Coincidence detection true coincidences

FIGURE 11 Principle of coincidence detection. True coincidence (solid line), random coincidence (dashed line), and scattered coincidence (broken line) are indicated. 

The residence time was determined for our neutron counter by measuring the time intervals between beta start signals and neutron stop signals. With a residence half-time of 11 ms and a coincidence resolving time of 40 ms. 92 of the true coincidence events were included. The fraction of true events not detected does not influence the present results because we normalize the Pn measurements to a known Pn value measured under identical conditions. The coincidence rate was measured by a simple overlap coincidence module where the beta pulse Input was stretched to 40 ms by a gate and delay generator. To measure the accidental coincidence rate, the same beta pulse was sent to a second coincidence module and overlapped with neutron pulses which had been delayed 45 ms. After correcting each coincidence rate for deadtime effects, the difference was the true coincidence rate. 

The observed intensity C(Ka, Kb) of true coincidences is then characterized by the settings of both spectrometers at Ka = a, a and Kb = b, detection efficiencies, the intensity C(Ka, Kb) then follows from an integration over the corresponding acceptance angles ... 

Figure 3.1. (a) True coincidence events (b) Random coincidence events detected by two detectors connected in coincidence along the dotted line. The two 511-keV photons originated from different positron annihilations, (c) Scattered coincidence events. Two scattered photons with little loss of energy originating from two annihilation events may fall within PHA window and also within coincidence time window to be detected as a coincidence event by two detectors. 

TRUE COINCIDENCE SUMMING (TCS) The simultaneous detection of two or more photons originating from a single nuclear disintegration that results in only one observed (summed) peak. This results in loss of counts from peaks leading to efficiency calibration errors. (See Chapter 8.)... 

Although the raw efficiency, or number of true coincidences acquired, is a basic determinant of the quality of a PET scanner, the complicating factors of scattered and random events and dead time have to be brought into the analysis. Details of the distribution of scattered events and correction methods can be found elsewhere, but for the present purposes it can be stated that scattered radiation (or scatter for short) produces a relatively flat background on the projection and image data, impairing contrast and reducing quantitative accuracy. The quantity of scatter detected, the scatter fraction (SF), is expressed simply in terms of the total true (unscattered -i- scattered) events (Tj j) and the scattered events S) by... 

The photomultipliers feed the coincidence-counting electronics, that includes a time-to-amplitude converter and a multichannel analyzer, yielding the time-delay spectrum of the two-photon detections (Fig. 11). This spectrum involves a flat background due to accidental coincidences (i.e. between photons emitted by different atoms). True coincidences yield a peak around the null-delay, with an exponential decrease (time constant t ). 

True coincidence Event detected in coincidence without scatter of either photon, generated from an annihilated positron, in the object. 

Hi. Sensitivity. Sensitivity in PET is defined as the capability of detecting the true coincidences (solid line. Fig. 11) with a given amount of radioactivity. Sensitivity has traditionally been measured with a phantom of diameter d = 20 cm, filled with a uniform activity concentration p (/u.Ci/cm ) (1/LrCi = 37,000 disintegrations per second). By considering several factors, including the activity in the field of view, the self-attenuation of y rays within the phantom, the solid angle subtended by the detector array, and the detection efficiency of the array, an empirical formula for sensitivity measure is derived and given by... 

Figure 2.4(a) shows normal error curves (B and S) with true means / and ns for blank and sample measurements respectively. It is assumed that for measurements made close to the limit of detection, the standard deviations of the blank and sample are the same, i.e. aB = a% — a. In most cases, a 95 % confidence level is a realistic basis for deciding if a given response arises from the presence of the analyte or not, i.e. there is a 5% risk in reporting the analyte detected when it is not present and vice versa. Thus, point L on curve B represents an upper limit above which only 5% of blank measure-mentswith true mean /tD will lie whilst point L on curve S represents a lower limit below which only 5% of sample measurements with true mean //s will lie. If /is now approaches /iB until points L on each curve coincide (figure... 

Coincidence events detected by two detectors within the time window are termed prompt events. The prompts include true, random, and scatter coincidence events. In many PET systems, in an attempt to eliminate random and scatter photons discussed later, annular septa ( -1 mm thick and radial width... 

More recently cyclic acetal-styrene systems were reinvestigated by the GPC technique 154,155). Using double detection (UV and RI), Yamashita et al. showed that products of copolymerization of styrene with tri- and tetraethylene glycol formals have a unimodal molecular weight distribution, and that the maxima of both RI and UV traces coincide indicating that the products are true copolymers. 

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