Analytic determination of the pinhole collimator's point-spread function and RMS resolution with penetration

Pinhole collimators are widely used to image small organs and animals. The pinhole response function (PRF) of knife-edge pinhole collimators has been estimated previously using geometric constructions without considering penetration and using "roll-off" models that employ an exponential model for the flux. An analytic expression for the PRF on the imaging plane that includes the effect of aperture penetration is derived in this paper by calculating the flux for photons passing through the aperture and those passing through the attenuating material. The PRF is then used to approximate the angular-dependent root-mean-square resolution in the directions parallel and perpendicular to the tilt of the point source. The corresponding aspect ratio is then obtained. The formulas are then compared with experimental data.