A method for improving the resolution of STEM images of thick samples. In STEM, the diameter of the cross-over depends on the opening half-angle .alpha. of the beam and can be as low as 0.1 nm. For optimum resolution an opening half-angle is chosen at which the diameter of the cross-over R(.alpha.) shows a minimum. For thick samples the resolution is, for those parts of the sample removed from the cross-over plane, limited by the convergence of the beam, resulting in a diameter D of the beam at the surface of the sample. The opening angle is chosen to balance the contribution of convergence and of diameter of the cross-over by choosing an opening half-angle smaller than the optimum opening half-angle. Effectively the sample is then scanned with a beam that has a substantially constant diameter over the length of the sample material through which the electrons have to travel.