Field-ion techniques have been used to create physical point sources for ions and electrons with emission areas and angles orders of magnitude smaller than in any other available source. The monatomic pyramidal tips emit electrons or ionize noble-gas atoms originating from the single front atom. The angular divergence from the normal direction above the single W atom is less than 0.5° for ion beams produced by field ionization. The angular spread for emission from small clusters is somewhat larger for field ionization and electron emission. By employing tips as sources for free electrons in an STM-like setup, we were able to obtain high-resolution images of surfaces with an electron beam of only 15 eV primary energy. The image information is contained in the yield of the secondary electrons created at the sample surface.