Methodology for spectrum evaluation in quantitative electron energy‐loss spectrometry using the Zeiss CEM902

Abstract

SUMMARY The spectral energy‐loss intensities acquired with the Zeiss CEM902 do not follow a Poisson law. The intensities are normally distributed and their variances are non‐uniform. When fitting the inverse power law after logarithmic transformation, it is expected that the power law coefficients and their uncertainties will be biased. Due to the particular dependence of the variance on the intensity which is observed in our experiments, it appears that no bias is introduced when using unweighted least‐squares fitting after log‐log transformation. Because the sample variances are estimated with low degrees of freedom, the residual variance of the fit is proposed as a criterion rather than the X 2 test to evaluate the optimum width of the fitting window. The optimal width for the integration window can be determined as the window where the signal‐to‐noise ratio is at a maximum. Critical limits for qualitative and quantitative analysis are proposed which are based on the variance of the net intensity. They can be used to test the analytical significance of the signals.