Gaussian-Lorentzian Ratios

Gaussian-Lorentzian SUM

Gaussian-Lorentzian PRODUCT

 

VOIGT (convolution of Gaussian and Lorentzian peak-shapes)

File:Voigt distributionPDF.png

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:  Gelius, Pearson…

 

Examples

Pure Gaussian peak-shape

Pure Lorentzian peak-shape

Pure Voigt peak-shape