PFChrom v5 Documentation Contents AIST Software Home AIST Software Support

Generalized Voigt

Voigt Generalization Convolution Models

PFChrom offers two different models for testing the integrity of Voigt model fits to spectroscopic data:

Gaussian Ä Student's t (Area)

This is an convolution model used to check the validity of Voigt model fits.

a_{0} = Area

a_{1} = Center

a_{2} = Gaussian Width

a_{3} = Lorentzian Width

a_{4}
= Student's t nu (1=Lorentzian, Infinite=Gaussian)

Built in model: Gauss<S>

User-defined peaks and view functions: Gauss[S]i[amp](x,a_{0},a_{1},a_{2},a_{3})
(Warning: computed as integral, very slow!)

This is a symmetric convolution of a Gaussian and a Student's t which
can be used to fit Voigt peaks where the Lorentzian component is estimated with a Student's t that will
be a Lorentzian only with the a_{4} nu=1. If the tails
of the non-Gaussian component of the convolution are not perfectly Lorentzian, this model will fit to
a value other an a_{3}=1. A Lorentzian has wide tails
which may be subject to instrumental sampling, digitization, and filtering. The Lorentzian component of
a pure Voigt should fit very close to a_{4}=1.0 if there
is a significant Lorentzian component to the Voigt. The peaks below vary from a_{4}=1
to a_{4}=1.5.

Lorentzian Ä Student's t (Area)

a_{0} = Area

a_{1} = Center

a_{2} = Lorentzian Width

a_{3} = Gaussian Width

a_{4}
= Student's t nu (1=Lorentzian, Infinite=Gaussian)

Built in model:Lorentz<S>

User-defined peaks and view functions: Lorentz[S]i(x,a_{0},a_{1},a_{2},a_{3})
(Warning: computed as integral, very slow!)

This is a symmetric convolution of a Lorentzian and a Student's t which
can be used to fit Voigt data where the Gaussian component is estimated with a Student's t that is a Gaussian
only with nu at infinity (PFChrom's upper bound on nu is 1,000,000). If the tails are not perfectly Gaussian,
this model will fit to a value with a nu lower than this maximum. This model can be used to test the integrity
of the Gaussian component of a Voigt peak. If any portion of that which contributes to the Gaussian line
spread function has wider tails, this will be strongly reflected in a_{4}.
If a pure Voigt is fit, you should expect values of a_{4} 10,000 or higher, if
there is a significant Gaussian component to the Voigt. The peaks below vary from a_{4}=5
to a_{4}=1,000,000.