An image processing approach to crystal structure determination

Abstract

An approach to crystal structure determination based on a single high-resolution electron microscope image and the corresponding electron diffraction pattern is introduced. The procedure contains two parts — image deconvolution and image resolution enhancement. The first part is to transform the image taken at an arbitrary defocused condition into the structural image by image deconvolution. The resolution of the deconvoluted image is limited by the resolution of the electron microscope so that only part of the atoms can be seen. The second part is to enhance the resolution of the deconvoluted image to about 1 Å so that all non-overlapped atoms can be resolved. The principle of the method is briefly described and the application to a conventional crystal structure and an incommensurate modulated structure is demonstrated. Since the principle is based on the weak phase object approximation, the validity of the latter is discussed by means of an approximate image contrast theory — pseudo weak phase object approximation — before the principle of the method is introduced.