title: Theoretical discussions on the geometrical phase analysis.
abstract: The Geometrical phase analysis, which is a very efficient method to measure deformation from High resolution transmission electron microscopy images, is studied from a theoretical point of view. We point out that the basic property of this method is its ability to measure local reciprocal lattice parameters with a high level of accuracy. We attempt to provide some insights into (a) different formula used in the geometrical phase analysis such as the well-known relation between phase and displacement: Pg(r)=-2pi g.u(r), (b) the two different definitions of strain, each of which corresponding to a different lattice reference and (c) the meaning of a continuous displacement in a dot-like high resolution image. The case of one-dimensional analysis is also presented. Finally, we show that the method is able to give the position of the dot that is nearest to a given pixel in the image.
authors.affiliation: CEA-Grenoble, Département de Recherche Fondamentale sur la Matière Condensée, SP2M, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France. rouvierej@cea.fr
authors.forename: J L
authors.initials: JL
authors.lastname: Rouvière
authors.forename: E
authors.initials: E
authors.lastname: Sarigiannidou