Study of ambiguities inherent to the spectral analysis of Voigt profiles—a modified Simplex approach

In pulsed spectrometries, temporal transients are often analyzed directly in the temporal domain, assuming they consist only of purely exponentially decaying sinusoids. When experimental spectra actually consist of Gaussian or Voigt profiles (Gauss–Lorentz profiles), we show that the direct methods may erroneously interpret such lines as the sum of two or more Lorentzian profiles. Using a Nelder and Mead Simplex method, modified by introducing new means to avoid degeneracies and quenchings in secondary minima, we demonstrate that a large number of different solutions can be obtained with equivalent accuracy over the limited acquisition time interval, with final peak parameters void of physical or chemical meaning.