Multiple Linear Least-Squares (MLLS)
Peak Fitting for EDS Analysis
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Multiple linear least squares (MLLS) fitting technique is well-known and may be applied to EDS spectra to determine the best fits against the known spectra of the elemental constituents of the specimen and then mathematically separate overlapping peaks and spectral background.

This technique is especially useful when one wants to identify trace elements. In this case, the procedure is:
        i) Locate the candidate peaks.
        ii) Determine the possible elemental families for the major peaks.
        iii) Fit the peak references over the full range of channels (the entire spectrum). The references may be obtained from pure elements.
        iv) Test, compare and then identify the residuals (the peaks of the trace elements).

However, the stability of such procedure described above becomes questionable when the relative peak height differences become large or when limited counting statistics are available.