Noise figure and figure of merit for nuclear-radiation detectors

The measurement of the energy of a nuclear particle by ionisation methods is limited in accuracy by the statistical fluctuations occurring in the detection process, including those in the associated electronic circuits as well as those occurring at the source of the particles. The noise figure defined in this note indicates the relative size of these two sources of fluctuations which limit the energy resolution. The generalised noise-figure definition is as given by Friis. The necessary statistical theorem is derived, which yields the fluctuations in the detection process, assuming a multiplicative process of detection; i.e. each primary particle produces a large number of secondary charge carriers. After adding the effects of the associated electronic circuits, the resulting noise figure FR contains as a figure of merit for nuclear-radiation detectors the excess noise figure FR ¿ 1.