- Email: [email protected]
A method of dead time measurement
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 551 (2005) 352–355 www.elsevier.com/locate/nima
A method of dead time measurement Chul-Young Yia,, Keeju Jeongb, Jang-Jin Ohc a
Ionizing Radiation Group, Korea Research Institute of Standards and Science, P.O. Box 102, Yuseong, Daejon 305-600, Korea b Department of Physics Education, Kongju National University, Sinkwan-dong 182, Kongju, Chungnam 314-701, Korea c Department of Radiation Protection, Radiation Safety Center, Korea Institute of Nuclear Safety, P.O. Box 114, Yuseong, Daejon 305600, Korea Received 10 December 2004; received in revised form 30 March 2005; accepted 8 June 2005 Available online 13 July 2005
Abstract A practical method for the dead time measurement of a counting system is proposed. The method is based on the irradiation of a counting system in the reference photon field for the calibration of dosimeters or dose rate meters. Using the method, we measured the dead time of a GM counting system. r 2005 Elsevier B.V. All rights reserved. PACS: 07.85.m; 29.40.n Keywords: Radiation detector; Radiation counter; GM counter; Dead time; Dead time measurement
1. Introduction In most detection systems of radiation, there is a certain amount of time required to separate two events in order that they be recorded as two different events, which is called the resolution time or dead time of a counting system. The dead time of a counting system affects inevitably the counting statistics. Even though two or more events occur, they are recorded as a single event if they come in the time interval shorter than the dead Corresponding author. Tel.: +82 42 868 5370;
fax: +82 42 868 5671. E-mail address: [email protected] (C.-Y. Yi).
time and, resultantly, the counting rate is measured lower than the true rate. Because of the random nature of radioactive decay, there is always some probability that a true event will be lost, since it may follow too quickly the preceding event. The dead time correction is one of the essential elements in the accurate counting measurement of radiation. In order to make dead time corrections, prior knowledge of the dead time is required. Sometimes this dead time can be associated with a known limiting property of the counting system (e.g., a fixed resolving time or pulse shaping time of an electronic circuit). More often, the dead time will not be known or may vary with operating
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.06.053
ARTICLE IN PRESS C.-Y. Yi et al. / Nuclear Instruments and Methods in Physics Research A 551 (2005) 352–355
conditions and must therefore be measured directly. The common example of dead time measurement is the decaying source method [1,2]. The method is practical when a radioisotope with a short half-life is available. The departure of the observed counting rate from the known exponential decay of the source can be used to determine the dead time. The short-lived radioisotope is obtainable from neutron irradiation facilities but only a few laboratories can get a timely access to neutron irradiation facilities. Vinagre and Conde [3] suggest a method for the measurement of effective dead time of a counting system, which was based on the artificial piling-up of the detector pulses with electronic pulses delayed by a specific time interval. The method requires extra instrumentation and the effect of the extra instrumentation on the dead time measurements should be analyzed. In the present paper we have proposed an efficient method for the dead time measurement of a counting system. The method is based on the irradiation of a counting system in the reference radiation field for the calibration of dosimeters or dose rate meters. The variation of counting rate per unit dose was used to evaluate the dead time.
2. Method Dead time corrections based on paralyzable and non-paralyzable models have been studied extensively and well summarized in Refs. [4–8]. In the non-paralyzable model, the relationship between the true and observed counting rates is given by n¼
m 1 mt
(1)
where n is the true counting rate, m is the observed counting rate and t is the dead time. The true rate of rays passing through a point in the reference radiation field for calibrating dose rate meters is proportional to the dose rate at the point: n ¼ kD
(2)
353
where n is the true rate, k is the proportionality constant and D is the dose rate at the point. Substituting Eq. (2) into Eq. (1), we have m ¼ k kmt. (3) D If we take the abscissa as m and the ordinate as m=D, then Eq. (3) is a straight line having a slope of kt and the intercept of k on the ordinate axis. In the paralyzable model, the relationship between the true and observed counting rates is given by m ¼ n expðntÞ.
(4)
Again, inserting Eq. (2) into Eq. (4), we have the equation m ln ¼ ln k kDt. (5) D Taking the abscissa as D and the ordinate as ln ðm=DÞ, we have another straight line. This time, the slope is also kt whereas the intercept is ln k. The dead time can be deduced from the slope and the intercept on the ordinate axis.
3. Result and discussion We applied the present method to determine the dead time of a GM counting system, which has been developed as a prototype alarm dose rate meter (ADR). We have not been involved in the development of the prototype ADR and the detailed information on the electronics of the prototype ADR has not been given. It was stated that the bias voltage of the GM tube was 550 V. The signal processing RC networks were designed as recommended by the manufacturer of the GM tube. Pulses generated in the GM tube were compared with a reference voltage by a comparator. A square output pulse was generated from the comparator when the height of the GM tube pulse was greater than the reference voltage. The square pulse was counted in the counting module. The prototype ADR was originally designed to convert the counting rate into the dose rate, but the specimen we have tested was programmed to transmit the counting rates to a PC via the serial RS-232 port.
ARTICLE IN PRESS C.-Y. Yi et al. / Nuclear Instruments and Methods in Physics Research A 551 (2005) 352–355
70
4.3 4.2
intercept : 4.1538 4.1
τ = 29.7 µs
4.0 3.9
slope : - 1.8894 x 10-3 3.8
(r2 = 0.994)
3.7 0
50
100
150
200
-1
Dose rate (mSv h ) Fig. 2. Logarithm of the counting rate per unit dose rate of the prototype ADR as a function of the dose rate.
The dead time can be estimated at 34.8 ms from Eq. (3) if we presume the dead time follows the nonparalyzable model. In order to analyze further, we took the logarithm of the data in Fig. 1 and presented the values in Fig. 2 as a function of the dose rate. The correlation coefficient of the straight fit line was 0.994. The dead time was deduced by Eq. (5) to be 29.7 ms with an assumption that the prototype ADR is paralyzable, differs by 17.2% from the dead time of the non-paralyzable case. However, the true counting rates estimated by Eqs. (1) and (4) with their corresponding dead times agreed within 71.5%. Along with the relative difference, the true counting rates estimated are given in Fig. 3. The agreement might come from the fact that the straight lines fit to data well in both cases. In the paralyzable case, n was found numerically from Eq. (4) using the bisection method [11].
intercept : 64.1092 (cps mSv-1 h)
Counting rate per unit dose rate
The prototype ADR was placed on the 30 30 15 cm PMMA slab phantom in the Cs137 reference radiation field and was irradiated in the dose rate range from 1 to 200 mSv h1. We used three irradiators with nominal activities of 185 GBq, 740 GBq and 4.8 TBq, respectively. About a 6-m-long rail was stretched out in front of each irradiator and a trolley was moved along the rail. The ADR and PMMA phantom were mounted on the trolley and aligned at the beam center. The air kerma rates for the three irradiators were determined for the movable range of the trolley 0.5–5.5 m from the sources with the expanded uncertainties (at 95% confidence level) less than 1.5%. The dose rate was the personal dose equivalent rate at 10 mm depth in soft tissue, which was defined by ICRU [9]. The factor for converting the air kerma rate to the personal dose equivalent rate at 10 mm depth in soft tissue is 1.21 Sv Gy1 [10]. In Fig. 1, the counting rate per unit dose rate of the prototype ADR is given as a function of counting rate per second (cps). The maximum counting rate recorded was around 9000 cps. The standard deviation of the measured counting rate ranged from 8% at 2 mSv h1 to 0.3% at 194 mSv h1. The background counting rate measured by the prototype ADR was less than one count per minute. As shown in the figure, the data were well fit to a straight line with the correlation coefficient 0.995. The commercially available software TableCurveTM 2D version 4.0 was used to fit.
ln (m/D)
354
60
τ = 34.8 µs
50
4. Concluding remarks
slope : - 2.2338 x 10-3 (r2 = 0.995)
40 0
2 4 6 8 Counting rate (x 1000 cps)
10
Fig. 1. Counting rate per unit dose rate of the prototype ADR as a function of the counting rate.
In the present paper, we have proposed a simple and efficient method for the dead time measurement of a counting system. The method is based on the irradiation of a counting system in the reference radiation field with varying dose rates. The dead time can be deduced from the slope and the intercept of the straight line fit to the scaled counting rates as given in Eqs. (3) and (5). Using
ARTICLE IN PRESS
Counting rate (x 1000 cps)
C.-Y. Yi et al. / Nuclear Instruments and Methods in Physics Research A 551 (2005) 352–355
Relative difference (%)
Acknowledgments
14 true counting rate (non-paralizable)
12
true counting rate (paralizable)
10
The present study has been supported in part by the mid- and long-term research fund for the development of nuclear energy granted by the Ministry of Science and Technology. The authors would like to express their gratitude to the referee for making valuable corrections and suggestions.
observed counting rate
8 6 4 2 0 0
(a)
50
100
150
200
2
References
1 0 -1 -2 0
(b)
355
50
100
150
200
Dose rate (mSv h-1)
Fig. 3. Comparison of the true rates with the observed counting rates (a) and difference of the true counting rates estimated using the paralyzable model from those of the nonparalyzable model (b). The difference is presented in percentage relative to the true counting rates of the non-paralyzable model.
the reference Cs-137 fields with dose rate range up to 200 mSv h1, the dead time of a prototype GM counter was measured by the proposed method.
[1] R.P. Gardner, L. Liu, Appl. Radiat. Isot. 48 (1997) 1605. [2] S.H. Lee, R.P. Gardner, Appl. Radiat. Isot. 53 (2000) 731. [3] F.L.R. Vinagre, C.A.N. Conde, Nucl. Instr. and Meth. A 462 (2001) 555. [4] R.D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955. [5] G.F. Knoll, Radiation Detection and Measurement, third ed., Wiley, New York, 2000. [6] J.W. Mueller, Nucl. Instr. and Meth. 112 (1973) 47. [7] J.W. Mueller, Nucl. Instr. and Meth. 117 (1974) 401. [8] J. Libert, Nucl. Instr. and Meth. 151 (1978) 555. [9] ICRU, ICRU Rep. 51, Bethesda, MD, 1993. [10] ISO, ISO 4037-3, Geneva, 1999. [11] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran, second ed., Cambridge University, New York, 1992.
Nuclear Instruments and Methods in Physics Research A 551 (2005) 352–355 www.elsevier.com/locate/nima
A method of dead time measurement Chul-Young Yia,, Keeju Jeongb, Jang-Jin Ohc a
Ionizing Radiation Group, Korea Research Institute of Standards and Science, P.O. Box 102, Yuseong, Daejon 305-600, Korea b Department of Physics Education, Kongju National University, Sinkwan-dong 182, Kongju, Chungnam 314-701, Korea c Department of Radiation Protection, Radiation Safety Center, Korea Institute of Nuclear Safety, P.O. Box 114, Yuseong, Daejon 305600, Korea Received 10 December 2004; received in revised form 30 March 2005; accepted 8 June 2005 Available online 13 July 2005
Abstract A practical method for the dead time measurement of a counting system is proposed. The method is based on the irradiation of a counting system in the reference photon field for the calibration of dosimeters or dose rate meters. Using the method, we measured the dead time of a GM counting system. r 2005 Elsevier B.V. All rights reserved. PACS: 07.85.m; 29.40.n Keywords: Radiation detector; Radiation counter; GM counter; Dead time; Dead time measurement
1. Introduction In most detection systems of radiation, there is a certain amount of time required to separate two events in order that they be recorded as two different events, which is called the resolution time or dead time of a counting system. The dead time of a counting system affects inevitably the counting statistics. Even though two or more events occur, they are recorded as a single event if they come in the time interval shorter than the dead Corresponding author. Tel.: +82 42 868 5370;
fax: +82 42 868 5671. E-mail address: [email protected] (C.-Y. Yi).
time and, resultantly, the counting rate is measured lower than the true rate. Because of the random nature of radioactive decay, there is always some probability that a true event will be lost, since it may follow too quickly the preceding event. The dead time correction is one of the essential elements in the accurate counting measurement of radiation. In order to make dead time corrections, prior knowledge of the dead time is required. Sometimes this dead time can be associated with a known limiting property of the counting system (e.g., a fixed resolving time or pulse shaping time of an electronic circuit). More often, the dead time will not be known or may vary with operating
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.06.053
ARTICLE IN PRESS C.-Y. Yi et al. / Nuclear Instruments and Methods in Physics Research A 551 (2005) 352–355
conditions and must therefore be measured directly. The common example of dead time measurement is the decaying source method [1,2]. The method is practical when a radioisotope with a short half-life is available. The departure of the observed counting rate from the known exponential decay of the source can be used to determine the dead time. The short-lived radioisotope is obtainable from neutron irradiation facilities but only a few laboratories can get a timely access to neutron irradiation facilities. Vinagre and Conde [3] suggest a method for the measurement of effective dead time of a counting system, which was based on the artificial piling-up of the detector pulses with electronic pulses delayed by a specific time interval. The method requires extra instrumentation and the effect of the extra instrumentation on the dead time measurements should be analyzed. In the present paper we have proposed an efficient method for the dead time measurement of a counting system. The method is based on the irradiation of a counting system in the reference radiation field for the calibration of dosimeters or dose rate meters. The variation of counting rate per unit dose was used to evaluate the dead time.
2. Method Dead time corrections based on paralyzable and non-paralyzable models have been studied extensively and well summarized in Refs. [4–8]. In the non-paralyzable model, the relationship between the true and observed counting rates is given by n¼
m 1 mt
(1)
where n is the true counting rate, m is the observed counting rate and t is the dead time. The true rate of rays passing through a point in the reference radiation field for calibrating dose rate meters is proportional to the dose rate at the point: n ¼ kD
(2)
353
where n is the true rate, k is the proportionality constant and D is the dose rate at the point. Substituting Eq. (2) into Eq. (1), we have m ¼ k kmt. (3) D If we take the abscissa as m and the ordinate as m=D, then Eq. (3) is a straight line having a slope of kt and the intercept of k on the ordinate axis. In the paralyzable model, the relationship between the true and observed counting rates is given by m ¼ n expðntÞ.
(4)
Again, inserting Eq. (2) into Eq. (4), we have the equation m ln ¼ ln k kDt. (5) D Taking the abscissa as D and the ordinate as ln ðm=DÞ, we have another straight line. This time, the slope is also kt whereas the intercept is ln k. The dead time can be deduced from the slope and the intercept on the ordinate axis.
3. Result and discussion We applied the present method to determine the dead time of a GM counting system, which has been developed as a prototype alarm dose rate meter (ADR). We have not been involved in the development of the prototype ADR and the detailed information on the electronics of the prototype ADR has not been given. It was stated that the bias voltage of the GM tube was 550 V. The signal processing RC networks were designed as recommended by the manufacturer of the GM tube. Pulses generated in the GM tube were compared with a reference voltage by a comparator. A square output pulse was generated from the comparator when the height of the GM tube pulse was greater than the reference voltage. The square pulse was counted in the counting module. The prototype ADR was originally designed to convert the counting rate into the dose rate, but the specimen we have tested was programmed to transmit the counting rates to a PC via the serial RS-232 port.
ARTICLE IN PRESS C.-Y. Yi et al. / Nuclear Instruments and Methods in Physics Research A 551 (2005) 352–355
70
4.3 4.2
intercept : 4.1538 4.1
τ = 29.7 µs
4.0 3.9
slope : - 1.8894 x 10-3 3.8
(r2 = 0.994)
3.7 0
50
100
150
200
-1
Dose rate (mSv h ) Fig. 2. Logarithm of the counting rate per unit dose rate of the prototype ADR as a function of the dose rate.
The dead time can be estimated at 34.8 ms from Eq. (3) if we presume the dead time follows the nonparalyzable model. In order to analyze further, we took the logarithm of the data in Fig. 1 and presented the values in Fig. 2 as a function of the dose rate. The correlation coefficient of the straight fit line was 0.994. The dead time was deduced by Eq. (5) to be 29.7 ms with an assumption that the prototype ADR is paralyzable, differs by 17.2% from the dead time of the non-paralyzable case. However, the true counting rates estimated by Eqs. (1) and (4) with their corresponding dead times agreed within 71.5%. Along with the relative difference, the true counting rates estimated are given in Fig. 3. The agreement might come from the fact that the straight lines fit to data well in both cases. In the paralyzable case, n was found numerically from Eq. (4) using the bisection method [11].
intercept : 64.1092 (cps mSv-1 h)
Counting rate per unit dose rate
The prototype ADR was placed on the 30 30 15 cm PMMA slab phantom in the Cs137 reference radiation field and was irradiated in the dose rate range from 1 to 200 mSv h1. We used three irradiators with nominal activities of 185 GBq, 740 GBq and 4.8 TBq, respectively. About a 6-m-long rail was stretched out in front of each irradiator and a trolley was moved along the rail. The ADR and PMMA phantom were mounted on the trolley and aligned at the beam center. The air kerma rates for the three irradiators were determined for the movable range of the trolley 0.5–5.5 m from the sources with the expanded uncertainties (at 95% confidence level) less than 1.5%. The dose rate was the personal dose equivalent rate at 10 mm depth in soft tissue, which was defined by ICRU [9]. The factor for converting the air kerma rate to the personal dose equivalent rate at 10 mm depth in soft tissue is 1.21 Sv Gy1 [10]. In Fig. 1, the counting rate per unit dose rate of the prototype ADR is given as a function of counting rate per second (cps). The maximum counting rate recorded was around 9000 cps. The standard deviation of the measured counting rate ranged from 8% at 2 mSv h1 to 0.3% at 194 mSv h1. The background counting rate measured by the prototype ADR was less than one count per minute. As shown in the figure, the data were well fit to a straight line with the correlation coefficient 0.995. The commercially available software TableCurveTM 2D version 4.0 was used to fit.
ln (m/D)
354
60
τ = 34.8 µs
50
4. Concluding remarks
slope : - 2.2338 x 10-3 (r2 = 0.995)
40 0
2 4 6 8 Counting rate (x 1000 cps)
10
Fig. 1. Counting rate per unit dose rate of the prototype ADR as a function of the counting rate.
In the present paper, we have proposed a simple and efficient method for the dead time measurement of a counting system. The method is based on the irradiation of a counting system in the reference radiation field with varying dose rates. The dead time can be deduced from the slope and the intercept of the straight line fit to the scaled counting rates as given in Eqs. (3) and (5). Using
ARTICLE IN PRESS
Counting rate (x 1000 cps)
C.-Y. Yi et al. / Nuclear Instruments and Methods in Physics Research A 551 (2005) 352–355
Relative difference (%)
Acknowledgments
14 true counting rate (non-paralizable)
12
true counting rate (paralizable)
10
The present study has been supported in part by the mid- and long-term research fund for the development of nuclear energy granted by the Ministry of Science and Technology. The authors would like to express their gratitude to the referee for making valuable corrections and suggestions.
observed counting rate
8 6 4 2 0 0
(a)
50
100
150
200
2
References
1 0 -1 -2 0
(b)
355
50
100
150
200
Dose rate (mSv h-1)
Fig. 3. Comparison of the true rates with the observed counting rates (a) and difference of the true counting rates estimated using the paralyzable model from those of the nonparalyzable model (b). The difference is presented in percentage relative to the true counting rates of the non-paralyzable model.
the reference Cs-137 fields with dose rate range up to 200 mSv h1, the dead time of a prototype GM counter was measured by the proposed method.
[1] R.P. Gardner, L. Liu, Appl. Radiat. Isot. 48 (1997) 1605. [2] S.H. Lee, R.P. Gardner, Appl. Radiat. Isot. 53 (2000) 731. [3] F.L.R. Vinagre, C.A.N. Conde, Nucl. Instr. and Meth. A 462 (2001) 555. [4] R.D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955. [5] G.F. Knoll, Radiation Detection and Measurement, third ed., Wiley, New York, 2000. [6] J.W. Mueller, Nucl. Instr. and Meth. 112 (1973) 47. [7] J.W. Mueller, Nucl. Instr. and Meth. 117 (1974) 401. [8] J. Libert, Nucl. Instr. and Meth. 151 (1978) 555. [9] ICRU, ICRU Rep. 51, Bethesda, MD, 1993. [10] ISO, ISO 4037-3, Geneva, 1999. [11] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran, second ed., Cambridge University, New York, 1992.