Unbiased method for signal estimation in electron energy loss spectroscopy, concentration measurements and detection limits in quantitative microanalysis: Methods and programs

Abstract

We present an unbiased method for the estimation of the background in EELS spectra. It looks for the maximum likelihood of a power law model whose two dependent parameters A and R are estimated together with their variances and covariance. Applying the usual rules of error propagation, core-loss characteristic signals and thier variances are estimated. Confidence intervals for the relevant atomic concentrations are then established. Special attention is paid to the first- and second-kind risks when detection limits are attained: they respectively correspond to the risk of stating that a concentration is positive when actually it is zero, and to the risk of stating that a concentration is zero when actually it is positive. A special algorithm, based on a chi-square test, is developed giving the weighted mean of successive estimations of the same unknown. This test can select significant data from a set of experimental results. We also present an algorithm which estimates the effective angle of collection β∗ in the case of convergent beam EELS experiments. These methods and algorithms are used in a set of five programs, written in DEC-FORTRAN 77. These programs can be obtained, upon request, from the author.