Optimal processing of information from detectors used for detecting explosives by neutron-radiation analysis

Abstract

The optimization is accomplished on the basis of methods used for checking statistical hypotheses. Two possible methods for processing information from γ-ray detectors are examined: setting a threshold according to a general likelihood ratio including all combinations of detectors or separate combinations of detectors. In the second case, all possible combinations of detectors must be sorted when the measurements are analyzed. Calculations for a specific setup with six detectors show that sorting detector combinations permits detection of smaller quantities of explosives than can be done with a general likelihood ratio. A sequential analysis instead of sorting detector combinations permits identifying explosives more quickly than can be done with a general likelihood ratio.Neutron-radiation analysis is one method for detecting exlosives in transportation hubs and in companies [1][2][3][4]. The method is based on the capture of thermal neutrons by nitrogen isotopes followed by the emission of γ rays, which are detected by a detector. Most explosives contain from 16 to 40% nitrogen (25% on the average) while ordinary materials in objects which are checked contain up to 28% nitrogen (10% on the average) [5]. The most informative part of the γ-ray spectrum in detecting nitrogen corresponds to the range 10-11 MeV [1,3]. Since an explosive can be found at any location of an object being checked, several detectors are used to detect γ rays. This makes it possible to indicate the relative location of an explosive and to estimate its quantity. The observable random quantities are the sums of the numbers of detector count n ik over N successive time intervals with duration ∆t:where k is the number of the successive time interval; i is the number of the detector, i = 1, 2, ..., Q; and Q is the number of detectors. The measurement time is N∆t. When analyzing measurements, the indications of each detector can be examined separately or the indications of several detectors can be summed. It is useful to divide the space of the measurement chamber into sections according to the number of detectors used. An explosive can be present in one or several of these sections. Thus, when measurements are analyzed, the relative configuration of the detectors and the explosive must be taken into account. The present paper analyzes methods of information processing that can be used to detect the smallest mass of explosives.Since γ-ray detection is of a random character, a judgement as to the presence or absence of an explosive on the basis of measurements must be regarded as a check of statistical hypotheses [6,7]. Two alternative hypotheses are checked: an explosive is present in one or several sections of the measurement chamber (hypothesis 1) and there is no explosive (hypothesis 0). An indicator that an effect is present (in this case an explosive) is that a selected threshold for the number K n i k i k N = = ∑ 1 ,

Optimal use of spectrometric information for discovering explosives by neutron-radiation analysis and inelastic neutron scattering

“…An excursion above threshold attests to the presence of the effect. The detection system with an method of analysis of the measurements is characterized by the mass G of the explosive, determined with a prescribed probability of false alarms and correct detection.The optimization of the processing of information coming from many detectors with different threshold setting methods is examined in [5]. In the present work, the considerations used in [5] are applied to optimal processing of γ-ray spectra.…”

“…The optimization of the processing of information coming from many detectors with different threshold setting methods is examined in [5]. In the present work, the considerations used in [5] are applied to optimal processing of γ-ray spectra.…”

“…In the present work, the considerations used in [5] are applied to optimal processing of γ-ray spectra.…”

“…For the ith channel, we denote the average number of counts in the presence of the effect by x i and in the absence of the effect by x 0i . The ratio of the likelihood lnl will include Q cofactors, the logarithm of this ratio L = ln l will contain Q terms [5]:…”

“…In this approximation, it follows from expression (1) that the difference of the average values of the logarithm of the ratio of the likelihood for the hypotheses H 0 and H 1 [5] is For a large number of counts in each channel, the distribution of the numbers of counts and the logarithm of the ratio of the likelihood L can be regarded as Gaussian with variance σ 2 L 1 ≅ σ 2 L 0 = ΔL. Then the ratio between the desired effect Δx and the probability of false alarms α and correct detection 1 -β can be determined according to the expression [6,7], relating the effect with quantiles of the normal distribution k 1−α and k 1−β :…”