The basis has been explored for the possible application of the various sch
emes that have been proposed for making use of the focusing properties of s
ingle heavy atoms, or rows of atoms extending through thin crystals in axia
l directions, for the attainment of ultra-high resolution in electron micro
scopy. Calculations are reported for the form of 200 keV electron beams cha
nneled along rows of atoms through crystals and propagated in the vacuum be
yond the crystals. The conditions for forming beams less than 0.05 nm in di
ameter have been established. Simulations of images having resolutions of t
his order are reported for the case that the specimen is placed at the Four
ier image position beyond the exit face of a thin crystal and the transmiss
ion of the periodic array of ultra-fine beams, translated laterally by tilt
ing the incident beam, may be observable using a conventional transmission-
electronmicroscopy (TEM) instrument.