Optimized acquisition parameters and statistical detection limit in quantitative EELS

Optimizing the acquisition parameters for EELS recording has to be accomplished simultaneously from the physical and the statistical points of view; the statistical aspect of the question is covered here. Approximate probability density functions of the variables of interest are derived, which provide a global measure of signal-to-noise ratio taking into account every step of the EELS edge area estimation process. Qualitative and quantitative advice is given regarding the critical choice of the estimation and integration energy regions. The notion of visual contrast is presented; it permits the introduction of the concept of statistical detection limit. It is found that for typical experimental conditions, when other factors are equal, the required analysis time for the sample varies approximately as the inverse square of the concentration.