Analytic Determination of Rectangular-Pinhole Sensitivity With Penetration

Modern small-animal SPECT systems use multiple pinhole collimators per detector to increase 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 pinhole collimators project onto the same detector, those with a rectangular field of view (FOV) can be packed more tightly than those with a circular FOV. In addition, a rectangular aperture can be used to obtain different resolution-sensitivity tradeoffs in the two orthogonal directions. Thus, these rectangular-pinhole collimators 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 pinholes (i.e., circular apertures with circular FOVs), where the pinhole walls were modeled as cones. In this work, a formula for the penetrative sensitivity for rectangular apertures with a rectangular FOV is determined. The formula was validated using numerical calculations for various combinations of acceptance angles, aperture sizes, linear attenuation coefficients, and incidence angles.