Generalized Voigt

Voigt Generalization Convolution Models

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

Gaussian � Student's t (Area)

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

a₀ = Area

a₁ = Center

a₂ = Gaussian Width

a₃ = Lorentzian Width

a₄ = Student's t nu (1=Lorentzian, Infinite=Gaussian)

Built in model: Gauss<S>

User-defined peaks and view functions: Gauss[S]i[amp](x,a₀,a₁,a₂,a₃) (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 a₄ 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 a₃=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 a₄=1.0 if there is a significant Lorentzian component to the Voigt. The peaks below vary from a₄=1 to a₄=1.5.

Lorentzian � Student's t (Area)

a₀ = Area

a₁ = Center

a₂ = Lorentzian Width

a₃ = Gaussian Width

a₄ = Student's t nu (1=Lorentzian, Infinite=Gaussian)

Built in model:Lorentz<S>

User-defined peaks and view functions: Lorentz[S]i(x,a₀,a₁,a₂,a₃) (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 a₄. If a pure Voigt is fit, you should expect values of a₄ 10,000 or higher, if there is a significant Gaussian component to the Voigt. The peaks below vary from a₄=5 to a₄=1,000,000.