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The Voigt profile is a spectral line profile named after Woldemar Voigt (seen in the upper left) in which a spectral line is broadened by two types of mechanisms, one which produces a Gaussian profile (e.g., Doppler broadening), and another which produces a Lorentzian, a Breit-Wigner, a Cauchy profile (e.g., collision broadening).
The driver and subroutines in test_voigt02.f compute the Voigt function H(a,v) given by M.R. Zaghloul in MNRAS, 375, 1043, 2007 , 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. I've made a modest contribution by adding the derivatives dH/da and dH/dv, and showing how the damped sinusoid integrals may be accurately calculated.
The Voigt function is also the real part of w(z) = exp(-z2) erfc(iz), the Faddeeva function, the complex probability function, the plasma dispersion function. One may want to compare the answers produced by code offered above to those produced by the TOMS 680, algorithm and from the codes given on Bob Wells' Voigt Function webpage. Click on an image for the corresponding vector graphics pdf file.
H(a,v) for smaller a. |
H(a,v) for larger a |
Derivative with respect to "a" profiles, dH/da
dH/da for smaller a |
dH/da for larger a |
Derivative with respect to "v" profiles, dH/dv
dH/dv for smaller a |
dH/dv for larger a |