Counting systems

In simple counting systems, the objective is to record the number of pulses that occur over a given measurement time, or alternatively, to indicate the rate at which these pulses are occurring. Some preselection may be applied to the pulses before they are recorded. A common method is to employ an electronic unit known as an integral discriminator to count only those pulses that are larger than a preset amplitude. This approach can eliminate small amplitude pulses that may be of no interest in the application. Alternatively, a differential discriminator (also known as a single-channel analyzer) will select only those pulses whose amplitudes lie within a preset window between a given minimum and maximum value. In this way, the accepted pulses can be restricted to those in which the charge Q from the detector is within a specific range. When the number of pulses meeting these criteria are accumulated in a digital register over the measurement time, the measurement consists of reporting the total number of accepted events over the time period.

One property that must be considered in counting systems is the concept known as dead time. Following each event in a detector, there is a period of time in which the measurement system is processing that event and is insensitive to other events. Because radiation events typically occur randomly distributed in time, there is always some chance that a true event will occur so soon after a previous event that it is lost. This behaviour is often accounted for by assigning a standard dead time to the counting system. It is assumed that each accepted event is followed by a fixed time period during which any additional true event will be ignored. As a result, the measured number of counts (or the counting rate) is always somewhat below the true value. The discrepancy can become significant at high radiation rates when the dead time is a significant fraction of the average spacing between true events in the detector. Corrections for dead-time losses can be made assuming that the behaviour of the counting system and length of its dead time are known.

As an alternative to simply registering the total number of accepted pulses over the counting time, the rate at which the accepted events are occurring in real time can be indicated electronically using a rate meter. This unit provides an output signal that is proportional to the rate at which accepted pulses are occurring averaged over a response time that is normally adjustable by the user. Long response times minimize the fluctuations in the output signal due to the random nature of the interaction times in the detector, but they also slow the response of the rate meter to abrupt changes in the radiation intensity.

Spectroscopy systems

The pulse-mode counting systems described above provide no detailed information on the amplitude of the pulses that are accepted. In many types of detectors, the charge Q and thus the amplitude of the signal pulse is proportional to the energy deposited by the incident radiation. Therefore, an important set of measurement systems are based on recording not only the number of pulses but also their distribution in amplitude. They are known as spectroscopy systems, and their main application is to determine the energy distribution of the radiation that is incident on the detector.

In spectroscopy systems the objective is to sort each pulse according to its amplitude. Every pulse from the linear amplifier is sorted into one of a large number of bins or channels. Each channel corresponds to signal pulses of a specific narrow amplitude range. As the pulses are sorted into the channels matching their amplitude, a pulse-height spectrum is accumulated that, after a given measurement time, might resemble the example given in Figure 3. In this spectrum, peaks correspond to those pulse amplitudes around which many events occur. Because pulse amplitude is related to deposited energy, such peaks often correspond to radiation of a fixed energy recorded by the detector. By noting the position and intensity of peaks recorded in the pulse-height spectrum, it is often possible to interpret spectroscopy measurements in terms of the energy and intensity of the incident radiation.

This pulse-height spectrum is recorded by sending the pulses to a multichannel analyzer, where the pulses are electronically sorted out according to their amplitude to produce the type of spectrum illustrated in Figure 3. Ideally, every incoming pulse is sorted into one of the channels of the multichannel analyzer. Therefore, when the measurement is completed, the sum of all the counts that have been recorded in the channels equals the total number of pulses produced by the detector over the measurement period. In order to maintain this correspondence at high counting rates, corrections must be applied to account for the dead time of the recording system or the pileup of two pulses spaced so closely in time that they appear to be only one pulse to the multichannel analyzer.

One important property of spectroscopy systems is the energy resolution. This concept is most easily illustrated by assuming that the detector is exposed to radiation quanta of a single fixed energy. (A radioisotope emitting a single gamma-ray energy in its decay comes very close to this ideal.) Many radiation quanta then deposit the same energy in the detector and ideally should produce exactly the same charge Q. Therefore, a number of pulses of precisely the same amplitude should be presented to the multichannel analyzer, and they all should be stored in a single channel. In actual systems, however, some fluctuations are observed in the amplitude of these pulses, and they are actually spread out over a number of channels in the spectrum, as illustrated in Figure 4. A formal definition of energy resolution is shown in the figure, expressed as the ratio of the full-width-at-half-maximum (FWHM) of the peak divided by the centroid position of the peak. This ratio is normally expressed as a percentage, and small values correspond to narrow peaks and good energy resolution. If the incident radiation consists of multiple discreet energies, good energy resolution will help in separating the resulting peaks in the recorded pulse-height spectrum.

Some potential causes of fluctuations that broaden the peaks include drifts in the detector-operating parameters over the course of the measurement, random fluctuations introduced by the noise in the pulse-processing electronics, and statistical fluctuations due to the fact that the charge Q consists of a finite number of charge carriers. This latter statistical limit is in some ways the most fundamental determinant in energy resolution since, as opposed to the other sources of fluctuation, it cannot be reduced by more careful experimental procedures. Poisson statistics predicts that the fractional standard deviation that characterizes these fluctuations about the average number of charge carriers N should scale as 1/Square root of√N. Therefore, detectors that produce the largest number of carriers per pulse show the best energy resolution. For example, the charge Q from a scintillation detector normally consists of photoelectrons in a photomultiplier tube. The average number produced by a 1-MeV particle is normally no more than a few thousand, and the observed energy resolution is typically 5–10 percent. In contrast, the same particle would produce several hundred thousand electron-hole pairs in a semiconductor, and the energy resolution is improved to a few tenths of a percent.