In any microscopy or spectroscopy, quantitative analysis of data requires some knowledge of the instrumental resolution function. Analysis in fact often involves image deconvolution, at least implicitly. However, for scanning tunneling microscopy (STM), the very definition of resolution becomes problematic and has until now been addressed only for metals, the simplest case. Here a natural general expression for the resolution of STM is developed. This definition gives a resolution function which may be strongly sample dependent in the case of semiconductors or semimetals, and which has an anomalous line shape and linewidth in certain cases. Thus image deconvolution is not generally possible, even in principle, without an understanding of the sample electronic structure. © 1989 The American Physical Society.