Modeling and Simulation of Scintillation Pulses for Crystal ...

Arab Journal of Nuclear Science and Applications, 94 (2 ), (123-131) 2016

Modeling and Simulation of Scintillation Pulses for Crystal Identification Applications H. I. Saleh and A. A. Arafa Radiation Engineering Department, National Center for Radiation Research and Technology , Atomic Energy Authority, Egypt.

Received: 6/9/2015

Accepted: 1/10/2015 ABSTRACT1

The crystal identification and particle identification require applying pulse shape discrimination (PSD) or Crystal Identification (CI) me thods to differentiate between two or more types of scintillation pulses according to their decay times. The characterizations of scintillation pulses significantly affect the performance and the complexity of the CI algorithm. This paper implements a mathematical model of different types of pulses and their typical noise. Furthermore, a generic LabVIEWbased module is implemented for simulation and generation of different types of scintillation pulses. The presented module provides a generic simulation too l to enable selection of different parameters and characteristics of generated pulses. The results of different simulated types of pulses are provided and compared with practically measured pulses. The discussed results show that the simulation and modeling of the scintillation pulses are accurately validated. Key Words: Crystal Identification/ Depth of Interaction/ Pulse Shape Discrimination/ Scintillation Pulses Modeling. INTRODUCTION Scintillation detectors have been used in various applications of radiation detection and spectroscopy including dosimetry (1, 2), particle physics (3), material science (4), medical imaging (5), high-energy physics (6, 7), fast-neutron detection (8), reactor instrumentation (9), nuclear safeguards and security (10), astrophysics (11) and homeland security (12). Scintillation detectors are usually composed of scintillators optically coupled to photomultiplier tubes (PMTs). Scintillator materials are used as convertors for ionizing radiations by emitting visible or UV photons. The scintillation crystal absorbs the incident radiation and emits a light pulse characterized by the special properties of the crystal such as the decay time (13). Subsequently, the PMT generates an electrical pulse with an overall decay time, which varies with the type of incident particle. Thus, based on the decay time of the pulse signal, the γ rays and α and β particles can be identified, i.e. particle identification (14-16), using the pulse shape discrimination (PSD). Furthermore, the phoswich detector (17) is a stack of two or more different scintillation crystals optically coupled to a single PMT. Based on the decay time of the pulses emitted from the phoswich detector, the crystal identification (CI) determines the Depth of Interaction (DOI) (18). Therefore, Positron Emission Tomography (PET) systems use phoswich detectors in order to reduce the parallax error (19, 20). Several techniques are used for PSD and CI applications (15, 18, 21-28). In order to test and compare these techniques, scintillation pulses must be generated and recorded which require a complex setup of radiation sources, scintillation detector, alongside data acquisition board. There is a great need for simulation of such scintillation pulses to unify the data set for comparison purposes as well as to avoid building such complex system.

1

Corresponding author E-mail: E-mail: [email protected] Tel: +201287587503

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Fax: +20222738665

Arab Journal of Nuclear Science and Applications, 94 (2 ), (123-131) 2016

In this paper, mathematical modeling and simulation of scintillation pulses are presented and implemented by a generic LabView-based module. This generic simulation module enables to input different parameters and specifications of scintillation detectors on which the scintillation pulses depend. The mathematical model of scintillation pulses is discussed in Section II. Section III introduces the noise sources modeling. The proposed simulation module of modeled pulses with noises is presented in Section IV. The results are shown and discussed in Section V. Finally, the conclusion is provided in Section VI. SCINTILLATION PULSES MODELING Scintillation detectors are composed of scintillators optically coupled to PMTs as shown in Fig. (1). Scintillator materials convert ionizing radiation such as X-ray, γ-ray into photons in form of light pulses. These light pulses are characterized by the special properties of the crystal such as the decay time (13). Subsequently, the photocathode absorbs scintillated photons and generates electrons which are focused into a beam by the focusing electrode. Then each initial electron is converted to between 104 and 105 electrons by successive stages of dynodes (i.e. electron multipliers); the tube in Fig. (1) has ten dynodes. The overall multiplication gain of the PMT ranges from 105 to 106. The PMT generates an electrical pulse derived from its anode with overall decay time, which varies with the type of incident radiation. Most of the gamma-ray detectors employed in PET applications afford output signals that need further amplifying and processing to perform an optimal analog-to-digital conversion. Front-end electronics include all the necessary analog processing from the detector’s output to the input of the data-acquisition system. An input pre-amplifying stage and an output shaping stage are typical frontend electronics. Due to their reduced amplitude and high sensibility to noise, the detector’s output signals must be carefully amplified by preamplifiers. An equivalent model of the detector will help throughout the simulation process.

Fig. (1) Cross-section of photomultiplier tube and its equivalent anode circuit. The principal component of light emitted from most scintillators can be adequately represented by a simple exponential decay pulse. If the spread of transit time of the PMT is smaller compared with this decay time, then the electron current arriving at the PMT anode can be realistically modeled as 𝑖(𝑡) = 𝑖0 𝑒 −𝜆𝑡, where λ is the scintillator decay constant. The initial current i0 can be expressed in terms of the total charge Q collected over the entire pulse by ∞

∞

𝑄 = ∫ 𝑖 (𝑡) 𝑑𝑡 = 𝑖 0 ∫ 𝑒 −𝜆𝑡 𝑑𝑡 = 𝑖 0 /𝜆

(1)

𝑖(𝑡 ) = 𝜆𝑄𝑒 −𝜆𝑡

(2)

0

0

So, 𝑖0 = 𝜆𝑄 and

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Arab Journal of Nuclear Science and Applications, 94 (2 ), (123-131) 2016

to derive the voltage pulse 𝑉(𝑡) expected at the anode. The shape of the voltage pulse generated at a PMT anode due to a scintillation event relys on the time constant of the anode circuit. The equivalent circuit for the PMT anode circuit and the front-end circuit consists of a combination of resistance R eq and capacitor Ctot connected in parallel as shown in Fig. (1. The current flowing into the parallel RC circuit must be the sum of the current flowing into the capacitance 𝑖𝐶 and the current through the resistance 𝑖𝑅 𝑖 (𝑡) = 𝑖 𝐶𝑡𝑜𝑡 + 𝑖 𝑅𝑒𝑞 = 𝐶𝑡𝑜𝑡

𝑑𝑉(𝑡) 𝑑𝑡

+

𝑉(𝑡) 𝑅𝑒𝑞

(3)

Substitute from (2) into (3) , one get the first order in-homogenous differential equation 𝑑𝑉(𝑡) 𝑑𝑡

+

𝑉(𝑡) 𝑅𝑒𝑞 𝐶𝑡𝑜𝑡

=

𝜆𝑄 𝐶𝑡𝑜𝑡

𝑒 −𝜆𝑡

(4)

The solution of this equation with initial condition 𝑉 (𝑡) = 0, is 𝑉(𝑡) =

where 𝛳 =

1 𝑅𝑒𝑞𝐶𝑡𝑜𝑡

1

𝜆𝑄

𝜆 − 𝛳 𝐶𝑡𝑜𝑡

(𝑒 −𝛳𝑡 − 𝑒 −𝜆𝑡 )

(5)

is the reciprocal of the anode time constant.

For most of scintillators, the emitted pulse is composed of two exponential decays; the fast and slow components of the scintillator. Because the slow component often depends on the nature of the absorbed radiation, this dependence is used to differentiate different kinds of radiation. Moreover, the CI uses PSD methods (21) in order to identify the scintillated crystal according to its pulse decay time, particularly the decay time of the slow component. The six-parameter model given in [29] describes scintillator pulse shapes as follows: 𝑉 (𝑡) =

𝑄 𝑄 ( ) (𝑒 −𝜃(𝑡−𝑡0) − 𝑒 −𝜆𝑓 𝑡 −𝑡0 ) + (𝑒 −𝜃(𝑡 −𝑡0) − 𝑒 −𝜆𝑠 (𝑡−𝑡0) ) 𝜃 𝜃 (1 − ) 𝐶 (1 − ) 𝐶 𝜆𝑓 𝜆𝑠

(6)

Where t 0 is the time reference for the start of the signal, and 𝜆𝑓 and 𝜆𝑠 are the decay constants (i.e. the reciprocals of decay times; 𝜆𝑓 = 1/𝜏𝑓 and 𝜆𝑠 = 1/𝜏𝑠 ) for the fast and slow components, respectively. For high rates counting applications, the anode circuit time constant is set to be much smaller than the scintillator decay time ( [13], (i.e., 𝜆𝑓 ≪ θ), to get a much faster pulse. Now equation (6) becomes: (𝑡 −𝑡0)

𝑥(𝑡) ≈ 𝐴(𝑒 −𝜆𝑓

Where 𝐴 =

𝜆𝑓𝑄 𝜃𝐶

and 𝐵 =

𝜆𝑠 𝑄 𝜃𝐶

−𝑒 −𝜃

( 𝑡−𝑡0)

) + 𝐵(𝑒 −𝜆𝑠(𝑡 −𝑡0) −𝑒 −𝜃(𝑡−𝑡0) )

(7)

are the amplitudes of the fast and slow components, respectively.

For simplicity, the pulse waveform is translated left by an amount 𝑡0 so that the start of the pulse is on the y-axis. Thus equation (7) can be expressed as: 𝑦 (𝑡) = 𝑉(𝑡 + 𝑡0 ) . 𝑢 (𝑡) ≈ [ 𝐴(𝑒 −𝜆𝑓 𝑡 −𝑒 −𝜃𝑡 ) + 𝐵(𝑒 −𝜆𝑠𝑡 −𝑒 −𝜃𝑡 )]. 𝑢 (𝑡 ) ,

(8)

where 𝑢(𝑡) is the unit step function. NOISE SOURCES MODELING There are a number of potential sources of fluctuation in the response of a given detector that result in imperfect energy resolution. These include any drift of the operating characteristics of the 125

Arab Journal of Nuclear Science and Applications, 94 (2 ), (123-131) 2016

detector during the course of the measurements, sources of random noise within the detector and instrumentation system, and statistical noise arising from the discrete nature of the measured signal itself. All of the noise components contributes to the overall noise, and can be computed from 2 2 𝜎𝑡𝑜𝑡 = √𝜎𝑠𝑡2 + 𝜎𝑏𝑘 + 𝜎𝑑2 + 𝜎𝑎𝑚𝑝

(9)

2 2 2 where 𝜎𝑠𝑡 , 𝜎𝑏𝑘 , 𝜎𝑑2 and 𝜎𝑎𝑚𝑝 are the individual noise component which can be computed when its relative individual currents are measured. 2 In a wide category of detector applications, the statistical noise 𝜎𝑠𝑡 represents the dominant source of fluctuation in the signal and thus sets an important limit on detector performance. The shot noise current 𝜎𝑠𝑡 corresponding to the overall statistical fluctuations in the photocathode and the dynodes can be written as

𝜎𝑠𝑡 = 𝜇 √2𝑒𝐼𝑝𝑒 𝐹𝐵

(10)

where 𝜇 is the PMT gain, 𝐼𝑝𝑒 is the photoelectric current, 𝐵 is the bandwidth of the measuring electronics, and 𝐹 is the PMT noise figure. The 𝐼𝑝𝑒 is the total charge being produced by the photocathode and collected by the first dynode per unit time. The terms 𝐹, 𝐵, and 𝜇 transform this current into the anode current. Furthermore, photomultiplier tubes are very sensitive devices and therefore unless the system has been made extremely light tight, there are always some background photons contributing to the signal. Hence, the corresponding background light shot noise 𝜎𝑏𝑘 can be written as 𝜎𝑏𝑔 = 𝜇 √2𝑒𝐼𝑏𝑔 𝐹𝐵

(11)

where 𝐼𝑏𝑔 is the background current, which is the average anode current measured without the incident light and can be computed from On the other hand, the dark current, which describes the average noise current due to a number of sources, is dominated by thermionic emission of electrons from the photocathode. The fluctuations of the dark current 𝜎𝑑 can introduce significant uncertainty in the final measurements. These fluctuations can be estimated from 𝜎𝑑 = 𝜇 √2𝑒𝐼𝑑 𝐹𝐵

(12)

where 𝐼𝑑 is the average dark current, which is highly desirable to be kept to the minimum possible value. Besides, the equivalent impedance of the amplifier circuit, which is connected to the PMT load for the measurement of anode current, is subject to thermal variations causing injection of thermal or Johnson noise in the system. The Johnson noise 𝜎𝑎𝑚𝑝 for an amplifier having noise figure 𝐹𝑎𝑚𝑝can be expressed as 𝜎𝑎𝑚𝑝 = √

4𝐹𝑎𝑚𝑝 𝐾𝑏 𝑇𝐵 𝑅𝑒𝑞

126

(13)

Arab Journal of Nuclear Science and Applications, 94 (2 ), (123-131) 2016

where 𝐾𝑏 is the Boltzmann’s constant, 𝑇 is the absolute temperature, and 𝑅 𝑒𝑞 is the equivalent circuit impedance. From equations (10), (11), (12) and (13) the total noise can be reformulated as follows:

𝜎𝑡𝑜𝑡 = √2𝑒 𝜇2 𝐹𝐵 {𝐼𝑝𝑒 + 𝐼𝑏𝑔 + 𝐼𝑑 } +

4𝐹𝑎𝑚𝑝 𝐾𝑏 𝑇𝐵 𝑅𝑒𝑞𝑣

(14)

Except for the statistical fluctuations, all the noise sources described above are instrumental in nature and therefore can be reduced by proper design and construction. For example decreasing the bandwidth of the readout circuitry improves the signal-to-noise ratio. This can be done in practical system provided it does not affect the dynamic range of the system. RESULTS AND DISCUSSIONS The discussed mathematical models of the decay pulse and its noise were implemented using LabVIEW virtual programming package. The LabVIEW-based simulation module (Fig. (2) provides ability to input and change different parameters and specifications of the scintillation detector such as scintillation material decay times, anode circuit and gain of the PMT, and different parameters of noise currents. This enables users to define different scintillation detectors and their simulated generated pulses. The introduced module uses the mathematical model of pulses (Equation (8)) and its noise model (Equation (14)) to generate simulated pulses within specified time window and sampling rate. The time window is selected to allow drawing the entire pulse and its decaying tail for better demonstration. The default values of different parameters and variables are shown in Fig. (2). The generated simulated pulse waveform and its noised waveform are shown in two adjacent panels within the simulation module.

Fig. (2) LabVIEW-based scintillation pulses module used to generate simulated pulses with different decay time constants.

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Arab Journal of Nuclear Science and Applications, 94 (2 ), (123-131) 2016

Simulated pulses with different decay times (20, 40, and 60 ns, respectively) were generated and their normalized (with respect to peak) waveforms are showed in Fig. (3). For comparison purposes, the simulated pluses with decay times 20 ns and 40ns were generated using specified parameters for each type to imitate the measured pulses of DATA_SET2 from LuYAP and LSO scintillation detectors (22). The DATA_SET2 which was used to test and compare different PSD algorithms (23), includes pulses generated from LSO/LuYAP(PML type2) phoswich detector where the slow component of LuYAP material does not affect the LuYAP total light output (22). LSO and LuYAP pulses of DATA_SET2 have decay times of 40 ns and 20 ns, respectively. On the other hand, LSO and LuYAP pulses of DATA_SET1 have decay times of 40 ns and 220 ns, respectively (24, 25,30).

(a)

(b)

(c)

Fig. (3) Simulated pulses with different decay times, (a) 20, (b) 40 and (c) 60 ns. Fig. (4) shows DATA_SET2 pulses recorded and sampled by a digital oscilloscope at sampling rate of 5 GHz. These pulses are generated from the PMT anode signals which are first inverted, amplified and then sampled. The LSO pulse has a larger voltage peak than LuYAP pulse complying with their relative light yields (31 , 32). All pulses are measured at anode, with Tectronix Oscilloscope and Sample-Test Board, where the anode signal is amplified with AD811 OpAmp inverting amplifier with 47  at input and 560  feedback resistor [33]. One pulse from each type (LuYAP and LSO) is normalized to its peak for comparison as shown in Fig. (4). It is noted that the noise in LuYAP pulse is higher than in LSO pulse due to the required high gain of amplification to compensate the low light yield of the LuYAP scintillator.

Fig. (4) Normalized recorded anode pulses of LuYAP and LSO detectors (sampled at 5 GHz rate by Tektronix Digital oscilloscope (33) ). 128

Arab Journal of Nuclear Science and Applications, 94 (2 ), (123-131) 2016

From Fig. (3) Simulated pulses with different decay times, (a) 20, (b) 40 and (c) 60 ns., the simulated LuYAP and LSO pulses are very similar to the measured ones shown in Fig. (4) Normalized recorded anode pulses of LuYAP and LSO detectors (sampled at 5 GHz rate by Tektronix Digital oscilloscope (33 ) ). The simulation module consists of three main parts. The first part is the transfer function used to give an exponential decay signal the pulse required. The second part is a random number generator governed by the used mathematical noise model which is used as a source of noise added to the generated pulses. Finally, amplification and normalization are applied on the generated pulses. To summarize, the proposed generic LabVIEW-based simulation module provides a flexible tool for simulating different types of scintillation pulses with different PMT arrangements. CONCLUSION The crystal identification and particle identification require applying CI methods to differentiate between two or more types of scintillation pulses according to their decay times. The characterizations of scintillation pulses significantly affect the performance and the complexity of the CI systems. A mathematical model has been implemented based on the six parameters model and the PMT noise model in order to generate different types of scintillation pulses. The discussed mathematical models of the decay pulse and its noise were implemented using the LabVIEW. The LabVIEW-based simulation module affords the ability to input and change different parameters and specifications of scintillation detectors such as scintillation material decay times, the gain and anode circuit of the PMT, and different parameters of noise currents. The presented module provides a generic simulation tool to enable selection of different parameters and characteristics of generated pulses. The results of simulated different types of pulses were provided and compared with practically measured pulses. The results showed that the simulation and modeling of the scintillation pulses are accurately validated. REFERENCES (1) L. Beaulieu, M. Goulet, L. Archambault, and S. Beddar, "Current status of scintillation dosimetry for megavoltage beams." p. 012013. (2) S. Stefanowicz, H. Latzel, L. R. Lindvold, C.E. Andersen, O. Jäkel, and S. Greilich, “Dosimetry in clinical static magnetic fields using plastic scintillation detectors,” Radiation Measurements, vol. 56, pp. 357-360, 2013. (3) W.R. Leo, Techniques for nuclear and particle physics experiments: a how-to approach: Springer Science & Business Media, 2012. (4) A. Peurrung, “Materials science for nuclear detection,” Materials Today, vol. 11, no. 3, pp. 50-54, 2008. (5) C.W. Van Eijk, “Inorganic scintillators in medical imaging,” Physics in medicine and biology, vol. 47, no. 8, pp. R85-R106, 2002. (6) P. Maoddi, “Microfluidic Scintillation Detectors for High Energy Physics,” ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE, 2015. (7) N. D'Ascenzo, and V. Saveliev, The New Photo-Detectors for High Energy Physics and Nuclear Medicine: INTECH Open Access Publisher, 2011. (8) C. Zhang, D.M. Mei, P. Davis, B. Woltman, and F. Gray, “Measuring fast neutrons with large liquid scintillation detector for ultra-low background experiments,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 729, pp. 138-146, 2013. (9) V. Belov, V. Brudanin, M. Danilov, V. Egorov, M. Fomina, A. Kobyakin, V. Rusinov, M. Shirchenko, Y. Shitov, and A. Starostin, “Registration of reactor neutrinos with the highly segmented plastic scintillator detector DANSSino,” Journal of Instrumentation, vol. 8, no. 05, pp. P05018, 2013. 129

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