Structure reconstruction with Ewald sphere curvature considerations

Abstract

An approach is proposed to determine the structure of a three-dimensional non-crystallineobject from a single two-dimensional x-ray scattering image. If x-ray absorption is ignored,this method, unlike what has been reported in the literature, always generates a structureof real electron density, even in the case that the Ewald sphere curvature is large. Inaddition, if the original object is thin, the reconstructed object is the integrated electrondensity of the original one along a path which makes an angle with the incoming x-rays(z-axis) in proportion to the maximum x-ray wavevector transfer magnitude along the axis,revealing the object’s depth information. It is demonstrated mathematically that the blursor ripples associated with a reconstructed object are due to a resolution function effect.Reconstructed structures of a hypothetical three-dimensional object are shown to agreewith the theoretical predictions.