Non-extending Dead Time Research Articles

Pseudo-fixed dead time circuit for designing and implementation of JEOL-type X-ray counting systems

Quantitative electron probe microanalysis (EPMA) of trace elements using wavelength dispersive spectrometers (WDS) requires high probe current and/or accelerating voltage and long X-ray sampling times to measure weak X-ray signals from target materials. The X-ray count rate of a standard material is extremely high when measured under the same conditions. Consequently, the accuracy of the dead time correction becomes a significant issue for quantification. Accurate dead time correction requires an exact knowledge of the X-ray counting system, including the behavior of the proportional counter and electronic circuits. Each spectrometer has a specific dead time that depends on factors such as electronic circuit design, counter bias, and X-ray energies. The dead time also changes with aging degradation. A pseudo-fixed dead time correction circuit with non-extendable approximation is described that prevents systematic errors in quantitative EPMA caused by inappropriate dead time corrections. The circuit, which is added to the output of the single channel analyzer, includes one extendable and two non-extendable dead time generators with dead times of 0.68μs, 1.08μs, and 1.92μs, respectively. The behavior of the whole system can be treated as non-extendable for most applications, with a dead time of approximately 2.01μs. The pseudo-fixed dead time circuit suppresses systematic error of the dead time correction to 0.6% or less when the original dead time is between 0.8–2.0μs and the true X-ray count rate is <200kcps. This makes it possible to perform accurate dead time corrections without periodic measurement of the dead time throughout the life of the proportional counter by implementing a high-precision crystal oscillator in the system.

Оптимальное оценивание состояний обобщенного MAP-потока событий в условиях непродлевающегося мертвого времени

Оптимальное оценивание состояний обобщенного MAP-потока событий в условиях непродлевающегося мертвого времени

Activity determination of 67Ga using 4πβ‒γ coincidence counting

The activity of a 67Ga solution was measured by means of the 4πβ–γ coincidence counting technique. A setup with a proportional counter and non-extending dead-time modules in the two detector channels was used. The influence of the delayed state affecting the measured count rates was taken into account by using appropriate correction formulae. The analysis requires a variation of the dead time and a subsequent extrapolation to infinite dead time. An uncertainty of about 0.5% was obtained and the result was used to make an intercomparison with the SIR of the BIPM.

Radiation Measurements without Posing the Inversion Problem

Purpose: Radiation measurement is an exponential analysis, which is an “illposed” problem, where the solution is not unique. Therefore, the accuracy of data points is critical. If the radiation detector is sensitive during the dead time, usually an extended dead time signal processing method is necessary and the calculation of the dead time and pile up rate invoke the inversion problem, which is difficult to solve, and only approximated. We have used two new approaches, where the inversion problem is not posed, and there is no need to assume the Poisson distribution or constant source strength. It goes beyond all previous techniques by handling the presence of discriminators. The preamplifier-signal processing chain has dead times and applies discriminators, as a consequence disturbs the randomness, and other distributions may also contribute. Although an undisturbed nuclear decay should be Poisson in nature, the measured spectrum usually does not have a Poisson distribution. The robustness of the two methods was investigated, focusing on the traceable derivation of statistical uncertainty. The two new methods were applied in gamma spectra measurements of 152Eu calibration sources, and nuclear half-life of 68Ga PET isotope, and compared with measurements using previous techniques. Methods: CSX (Cambridge Scientific) digital signal processors were used with five HPGe detectors in two operation modes in two measurement series. In quality assurance mode, the CSX processes all events, both the accepted and rejected ones, placing each event into one or more spectra based on the applied discriminators. Based on the accepted spectrum, the rejected spectra were analyzed to determine the single, double and triple events, the rate of unrelated, and noise events all to obtain the true input counts. The second and independent approach was a time interval histogram analysis for the measurement of the gamma ray intensities. In time interval histogram mode, the CSX creates an energy spectrum as well as an interval histogram of arrival times between successive events. This operation mode does not apply discriminators and has no dead time. The CSX signal processor was selected, as it offers a dead time free and less than 1% pile up rate up to about a million counts per second input rate, as well as quality assurance at the signal processing level. Results: The CSX processors employ a non-extended dead time approach and in quality assurance mode the true input rate is readily determined. As a consequence, the inversion problem was avoided. The uncertainties and uncertainty propagation are clearly justified. For the half-life measurement of 68Ga, the time interval histogram analysis gave six times smaller standard uncertainty than the square root of the counts. The inter-arrival time histogram was sensitive to non-deterministic behaviour of the detectors, and electronic disturbances, discrediting several measurement series. This additional ability is significant for quality measurements. Conclusion: Spectroscopy with HPGe detectors has lacked a method to credibly determine the uncertainties when discrimination is applied. In addition, a calibration procedure was required to establish the output rate versus input rate relations for each input rate preferably with a similar spectral distribution as the spectrum of interest. The preamplifier signal shape varied as a function of the input rate for each of the HPGe detectors studied. In such cases both the accepted and rejected event spectra are necessary for a proper evaluation. Accounting for all the events allows the determination of the uncertainties. The time interval histogram analysis is simple and straightforward, and offers an elegant way to determine the true input rate and uncertainty. The measurement can be applied over large input counting ranges, and does not require calibration.

Corrections for the combined effects of decay and dead time in live-timed counting of short-lived radionuclides

Studies and calibrations of short-lived radionuclides, for example 15O, are of particular interest in nuclear medicine. Yet counting experiments on such species are vulnerable to an error due to the combined effect of decay and dead time. Separate decay corrections and dead-time corrections do not account for this issue. Usually counting data are decay-corrected to the start time of the count period, or else instead of correcting the count rate, the mid-time of the measurement is used as the reference time. Correction factors are derived for both those methods, considering both extending and non-extending dead time. Series approximations are derived here and the accuracy of those approximations are discussed.

A High Performance Digital Time Interval Spectrometer: An Embedded, FPGA-Based System With Reduced Dead Time Behaviour

AbstractIn this work, a fast 32-bit one-million-channel time interval spectrometer is proposed based onfield programmable gate arrays(FPGAs). The time resolution is adjustable down to 3.33 ns (=T, the digitization/discretization period) based on a prototype system hardware. The system is capable to collect billions of time interval data arranged in one million timing channels. This huge number of channels makes it an ideal measuring tool for very short to very long time intervals of nuclear particle detection systems. The data are stored and updated in a built-in SRAM memory during the measuring process, and then transferred to the computer. Twotime-to-digital converters(TDCs) working in parallel are implemented in the design to immune the system against loss of the first short time interval events (namely below 10 ns considering the tests performed on the prototype hardware platform of the system). Additionally, the theory of multiple count loss effect is investigated analytically. Using the Monte Carlo method, losses of counts up to 100million events per second(Meps) are calculated and the effective system dead time is estimated by curve fitting of a non-extendable dead time model to the results (τNE= 2.26 ns). An important dead time effect on a measured random process is the distortion on the time spectrum; using the Monte Carlo method this effect is also studied. The uncertainty of the system is analysed experimentally. The standard deviation of the system is estimated as ± 36.6 ×T(T= 3.33 ns) for a one-second time interval test signal (300 millionTin the time interval).

Uncertainty of nuclear counting

Nuclear counting is affected by pulse pileup and system dead time, which induce rate-related count loss and alter the statistical properties of the counting process. Fundamental equations are presented to predict deviations from Poisson statistics due to non-random count loss in nuclear counters and spectrometers. Throughput and dispersion of counts are studied for systems with pileup, extending and non-extending dead time, before and also after compensation for count loss. Equations are provided for random fractions of the output events, applicable to spectrometry applications. Methods for loss compensation are discussed, including inversion of the throughput equation, live-time counting and loss-free counting. Secondary effects in live-time counting are addressed: residual interference from pileup in systems with imposed dead times and errors due to varying count rate when measuring short-lived radionuclides.

Cascades of pile-up and dead time

Count loss through a cascade of pile-up and dead time is studied. Time interval density-distribution functions and throughput factors are presented for counters with a series arrangement of pile-up and extending or non-extending dead time. A counter is considered, where an artificial dead time is imposed on every counted event, in order to control the length and type of dead time. For such a system, it is relatively easy to determine an average count-loss correction factor via a live-time clock gated by the imposed dead-time signal (‘live-time mode’), or otherwise to apply a correction factor based on the inversion of the throughput function (‘real-time mode’). However, these techniques do not account for additional loss through pulse pile-up. In this work, counting errors associated with neglecting cascade effects are calculated for measurements in live-time and real-time mode.

Monte Carlo simulation of the effect of counting losses on measured X-ray intensities

The statistical properties of intensities affected by counting loss based on conventional non-extended and extended dead-time models are examined by a Monte Carlo method. It has been confirmed that the variance of the counted pulses for the non-extended dead-time model with the rate of generated pulsesr and the dead-time τ is given by \sigma_{\rm non}^2 = \mu_{\rm non}/(1+r \tau)^2, while that for the extended dead-time model is given by \sigma_{\rm ext}^2 = \mu_{\rm ext} [1 - 2r\tau \exp(-r \tau)], as proposed by Laundy &amp; Collins [(2003).J. Synchrotron Rad.10, 214–218], for the mean values of counted pulses μnonand μext, respectively. Practical formulae to estimate the statistical errors of the corrected intensities are also presented.

Measurement of beta surface emission rate from an extended area [formula omitted]Cl source using a multiwire proportional counter

We have developed, as a national standard, a windowless multiwire proportional counting (MWPC) system for gross measurements of α - and β -emitting radionuclides at an uncertainty level below 1%. Various detector characteristics have been studied and several working parameters of the system have been determined in order to achieve an optimized detection capability. The detector is commissioned through an international comparison of the β emission rate from an extended area 36 Cl source. Correction for the dead time loss is made by the non-extendable dead time method. A linear extrapolation of pulse height spectrum is employed to correct for the loss in the detection efficiency due to discriminating against the events formed from a small number of original ion pairs. The surface emission rate was measured to be 1.84 × 10 3 counts/s with the relative combined standard uncertainty of 0.46%. The measured uncertainty indicates that the constructed MWPC is capable of serving as a national standard.

Practical correction of dead time effect in variance-to-mean ratio measurement

A practical technique to correct the dead time effect in the variance-to-mean ratio measurement is proposed. A correction formula used in the technique is derived based on a simple mechanism of count loss due to a non-extending dead time. The technique was verified with a Monte Carlo simulation and an experiment in Deuterium Critical Assembly. It was confirmed that the formula can make a reasonable correction to the case that the count loss is as large as 50%. This correction technique is extremely simple and can make the correction only with data obtained in the original measurement.

Is loss-free counting under statistical control?

A new formula for the statistical uncertainty of "loss-free counting" (LFC) is presented. Its validity is demonstrated by comparing with experimental data obtained with a HPGe gamma-ray spectrometer. Also, computer simulation data of nuclear counting with different types of count loss (pileup rejection, extending and nonextending dead time) are in agreement with the predicted counting uncertainty. The proposed formula for LFC uncertainty is applicable to spectrometers with a classical semi-Gaussian pulse-shaping amplifier as well as with a gated-integrator amplifier. Hence, achieving statistical control seems to be a feasible goal.

Time-interval distributions and counting statistics with a non-paralysable spectrometer

Time-interval density distributions of subsequently counted events with a non-paralysable spectrometer are scrutinised; a theoretical expression is presented and its results are compared with computer simulations of nuclear counting. The corresponding counting uncertainty formula is derived from the Laplace transform of the time-interval distribution formula. A clear difference is found in the counting statistics for the count integral of the full spectrum as compared to arbitrary fractions of the spectrum. New counting uncertainty formulas are presented for use in spectrometry. In addition, time-intervals and counting statistics are investigated theoretically for spectra taken with an ADC of the Wilkinson type, in which the characteristic non-extending deadtime varies linearly with the channel number.

An exact solution for a non-extending dead time problem in passive neutron assay

The Markov Chain method is used to obtain an exact solution to the problem of deriving the count rate, for time correlated pulses arising in passive neutron assay, in the presence of a non-extending dead time. While the discussion presented in the main text assumes only singlets and doublets in the pulse train, extension to include higher multiplicities is described in the Appendix.

The half-lives of 42Sc, 46V, 50Mn and 54Co

As part of a broad program to determine ft values for superallowed O + → O − β transitions, the half-lives of 42Sc, 46V, 50Mn and 54Co have been measured with isotopically pure samples prepared with an on-line isotope separator. Emitted β + particles were observed with a large-solid-angle, high-efficiency, low-background gas proportional counter, from which signals were multiscaled. The counting electronics had a well-defined, non-extendable dead time. As no exact data analysis is possible, three different procedures were compared. The most stringent method involved regression analysis where a common half-life was simultaneously fitted to the individual decay curves of hundreds of samples and their Poisson statistical weights were distorted to reflect dead-time losses. The analysis procedures were tested on hypothetical decay data that were created by binning a time sequence of events, obtained from interval distributions reflecting the given half-lives and intensities of two decay components, and allowing for series and non-extendible dead times that reflected experimental conditions. On the basis of these tests it is demonstrated that the analysis does not introduce any bias at the 0.01% level. The deduced half-lives are 42 Sc: (680.67 ± 0.28) ms, 46 V: (422.57 ± 0.13) ms, 50 Mn: (283.29 ± 0.08) ms, 54 Co: (193.28 ± 0.07) ms. These results establish important elements in a demanding test of the Electroweak Standard Model.

The markov chain method for solving dead time problems in the space dependent model of reactor noise

The discrete time Markov chain approach for deriving the statistics of time-correlated pulses, in the presence of a non-extending dead time, is extended to include the effect of space energy distribution of the neutron field. Equations for the singlet and doublet densities of follower neutrons are derived by neglecting correlations beyond the second order. These equations are solved by the modal method. It is shown that in the unimodal approximation, the equations reduce to the point model equations with suitably defined parameters.

Dead-time effects in time-of-flight measurements

Abstract It is shown that the counting losses due to dead-time effects in detection systems associated with pulsed sources, follow a behavior essentially different from the continuous counting experiments. Extended and nonextended dead-time cases are examined and general expressions for the recorded spectra are obtained. Analytical expressions for particles with a time-independent distribution are given and compared with Monte Carlo simulations. Previous publications related to the present work are discussed.

Practical equation for deadtime determination in X-ray counting systems

A practical equation is presented to determine the deadtime τd in conventional X-ray counting systems when the amount of deadtime is greater than that which can be accounted for by non-extended deadtime theory. The use of this equation to determine the deadtime increases the practical range over which conventional X-ray detection systems can be used.

Theoretical analysis of the variable dead time counter technique for passive neutron assay of plutonium

The variable dead time counter employing non-extendable dead time has been used in the past for the passive neutron assay of Pu. However, as no exact theory of the technique is available, the results are analyzed in terms of semi-empirical relations between the measured count rates and the system parameters of interest. Since these relations have limited validity, the scope of the technique is rather restricted. In this paper a series of formulae for the count rate in the presence of non-extendable dead time, which represent successive approximations to the exact result, are derived. The formulae are compared with Monte-Carlo calculations and may be useful in interpreting the results of this technique over a wider range of parameters.

Another method of dead time correction

A new method of the correction of counting losses caused by a non-extended dead time of pulse detection systems is presented. The approach is based on the distribution of time intervals between pulses at the output of the system.