Counting loss

The crystal of the Ge(Li) detector was 35 mm in diameter and 27 mm long. It had a nominal active volume of 20 cm3 and resolutions of the 1332.5 keV photons of 2.18 (full width—half maximum) and 4.09 keV (full width—0.1 maximum). Counting losses at 20% dead time were about 6%. 

What is the maximum allowed counting rate with a scintillation detector with a 0.25-p,s dead time if you can only tolerate a 3% counting loss ... 

The pulser pulses are generated at a constant frequency, so that the variance of the pulser peak area that results from the statistical nature of spectrum acquisition is approximated at counting losses well below 50% by... 

At low count rates the relative uncertainty of the pulser peak area in 1-day measurements remains below 10 3. At counting losses of 30% and at acquisition times of 1 h the relative uncertainty of the counting time does not exceed 1%. To cover the possible influence of systematic effects on the effective duration of the effective acquisition time originating in different counting conditions, a 1% uncertainty is included in the uncertainty budget at count rates exceeding 5000 s1. 

Although it is common practice to calibrate the Coulter Counter using a standard powder, it is possible to calibrate the instrument with the powder being examined. This is the preferred British Standard method [17]. It is reiterated that this procedure cannot be carried out with some instruments due to count loss. Essentially one balances the volume of particles passing through the measuring aperture with the known volume in the measurement sample. This serves a multiple purpose in that ... 

The classical method of 4ji p counting with a 4jt gas flow proportional counter is still useful for the absolute measurements of P-emitting nuclides provided that good sources with small self-absorption can be prepared. From the observed counting rate, after fundamental corrections for background and counting loss due to dead time, the radioactivity, n, can be calculated as... 

Fig. 7-10 The effect of counting rate on counting losses for three kinds of counter (schematic).

All counters have a thin window, usually of mica or beryllium, through which the x-rays must pass before reaching the active volume of the counter. The fraction of the incident radiation absorbed by the window/ bs, should be as small as possible, and the fraction absorbed by the counter itself /abs.c as large as possible. The absorption efficiency abs> expressed as a fraction, is given by 0 -/abs.wX/abs.c)- The dctcction efficiency is simply (1 -/, sses). where /losses represents the fractional counting losses described above. The overall efficiency is then... 

The counting rate varies linearly with x-ray intensity up to rates of about 5,000-10,000 cps. Counting losses in the counter-electronics system occur in the electronics rather than the counter. The electronics are more complex than usual and include, besides the usual pulse amplifiers and shapers, a multichannel pulse-height analyzer (Sec. 7-9). 

According to NEMA NU 2-2001 and NEMA NU 2-2007 standards, a 70-cm-long plastic tube filled with a known amount (Acai) of a radionuclide is used (Fig. 6.3c, d) (Daube-Witherspoon et al, 2002). The level of activity is kept low so as to have random rate less than 5% of the true counts and count loss less than 1%. The source is encased in metal sleeves of various thicknesses and suspended at the center of the transverse FOV in parallel to the axis of the scanner in such a way that the supporting unit stays outside the FOV. 

The percent dead time count loss (%DT) as function of activity is calculated by... 

This is determined by both the absorption efficiency and the noise, if present, in the detector. The absorption or quantum efficiency of a detector is the fraction of photons absorbed in the active region of the detector. The factor should also be multiplied by a loss factor associated with any losses of photons in an entrance window or inactive layer. For a pure photon counter, in the absence of counting losses, these effects are the only ones of interest because the detector does not introduce any noise. 

This derivation ignores the possibility of more than two pulses piling up and is therefore applicable only when the counting losses are not too high. 

Because of counter dead time, the possibility exists that some particles will not be recorded since the counter will not produce pulses for them. Pulses will not be produced because the counter will be occupied with the formation of the signal generated by particles arriving earlier. The counting loss of particles is particularly important in the case of high counting rates. Obviously, the observed counting rate should be corrected for the loss of counts due to counter dead time. The rest of this section presents the method for correction as well as a method for the measurement of the dead time. 

Of course, the multidetector technique does not increase the maximum throughput rate of a TCSPC system. In any TCSPC device there is a small but noticeable loss of photons due to the dead time" of the processing electronics. The dead time of advanced TCSPC devices is of the order of 100 ns, and for count rates above 1 MHz the counting loss becomes noticeable (see Sect 7.9, page 332). The counting loss for a multidetector TCSPC system is the same as for a single detector system operated at the total count rate of the detectors of a multidetector system. 

An important and sometimes confusing feature of the multidetector technique is that the relative counting loss is the same for all channels, independent of the distribution of the rates over the detectors. The reason is that the photons detected by all detectors are processed by the same TCSPC channel so that the counting loss depends on the overall count rate. However, the photons appear randomly in the particular detector channels. Therefore the dead time caused by a detection event in one detector on average causes the same relative loss for all detector... 

The maximum count rate of a single TCSPC channel is limited not only by the counting loss due to the dead time of the TCSPC channel, but also by pile-up effects and the counting capability of the detector. 

Compared with classic systems, the dead time of advanced TCSPC systems has been considerably reduced. It is however, still on the order of 100 to 150 ns. The fraction of photons lost in the dead time - the counting loss - becomes noticeable at detector count rates higher than 10% of the reciprocal dead time (see Sect. 7.9.2, page 338). The counting loss can be compensated for by a dead-time-compensated acquisition time. Therefore, often a relatively high loss can be tolerated. The practical limit is the maximum useful" count rate, which is defined as the recorded rate at which 50% of the photons are lost. For currently available TCSPC modules, the maximum useful count rate ranges from 3 to 5 MHz, corresponding to a detector count rate from 6 to 10 MHz. 

The recorded intensities may also be changed by possible counting loss in the TCSPC module. If and are measured consecutively, a count rate of a few percent of the reciprocal dead time should not be exceeded, or dead-time compensation should be used (see Sect. 7.9.2, page 338). Moreover, often a different IRF of both channels has to be taken into account. 

The sample (usually a cuvette) is measured from both sides under different polarisation angles. Two detectors and a router are used to detect Ip and L simultaneously [58, 59]. The T geometry with routed detection has twice the efficiency of a sequential measurement. Moreover, possible counting loss due to the dead time of the TCSPC module affects both channels in the same way and therefore does not affect the measured intensity ratio. The dual-detector routing technique is even able to record dynamic changes of the lifetime and depolarisation time. The drawback is that the instrument response functions of the two detectors are different,... 

For the results shown below, a Becker Hickl BHL-600 laser module was used, with a wavelength of 650 nm, 80 ps pulse duration, and 50 MHz repetition rate. The incident power density at the surface of the leaf was approximately 1 mW/mm. The measurement wavelength was selected by a 700 15 nm bandpass filter. The fluoreseenee deeay curves were recorded in one TCSPC channel of a Beeker Hickl SPC-134 system. One fluorescence decay curve was recorded eaeh 2 seconds, at a count rate of about 2-10 s Dead time compensation was used to avoid the influenee of counting loss on the recorded intensity. Typical results are shown in Fig. 5.32. 

It should be noted that the a count rate of 4.510 s is close to the limit of a single channel in currently available TCSPC devices. Intensity measurements at rates this high require a correction for counting loss (see Sect. 7.9.2, page 338). The moments of the time-of-flight distributions are not influenced by eounting loss. Certainly, there is a small pulse-shape error due to classic pile-up. However, because only small changes in the moments are of interest, the pile-up-error is not substantial. 

---