Analytic determination of rectangular-pinhole sensitivity with penetration

Modern small-animal SPECT systems use multiple pinhole apertures per detector to obtain high sensitivity while still maintaining high resolution. This resolution is a combination of aperture resolution combined with detector resolution, which is mitigated by magnification. Higher magnification results in better resolution, but fewer apertures per detector. When multiple apertures project onto the same detector, apertures with a rectangular field of view (FOV) can be packed more tightly than circular apertures. In addition, a rectangular aperture can be used to obtain different resolution-sensitivity tradeoffs in the two orthogonal directions. Thus, these apertures can have independent FOVs and independent resolution values in the two directions of the rectangular aperture. Previous work has determined the amount of penetration for circular apertures, where the pinhole walls were modeled as cones. In this work, a formula for the penetrative sensitivity for rectangular apertures with a rectangular FOV was determined. The formula was vali- dated using numerical calculations for numerous combinations of acceptance angles, aperture sizes, linear attenuation coefficients, and incidence angles.