“…To see the effect when this is not the case, we introduce the rate of oversampling, , to denote the ratio of the magnified geometric resolution to the intrinsic resolution, defined as (22) In combination with (1) we obtain (23) Inserting this expression in (19), we find that, for a fixed rate of oversampling, the upper bound of the sensitivity is reduced with a factor of resulting in (24) For example, a rate of oversampling of reduces the maximum sensitivity with a factor of 0.5, with a factor of 0.8, with a factor of 0.9, and so on. Another study, [25], concurrent with ours, derives the maximum sensitivity while incorporating the effects of penetration in the pinhole knife edge, in the context of brain SPECT. Through an approximation using a first-order Taylor expansion they identify two regimes, one for low-resolution and one for high-resolution detectors.…”