Voigt profile

In spectroscopy, the Voigt profile is a spectral line profile named after Woldemar Voigt and found in all branches of spectroscopy in which a spectral line is broadened by two types of mechanisms, one of which alone would produce a Doppler profile, and the other of which would produce a Lorentzian profile.

Related Topics:
Spectroscopy - Woldemar Voigt - Spectral line - Doppler profile - Lorentzian profile

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

Related Topics:
Probability distribution - Normal distribution - Cauchy distribution - Convolution - Lorentzian profile - Doppler profile

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

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where x is frequency from line center, D(x;sigma) is the centered Doppler profile:

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D(x;sigma)equivrac{e^{-x^2/2sigma^2}}{sigma sqrt{2pi}}

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and L(x;gamma) is the centered Lorentzian profile:

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

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The defining integral can be evaluated as:

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V(x;sigma,gamma)=rac{ extrm{Re}}{sigmasqrt{2 pi}}

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where Re is the real part of the complex error function of z  and

Related Topics:
Real - Error function

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z=rac{x+igamma}{sigmasqrt{2}}.

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