The point spread function (PSF) of a ring PET tomograph is known to be spatially variant and difficult to obtain because it must be reconstructed from projections. A mathematical model was developed to simulate the data acquisition from a point source and to reconstruct the PSF, taking into account weighting functions to describe the detector response functions. In order to investigate the effect of the detector weighting function on the PSF, the reconstruction, based on the filtered backprojection algorithm, was implemented with three classes of weighting functions of decreasing complexity: exact, locally invariant, and constant. Significant differences are observed to result from the three hypotheses, and this is shown to lead to distorted PSFs and to erroneous estimates of the intrinsic resolution off the center of the tomograph.