Digital darkfield decompositions

Lattice imaging facilitates digital implementation of optical darkfield strategies that have for decades played a key role in the conventional electron microscopy of materials. Applications to the microscopy of periodic structures are described in the context of recent developments in the mathematical harmonic analysis community, with hopes of inspiring further development along these lines. Applications here, which push present day limits using sharp-edged Fourier windows alone, include the location of weak periodicities in images by virtue of their spatial correlations, and the quantitative mapping of projected strain in a variety of nanostructures.