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This paper shows that it is possible markedly to improve the resolution obtainable in electron micrographs by deliberately using low beam divergence (2 x 10 -4 rad) and by minimizing thermal spread in the electron gun. Point-to-point resolutions in the sub-3 A range will be illustrated for the hollandite structure. Image matching, including the effects of both beam divergence and chromatic aberration, showed that the experimental images could be fitted using 2 A objective aperture, with no divergence and defocus ripple of only 50 ,~. In fact, these stringent experimental requirements must be met if useful structural information is to be obtained in the 2-3 A range.

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