Crystal lattice image reconstruction from Moiré sampling scanning transmission electron microscopy

A wide range of reconstruction methods exist nowadays to retrieve data from their undersampled acquisition schemes. In the context of Scanning Transmission Electron Microscopy (STEM), compressed sensing methods successfully demonstrated the ability to retrieve crystalline lattice images from undersampled electron micrographs. In this manuscript, an alternative method is proposed based on the principles of Moiré sampling by intentionally generating aliasing artifacts and correcting them afterwards. The interference between the scanning grid of the electron beam raster and the crystalline lattice results in the formation of predictable sets of Moiré fringes (STEM Moiré hologram). Since the aliasing artifacts are simple spatial frequency shifts applied on each crystalline reflection, the crystal lattices can be recovered from the STEM Moiré hologram by reverting the aliasing frequency shifts from the Moiré reflections. Two methods are presented to determine the aliasing shifts for all the resolved crystalline reflections. The first approach is a prior knowledge-based method using information on the spatial frequency distribution of the crystal lattices (a common case in practice). The other option is a multiple sampling approach using different sampling parameters and does not require any prior knowledge. As an example, the Moiré sampling recovery method detailed in this manuscript is applied to retrieve the crystalline lattices from a STEM Moiré hologram recorded on a silicon sample. The great interest of STEM Moiré interferometry is to increase the field of view (FOV) of the electron micrograph (up to several microns). The Moiré sampling recovery method extends the application of the STEM imaging of crystalline materials towards low magnifications.