Contrast transfer and resolution limits for sub-angstrom high-resolution transmission electron microscopy

The optimum imaging of an object structure at the sub-angstrom length scale requires precise adjustment of the lens aberrations of a high-resolution instrument up to the fifth order. A least-squares optimization of defocus aberration C-1, third-order spherical aberration C-3, and fifth-order spherical aberration C-5 yields two sets of aberration coefficients for strong phase contrast up to the information limit: one for variable C-1 and C-3, at fixed C-5, another for variable C-1, C-3, and C-5. An additional correction to the defocus aberration, dependent on object thickness, is described, which becomes important for the use of image simulation programs in predicting optimum high-resolution contrast from thin objects at the sub-angstrom scale. For instruments with a sub-angstrom information limit the ultimate structure resolution, the power to resolve adjacent atom columns in a crystalline object, depends on both the instrumental pointspread and an object pointspread due to finite width of the atomic column potentials. A simulation study on a simple double-column model yields a range for structure resolutions, dependent on the atomic scattering power, from 0.070 nm down to 0.059 nm, for a hypothetical 300-kV instrument with an information limit of 0.050 nm.