The application of electron channelling theory to dynamical exit wave calculations is briefly reviewed, and a comparison of channelling results with full dynamical calculations is presented. The channelling expression to the exit wave is combined with conventional imaging theory, and it is shown that a simple expression can be obtained for a dynamical contrast transfer function (D-CTF), which incorporates imaging aberrations and thickness-dependent dynamical scattering effects. The D-CTF can provide detailed insight into HREM images of a mixed cation oxide at thicknesses up to 200 Å, whereby an approximate correction for non-linear effects is utilized in the larger thickness regime.