The structure of twin walls and their interaction with defects has important implications for the behaviour of a variety of materials including ferroelectric, ferroelastic, co-elastic and superconducting crystals. Here, we present a method for investigating the structure of twin walls with nanometre-scale resolution. In this method, the surface topography measured using atomic force microscopy is compared with candidate displacement fields, and this allows for the determination of the twin-wall thickness and other structural features. Moreover, analysis of both complete area images and individual line-scan profiles provides essential information about local mechanisms of twin-wall broadening, which cannot be obtained by existing experimental methods. The method is demonstrated in the ferroelectric material PbTiO3, and it is shown that the accumulation of point defects is responsible for significant broadening of the twin walls. Such defects are of interest because they contribute to the twin-wall kinetics and hysteresis.