In this paper, we use a Bloch wave approach to show that the elastically scattered electrons from neighbouring atomic columns in a zone-axis oriented crystal contribute incoherently to a Z-contrast image regardless of the fact that we have coherent dynamical scattering from a stationary lattice with no absorption. This incoherent nature of the elastic scattering means that through the filtering of the ls-type Bloch states by the detector geometry we approach the Rutherford Z2 dependence of the column intensity for sufficiently large inner detector angle. Thus, annular dark-field (ADF) imaging provides us with a direct incoherent structure image of the atomic-column positions in a zone-axis oriented crystal.

Bloch wave simulations were carried out at 300 kV for the 〈110〉 orientation of InAs (a = 6.06Å) with full, half and empty columns of In atoms. Calculations including 411-beams were carried out for each of the above structural configurations for a single incident partial plane wave vector parallel to the optic axis.