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The periodic integrator: An instrument for recording rapid variations of counting rate
The Periodic Integrator: for Recording Rapid of Counting
An Instrument Variations
+150
INPUT.+,
1
Rate*
(First received 8 Mgy 1962 and injinalform
18 June 1962)
SCHEMATICALLY any ratemeter can be considered as consisting of the following three parts: (a) Current generator (pump circuit), the average value I of the current supplied in any given interval of time being proportional to the counting rate during that time. (b) Tank capacitor C, in parallel with a resistor R, in which the current I is fed by (a). (c) Voltmeter circuit which reads the voltage V across C. In the circuit (b), it is readily shown that
-105
FIG. 1. Basic circuit
=;(V+RCg).
The recorded value of V is thus accurately proportional to the counting rate only when the term in dV/dt is negligible. For applications, such as radiocardiography, in which rapid changes of counting rate occur and the time constant RC cannot be further reduced because of statistical fluctuations, a large error can be introduced by this term. Various systems have been proposed in order to avoid or account for this error. These systems include magnetic tape recordingt1+2) printing scalers(s*4) or differentiation of the ratemeter tracet3). Such procedures may all work quite properly, but they have at least one of the following drawbacks: (1) High cost. (2) Impossibility of monitoring the curve during recording. (3) Time-consuming analysis of the data. An instrument has been developed, by modifying a commercial ratemeter, which provides direct, undamped records of radiocardiography changes. * This work has been supported States Atomic Energy Commission (30-l)-2648).
of the periodic
integrator.
The circuit developed (see Fig. 1) substitutes the parts (b) and (c) of the ratemeter. We will refer to it as “periodic integrator”. Its principle of operation is the following: The charge supplied by (a) t is fed into the tank capacitor C with an effectively infinite time constant. C is periodically discharged through a fast mercury relay triggered by a Thyratron oscillator (the period is adjustable between l/20 and l/2 set). The output of the circuit, which measures the instantaneous value of the charge stored in the capacitor (proportional to the number of pulses having occurred since the previous reset), is fed to the recording oscilloscope. Operating with resetting periods much longer than the time during which the relay is closed (with the circuit of Fig. 1, 1.5 x 10F3 set) the heights of the peaks reached at the end of each integrating period are proportional to the average counting rate during the period itself. In Fig. 2, is reported a radiocardiogram recorded 7 The ratemeter used was a Tracerlab SC-79. The input of the periodic integrator consisted in having the input terminal raised from the ground potential to about 130 V each time a pulse was registered. With the value for the various components as indicated in Fig. 1, it can be shown that the charge fed each time in C is proportional to (130 lr/lO), lJ (in itself) being the voltage across C. Operating with maximum output voltage of 10 V, the linearity is therefore better than 1 per cent.
by the United (Contract AT 582
FIG. 2. Radiocardiogram recorded by means of a periodic integrator, with an integrating period of 0.088 sec. The upper tracing is an electrocardiogram.
582
583
Technical notes
by means of the periodic integrator
with an integrating period of 0.088 sec. It may be interesting to note that if a sudden change in the counting rate occurs during a period of integration, its time of occurrence can be found accurately by locating the corresponding point of change in the shape of the trace recorded. Finally we point out that the r.m.s. fluctuation on the height of each peak is given by the square root of the height itself, thus making very simple the statistical analysis of the data recorded. Acknowledgment-Thanks
are due to MR. N. VEALL
for a very helpful discussion. I. MANNELLI
lstituto di Fisica
dell' Uniuersitadi Pisa Piss, Italy Centro di Medicina Nucleare Clinica Medica deN’lJniversita di Pisa,
Calculated Efficiencies of a 3 x 3 in. NaI(T1) Well-Type Scintillation Crystal (Received16 March 1962) CALCULATED efficiencies of solid NaI(T1) scintillation crystals have been published on several occasions.(1-3) As far as we know, calculated efficiencies for well-type crystals have never yet been reported. Experimental values, however, were given by some authors (e.g. GUNNIKand STONER(~)),but not for the crystal-type we use in our laboratories. Our crystal is a 3 x 3 in. well-type 12AW12 obtained from the Harshaw Chemical Company, the dimensions of the well being is in. deep and 8 in. in diameter. ‘Our efficiency calculations were based on the formula T(E,
L. DONATO
a) = 4
where
Pisa, Italy
w{l - ebT(E)z@,a)} sin 0 d0 s0
a) = total absolute efficiency with which the crystal detects y-rays of energy E, originating from a point source on the crystal axis; a being the distance between the source and the bottom of the well T(E) = total absorption coefficient for y-rays of energy Ec6) 0 = angle between any given y-ray and the crystal axis ~(0, a) = distance travelled by that y-ray through the crystal material.
T(E,
References HUFF R. L., PARRISHD., CROCKETTW. A. and HANKENESSS. J. Strahlentherapie (Sonderbericht) 48, 161 (1958).
BERNE E., HALLBERCL. and LINDELLS. E. Sand. J. clin. Lab. Invest.14, 3 (1961). GIUNTINIC., BIANCHIR., TONI P. and DONATOL. Minema Nucleare 5, 2 18 ( 196 1). EICH R. H., CHAFFERW. R. and CHODOSR. B. Circ. Res. 9, 626 (1961).
TABLE 1. Total absolute efficiencies
(M:V)
a = 3.81
a = 6.81
a = 13.81
(cm) h = 3.00
(cm) h = 10.00
a = 0.00
a = 0.50
a = 1.00
a = 1.569
a = 2.00
(cm) h = 0.00
(cm)
(cm)
(cm)
(cm)
(cm)
(cm)
(cm)
0.980
0.974 0.973 0.973
0.964 0.964 0.963
0.971 0.963 0.926 0.790
0.961 0.949 0.907 0.765 0.660 0.590 0.545 0.484 0443 0.377 0.344 0.315 0.304 0.300
0.947 0.946 0.944 0.941 0.923
0.925 0.924 0.92 1 0.915 0.891
0.500 0.500 0.500 0.500 0.499 0.486 0.424 0.372 0.336 0.312 0.280 0.257 0.221 0.202 0.186 0.179
0.190 0.189 0.187 0.184 0.172 0.158 0.133 0.117 0.107 0.0994 0.0898 0.0832 0.0724 0.0664 0.0613 0.0593 0.0586
0.0500 0.0600 0.0800 0.100
o-979 0.978
0.150 0.200 0.300 0400 0.500 0.600 0.800 1 .oo 1.50 2.00 3.00 4.00 5.00
0.972 0.946 0.833 0.735 0.667 0.620 0.557 0.513 0443 0.405 0.372 0.359 0.355
0.980
0.686 0.616 0.569 0.507 0.465 0.399 0.363 0.332 0.32 1 0.317
0.875 0.732 0.630 0.562 0.518 0.460 0.42 1 0.360 0.327 0.299 0.288 0.284
0.840 0.699 0.601 0.536 0.494 0.439 0401 0.342 0.311 0.284 0.274 0.271
0.177
(cm)
0.0326 0.0325 0.0323 0.0318 0.0304 0.0286 0.0254 0.023 1 0.0214 0.0202 0.0186 0.0174 0.0154 0.0142 0.0132 0.0128 0.0127
An Instrument Variations
+150
INPUT.+,
1
Rate*
(First received 8 Mgy 1962 and injinalform
18 June 1962)
SCHEMATICALLY any ratemeter can be considered as consisting of the following three parts: (a) Current generator (pump circuit), the average value I of the current supplied in any given interval of time being proportional to the counting rate during that time. (b) Tank capacitor C, in parallel with a resistor R, in which the current I is fed by (a). (c) Voltmeter circuit which reads the voltage V across C. In the circuit (b), it is readily shown that
-105
FIG. 1. Basic circuit
=;(V+RCg).
The recorded value of V is thus accurately proportional to the counting rate only when the term in dV/dt is negligible. For applications, such as radiocardiography, in which rapid changes of counting rate occur and the time constant RC cannot be further reduced because of statistical fluctuations, a large error can be introduced by this term. Various systems have been proposed in order to avoid or account for this error. These systems include magnetic tape recordingt1+2) printing scalers(s*4) or differentiation of the ratemeter tracet3). Such procedures may all work quite properly, but they have at least one of the following drawbacks: (1) High cost. (2) Impossibility of monitoring the curve during recording. (3) Time-consuming analysis of the data. An instrument has been developed, by modifying a commercial ratemeter, which provides direct, undamped records of radiocardiography changes. * This work has been supported States Atomic Energy Commission (30-l)-2648).
of the periodic
integrator.
The circuit developed (see Fig. 1) substitutes the parts (b) and (c) of the ratemeter. We will refer to it as “periodic integrator”. Its principle of operation is the following: The charge supplied by (a) t is fed into the tank capacitor C with an effectively infinite time constant. C is periodically discharged through a fast mercury relay triggered by a Thyratron oscillator (the period is adjustable between l/20 and l/2 set). The output of the circuit, which measures the instantaneous value of the charge stored in the capacitor (proportional to the number of pulses having occurred since the previous reset), is fed to the recording oscilloscope. Operating with resetting periods much longer than the time during which the relay is closed (with the circuit of Fig. 1, 1.5 x 10F3 set) the heights of the peaks reached at the end of each integrating period are proportional to the average counting rate during the period itself. In Fig. 2, is reported a radiocardiogram recorded 7 The ratemeter used was a Tracerlab SC-79. The input of the periodic integrator consisted in having the input terminal raised from the ground potential to about 130 V each time a pulse was registered. With the value for the various components as indicated in Fig. 1, it can be shown that the charge fed each time in C is proportional to (130 lr/lO), lJ (in itself) being the voltage across C. Operating with maximum output voltage of 10 V, the linearity is therefore better than 1 per cent.
by the United (Contract AT 582
FIG. 2. Radiocardiogram recorded by means of a periodic integrator, with an integrating period of 0.088 sec. The upper tracing is an electrocardiogram.
582
583
Technical notes
by means of the periodic integrator
with an integrating period of 0.088 sec. It may be interesting to note that if a sudden change in the counting rate occurs during a period of integration, its time of occurrence can be found accurately by locating the corresponding point of change in the shape of the trace recorded. Finally we point out that the r.m.s. fluctuation on the height of each peak is given by the square root of the height itself, thus making very simple the statistical analysis of the data recorded. Acknowledgment-Thanks
are due to MR. N. VEALL
for a very helpful discussion. I. MANNELLI
lstituto di Fisica
dell' Uniuersitadi Pisa Piss, Italy Centro di Medicina Nucleare Clinica Medica deN’lJniversita di Pisa,
Calculated Efficiencies of a 3 x 3 in. NaI(T1) Well-Type Scintillation Crystal (Received16 March 1962) CALCULATED efficiencies of solid NaI(T1) scintillation crystals have been published on several occasions.(1-3) As far as we know, calculated efficiencies for well-type crystals have never yet been reported. Experimental values, however, were given by some authors (e.g. GUNNIKand STONER(~)),but not for the crystal-type we use in our laboratories. Our crystal is a 3 x 3 in. well-type 12AW12 obtained from the Harshaw Chemical Company, the dimensions of the well being is in. deep and 8 in. in diameter. ‘Our efficiency calculations were based on the formula T(E,
L. DONATO
a) = 4
where
Pisa, Italy
w{l - ebT(E)z@,a)} sin 0 d0 s0
a) = total absolute efficiency with which the crystal detects y-rays of energy E, originating from a point source on the crystal axis; a being the distance between the source and the bottom of the well T(E) = total absorption coefficient for y-rays of energy Ec6) 0 = angle between any given y-ray and the crystal axis ~(0, a) = distance travelled by that y-ray through the crystal material.
T(E,
References HUFF R. L., PARRISHD., CROCKETTW. A. and HANKENESSS. J. Strahlentherapie (Sonderbericht) 48, 161 (1958).
BERNE E., HALLBERCL. and LINDELLS. E. Sand. J. clin. Lab. Invest.14, 3 (1961). GIUNTINIC., BIANCHIR., TONI P. and DONATOL. Minema Nucleare 5, 2 18 ( 196 1). EICH R. H., CHAFFERW. R. and CHODOSR. B. Circ. Res. 9, 626 (1961).
TABLE 1. Total absolute efficiencies
(M:V)
a = 3.81
a = 6.81
a = 13.81
(cm) h = 3.00
(cm) h = 10.00
a = 0.00
a = 0.50
a = 1.00
a = 1.569
a = 2.00
(cm) h = 0.00
(cm)
(cm)
(cm)
(cm)
(cm)
(cm)
(cm)
0.980
0.974 0.973 0.973
0.964 0.964 0.963
0.971 0.963 0.926 0.790
0.961 0.949 0.907 0.765 0.660 0.590 0.545 0.484 0443 0.377 0.344 0.315 0.304 0.300
0.947 0.946 0.944 0.941 0.923
0.925 0.924 0.92 1 0.915 0.891
0.500 0.500 0.500 0.500 0.499 0.486 0.424 0.372 0.336 0.312 0.280 0.257 0.221 0.202 0.186 0.179
0.190 0.189 0.187 0.184 0.172 0.158 0.133 0.117 0.107 0.0994 0.0898 0.0832 0.0724 0.0664 0.0613 0.0593 0.0586
0.0500 0.0600 0.0800 0.100
o-979 0.978
0.150 0.200 0.300 0400 0.500 0.600 0.800 1 .oo 1.50 2.00 3.00 4.00 5.00
0.972 0.946 0.833 0.735 0.667 0.620 0.557 0.513 0443 0.405 0.372 0.359 0.355
0.980
0.686 0.616 0.569 0.507 0.465 0.399 0.363 0.332 0.32 1 0.317
0.875 0.732 0.630 0.562 0.518 0.460 0.42 1 0.360 0.327 0.299 0.288 0.284
0.840 0.699 0.601 0.536 0.494 0.439 0401 0.342 0.311 0.284 0.274 0.271
0.177
(cm)
0.0326 0.0325 0.0323 0.0318 0.0304 0.0286 0.0254 0.023 1 0.0214 0.0202 0.0186 0.0174 0.0154 0.0142 0.0132 0.0128 0.0127