The Reconstruction of Displacement Fields of Defects in Crystals from Electron Micrographs. I. Analytic Fields

Abstract

The following theorem and corollaries are proved. If the two-beam column approximation theory of electron microscope image formation is assumed and if the displacement field of the object is analytic with zero derivative at infinity, and such that there is a direction in the object along which displacements are constant, then from an electron micrograph that records intensities but no phase information there is an explicit and unique reconstruction of the component of the displacement field of the object in the direction of the diffracting vector, except possibly in some specified singular cases for which the reconstruction cannot be started uniquely.