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== | {{Other uses|Dead Time (disambiguation)}} | ||
For detection systems that record discrete events, such as [[particle physics|particle]] and [[nuclear physics|nuclear]] [[particle detector|detectors]], the '''dead time''' is the time after each event during which the system is not able to record another event.<ref name="Leo">{{cite book | author=W. R. Leo | title=Techniques for Nuclear and Particle Physics Experiments |pages=122–127| publisher=Springer | year=1994 |isbn=3-540-57280-5}}</ref> | |||
An everyday life example of this is what happens when someone takes a photo using a flash - another picture cannot be taken immediately afterward because the flash needs a few seconds to recharge. In addition to lowering the detection efficiency, dead times can have other effects, such as creating possible exploits in [[quantum cryptography]].<ref>{{cite journal | |||
|first1=H. | |||
|last1=Weier | |||
|first2=H. | |||
|last2=Krauss | |||
|display-authors=1 | |||
|journal=New Journal of Physics | |||
|volume=13 | |||
|year=2011 | |||
|pages=073024 | |||
|title=Quantum eavesdropping without interception: an attack exploiting the dead time of single-photon detectors | |||
|url=http://iopscience.iop.org/1367-2630/13/7/073024 | |||
|doi=10.1088/1367-2630/13/7/073024|bibcode = 2011NJPh...13g3024W |arxiv = 1101.5289 }}</ref> | |||
==Overview== | |||
The total dead time of a detection system is usually due to the contributions of the intrinsic dead time of the detector (for example the drift time in a [[gaseous ionization detector]]), of the analog front end (for example the shaping time of a spectroscopy amplifier) and of the [[Data acquisition|DAQ]] (the conversion time of the [[Analog-to-digital converter|ADC]]s and the readout and storage times). | |||
The intrinsic dead time of a detector is often due to its physical characteristics; for example a [[spark chamber]] is "dead" until the potential between the plates recovers above a high enough value. In other cases the detector, after a first event, is still "live" and does produce a signal for the successive event, but the signal is such that the detector readout is unable to discriminate and separate them, resulting in an event loss or in a so-called "pile-up" event where, for example, a (possibly partial) sum of the deposited energies from the two events is recorded instead. In some cases this can be minimised by an appropriate design, but often only at the expense of other properties like energy resolution. | |||
The analog electronics can also introduce dead time; in particular a shaping spectroscopy amplifier needs to integrate a fast rise, slow fall signal over the longest possible time (usually from .5 up to 10 microseconds) to attain the best possible resolution, such that the user needs to choose a compromise between event rate and resolution. | |||
Trigger logic is another possible source of dead time; beyond the proper time of the signal processing, spurious triggers caused by noise need to be taken into account. | |||
Finally, digitisation, readout and storage of the event, especially in detection systems with large number of channels like those used in modern High Energy Physics experiments, also contribute to the total dead time. To alleviate the issue, medium and large experiments use sophisticated pipelining and multi-level trigger logic to reduce the readout rates.<ref>{{cite report|title=[[A Large Ion Collider Experiment|ALICE]] DAQ and ECS Manual |year=2010 |month=December |url=https://ph-dep-aid.web.cern.ch/ph-dep-aid/dateUserGuide/dateUserGuide.pdf |type=ALICE Internal Note/DAQ ALICE-INT-2010-001 |first1=F. |last1=Carena |first2=W. |last2=Carena |display-authors=1}}</ref> | |||
From the total time a detection system is running, the dead time must be subtracted to obtain the [[live time]]. | |||
==Paralyzable and non-paralyzable behaviour== | |||
A detector, or detection system, can be characterized by a ''paralyzable'' or ''non-paralyzable'' behaviour.<ref name="Leo"/> | |||
In a non-paralyzable detector, an event happening during the dead time since the previous event is simply lost, so that with an increasing event rate the detector will reach a saturation rate equal to the inverse of the dead time. | |||
In a paralyzable detector, an event happening during the dead time since the previous one will not just be missed, but will restart the dead time, so that with increasing rate the detector will reach a saturation point where it will be incapable of recording any event at all. | |||
A semi-paralyzable detector exhibits an intermediate behaviour, in which the event arriving during dead time does extend it, but not by the full amount, resulting in a detection rate that decreases when the event rate approaches saturation. | |||
== | == Analysis == | ||
It will be assumed that the events are occurring randomly with an average frequency of ''f''. That is, they constitute a [[Poisson process]]. The probability that an event will occur in an infinitesimal time interval ''dt'' is then ''f dt''. It follows that the probability ''P(t)'' that an event will occur at time ''t'' to ''t+dt'' with no events occurring between ''t=0'' and time ''t'' is given by the [[exponential distribution]] (Lucke 1974, Meeks 2008): | |||
:<math>P(t)dt=fe^{-ft}dt\,</math> | |||
The expected time between events is then | |||
:<math>\langle t \rangle = \int_0^\infty tP(t)dt = 1/f</math> | |||
== | === Non-paralyzable analysis === | ||
For the non-paralyzable case, with a dead time of <math>\tau</math>, the probability of measuring an event between <math>t=0</math> and <math>t=\tau</math> is zero. Otherwise the probabilities of measurement are the same as the event probabilities. The probability of measuring an event at time ''t'' with no intervening measurements is then given by an exponential distribution shifted by <math>\tau</math>: | |||
:<math>P_m(t)dt=0\,</math> for <math>t\le\tau\,</math> | |||
== | :<math>P_m(t)dt=\frac{fe^{-ft}dt}{\int_\tau^\infty fe^{-ft}dt} = fe^{-f(t-\tau)}dt</math> for <math>t>\tau\,</math> | ||
The expected time between measurements is then | |||
:<math>\langle t_m \rangle = \int_\tau^\infty tP_m(t)dt = \langle t \rangle+\tau</math> | |||
In other words, if <math>N_m</math> counts are recorded during a particular time interval <math>T</math> and the dead time is known, the actual number of events (''N'') may be estimated by | |||
:<math>N \approx \frac{N_m}{1- N_m \tau / T}</math> | |||
If the dead time is not known, a statistical analysis can yield the correct count. For example (Meeks 2008), if <math>t_i</math> are a set of intervals between measurements, then the <math>t_i</math> will have a shifted exponential distribution, but if a fixed value ''D'' is subtracted from each interval, with negative values discarded, the distribution will be exponential as long as ''D'' is greater than the dead time <math>\tau</math>. For an exponential distribution, the following relationship holds: | |||
:<math>\frac{\langle t^n \rangle}{\langle t \rangle^n} = n!</math> | |||
where ''n'' is any integer. If the above function is estimated for many measured intervals with various values of ''D'' subtracted (and for various values of ''n'') it should be found that for values of ''D'' above a certain threshold, the above equation will be nearly true, and the count rate derived from these modified intervals will be equal to the true count rate. | |||
==Time-To-Count== | |||
With a modern microprocessor based [[ratemeter]] one technique for measuring field strength with detectors (e.g., [[Geiger–Müller_tube#Quenching_and_dead_time|Geiger–Müller tubes]]) with a recovery time is Time-To-Count. In this technique, the detector is armed at the same time a counter is started. When a strike occurs, the counter is stopped. If this happens many times in a certain time period (e.g., two seconds), then the mean time between strikes can be determined, and thus the count rate. Live time, dead time, and total time are thus measured, not estimated. This technique is used quite widely in radiation monitoring systems used in nuclear power generating stations. | |||
==See also== | |||
* [[Data acquisition]] (DAQ) | |||
* [[Allan_variance#Dead_time_in_measurements|Allan variance]] | |||
* [[Photomultiplier]] | |||
* [[Positron emission tomography#Image_reconstruction|Positron emission tomography]] | |||
* [[Class-D_amplifier#Design_challenges|Class-D amplifier]] | |||
==References== | |||
<references/> | |||
==Further reading== | |||
* {{cite journal | last =Lucke | first =Robert L. |date=June 1976 | title =Counting Statistics for Nonnegligible Dead Time Corrections | journal =Rev. Sci. Instrum. | volume =47 | issue =6 | doi =10.1063/1.1134733 | page =766|bibcode = 1976RScI...47..766L }} | |||
* {{cite journal | last =Meeks | first =Craig | coauthors=Siegel, P.B. |date=June 2008 | title =Dead time correction via the time series | journal =Am.J. Phys | volume =76 | issue =6 | doi =10.1119/1.2870432 | page =589|bibcode = 2008AmJPh..76..589M }} | |||
[[Category:Nuclear physics]] | |||
Morris, S.L. and Naftilan, S.A., "Determining Photometric Dead Time by Using Hydrogen Filters", Astron. Astrophys. Suppl. Ser. 107, 71-75, Oct. 1994 | |||
Revision as of 17:33, 8 January 2014
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I'm learning Norwegian literature at a local college and I'm just about to graduate.
I have a part time job in a the office.
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For detection systems that record discrete events, such as particle and nuclear detectors, the dead time is the time after each event during which the system is not able to record another event.[1]
An everyday life example of this is what happens when someone takes a photo using a flash - another picture cannot be taken immediately afterward because the flash needs a few seconds to recharge. In addition to lowering the detection efficiency, dead times can have other effects, such as creating possible exploits in quantum cryptography.[2]
Overview
The total dead time of a detection system is usually due to the contributions of the intrinsic dead time of the detector (for example the drift time in a gaseous ionization detector), of the analog front end (for example the shaping time of a spectroscopy amplifier) and of the DAQ (the conversion time of the ADCs and the readout and storage times).
The intrinsic dead time of a detector is often due to its physical characteristics; for example a spark chamber is "dead" until the potential between the plates recovers above a high enough value. In other cases the detector, after a first event, is still "live" and does produce a signal for the successive event, but the signal is such that the detector readout is unable to discriminate and separate them, resulting in an event loss or in a so-called "pile-up" event where, for example, a (possibly partial) sum of the deposited energies from the two events is recorded instead. In some cases this can be minimised by an appropriate design, but often only at the expense of other properties like energy resolution.
The analog electronics can also introduce dead time; in particular a shaping spectroscopy amplifier needs to integrate a fast rise, slow fall signal over the longest possible time (usually from .5 up to 10 microseconds) to attain the best possible resolution, such that the user needs to choose a compromise between event rate and resolution.
Trigger logic is another possible source of dead time; beyond the proper time of the signal processing, spurious triggers caused by noise need to be taken into account.
Finally, digitisation, readout and storage of the event, especially in detection systems with large number of channels like those used in modern High Energy Physics experiments, also contribute to the total dead time. To alleviate the issue, medium and large experiments use sophisticated pipelining and multi-level trigger logic to reduce the readout rates.[3]
From the total time a detection system is running, the dead time must be subtracted to obtain the live time.
Paralyzable and non-paralyzable behaviour
A detector, or detection system, can be characterized by a paralyzable or non-paralyzable behaviour.[1] In a non-paralyzable detector, an event happening during the dead time since the previous event is simply lost, so that with an increasing event rate the detector will reach a saturation rate equal to the inverse of the dead time. In a paralyzable detector, an event happening during the dead time since the previous one will not just be missed, but will restart the dead time, so that with increasing rate the detector will reach a saturation point where it will be incapable of recording any event at all. A semi-paralyzable detector exhibits an intermediate behaviour, in which the event arriving during dead time does extend it, but not by the full amount, resulting in a detection rate that decreases when the event rate approaches saturation.
Analysis
It will be assumed that the events are occurring randomly with an average frequency of f. That is, they constitute a Poisson process. The probability that an event will occur in an infinitesimal time interval dt is then f dt. It follows that the probability P(t) that an event will occur at time t to t+dt with no events occurring between t=0 and time t is given by the exponential distribution (Lucke 1974, Meeks 2008):
The expected time between events is then
Non-paralyzable analysis
For the non-paralyzable case, with a dead time of , the probability of measuring an event between and is zero. Otherwise the probabilities of measurement are the same as the event probabilities. The probability of measuring an event at time t with no intervening measurements is then given by an exponential distribution shifted by :
The expected time between measurements is then
In other words, if counts are recorded during a particular time interval and the dead time is known, the actual number of events (N) may be estimated by
If the dead time is not known, a statistical analysis can yield the correct count. For example (Meeks 2008), if are a set of intervals between measurements, then the will have a shifted exponential distribution, but if a fixed value D is subtracted from each interval, with negative values discarded, the distribution will be exponential as long as D is greater than the dead time . For an exponential distribution, the following relationship holds:
where n is any integer. If the above function is estimated for many measured intervals with various values of D subtracted (and for various values of n) it should be found that for values of D above a certain threshold, the above equation will be nearly true, and the count rate derived from these modified intervals will be equal to the true count rate.
Time-To-Count
With a modern microprocessor based ratemeter one technique for measuring field strength with detectors (e.g., Geiger–Müller tubes) with a recovery time is Time-To-Count. In this technique, the detector is armed at the same time a counter is started. When a strike occurs, the counter is stopped. If this happens many times in a certain time period (e.g., two seconds), then the mean time between strikes can be determined, and thus the count rate. Live time, dead time, and total time are thus measured, not estimated. This technique is used quite widely in radiation monitoring systems used in nuclear power generating stations.
See also
- Data acquisition (DAQ)
- Allan variance
- Photomultiplier
- Positron emission tomography
- Class-D amplifier
References
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Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ Template:Cite report
Further reading
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In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
Morris, S.L. and Naftilan, S.A., "Determining Photometric Dead Time by Using Hydrogen Filters", Astron. Astrophys. Suppl. Ser. 107, 71-75, Oct. 1994