Determination of Detector Efficiency

The efficiency of a detector can be determined either by measurement or by calculation. Many methods have been used for the measurement of detection efficiency, but the simplest and probably the most accurate is the method of using a calibrated source, i.e., a source of known strength. In Fig. 8.19, assume that the source is a monoenergetic point isotropic source emitting S particles per second. If the true net counting rate is r counts per second, the solid angle is D, and the efficiency is e, the equation giving the efficiency is 

Accurate absolute measurements rely on measured rather than calculated efficiencies. Nevertheless, an efficiency calculation is instructive because it brings forward the parameters that are important for this concept. For this reason, two cases of efficiency calculation for a photon detector are presented below. 

Consider first a parallel beam of photons of energy E impinging upon a detector of thickness L (Fig. 8.20). The probability that a photon will have at least one interaction in the detector is 1 — e where fiiE) is the total 

Example 8.3 What is the efficiency of a 50-mm-long Nal(Tl) crystal for a parallel beam of (a) 2-MeV gammas or (b) 0.5-MeV gammas  

The next case to consider is that of a point isotropic monoenergetic source, at a distance d away from a cylindrical detector of length L and radius R (see Fig. 8.21). For photons emitted at an angle 0, measured from the axis of the detector, the probability of interaction is 1 — exp[ —/u,( )r(0)] and the probability of emission between angles 0 and 0 -I- is sin 0 d0. Assuming, as before, that one interaction is enough to produce a detectable pulse, the efficiency is given by 

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