1094:) 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
109:
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.
74:
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.
41:
is the time after each event during which the system is not able to record another event. 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
108:
behaviour. In a non-paralyzable detector, an event happening during the dead time 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 will not just be
84:
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
77:
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
73:
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,
651:
781:
1057:
903:
307:
222:
463:
490:
678:
498:
81:
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.
689:
387:
988:
960:
933:
811:
411:
335:
1078:
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.
361:
831:
54:
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 ion drift time in a
1316:
Morris, S.L. and
Naftilan, S.A., "Determining Photometric Dead Time by Using Hydrogen Filters", Astron. Astrophys. Suppl. Ser. 107, 71-75, Oct. 1994
996:
1175:
Weier, H.; et al. (2011). "Quantum eavesdropping without interception: an attack exploiting the dead time of single-photon detectors".
389:
is zero. Otherwise the probabilities of measurement are the same as the event probabilities. The probability of measuring an event at time
843:
233:
1159:
1239:
1123:
63:
55:
20:
1091:
966:
is subtracted from each interval, with negative values discarded, the distribution will be exponential as long as
908:
If the dead time is not known, a statistical analysis can yield the correct count. For example, (Meeks 2008), if
1328:
154:
1221:
42:
lowering the detection efficiency, dead times can have other effects, such as creating possible exploits in
163:
1241:
Dead time and count loss determination for radiation detection systems in high count rate applications
1066:
is any integer. If the above function is estimated for many measured intervals with various values of
1296:
1267:
1194:
1095:
646:{\displaystyle P_{m}(t)dt={\frac {fe^{-ft}dt}{\int _{\tau }^{\infty }fe^{-ft}dt}}=fe^{-f(t-\tau )}dt}
43:
419:
468:
656:
88:
From the total time a detection system is running, the dead time must be subtracted to obtain the
69:
The intrinsic dead time of a detector is often due to its physical characteristics; for example a
1184:
58:), of the analog front end (for example the shaping time of a spectroscopy amplifier) and of the
776:{\displaystyle \langle t_{m}\rangle =\int _{\tau }^{\infty }tP_{m}(t)dt=\langle t\rangle +\tau }
1087:
89:
1155:
1128:
34:
1258:
Lucke, Robert L. (June 1976). "Counting
Statistics for Nonnegligible Dead Time Corrections".
366:
1304:
1275:
1202:
1107:
59:
27:
973:
938:
911:
789:
396:
320:
1118:
122:
31:
393:
with no intervening measurements is then given by an exponential distribution shifted by
340:
1300:
1271:
1206:
1198:
1113:
816:
117:
It will be assumed that the events are occurring randomly with an average frequency of
1322:
70:
1287:
Meeks, Craig; Siegel, P.B. (June 2008). "Dead time correction via the time series".
125:. The probability that an event will occur in an infinitesimal time interval
1052:{\displaystyle {\frac {\langle t^{n}\rangle }{\langle t\rangle ^{n}}}=n!}
1308:
1279:
990:. For an exponential distribution, the following relationship holds:
962:
will have a shifted exponential distribution, but if a fixed value
898:{\displaystyle N\approx {\frac {N_{m}}{1-N_{m}{\frac {\tau }{T}}}}}
1189:
1090:
one technique for measuring field strength with detectors (e.g.,
302:{\displaystyle \langle t\rangle =\int _{0}^{\infty }tP(t)dt=1/f}
16:
Time after an event when a detector can't record another event
100:
A detector, or detection system, can be characterized by a
85:
and multi-level trigger logic to reduce the readout rates.
26:
For detection systems that record discrete events, such as
833:
and the dead time is known, the actual number of events (
1152:
Techniques for
Nuclear and Particle Physics Experiments
935:
are a set of intervals between measurements, then the
813:
counts are recorded during a particular time interval
999:
976:
941:
914:
846:
819:
792:
692:
659:
501:
471:
422:
399:
369:
343:
323:
236:
166:
1098:systems used in nuclear power generating stations.
1051:
982:
954:
927:
897:
825:
805:
775:
672:
645:
484:
457:
405:
381:
355:
329:
317:For the non-paralyzable case, with a dead time of
301:
216:
337:, the probability of measuring an event between
683:The expected time between measurements is then
78:compromise between event rate and resolution.
1227:(ALICE Internal Note/DAQ ALICE-INT-2010-001).
8:
1028:
1021:
1016:
1003:
764:
758:
706:
693:
243:
237:
1220:Carena, F.; et al. (December 2010).
1188:
1031:
1010:
1000:
998:
975:
946:
940:
919:
913:
882:
876:
859:
853:
845:
818:
797:
791:
734:
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342:
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291:
258:
253:
235:
227:The expected time between events is then
213:
195:
165:
96:Paralyzable and non-paralyzable behaviour
1074:) it should be found that for values of
1139:
1070:subtracted (and for various values of
1145:
1143:
7:
66:and the readout and storage times).
1086:With a modern microprocessor based
217:{\displaystyle P(t)dt=fe^{-ft}dt\,}
722:
570:
259:
133:. It follows that the probability
14:
145:with no events occurring between
137:that an event will occur at time
1154:. Springer. pp. 122–127.
970:is greater than the dead time
746:
740:
632:
620:
518:
512:
458:{\displaystyle P_{m}(t)dt=0\,}
439:
433:
276:
270:
176:
170:
1:
1207:10.1088/1367-2630/13/7/073024
485:{\displaystyle t\leq \tau \,}
121:. That is, they constitute a
1124:Positron emission tomography
673:{\displaystyle t>\tau \,}
64:analog-to-digital converters
62:(the conversion time of the
1244:(PhD Thesis). p. 2148.
56:gaseous ionization detector
1345:
157:(Lucke 1974, Meeks 2008):
21:Dead Time (disambiguation)
18:
1222:ALICE DAQ and ECS Manual
313:Non-paralyzable analysis
155:exponential distribution
837:) may be estimated by
382:{\displaystyle t=\tau }
153: is given by the
1177:New Journal of Physics
1053:
984:
956:
929:
899:
827:
807:
777:
674:
647:
486:
459:
407:
383:
357:
331:
303:
218:
1054:
985:
983:{\displaystyle \tau }
957:
955:{\displaystyle t_{i}}
930:
928:{\displaystyle t_{i}}
900:
828:
808:
806:{\displaystyle N_{m}}
778:
675:
648:
487:
460:
408:
406:{\displaystyle \tau }
384:
358:
332:
330:{\displaystyle \tau }
304:
219:
1238:Patil, Amol (2010).
1096:radiation monitoring
997:
974:
939:
912:
844:
817:
790:
690:
657:
499:
469:
420:
397:
367:
341:
321:
234:
164:
44:quantum cryptography
19:For other uses, see
1301:2008AmJPh..76..589M
1272:1976RScI...47..766L
1199:2011NJPh...13g3024W
1092:Geiger–Müller tubes
786:In other words, if
726:
574:
356:{\displaystyle t=0}
263:
1150:W. R. Leo (1994).
1049:
980:
952:
925:
895:
823:
803:
773:
712:
670:
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560:
482:
455:
403:
379:
353:
327:
299:
249:
214:
1309:10.1119/1.2870432
1280:10.1063/1.1134733
1260:Rev. Sci. Instrum
1129:Class-D amplifier
1038:
893:
890:
826:{\displaystyle T}
601:
1336:
1312:
1283:
1246:
1245:
1235:
1229:
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1226:
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1108:Data acquisition
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60:data acquisition
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1329:Nuclear physics
1319:
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1286:
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1252:Further reading
1249:
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1219:
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1119:Photomultiplier
1104:
1084:
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1020:
1006:
1002:
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994:
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395:
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365:
364:
339:
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319:
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232:
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191:
162:
161:
123:Poisson process
115:
106:non-paralyzable
98:
52:
24:
17:
12:
11:
5:
1342:
1340:
1332:
1331:
1321:
1320:
1314:
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1212:
1167:
1160:
1138:
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1133:
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1126:
1121:
1116:
1114:Allan variance
1111:
1103:
1100:
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1200:
1196:
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1186:
1183:(7): 073024.
1182:
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1171:
1168:
1163:
1161:3-540-57280-5
1157:
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1120:
1117:
1115:
1112:
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1101:
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1097:
1093:
1089:
1082:Time-To-Count
1081:
1079:
1077:
1073:
1069:
1065:
1046:
1043:
1040:
1032:
1024:
1011:
1007:
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947:
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916:
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72:
71:spark chamber
67:
65:
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57:
49:
47:
45:
40:
36:
33:
29:
22:
1315:
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1288:
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1215:
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1151:
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682:
390:
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150:
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118:
116:
105:
101:
99:
87:
83:
80:
76:
68:
53:
38:
25:
1289:Am. J. Phys
102:paralyzable
1295:(6): 589.
1266:(6): 766.
1135:References
141: to
1190:1101.5289
1088:ratemeter
1029:⟩
1022:⟨
1017:⟩
1004:⟨
978:τ
885:τ
870:−
851:≈
771:τ
765:⟩
759:⟨
723:∞
718:τ
714:∫
707:⟩
694:⟨
667:τ
630:τ
627:−
615:−
584:−
571:∞
566:τ
562:∫
542:−
479:τ
476:≤
401:τ
377:τ
325:τ
260:∞
251:∫
244:⟩
238:⟨
197:−
149:and time
90:live time
39:dead time
35:detectors
1323:Category
1102:See also
129:is then
113:Analysis
50:Overview
28:particle
1297:Bibcode
1268:Bibcode
1195:Bibcode
32:nuclear
1158:
1062:where
37:, the
1225:(PDF)
1185:arXiv
1110:(DAQ)
1156:ISBN
664:>
653:for
465:for
363:and
143:t+dt
135:P(t)
131:f dt
30:and
1305:doi
1276:doi
1203:doi
147:t=0
104:or
1325::
1303:.
1293:76
1291:.
1274:.
1264:47
1262:.
1201:.
1193:.
1181:13
1179:.
1142:^
413::
127:dt
92:.
46:.
1311:.
1307::
1299::
1282:.
1278::
1270::
1209:.
1205::
1197::
1187::
1164:.
1076:D
1072:n
1068:D
1064:n
1047:!
1044:n
1041:=
1033:n
1025:t
1012:n
1008:t
968:D
964:D
948:i
944:t
921:i
917:t
888:T
878:m
874:N
867:1
861:m
857:N
848:N
835:N
821:T
799:m
795:N
768:+
762:t
756:=
753:t
750:d
747:)
744:t
741:(
736:m
732:P
728:t
710:=
702:m
698:t
661:t
641:t
638:d
633:)
624:t
621:(
618:f
611:e
607:f
604:=
598:t
595:d
590:t
587:f
580:e
576:f
556:t
553:d
548:t
545:f
538:e
534:f
528:=
525:t
522:d
519:)
516:t
513:(
508:m
504:P
473:t
452:0
449:=
446:t
443:d
440:)
437:t
434:(
429:m
425:P
391:t
374:=
371:t
351:0
348:=
345:t
297:f
293:/
289:1
286:=
283:t
280:d
277:)
274:t
271:(
268:P
265:t
255:0
247:=
241:t
211:t
208:d
203:t
200:f
193:e
189:f
186:=
183:t
180:d
177:)
174:t
171:(
168:P
151:t
139:t
119:f
23:.
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