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Development of a single-chip digital radiation spectrometer based on ARM Cortex-M7 micro-controller unit
Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
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Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Development of a single-chip digital radiation spectrometer based on ARM Cortex-M7 micro-controller unit S. Boorboor, M. Khorsandi ∗ Radiation Application Department, Shahid Beheshti University, Tehran, Iran
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Keywords: Radiation spectroscopy Digital signal processing Energy resolution Trapezoidal filter ARM micro-controller
ABSTRACT Digital signal processing is a flexible and effective approach for development of radiation spectroscopy systems. However, the conventional digital spectrometers are built using many hardware components resulted in a more complex and costly system. In this work, a complete digital spectrometer has been implemented in an ARM-based STM32F730 micro-controller. The proposed approach was benefited from a high signal to noise ratio of the trapezoidal filter to extract the particle energies. The recorded pulse height spectra using a large HPGe detector proved the good performance of the implemented system in the experiments. The proposed spectroscopy system provided an energy resolution better than 0.15% at 1332.5 keV along with a maximum nonlinearity of 0.34%, over a wide energy range. The overall results revealed that modern MCUs can be efficiently employed to develop a compact low-powered and cost-effective digital radiation spectrometer.
1. Introduction Digital signal processing is a very promising approach for the development of radiation spectroscopic systems. It demonstrates significant advantages over the traditional analog chain such as high stability, high noise immunity, simple design, and unlimited flexibility in choosing the shaping parameters. The digital approach also provides the opportunity to easily implement a high performance triangular, trapezoidal, or cusp-like shaping filters [1–5]. An ordinary digital spectroscopy system hardware contains many different components including ADC, volatile and non-volatile memories, communication interfaces, and some processing units such as DSP and/or FPGA [3,5,6]. These may make the system bulky, fragile, vulnerable and expensive that limits its applicability in some cases. However, in recent years, the micro-controller technology has been revolutionized by the advent of ARM Cortex-M7 processor series. Most of the modern ARM-based micro-controllers provide high computation capabilities for real-time digital signal processing besides many useful peripheral components such as high-speed ADCs, direct memory access (DMA) units, Ethernet and USB communication bridges [7]. The features of modern micro-controller units (MCUs) make them interesting tools in the field of digital spectroscopy. The performance of an MCU had been previously evaluated using STM32F746 micro-controller in which the Lagrange interpolation had been used for precise pulse height extraction of quasi-Gaussian pulses [8]. The demands of environmental radiation monitoring spectroscopy have been led to the development of portable low-power data acquisition systems [9]. These devices have been designed with different processing capabilities in a variety of dimensions and power consumption.
As an example, MCA8000D made by Amptek is a portable complete pulse height analysis system which measures the peak amplitude and produces a histogram representing the pulse height spectrum [10]. The device dimension is about 12.5 × 7.1 × 2 cm3 which limits its application as a compact device. Amptek has also developed PD5, a single board digital signal processing in place of both the shaping amplifier and MCA used in a traditional analog spectroscopy system [11]. PD5 provides a trapezoidal filter with commendable peaking time and flattop duration up to 102 and 51 μs, respectively. Physical dimensions of the PD5 board are 8.9 cm × 6.3 cm (3.5 in. × 2.5 in.) and its typical power consumption is quoted about 600 mW. There are also integrated radiation spectroscopy systems including digital pulse processing, MCA, and high voltage supply. The power dissipation of these systems can be as large as a few watts [12,13]. In the present work, a digital pulse processing system has been developed based on a single STM32F730 chip for portable batterypowered radiation spectroscopy. It was intended for the applications in which the count-rate are typically lower than 104 cps. For such system, although the count-rate can be increased more than ten thousand at the expense of resolution degradation to 2.2 keV at 1332 keV of 60 Co, it still provides much lower throughput compared to the FPGA based systems and flash ADCs. In the proposed system, the exponentially decaying signal of a charge-sensitive preamplifier is directly sampled by the MCU’s ADC without any extra analog pulse processing circuits. Physical dimensions of the developed system including MCU, antialiasing filter and gain adjustment amplifier are 3 cm × 2 cm (1.2 in. × 0.8 in.), which makes it easily possible to embed the circuitry in a compact
∗ Corresponding author. E-mail address: [email protected] (M. Khorsandi).
https://doi.org/10.1016/j.nima.2019.162685 Received 28 April 2019; Received in revised form 6 August 2019; Accepted 1 September 2019 Available online 5 September 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.
S. Boorboor and M. Khorsandi
Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
portable device. The maximum power dissipation of the system is limited to 190 mW. This feature makes the system potentially a preferable candidate for portable battery-operated data acquisition. The firmware of the system can be easily updated by developing C and/or assembly signal processing subroutines. It is rather hard or maybe in some cases impossible to make such flexibility in commercially available data acquisition systems. In terms of cost, the cost price of the developed system is less than $15. Therefore, the proposed system can be quite cost-effective compared to the commercial or custom-made FPGA based systems. This approach will result in a more versatile platform in which any demanded pulse and data processing algorithms can be easily implemented for particle energy measurement or timing applications in which the time resolution is to be in the order of tens of nanoseconds. 2. Methodology 2.1. Pulse processing method Fig. 1. Typical output of digital pulse shaping with the peaking time of 9.3 μs and the flat-top duration of 1.86 μs.
The goal of the pulse processing is the conversion of the preamplifier signal to an appropriate pulse shape whose height is linearly proportional to the deposited energy of the particle in the active region of the detector. The shaping filters such as trapezoidal, triangular, cusplike, quasi-Gaussian, etc. can be used for particle energy measurement. Any filter is favored under some specific circumstances. Cusp-like filter theoretically provides the best signal to noise ratio, especially in systems with high series and parallel white noise, in cost of a rather low throughput. The quasi-Gaussian shaper is a very interesting filter which can be easily implemented in an analog circuitry using passive components in the form of CR-RC4 network. However, the signal to noise ratio of a quasi-Gaussian filter is relatively poor compared to that of cusp-like and triangular filters [3,14]. The trapezoidal shaper is an appropriate filter which handles well the tradeoff between the minimization of resolution and throughput maximization by providing adjustable parameters of peaking time and flat-top duration. As well, it is shown that the trapezoidal shaper provides a better energy resolution than the cusp-like filter for short peaking time in gamma spectroscopy by coaxial HPGe detector [4]. The implementation of high-performance filters such as trapezoidal and triangular one is straight forward on a digital platform. In this regard, the input is an exponentially decaying pulse of the chargesensitive preamplifier that can be ideally expressed by the following equation: { 𝑡 𝑚𝑒− 𝜏 𝑡 ≥ 0 𝑥(𝑡) = (1) 0 𝑡<0
Integration of the rectangular pulse over a period of l can be done using the following recursive formula: 𝑎𝑛 = 𝑎𝑛−1 + 𝑟𝑛 − 𝑟𝑛−𝑙
where 𝑎𝑛 is the trapezoidal signal value of nth sample. It is more convenient to present the filter shaping controls as peaking time and flat-top duration. In this respect, the averaging length (l) can be considered to be equal to the peaking time of the pulse. The flat-top duration can be also calculated by subtracting the averaging length from the rectangle width (k). A typical output of the proposed digital pulse processing has been presented in Fig. 1. The input signal is obtained from a charge sensitive preamplifier connected to an HPGe detector. The preamplifier is an RC-type with a time constant of ∼47 μs. The preamplifier signal was sampled at a rate of 5.4 MS/s and transferred to MATLAB software via USB port. In the present approach, the decaying pulse was converted to the trapezoidal form through the Eqs. (4) and (5). Here, the peaking time and the flat-top duration of the trapezoid are equal to 9.3 μs and 1.86 μs, respectively. 2.2. Logical block diagram of spectroscopy system The logical block diagram of the spectroscopy system has been shown in Fig. 2. The sampled input signal has been fed into two separate branches, one of which has a slow shaping time and the other has a fast shaping time constant. In both branches, at first, the exponential signal is converted to a rectangular shape. Then, a moving average filter acts on the rectangular pulse to produce a trapezoidal signal shape. The slow branch provides a good signal to noise ratio that is required for energy measurement purposes, whereas the fast signal is short enough to drive pulse edge detection and pile-up rejection units. The peak detection block is triggered by a pulse flag which is raised by the pulse edge detection unit when the fast trapezoidal signal exceeds a predefined threshold level. The energy measurement is accomplished by calculating the trapezoid height with respect to the baseline in the slow branch. The baseline of each pulse is determined separately by measuring the trapezoidal filter output 0.56 μs before pulse edge. At the same time, the pile-up rejection block inspects any pile-up events. Finally, if the pile-up flag is off, the slow signal pulse height is recorded by the histogram unit.
where m, 𝜏, and t represent the pulse amplitude, decaying time constant of the preamplifier with resistor feedback, and the elapsed time, respectively. A discretized form of the signal may be represented as: { 𝑇 𝑚𝑒− 𝜏 𝑛 𝑛 ≥ 0 𝑥𝑛 = (2) 0 𝑛<0 where, T and n denote sampling period time and sample index, respectively. The desired form of the signal for further processing is a finite rectangular pulse which have a height of 𝑚 and an arbitrary width of k. It can also be shown by the following expression: { 𝑚 0<𝑛<𝑘 𝑟𝑛 = (3) 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 The conversion of exponential signal to rectangle one can be performed easily by employing Z-transform [15]. The simplified recursive form of the conversion can be written by Eq. (4). 𝑇
2.3. Implementation of the system
𝑇
𝑟𝑛 = 𝑟𝑛−1 + 𝑥𝑛 − 𝑥𝑛−1 𝑒− 𝜏 + 𝑥𝑛−𝑘 − 𝑥𝑛−𝑘−1 𝑒− 𝜏
(5)
(4)
A digital spectroscopy system has been implemented using an STM32F730 micro-controller which is based on the ARM Cortex-M7
The rectangular pulse is converted to a trapezoidal shape using a moving integration filter having finite width which is smaller than k. 2
S. Boorboor and M. Khorsandi
Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
Fig. 2. The logical block diagram of the developed spectroscopy system.
Fig. 3. Schematic configuration of the implemented system on STM32f730 MCU.
Fig. 4. Block diagram of the experimental setup.
32-bit RISC core, operating at frequency up to 216 MHz. The device offers three 12-bit ADC with a maximum sampling rate of 2.4 MS/s and 7.2 MS/s, respectively in the single and the triple interleaved modes, two DMA units operating at a frequency of 108 MHz, several communication interfaces, timers, and the other components [7]. The schematic configuration of the implemented system has been presented in Fig. 3. The ADC unit has been configured in triple interleaved mode at a sampling rate of 5.4 MS/s. The ADC samples are automatically transferred to a cyclic buffer with a length of 10,000 2byte words per 186 ns using a DMA. The sampled pulse was shaped by slow and fast signal processing units, simultaneously. The implemented program benefits from some intrinsic advantages of the Cortex-M7 such as the same operation on multiple data (SIMD), multiply-accumulate (MAC) capability of DSP, and also branch prediction [16]. The moving
average filter has been also implemented by designing an efficient FIFO buffer in stack region. The spectrum buffer showed in Fig. 3, is an array with the length of 4096 Q-words (32-bits) that stores pulse height histogram. The content of this buffer is updated at the end of pulse height measurement of the valid events. There is also a pulse buffer to store a slice of DMA cyclic buffer for debugging purposes and displaying the input signal on the PC/Laptop screen. The content of both spectrum and pulse buffer can be read by the communication unit via USB port. 2.4. Experimental setup An experimental setup has been implemented to evaluate the performance of the developed system for gamma-ray spectroscopy using 3
S. Boorboor and M. Khorsandi
Fig. 5. (a) Pulse height spectrum from along with a fitted Gaussian curve.
Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
60
Co, (b) magnified 1332.5 keV peak region
Fig. 6. The measured FWHM for different peaking time and flat-top duration, (a) due to the electronic noise, and (b) due to the combination of electronic noise, charge generation, and charge collection of 1332.5 keV gamma-ray energy.
HPGe detector. As illustrated in Fig. 4, a GC1320 HPGe made by CANBERRA Industries has been used as the gamma-ray detector. The detector is a p-type germanium diode with the nominal relative detection efficiency of 13% and guarantied energy resolution of 2 keV for 6 μs shaping time at 1332.5 keV. The charge carries created by gamma absorption in the detector is converted to an exponentially decaying pulse through a charge sensitive preamplifier with a time constant of 47 μs [17]. A precision pulser module used along with the detector to measure electronic noise of the system. After eliminating the aliasing components and also doing gain adjustment, the preamplifier signal was fed into the analog input of the MCU. The pulse processing was accomplished in the MCU and then the pulse height histogram was recorded in the internal memory of the device that can be read by PC/Laptop. It should be mentioned that the count-rate for all the spectra measured by this experimental setup was lower than 104 cps which is usually required in a low count-rate application.
electronic noise amplitude. This behavior can be explained based on the fact that the contribution of the series noise becomes less important at larger integration times. As well, by averaging the processed ADC’s samples, the ADC noise is also reduced efficiently. However, because of the parallel noise, further increases in the peaking time (above 15 μs) causes a degradation in the signal to noise ratio of the filters. It can be also seen that the parallel noise effect is more severe for the pulses with longer flat-top duration. The performance of the quasi-Gaussian filter is worse than the trapezoidal one in the range of investigated peaking time, as shown in the figure. According to Fig. 6b, the peak broadening of 1332.5 keV has been decreased by increasing the peaking time. A two-fold phenomenon can cause this behavior. On the one hand, increasing the integration time up to 10–15 μs has led to a smaller electronic noise. On the other hand, the longer shaping time has provided the opportunity for a better charge collection that limits the contribution of charge collection fluctuation to the peak broadening. Furthermore, the peak broadening caused by the imperfect charge collection can be ameliorated by adding a flat-top part into the synthesized pulse. Then, the longer flat-top duration leads to a smaller FWHM, specifically for the peaking time below 10 μs. For longer peaking times, the charge collection fluctuation becomes almost constant. Nevertheless, the resolution of the system was degraded in much longer peaking times because the parallel noise contribution has become more significant. As expected, the resolution degradation is more severe for filters with longer flat-top durations. Moreover, it can be seen that the measured broadening of pseudoGaussian pulses is obviously larger than that of trapezoidal pulses in the region of the shorter peaking times, whereas, for very long peaking times (>18 μs), the performance of both filters is almost the same. As a result, the Gaussian shaping is more sensitive to fluctuations in the charge collection process.
3. Results and discussions Fig. 5a shows a pulse height spectrum recorded from 1173.2 keV and 1332.5 keV gamma rays emitted by 60 Co using the experimental setup. The peaking time and the flat-top duration of the filter were chosen to be 5.9 μs and 8.9 μs, respectively. To give more details about the pulse height distribution of the fully absorbed gamma quanta, the photo-peak region of 1332.5 keV energy is presented in Fig. 5b. As seen in the spectrum, the shape of the full-energy peak is very nearly Gaussian. The full width at half maximum (FWHM) of the peak is 4.7 ± 0.05 channels (1.96 ± 0.02 keV) translated to a resolution of about 0.15% at 1332.5 keV. Furthermore, some experiments have been carried out to investigate the effect of processing parameters on the energy resolution. The electronic noise of the implemented trapezoidal filter, as well as an analog quasi-Gaussian filter, are presented as a function of peaking time in Fig. 6a. Here, it is evident that increasing the peaking time up to 10–15 μs, depending on the flat-top duration, has led to a smaller 4
S. Boorboor and M. Khorsandi
Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
Co,
137
Cs, and
152
Fig. 7. The recorded pulse height spectrum from sources. Table 1 Energy, central channel and FWHM for
60
Energy (keV)
Peak Central Channel
FWHM (keV)
121.8 244.7 344.2 411.1 443.9 661.7 778.9 867.3 964 1085.8 1112 1173.2 1299.1 1332.5 1408
330.4 ± 0.01 662.1 ± 0.02 930.9 ± 0.03 1112.7 ± 0.04 1200.1 ± 0.07 1787.1 ± 0.05 2104.9 ± 0.06 2344.1 ± 0.12 2605.5 ± 0.10 2934.1 ± 0.21 3006.1 ± 0.13 3171.7 ± 0.10 3512.6 ± 0.14 3602.9 ± 0.10 3807.4 ± 0.08
1.13 1.22 1.29 1.33 1.38 1.53 1.62 1.66 1.79 1.92 1.92 1.93 1.99 2.00 2.07
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
Co,
0.01 0.02 0.02 0.03 0.06 0.03 0.06 0.07 0.04 0.06 0.05 0.03 0.06 0.03 0.03
137
60
Cs, and
152
Eu radioisotope
Eu peaks.
FWHM (Channel)
Resolution (%)
3.05 3.31 3.49 3.61 3.73 4.14 4.39 4.50 4.78 5.18 5.19 5.19 5.38 5.42 5.61
0.93 0.50 0.37 0.32 0.31 0.23 0.20 0.19 0.18 0.17 0.17 0.16 0.15 0.15 0.15
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.03 0.06 0.06 0.08 0.17 0.09 0.16 0.19 0.10 0.16 0.14 0.09 0.17 0.08 0.08
Fig. 8. (a) The relation between photo-peak central channel and photon energy, (b) deviation of data points from the fitted line.
maximum nonlinearity of 0.042%. This value is negligible compared with the maximum observed nonlinearity of 0.34% in the energychannel relationship. It is deduced that the observed nonlinearity of the energy peaks can be originated from incomplete charge collection in the detector side and ballistic deficit as well. Moreover, investigation of the energy-channel linearity for different shaping parameters shows that the maximum non-linearity is generally decreased as the shaping time is increased. As an example, the maximum nonlinearity in energy peak distribution is limited to 0.19% for peaking time and flat-top duration of 14.8 μs and 5.6 μs, respectively. The total broadening of the photo-peaks, as well as contribution of the electronic noise, were measured as a function of energy, for peaking time of 5.9 μs and flat-top of 5.2 μs, as shown in Fig. 9. The total broadening is caused by different factors including charge carrier generation statistics, charge collection, and electronic readout noise which itself contains the preamplifier noise, gain controller noise, ADC error, and DSP operations round-off error. As shown in Fig. 9, the measured peak broadening due to the electronic noise is almost constant (∼0.86 keV) over the entire ADC range. The contribution of the baseline fluctuations and pile-up effects to the noise were investigated through the measurement of the peak broadening at the count-rate between 500 to 7000 cps made by changing the source-detector distance. Thereupon, no expressive effect was observed in the peak broadening in the range of the investigated count-rate. So, the major contributor to the noise can be due to the imperfect charge collection. This imperfection may be originated from trapping centers created in the semiconductor material, acceleration/deceleration of primary electrons, etc. However, due to the energy dependence of charge generation and collection statistics, the total FWHM is a function of incident gamma-ray energy. To have an estimation, the model discussed by Owen [18] was fitted on the measured total FWHM data illustrated in Fig. 9. By the model, the total
The linearity and the energy resolution of the spectrometer were determined over a wide range of energies. In this respect, the pulse height spectrum from gamma quanta emitted by 60 Co, 137 Cs, and 152 Eu sources was measured considering a peaking time and flat-top duration of 5.9 μs and 5.2 μs, respectively. As shown in Fig. 7, 15 photo-peaks expanded from 121.78 keV to 1408 keV can be well recognized in the recorded spectrum. Here, the best energy resolution was obtained about 0.15% pertaining to 1408 keV energy peak of 152 Eu. The resolution is degraded with decreasing the energy and reaches to 0.93% for the 121.78 keV peak. Details about the central channel and FWHM of all peaks are reported in Table 1. The relation between the different photon energy in the pulse height histogram and the corresponding central channel of the photo-peak is shown in Fig. 8a. According to the figure, the proposed spectrometer provides a linear relation between the photo-peak channel and gammaray energy with the slop of 2.7 channels/keV. Deviation of the data points from the fitted line has been also given in Fig. 8b. The maximum observed nonlinearity is 0.34% which belongs to 121.78 keV photon. However, the nonlinearity is drastically decreased for higher energy photons and limited to only about 0.09%. The linearity of the electronic chain including the preamplifier, gain adjustment, ADC, and DSP was also measured by applying a pulser module. The measurement results at different pulse heights showed a 5
S. Boorboor and M. Khorsandi
Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
benefits from the advantages of low-power consumption, low cost, small dimensions, and flexibility in development of the Cortex-M7 to perform a digital pulse processing in an efficient way. The experimental results showed that the spectrometer was able to resolve 1332.5 keV photons peak with FWHM of 1.96 keV. In addition, good linearity was observed between the central peak channels and gamma-ray energies so that the maximum nonlinearity was limited to 0.34%. This value mainly originated from incomplete charge collection in the detector side and ballistic deficit as well. The overall results revealed that the modern MCU along with the proposed approach can be efficiently employed as a compact and cost-effective digital radiation spectrometers. It seems that these devices have many potentials to be used as the next platform of the digital spectrometers in various low-rate applications. Acknowledgment The authors are gratefully indebted to Shahid Beheshti University, Iran, G. C., for researching support of this work. We would also like to show our gratitude to the professor S. A. H. Feghhi and we thank specially reviewers for their so-called insights. References [1] V.T. Jordanov, G.F. Knoll, Digital synthesis of pulse shapes in real time for high resolution radiation spectroscopy, Nucl. Instrum. Methods Phys. Res. A 345 (1994) 337–345, http://dx.doi.org/10.1016/0168-9002(94)91011-1. [2] V.T. Jordanov, G.F. Knoll, A.C. Huber, J.A. Pantazis, Digital techniques for realtime pulse shaping in radiation measurements, Nucl. Instrum. Methods Phys. Res. A 353 (1994) 261–264, http://dx.doi.org/10.1016/0168-9002(94)91652-7. [3] G.F. Knoll, Radiation Detection and Measurement, fourth ed., Wiley, 2010, pp. 630–670. [4] N. Menaa, P. D’Agostino, B. Zakrzewski, V.T. Jordanov, Evaluation of real-time digital pulse shapers with various HPGe and silicon radiation detectors, Nucl. Instrum. Methods Phys. Res. A 652 (2011) 512–515, http://dx.doi.org/10.1016/ j.nima.2010.08.095. [5] A. Messai, A. Nour, I. Abdellani, Digital signal processing for optimal resolution in gamma ray spectroscopy, in: Instrum. Digit. Nucl. Spectrosc. Proc. IAEA Tech. Meet. Held Vienna, Austria, 2010, pp. 123. [6] D. Bazzacco, et al., AGATA, technical proposal for an advanced gamma tracking array for the european gamma spectroscopy community, 2001, https://hal. archives-ouvertes.fr/hal-00729050. [7] STMicroelectronics, STM32F730xx datasheet, 2017, https://www.st.com/en/ microcontrollers-microprocessors/stm32f730r8.html. [8] S. Boorboor, H. Jafari, S.A.H. Feghhi, Development of a novel approach for precise pulse height extraction using Lagrange interpolation, Nucl. Instrum. Methods Phys. Res. A 919 (2019) 82–88, http://dx.doi.org/10.1016/j.nima.2018. 12.028. [9] P. Shebell, Portable Gamma-Ray Spectrometers and Spectrometry Systems, International Atomic Energy Agency (IAEA), 1999, http://inis.iaea.org/search/search. aspx?orig_q=RN:30060366. [10] MCA-8000D, Digital multichannel analyzer, (n.d.) https://www.amptek.com/ products/multichannel-analyzers/mca-8000d-digital-multichannel-analyzer. [11] DP5 OEM, Digital signal processor, (n.d.) https://www.amptek.com/products/ digital-pulse-processors/dp5-digital-pulse-processor-and-mca. [12] DSA-LX, Digital signal analyzer, (n.d.) https://www.mirion.com/products/dsa-lxdigital-signal-analyzer. [13] PX5-HPGe, Digital pulse processor, (n.d.) https://www.amptek.com/products/ digital-pulse-processors/px5-hpge-for-germanium-detectors. [14] Gordon R. Gilmore, Practical Gamma-Ray Spectrometry, second ed., John Wiley & Sons, Ltd, 2008. [15] A.V. Oppenheim, R.W. Schafer, Discrete-Time Signal Processing, Pearson, 2010. [16] STM32F7 series and STM32H7 series Cortex® -M7 processor programming manual, 2017, https://www.st.com/resource/en/programming_manual/dm00237416. pdf. [17] www.canberra.com, SEGe detectors datasheet, https://www.mirion.com/ products/sege-standard-electrode-coaxial-ge-detectors. [18] A. Owens, Spectral degradation effects in an 86 cm3 Ge(HP) detector, Nucl. Instrum. Methods Phys. Res. A 238 (1985) 473–478, http://dx.doi.org/10.1016/ 0168-9002(85)90487-5. [19] S. Croft, D.S. Bond, A determination of the Fano factor for germanium at 77.4 K from measurements of the energy resolution of a 113 cm3 HPGe gammaray spectrometer taken over the energy range from 14 to 6129 keV, Int. J. Radiat. Appl. Instrum. A 42 (1991) 1009–1014, http://dx.doi.org/10.1016/08832889(91)90002-I.
Fig. 9. The FWHM as a function of energy for the peaking time of 5.9 μs and the flat-top duration of 5.2 μs.
peak broadening can be expressed by: [ ]0.5 𝛥 (𝐸) = 2.355 𝐹 𝜀𝐸 + (𝛼𝐸 + 𝛽)2 + 𝜎𝑒2
(6)
where, F, 𝜀, E, and 𝜎𝑒 are respectively Fano-factor, the energy required to produce an electron–hole pair, photon energy, and standard deviation of electronic noise. The term 𝐹 𝜀𝐸 is the variance of charge generation inside the crystal active region. The standard deviation of charge collection may be considered as a linear function with constants of 𝛼 and 𝛽. By Taking 𝜀= 2.97 eV, 2.355𝜎𝑒 = 0.86 keV and by fitting Eq. (6) on the total FWHM data points, we will obtain F =0.081, 𝛼 = 2.4 × 10−4 and 𝛽= 213.5 eV. The value of the Fano-factor is therefore consistent with that of the other works [19]. However, the non-zero value of 𝛽 results in a slightly greater value of 𝛥 (𝐸) than electronic noise at zero energy. The calculated values of the broadening due to the charge generation and collection are also shown in Fig. 9. The contribution of different factors to the peak broadening can be estimated based on the resulting curves. One can deduce that the electronic readout noise is a significant contributor to the total broadening in the low energy region (< 250 keV). However, the quadrature sum of the charge generation and the charge collection fluctuations has become a dominant factor of the energy resolution degradation in the higher energy region. As an example, the values of fluctuation in charge generation and collection are obtained respectively 1.33 keV and 1.26 keV at the gamma-ray energy of 1332.5 keV. 4. Conclusion A digital radiation spectrometer has been developed using a single STM32F730 MCU chip. The particle energy was measured by converting the preamplifier signal to the trapezoidal one. The proposed system
6
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Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Development of a single-chip digital radiation spectrometer based on ARM Cortex-M7 micro-controller unit S. Boorboor, M. Khorsandi ∗ Radiation Application Department, Shahid Beheshti University, Tehran, Iran
ARTICLE
INFO
Keywords: Radiation spectroscopy Digital signal processing Energy resolution Trapezoidal filter ARM micro-controller
ABSTRACT Digital signal processing is a flexible and effective approach for development of radiation spectroscopy systems. However, the conventional digital spectrometers are built using many hardware components resulted in a more complex and costly system. In this work, a complete digital spectrometer has been implemented in an ARM-based STM32F730 micro-controller. The proposed approach was benefited from a high signal to noise ratio of the trapezoidal filter to extract the particle energies. The recorded pulse height spectra using a large HPGe detector proved the good performance of the implemented system in the experiments. The proposed spectroscopy system provided an energy resolution better than 0.15% at 1332.5 keV along with a maximum nonlinearity of 0.34%, over a wide energy range. The overall results revealed that modern MCUs can be efficiently employed to develop a compact low-powered and cost-effective digital radiation spectrometer.
1. Introduction Digital signal processing is a very promising approach for the development of radiation spectroscopic systems. It demonstrates significant advantages over the traditional analog chain such as high stability, high noise immunity, simple design, and unlimited flexibility in choosing the shaping parameters. The digital approach also provides the opportunity to easily implement a high performance triangular, trapezoidal, or cusp-like shaping filters [1–5]. An ordinary digital spectroscopy system hardware contains many different components including ADC, volatile and non-volatile memories, communication interfaces, and some processing units such as DSP and/or FPGA [3,5,6]. These may make the system bulky, fragile, vulnerable and expensive that limits its applicability in some cases. However, in recent years, the micro-controller technology has been revolutionized by the advent of ARM Cortex-M7 processor series. Most of the modern ARM-based micro-controllers provide high computation capabilities for real-time digital signal processing besides many useful peripheral components such as high-speed ADCs, direct memory access (DMA) units, Ethernet and USB communication bridges [7]. The features of modern micro-controller units (MCUs) make them interesting tools in the field of digital spectroscopy. The performance of an MCU had been previously evaluated using STM32F746 micro-controller in which the Lagrange interpolation had been used for precise pulse height extraction of quasi-Gaussian pulses [8]. The demands of environmental radiation monitoring spectroscopy have been led to the development of portable low-power data acquisition systems [9]. These devices have been designed with different processing capabilities in a variety of dimensions and power consumption.
As an example, MCA8000D made by Amptek is a portable complete pulse height analysis system which measures the peak amplitude and produces a histogram representing the pulse height spectrum [10]. The device dimension is about 12.5 × 7.1 × 2 cm3 which limits its application as a compact device. Amptek has also developed PD5, a single board digital signal processing in place of both the shaping amplifier and MCA used in a traditional analog spectroscopy system [11]. PD5 provides a trapezoidal filter with commendable peaking time and flattop duration up to 102 and 51 μs, respectively. Physical dimensions of the PD5 board are 8.9 cm × 6.3 cm (3.5 in. × 2.5 in.) and its typical power consumption is quoted about 600 mW. There are also integrated radiation spectroscopy systems including digital pulse processing, MCA, and high voltage supply. The power dissipation of these systems can be as large as a few watts [12,13]. In the present work, a digital pulse processing system has been developed based on a single STM32F730 chip for portable batterypowered radiation spectroscopy. It was intended for the applications in which the count-rate are typically lower than 104 cps. For such system, although the count-rate can be increased more than ten thousand at the expense of resolution degradation to 2.2 keV at 1332 keV of 60 Co, it still provides much lower throughput compared to the FPGA based systems and flash ADCs. In the proposed system, the exponentially decaying signal of a charge-sensitive preamplifier is directly sampled by the MCU’s ADC without any extra analog pulse processing circuits. Physical dimensions of the developed system including MCU, antialiasing filter and gain adjustment amplifier are 3 cm × 2 cm (1.2 in. × 0.8 in.), which makes it easily possible to embed the circuitry in a compact
∗ Corresponding author. E-mail address: [email protected] (M. Khorsandi).
https://doi.org/10.1016/j.nima.2019.162685 Received 28 April 2019; Received in revised form 6 August 2019; Accepted 1 September 2019 Available online 5 September 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.
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Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
portable device. The maximum power dissipation of the system is limited to 190 mW. This feature makes the system potentially a preferable candidate for portable battery-operated data acquisition. The firmware of the system can be easily updated by developing C and/or assembly signal processing subroutines. It is rather hard or maybe in some cases impossible to make such flexibility in commercially available data acquisition systems. In terms of cost, the cost price of the developed system is less than $15. Therefore, the proposed system can be quite cost-effective compared to the commercial or custom-made FPGA based systems. This approach will result in a more versatile platform in which any demanded pulse and data processing algorithms can be easily implemented for particle energy measurement or timing applications in which the time resolution is to be in the order of tens of nanoseconds. 2. Methodology 2.1. Pulse processing method Fig. 1. Typical output of digital pulse shaping with the peaking time of 9.3 μs and the flat-top duration of 1.86 μs.
The goal of the pulse processing is the conversion of the preamplifier signal to an appropriate pulse shape whose height is linearly proportional to the deposited energy of the particle in the active region of the detector. The shaping filters such as trapezoidal, triangular, cusplike, quasi-Gaussian, etc. can be used for particle energy measurement. Any filter is favored under some specific circumstances. Cusp-like filter theoretically provides the best signal to noise ratio, especially in systems with high series and parallel white noise, in cost of a rather low throughput. The quasi-Gaussian shaper is a very interesting filter which can be easily implemented in an analog circuitry using passive components in the form of CR-RC4 network. However, the signal to noise ratio of a quasi-Gaussian filter is relatively poor compared to that of cusp-like and triangular filters [3,14]. The trapezoidal shaper is an appropriate filter which handles well the tradeoff between the minimization of resolution and throughput maximization by providing adjustable parameters of peaking time and flat-top duration. As well, it is shown that the trapezoidal shaper provides a better energy resolution than the cusp-like filter for short peaking time in gamma spectroscopy by coaxial HPGe detector [4]. The implementation of high-performance filters such as trapezoidal and triangular one is straight forward on a digital platform. In this regard, the input is an exponentially decaying pulse of the chargesensitive preamplifier that can be ideally expressed by the following equation: { 𝑡 𝑚𝑒− 𝜏 𝑡 ≥ 0 𝑥(𝑡) = (1) 0 𝑡<0
Integration of the rectangular pulse over a period of l can be done using the following recursive formula: 𝑎𝑛 = 𝑎𝑛−1 + 𝑟𝑛 − 𝑟𝑛−𝑙
where 𝑎𝑛 is the trapezoidal signal value of nth sample. It is more convenient to present the filter shaping controls as peaking time and flat-top duration. In this respect, the averaging length (l) can be considered to be equal to the peaking time of the pulse. The flat-top duration can be also calculated by subtracting the averaging length from the rectangle width (k). A typical output of the proposed digital pulse processing has been presented in Fig. 1. The input signal is obtained from a charge sensitive preamplifier connected to an HPGe detector. The preamplifier is an RC-type with a time constant of ∼47 μs. The preamplifier signal was sampled at a rate of 5.4 MS/s and transferred to MATLAB software via USB port. In the present approach, the decaying pulse was converted to the trapezoidal form through the Eqs. (4) and (5). Here, the peaking time and the flat-top duration of the trapezoid are equal to 9.3 μs and 1.86 μs, respectively. 2.2. Logical block diagram of spectroscopy system The logical block diagram of the spectroscopy system has been shown in Fig. 2. The sampled input signal has been fed into two separate branches, one of which has a slow shaping time and the other has a fast shaping time constant. In both branches, at first, the exponential signal is converted to a rectangular shape. Then, a moving average filter acts on the rectangular pulse to produce a trapezoidal signal shape. The slow branch provides a good signal to noise ratio that is required for energy measurement purposes, whereas the fast signal is short enough to drive pulse edge detection and pile-up rejection units. The peak detection block is triggered by a pulse flag which is raised by the pulse edge detection unit when the fast trapezoidal signal exceeds a predefined threshold level. The energy measurement is accomplished by calculating the trapezoid height with respect to the baseline in the slow branch. The baseline of each pulse is determined separately by measuring the trapezoidal filter output 0.56 μs before pulse edge. At the same time, the pile-up rejection block inspects any pile-up events. Finally, if the pile-up flag is off, the slow signal pulse height is recorded by the histogram unit.
where m, 𝜏, and t represent the pulse amplitude, decaying time constant of the preamplifier with resistor feedback, and the elapsed time, respectively. A discretized form of the signal may be represented as: { 𝑇 𝑚𝑒− 𝜏 𝑛 𝑛 ≥ 0 𝑥𝑛 = (2) 0 𝑛<0 where, T and n denote sampling period time and sample index, respectively. The desired form of the signal for further processing is a finite rectangular pulse which have a height of 𝑚 and an arbitrary width of k. It can also be shown by the following expression: { 𝑚 0<𝑛<𝑘 𝑟𝑛 = (3) 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 The conversion of exponential signal to rectangle one can be performed easily by employing Z-transform [15]. The simplified recursive form of the conversion can be written by Eq. (4). 𝑇
2.3. Implementation of the system
𝑇
𝑟𝑛 = 𝑟𝑛−1 + 𝑥𝑛 − 𝑥𝑛−1 𝑒− 𝜏 + 𝑥𝑛−𝑘 − 𝑥𝑛−𝑘−1 𝑒− 𝜏
(5)
(4)
A digital spectroscopy system has been implemented using an STM32F730 micro-controller which is based on the ARM Cortex-M7
The rectangular pulse is converted to a trapezoidal shape using a moving integration filter having finite width which is smaller than k. 2
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Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
Fig. 2. The logical block diagram of the developed spectroscopy system.
Fig. 3. Schematic configuration of the implemented system on STM32f730 MCU.
Fig. 4. Block diagram of the experimental setup.
32-bit RISC core, operating at frequency up to 216 MHz. The device offers three 12-bit ADC with a maximum sampling rate of 2.4 MS/s and 7.2 MS/s, respectively in the single and the triple interleaved modes, two DMA units operating at a frequency of 108 MHz, several communication interfaces, timers, and the other components [7]. The schematic configuration of the implemented system has been presented in Fig. 3. The ADC unit has been configured in triple interleaved mode at a sampling rate of 5.4 MS/s. The ADC samples are automatically transferred to a cyclic buffer with a length of 10,000 2byte words per 186 ns using a DMA. The sampled pulse was shaped by slow and fast signal processing units, simultaneously. The implemented program benefits from some intrinsic advantages of the Cortex-M7 such as the same operation on multiple data (SIMD), multiply-accumulate (MAC) capability of DSP, and also branch prediction [16]. The moving
average filter has been also implemented by designing an efficient FIFO buffer in stack region. The spectrum buffer showed in Fig. 3, is an array with the length of 4096 Q-words (32-bits) that stores pulse height histogram. The content of this buffer is updated at the end of pulse height measurement of the valid events. There is also a pulse buffer to store a slice of DMA cyclic buffer for debugging purposes and displaying the input signal on the PC/Laptop screen. The content of both spectrum and pulse buffer can be read by the communication unit via USB port. 2.4. Experimental setup An experimental setup has been implemented to evaluate the performance of the developed system for gamma-ray spectroscopy using 3
S. Boorboor and M. Khorsandi
Fig. 5. (a) Pulse height spectrum from along with a fitted Gaussian curve.
Nuclear Inst. and Methods in Physics Research, A 946 (2019) 162685
60
Co, (b) magnified 1332.5 keV peak region
Fig. 6. The measured FWHM for different peaking time and flat-top duration, (a) due to the electronic noise, and (b) due to the combination of electronic noise, charge generation, and charge collection of 1332.5 keV gamma-ray energy.
HPGe detector. As illustrated in Fig. 4, a GC1320 HPGe made by CANBERRA Industries has been used as the gamma-ray detector. The detector is a p-type germanium diode with the nominal relative detection efficiency of 13% and guarantied energy resolution of 2 keV for 6 μs shaping time at 1332.5 keV. The charge carries created by gamma absorption in the detector is converted to an exponentially decaying pulse through a charge sensitive preamplifier with a time constant of 47 μs [17]. A precision pulser module used along with the detector to measure electronic noise of the system. After eliminating the aliasing components and also doing gain adjustment, the preamplifier signal was fed into the analog input of the MCU. The pulse processing was accomplished in the MCU and then the pulse height histogram was recorded in the internal memory of the device that can be read by PC/Laptop. It should be mentioned that the count-rate for all the spectra measured by this experimental setup was lower than 104 cps which is usually required in a low count-rate application.
electronic noise amplitude. This behavior can be explained based on the fact that the contribution of the series noise becomes less important at larger integration times. As well, by averaging the processed ADC’s samples, the ADC noise is also reduced efficiently. However, because of the parallel noise, further increases in the peaking time (above 15 μs) causes a degradation in the signal to noise ratio of the filters. It can be also seen that the parallel noise effect is more severe for the pulses with longer flat-top duration. The performance of the quasi-Gaussian filter is worse than the trapezoidal one in the range of investigated peaking time, as shown in the figure. According to Fig. 6b, the peak broadening of 1332.5 keV has been decreased by increasing the peaking time. A two-fold phenomenon can cause this behavior. On the one hand, increasing the integration time up to 10–15 μs has led to a smaller electronic noise. On the other hand, the longer shaping time has provided the opportunity for a better charge collection that limits the contribution of charge collection fluctuation to the peak broadening. Furthermore, the peak broadening caused by the imperfect charge collection can be ameliorated by adding a flat-top part into the synthesized pulse. Then, the longer flat-top duration leads to a smaller FWHM, specifically for the peaking time below 10 μs. For longer peaking times, the charge collection fluctuation becomes almost constant. Nevertheless, the resolution of the system was degraded in much longer peaking times because the parallel noise contribution has become more significant. As expected, the resolution degradation is more severe for filters with longer flat-top durations. Moreover, it can be seen that the measured broadening of pseudoGaussian pulses is obviously larger than that of trapezoidal pulses in the region of the shorter peaking times, whereas, for very long peaking times (>18 μs), the performance of both filters is almost the same. As a result, the Gaussian shaping is more sensitive to fluctuations in the charge collection process.
3. Results and discussions Fig. 5a shows a pulse height spectrum recorded from 1173.2 keV and 1332.5 keV gamma rays emitted by 60 Co using the experimental setup. The peaking time and the flat-top duration of the filter were chosen to be 5.9 μs and 8.9 μs, respectively. To give more details about the pulse height distribution of the fully absorbed gamma quanta, the photo-peak region of 1332.5 keV energy is presented in Fig. 5b. As seen in the spectrum, the shape of the full-energy peak is very nearly Gaussian. The full width at half maximum (FWHM) of the peak is 4.7 ± 0.05 channels (1.96 ± 0.02 keV) translated to a resolution of about 0.15% at 1332.5 keV. Furthermore, some experiments have been carried out to investigate the effect of processing parameters on the energy resolution. The electronic noise of the implemented trapezoidal filter, as well as an analog quasi-Gaussian filter, are presented as a function of peaking time in Fig. 6a. Here, it is evident that increasing the peaking time up to 10–15 μs, depending on the flat-top duration, has led to a smaller 4
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Co,
137
Cs, and
152
Fig. 7. The recorded pulse height spectrum from sources. Table 1 Energy, central channel and FWHM for
60
Energy (keV)
Peak Central Channel
FWHM (keV)
121.8 244.7 344.2 411.1 443.9 661.7 778.9 867.3 964 1085.8 1112 1173.2 1299.1 1332.5 1408
330.4 ± 0.01 662.1 ± 0.02 930.9 ± 0.03 1112.7 ± 0.04 1200.1 ± 0.07 1787.1 ± 0.05 2104.9 ± 0.06 2344.1 ± 0.12 2605.5 ± 0.10 2934.1 ± 0.21 3006.1 ± 0.13 3171.7 ± 0.10 3512.6 ± 0.14 3602.9 ± 0.10 3807.4 ± 0.08
1.13 1.22 1.29 1.33 1.38 1.53 1.62 1.66 1.79 1.92 1.92 1.93 1.99 2.00 2.07
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
Co,
0.01 0.02 0.02 0.03 0.06 0.03 0.06 0.07 0.04 0.06 0.05 0.03 0.06 0.03 0.03
137
60
Cs, and
152
Eu radioisotope
Eu peaks.
FWHM (Channel)
Resolution (%)
3.05 3.31 3.49 3.61 3.73 4.14 4.39 4.50 4.78 5.18 5.19 5.19 5.38 5.42 5.61
0.93 0.50 0.37 0.32 0.31 0.23 0.20 0.19 0.18 0.17 0.17 0.16 0.15 0.15 0.15
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.03 0.06 0.06 0.08 0.17 0.09 0.16 0.19 0.10 0.16 0.14 0.09 0.17 0.08 0.08
Fig. 8. (a) The relation between photo-peak central channel and photon energy, (b) deviation of data points from the fitted line.
maximum nonlinearity of 0.042%. This value is negligible compared with the maximum observed nonlinearity of 0.34% in the energychannel relationship. It is deduced that the observed nonlinearity of the energy peaks can be originated from incomplete charge collection in the detector side and ballistic deficit as well. Moreover, investigation of the energy-channel linearity for different shaping parameters shows that the maximum non-linearity is generally decreased as the shaping time is increased. As an example, the maximum nonlinearity in energy peak distribution is limited to 0.19% for peaking time and flat-top duration of 14.8 μs and 5.6 μs, respectively. The total broadening of the photo-peaks, as well as contribution of the electronic noise, were measured as a function of energy, for peaking time of 5.9 μs and flat-top of 5.2 μs, as shown in Fig. 9. The total broadening is caused by different factors including charge carrier generation statistics, charge collection, and electronic readout noise which itself contains the preamplifier noise, gain controller noise, ADC error, and DSP operations round-off error. As shown in Fig. 9, the measured peak broadening due to the electronic noise is almost constant (∼0.86 keV) over the entire ADC range. The contribution of the baseline fluctuations and pile-up effects to the noise were investigated through the measurement of the peak broadening at the count-rate between 500 to 7000 cps made by changing the source-detector distance. Thereupon, no expressive effect was observed in the peak broadening in the range of the investigated count-rate. So, the major contributor to the noise can be due to the imperfect charge collection. This imperfection may be originated from trapping centers created in the semiconductor material, acceleration/deceleration of primary electrons, etc. However, due to the energy dependence of charge generation and collection statistics, the total FWHM is a function of incident gamma-ray energy. To have an estimation, the model discussed by Owen [18] was fitted on the measured total FWHM data illustrated in Fig. 9. By the model, the total
The linearity and the energy resolution of the spectrometer were determined over a wide range of energies. In this respect, the pulse height spectrum from gamma quanta emitted by 60 Co, 137 Cs, and 152 Eu sources was measured considering a peaking time and flat-top duration of 5.9 μs and 5.2 μs, respectively. As shown in Fig. 7, 15 photo-peaks expanded from 121.78 keV to 1408 keV can be well recognized in the recorded spectrum. Here, the best energy resolution was obtained about 0.15% pertaining to 1408 keV energy peak of 152 Eu. The resolution is degraded with decreasing the energy and reaches to 0.93% for the 121.78 keV peak. Details about the central channel and FWHM of all peaks are reported in Table 1. The relation between the different photon energy in the pulse height histogram and the corresponding central channel of the photo-peak is shown in Fig. 8a. According to the figure, the proposed spectrometer provides a linear relation between the photo-peak channel and gammaray energy with the slop of 2.7 channels/keV. Deviation of the data points from the fitted line has been also given in Fig. 8b. The maximum observed nonlinearity is 0.34% which belongs to 121.78 keV photon. However, the nonlinearity is drastically decreased for higher energy photons and limited to only about 0.09%. The linearity of the electronic chain including the preamplifier, gain adjustment, ADC, and DSP was also measured by applying a pulser module. The measurement results at different pulse heights showed a 5
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benefits from the advantages of low-power consumption, low cost, small dimensions, and flexibility in development of the Cortex-M7 to perform a digital pulse processing in an efficient way. The experimental results showed that the spectrometer was able to resolve 1332.5 keV photons peak with FWHM of 1.96 keV. In addition, good linearity was observed between the central peak channels and gamma-ray energies so that the maximum nonlinearity was limited to 0.34%. This value mainly originated from incomplete charge collection in the detector side and ballistic deficit as well. The overall results revealed that the modern MCU along with the proposed approach can be efficiently employed as a compact and cost-effective digital radiation spectrometers. It seems that these devices have many potentials to be used as the next platform of the digital spectrometers in various low-rate applications. Acknowledgment The authors are gratefully indebted to Shahid Beheshti University, Iran, G. C., for researching support of this work. We would also like to show our gratitude to the professor S. A. H. Feghhi and we thank specially reviewers for their so-called insights. References [1] V.T. Jordanov, G.F. Knoll, Digital synthesis of pulse shapes in real time for high resolution radiation spectroscopy, Nucl. Instrum. Methods Phys. Res. A 345 (1994) 337–345, http://dx.doi.org/10.1016/0168-9002(94)91011-1. [2] V.T. Jordanov, G.F. Knoll, A.C. Huber, J.A. Pantazis, Digital techniques for realtime pulse shaping in radiation measurements, Nucl. Instrum. Methods Phys. Res. A 353 (1994) 261–264, http://dx.doi.org/10.1016/0168-9002(94)91652-7. [3] G.F. Knoll, Radiation Detection and Measurement, fourth ed., Wiley, 2010, pp. 630–670. [4] N. Menaa, P. D’Agostino, B. Zakrzewski, V.T. Jordanov, Evaluation of real-time digital pulse shapers with various HPGe and silicon radiation detectors, Nucl. Instrum. Methods Phys. Res. A 652 (2011) 512–515, http://dx.doi.org/10.1016/ j.nima.2010.08.095. [5] A. Messai, A. Nour, I. Abdellani, Digital signal processing for optimal resolution in gamma ray spectroscopy, in: Instrum. Digit. Nucl. Spectrosc. Proc. IAEA Tech. Meet. Held Vienna, Austria, 2010, pp. 123. [6] D. Bazzacco, et al., AGATA, technical proposal for an advanced gamma tracking array for the european gamma spectroscopy community, 2001, https://hal. archives-ouvertes.fr/hal-00729050. [7] STMicroelectronics, STM32F730xx datasheet, 2017, https://www.st.com/en/ microcontrollers-microprocessors/stm32f730r8.html. [8] S. Boorboor, H. Jafari, S.A.H. Feghhi, Development of a novel approach for precise pulse height extraction using Lagrange interpolation, Nucl. Instrum. Methods Phys. Res. A 919 (2019) 82–88, http://dx.doi.org/10.1016/j.nima.2018. 12.028. [9] P. Shebell, Portable Gamma-Ray Spectrometers and Spectrometry Systems, International Atomic Energy Agency (IAEA), 1999, http://inis.iaea.org/search/search. aspx?orig_q=RN:30060366. [10] MCA-8000D, Digital multichannel analyzer, (n.d.) https://www.amptek.com/ products/multichannel-analyzers/mca-8000d-digital-multichannel-analyzer. [11] DP5 OEM, Digital signal processor, (n.d.) https://www.amptek.com/products/ digital-pulse-processors/dp5-digital-pulse-processor-and-mca. [12] DSA-LX, Digital signal analyzer, (n.d.) https://www.mirion.com/products/dsa-lxdigital-signal-analyzer. [13] PX5-HPGe, Digital pulse processor, (n.d.) https://www.amptek.com/products/ digital-pulse-processors/px5-hpge-for-germanium-detectors. [14] Gordon R. Gilmore, Practical Gamma-Ray Spectrometry, second ed., John Wiley & Sons, Ltd, 2008. [15] A.V. Oppenheim, R.W. Schafer, Discrete-Time Signal Processing, Pearson, 2010. [16] STM32F7 series and STM32H7 series Cortex® -M7 processor programming manual, 2017, https://www.st.com/resource/en/programming_manual/dm00237416. pdf. [17] www.canberra.com, SEGe detectors datasheet, https://www.mirion.com/ products/sege-standard-electrode-coaxial-ge-detectors. [18] A. Owens, Spectral degradation effects in an 86 cm3 Ge(HP) detector, Nucl. Instrum. Methods Phys. Res. A 238 (1985) 473–478, http://dx.doi.org/10.1016/ 0168-9002(85)90487-5. [19] S. Croft, D.S. Bond, A determination of the Fano factor for germanium at 77.4 K from measurements of the energy resolution of a 113 cm3 HPGe gammaray spectrometer taken over the energy range from 14 to 6129 keV, Int. J. Radiat. Appl. Instrum. A 42 (1991) 1009–1014, http://dx.doi.org/10.1016/08832889(91)90002-I.
Fig. 9. The FWHM as a function of energy for the peaking time of 5.9 μs and the flat-top duration of 5.2 μs.
peak broadening can be expressed by: [ ]0.5 𝛥 (𝐸) = 2.355 𝐹 𝜀𝐸 + (𝛼𝐸 + 𝛽)2 + 𝜎𝑒2
(6)
where, F, 𝜀, E, and 𝜎𝑒 are respectively Fano-factor, the energy required to produce an electron–hole pair, photon energy, and standard deviation of electronic noise. The term 𝐹 𝜀𝐸 is the variance of charge generation inside the crystal active region. The standard deviation of charge collection may be considered as a linear function with constants of 𝛼 and 𝛽. By Taking 𝜀= 2.97 eV, 2.355𝜎𝑒 = 0.86 keV and by fitting Eq. (6) on the total FWHM data points, we will obtain F =0.081, 𝛼 = 2.4 × 10−4 and 𝛽= 213.5 eV. The value of the Fano-factor is therefore consistent with that of the other works [19]. However, the non-zero value of 𝛽 results in a slightly greater value of 𝛥 (𝐸) than electronic noise at zero energy. The calculated values of the broadening due to the charge generation and collection are also shown in Fig. 9. The contribution of different factors to the peak broadening can be estimated based on the resulting curves. One can deduce that the electronic readout noise is a significant contributor to the total broadening in the low energy region (< 250 keV). However, the quadrature sum of the charge generation and the charge collection fluctuations has become a dominant factor of the energy resolution degradation in the higher energy region. As an example, the values of fluctuation in charge generation and collection are obtained respectively 1.33 keV and 1.26 keV at the gamma-ray energy of 1332.5 keV. 4. Conclusion A digital radiation spectrometer has been developed using a single STM32F730 MCU chip. The particle energy was measured by converting the preamplifier signal to the trapezoidal one. The proposed system
6