Voigt Profile

In spectroscopy, the Voigt profile (named after Woldemar Voigt) is a line profile resulting from the convolution of two broadening mechanisms, one of which alone would produce a Gaussian profile (usually, as a result of the Doppler broadening), and the other would produce a Lorentzian profile. Voigt profiles are common in many branches of spectroscopy and diffraction. Due to the computational expense of the convolution operation, the Voigt profile is often approximated using a pseudo-Voigt profile.

All normalized line profiles can be considered to be probability distributions. The Gaussian profile is equivalent to a Gaussian or normal distribution and a Lorentzian profile is equivalent to a Lorentz or Cauchy distribution. Without loss of generality, we can consider only centered profiles which peak at zero. The Voigt profile is then a convolution of a Lorentz profile and a Gaussian profile:

V(x;\sigma,\gamma)=\int_{-\infty}^\infty G(x';\sigma)L(x-x';\gamma)\, dx'

where x is frequency from line center, is the centered Gaussian profile:

G(x;\sigma)\equiv\frac{e^{-x^2/(2\sigma^2)}}{\sigma \sqrt{2\pi}}

and is the centered Lorentzian profile:

L(x;\gamma)\equiv\frac{\gamma}{\pi(x^2+\gamma^2)}.

The defining integral can be evaluated as:

V(x;\sigma,\gamma)=\frac{\textrm{Re}}{\sigma\sqrt{2 \pi}}

where Re is the real part of the Faddeeva function evaluated for

z=\frac{x+i\gamma}{\sigma\sqrt{2}}.

Read more about Voigt Profile:  Properties, Voigt Functions

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