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NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A

Nuclear pulse discrimination using statistical detection theory a, J.M . Perez b Unioersitat Jaume 1, Dpt. Ciències Experimentals, 12080 Caste116, Spain b CIEMAT, Acda . Complutense 22, 28040 Madrid, Spain

G . Garcia-Belmonte

(Received 2 August 1993 ; revised form received 17 November 1993)

The introduction of modern materials, like HgI2, into the field of nuclear detection is not fulfilling previous expectations. Due to technological problems, a significant percentage of H9I 2 detectors do not respond to the theoretical behaviour in the detection of radiation. This is mainly the case when high efficiency is desired and thick detectors must be employed . In particular, standard discriminators are sensitive to evolution in time of the pulse parameters, such as amplitude or rise time . This phenomenon has been related to polarization effects . In order to improve the response of these "bad quality" detectors, we have studied the possibility of using statistical discrimination methods implemented by means of digital processing techniques, aiming to keep the counting behaviour stable in time when thick Hg12 detectors (1 cm) are employed . Some theoretical aspects of these procedures are presented and a discrimination algorithm is implemented with the help of a real-time fast digital processor.

1. Introduction Detection is basically understood as the discrimination of pulses produced in a nuclear detector by the incoming radiation from the intrinsic noise inherent in the nuclear electronic chain . This paper deals with the possibility of using digital processing techniques in the detection of nuclear (gamma) radiation. A standard (NIM) discriminator delivers a logic pulse when the amplitude of a useful nuclear pulse exceeds a prefixed threshold level. These circuits are designed to operate in a wide variety of signal input conditions (different photon fluences, nonuniform pulses rise times, . . . ) or in different environmental characteristics such as temperature or irradiation dose [1]. The output of matched filters or pulse shape discriminators [2] depends on the similarity between the filter response and the signal shape . Therefore, these devices are very sensitive to incoming signal changes. The increasing interest in a new set of detectors, based on wide band gap semiconductors and their particular characteristics, has led us to view these classical discriminators as not entirely suitable for some applications . In this paper we will consider one of the most promising among these types of materials: the HgI Z detectors. Unfortunately, a significant percentage of the HgI2 detectors [3] do not respond to the theoretical expectations in the detection of radiation, due to technological problems . This limitation stands out in

thick (- 1 cm) detectors and energies greater than 300 keV [4]. Lack of detector homogeneity and quality results in a decrease of the pulses' amplitude. Consequently, there is a reduction in the number of pulses detected by standard discriminators . This results in a series of drawbacks: the most evident ones are poor energetic resolution and even low signal to noise ratio. The above considerations have led us to search for other more sophisticated methods for radiation discrimination in order to improve the response of these detectors. Detection theory has been successfully applied in many scientific areas: radio and radar astronomy, seismology, speech processing, communications, . . . Its statistical criteria are well-known . The technique of matched filter estimation, currently employed in nuclear electronics, is based on the same statistical assumptions [5]. However, little attention has been paid to digital implementations. It must be stressed, nonetheless, that matched analog filters do not improve bad quality signals provided by thick HgIZ sensors [6]. Poor SNR, rise time dispersion and polarization effects all degrade the sensor response and it is very difficult to design a suitable filter that avoids all these problems . Mathematical models of expected pulses generated by nuclear detectors and electronic noise are provided . It will be shown that a simple digital algorithm allows us to discriminate efficiently real signals from 1 cm thick HgIZ crystals . A digital version of such discrimi-

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nator is implemented with the help of a real-time fast processor. Its features are studied for different -treatment times. 2. Detection theory

L >-A :

2.1 . Statistical criteria In order to determine the optimum discrimination algorithm, statistical discrete models for both useful signal and noise are needed. For the sake of simplicity, noise will be represented by a zero mean Gaussian random process with a correlation matrix R. On the other hand, no assumption about useful signal profile will be done . A random time of arrival to the receiver following a Poisson distribution will be considered . Making use of the usual terminology in Detection theory [7] our problem is stated as follows, 110 : x(i)=n(i) ; x(i) H, : =s(i) +n(i) ;

- f(x/H1,k) is the probability distribution of x when both useful signal at time k and noise are present, - L is the likelihood ratio. If a threshold level A can be found for the values of L such that

i=0, . . .,N-1,

i = 0, . . . . N- 1,

where Ho and H, represent the absence and presence of useful signal hypotheses, x is the signal received by the discriminator, s represents the useful signal and n is the electronic noise. Discriminator processes N samples with i as time digital index. Vectors s and n can both be considered discrete random processes [8]. We will assume that the only known data is at the receiver. Thus, the additional data that could be obtained from parameters such as desintegration rate or geometrical source dispositions is not taken into account. Therefore, the design of an optimum filter requires a posteriori probabilities calculations [9, p. 142] . Composite detection makes reference to the situation where the expected signal, s, depends on random parameters that are not measured . In this case, the random variable can be considered the time of arrival at the receiver . According to this statement the samples are related not only to the digitalization index i but also to a discrete representation k of the arrival time . A simple test allows to make a decision between the two possible hypotheses Ho and Hl. To do this likelihood ratio functions must be constructed [10], L(k) = P,(k)f(xlH1,k)lf(xlHo) , N-1 L - (2) Y_ L(k), k=0

where: - P,s(k) is the probability that an expected signal arrives at the detector at time k = 0, . . . , N - 1, - f(x/Ho) is the probability distribution of x when only noise is present,

Ho; Hl ;

only noise is present, useful signal is present,

is verified, the decision about the presence of useful pulse in the incoming signal can be taken by means of Eq . (3). There is a number of different criteria to determine the threshold level A [10, p. 126-137] . The selection of the most suitable criterion depends on the data available in the particular experiment and on the fixed cost of errors that can be committed if the discriminator does not assume the right hypothesis . We will apply the Neyman-Pearsons criterion since it assures maximum detection probability when the false-alarm probability has been prefixed . 2.2 . Step function detection We shall next regard a simplified case by modeling each pulse obtained from the nuclear electronic chain as a step signal with height a. This is only an approximation to the real pulse shape, but the model does allow to observe the most important features of the statistical methods. The model considered for the noise is very simple too : it has been set as a bandlimited white process. However, the noise that is produced by an amplification electronic chain presents a colored power spectrum, with a frequency dependence equal to 1/W2 for frequencies lower than the inverse of noise corner time constant, and a white power spectrum for frequencies higher than this limit. Other dependencies, like 11to noises, will not be considered . In spite of this, an overall white power spectrum can be obtained by means of whitening analog or digital filters in an experimental setup [8,17] . Therefore, the model chosen to represent the useful signal and noise is given by the next expression, sk(i)

_ 0, - {a,

i = 0, . . ., k - 1 i=k, . ,N-1

Rn = o, 21, where o- is the noise rms and I is the unity matrix. Processing time NAt has been supposed shorter than the time elapsed between the arrival of two consecutive incoming photons. To a good approximation, the probability that a pulse reaches the receiver at time k is constant during the treatment, that is, P,(k) = 1/N.

G. Garcia-Belmone, J.M. Perez /Nucl. Instr and Meth . in Phys. Res. A 342 (1994) 591-595

593

After some basic calculations, the likelihood ratio can be written as follows [9, p. 155], 1 L(k) = N exp(x T Rn tsk - 1ST Rn t sk),

L

N-1

= Y-' L(k) . k=0

Applying the Neyman-Pearsons criterion, the threshold level to compare likelihood ratio could be obtained. In this evaluation, the false-alarm probability must have a prefixed value imposed for the particular application of the device . Typical operation characteristic diagrams in which detection probability vs the signal-to-noise ratio for a given false-alarm probability are depicted in Fig. 1, showing them for different values of N. In this case the signal-to-noise ratio is defined as (a/o )2 . However, the implementation of the optimum discriminator described above may be excessively cumbersome, and even impossible if real-time processing is required . Thus, keeping in mind the need to construct a digital version of such a discriminator, the simplest try will be to consider only the case k = 0 at the evaluation of L . This choice results in the sample addition as a hypotheses test, N-1

Lnop

T

1=o

(6)

X(*

whose implementation does not bear any complexity at all.

9

SNR

Fig. 2. Operation characteristics for optimum discrimination (solid curves) and sample adder (dashed curves) with different false-alarm probabilities f = 10 -1 , 10 -2, 10 -3 and N= 100 processed samples. In order to compare optimum and non-optimum (sample adder) treatment, we have calculated the operation characteristics of two processors for the signal model given in Eq . (4). In Fig. 2 these curves are plotted for a fixed number of samples. It is evident that the detection probability for optimum treatment does not excessively improve the result obtained using the simpler processing performed by means of Eq . (6), at least for low SNR values . 2.3 . Nonparametric detection

0

â

N-ia

06

04

02

9

,0 SNR

Fig. 1 . Operation characteristics for optimum discrimination with a false-alarm probability f = 0.01 and N =10, 50, 100 processed samples.

Nonparametric (also called model-free) methods [11] make use of very poor previous information about useful signal and noise in the design of a suitable discriminator . The model employed to describe useful signal and noise is based on general statistical assumptions, and therefore, no exhaustive description of the expected signal is required . These approaches present some advantages when compared with optimum filters . It is clear that optimum detectors are very sensitive to signal parameters' changes in time and their good features may be destroyed by such parameter evolutions. In particular, temporal variations in rise time and height for Hg12 pulses due to polarization phenomena have been observed [13] . Not only intrinsic changes in signal profile but changes in the environmental parameters, like temperature or radiation dose fluence, may produce evolutions in the characteristic parameters of signal and noise. Thus, it is necessary to design discrim-

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inators insensitive to signal changes, in order to obtain constant outputs in time when the geometrical locations of sources and sensor are maintained . In the signal representation, the simplest assumption that could be proposed consists of regarding the noise as a zero mean random process, and the useful signal with a positive mean value . Obviously, a method for mean estimation is the sample addition . Therefore, Eq . (6) performs the hypotheses test from a different and more general point of view without need for an exhaustive knowledge of noise parameters and useful signal shape. Accordingly, the null and alternative hypotheses [12] that we will test are simply

where A represents the sample mean . Instead of A, sample addition can be used to perform the same test, because both functions are linear related statistics .

Fig. 3. Typical counting behaviour of the discriminator, that implements the sample adder algorithm, in background exposure . Note the plateau between 2-5 As .

3. Discriminator implementation We have constructed a digital filter that performs the addition of N samples and compares it with a prefixed threshold, using an 8-bit flash ADC and a 16-bit fast adder. Two's complement coding allows us to achieve work frequencies near 20 MHz. The presence of a useful pulse is established when the sample addition surpasses a known threshold level during the treatment time . Absence of useful signal will be the output whenever sample addition does not reach the threshold. The treatment time covered a range of 0-10 As for the processing of a number of samples varying from 1 to 175 . We have considered this range large enough to detect pulses with a rise time ranging from 1 to 5 As, which is expected in this type of sensor material . The analog part of the experiment is composed of a 1-cm thick HgIZ detector biased with a voltage of 1000 V and a charge sensitive preamplifier (A250, from Amtek, Inc .) coupled in AC mode . Its output is amplified in order to scale the signal amplitude into the ADC voltage range. 4. Discriminator behaviour Stability has been stated by observing the reproducible output pattern for background exposure (no radiation sources present) . During 18 days, the evolution of the counting rate vs treatment time remained unaltered . As can be see in Fig. 3, up to 2 /is the detected counts (s -t) rise up with treatment time,

between 2-5 As a plateau is observed, that is, no other pulses are discriminated and for times greater than this last limit noise detections appear. The most important feature is that a threshold level in treatment time (near 5 As), can be found. Therefore, the method allows us to discriminate nuclear pulses from noise and, as shown in ref. [14], it is more efficient than standard voltage discriminators (single channel analyzers) . An improvement of 15% with respect to the values obtained by the standard discriminator could be observed by the authors when a 133 Ba source was employed . The result in the case of high energy sources, like 6° Co, is 20% better than the values achieved using classical methods. As an example, we show in Fig. 4 the typical discriminator behaviour when the detector is irradiated with a 133Ba radioactive source . The counting rises as the treatment time is increased. This takes place up to near 5 As . This fact is due to an increase in the real photon detection. For larger treatment times, rise rate of counting achieves the same value than in background exposure, and thus, no more useful signal detections have to be considered . 5. Conclusions and comments In this paper, we have presented some theoretical aspects of impulsive nuclear signal discrimination based on statistical Detection theory . We have provided a comparison between optimum and non-optimum, but easily implementable, detectors. The non-optimum ver-

G . Garcia-Belmone, J.M. Perez /Nucl. Instr. and Meth. i n Phys Res . A 342 (1994) 591-595

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In conclusion, digital methods in nuclear electronics are becoming promising in order to improve some aspects of signal processing, not completely resolved using standard approaches .

References

Fig . 4 . Counting behaviour of the discriminator, that imple ments the sample adder algorithm, in a "3 Ba exposure of low activity . sion, the sample adder, also performs the hypotheses test under the adoption of a nonparametric point of view of the algorithm determination . We constructed a digital filter that implements the detection algorithm, and a thick HgI 2 sensor was tested in absence of radiation sources (background) and irradiated with low energy y-sources (E < 400 keV). This method permits to discriminate between pulses and noise, making evident that polarization effects do not produce changes in the discriminator output . It is important to note that the method discussed here is related to the classical gated-integrator filter proposed in the 1970's [15] in order to improve bad quality spectra caused by pulse rise time dispersion . In both analog and digital cases, an integration during a fixed time is performed but in the second case we are dealing with discrimination and, therefore, no time reference exists . A digital version of gated-integrators has been presented in another paper [16] .

[1] Technical data, Nuclear Products Catalog 1989, LeCroy Corporation . [2] K . Neelakantan and V .R . Seshadri, Nucl . Instr . and Meth . A 256 (1987) 112 . [3] V . Gerrish and L . van der Berg, Nucl . Instr . and Meth . A 299 (1990) 41 . [4] J.M . Perez, Ph . D . Thesis, Universidad Complutense de Madrid (1992) . [5] E . Gatti and P .F. Manfredi, Riv . Nuovo Cimento 9 (1) (1986) 1 . [6] P . Olmos, J .M. Perez, G . Garcia-Belmonte, A . Bru and J .L . de Pablos, Nucl . Instr . and Meth . A 302 (1991) 91 . [7] W .L. Root, Proc . IEEE May 1970, ed . P .E. Green, sr ., vol . 58, nr. 5, p . 610 . [8] C .W . Therrien, Discrete Random Signals and Statistical Signal Processing (Prentice-Hall, Englewood Cliffs, 1992) . [9] LA . Warnstein and V .D. Zubakov, Extraction of Signals from Noise, (Dover, New York, 1962). [10] A .D . Whalen, Detection of Signals in Noise (Academic Press, New York, 1971) . [11] J .D . Gidson and J .L . Melsa, Introduction to Nonparametric Detection with Applications (Academic Press, New York, 1975). [12] J .W . Pratt and J .D . Gibbons, Concepts of Nonparametric Theory (Springer, New York, 1981) . [131 T . Mohamed-Brahim, A . Friant and J . Mellet, IEEE Trans . Nucl . Sci . NS-32 (1985) 581 . [14] P . Olmos, G . Garcia-Belmonte and J .M . Perez, Nucl . Instr . and Meth . A 322 (1992) 557 . [15] V . Radeka, Nucl . Instr . and Meth . 99 (1972) 525 . [16] R .E . Chrien and R .J . Sutter, Nucl Instr . and Meth . A 249 (1986) 421 [17] V . Radeka and N . Karlovac, Nucl . Instr. and Meth . 52 (1967) 86 .

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