We have shown that a scanning transmission electron microscope with a high brightness field emission source is capable of obtaining better than 3 A resolution using 30 to 40 keV electrons. Elastic dark field images of single atoms of uranium and mercury are shown which demonstrate this fact as determined by a modified Rayleigh criterion. Point-to-point micrograph resolution between 2.5 and 3.0 A is found in dark field images of micro-crystallites of uranium and thorium compounds. Furthermore, adequate contrast is available to observe single atoms as light as silver.The ability to obtain high resolution images of very small objects is of considerable importance in the biological and material sciences. The only instrument heretofore available for this purpose has been the conventional transmission electron microscope (CTEM).Invented in the 1930's, the basic design of this instrument is an electron analog of the light microscope. The performance of the CTEM has steadily improved during the last few decades, and it is now limited primarily by diffraction effects and the large aberrations inherent in electromagnetic lenses.For the moment, we will ignore the effects of chromatic aberration. This is justifiable if the electron energy is high enough. Then one can minimize the combined effect of diffraction and spherical aberration to calculate the objective aperture which gives the best instrumental resolution. In this case, a hypothetical point source of scattered electrons in the specimen plane would be imaged as a modified Airy disc whose radius to the first intensity minimum is given by a = 0.43 Cs1/4X" [1] where C, is the coefficient of spherical aberration (generally of the order of 1 mm in high quality objective lenses) and X is the wavelength of the incident electron (0.037 A for 100-keV electrons) (1). The image of two incoherent point objects separated by this distance 6 will have an intensity minimum between them of 0.75 of the peak intensity and will be resolved according to the modified Rayleigh criterion of Scherzer (1). In order to obtain this resolution, the objective aperture should subtend a half-angle at the specimen given by (2) a(pt = (4X/Cs) 1/4.