Determination of the analytical point spread function of a pinhole aperture SPECT system

Pinhole aperture in single photon emission computed tomography (SPECT) imaging system provides high spatial resolution for quantitative measurement. In this paper, we propose a new analytical method to calculate the PSF of a pinhole SPECT system where the response of the crystal is taken into account. The PSF is calculated as the convolution of the pinhole and the crystal responses. A general method to calculate the pinhole response is introduced using a decomposition of the pinhole geometry in single mathematical elements. The crystal response is derived analytically using the distribution of the optical photons on the photodetector surface. As a conclusion, both the pinhole response and the optical distribution give similar results compared to the one obtained with Monte Carlo simulation for a reduced computing time.