Improved precision and accuracy of electron energy-loss spectroscopy quantification via fine structure fitting with constrained optimization.

By working out the Bethe sum rule, a boundary condition that takes the form of a linear equality is derived for the fine structure observed in ionization edges present in electron energy-loss spectra. This condition is subsequently used as a constraint in the estimation process of the elemental abundances, demonstrating starkly improved precision and accuracy and reduced sensitivity to the number of model parameters. Furthermore, the fine structure is reliably extracted from the spectra in an automated way, thus providing critical information on the sample's electronic properties that is hard or impossible to obtain otherwise. Since this approach allows dispensing with the need for user-provided input, a potential source of bias is prevented.