A Study of Systematic Errors in Multiple Linear Regression Peak Fitting Using Generated Spectra

Abstract

Quantitative analysis using electron, x-ray, or ion beam excited x rays depends on accurate measurement of characteristic peak intensities in the spectrum. Multiple-linear-least-squares (ML) procedures are routinely used to extract peak areas even from spectra with severe peak overlaps. In an ML fitting procedure, a factor is found that scales a reference distribution for each peak or family of peaks from each element of interest contributing to the specimen spectrum. The area of the reference is known, so the fitting factor may be used to calculate the area of the fitted peak. Most conveniently, the reference distributions are segments of spectra from pure element specimens and thus are assumed to include all spectrum features associated with a particular family of lines as well as any spectral artifacts peculiar to the spectrometer.^(l) For electron excited x rays, some implementations of ML peak fitting utilize reference distributions that are background-free.^(2,3) Others fit distributions that include the continuum background and assume that a correction can be made for the reference background contribution in the fitted area.⁽⁴⁾ Continuum can be suppressed before the fitting procedure by digitally filtering both the spectrum and references with a “top-hat” filter of dimensions chosen to preferentially pass only higher frequency features.^(5,6) For spectra from bulk specimens, these high frequency features include not only characteristic peaks but also abrupt decreases in continuum due to absorption edges that may introduce an error in calculating fitted peak areas. In fact, as pointed out by Statham,⁽⁶⁾ any region of the continuum a residual in the filtered spectrum that will introduce an error in the fitted area of a peak in that region. For example, Kitazawa et al. demonstrated a systematic error for Na in spectra from a thin specimen acquired with a beryllium window detector. This error arises from the change in curvature of the continuum near the Na Ka energy due to strong absorption of the low energy x rays by the detector.