Wave field restoration using three-dimensional Fourier filtering method

A wave field restoration method in transmission electron microscopy (TEM) was mathematically derived based on a three-dimensional (3D) image formation theory. Wave field restoration using this method together with spherical aberration correction was experimentally confirmed in through-focus images of amorphous tungsten thin film, and the resolution of the reconstructed phase image was successfully improved from the Scherzer resolution limit to the information limit. In an application of this method to a crystalline sample, the surface structure of Au(1 1 0) was observed in a profile-imaging mode. The processed phase image showed quantitatively the atomic relaxation of the topmost layer.