Gaussian-Lorentzian Ratios
Gaussian-Lorentzian SUM
Gaussian-Lorentzian PRODUCT
VOIGT (convolution of Gaussian and Lorentzian peak-shapes)
Plot of the centered Voigt profile for four cases. Each case has a full width at half-maximum (FWHM) of very nearly 3.6.
The black and red profiles are the limiting cases of the Gaussian (γ =0) and the Lorentzian (σ =0) profiles respectively.
Voigt (convolution of Gaussian and Lorentzian peak-shapes)
The third line shape that has a theoretical basis is the Voigt function, a convolution of a Gaussian and a Lorentzian,
- {\displaystyle V(x;\sigma ,\gamma )=\int _{-\infty }^{\infty }G(x’;\sigma )L(x-x’;\gamma )\,dx’,}
where σ and γ are half-widths. The computation of a Voigt function and its derivatives are more complicated than a Gaussian or Lorentzian.[4]
Other peak-shapes:Â Gelius, Pearson…
Examples
Pure Gaussian peak-shape
Pure Lorentzian peak-shape
Pure Voigt peak-shape