In this paper, we demonstrate that the shift between similar features in two electron backscatter diffraction (EBSD) patterns can be measured using cross-correlation based methods to +/- 0.05 pixels. For a scintillator screen positioned to capture the usual large solid angle employed in EBSD orientation mapping this shift corresponds to only approximately 8.5 x 10(-5)rad at the pattern centre. For wide-angled EBSD patterns, the variation in the entire strain and rotation tensor can be determined from single patterns. Repeated measurements of small rotations applied to a single-crystal sample, determined using the shifts at four widely separated parts of the EBSD patterns, showed a standard deviation of 1.3 x 10(-4) averaged over components of the displacement gradient tensor. Variations in strains and rotations were measured across the interface in a cross-sectioned Si1-x Gex epilayer on a Si substrate. Expansion of the epilayer close to the section surface is accommodated by tensile strains and lattice curvature that extend a considerable distance into the substrate. Smaller and more localised shear strains are observed close to the substrate-layer interface. EBSD provides an impressive and unique combination of high strain sensitivity, high spatial resolution and ease of use.