On the phase-object function, used in dynamical electron diffraction calculations

Abstract

A systematic study is presented of methods employed to calculate a phase-object function which can be used in HRTEM image calculations (multislice and real space). The influence of errors introduced by the discrete sampling of the crystal potential and the electron beam wavefunction is examined. Several possible ways of suppressing these errors are quantitatively tested. Using an anti-aliased phase-object function in a dynamical calculation improves the accuracy considerably for a given number of calculation points. The calculation of an anti-aliased phase-object function is very time-consuming, which will become a problem when there is a structural variation in the direction of the electron beam, and the calculation has to be done for each slice. Two new methods are presented for calculating anti-aliased phase-object functions. One, which applies the anti-aliasing a priori to the individual atoms, is quite generally applicable but some accuracy is lost. The other, which applies anti-aliasing a priori to rectangular building blocks, is not so general in application but is very fast and accurate.