Real-space analysis of lattice images and its link to conventional theory

We show that real-space analysis of lattice images in terms of multidimensional vectors rests on a small number of physically significant dimensions, each representing the contribution of a characteristic pattern forming a basis vector. In many cases, these basis vectors can be linked to 'spatial periodicities', and expressed in terms of conventional formalisms of dynamical scattering. This provides a link between the more abstract (but convenient) real-space image analysis and the more familiar formalisms of image formation in terms of Bloch waves. Within this framework, the simplest implementations of QUANTITEM and Chemical Mapping may be viewed as limiting cases of a more general approach. This helps delineate the application domain for each. The paper is illustrated by reference to the A1(x)Ga₁-(x)As system in the <1 0 0>, <1 1 0> and <1 1 1> projections. The historically popular <1 1 0> projection is shown to be the most complex for quantitative data extraction.