The geometric transfer function for a slat collimator mounted on a strip detector

A theoretical formulation of the effective point spread function of a slat collimator on a strip detector has been derived. The used technique to obtain the geometric transfer function, which is the Fourier transform of the effective point source image, is based on the geometric characteristics of a single gap and it accurately describes the performance of the collimation system for system analysis. Valuable conclusions resulting from this geometric transfer function could be made on the sensitivity, on the spatial resolution, and on the line spread function of the imaging system. We found that the sensitivity was dependent on the angle of incidence and on the distance to the detector. The spatial resolution was constant in a plane at a fixed distance to the detector and closed analytical expressions were derived for transaxial line spread profiles. These results were confirmed by the appropriate Monte Carlo simulations. The presented formulation of the geometric transfer function will be useful with usage in iterative reconstruction algorithms to incorporate distance dependent effects.