Pseudo Voigt

Someone models instrument response function as voigt profile. Since convolution with voigt profile is hard, I approximate voigt profile to linear combination of cauchy and gaussian distribution. Such approximated function is usually called pseudo voigt profile.

\[\begin{equation*} {IRF}(t) = \eta C({fwhm}_L, t) + (1-\eta)G({fwhm}_G, t) \end{equation*}\]

where, \({fwhm}_L\), \({fwhm}_G\) is full width at half maximum value of cauchy and gaussian distribution, respectively. \(C(t)\), \(G(t)\) is normalized cauchy and gaussian distribution, each. \(\eta\) is mixing parameter (\(0 \leq \eta \leq 1\)).