[en] We have characterized the effects of crystal penetration by annihilation photons in circular ring positron tomographs. They are most serious in high resolution instruments having small detectors. When annihilation photons are not normally incident and penetrate some distance into the scintillator before interacting, the measurement of their transverse position becomes uncertain. This penetration of photons into the detector material before interaction is a statistical process which leads to significant displacement and anisotropy of the point spread function. The subject of this work is mathematical correction of emission datasets by performing a two-dimensional spatially variant deconvolution of the emission data in sinogram format. Examples for the Donner 600-Crystal Positron Tomograph are presented, and the amplification of statistical errors resulting from the correction procedure is also discussed. 7 refs., 9 figs., 2 tabs