Dead time (particle measurement technology)

The dead time of a particle detector (also correspondingly in the case of radiation detectors ) is a period of time immediately after the detection of a particle, during which the detector is not yet ready to detect another particle. This means that if two particles arrive shortly after one another, the second is not registered.

Depending on the type of detector and the electronic apparatus connected to it, the dead time can be constant or it can depend on the particle energy, the counting rate and / or other parameters. In addition to the detector itself, electronic components such as B. Discriminators , pile-up rejectors and multi-channel analyzers or coincidence circuits dead times. The overall dead time behavior of more complicated detector equipment can therefore be confusing.

For many measurement tasks, the conditions can be set up so that the counting loss due to dead time remains negligibly small or can be remedied with sufficient accuracy by means of an approximate computational correction.

Mathematical correction of the loss of counting

In the following, the “true” rate (number per unit of time) of detection events sought means the registered rate and the dead time. It is assumed that (more precisely: the probability of a detection event per short time interval ) remains constant over the measurement period and that it is constant. The difficulty with this correction method usually lies in precisely determining the dead time of the detector apparatus; complex measurements may be necessary for this. ${\ displaystyle n}$ ${\ displaystyle m}$ ${\ displaystyle \ tau}$ ${\ displaystyle n}$ ${\ displaystyle \ mathrm {d} t}$ ${\ displaystyle \ tau}$

Two types of dead times

Two types of dead time are distinguished for calculating the counting loss: the non-extendable and the extendable dead time.

Dead time that can not be extended means that a detection event that occurs during a dead time that is already running does nothing: it is not registered, but does not cause any further dead time, but dead times only arise from the registered events. The number of events registered during a measurement multiplied by is then the time during which the apparatus was overall "dead". The proportion of lost events must correspond to the proportion of this total dead time in the measurement duration. This results in the correction formula ${\ displaystyle \ tau}$

{\ displaystyle n = {\ frac {m} {1-m \ tau}} \ ,.}

Extendable dead time means, however, that even if it falls into a gentle current dead time, a new full dead time starts with each detection event. The dead times can therefore overlap. In this case, the frequency distribution of the time intervals between successive events must be taken into account for the calculation. This interval distribution is known because the events themselves form a Poisson distribution . The corresponding equation is

{\ displaystyle m = n \ cdot \ mathrm {e} ^ {- n \ tau} \ ,.}

From this, it must be calculated in individual cases by means of iteration starting from an estimated value. ${\ displaystyle n}$

In both formulas it is neglected that in a dead time, two or more events can also be lost - with less probability.

In the case of an extremely high count rate of the actual events, the registered rate in the former case is equal to the reciprocal of the dead time. In the second case, the apparatus is permanently paralyzed by a high event rate, the registered rate becomes zero.

According to Krieger, the classic Geiger-Müller counter tube is an example of extendable dead time. In general, however, the two dead time types are only idealized extreme cases; the dead time behavior of many real counting devices lies in between.

Artificial dead time

Sometimes an artificial dead time is built into the signal processing chain . This is an additional processing stage with a fixed, precisely known dead time which is selected to be longer than all dead times already given by the other components, so that it dominates the behavior. The loss of counting becomes larger, but more precisely calculable.

Direct measurement of the counting loss

It is also possible to measure the loss of counting during the actual measurement. In addition, artificial impulses are fed in at a known rate and their losses are observed. If the experiment involves pulse height spectroscopy rather than pulses of uniform height, the artificial pulses must follow the spectrum pulses at different heights at random, and the rate of injection must be a constant fraction of the total count rate of the spectrum.

Use of the time interval distribution

The above-mentioned interval distribution of the events, like the count rate, is changed by dead times, because shorter intervals than the dead time do not occur. In the case of dead time that cannot be extended, the true event rate can be determined directly from the measurement of two different integrals of the interval distribution.

Live time with multi-channel analyzers

The digital-to-analog converter (ADC) of a multichannel analyzer has a relatively long dead time, which depends on the pulse height, but cannot be extended, depending on the type. In many applications such as gamma spectrometers , this is by far the dominant contribution. That is why many devices offer the choice between true time and live time when preselecting the desired measurement duration . With true time is meant the real time that elapses from the beginning to the end of the registration. Live time, on the other hand, means that the measuring time clock is stopped during every dead time of the ADC; the total duration of the measurement is thereby extended by the sum of the dead times that have occurred. Provided that the true event rate and the pulse height spectrum do not change noticeably during the measurement period, the live time option results in an automatic compensation of the dead time-related loss of counting.

If the count rate is high, the loss of dead time can be compensated immediately during the measurement, even if the count rate is not constant, by continuously measuring the live time / true time ratio and inserting a fast digital processor that provides the registered events with weighting factors.

Pulsed radiation

If the particles or quanta do not reach the detector at a constant rate but in a pulsed manner, i.e. with regular interruptions, the dead time-related counting loss depends on the ratio of the dead time to the pulse and pause duration. Let it be the dead time, the duration of the radiation pulse and the duration of the pause between the pulses. The repetition frequency - determined for example by the particle accelerator - is . The duration can correspond to that of the accelerator macro pulse , but can also be longer if, for. B. delayed emissions or particle flight times play a role. ${\ displaystyle \ tau}$ ${\ displaystyle T_ {1}}$ ${\ displaystyle T_ {0}}$ ${\ displaystyle f = 1 / (T_ {1} + T_ {0})}$ ${\ displaystyle T_ {1}}$

It is particularly interesting that the dead time is longer than the pulse but shorter than the pause:

{\ displaystyle T_ {1} <\ tau <T_ {0} \ ,.}

Under these circumstances, the first and only the first detection event of each radiation pulse is registered. The mean true number of events per pulse results from the mean number of registered events per pulse - a number between 0 and 1 ${\ displaystyle N}$ ${\ displaystyle M}$

{\ displaystyle N = - \ ln (1-M) \ ,.}

The corrected count rate is thus

{\ displaystyle n = N \ cdot f}

.

Such a combination of , and has the important practical advantage that the counting loss is not influenced by the exact value of the dead time, its possible variability, elongation behavior, etc., and also not by the shape of the radiation pulse; the restriction to rectangular radiation pulses sometimes found in the literature is not necessary here. The radiation pulse can e.g. B. be subdivided into the unavoidable micropulses in high frequency accelerators. It is only necessary that the above inequality is observed (for the macro pulse) and that no detection events occur in the pauses. If necessary, the latter condition can be met by interrupting the signal chain before the component with the determining dead time during the pauses. The validity of the correction formula under these conditions was proven in an experiment with artificial dead times with counting losses of up to 80% with an accuracy of 1 to 2%. A comparable evidence was provided with the spectroscopy of pulsed X-rays. ${\ displaystyle T_ {1}}$ ${\ displaystyle T_ {0}}$ ${\ displaystyle \ tau}$

literature

Glenn F. Knoll: Radiation detection and measurement. 2nd edition, New York: Wiley, 1989. ISBN 0-471-81504-7 , pages 120-130.
Konrad Kleinknecht: Detectors for particle radiation . 4th edition, Teubner 2005, ISBN 978-3-8351-0058-9 .
Hanno Krieger: Radiation measurement and dosimetry . 2nd edition, Springer 2013, ISBN 978-3-658-00385-2 .

Individual evidence

↑ ^a ^b Knoll (see list of literature), page 121
↑ Knoll (see list of literature) p. 122
↑ Krieger (see literature list), page 162
^ JW Müller: Generalized dead times. Nuclear Instruments and Methods in Physics Research , Vol. A 301 (1991) 543-551
↑ HH Bolotin et a .: Simple technique for precise determination of counting losses in nuclear pulse processing systems. Nuclear Instruments and Methods Vol. 83 (1970) pp. 1-12
↑ W. Görner: An adaptation of the pulser method for the determination of losses in counting short-lived nuclides. Nuclear Instruments and Methods Vol. 120 (1974) 363-364
↑ J. Sabol: Another method of dead time correction. Journal of Radioanalytical and Nuclear Chemistry - Letters 127/5 / (1988) pages 389-394
^ GP Westphal: Loss-free counting - a concept for real-time compensation of dead-time and pile-up losses in nuclear pulse spectroscopy. Nuclear Instruments and Methods Vol. 146 (1977) pp. 605-606
^ S. Pommé et al .: Accuracy and precision of loss-free counting in gamma-ray spectrometry. Nuclear Instruments and Methods in Physics Research Vol. S 422 (1999) pages 388-394
↑ Knoll (see list of literature), page 127
↑ Knoll (see list of literature), page 126
↑ ^a ^b U. von Möllendorff, H. Giese: Experimental tests of dead-time corrections. Nuclear Instruments and Methods in Physics Research Vol. A 498 (2003) pages 453-458
^ Y. Danon et al .: Dead time and pileup in pulsed parametric X-ray spectroscopy. Nuclear Instruments and Methods in Physics Research Vol. A 524 (2004) pages 287-294

Web links

S. Pommé: Pile-up, dead time, and counting statistics. BIPM Uncertainty Workshop, 2007. ( PDF )

[Knoll121-1] Knoll (see list of literature), page 121

[2] Knoll (see list of literature) p. 122

[3] Krieger (see literature list), page 162

[4] JW Müller: Generalized dead times. Nuclear Instruments and Methods in Physics Research , Vol. A 301 (1991) 543-551

[5] HH Bolotin et a .: Simple technique for precise determination of counting losses in nuclear pulse processing systems. Nuclear Instruments and Methods Vol. 83 (1970) pp. 1-12

[6] W. Görner: An adaptation of the pulser method for the determination of losses in counting short-lived nuclides. Nuclear Instruments and Methods Vol. 120 (1974) 363-364

[7] J. Sabol: Another method of dead time correction. Journal of Radioanalytical and Nuclear Chemistry - Letters 127/5 / (1988) pages 389-394

[8] GP Westphal: Loss-free counting - a concept for real-time compensation of dead-time and pile-up losses in nuclear pulse spectroscopy. Nuclear Instruments and Methods Vol. 146 (1977) pp. 605-606

[9] S. Pommé et al .: Accuracy and precision of loss-free counting in gamma-ray spectrometry. Nuclear Instruments and Methods in Physics Research Vol. S 422 (1999) pages 388-394

[10] Knoll (see list of literature), page 127

[11] Knoll (see list of literature), page 126

[MG-12] U. von Möllendorff, H. Giese: Experimental tests of dead-time corrections. Nuclear Instruments and Methods in Physics Research Vol. A 498 (2003) pages 453-458

[13] Y. Danon et al .: Dead time and pileup in pulsed parametric X-ray spectroscopy. Nuclear Instruments and Methods in Physics Research Vol. A 524 (2004) pages 287-294