Convexity constraints on linear background models for electron energy-loss spectra

Wouter Van den Broek; Daen Jannis; Jo Verbeeck

doi:10.1016/j.ultramic.2023.113830

Convexity constraints on linear background models for electron energy-loss spectra

Ultramicroscopy. 2023 Dec:254:113830. doi: 10.1016/j.ultramic.2023.113830. Epub 2023 Aug 14.

Authors

Wouter Van den Broek¹, Daen Jannis², Jo Verbeeck²

Affiliations

¹ Thermo Fischer Scientific, Achtseweg Noord 5, 5651 GG Eindhoven, Netherlands. Electronic address: wouter.vandenbroek@thermofisher.com.
² Electron Microscopy for Materials Research (EMAT), University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium; Nanolab center of excellence, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium.

PMID: 37633170
DOI: 10.1016/j.ultramic.2023.113830

Abstract

In this paper convexity constraints are derived for a background model of electron energy loss spectra (EELS) that is linear in the fitting parameters. The model outperforms a power-law both on experimental and simulated backgrounds, especially for wide energy ranges, and thus improves elemental quantification results. Owing to the model's linearity, the constraints can be imposed through fitting by quadratic programming. This has important advantages over conventional nonlinear power-law fitting such as high speed and a guaranteed unique solution without need for initial parameters. As such, the need for user input is significantly reduced, which is essential for unsupervised treatment of large datasets. This is demonstrated on a demanding spectrum image of a semiconductor device sample with a high number of elements over a wide energy range.

Keywords: Constrained optimization; Convexity constraints; Electron energy-loss spectroscopy; Linear background model; Power-law; Quadratic programming.