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Generalized Voigt

Voigt Generalization Convolution Models

PeakLab 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 (PeakLab'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.