- Email: [email protected]
Simulation and characterization of different setups for gamma ray detection using SiPMs and LYSO scintillators
Nuclear Instruments and Methods in Physics Research A 658 (2011) 61–65
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Simulation and characterization of different setups for gamma ray detection using SiPMs and LYSO scintillators M. Benetti a,, A. Tarolli b, G. Giacomini b, C. Piemonte b, G.-F. Dalla Betta a a
INFN, Sezione di Padova (Gruppo Collegato di Trento) and Dipartimento di Ingegneria e Scienza dell’Informazione, Universita di Trento, Via Sommarive, 14, I-38123 Povo di Trento (TN), Italy b Fondazione Bruno Kessler, Centro per i Materiali e i Microsistemi (FBK-CMM), Via Sommarive, 18, I-38123 Povo di Trento (TN), Italy
a r t i c l e i n f o
abstract
Available online 18 July 2011
Silicon photomultipliers (SiPMs) coupled to fast bright scintillators, like cerium doped silicate based crystals, allow the construction of compact gamma ray detectors. In this paper we discuss simulation results obtained from Monte Carlo ray tracing tools applied to SiPM and LYSO systems. We address the importance of three key factors in light propagation: the scintillator wrapping, the coupling medium, and the detector coating. We also propose a simple experiment to verify some of the findings related to the investigation of diffusive wrappings. & 2011 Elsevier B.V. All rights reserved.
Keywords: Scintillator Monte Carlo optical simulation SiPM Gamma ray detectors
1. Introduction Silicon photomultipliers (SiPMs) are detectors with single photon sensing capability that, owing to their fast response and small sizes, are candidate to substitute photomultiplier tubes (PMTs) in a large number of applications involving gamma ray detection [1]. In order to estimate the number of photons detected by a SiPM for a given incident photon flux we can multiply the flux of photons by the SiPM Photon Detection Efficiency (PDE). PDE is a parameter that depends on the light wavelength l and that can be experimentally measured using a collimated monochromatic light [2]. The application of SiPMs in the detection of gamma rays implies the use of a scintillator crystal that converts the highenergy gamma rays into light photons. Scintillator light output is spread with a large angular power distribution that depends on many system factors. In a particular assembly, the performance is critically dependent on some practical setup choices, such as the optical grease used as coupling medium, the geometry of the crystals and their wrappings. In the literature, some studies of systems composed of detector–scintillator assemblies are carried out using experimental practice, optical simulations or a mixed approach (see for example Refs. [3–7]). In this work we propose a method to calculate the output of a detector for a non-collimated light flux. This method is based on our optical simulation framework, and we apply it to SiPMs Corresponding author. Tel.: þ 39 461 414130; fax: þ 39 461 282093.
E-mail address: [email protected] (M. Benetti). 0168-9002/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2011.06.105
devices developed at FBK (Trento, Italy). We study how the light propagation inside the scintillator crystal is affected by the properties of different wrappings and interfaces, and we estimate the relative importance of different factors in determining the light output. Simulation results are compared to experimental data achieved with a simple setup.
2. Optical simulation In this section, we define the quantities extracted from the simulations. In the following, we will refer to the set-up depicted in Fig. 1. In our simulation gamma rays travel parallel to the crystal axis entering from the surface Ai in Fig. 1. We define as ‘‘light output’’, Z, the ratio of detected photons, Pdetected, to the photons generated by the deposition of the whole energy of a gamma ray, Pgamma, as suggested in Ref. [8]. We express it as the product of three factors with the PDE:
Z
Pdetected ¼ Zcris Zmed Zcoat PDE Pgamma
Zcris ¼ f ða,x,yÞ is the light output at interface A of Fig. 1. This quantity describes the light propagation inside the crystal and is dependent on the angle of incidence a, formed by the light and the normal to the surface A, and on the position of the light generation inside the crystal (x indicates the position along the crystal axis while y indicates the distance between the point of interaction and the axis in a section parallel to the surface A. The points with x ¼0 correspond to surface Ai). We will study this dependence in Section 2.2, where we discuss how the simulated
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Teflon wrapping: light output for different points of interaction 17.3 mm 12.9 mm 10.0 mm 7.8 mm 6.0 mm 4.6 mm 3.4 mm 2.3 mm 1.4 mm 0.5 mm
2.1. Energy deposition We used the simplest approximation of gamma-crystal interaction, namely the Lambert–Beer Law, stating that a gamma ray has probability equal to x=d
PðxÞ ¼ e
of no interaction after having traveled a distance x, with d, the extinction coefficient or absorption length, a value that is normally given by the crystal producer. In the interaction with the crystal, the gamma ray deposits all its energy. In our experimental activity we have being using LYSO scintillators, produced by Hilger Crystals having a d, defined in the previous equation, of 1.14 cm at 511 keV. We used the value of the extinction coefficient to divide the crystal into subsequent volumes. In each of these volumes the gamma ray has a similar probability of depositing its energy. In the following we call volumes calculated in this way ‘‘equal probability volumes’’. In our Monte Carlo optical simulations we have assumed that all the light produced by the energy deposition of the gamma ray at 511 keV is generated from one single point, located along the crystal axis at the center of an equal probability volume. This simplification is similar to that introduced in Ref. [8]. 2.2. Relative light distribution at crystal interface The histograms in Figs. 2 and 3 give the simulated angular distribution of the incident light at surface A of Fig. 1, in the case of a diffusive and a mirror wrapping. We assumed a perfect adhesion between the wrap and the crystal. This assumption is due to the difficulties in modeling properly some characteristics of the air gap such as thickness, shape, presence of bubbles. The light propagation inside the crystal is modeled assuming a light attenuation length of 40 cm [9]. The diffusive coating is assumed to be 99% lambertian. The diffusive wrapping is typically obtained in experimental practice wrapping the crystal with Teflon and for this reason in the following we will use the term Teflon wrapping
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Fig. 2. Light power distribution at the crystal interface for different points of interaction—Teflon diffusive wrapping.
Mirror wrapping: light output for different points of interaction
[%] of the light produced by the gamma interaction
angular distribution of Zcris changes varying the point of interaction. Zmed ¼ f ða,nmedium Þ is the light output at interface B of Fig. 1. The angular distribution of Zmed depends on the refractive index of the medium. This dependence is analyzed in Section 2.3. In this case we study the average light output after a large number of gamma interactions. To model the energy deposition of a large number of gamma rays inside the crystal we used the model presented in Section 2.1. Zcoat ¼ f ða,coatingÞ is the light output of the coating. Its angular distribution is determined by the number, the thickness and the refractive index of the dielectric layers that are deposited over the SiPM. We examine this quantity in Section 2.4. Results for the average light outputs (i.e. the sum of light outputs calculated for different angles, Zcris , Zmed and Zcoat ) are reported in Section 2.5.
[%] of the light produced by the gamma interaction
10 Fig. 1. Sketch of the simulated setup, showing the radioactive source, the crystal, the optical grease and the detector (SiPM).
17.3 mm 12.9 mm 10.0 mm 7.8 mm 6.0 mm 4.6 mm 3.4 mm 2.3 mm 1.4 mm 0.5 mm
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Fig. 3. Light power distribution at the crystal interface for different points of interaction—mirror wrapping.
to indicate the diffusive wrapping. All the surfaces are assumed as ideal, i.e. the surface roughness is not modeled. The light distribution is expressed in terms of percentage of light incident with respect to the light generated. The axial coordinates that we used in this calculation are the centers of the previously introduced equal probability volumes and are reported in the legend of Figs. 2 and 3 as axial distance from surface Ai. We can note that in the Teflon case the light distribution changes, for a given angle of incidence, changing the point of interaction. In particular it increases for interactions that occur closer to the surface A and this increment is greater for low angles of incidence. In Fig. 3 we can note that with mirror wrapping only minor changes are predicted from simulator. To explain this effect we can consider that the number of interactions between the light generated by the gamma and the wrap is greater for gamma absorptions that occur far from the sensor. In the case of a perfect mirror reflection only the sign of the incident light angle is modified as a result of the light–wrap interaction while in the case of a lambertian reflection the light is
M. Benetti et al. / Nuclear Instruments and Methods in Physics Research A 658 (2011) 61–65
redistributed in the whole half solid angle. For this reason we can expect that in the case of the mirror coating the shape of the light distribution is less dependent on the number of light–wrap interactions.
Teflon wrapping: light output for different index of refraction n n=1.7 n=1.6 n=1.5 n=1.4 n=1
[%] of the light produced by the gamma interaction
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The angular distribution of incident light at interface A of Fig. 1 is modified according to Snell Law when the light enters in the subsequent medium. Lutetium orthosilicate-based crystals have a high refractive index, so that, passing through the interface to a medium with a lower index of refraction, it causes a decrease of the transmitted power and a redistribution of the light power incident at low angle. In Fig. 4 we show how the two light distributions, relative to the diffusive wrapping (top) and the mirror wrapping (bottom), are modified by the coupling medium properties. The initial distributions are obtained by summing all the light distributions of calculated equal probability volumes. The cumulative light distribution for the diffusive wrapping is higher for small angles and therefore is less affected by medium at the interface with respect to the cumulative light distribution calculated for the mirror wrapping. Simulations predict that a larger quantity of light reaches the detector if the crystal is coated with a diffusive layer, and this observation is confirmed by experimental practice [10]. 2.4. Light transport across SiPM coating
n=1.7 n=1.6 n=1.5 n=1.4 n=1
12
2.3. Light distribution at sensor interface
0
Mirror wrapping: light output for different index of refraction n
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63
34
Light propagation through an arbitrary number of dielectrics layer is modeled solving optics with the calculation procedure explained in Ref. [11]. By this procedure, knowing the thickness and the refractive index of every layer deposited over SiPMs, we can calculate the transmission coefficient at a given l (which in our case is 425 nm, the peak emission of the crystal), as a function of the angles of incidence at the outermost layer (surface B of Fig. 1). In Fig. 5 we report some examples of such calculations for different semi-infinite mediums (with a different index of refraction) which simulate the grease coupling the scintillator to the SiPM. We used these values to modify the cumulative light distributions and we did not simulate the behavior of the reflected photons.
5
0
Fig. 4. Angular distribution of the light output for different refractive indexes of the coupling medium: (top) diffusive wrapping and (bottom) mirror wrapping.
2.5. Simulation resume Results for the light outputs at each interface, Zcris , Zmed and Zcoat , summed over the angles, are reported in Table 1. Multiplying the products of one column for the PDE gives Z, the total light output in that configuration.
Fig. 5. Light transmission to the SiPM for different angles of incidence at the surface B, and for different mediums, i.e. the coupling grease between the crystal and the SiPM. In the legend n is the index of refraction of such medium.
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Table 1 Calculated value for light output at different refraction indexes. In the first half light outputs for Teflon wrapping are tabulated and in the second half we report data for mirror wrapping. Light outputs
n¼ 1.7
n¼ 1.6
n ¼1.5
n¼1.4
n¼ 1
0.47 0.98 0.69
0.47 0.96 0.76
0.47 0.94 0.83
0.47 0.90 0.84
0.47 0.68 0.80
0.83 0.67 0.53
0.83 0.55 0.67
0.83 0.46 0.81
0.83 0.38 0.82
0.83 0.17 0.80
Teflon wrapping
Zcris Zmed Zcoat Mirror wrapping
Zcris Zmed Zcoat
(expressed in [V s])) is directly proportional to the number of photons detected. We put a 22Na gamma source near the center of the crystal. In this configuration we can assume that all the points of the crystal absorb a gamma ray with a probability that depends on the distance between that point and the source and on the amount of material placed in between. The energy spectra for the two individual SiPMs are reported in Fig. 7. In both graphs we can recognize two peaks corresponding to the two characteristics photo-peaks of 22Na gamma rays, having energies at 511 keV and 1.275 MeV. Values extracted from the Gaussian fitting of the 511 keV peak are reported in the caption. It can be seen that the signals from the two devices are different: this is due to the different gains resulting from using the same bias voltage for both SiPMs although their breakdown voltages are slightly different. The two energy resolution values calculated from the two Gaussian fits of Fig. 7 are poor (46.72% and 31.15%). This is not surprising with this setup, because the light output depends heavily on the point of interaction which has a detrimental effect on the energy resolution.
Fig. 6. Simulated light output at the interface corresponding to x ¼20 as a function of the event position along the crystal axis, with the crystal wrapped by a Teflon wrapping.
3. Case history We adopted the setup proposed in Ref. [12], in which the event position inside the crystal is extrapolated from the light outputs measured at both ends of the crystal, where two detectors are placed. To exploit this effect fully, the crystal needs to be wrapped with a diffusive wrapping as pointed out in Section 2.2. In Fig. 6 the simulated light output is shown as a function of the event position along the crystal axis. Apart from the very ends of the crystal, where the number of interactions between light and wrap is fewer, a quite good linear dependence of the light output on the position is observed. The maximum ratio between the light outputs at the two ends of the crystal is equal to 1.33, meaning that when a gamma ray interacts near one end of the crystal, i.e. in the proximity of one of the two detectors, the ratio between the two signals yielded by the two sensors should be 1.33. In our experimental setup, we used an optical grease TM (Rhodorsil pate 7), having an index of refraction of 1.4, to couple two nominally identical SiPMs placed at the opposite faces of a 20 mm Teflon coated crystal. The two SiPMs have 3600 cells, each of 50 50 mm2 , with a total area of 3 3 mm2. We used two channels of a digital scope (zt4210 from ztec instruments) to read-out the voltage drop on the 50-O input resistance produced by the current bursts of each SiPM. No further amplification or signal shaping was used, so that the area of the digitized output
Fig. 7. Energy spectra of the signal read on Ch1 (top) and Ch2 (bottom). The values of peak positions are Ch1 1.129 and Ch2 1.69 [V se 8] The values of energy resolutions are Ch1 46.72% and Ch2 31.15%.
M. Benetti et al. / Nuclear Instruments and Methods in Physics Research A 658 (2011) 61–65
65
By chance this number is very close to the simulated ratio of maximum and minimum light outputs of Fig. 6. This is the reason why the bisector in Fig. 9 well fits the lower border of the scatter plot. Although this aspect should be further investigated, it is indicating that simulations correctly predict the position dependence of the light output.
4. Conclusions
Fig. 8. Energy spectrum of the signal obtained by the linear combination of the two channels. The value for energy resolutions is 16.12%. Peak position is 3.32 ½108 V s.
We proposed a simulation framework that allows us to apply the measured value of PDE to not collimated light sources. The simulation calculates the angular power distribution of a light source and how it is modified by the interaction with a series of optical elements before light absorption. We applied this method to the investigation of light output of a scintillator crystal and we studied the weights of three factors in the optical system composed of a LYSO crystal and a SiPM, namely the three indexes of refraction of the coupling medium, of the crystal and of the detector wrapping. According to the predicted behavior, a mirror wrapping seems to give some advantages in terms of energy resolution, since the light output is not position dependent. On the other hand the same simulations predict that the overall light output is more prone to be affected crossing successive optical elements due to an angular distribution shifted toward large angles. In Section 2.4 we have presented the calculated light transmission of a SiPM, produced at FBK, once the indexes of refraction and the thickness of the different layers of a detector coating are known. We proposed a simple experimental setup to verify the detection properties of two SiPMs, coupled to a scintillator, wrapped with white diffusive Teflon wrapping, which was studied with the above-mentioned simulation framework. We observe well-correlated signals. The difference in the observed experimental light outputs at the two sides of the crystal are coherent with simulation results. A more accurate experimental verification of the simulation framework will be carried out testing crystals with different lengths and testing mediums with different refractive indexes.
References Fig. 9. Correlation of signals of the two SiPMs coupled at the opposite sides of a 3 3 20 mm3 crystal coated with Teflon wrap.
If we linearly combine the output of the two detectors, we obtain the energy spectrum shown in Fig. 8, which exhibits an energy resolution of 16.72%, still not optimized but definitely much better than the two energy resolutions measured with the single detectors. This confirms that the outputs of the two single channels are strongly correlated. This effect is further demonstrated by the graph of the signal correlation shown in Fig. 9, where a symmetrical accumulation of points can be observed. The lowest border of this scatter plot is due to the interactions occurring near the SiPM connected to Ch1 of the scope (corresponding to the x-axis), whereas the upper border is due to the interactions occurring at the other end (SiPM connected to Ch2, y-axis). In this scatter plot, points relevant to the peak at 1.275 MeV are easily found in the upper right zone, as isolated points. As expected, they are well aligned perpendicularly to the symmetry axes of the scatter plot. The linear regression fit to the data is found to have a slope of C1:32, in agreement with the different gains of the two SiPMs.
[1] P. Buzhan, et al., Nuclear Instruments and Methods in Physics Research A 504 (2003) 48. [2] G. Collazuol, et al., Nuclear Instruments and Methods in Physics Research A 581 (2007) 461. [3] P. Liaparinos, I. Kandarakis, D. Cavouras, H. Delis, G. Panayiotakis, Nuclear Instruments and Methods in Physics Research A 569 (2006) 355. [4] D. Wahl, V. Mikhailik, H. Kraus, Nuclear Instruments and Methods in Physics Research A 570 (2007) 529. [5] N. Ghal-Eh, M. Scott, R. Koohi-Fayegh, M.F. Rahimi, Nuclear Instruments and Methods in Physics Research A 516 (2004) 116. [6] Y.A. Berdnikov, V.V. Grebenshchikov, V.F. Kosmach, I. Leonov, V. Samsonov, O.Y. Krushcheva, A.P. Shishlo, Instruments and Experimental Techniques 44 (4) (2001) 466. [7] M. Kronberger, E. Auffray, P. Lecoq, Improving light extraction from heavy inorganic scintillators by photonic crystals, Nuclear Science Symposium Conference Record, vol. M06-179(22), 2008, pp. 3914–3919. + [8] E. Lorincz, G. Erdei, I. Pe´czeli, C. Steinbach, F. Ujhelyi, T. Bukki, IEEE Transactions on Nuclear Science NS-57 (1) (2010) 48. [9] I. Vilardi, F. Ciocia, N. Colonna, R. De Leo, L. Lagamba, S. Marrone, E. Nappi, G. Tagliente, A. Valentini, A. Braem, E. Chesi, C. Joram, et al., Nuclear Instruments and Methods in Physics Research A 564 (2006) 506. [10] H. Heinrichs, A. Blume, N. Bußmann, R. Engels, G. Kemmerling, S. Weber, K. Ziemons, Nuclear Instruments and Methods in Physics Research A 486 (2002) 60. [11] F. Tommasini, A. Morgante, Correnti radiazioni e quanti, 2007. [12] A.V. Getkin, V. Gavrylyuk, D. Zosim, V. Yankelevich, Unidimensional position sensitive detector, Nuclear Science Symposium Conference Record 3, 2000.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Simulation and characterization of different setups for gamma ray detection using SiPMs and LYSO scintillators M. Benetti a,, A. Tarolli b, G. Giacomini b, C. Piemonte b, G.-F. Dalla Betta a a
INFN, Sezione di Padova (Gruppo Collegato di Trento) and Dipartimento di Ingegneria e Scienza dell’Informazione, Universita di Trento, Via Sommarive, 14, I-38123 Povo di Trento (TN), Italy b Fondazione Bruno Kessler, Centro per i Materiali e i Microsistemi (FBK-CMM), Via Sommarive, 18, I-38123 Povo di Trento (TN), Italy
a r t i c l e i n f o
abstract
Available online 18 July 2011
Silicon photomultipliers (SiPMs) coupled to fast bright scintillators, like cerium doped silicate based crystals, allow the construction of compact gamma ray detectors. In this paper we discuss simulation results obtained from Monte Carlo ray tracing tools applied to SiPM and LYSO systems. We address the importance of three key factors in light propagation: the scintillator wrapping, the coupling medium, and the detector coating. We also propose a simple experiment to verify some of the findings related to the investigation of diffusive wrappings. & 2011 Elsevier B.V. All rights reserved.
Keywords: Scintillator Monte Carlo optical simulation SiPM Gamma ray detectors
1. Introduction Silicon photomultipliers (SiPMs) are detectors with single photon sensing capability that, owing to their fast response and small sizes, are candidate to substitute photomultiplier tubes (PMTs) in a large number of applications involving gamma ray detection [1]. In order to estimate the number of photons detected by a SiPM for a given incident photon flux we can multiply the flux of photons by the SiPM Photon Detection Efficiency (PDE). PDE is a parameter that depends on the light wavelength l and that can be experimentally measured using a collimated monochromatic light [2]. The application of SiPMs in the detection of gamma rays implies the use of a scintillator crystal that converts the highenergy gamma rays into light photons. Scintillator light output is spread with a large angular power distribution that depends on many system factors. In a particular assembly, the performance is critically dependent on some practical setup choices, such as the optical grease used as coupling medium, the geometry of the crystals and their wrappings. In the literature, some studies of systems composed of detector–scintillator assemblies are carried out using experimental practice, optical simulations or a mixed approach (see for example Refs. [3–7]). In this work we propose a method to calculate the output of a detector for a non-collimated light flux. This method is based on our optical simulation framework, and we apply it to SiPMs Corresponding author. Tel.: þ 39 461 414130; fax: þ 39 461 282093.
E-mail address: [email protected] (M. Benetti). 0168-9002/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2011.06.105
devices developed at FBK (Trento, Italy). We study how the light propagation inside the scintillator crystal is affected by the properties of different wrappings and interfaces, and we estimate the relative importance of different factors in determining the light output. Simulation results are compared to experimental data achieved with a simple setup.
2. Optical simulation In this section, we define the quantities extracted from the simulations. In the following, we will refer to the set-up depicted in Fig. 1. In our simulation gamma rays travel parallel to the crystal axis entering from the surface Ai in Fig. 1. We define as ‘‘light output’’, Z, the ratio of detected photons, Pdetected, to the photons generated by the deposition of the whole energy of a gamma ray, Pgamma, as suggested in Ref. [8]. We express it as the product of three factors with the PDE:
Z
Pdetected ¼ Zcris Zmed Zcoat PDE Pgamma
Zcris ¼ f ða,x,yÞ is the light output at interface A of Fig. 1. This quantity describes the light propagation inside the crystal and is dependent on the angle of incidence a, formed by the light and the normal to the surface A, and on the position of the light generation inside the crystal (x indicates the position along the crystal axis while y indicates the distance between the point of interaction and the axis in a section parallel to the surface A. The points with x ¼0 correspond to surface Ai). We will study this dependence in Section 2.2, where we discuss how the simulated
62
M. Benetti et al. / Nuclear Instruments and Methods in Physics Research A 658 (2011) 61–65
Teflon wrapping: light output for different points of interaction 17.3 mm 12.9 mm 10.0 mm 7.8 mm 6.0 mm 4.6 mm 3.4 mm 2.3 mm 1.4 mm 0.5 mm
2.1. Energy deposition We used the simplest approximation of gamma-crystal interaction, namely the Lambert–Beer Law, stating that a gamma ray has probability equal to x=d
PðxÞ ¼ e
of no interaction after having traveled a distance x, with d, the extinction coefficient or absorption length, a value that is normally given by the crystal producer. In the interaction with the crystal, the gamma ray deposits all its energy. In our experimental activity we have being using LYSO scintillators, produced by Hilger Crystals having a d, defined in the previous equation, of 1.14 cm at 511 keV. We used the value of the extinction coefficient to divide the crystal into subsequent volumes. In each of these volumes the gamma ray has a similar probability of depositing its energy. In the following we call volumes calculated in this way ‘‘equal probability volumes’’. In our Monte Carlo optical simulations we have assumed that all the light produced by the energy deposition of the gamma ray at 511 keV is generated from one single point, located along the crystal axis at the center of an equal probability volume. This simplification is similar to that introduced in Ref. [8]. 2.2. Relative light distribution at crystal interface The histograms in Figs. 2 and 3 give the simulated angular distribution of the incident light at surface A of Fig. 1, in the case of a diffusive and a mirror wrapping. We assumed a perfect adhesion between the wrap and the crystal. This assumption is due to the difficulties in modeling properly some characteristics of the air gap such as thickness, shape, presence of bubbles. The light propagation inside the crystal is modeled assuming a light attenuation length of 40 cm [9]. The diffusive coating is assumed to be 99% lambertian. The diffusive wrapping is typically obtained in experimental practice wrapping the crystal with Teflon and for this reason in the following we will use the term Teflon wrapping
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Fig. 2. Light power distribution at the crystal interface for different points of interaction—Teflon diffusive wrapping.
Mirror wrapping: light output for different points of interaction
[%] of the light produced by the gamma interaction
angular distribution of Zcris changes varying the point of interaction. Zmed ¼ f ða,nmedium Þ is the light output at interface B of Fig. 1. The angular distribution of Zmed depends on the refractive index of the medium. This dependence is analyzed in Section 2.3. In this case we study the average light output after a large number of gamma interactions. To model the energy deposition of a large number of gamma rays inside the crystal we used the model presented in Section 2.1. Zcoat ¼ f ða,coatingÞ is the light output of the coating. Its angular distribution is determined by the number, the thickness and the refractive index of the dielectric layers that are deposited over the SiPM. We examine this quantity in Section 2.4. Results for the average light outputs (i.e. the sum of light outputs calculated for different angles, Zcris , Zmed and Zcoat ) are reported in Section 2.5.
[%] of the light produced by the gamma interaction
10 Fig. 1. Sketch of the simulated setup, showing the radioactive source, the crystal, the optical grease and the detector (SiPM).
17.3 mm 12.9 mm 10.0 mm 7.8 mm 6.0 mm 4.6 mm 3.4 mm 2.3 mm 1.4 mm 0.5 mm
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Fig. 3. Light power distribution at the crystal interface for different points of interaction—mirror wrapping.
to indicate the diffusive wrapping. All the surfaces are assumed as ideal, i.e. the surface roughness is not modeled. The light distribution is expressed in terms of percentage of light incident with respect to the light generated. The axial coordinates that we used in this calculation are the centers of the previously introduced equal probability volumes and are reported in the legend of Figs. 2 and 3 as axial distance from surface Ai. We can note that in the Teflon case the light distribution changes, for a given angle of incidence, changing the point of interaction. In particular it increases for interactions that occur closer to the surface A and this increment is greater for low angles of incidence. In Fig. 3 we can note that with mirror wrapping only minor changes are predicted from simulator. To explain this effect we can consider that the number of interactions between the light generated by the gamma and the wrap is greater for gamma absorptions that occur far from the sensor. In the case of a perfect mirror reflection only the sign of the incident light angle is modified as a result of the light–wrap interaction while in the case of a lambertian reflection the light is
M. Benetti et al. / Nuclear Instruments and Methods in Physics Research A 658 (2011) 61–65
redistributed in the whole half solid angle. For this reason we can expect that in the case of the mirror coating the shape of the light distribution is less dependent on the number of light–wrap interactions.
Teflon wrapping: light output for different index of refraction n n=1.7 n=1.6 n=1.5 n=1.4 n=1
[%] of the light produced by the gamma interaction
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30 20 [degree]
10
The angular distribution of incident light at interface A of Fig. 1 is modified according to Snell Law when the light enters in the subsequent medium. Lutetium orthosilicate-based crystals have a high refractive index, so that, passing through the interface to a medium with a lower index of refraction, it causes a decrease of the transmitted power and a redistribution of the light power incident at low angle. In Fig. 4 we show how the two light distributions, relative to the diffusive wrapping (top) and the mirror wrapping (bottom), are modified by the coupling medium properties. The initial distributions are obtained by summing all the light distributions of calculated equal probability volumes. The cumulative light distribution for the diffusive wrapping is higher for small angles and therefore is less affected by medium at the interface with respect to the cumulative light distribution calculated for the mirror wrapping. Simulations predict that a larger quantity of light reaches the detector if the crystal is coated with a diffusive layer, and this observation is confirmed by experimental practice [10]. 2.4. Light transport across SiPM coating
n=1.7 n=1.6 n=1.5 n=1.4 n=1
12
2.3. Light distribution at sensor interface
0
Mirror wrapping: light output for different index of refraction n
15
63
34
Light propagation through an arbitrary number of dielectrics layer is modeled solving optics with the calculation procedure explained in Ref. [11]. By this procedure, knowing the thickness and the refractive index of every layer deposited over SiPMs, we can calculate the transmission coefficient at a given l (which in our case is 425 nm, the peak emission of the crystal), as a function of the angles of incidence at the outermost layer (surface B of Fig. 1). In Fig. 5 we report some examples of such calculations for different semi-infinite mediums (with a different index of refraction) which simulate the grease coupling the scintillator to the SiPM. We used these values to modify the cumulative light distributions and we did not simulate the behavior of the reflected photons.
5
0
Fig. 4. Angular distribution of the light output for different refractive indexes of the coupling medium: (top) diffusive wrapping and (bottom) mirror wrapping.
2.5. Simulation resume Results for the light outputs at each interface, Zcris , Zmed and Zcoat , summed over the angles, are reported in Table 1. Multiplying the products of one column for the PDE gives Z, the total light output in that configuration.
Fig. 5. Light transmission to the SiPM for different angles of incidence at the surface B, and for different mediums, i.e. the coupling grease between the crystal and the SiPM. In the legend n is the index of refraction of such medium.
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Table 1 Calculated value for light output at different refraction indexes. In the first half light outputs for Teflon wrapping are tabulated and in the second half we report data for mirror wrapping. Light outputs
n¼ 1.7
n¼ 1.6
n ¼1.5
n¼1.4
n¼ 1
0.47 0.98 0.69
0.47 0.96 0.76
0.47 0.94 0.83
0.47 0.90 0.84
0.47 0.68 0.80
0.83 0.67 0.53
0.83 0.55 0.67
0.83 0.46 0.81
0.83 0.38 0.82
0.83 0.17 0.80
Teflon wrapping
Zcris Zmed Zcoat Mirror wrapping
Zcris Zmed Zcoat
(expressed in [V s])) is directly proportional to the number of photons detected. We put a 22Na gamma source near the center of the crystal. In this configuration we can assume that all the points of the crystal absorb a gamma ray with a probability that depends on the distance between that point and the source and on the amount of material placed in between. The energy spectra for the two individual SiPMs are reported in Fig. 7. In both graphs we can recognize two peaks corresponding to the two characteristics photo-peaks of 22Na gamma rays, having energies at 511 keV and 1.275 MeV. Values extracted from the Gaussian fitting of the 511 keV peak are reported in the caption. It can be seen that the signals from the two devices are different: this is due to the different gains resulting from using the same bias voltage for both SiPMs although their breakdown voltages are slightly different. The two energy resolution values calculated from the two Gaussian fits of Fig. 7 are poor (46.72% and 31.15%). This is not surprising with this setup, because the light output depends heavily on the point of interaction which has a detrimental effect on the energy resolution.
Fig. 6. Simulated light output at the interface corresponding to x ¼20 as a function of the event position along the crystal axis, with the crystal wrapped by a Teflon wrapping.
3. Case history We adopted the setup proposed in Ref. [12], in which the event position inside the crystal is extrapolated from the light outputs measured at both ends of the crystal, where two detectors are placed. To exploit this effect fully, the crystal needs to be wrapped with a diffusive wrapping as pointed out in Section 2.2. In Fig. 6 the simulated light output is shown as a function of the event position along the crystal axis. Apart from the very ends of the crystal, where the number of interactions between light and wrap is fewer, a quite good linear dependence of the light output on the position is observed. The maximum ratio between the light outputs at the two ends of the crystal is equal to 1.33, meaning that when a gamma ray interacts near one end of the crystal, i.e. in the proximity of one of the two detectors, the ratio between the two signals yielded by the two sensors should be 1.33. In our experimental setup, we used an optical grease TM (Rhodorsil pate 7), having an index of refraction of 1.4, to couple two nominally identical SiPMs placed at the opposite faces of a 20 mm Teflon coated crystal. The two SiPMs have 3600 cells, each of 50 50 mm2 , with a total area of 3 3 mm2. We used two channels of a digital scope (zt4210 from ztec instruments) to read-out the voltage drop on the 50-O input resistance produced by the current bursts of each SiPM. No further amplification or signal shaping was used, so that the area of the digitized output
Fig. 7. Energy spectra of the signal read on Ch1 (top) and Ch2 (bottom). The values of peak positions are Ch1 1.129 and Ch2 1.69 [V se 8] The values of energy resolutions are Ch1 46.72% and Ch2 31.15%.
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By chance this number is very close to the simulated ratio of maximum and minimum light outputs of Fig. 6. This is the reason why the bisector in Fig. 9 well fits the lower border of the scatter plot. Although this aspect should be further investigated, it is indicating that simulations correctly predict the position dependence of the light output.
4. Conclusions
Fig. 8. Energy spectrum of the signal obtained by the linear combination of the two channels. The value for energy resolutions is 16.12%. Peak position is 3.32 ½108 V s.
We proposed a simulation framework that allows us to apply the measured value of PDE to not collimated light sources. The simulation calculates the angular power distribution of a light source and how it is modified by the interaction with a series of optical elements before light absorption. We applied this method to the investigation of light output of a scintillator crystal and we studied the weights of three factors in the optical system composed of a LYSO crystal and a SiPM, namely the three indexes of refraction of the coupling medium, of the crystal and of the detector wrapping. According to the predicted behavior, a mirror wrapping seems to give some advantages in terms of energy resolution, since the light output is not position dependent. On the other hand the same simulations predict that the overall light output is more prone to be affected crossing successive optical elements due to an angular distribution shifted toward large angles. In Section 2.4 we have presented the calculated light transmission of a SiPM, produced at FBK, once the indexes of refraction and the thickness of the different layers of a detector coating are known. We proposed a simple experimental setup to verify the detection properties of two SiPMs, coupled to a scintillator, wrapped with white diffusive Teflon wrapping, which was studied with the above-mentioned simulation framework. We observe well-correlated signals. The difference in the observed experimental light outputs at the two sides of the crystal are coherent with simulation results. A more accurate experimental verification of the simulation framework will be carried out testing crystals with different lengths and testing mediums with different refractive indexes.
References Fig. 9. Correlation of signals of the two SiPMs coupled at the opposite sides of a 3 3 20 mm3 crystal coated with Teflon wrap.
If we linearly combine the output of the two detectors, we obtain the energy spectrum shown in Fig. 8, which exhibits an energy resolution of 16.72%, still not optimized but definitely much better than the two energy resolutions measured with the single detectors. This confirms that the outputs of the two single channels are strongly correlated. This effect is further demonstrated by the graph of the signal correlation shown in Fig. 9, where a symmetrical accumulation of points can be observed. The lowest border of this scatter plot is due to the interactions occurring near the SiPM connected to Ch1 of the scope (corresponding to the x-axis), whereas the upper border is due to the interactions occurring at the other end (SiPM connected to Ch2, y-axis). In this scatter plot, points relevant to the peak at 1.275 MeV are easily found in the upper right zone, as isolated points. As expected, they are well aligned perpendicularly to the symmetry axes of the scatter plot. The linear regression fit to the data is found to have a slope of C1:32, in agreement with the different gains of the two SiPMs.
[1] P. Buzhan, et al., Nuclear Instruments and Methods in Physics Research A 504 (2003) 48. [2] G. Collazuol, et al., Nuclear Instruments and Methods in Physics Research A 581 (2007) 461. [3] P. Liaparinos, I. Kandarakis, D. Cavouras, H. Delis, G. Panayiotakis, Nuclear Instruments and Methods in Physics Research A 569 (2006) 355. [4] D. Wahl, V. Mikhailik, H. Kraus, Nuclear Instruments and Methods in Physics Research A 570 (2007) 529. [5] N. Ghal-Eh, M. Scott, R. Koohi-Fayegh, M.F. Rahimi, Nuclear Instruments and Methods in Physics Research A 516 (2004) 116. [6] Y.A. Berdnikov, V.V. Grebenshchikov, V.F. Kosmach, I. Leonov, V. Samsonov, O.Y. Krushcheva, A.P. Shishlo, Instruments and Experimental Techniques 44 (4) (2001) 466. [7] M. Kronberger, E. Auffray, P. Lecoq, Improving light extraction from heavy inorganic scintillators by photonic crystals, Nuclear Science Symposium Conference Record, vol. M06-179(22), 2008, pp. 3914–3919. + [8] E. Lorincz, G. Erdei, I. Pe´czeli, C. Steinbach, F. Ujhelyi, T. Bukki, IEEE Transactions on Nuclear Science NS-57 (1) (2010) 48. [9] I. Vilardi, F. Ciocia, N. Colonna, R. De Leo, L. Lagamba, S. Marrone, E. Nappi, G. Tagliente, A. Valentini, A. Braem, E. Chesi, C. Joram, et al., Nuclear Instruments and Methods in Physics Research A 564 (2006) 506. [10] H. Heinrichs, A. Blume, N. Bußmann, R. Engels, G. Kemmerling, S. Weber, K. Ziemons, Nuclear Instruments and Methods in Physics Research A 486 (2002) 60. [11] F. Tommasini, A. Morgante, Correnti radiazioni e quanti, 2007. [12] A.V. Getkin, V. Gavrylyuk, D. Zosim, V. Yankelevich, Unidimensional position sensitive detector, Nuclear Science Symposium Conference Record 3, 2000.