A MONTE CARLO CODE FOR SIMULATION OF PULSE PILE-UP SPECTRAL DISTORTION IN PULSE-HEIGHT MEASUREMENT

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1 Copyright JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume A MONTE CARLO CODE FOR SIMULATION OF PULSE PILE-UP SPECTRAL DISTORTION IN PULSE-HEIGHT MEASUREMENT ABSTRACT Weijun Guo, Robin P. Gardner, and Fusheng Li Center for Engineering Applications of Radioisotopes (CEAR) Nuclear Engineering Department, PO Box 7909 North Carolina State University Raleigh, NC The Monte Carlo simulation code CEARPPU has been improved to obtain better accuracy for predicting pulse-height spectra measured at high counting rates. Experimental verification was carried out by measuring an Fe-55 spectrum with a Si(Li) X-ray spectrometer. Based on the spectrum measured at low counting rate, which is considered to be the true spectrum with no pulse pile-up distortion, the predicted high counting-rate spectrum by CEARPPU is in excellent agreement with the measured one for all of the folded regions due to pulse pile-up. This code is available for public dissemination at Oak Ridge National Laboratory (ORNL) through RSICC. By iteratively using this code, a Monte Carlo approach MCPUT has been proposed and demonstrated for solving the inverse problem to make pulse pile-up corrections for pulseheight spectra measured at high counting rates. INTRODUCTION Pulse pile-up distortion is a common problem for pulse-height measurement at high counting rates. High counting rates are a must for many medical and industrial applications of radiation measurement to ensure good counting statistics in the shortest possible diagnosis or on-line measurement times. The electronics of a spectrometer for pulse-height measurement are illustrated in Figure 1. Two signal acquisition options are now available, analog and digital pulse processing. Detector Current Pulses Preamplifier Tail Pulses Tail Pulses Digital Digitizer Digitized Pulses Display Analog Linear Amplifier Shaped Pulses MCA MCB (ADC+Memory) Display Figure 1. Schematic diagram of a generalized chain of electronics for energy pulse-height measurement

2 This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website ICDD Website -

3 Copyright JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume For analog pulse processing, the incident radiation particles interact in the detector and generate relatively fast current pulses. These current pulses are amplified and shaped before being digitized and stored by the Multi-Channel Analyzer. These stored values accumulate to form the measured spectrum. For digital pulse processing, the main difference comes after the preamplifier. The tail pulse will be digitized directly and thereafter shaped by digital filters. The occurrences of radiation are random, and may be characterized by the Poisson distribution. However, the shaped pulses have finite width so that two or more adjacent pulses may overlap each other. The individual components of each folded pulse are not directly measurable. The maximum counting rate that could be used otherwise is therefore limited by pulse pile up. The analytical relationship between measured counting rate and true counting rate is as follows: Rm = Rt exp( λ Rt ). (1) Where Rm and Rt are the measured and true counting rate respectively and λ is the total system dead time. Typically, for analog pulse processing, this system dead time could be characterized by the width of the main amplifier output pulse. According to this equation, if we could reduce the pulse width, the maximum achievable counting rate would be increased as well. However, the optimal setting of pulse width is limited by the ballistic deficit and the signal to noise ratio. Figure 2 plots Equation 1 with λ equal to 10 µ s, which is typical for a Si(Li) spectrometer. The Monte Carlo simulation code, CEARPPU, was previously developed by Figure 2. Counting rate curve. our research center [1] to simulate the pulse pile-up distortion of a Si(Li) spectroscopy system measuring an annular Fe-55 radioisotope source at high counting rate. A low counting rate Fe-55 spectrum was measured with the same spectrometer and used as the true spectrum shape for the Monte Carlo simulation. As one of the inputs for the Monte Carlo simulation, the normalized true spectrum serves as the probability density function (pdf) for sampling the pulse heights of the linear amplifier s output pulse. A semi-empirical function was applied to model the pulse shape of the linear amplifier output. The occurrence time of pulses are sampled with the exponential interval distribution characterized by the counting rate. Pulse pile-up distortion is automatically simulated by the Monte Carlo code when two pulses occur within an interval less than the pulse width of a single pulse. The simulation showed good agreement with a benchmark experiment. Discrepancies were observed for the regions with three or more pulses piled-up or folded together. In recent efforts, the dead time model has been modified by double weighting the rise time of amplifier output pulse [2]. The new simulation results are reported in this paper and show significant improvement. The linear amplifier output is now directly digitized for use in pointwise format. This enhancement makes it easier for other researchers to use the CEARPPU code for their own spectroscopy system. This code is available from the Radiation Safety Information

4 Copyright JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume Computational Center (RSICC) at ORNL for general dissemination [3]. By iteratively using this forward algorithm for predicting pulse pile-up distortion, the MCPUT approach has been reported for correcting spectral distortion by pulse pile up [4]. MONTE CARLO SIMULATION In general, Monte Carlo simulation solves problems by sampling individual events one by one. These events are tracked from birth to death. The contribution of each event to the quantities of interest is tallied and both the average and the variance of the average can be predicted. For pulse pile- up simulation, individual pulses are sampled for both occurrence time and pulse height. Pile up is determined according to the time-interval criterion. The pulse-height value of each pulse train is sorted to the appropriate ADC channel to form the pulse-height spectrum. The code flow diagram of the CEARPPU code is presented in Figure 3. The sampling algorithms for single pulses are the kernel of the CEARPPU code. Two random variables need to be sampled for each single pulse: the occurrence time (that is relative to the previous pulse, thereby, time interval between two adjacent pulses) and the pulse height. Radiation emission from a source is characterized by the Poisson process. The time interval of two adjacent emissions is described by the exponential interval distribution: f ( t) = Rt exp( Rt t). (2) The cumulative density function (CDF) is equal to the integration of this pdf from time 0 to t : F( t) = t 0 f ( x) dx = 1 exp( R t) Code Initialization - Load experiment settings (Counting rate, amplifier parameters, etc.) t Single Pulse Sampling. (3) To sample one value of time interval ( t ), we sample a uniformly distributed number R first. R is greater than or equal to 0 and less than or equal to 1. Then we apply the inverse function of CDF to this R. A value of t can then be sampled. To verify the sampling process and also show the effect of sampling history number, two sampling cases were made. It is noted that the sampling history number is linearly proportional to the actual experiment time. The comparison for simulated and true distribution for time interval is plotted in Figure 4(a) and Figure 4(b) for 1k and 1M histories, respectively. Obviously, for fewer histories, the trend of the distribution is kept but the variance is much larger. PPU?. Histogram the pulse height of the preceding pulse train. Reset the pulse train storage to the current pulse No No Yes Complete? End Reject? No Update Pulse Train Figure 3. CEARPPU code flow diagram. Yes

5 Copyright JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume Simulated distribution True distribution Simulated distribution True distribution PDF 3000 PDF TIME(ms) a TIME(ms) Figure 4. Comparison of simulated and true time interval distribution (a) 1k histories (b) 1M histories The pulse heights are sampled in similar fashion to the time interval. One major difference is that the pdf of the pulse height is the normalized low counting-rate spectrum. It is in discrete form and the normalization factor is the total number of counts in the measurement. The CDF is calculated from the cumulative sum of the pdf instead of by integration. To sample each pulseheight value, a uniform random number is sampled first. Then an index i is obtained by forcing the random number to be within the range of two adjacent CDF values. The pulse height is finally found by interpolation according to the following equation: H = H i ( F(H i ) - r)( H i+ 1 H i ) /[F(Hi+ 1) F(Hi )] (4) The simulated pulse height distributions are also compared to the true distribution for different numbers of sampled pulses in Figure 5. We see that the simulation does a good job when enough pulses have been sampled. b Simulated distribution True distribution Simulated distribution True distribution dn/dh dn/dh CHANNEL NO. CHANNEL NO. a b Figure 5. Comparison of simulated and true pulse height distribution (a) 1k histories (b) 1M histories A new dead time model has been implemented in CEARPPU by double weighting the rise time of each pulse [2]. A cubic spline pulse model is now available in the code to model the linear amplifier output pulses. By digitizing the output pulse into a point-wise table, different application-specific linear amplifiers are modeled easily and accurately. So far, three different pulse shapes of general interest are available, namely, Gaussian, trapezoidal and triangular pulses,

6 Copyright JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume respectively. For a pulse with unit pulse height from an ORTEC-572 amplifier, 20 digitized points were used to construct the pulse model. The comparison of the interpolated model with 64 digitization values is presented in Figure 6. EXPERIMENTAL VERIFICATION To benchmark the CEARPPU code, two pulseheight spectra with an annular Fe-55 radioisotope source were measured with an X-ray Si(Li) detector. The ORTEC 572 linear amplifier and the ORTEC 919 ADC were used. The shaping time of the linear amplifier was set to be 2 µs, which produced an Figure 6. Cubic spline pulse model verification. output pulse with a width of 12.8 µs. According to the classification criterion introduced on page 627 of Knoll s book [5], this pulse width identifies measurements with counting rates lower than 78 counts per second as low counting-rate measurements and 7812 counts per second as the lower limit for high counting-rate measurements. Observed counting rates for benchmark experiments here were 74 and 18,169 counts per second, respectively. The gain and zero for energy calibration were ev/channel and ev, respectively. Two measured spectra for low and high counting-rate measurements are compared in Figure 7. Based on the previous discussion, the low counting-rate spectrum may be considered to be free of pulse pile-up distortion. Due to the simplicity of the source spectrum of Fe-55, those counts for channels with related energy greater than the Manganese X-rays (5.9 kev and 6.5 kev) are considered to be from background sources. Figure 7 shows the true, double, triple, and quadruple and higher piled-up regions of a high counting-rate spectrum. The first region is the region that corresponds to the true region of the low counting-rate measurement, from channel 1 to 510. Regions following that are caused mainly by piled-up pulses, and the upper limits of the double pile-up region, triple pile-up region, and quadruple and more pile-up region are shown Low Counting Rate High Counting Rate 10 6 COUNTS 10 4 "True" "Double" "Quadruple and more" "Triple" CHANNEL NUMBER Figure 7. Comparison of the Fe-55 spectra measured with low counting rate and high counting rate. Four regions are marked according to their major contribution of pulses. More accurately, double piled-up pulses contribute to both True and Double regions, and so on.

7 Copyright JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume The CEARPPU code was used to simulate the high counting-rate measurement by using the low counting-rate measurement and the electronics parameters as input. The simulated spectrum is compared with the experimental one in Figure 8 with excellent agreement. CONCLUSIONS AND DISCUSSION The CEARPPU code has been successfully improved in accuracy to predict the high counting rate performance of a spectrometer based on a low counting-rate measurement. The Monte Carlo solution for the inverse problem of correcting pulse pile-up distortion for high counting- rate measurement becomes possible based on an accurate forward simulation tool like CEARPPU. The iterative approach MCPUT has been published [4] by our group. Moreover, the pulse pile-up problem might be dealt with in real time. MCPUT solves the problem in the offline mode and it has an advantage for pulse pile-up that occurs in extremely small time intervals (true coincidences at the nanosecond level). However, it has a potential limit in recovering information that was lost during the measurement, such as that of variable counting rates. The computer is becoming cheaper and faster and the same applies for instrument electronics. It is realistic to predict that direct digitization and storage of incoming pulse trains from the radiation detectors will be possible very soon. Two simple approaches for pulse pile-up real-time deconvolution have been proposed in a recent publication by our group [6]. Figure 8. Spectrum comparisons between simulated high counting-rate spectrum and experimental spectrum. ACKNOWLEDGMENTS The work described was supported by Grant Number 2R01ES06671 from the National Institute of Environmental Health Sciences, National Institutes of Health, US Public Health Service. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIEHS, NIH. The authors are also grateful for the financial support from the

8 Copyright JCPDS - International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume Associates Program for Nuclear Techniques in Oil Well Logging presently supported by Baker Atlas, Advantage Engineering, Shell, and EXXON Mobil. REFERENCES [1] Gardner, R.P. and S.H. Lee, Monte Carlo Simulation of pulse pile up. Advances in X-ray Analysis, : p [2] Ortec, ORTEC Modular Pulse-Processing Electronics Catalog [3] Gardner, R.P., et al., CEAR-PPU: A Monte Carlo Code for Predicting Pulse Pile-up Distortion for High Counting-Rate Radiation Spectra. PSR , Radiation Safety Information Computational Center, Oak Ridge National Laboratory. [4] Guo, W., S.H. Lee, and R.P. Gardner, The Monte Carlo Approach MCPUT for Correcting Pile-up Distorted Pulse-height Spectra. Nuclear Instruments and Methods in Physics Research A, In Press: p. pp. TBD. [5] Knoll, G.F., Radiation Detection and Measurement. 3rd ed. 2000, New York: Wiley. [6] Guo, W., R.P. Gardner, and C.W. Mayo, On the development of approaches for the real- time deconvolution of pulse pile-up for digital radiation spectroscopy. ANS Winter Meeting, Invited Paper for Mark Mills Award.