Paralyzable and nonparalyzable deadtime analysis in spatial photon counting

Inherent in particle and photon-counting systems is a deadtime period that affects the measured counting distribution. The effects of deadtime on counting distributions in single-channel detectors have been extensively studied. These results, however, are not generally applicable to two-dimensional detectors which measure both spatial and temporal photon event coordinates. Deadtime is attributed to the finite recovery characteristics (which include adjacency effects) in the microchannel plate intensifier part of the system and this process is modeled by introducing concepts of a temporal deadtime extending over a rigid or variable spatial dead area. Novel theoretical analyses are presented to predict the effect of paralyzable and nonparalyzable deadtime on the reduced mean count rate in a 2D imaging array. In the limits where the system resembles a one-dimensional detector, the analytic expressions agree exactly with previously published results. The accuracy of the analyses is examined by comparison with computer simulations. The paralyzable analysis is shown to be accurate at all count rates. The accuracy of the nonparalyzable analysis is excellent over count rates relevant in practical situations, but is in general count rate dependent. An inversion procedure is proposed which is applicable to both the paralyzable and nonparalyzable cases. This procedure allows an ‘‘ideal’’ incident image to be estimated by correcting for deadtime losses in the ‘‘measured’’ image. Computer results are presented which demonstrate the effectiveness of this inversion method and thus illustrate an important practical application of the work.