Computing Information from Nanoscale Imaging (and Vice Versa)

We employ mathematical transformations to analyze the atomic-scale chemical and physical properties of materials imaged by scanning tunneling microscopy. Initial discussions will include the role of Fourier transformation in understanding nanoscale images of layered systems that include graphene and topological insulators. The next section will highlight the use of morphological operators to quantify the temperature dependent intramolecular mechanics of nanocar molecules. Finally, the discussion will center on how image information theory can guide the design of new optical microscopy instrumentation for sum-frequency generation imaging of self-assembled monolayers and darkfield imaging of metallic nanostructures.