Atomic level characterization based on focus modulation electron microscopy

Defocus image modulation processing and three-dimensional Fourier filtering methods are compared from the viewpoint of application to high-resolution phase transmission electron microscopy. Both methods can successfully correct the spherical aberration in TEM by image processing using through-focus images resulting in resolution improvement from the Scherzer resolution limit to the information limit. Comparing the processed images demonstrates that the potential to determine localized atomic structures between the two methods is at the same level when the sample thickness is thin. However, the achieved signal-to-noise ratio is better in images processed by the three-dimensional Fourier filtering method because the filtering process in Fourier space effectively reduces quantum noises involved in the original images. Spherical aberration-free phase observation by the latter method clearly shows the existence of individual gadolinium atoms in C-82 molecules encapsulated in single wall carbon nanotubes. It is demonstrated that the three-dimensional Fourier filtering method works effectively for atomic level characterization even when a sample consisting of light atoms is observed under the condition of a low electron dose.