100% Gaussian and 100% Lorentzian

 

Examples of 100% Gaussian and 100% Lorentzian peak-shapes used to Peak-fit O (1s) signal

 

 

Peak-shape functions
(from Wikipedia)

 

Comparison of Gaussian (red) and Lorentzian (blue) synthetic peak shapes. The HWHM (w/2) is 1.

 

 

Plot of the centered synthetic Voigt peak shape for four cases.

Each case has a full width at half-maximum 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.

 

Lorentzian    (from Wikipedia)

A Lorentzian peak shape function can be represented as

where L signifies a Lorentzian function standardized, for spectroscopic purposes, to a maximum value of 1;[note 1]  is a subsidiary variable defined as

where p0 is the position of the maximum (corresponding to the transition energy E), p is a position, and w is the full width at half maximum(FWHM), the width of the curve when the intensity is half the maximum intensity (this occurs at the points p = p0±w/2). The unit of p0, p and w is typically wavenumber or frequency. The variable x is dimensionless and is zero at p=p0.

Gaussian    (from Wikipedia)

The Gaussian peak shape has the standardized form,

 

 

The subsidiary variable, x, is defined in the same way as for a Lorentzian shape. Both this function and the Lorentzian have a maximum value of 1 at x = 0 and a value of 1/2 at x=±1.

Voigt   (from Wikipedia)

The third peak shape that has a theoretical basis is the Voigt function, a convolution of a Gaussian and a Lorentzian,

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]