Method and apparatus for determining random coincidence count rate in a scintillation counter utilizing the coincidence technique

A method and related apparatus for the reliable determination of a random coincidence count attributable to chance coincidences of single-photon events which are each detected in only a single detector of a scintillation counter utilizing two detectors in a coincidence counting technique. A first delay device is employed to delay output pulses from one detector, and then the delayed signal is compared with the undelayed signal from the other detector in a coincidence circuit, to obtain an approximate random coincidence count. The output of the coincidence circuit is then applied to an anti-coincidence circuit, where it is corrected by elimination of pulses coincident with, and attributable to, conventionally detected real coincidences, and by elimination of pulses coincident with, and attributable to, real coincidences that have been delayed by a second delay device having the same time parameter as the first.

BACKGROUND OF THE INVENTION 
This invention relates generally to the measurement of radioactivity 
utilizing what is generally referred to as the coincidence counting 
technique, wherein events relating to radioactive decay are detected in 
two or more detectors within a given time interval, in order to eliminate 
various sources of error which would be introduced if only one detector 
were used. More particularly, the invention relates to a new and improved 
method, and related apparatus, for eliminating a further source of error 
due to the detection of chance or random coincidences in the multiple 
detectors. 
One of the most widely used devices for the measurement of radiation from 
radioactive substances is the scintillation counter. The basic element of 
a scintillation counter is a scintillation medium which absorbs incident 
radiation and emits photons as a result. Many of the emitted photons are 
incident upon a photocathode in a nearby multiplier phototube, and are 
converted to photoelectrons emitted from the photocathode. The electrons 
emitted from the photocathode are multiplied in number at a succession of 
phototube electrodes, called dynodes, and the output of the multiplier 
phototube is a measurable electrical pulse having a magnitude which is 
approximately proportional to the energy of the incident radiation. 
A liquid scintillation counter operates on the same basic principle, except 
that the scintillation medium is a liquid into which is dissolved, 
suspended or otherwise intermixed with sample being tested. The 
radioactivity of the sample can then be measured by collecting the photons 
emitted from the scintillation medium in a multiplier phototube positioned 
near the sample, and counting the pulses generated by the tube in 
appropriate electrical circuitry. Depending on the characteristics of the 
sample being measured, and on the particular tests being performed, this 
electrical circuitry usually performs some type of pulse height analysis 
on the pulse output from the phototube, since it is usually desired to 
detect and count radioactive events within a particular range or window of 
energy levels. 
A significant problem encountered in the measurement of radioactivity by 
means of scintillation counters is that there are a number of phenomena 
unrelated to the radioactivity of the sample which nevertheless result in 
the generation of output pulses from the multiplier phototube of a 
scintillation counter. These phenomena are frequently referred to as 
"singles" events since they are all characterized by the emission of 
single photons or photoelectrons. A relatively large source of "singles" 
events is the thermionic emission of electrons from the photocathode or 
from the dynodes of the multiplier phototube itself. Such electrons are 
emitted independently of any detected radiation, and can result in 
significant error, especially if the tubes are operated at relatively high 
voltages, the typical case where high amplification factors are being 
used, as in the measurement of relatively low radiation levels. This 
thermionic emission of electrons is also referred to as "tube noise." 
In liquid scintillation counters, the sample itself may emit photons by 
some process unrelated to its radioactivity. The sample material could 
exhibit some degree of chemiluminescence, i.e., there may be some chemical 
reaction or reactions ocurring within the sample material which result in 
the emission of photons. The sample material may also be subject to the 
processes of bioluminescence or photoluminescence, which also generate 
photons independently of the level of radioactivity of the sample 
material. In addition, the presence of low-level background radiation, 
static electrical discharges, or a leakage of ambient light into the 
counter, could give rise to "singles" events detectable by the 
scintillation counter. 
Use of the well known coincidence counting technique substantially reduces 
the detection of "singles" events by a scintillation counter. In a liquid 
scintillation counter, this technique is utilized by employing at least 
two multiplier phototubes disposed one on each side of the sample. The 
emission of many single radioactive particles by the sample can typically 
result in the emission of about seven or more photons simultaneously, or 
nearly simultaneously. Thus, there is a high probability that such an 
event will be detected by both phototubes at nearly the same time. A 
"singles" event, however, such as one resulting from chemiluminescence, or 
from a thermionically emitted electron in one of the tubes, would result 
in an output pulse from only one of the tubes. It can be appreciated, 
then, that the use of the coincidence counting technique results in the 
elimination of most of the "singles" events from the counting process. 
It will also be apparent, however, that, because of the random nature of 
the "singles" events, there is a significant probability that a "singles" 
event could be detected in one tube at nearly the same instant in time 
that one is detected in the other tube. There is, therefore, a random 
coincidence rate resulting from random or chance coincidences of unrelated 
"singles" events. Mathematically, the random coincidence count rate 
S.sub.c is given by: 
EQU S.sub.c =2.tau..sub.c S.sub.1 S.sub.2, (1) 
where: 
.tau..sub.c =the resolving time of the coincidence counter, i.e., the 
longest time separating two pulses which would still be considered 
coincident, 
S.sub.1 =the "singles" count rate measured by one of the multiplier 
phototubes, and 
S.sub.2 =the "singles" count rate measured by the other of the multiplier 
phototubes. 
Under normal operation, a liquid scintillation counter will give a measured 
count rate (S.sub.m) which will be the sum of the sample coincidence count 
rate (S.sub.a) and the "singles" random coincidence count rate (S.sub.c). 
That is: 
EQU S.sub.m =S.sub.a +S.sub.c. (2) 
Any user of a liquid scintillation counter ideally needs to know the value 
of S.sub.c so that, where possible, a correction can be made to obtain the 
correct value of radiation attributable to the sample only. Even where 
direct correction is not possible, because testing is being performed in 
specific energy level "windows," the user of the counter could still use 
the value of S.sub.c as an indication of the reliability of the measured 
count rate. 
Prior to this invention, a precise determination of the random coincidence 
rate has not been possible, except as disclosed and claimed in U.S. Pat. 
No. 4,071,761 bearing the same title and having the same inventor as the 
present application. Although the technique disclosed in the prior 
application provides a highly satisfactory solution to the problem posed 
by the occurrence of random coincidences, it requires the use of a 
counting channel for measurement of a single-photon count. Accordingly, 
there is still a need for an alternative solution to the problem. 
Prior art techniques have been limited to making a qualitative estimate of 
the presence of those "singles" events which decrease with time. Usually 
chemiluminescence, bioluminescence and photoluminescence have this decay 
characteristic. In accordance with such prior art techniques, the 
radioactivity of a sample would be measured at different times, and the 
measured count rates compared, so that any decrease in the measured 
coincidence rates could be noted. If there was little or no decrease in 
the measured coincidence rates over a substantial time period, it was 
generally assumed that the random coincidence count was insignificant. 
This method is, of course, quite time consuming, and does not take into 
account at all those "singles" events derived from tube noise, or from 
other sources which do not rapidly decay. 
U.S. Pat. No. 3,772,512 issued in the name of Laney, suggests that real 
coincidences can be distinguished from chance or random coincidences in 
multiple detectors by delaying the output pulses from one of the 
detectors. The theory underlying the use of the delay circuit is that the 
real coincidences will be eliminated by delaying the signals from one of 
the detectors, but the chance coincidences will occur at the same 
measurable rate, since they are random by nature and a time delay does not 
affect this characteristic of randomness. Accordingly, if the delayed 
signal from one detector and the undelayed signal from the other detector 
are applied to a coincidence determination circuit, this should yield an 
indication of the random coincidence rate. However, the technique is still 
subject to significant error, especially at relatively high sample 
radiation counts. At high count rates, there is an increased probability 
that pulses due to real coincidences, although shifted out of coincidence 
with each other, will nevertheless be coincident with singles events or 
with other "real" events. 
Accordingly, there is still a need for improvement in the coincidence 
counting technique which utilizes a delay circuit, to provide an 
alternative to the solution set forth in the aforementioned patent 
application for the reliable estimation of the error attributable to 
random or chance coincidences of singles events. The present invention 
fulfills this need. 
SUMMARY OF THE INVENTION 
The present invention resides in a method and related apparatus for 
determining the random coincidence count due to different events which 
each generate single quanta of energy and which happen to be detected at 
substantially the same time at different ones of the two independent 
detectors in a scintillation counter. Briefly, and in general terms, the 
method of the invention comprises the steps of counting the number of 
measured coincidences or events detected essentially simultaneously by 
both detectors in the scintillation counter, delaying the pulses from one 
of the detectors by a fixed time delay, detecting the essentially 
simultaneous pulses derived from the delayed pulses from one detector and 
the undelayed pulses from the other detector, to obtain an approximate 
measure of a random coincidence count rate attributable to chance 
coincidences of single-quantum events, and correcting the approximate 
random coincidence count rate to compensate for coincidences involving at 
least one pulse attributable to a real coincidence. More specifically, the 
step of correcting the random coincidence count rate includes eliminating 
pulses that are coincident with pulses detected simultaneously by both 
detectors, delaying the signal indicative of pulses detected 
simultaneously by both detectors, and further eliminating pulses 
coincident with the delayed signal indicative of pulses simultaneously 
detected by both detectors. 
Since the approximate random coincidence count rate is derived by detecting 
coincidences between delayed pulses from one detector and undelayed pulses 
from the other detector, the approximate count rate will include four 
categories of coincident pulse pairs. The most significant of these, of 
course, is that which includes coincidences between undelayed singles 
events and delayed singles events, since these represent the random 
coincidence count rate. The other three categories are coincidences 
between undelayed real events and delayed real events, coincidences 
between undelayed real events and delayed singles events, and coincidences 
between undelayed singles events and delayed real events. The first two of 
these three unwanted categories, both involving undelayed real events, can 
be eliminated by removing from consideration all of those pulses which are 
coincident with originally measured undelayed real coincidences. The third 
category, involving a delayed real event, can be eliminated by removing 
from consideration those pulses which are coincident with delayed real 
coincidences. 
In terms of novel apparatus, the invention comprises first coincidence 
detection means for detecting real and chance coincidences between the 
signals from the two detectors, a first time delay means for delaying the 
signals from one of the detectors, and second coincidence detection means 
for determining the coincidences between a delayed signal from one 
detector and an undelayed signal from the other detector, to obtain an 
approximate random coincidence count rate. Also included are a second time 
delay means, having a time delay identical with the first, and 
anti-coincidence detection means for eliminating from the approximate 
random coincidence count rate pulses that are coincident with a signal 
from the first coincident detection means, and also those that are 
coincident with a delayed signal from the first coincidence detection 
means. The invention apparatus may also include counting means for 
accumulating a corrected count of random coincidences and a count of 
measured coincidences, and comparison means for comparing the corrected 
random coincidence count rate with an acceptable random coincidence count 
rate. 
It will be appreciated from the foregoing that the present invention 
provides a simple alternative to the single photon counting technique 
described and claimed in the aforementioned Horrocks patent. The random 
coincidence count rate as thus determined may be used for comparison with 
an acceptable count rate, or percentage corrections can be calculated in 
the manner set forth in the aforementioned patent. Other aspects and 
advantages of the present invention will become apparent from the 
following more detailed description taken in conjunction with the 
accompanying drawings.

DETAILED DESCRIPTION 
As shown in the drawings for purposes of illustration, the present 
invention is principally concerned with a method for determining the error 
due to chance coincidences detected by utilizing the coincidence counting 
technique in a scintillation counter. As previously indicated, the 
coincidence counting technique utilizes at least two radiation detectors, 
usually multiplier phototubes, in order to avoid counting single-photon 
events resulting from chemiluminescence or similar phenomena in the sample 
being measured, or resulting from phototube noise which arises from 
thermionic emission of electrons. Although these "singles" events will 
normally be detected in only one multiplier phototube, the random nature 
of their occurrence results in the detection of a significant number of 
apparent coincidences that are unrelated to the radioactivity being 
monitored. 
FIG. 1 shows in block diagram form a typical arrangement for radioactivity 
measurement using a liquid scintillation counter. A sample 10, is placed 
between a pair of photon detectors 12, which usually take the form of 
multiplier phototubes. In liquid scintillation counters, radioactive 
particles emitted by the sample material are absorbed by a liquid 
scintillation medium mixed with the sample itself, and the generation of a 
number of photons results from each emission of a radioactive particle. 
The photons are simultaneously, or nearly simultaneously, detected by the 
multiplier phototubes 12 and converted into measurable electrical pulses 
for output on lines 14 and 15, respectively. The output pulses from the 
multiplier phototubes 12 are transmitted to a summing amplifier 16, the 
output of the amplifier being fed to three pulse height analyzers 18, each 
of which can be adjusted to ignore pulses which do not fall within a 
selectable range of pulse heights or energy levels. The output pulses from 
the multiplier phototubes 12 are also transmitted to a coincidence 
detection circuit 20, which provides an output on line 22 if the pulses 
from the tubes are in coincidence, to within some preselected resolution 
time interval. 
The coincidence signal on line 22 and the outputs from the pulse height 
analyzers 18 are applied to three coincidence gates 24, which function as 
AND gates, producing an output only when both input signals are in the 
same selected condition. Three scalers 26 receive output pulses from the 
respective coincidence gates 24, and accumulate counts in the three 
channels. 
In accordance with the present invention, the output signals from one of 
the multiplier phototubes 12, on line 15, is also applied to a delay 
device 30, and the delayed signal is applied to a second coincidence 
detection circuit 32 along with the undelayed signal from the other 
multiplier phototube on line 14. Then, an approximate random coincidence 
count obtained from the second coincidence detection circuit 32 is further 
corrected by means of an anti-coincidence circuit 34 to which signals 
indicative of the approximate random coincidence rate are applied over 
line 36. Also applied to the anti-coincidence circuit 34 are a signal 
indicative of the measured coincidences, derived from line 22, and a 
signal indicative of the original coincidences on line 22 delayed by a 
second delay device 38, having the same inherent time delay as the first 
time delay device 30. As will be further explained, the anti-coincidence 
circuit 34 yields signal pulses, on output line 40, that are indicative of 
a corrected rate of random coincidences, i.e., coincidences that are 
attributable to "singles" events. 
The chance coincidence pulses thus obtained on line 40 are accumulated in a 
scaler 42, and the measured coincidence pulses on line 22 are accumulated 
in another scaler 44. The accumulated count in scaler 42, indicative of 
the corrected random coincidence count rate, is transmitted over line 46 
to a display device 48, and to a comparison circuit 50, which also 
receives data from the scaler 44 over line 52. The comparison circuit 50 
can include any desired circuitry for comparing the value of the random 
coincidence count rate with an acceptable random rate, indicated at 54. 
The comparison circuit 50 may also have the function of generating a 
scaler reset signal, as indicated at 56, so that counting may be restarted 
automatically if the random coincidence count rate is not down to an 
acceptable level. This latter feature would, of course, be useful only if 
the chance coincidences were attributable primarily to some phenomena, 
such as chemiluminescence, which decayed rapidly with time. 
Operation of the apparatus illustrated in FIG. 1 can be better appreciated 
by considering the various categories of pulses that can occur, as 
illustrated in simplified form in FIGS. 2 and 3. FIG. 2a shows two real 
coincident pulses, designated as R.sub.1 and R.sub.2, respectively. Since 
the pulses R.sub.1 and R.sub.2 result from only one event, they are 
practically coincident in time, and give rise to a real coincidence pulse, 
indicated as R.sub.0. In relation to the block diagram of FIG. 1, if 
R.sub.1 were to appear on line 14 and R.sub.2 were to appear on line 15, 
the coincidence detection circuit 20 would yield the pulse R.sub.0 on line 
22. 
FIG. 2b illustrates by way of contrast two "singles" pulses which are 
unrelated and non-coincident in time, and are designated S.sub.1 and 
S.sub.2, respectively. FIG. 2c indicates two unrelated singles pulses 
S.sub.1 and S.sub.2 which happen to coincide in time within the tolerance 
selected for the widths of the coincidence gate included in the 
coincidence detection circuit 20. These pulses therefore give rise to a 
chance coincidence pulse S.sub.c. Again, in terms of the apparatus shown 
in FIG. 1, if pulses S.sub.1 and S.sub.2 were to appear on lines 14 and 
15, respectively, the coincidence detection circuit 20 would yield the 
pulse S.sub.c on line 22. 
In FIG. 3, waveform (a) indicates in simplified form a train of pulses of 
the kind that might appear on line 14 (FIG. 1) from one of the multiplier 
phototubes 12. It will be seen that waveform (a) includes two types of 
pulses, real pulses indicated by R.sub.1 and "singles" pulses indicated by 
S.sub.1. For purposes of further identification, the real pulses are 
indicated sequentially as R.sub.1-1, R.sub.1-2, R.sub.1-3, etc., and the 
singles pulses are designated S.sub.1-1, S.sub.1-2, S.sub.1-3, etc. In 
similar fashion, waveform (b) of FIG. 3 shows a corresponding waveform of 
the signal pulses appearing on line 15 from the other multiplier phototube 
12. It will be observed that the same nomenclature is utilized, and that 
the pulses due to real events are time coincident in the two waveforms. 
Thus, pulse R.sub.1-1 is time coincident with pulse R.sub.2-1, pulse 
R.sub.1-2 is time coincident with R.sub.2-2, and so forth. The singles 
pulses are, of course, not generally coincident, but, for purposes of 
illustration, singles pulse S.sub.1-2 is shown as being coincident in time 
with singles pulse S.sub.2-2. The signal content of waveform (a) may be 
indicated in shorthand form as R.sub.1 +S.sub.1, and the signal content of 
waveform (b) may be indicated in shorthand as R.sub.2 +S.sub.2. 
Waveform (c) represents the output of the first coincidence detection 
circuit 20 on line 22. It will be seen that it contains coincidence pulses 
for the real events, indicated as R.sub.0-1, R.sub.0-2, etc., and contains 
one chance or random coincidence, indicated as S.sub.c-1. Waveform (c) may 
be designated R.sub.0 +S.sub.c in shorthand form. For convenience, 
waveform (a) is repeated as waveform (d). Waveform (e) is the result of 
time delaying waveform (b). In other words, waveform (e) represents the 
delayed signal output from the time delay device 30 to the second 
coincidence detection circuit 32. In shorthand form, waveform (e) may be 
indicated as (R.sub.2 +S.sub.2).sub.D. 
Waveform (f) depicts the signal that is obtained on line 36 from the second 
coincidence circuit, and represents coincidences between pulses in 
waveforms (d) and (e). As will be discussed in more detail, this signal 
contains pulses of four types, which may be represented in the same 
shorthand form as: R.sub.1 +R.sub.2D, R.sub.1 +S.sub.2D, S.sub.1 
+R.sub.2D, and S.sub.1 +S.sub.2D. 
The theory underlying the use of a delay to distinguish real coincidences 
from random ones is that the number of random coincidences between 
"singles" events will be unchanged if the signals from one of the 
multiplier phototubes is delayed in time, but that the delay destroys the 
time coincidence relationship between the real coincident pulses. It can 
be seen from FIG. 3, however, that, since waveforms (d) and (e) both 
contain pulses resulting from real and singles events, there is a 
possibility that, when the shifted and unshifted signals are compared, 
there will be coincidences due to pulses attributable to real events as 
well as due to pulses attributable to singles events. More specifically, 
the coincidences detected in coincidence detection circuit 32 include four 
distinguishable categories: an undelayed real pulse and a delayed real 
pulse, and undelayed real pulse and a delayed singles pulse, an undelayed 
singles pulse and a delayed real pulse, and an undelayed singles pulse and 
a delayed singles pulse. Clearly, the random coincidence count rate in 
which the user is interested is the one derived from coincidences in the 
last category of the four, i.e., between singles pulses. For an accurate 
determination of the random coincidence count rate, coincidences in the 
first three categories must therefore be eliminated. 
For purposes of illustration, waveform (f) is shown as including one pulse 
from each of the four categories of coincident pulse pairs. Delayed pulse 
R.sub.2-1 is shown as being coincident with undelayed singles pulse 
S.sub.1-1, undelayed pulse R.sub.1-3 is shown as being coincident with 
delayed singles pulse S.sub.2-3, undelayed pulse R.sub.1-5 is shown as 
being coincident with delayed pulse R.sub.2-4, and undelayed singles pulse 
S.sub.1-4 is shown as being coincident with delayed singles pulse 
S.sub.2-4. 
In order to eliminate the unwanted categories of coincident pulses from the 
approximately determined random coincidence count, the anti-coincidence 
circuit 34 is utilized. The output from the first coincidence detection 
circuit 20 on line 22, is employed in the anti-coincidence circuit to 
eliminate those coincidences due to undelayed pulses attributable to real 
events. As shown in waveform (g), which is identical to waveform (c), the 
pulse R.sub.0-3 can be used to eliminate the coincidence in waveform (f) 
indicated as R+S.sub.D, and the pulse R.sub.0-5 can be used to eliminate 
the coincidence between unshifted and shifted real event pulses indicated 
in waveform (f) as R+R.sub.D. 
The signal representing measured coincidences, indicated by waveform (c), 
is also applied to the delay device 38, and the delayed signal, shown in 
waveform (h), is then applied, over line 39, to the anti-coincidence 
circuit 34. It will be seen from waveform (h) that the pulses can be 
utilized to eliminate the coincidence indicated as S+R.sub.D, involving an 
delayed singles pulse and a delayed real pulse. Once the three unwanted 
categories of coincidences have been eliminated from waveform (f), what 
remains on line 40 is a signal illustrated in waveform (i), i.e., 
containing only pulses attributable to chance coincidences of "singles" 
events. 
The anti-coincidence circuit 34 can be implemented in any of a variety of 
specific forms. In principle, it functions as an AND gate having three 
inputs. One input is supplied from the signals indicative of the 
approximate random coincidence count rate, on line 36, and the other two 
inputs are derived from inverted forms of the signals on lines 22 and 39, 
respectively. It will be appreciated, however, that somewhat more complex, 
yet perfectly conventional, logic will be needed to take care of 
situations in which pulses to be eliminated from waveform (f) are not 
exactly in coincidence with corresponding pulses in waveforms (g) and (h). 
There is a very small probability that coincidence pulses even of the type 
attributable to "singles" pulses only will be eliminated by the 
aforedescribed technique. The possibility exists that the time of 
occurrence of one of the random pulses S+S.sub.D in waveform (f) will 
almost exactly correspond with the time of occurrence of a chance 
coincidence as indicated by S.sub.c in waveform (g) or waveform (h). It is 
believed, however, that the probability of this occurring is extremely 
low, and that the probability can be ignored for most practical purposes. 
It will be appreciated from the foregoing that the present invention 
provides a simple and practical alternative technique for obtaining an 
indication of the random coincidence count rate in a scintillation counter 
using the coincidence technique. It will also be appreciated that, 
although a specific embodiment of the invention has been described in 
detail for purposes of illustration, various modifications may be made 
without departing from the spirit and scope of the invention. Accordingly, 
the invention is not to be limited except as by the appended claims.