Complex atomic scattering amplitudes calculated by the WKB-method and verified experimentally in earlier work are used to compute the decrease in intensity if imaging single atoms, plane arrays of atoms or atomic monolayers, especially of platinum atoms. By calculating the decrease of intensity in the centre of an atomic image for a large number of different objective apertures α and defocussing parameters Δf one gets a better survey for the limits of optimal underfocus. We used constants of spherical aberration Cö = 0.5, 1, 2 and 4 mm. The energy of the electrons is 100 keV. Some calculations are done up to 1200 keV. The use of complex scattering amplitudes does not justify to distinguish between amplitude and phase contrast. Both limiting cases are obtatined in the used theory. Two platinum atoms in nearest distance can be resolved in the optimal underfocus only for Cö= 0 .5 and 1 mm. But for larger Cö there exists a region at larger α with a much better resolution. These results show that there is a continuous transition from the resolution of an atomic pair up to that of the lattice planes in crystal films. Disks of 7 and 19 atoms in a two-dimensional dense packing are calculated and some deviations in optimal focus are found compared to the results of single atoms. At low α beyond the Bragg angle of the dense packed atomic rows no large difference exist if varying Cö and α. The single atoms are not resolved, but the decrease of intensity should be large enough for observation. Further calculations have been done about the contrast of a mono-atomic layer considering the influence of a vacancy too. The influence of a finite aperture of illumination and the energy distribution of the electrons are considered by folding the results with a distribution like a Gaussian error function.
