Convolution, deconvolution and small-angle plural electron scattering

A method is given for the evaluation of two-dimensional small-angle folding integrals in the particular case of cylindrical symmetry. The associated problem of deconvolution of scattering patterns with cylindrical symmetry is also considered. The present results are particularly applied to problems in the small-angle scattering of electrons (incident energy range 20 kev-1 Mev). The good accuracy of the method of computation is illustrated by calculating the angular distribution of electrons after ten scattering events using a test first scattering distribution of Gaussian form. The general procedure also allows the correction of the electron scatter patterns for convolution effects due to the finite angular divergence of the incident electron beam and the finite size of the collector aperture.