant4 version 10.3 which used G4EMLOW 6.50 data library. The described detector in Section 2.1.1 was simulated using Geant4. Geant4 with an ability to model different aspects of a scintillation detector including the nuclear particle interactions along with the transport of the optical photons inside the materials for different kinds of the boundaries and geometries [15–18] is a powerful tool for our simulations. The scintillation yield, absorption length and refractive index of the plastic are set to 10000, 250 cm and 1.58, respectively [26,27]. All optical properties of the BC400 was considered at its max emission wavelength 423 nm [27]. G4OpBoundaryProcess class using G4OpticalSurface object is responsible for the transport of the optical photon at the optical boundaries. The type of the interfaces was set to dielectric-metal for the selected reflectors and dielectric-dielectric for the bare detector which is actually covered with (encompassed by) air. In the case of a dielectric-metal interface, the optical photons can be absorbed in the metal or be reflected in the dielectric medium. The surfaces of the employed scintil-
88
M. Askari et al. / Optik 163 (2018) 86–90
Fig. 2. Experimental gamma spectra of 137 Cs; Al-foil wrapped, Al-Mylar wrapped, steel wrapped and a bare plastic scintillator.
Fig. 3. The geant4 simulated gamma spectra of ranging from 40% to 90%.
137
Cs for a bare plastic scintillator along with the metal wrapped detectors with different reflectivities
lator and the reflectors were completely polished, so the roughness of the surfaces was not considered in the simulations. On the other side, at a dielectric-dielectric interface, the critical angle which is determined by the refractive indices of the two sides ascertains the optical transmission or refraction and there is no reflectivity. 2.2. Diffuse reflection spectroscopy To validate the calculated reflectivity values, necessitated a standard optical reflection spectroscopy. The reflectivity of all three employed reflectors were determined using diffuse reflection spectroscopy (DRS) method. An Avantes Spectrometer (Model Avaspec-2048-TEC) with AvaLamp DH-S Setup was used to carry out the DRS test. The measurements were made in the range of 300–900 nm. 3. Results 3.1. Experimental tests The experimentally recorded gamma spectra of 137 Cs for the plastic scintillator wrapped with the three reflectors mentioned above along with the case without any reflector are shown in Fig. 2. According to the channel of CMs, Al-foil wrapped, Al-Mylar wrapped, steel wrapped, and bare plastic scintillators are ranked from the highest to the lowest output pulse heights. CMrefl /CMbare for Al-foil wrapped, Al-Mylar wrapped, steel wrapped detectors were obtained to be 1.66, 1.55 and 1.12, respectively. This means that we should expect the Al-foil to have the highest and the steel to have the lowest reflectivities. 3.2. Geant4 simulations The aim of this part of the study, was to find the relation between the effective reflectivity and CMrefl /CMbare . For this purpose, the gamma spectra of 137 Cs for a bare plastic scintillator along with the metal wrapped detectors with different reflectivities ranging from 0.4 to 0.9 were simulated. The obtained results are shown in Fig. 3. As it was expected, the channel
M. Askari et al. / Optik 163 (2018) 86–90
89
Fig. 4. The effective reflectivity as a function of CMrefl /CMbare ratio, simulated data and fitting result. Table 1 Effective reflectivities of the selected reflectors obtained using GRS and DRS. Reflector
CMrefl /CMbare
EF-GRS (%)
EF-DRS (%)a
Relative error (%)
Steel Al-Mylar Al-foil
1.12 1.55 1.66
48.9 69.6 73.9
38.2 73.0 74.4
27.9 4.6 0.7
a
423 nm.
Fig. 5. Diffuse reflectivity of the three selected reflectors, DRS method.
of the CM increases, according to the reflectivity of the metal reflectors. Based on the results of the simulations, the bare scintillator is almost equal to a metal wrapped scintillator with an effective reflectivity of 40%. The effective reflectivity as a function of CMrefl /CMbare ratio is plotted in Fig. 4. A second order polynomial was fitted to the calculated data and Eq. 1 was obtained to predict the effective reflectivity as a function of x = CMrefl /CMbare . ER = −0.1743x2 + 0.948x − 0.3545
(1)
Finally, three CMrefl /CMbare derived from the measurements in Subsection 3.1 were replaced in Eq. (1) to obtain their corresponding reflectivities. The obtained results are presented in Table 1. Based on the obtained results the Al-foil and steel showed the highest and lowest reflectivities as expected. 3.3. DRS test The results of the DRS method for the employed reflectors are shown in Fig. 5. The measured reflectivities for Al-foil, Al-Mylar and steel are listed in Table 1. The arrangement of the reflectors in terms of the reflectivity magnitude was the same for both DRS and GRS methods. Considering the results of the DRS as references, the errors related to the GRS results were calculated as reported in Table 1. As shown in this table, the relative errors for Al- foil and Al-Mylar are acceptable, albeit excluding steel. The relative error decreases dramatically as the reflectivity is increased. Considering the reduction of the relative error, we can conclude that this method is likely to show an error of less than 10% in predicting the reflectivities of more than 60%.
90
M. Askari et al. / Optik 163 (2018) 86–90
4. Conclusion A new method based on gamma ray spectroscopy (GRS), a combination of the experimental tests and the Geant4 simulations, was proposed to calculate the optical reflectivities of the materials to be used as reflectors in scintillators. Furthermore, the DRS as a standard method was used to validate the obtained results. The calculated reflectivities using GRS method were 48.9%, 69.6% and 73.9% for steel, Al-Mylar and Al-foil, respectively. The corresponding values at 423 nm obtained with the DRS method were 38.2%, 73.0% and 74.4%. The calculated relative errors revealed that the proposed method can be successfully employed to predict the reflectivities more than 60%. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
M. Janecek, W.W. Moses, Optical reflectance measurements for commonly used reflectors, IEEE Trans. Nucl. Sci. 55 (4) (2008). P. Beckmann, A. Spizzichino, The Scattering of Electro-Magnetic Waves from Rough Surfaces, The Macmillan Company, 1963. S.O. Rice, Reflection of electromagnetic waves from slightly rough surfaces, Commun. Pure Appl. Math. 4 (1951) 361–378. H. Davies, The reflection of electromagnetical waves from rough surfaces, Proc. Inst. Electr. Eng. 101 (1954) 209–214. A.K. Fung, Z. Li, K.S. Chen, Backscattering from a randomly rough dielectric surface, IEEE Trans. Geosci. Remote Sens. 30 (2) (1992) 356–369. A.K. Fung, G.W. Pan, A scattering model for perfectly conducting random surfaces I. Model development, Int. J. Remote Sens. 8 (11) (1987) 1579–1593. L. Tsang, J.A. Kong, K.H. Ding, C.O. Ao, Scattering of Electromagnetic Waves, Numerical Simulations, Wiley, 2001. M. Saillard, A. Sentenac, Rigorous solutions for electromagnetic scattering from rough surfaces, Waves Random Media 11 (2001) 103–137. K. Torrance, E. Sparrow, Theory for off-specular reflection from roughened surfaces, J. Opt. Soc. Am. 57 (1967) 1105–1114. T. Whitted, An improved illumination model for shaded display, Commun. ACM 23 (6) (1980) 343–349. B.T. Phong, Illumination for computer generated pictures, Commun. ACM 18 (6) (1975) 311–317. J.F. Blinn, Models of light reflection for computer synthesized pictures, Computer Gr. 11 (2) (1977) 192–198. A. Taheri, R.G. Peyvandi, M.T. Sasanpour, M. Askari, Spectral response evaluation of plastic rod scintillators as position sensitive beta particle detectors, JINST 10 (2015) T12006. A. Taheri, R.G. Peyvandi, The impact of wrapping method and reflector type on the performance of rod plastic scintillators, Measurement 97 (2017) 100. A. Taheri, S. Saramad, S. Setayeshi, ZnO nanowires in polycarbonate membrane as a high resolution X-ray detector (a Geant4 simulation), Nucl. Instrum. Methods A 716 (2013) 15. A. Taheri, S. Saramad, S. Ghalenoi, S. Setayeshi, Fabrication, testing and simulation of a high spatial resolution alpha-particle imager based on ZnO nanowires in a polycarbonate nanoporous membrane, Eur. Phys. J. C 73 (2013) 2649. A. Taheri, M. Sheidaiy, Scintillation and optical behavior of GaN nanowires in the presence of low-energy X-ray photons: a Geant4 simulation, Radiat. Meas. 77 (2015) 5. A. Taheri, M. Sheidaiy, Wurtzite gallium nitride as a scintillator detector for alpha particles (a Geant4 simulation), JINST 10 (2015) T05003. A. Taheri, M. Askari, M. Taghan Sasanpour, Lead foil wrapping of the plastic scintillators for the gamma ray detection: optical reflector or spectrum intensifier? JINST 12 (2017) T08006. F.X. Gentit, Litrani: a general purpose Monte-Carlo program simulating light propagation in isotropic or anisotropic media, Nucl. Instr. Meth. A 486 (June (1–2)) (2002) 35. G. Santin, D. Strul, D. Lazaro, et al., GATE: A Geant4-based simulation platform for PET and SPECT integrating movement and time management, IEEE Trans. Nucl. Sci. 50 (October (5)) (2003) 1516–1521. F. Cayouette, D. Laurendeau, C. Moisan, DETECT2000: An improved Monte-Carlo simulator for the computer aided design of photon sensing devices, in: Proc. SPIE Photonic, North, Quebec, Canada, June, 2002. S. Agostinelli, et al., Geant4 – A simulation toolkit, Nucl. Instr. Meth. A 506 (2003) 250–303. R.G. Peyvandi, A. Taheri, M.A. Lehdarboni, Evaluation of a new position sensitive detector based on the plastic rod scintillators, JINST 10 (2015) T06004. A. Taheri, M.A. Lehdarboni, R. Gholipour, Determination of Gaussian energy broadening parameters for organic scintillators, JINST 11 (2016) P05020. G.F. Knoll, Radiation Detection and Measurement, 4th edition, Wiley, U.S.A., 2010. Saint-Gobain Ceramics and Plastics, BC-400, BC-404, BC-408, BC-412, BC-416 datasheet, URL: http://www.crystals.saint-gobain.com/sites/imdf.crystals.com/files/documents/sgc-bc400-404-408-412-416-data-sheet.pdf.