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Measurement of system dead time with commercially available NIM modules
NUCLEAR
INSTRUMENTS
AND
METHODS
97 ( / 9 7 I ) 3o9-313;
© NORTH-HOLLAND
PUBLISHING
CO.
MEASUREMENT OF SYSTEM DEAD TIME WITH COMMERCIALLY AVAILABLE NIM MODULES C . B . N E L S O N N E L S O N , J. M. H A R D I N and G . I . COATS
Northeastern Radiological Health Laboratory, 109 tfolton Street, Winchester, Massachusetts 01890, U.S.A. Received 23 August 1971 A procedure to measure the dead time of a counting system with a commercially available N I M type gate and delay generator and a gated scaler is described. A gate method was used to determine
the dead time of a 4~r proportional counter to within 0.1/~sec as a routine part o f the counting procedure; agreement was found when comparison was made with the two source method.
1. Introduction
records the n u m b e r o f events during the period t,. In a counting period o f length T, the n u m b e r o f counts in this scaler is called C. A second scaler counts the number o f gate pulses, G. In effect the gate sorts all pulses into one o f two bins so that C + G = No, the observed n u m b e r o f discriminator output pulses. The rate or counts per unit time is designated as c + g = no, where c = C / T , 9 = G / T , and n o = No/T. The dead time corrected count rate is:
Several systems have been described to measure and even automatically correct for dead time losses 1-4) but all require specialized equipment. Using the following system, the dead time can be measured with a standard N I M type gate and delay generator and a gated scaler as shown in fig. 1. The gate and delay generator is used to gate on a scaler for a period tg (approximately 20/~sec for proportional counters). The scaler then N.B. The mention of commercial products, their source, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health, Education, and Welfare, Public Health Service.
n = n 0 / ( 1 - n o td),
where td is the system dead time up to the discriminator. This model assumes that the dead time is non-extending, i.e., that a detector pulse occurring during the dead
_[ --[
EVENT SCALER "No "
SINGLE CHANNEL
ANALYZER
_l
LA v I
GATED SCALER "C
"
(GATE INPUT)
AMPLIFIER
GATE AND DELAY GENERATOR DETECTOR
GATE SCALER "G"
Fig. 1. Block diagram o f electronics.
309
(1)
310
c . B . NELSON et al.
time of a previous pulse does not extend the dead time. In addition, it is assumed that the pulse separations can be considered Poisson distributed. Since the dead time for any individual pulse is dependent on pulse height, td is actually the mean of a distribution. In standardization counting, the dead time correction is usually less than a few percent so that the first two assumptions are reasonable if not exact. Since many pulses are counted, the concept of a mean dead time is also reasonable. At the output of the gate generator, the true count rate is: n = g/(1-g
tg),
(2)
where tg is the gate width. The gate is also assumed to be non-extending and to be longer than any value of the dead time distribution. The count rate given by eq. (2) is just that obtained by substituting a known time t, for the system dead time where tg > t d. Combining eqs. (1) and (2) and solving for td, we get t o = tg-- (n o -- g ) / ( n o g), t a = t g - - C / ( n o g ).
(3)
Thus, by knowing the gate width and two of the three quantities; G, N o, and C, one can obtain the dead time during the actual measurement of a sample. This procedure has the advantage over the artificial dead time method in that the system dead time is directly measured. Any change in system performance affecting the dead time will be detected. In addition, once the system dead time has been measured, the gate and delay generator and the additional scalers are not a necessary part of the system and can be used for other purposes.
then tg --
cd
(5)
nogd
3. Overlap correction
The above models are not entirely accurate because dead time from secondary C pulses can, by overlap, extend in time past the gate pulse and thereby subtract from the time available for gate pulses. In the delayed gate case, the overlap is symmetrical at the start and end of the gate and so does not change the effective gate width. In the prompt gate case, the dead time associated with the gate pulse lies completely within the gate but those C pulses occurring within a time td before the end of the gate will only reduce the live time of the gate by that portion of the dead time which lies within the gate; the remainder of the dead time which may be outside the gate reduces the time available for counting gate pulses. Assuming an average overlap of the ½ td, and that C pulses are uniformly distributed in the interval between the end of the gate pulse dead time and end of the gate pulse, the time available for counting C pulses will be: Tc = G(tg - td) - C It d - ½ td • td/(tg -- td)],
which in terms of count rate is c=ng(tg--td)--nctd+nc[½ta'td/(tg--td)
The t~ may be measured directly (with a calibrated oscilloscope) or indirectly by delaying the gate beyond the longest dead time interval and observing the count rate in the C scaler. The total live time for the C scaler where Gd is the number of delayed gates is: Tc = Gd t g - C t d,
(7)
] .
Since n = n o / ( 1 - n o td), C-- n o ¢ t d = n Og (tg -- td) -- no c t d + ½ n o c t d • td/(tg -- td). Collecting terms and solving for t o w e have Clg--Ct d = n o g t Z - - 2 n o g t g t d + n o g t d + T n o 2
2. Gate width measurement
(6)
1
c t~ ,
tZ ( no g + ½ no c) + td( c - - 2 no g tg) + tg( no g tg--C) = O,
td2 (1 + ½c / g ) - - t d [2 tg-- c/(n o g)] + tg [tg-- c/(n o g)] = O. Let A = tg-C/n og.
(4) Then
or in rate units:
t~ (1 + ½ c/g ) - ta (tg + A) + tg A = O. C =
ngdtg--nct
d.
Let
Since n no
B=
-
l+n
td '
tg A tg+A
_ tg[tg-c/(nog)] 2tg-c/(nog)
_ tg(n o g tg--C) 2nogtg--C
MEASUREMENT 8.2
I
OF
I
SYSTEM
I
DEAD
311
TIME
I
I
I
0
O
8.0 m
O
O
O O 0
0~-
0
0
7.8 m
7.6 m ~t
2~ 7.4 m
7.
m
O
O
7.1
I
I
I
I
I
I
5
lO
15
20
25
30
t
g, ~Sec
Fig. 2. D e a d t i m e as a f u n c t i o n o f g a t e w i d t h . 9 ° S r - 9 ° Y s o u r c e ; 2/~sec, b i p o l a r p u l s e s h a p i n g . M e a n 4250
I
I
35
I
(1/4 ~Sec)(l/2,~Sec) (l~Sec)
I (2,~Sec)
I
I
7.9844-S.D. -0.060.
i
( s h a p i n g time c o n s t a n t )
(4~Sec)
4240
0 4230
o--
O
4220
--
4210
m
4200 0,0
0
I
I
I
I
I
I
2°0
4.0
6.0
8.0
I0.0
12.0
I 14.0
16.
td, ,~Sec F i g . 3. C o r r e c t e d c o u n t i n g r a t e as a f u n c t i o n o f d e a d t i m e . D e a d t i m e is a d j u s t e d b y c h a n g i n g a m p l i f i e r d e a d t i m e c o n s t a n t . 9 ° S r - 9 ° Y source; bipolar shaping.
312
c.B.
N E L S O N et al.
Then
TABLE 1
t2(1 +½c/g)
tg+A
Dead time by gate and two source method. 90Sr 90y source between a l u m i n u m foil, 2 # s e c bipolar s h a p i n g time-bipolar pulse shaping.
td+B = 0
Finally td =
Run
2 B {1 + [1 -- 4 B (1 + ½c/g)/(tg + A)] +} - 1 .
(8)
For very long gate pulse widths eq. (8) approaches eq. (3). However, if tg is only a few times t d, the error in eq. (3) is appreciable and eq. (8) should be used. 4. Comparison with two source method The gate method of determining dead time was tested using a 4n beta counting system which included a straight wire, gas flow, proportional counter detector, preamplifier (Ortec 109Pc), a linear selectable active filter amplifier (Ortec 440A) and a logic shaper and delay (Canberra Model 1455). The logic shaper was modified to inhibit setting the delay flip flop until the gate was terminated to prevent a pulse during the gate from starting a new gate. An additional gate input was added to the C scaler to allow it to be gated by the timer. For convenience the prompt gate was started 1.00 psec after the rise time of No pulses. This 1 /~sec was then added t o " t g " after " t g " w a s determined by direct measurement (eq. 8). The gate method was compared to the two source method of determining dead time using split sources o f 9 ° S r - 9 ° Y sandwiched between aluminum foil. Each data point normally contained greater than l 0 6 counts on the No scaler. Fig. 2 demonstrates that the dead time provided by the gate method is independent of the width of the gate if the gate is at least 50% greater than the system dead time. Fig. 3 shows that N remains constant as the dead time of the system is altered by changing the shaping time of the amplifier. For shaping constants of the same order of magnitude as the pulse length provided by the detector, an improper mode of operation, N is biased low. The accuracy of the gate procedure was tested by comparison with the two source method. The gate method dead time was calculated from eqs. (5) and (8) while for the two source method z - {1 --[-1 - m , 2 ( m l + r n 2 - m l z - B ) / ( m l mz)J+}/rn12. Results shown in table 1 show agreement within statistical error between the two methods. The gate method has better precision and is less subject to
1 2 3 4 5 6 7
Two source method (#sec)
Gate method (/~sec)
7.93 7.85 8.07 8.25 7.99 (9.14) rejected 8.22
8.071 8.098 7.968 7.939 8.011 7.957 7.999
Average
8.05
8.006
Standard deviation o f average
0.15
0.059
outlying results because the gate method essentially measures the dead time as the difference between the full gate width and the effective gate width in a single counting run. By comparison the two source method requires the accurate determination of small differences between three separate counts and a background count. Small unaccountable changes in the system between counts can cause appreciable errors in the two source method of dead time determination. In addition, the two source method can only provide the correct result for the radionuclide and source configuration actually used for the determination of the system dead time. 5. Effect of pulse height distribution ff a weightless source of 9 ° S r - 9 ° Y is mounted on a thin film (50/tg/cm 2) rather than between aluminum, TABLE 2 Dead time as a function o f pulse height distribution. Shaping: 2/tsec, bipolar, 21/~sec gate pulse; detector: 4 ~ gas proportional counter; source m o u n t i n g : thin film.
Radionuclide
60Co 90Sr-9°Y 204T1
Dead time (/*sec) 7.14 7.34 7.52 7.29 7.71 7.72
M E A S U R E M E N T OF S Y S T E M D E A D TIME
the energy spectrum of pulses seen by the detector will be different because of less interaction of the beta particles with source mounting material. Since the dead time distribution depends on the pulse height distribution, dead time for the two sources will not be the same. Dead time losses for three different radionuclides mounted on thin films are shown in table 2. Small but significant differences are seen between radionuclides and between 9 ° S r - 9 ° Y s o u r c e s mounted on film and between aluminum foil. A 0.5/~sec error in dead time at a count rate of 2000 cps would cause a resulting error in N O of 1 part per 1000. Since the dead time is apparently a mean value of a distribution, the counting system dead time must be determined for each different spectrum of pulses that
313
are presented to the linear amplifier. The gate procedure has the advantage that dead time may be determined easily and quickly and with accuracy and precision for each source as a routine part of a counting procedure. If used with normal standardization counting procedures, the uncertainty due to dead time is considerably less than one part per 1000.
References 1) G. I. Coats, IEEE Trans. Nucl. Sci. NS-13, no. 1 (1966) 301. 2) D. Taylor, S. J. Blatt and I. A. Henderson, Nu¢l. Instr. and Meth. 77 (1970) 177. 3) j. Seda, Nucl. Instr. and Meth. 70 (1969) 121.
a) F. Rau and G. H. Wolf, Nucl. Instr. and Meth. 27 (1963) 321.
INSTRUMENTS
AND
METHODS
97 ( / 9 7 I ) 3o9-313;
© NORTH-HOLLAND
PUBLISHING
CO.
MEASUREMENT OF SYSTEM DEAD TIME WITH COMMERCIALLY AVAILABLE NIM MODULES C . B . N E L S O N N E L S O N , J. M. H A R D I N and G . I . COATS
Northeastern Radiological Health Laboratory, 109 tfolton Street, Winchester, Massachusetts 01890, U.S.A. Received 23 August 1971 A procedure to measure the dead time of a counting system with a commercially available N I M type gate and delay generator and a gated scaler is described. A gate method was used to determine
the dead time of a 4~r proportional counter to within 0.1/~sec as a routine part o f the counting procedure; agreement was found when comparison was made with the two source method.
1. Introduction
records the n u m b e r o f events during the period t,. In a counting period o f length T, the n u m b e r o f counts in this scaler is called C. A second scaler counts the number o f gate pulses, G. In effect the gate sorts all pulses into one o f two bins so that C + G = No, the observed n u m b e r o f discriminator output pulses. The rate or counts per unit time is designated as c + g = no, where c = C / T , 9 = G / T , and n o = No/T. The dead time corrected count rate is:
Several systems have been described to measure and even automatically correct for dead time losses 1-4) but all require specialized equipment. Using the following system, the dead time can be measured with a standard N I M type gate and delay generator and a gated scaler as shown in fig. 1. The gate and delay generator is used to gate on a scaler for a period tg (approximately 20/~sec for proportional counters). The scaler then N.B. The mention of commercial products, their source, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health, Education, and Welfare, Public Health Service.
n = n 0 / ( 1 - n o td),
where td is the system dead time up to the discriminator. This model assumes that the dead time is non-extending, i.e., that a detector pulse occurring during the dead
_[ --[
EVENT SCALER "No "
SINGLE CHANNEL
ANALYZER
_l
LA v I
GATED SCALER "C
"
(GATE INPUT)
AMPLIFIER
GATE AND DELAY GENERATOR DETECTOR
GATE SCALER "G"
Fig. 1. Block diagram o f electronics.
309
(1)
310
c . B . NELSON et al.
time of a previous pulse does not extend the dead time. In addition, it is assumed that the pulse separations can be considered Poisson distributed. Since the dead time for any individual pulse is dependent on pulse height, td is actually the mean of a distribution. In standardization counting, the dead time correction is usually less than a few percent so that the first two assumptions are reasonable if not exact. Since many pulses are counted, the concept of a mean dead time is also reasonable. At the output of the gate generator, the true count rate is: n = g/(1-g
tg),
(2)
where tg is the gate width. The gate is also assumed to be non-extending and to be longer than any value of the dead time distribution. The count rate given by eq. (2) is just that obtained by substituting a known time t, for the system dead time where tg > t d. Combining eqs. (1) and (2) and solving for td, we get t o = tg-- (n o -- g ) / ( n o g), t a = t g - - C / ( n o g ).
(3)
Thus, by knowing the gate width and two of the three quantities; G, N o, and C, one can obtain the dead time during the actual measurement of a sample. This procedure has the advantage over the artificial dead time method in that the system dead time is directly measured. Any change in system performance affecting the dead time will be detected. In addition, once the system dead time has been measured, the gate and delay generator and the additional scalers are not a necessary part of the system and can be used for other purposes.
then tg --
cd
(5)
nogd
3. Overlap correction
The above models are not entirely accurate because dead time from secondary C pulses can, by overlap, extend in time past the gate pulse and thereby subtract from the time available for gate pulses. In the delayed gate case, the overlap is symmetrical at the start and end of the gate and so does not change the effective gate width. In the prompt gate case, the dead time associated with the gate pulse lies completely within the gate but those C pulses occurring within a time td before the end of the gate will only reduce the live time of the gate by that portion of the dead time which lies within the gate; the remainder of the dead time which may be outside the gate reduces the time available for counting gate pulses. Assuming an average overlap of the ½ td, and that C pulses are uniformly distributed in the interval between the end of the gate pulse dead time and end of the gate pulse, the time available for counting C pulses will be: Tc = G(tg - td) - C It d - ½ td • td/(tg -- td)],
which in terms of count rate is c=ng(tg--td)--nctd+nc[½ta'td/(tg--td)
The t~ may be measured directly (with a calibrated oscilloscope) or indirectly by delaying the gate beyond the longest dead time interval and observing the count rate in the C scaler. The total live time for the C scaler where Gd is the number of delayed gates is: Tc = Gd t g - C t d,
(7)
] .
Since n = n o / ( 1 - n o td), C-- n o ¢ t d = n Og (tg -- td) -- no c t d + ½ n o c t d • td/(tg -- td). Collecting terms and solving for t o w e have Clg--Ct d = n o g t Z - - 2 n o g t g t d + n o g t d + T n o 2
2. Gate width measurement
(6)
1
c t~ ,
tZ ( no g + ½ no c) + td( c - - 2 no g tg) + tg( no g tg--C) = O,
td2 (1 + ½c / g ) - - t d [2 tg-- c/(n o g)] + tg [tg-- c/(n o g)] = O. Let A = tg-C/n og.
(4) Then
or in rate units:
t~ (1 + ½ c/g ) - ta (tg + A) + tg A = O. C =
ngdtg--nct
d.
Let
Since n no
B=
-
l+n
td '
tg A tg+A
_ tg[tg-c/(nog)] 2tg-c/(nog)
_ tg(n o g tg--C) 2nogtg--C
MEASUREMENT 8.2
I
OF
I
SYSTEM
I
DEAD
311
TIME
I
I
I
0
O
8.0 m
O
O
O O 0
0~-
0
0
7.8 m
7.6 m ~t
2~ 7.4 m
7.
m
O
O
7.1
I
I
I
I
I
I
5
lO
15
20
25
30
t
g, ~Sec
Fig. 2. D e a d t i m e as a f u n c t i o n o f g a t e w i d t h . 9 ° S r - 9 ° Y s o u r c e ; 2/~sec, b i p o l a r p u l s e s h a p i n g . M e a n 4250
I
I
35
I
(1/4 ~Sec)(l/2,~Sec) (l~Sec)
I (2,~Sec)
I
I
7.9844-S.D. -0.060.
i
( s h a p i n g time c o n s t a n t )
(4~Sec)
4240
0 4230
o--
O
4220
--
4210
m
4200 0,0
0
I
I
I
I
I
I
2°0
4.0
6.0
8.0
I0.0
12.0
I 14.0
16.
td, ,~Sec F i g . 3. C o r r e c t e d c o u n t i n g r a t e as a f u n c t i o n o f d e a d t i m e . D e a d t i m e is a d j u s t e d b y c h a n g i n g a m p l i f i e r d e a d t i m e c o n s t a n t . 9 ° S r - 9 ° Y source; bipolar shaping.
312
c.B.
N E L S O N et al.
Then
TABLE 1
t2(1 +½c/g)
tg+A
Dead time by gate and two source method. 90Sr 90y source between a l u m i n u m foil, 2 # s e c bipolar s h a p i n g time-bipolar pulse shaping.
td+B = 0
Finally td =
Run
2 B {1 + [1 -- 4 B (1 + ½c/g)/(tg + A)] +} - 1 .
(8)
For very long gate pulse widths eq. (8) approaches eq. (3). However, if tg is only a few times t d, the error in eq. (3) is appreciable and eq. (8) should be used. 4. Comparison with two source method The gate method of determining dead time was tested using a 4n beta counting system which included a straight wire, gas flow, proportional counter detector, preamplifier (Ortec 109Pc), a linear selectable active filter amplifier (Ortec 440A) and a logic shaper and delay (Canberra Model 1455). The logic shaper was modified to inhibit setting the delay flip flop until the gate was terminated to prevent a pulse during the gate from starting a new gate. An additional gate input was added to the C scaler to allow it to be gated by the timer. For convenience the prompt gate was started 1.00 psec after the rise time of No pulses. This 1 /~sec was then added t o " t g " after " t g " w a s determined by direct measurement (eq. 8). The gate method was compared to the two source method of determining dead time using split sources o f 9 ° S r - 9 ° Y sandwiched between aluminum foil. Each data point normally contained greater than l 0 6 counts on the No scaler. Fig. 2 demonstrates that the dead time provided by the gate method is independent of the width of the gate if the gate is at least 50% greater than the system dead time. Fig. 3 shows that N remains constant as the dead time of the system is altered by changing the shaping time of the amplifier. For shaping constants of the same order of magnitude as the pulse length provided by the detector, an improper mode of operation, N is biased low. The accuracy of the gate procedure was tested by comparison with the two source method. The gate method dead time was calculated from eqs. (5) and (8) while for the two source method z - {1 --[-1 - m , 2 ( m l + r n 2 - m l z - B ) / ( m l mz)J+}/rn12. Results shown in table 1 show agreement within statistical error between the two methods. The gate method has better precision and is less subject to
1 2 3 4 5 6 7
Two source method (#sec)
Gate method (/~sec)
7.93 7.85 8.07 8.25 7.99 (9.14) rejected 8.22
8.071 8.098 7.968 7.939 8.011 7.957 7.999
Average
8.05
8.006
Standard deviation o f average
0.15
0.059
outlying results because the gate method essentially measures the dead time as the difference between the full gate width and the effective gate width in a single counting run. By comparison the two source method requires the accurate determination of small differences between three separate counts and a background count. Small unaccountable changes in the system between counts can cause appreciable errors in the two source method of dead time determination. In addition, the two source method can only provide the correct result for the radionuclide and source configuration actually used for the determination of the system dead time. 5. Effect of pulse height distribution ff a weightless source of 9 ° S r - 9 ° Y is mounted on a thin film (50/tg/cm 2) rather than between aluminum, TABLE 2 Dead time as a function o f pulse height distribution. Shaping: 2/tsec, bipolar, 21/~sec gate pulse; detector: 4 ~ gas proportional counter; source m o u n t i n g : thin film.
Radionuclide
60Co 90Sr-9°Y 204T1
Dead time (/*sec) 7.14 7.34 7.52 7.29 7.71 7.72
M E A S U R E M E N T OF S Y S T E M D E A D TIME
the energy spectrum of pulses seen by the detector will be different because of less interaction of the beta particles with source mounting material. Since the dead time distribution depends on the pulse height distribution, dead time for the two sources will not be the same. Dead time losses for three different radionuclides mounted on thin films are shown in table 2. Small but significant differences are seen between radionuclides and between 9 ° S r - 9 ° Y s o u r c e s mounted on film and between aluminum foil. A 0.5/~sec error in dead time at a count rate of 2000 cps would cause a resulting error in N O of 1 part per 1000. Since the dead time is apparently a mean value of a distribution, the counting system dead time must be determined for each different spectrum of pulses that
313
are presented to the linear amplifier. The gate procedure has the advantage that dead time may be determined easily and quickly and with accuracy and precision for each source as a routine part of a counting procedure. If used with normal standardization counting procedures, the uncertainty due to dead time is considerably less than one part per 1000.
References 1) G. I. Coats, IEEE Trans. Nucl. Sci. NS-13, no. 1 (1966) 301. 2) D. Taylor, S. J. Blatt and I. A. Henderson, Nu¢l. Instr. and Meth. 77 (1970) 177. 3) j. Seda, Nucl. Instr. and Meth. 70 (1969) 121.
a) F. Rau and G. H. Wolf, Nucl. Instr. and Meth. 27 (1963) 321.