Voigt Function


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Contact: F.X.Timmes
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$ \def\drvop#1{{\frac{d}{d{#1}}}} \DeclareMathOperator\erfc{erfc} $ A spectral line profile which is Doppler broadened (a Gaussion profile) and collision broadened (a Lorentzian, Breit-Wigner, or Cauchy profile) is named after Woldemar Voigt. The tool voigt.tbz computes the Voigt function H(a,v) given by Zaghloul 2007 as \begin{equation} H(a,v) = \exp(a^2) \ \erfc(-v^2) \ \cos(2av) + \frac{2}{\sqrt{\pi}} \ \int_0^v \exp[-(v^2 - u^2)] \ \sin[2a(v - u)] \ {\rm d}u \label{eq1} \tag{1} \end{equation} where "a" is the ratio of the natural width to the Doppler width and "v", distance from line center in units of the Doppler width. A modest contribution has been adding the derivatives dH/da and dH/dv, and showing how the damped sinusoid may be accurately integrated.

The Voigt function is also the real part of w(z)=exp(-z2) erfc(iz) with z = a + i v, the Faddeeva function, the complex probability function, the plasma dispersion function. One may want to compare the answers and performance produced by voigt.tbz to those produced by TOMS 916.

H(a,v) profiles

H(a,v) for smaller a.

H(a,v) for larger a

Derivative dH/da

dH/da for smaller a

dH/da for larger a

Derivative dH/dv

dH/dv for smaller a

dH/dv for larger a


Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.