  We describe a lattice-based crystallographic approximation for the analysis
of distorted crystal structures via Electron Backscatter Diffraction (EBSD) in
the scanning electron microscope. EBSD patterns are closely linked to local
lattice parameter ratios via Kikuchi bands that indicate geometrical lattice
plane projections. Based on the transformation properties of points and lines
in the real projective plane, we can obtain continuous estimations of the local
lattice distortion based on projectively transformed Kikuchi diffraction
simulations for a reference structure. By quantitative image matching to a
projective transformation model of the lattice distortion in the full solid
angle of possible scattering directions, we enforce a crystallographically
consistent approximation in the fitting procedure of distorted simulations to
the experimentally observed diffraction patterns. As an application example, we
map the locally varying tetragonality in martensite grains of steel.
