Influence of background subtraction and deconvolution on calculation of
EELS
core‐loss intensities
Authors: Angadi Veerendra C , Walther Thomas 
Published: December 2016

Quantitative analysis of electron energy‐loss spectra (EELS) can be highly influenced by plural scattering for large thicknesses (t/λ>0.5) and background modelling. For quantification by integration [1], plural scattering can be accounted for by choosing large integration ranges or by deconvolving with the low‐loss function. Richardson‐Lucy (maximum likelihood) or Fourier‐Ratio deconvolution are state‐of‐the‐art techniques. Fourier‐Ratio deconvolution enhances noise which can be partially compensated by re‐convolving with a Gaussian kernel. The height of the edge onset of the deconvolved core‐loss will usually be lower than the actual onset, see figure 1. Richardson‐Lucy (RL) deconvolution is frequently used to improve astronomical observations, de‐blur images and resolve near edge structures from monochromated EELS in transmission electron microscopy (TEM) [2]. The iterative RL method produces ringing artefacts which are studied in figure 1. The amplitude and position of the artefacts changes depending on the number of iterations as shown in figure 2 for a simulated hydrogenic line without background. The deconvolved core‐loss is sharper and the onset is almost at the precise location it should be. The other effect that influences quantification is background subtraction. Background subtraction is usually done by fitting an inverse power‐law (AE
‐r
) function to the pre‐edge region. The errors associated with background fit and extrapolation have been discussed by Egerton in terms of so‐called h‐parameters. Other methods such as multiple linear least‐squares fits have been implemented in software packages such as Hyperspy [3], EELSMODEL [4] and Digital Micrograph [5]. In background subtraction, there is always a trade‐off between systematic and statistical errors in quantification of core‐losses. In some cases, due to noise, near edge or extended fine structures in preceding edges, the extrapolated background can cross the spectrum, which leads to large systematic under‐estimate of the net core‐loss intensity. Background subtraction techniques with exponential fitting can be explored more systematically and a new approach on how quantification can be improved by choosing different functions to fit in pre‐edge regions will be discussed. In particular, modelled pre‐edge backgrounds can be forced to not cross the spectrum by introducing a linear offset function, thereby minimizing the under‐estimate of the core‐loss. Modelling the background can also be explored more extensively by fitting an inverse power‐law or exponential fit to the post‐ionisation range and shifting the fitted curve downwards to pass though the edge onset. This leads to an overestimate of the core‐loss intensity. The possible best background fit and its reliability can be calculated from the error bars associated with the under and over‐estimated intensities as described in figure 3. The histograms in figure 4 show that the over‐ and under‐estimate of the As‐L edge intensity influences the quantification while optimal fitting provides quantification in better agreement with Ga/As ratio of unity for GaAs.