Adaptive digital filter for high-rate high-resolution gamma spectrometry

IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 48, NO. 3, JUNE 2001

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Adaptive Digital Filter for High-Rate High-Resolution Gamma Spectrometry G. P. Westphal, K. Jöstl, P. Schröder, and W. Winkelbauer

Abstract—By automatically adapting the noise filtering time to individual pulse intervals, the preloaded digital filter (PLDF) combines low- to medium-rate resolutions comparable to those of highquality Gaussian amplifiers with throughput rates of up to 100 kc/s and high-rate resolutions superior to those of state-of-the-art gated integrator systems. In contrast to commercially available digital filters, the PLDF in its new implementation performs pulse shortening as well as pole-zero cancellation in the analog domain. This not only results in a simpler digital core, but also, for the first time, makes possible the use of a low-cost analog–digital converter in a spectrometric application. Combined with real-time correction of counting losses according to the loss-free counting method, the PLDF is the core of a novel multichannel analyzer system for neutron activation analysis of short-lived isomeric transition. Index Terms—Adaptive digital filtering, digital spectroscopy, high counting rates.

I. INTRODUCTION

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O RESOLVE the “resolution or throughput rate” dilemma, the ideal so-called adaptive pulse processing system has been postulated by Bertolaccini et al. [1], sensing the time positions of all the pulses and providing for each pulse the optimum filtering in the time available between the preceding and the following pulses. In this way, pileup should be avoided and, theoretically, optimum resolution attained at any counting rate. Implementation proposals in their paper, however, are purely illustrative and technically not feasible. The first to answer Bertolaccini’s challenge was Koeman [7], [20], who proposed at least two symmetrical weighting functions of different duration with equal integration periods before and after a pulse wherefrom a matching one should be selected to fit the actual pulse intervals. He was followed by Lakatos [8] and Farrow [9] with nearly identical designs. Common drawbacks are the coarse approximation of intervals and the loss of information from the longer weighting functions as intervals before and after an event are unequal in most instances. A completely different approach is based on signal recognition of the of an antialiasing filter according to the known pulse shape maximum likelihood method [10], [11]. Together with a nearly optimum signal-to-noise ratio (SNR), it also makes possible the adaptive utilization of pulse intervals for noise reduction, but cannot be used for gamma spectrometry due to its sensitivity to

Manuscript received October 27, 2000; revised January 26, 2001. This work was supported in part by the International Atomic Energy Agency, Vienna, Austria. The authors are with the Atominstitut der Österreichischen Universitäten, A-1020 Vienna, Austria (e-mail: [email protected]). Publisher Item Identifier S 0018-9499(01)05082-1.

Fig. 1.

Operating principle of the PLF.

charge collection time variations and the not yet sufficient computational power of today’s digital signal processors.

II. PRELOADED FILTER A. Operating Principle The first system to realize Bertolaccini’s postulate completely and this in the simplest possible manner is the preloaded filter (PLF) pulse processor [2], [3], which automatically adapts its noise filtering time to the pulse intervals occurring just then. Matched to the system’s noise corner time constant, the PLF is a low-pass filter working immediately on the step output of a preamplifier. Consisting essentially of a resistor and a capacitor (Fig. 1), it is charged up rapidly (“preloaded”) to the step amplitude by closing a switch across the resistor during the rise time of the step. At the same time, the previous amplitude is subtracted, providing for ground referred output amplitudes with high baseline stability. After acquisition, the switch is opened and noise filtering commences, extending up to the optimum filtering time or, if this comes earlier, up to the next event. Subsequently, the filter output is sampled and transferred to the multichannel analyzer while, simultaneously, the next step acquisition may take place.

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B. Adaptivity and Resolution The PLF lends itself to adaptivity in a unique manner due to the fact that its momentary output value never differs from the final value by more than the actual noise band, which decays exponentially with the filter time constant from the initial value during acquisition to its minimum value after three time constants. This renders possible the readout of the current event and the acquisition of the next one at any time and thus fully utilizes the available pulse intervals for noise reduction. at a filtering time is given by quadratic Total noise to the exponentially deaddition of the noise in filter mode caying noise in acquisition mode (1) ), noise contributions from At optimum filtering time ( the signal acquisition period are already negligible and the PLF ) operating on a may be described as a low-pass filter ( step function. This, in turn, is equivalent to a differentiated step ) integrated in a gated integrator. For , gated ( integration of a differentiated step yields a step noise index of 0.89 and a delta noise index of 1.87 / , which compares to 0.90 and 2.04 / for a fourth-order Gaussian filter with the same peaking time [12]. Noise figures during signal capture are governed by similar relations with the only exception of a much shorter time constant corresponding to system bandwidth in acquisition mode. By controlled bandwidth limitation in acquisition mode, the speed and with it the throughput rate may be traded against improved high-rate resolution. C. Digital Implementation Elsewhere described in more detail [4], the design of the preloaded digital filter (PLDF) is based on an analog–digital converter (ADC) with 10-MHz sampling rate and 14-bit resolution followed by a large field programmable gate array (FPGA), which implements the filtering algorithm as a fast pipelined data processing system. Briefly sketched, pole-zero cancelled digital differentiation 0.8 s) is followed by gated digital (see [13, Fig. 3], baseline restoration, feeding a digital integrator which reconstitutes a clean zero-slope step function. On that step operates the digital equivalent of a switched (“preloaded”) low-pass filter, which in turn is followed by a 32-stage firtst in-first out (FIFO) memory to accommodate even slow multichannel analyzers. D. Alternative Method of Step Reconstitution Another method for the reconstitution of a step from a resistance–capacitance (RC) differentiated step is the addition of the integral of the differentiated step [16] (2) Probably used for the first time by Westphal in an analog implementation of the PLF (see [3, C-C amp in Fig. 5]), the technique was described some years later under the name of “moving window deconvolution” by Georgiev and Gast [14]. They in turn were followed by Jordanov et al. [15] and Kuwata et al. [16], again with an application in the analog domain.

Fig. 2. Pulse response of pseudorectangular filter 1) and preceding differentiator 2).

E. Linearity and Pileup As with all filters with digital differentiation, exceptionally high-gain linearity of the ADC is a prerequisite for the processing of elevated counting rates. Otherwise, signal pileup at the ADC would result in virtual peak shifts and line broadenings. An adequate, but expensive choice (also by Ortec in its DSPEC spectrometers) was Datel’s hybrid ADS 945 with 14-bit resolution at 10-MHz conversion rate, a differential nonlinearity (DNL) of 0.5 least significant bit (LSB), an integral nonlinearity (INL) of 0.5 LSB, and a signal-to-noise and distortion ratio (SINAD) of 76 dB. F. Analog Differentiation To render possible the use of cheap monolithic converters such as the AD9240 by Analog Devices with a slightly better SINAD of 77.5 dB, a comparable DNL of 0.7 LSB, but a much poorer INL of 2.5 LSB, we decided to perform differentiation in the analog domain. By presenting to the ADC very short signals as near as possible to the current pulses originating in the detector, pulse pileup at elevated counting rates, and the consequent, INL-related degradation of system resolution is completely avoided. At the same time, much better use may be made of the dynamic range of the converter as allowances for pulse pileup are no longer necessary. Added benefits are a much simpler digital circuit and conventional instead of digital pole-zero cancellation [18]. To further optimize the SNR, a pseudorectangular prefilter [5] with a pulse duration of 1.5 s has been chosen (Fig. 2), which makes possible a maximum throughput rate after pileup rejection of 92 kc/s (Fig. 5). is The PLDF’s throughput rate after pileup rejection given by (3) is the input rate and the acquisition time. The where acquisition time may be set to take into account even strongly varying charge collection times of large detectors.

WESTPHAL et al.: ADAPTIVE DIGITAL FILTER FOR HIGH-RATE HIGH-RESOLUTION GAMMA SPECTROMETRY

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Fig. 3. Block diagram of PLDF with differentiation and pole-zero cancellation in the analog domain.

Low-noise differentiation based on active feedback loops as described by Casoli et al. [17] yields the signal of Fig. 2, Channel 2. Together with two subsequent second-order low-pass filters of 100 ns each, it constitutes the pseudorectangular signal of Channel 1 and also serves as input to the system’s signal recognition discriminator. The pseudorectangular signal is digitized by the above mentioned AD9240 converter with 14-bit resolution and a 10-MHz conversion rate. In the subsequent Xilinx 4010 FPGA digital baseline restoration takes place, followed by integration, preloaded filtering, and intermediate storage of results in a 32-stage FIFO memory. Fig. 3 is a block diagram of the instrument and Fig. 4 a photograph of the PLF. G. Correction of Counting Losses is system dead-time and The filter acquisition time pileup sensitive period at the same time. Consequently, the or the combined probability pulse processing probability and pulse pileup escape for the of dead-time escape PLDF is given by (4) is the true input counting rate. It is measured quantiwhere , extended to 2 by tatively by a live-time clock gated by means of a monostable multivibrator [6], [19], [21]. By taking , weighting factors are short-time samples of the inverse of generated by loss-free counting [6], [19], [21] to be added to the channels addressed during the measurement of a spectrum instead of incrementing them by one as in ordinary pulse height analysis. H. System for Activation Analysis ) of A software implementation (in Assembler and C a loss-free counting multichannel analyzer, storing immedi-

Fig. 4. PLDF is a double width NIM module compatible with multichannel analyzers of the Canberra type.

ately into the multimegabyte memory of a low-cost 486- or Pentium-type PC, enables the collection of up to 1000 pairs of simultaneously recorded loss-corrected and noncorrected spectra of 16-k channels each in a true sequence without time gaps in between at throughput rates of up to 200 kc/s [19]. Intended for activation analysis of short-lived isomeric transitions, the system renders possible peak to background optimizations and separations of lines with different half lives without an a priori knowledge of sample composition by summing up appropriate numbers of spectra over appropriate intervals of time. The combination of a PLDF with analog preshaping and an inexpensive ADC with a software-based loss-free counting multichannel analyzer provides a low-cost, but powerful solution for the instrumentation of neutron activation analysis at Triga reactors in developing countries, a forthcoming research project of the International Atomic Energy Agency, Vienna, Austria. III. MEASUREMENTS A. Low Counting Rates Basic resolution of the PLDF with analog preshaping has been measured at 1.4 kc/s by means of an -type HpGe detector from Ortec with 20% relative efficiency and a transistor reset preamplifier, as 0.95 keV at 59.5 keV, 1.4 keV at 661.6 keV, 1.7 keV at 1173.3 keV, and 1.8 keV at 1332.5 keV, at an optimum

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Fig. 5.


Resolution versus counting rate of PLDF with analog preshaping.

Fig. 6. Peak position versus counting rate of PLDF with analog preshaping.

shaping time of 1.6 s. This compares to 1.0 keV at 59.5 keV, 1.5 keV at 661.6 keV, 1.9 keV at 1173.3 keV, and 2.0 keV at 1332.5 keV, measured under similar conditions, but with a Canberra 2020 semi-Gaussian amplifier at an optimum shaping time of 3 s. A slightly better performance of the PLDF is attributed to its insensitivity to charge collection time variations in large coaxial detectors. B. High Counting Rates Resolution versus counting rate of the PLDF is given in Fig. 5, while peak position versus counting rate is given in Fig. 6. Both Cs source. This have been measured up to 400 kc/s with a compares favorably to the PLDF with digital differentiation and the expensive ADC, which exhibited a slightly higher maximum peak shift of 0, 4 keV and a worst resolution of 2.1 keV at 400 kc/s. Digital differentitation with the cheap ADC results in a peak shift of 1.5 keV and a line width of more than 3 keV at 400 kc/s.

Fig. 7. Throughput after pileup rejection versus counting rate of PLDF with analog preshaping.

Fig. 8. Performance of LFC counting loss correction measured with Co (reference) and Cs (modulation). Dashed lines correspond to 3 standard deviations of the noncorrected reference intensities.

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Fig. 7 shows the throughput rate after pileup rejection versus input counting rate of the PLDF with analog preshaping and a low-cost ADC. C. Real-Time Correction of Counting Losses Finally, Fig. 8 shows the performance of the loss-free counting system. As a reference sample, the relative net peak area of the 1173 keV line of Co is shown versus a rising Cs. input counting rate that has been increased by means of The dashed lines correspond to 3 standard deviations of the noncorrected net peak areas of the reference line. ACKNOWLEDGMENT The authors would like to thank P. P. de Regge, Head of PCI Laboratories, IAEA Seibersdorf, for valuable discussions and R. Arlt, Nuclear Safeguards Division, IAEA Vienna, for the loan of an HPGe detector.

WESTPHAL et al.: ADAPTIVE DIGITAL FILTER FOR HIGH-RATE HIGH-RESOLUTION GAMMA SPECTROMETRY

REFERENCES [1] M. Bertolaccini, C. Bussolati, S. Cova, I. de Lotto, and E. Gatti, “Optimum processing for amplitude distribution evaluation of a sequence of randomly spaced pulses,” Nucl. Instr. Meth., vol. 61, pp. 84–88, 1968. [2] G. P. Westphal, “Nuclear and X-ray spectrometry and low-pass filter and filtering method therefore,” U.S. Pat. 4 692 626, Sept. 1987. , “A preloaded filter for high-rate, high-resolution gamma spec[3] trometry,” Nucl. Instr. Meth, vol. A 299, pp. 261–267, 1990. [4] G. P. Westphal, G. R. Cadek, N. Kerö, T. Sauter, and P. C. Thorwartl, “Digital implementation of the preloaded filter pulse processor,” J. Rad. Chem., vol. 193, no. 1, pp. 81–88, 1995. [5] K. Husimi and S. Ohkawa, “Trapezoidal filtering of signals realized by the directly synthesized Gaussian filter,” IEEE Trans. Nucl. Sci., vol. 36, pp. 396–400, Feb. 1989. [6] G. P. Westphal, “Real-time correction of counting losses in nuclear pulse spectroscopy,” J. Rad. Chem., vol. 70, no. 1-2, p. 387, 1982. [7] H. Koeman, “Method of, and apparatus for, determining radiation energy distributions,” U.S. Patent 3 872 287, Mar. 1975. [8] T. Lakatos, “Adaptive digital signal processing for X-ray spectrometry,” Nucl. Instr. Meth., vol. B47, pp. 307–310, 1990. [9] R. C. Farrow, J. Headspith, A. J. Dent, B. R. Dobson, R. L. Bilsborrow, C. A. Ramsdale, P. C. Stephenson, S. Brierly, G. E. Derbyshire, P. Sangsingkeow, and K. Buxton, “Initial data from the 30-element ORTEC HPGe detector array and the XSPRESS pulse-processing electronics at the SRS, Daresbury laboratory,” J. Synchrotron Rad., vol. 5, pp. 845–847, 1998. [10] G. Bertuccio, E. Gatti, M. Sampietro, P. Rehak, and S. Rescia, “Sampling and optimum data processing of detector signals,” Nucl. Instr. Meth., vol. A322, pp. 271–279, 1992. [11] M. Sampietro, G. Bertuccio, and A. Geraci, “A digital system for ‘optimum’ resolution in x-ray spectroscopy,” Rev. Sci. Instrum., vol. 66, no. 2, pp. 975–981, 1995.

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[12] F. S. Goulding, “Pulse-shaping in low-noise nuclear amplifiers: A physical approach to noise analysis,” Nucl. Instr. Meth., vol. 100, pp. 493–504, 1972. [13] G. Ripamonti, A. Castoldi, and E. Gatti, “Multiple delay line shaping: A new class of weighting functions suitable for digital signal processing,” Nucl. Instr. Meth., vol. A340, pp. 584–585, 1994. [14] A. Georgiev and W. Gast, “Digital processing in high resolution, high throughput gamma-ray spectroscopy,” IEEE Trans. Nucl. Sci., vol. 40, pp. 770–779, Aug. 1993. [15] V. T. Jordanov, G. F. Knoll, A. C. Huber, and J. A. Pantazis, “Digital techniques for real-time pulse shaping in radiation measurements,” Nucl. Instr. Meth., vol. A353, pp. 261–264, 1994. [16] M. Kuwata and H. Maeda, “A trapezoidal shaper using a rectangular prefilter,” IEEE Trans. Nucl. Sci., vol. 42, pp. 705–708, Aug. 1995. [17] P. Casoli, L. Isabella, P. F. Manfredi, and P. Maranesi, “Active zero-pole feedback loop to enhance high-rate performances of nuclear spectroscopy systems,” Nucl. Instr. Meth., vol. 156, pp. 559–566, 1978. [18] A. Geraci, A. Pullio, and G. Ripamonti, “Automatic pole-zero/zero-pole digital compensator for high resolution spectroscopy: design and experiments,” IEEE Trans. Nucl. Meth., vol. 46, pp. 817–821, Aug. 1999. [19] G. P. Westphal, H. Lemmel, F. Grass, R. Gwozdz, K. Jöstl, P. Schröder, and E. Hausch, “A gamma spectrometry system for activation analysis,” presented at the 5th Int. Conf. Methods Applications Radioanalytical Chemistry, Kona, HI, 2000. [20] H. Koeman, “Discussion on optimum filtering in nuclear radiation spectrometers, principle of operation and properties of a transversal digital filter, and practical performance of the transversal digital filter in conjunction with X-ray detector and preamplifier,” Nucl. Instr. Meth., vol. 123, pp. 161–187, 1975. [21] G. P. Westphal, “Method of, and system for, determining a spectrum of radiation characteristics with full counting-loss compensation,” U.S. Pat. 4 476 384, Oct. 1984.