Imaging of Single Atoms with the Electron Microscope by Phase Contrast

Abstract

Calculations have been made on image contrast by computing the Kirchhoff diffraction integral assuming the amplitudes of elastic scattering from single atoms and linear chains of atoms given by the first Born approximation using either the Hartree-Fock or Thomas-Fermi atomic models. Phase shifts occur due to diffraction, spherical aberration, and defocusing which can be optimized by suitable choices of defocus and aperture size. Balancing of phase shifts due to defocus and spherical aberration produces a relatively uniform phase shift over a considerable part of the objective aperture and allows maximum contrast in the image which does not depend critically on atomic spacing. For atoms with Z>10 image contrasts of at least 5%−10% are indicated with presently available objective lenses. Resolutions down to ∼2.5 Å may be achieved at 100 kV and as low as ∼1.5 Å at 750 kV if spherical aberration sets the ultimate limit.