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 C1, third-order spherical aberration C3, and fifth-order spherical aberration C5 yields two sets of aberration coefficients for strong phase contrast up to the information limit: one for variable C1 and C3, at fixed C5, another for variable C1, C3, and C5. 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.