Geometric Phase Analysis of High Resolution Electron Microscope Images

A new method is described for analysing high resolution lattice fringe images. The image is considered to be composed of a reduced set of major image periodicities. Each periodicity has an associated Fourier component which is allowed to vary as a function of position. It is shown that the local amplitude and geometric phase of lattice fringes can be determined in this way by filtering in Fourier space. A direct relationship is then established between the phase and the displacement of lattice fringes, and between the gradient of the phase and the local reciprocal lattice vector. Examples are given illustrating the use of the phase images for analysing variations in structure from high resolution images. The errors in the amplitude and phase measurement induced by noise are estimated and the circumstances under which the lattice fringe positions correspond to atomic plane positions are outlined.