  At radio wavelengths, scattering in the interstellar medium distorts the
appearance of astronomical sources. Averaged over a scattering ensemble, the
result is a blurred image of the source. However, Narayan & Goodman (1989) and
Goodman & Narayan (1989) showed that for an incomplete average, scattering
introduces refractive substructure in the image of a point source that is both
persistent and wideband. We show that this substructure is quenched but not
smoothed by an extended source. As a result, when the scatter-broadening is
comparable to or exceeds the unscattered source size, the scattering can
introduce spurious compact features into images. In addition, we derive
efficient strategies to numerically compute realistic scattered images, and we
present characteristic examples from simulations. Our results show that
refractive substructure is an important consideration for ongoing missions at
the highest angular resolutions, and we discuss specific implications for
RadioAstron and the Event Horizon Telescope.
