    One dimensional Voigt profile.

voigt1d

The Voigt profile is a convolution between a Gaussian distribution a Cauchy-Lorentz distribution [Voigt_1912] , [wiki_voigt] . It is often used in analyzing spectroscopy data.

>>> create_model_component("voigt1d", "mdl")
>>> print(mdl)

Create a component of the voigt1d model and display its default parameters. The output is:

mdl Param Type Value Min Max Units ----- ---- ----- --- --- ----- mdl.fwhm_g thawed 10 1.17549e-38 3.40282e+38 mdl.fwhm_l thawed 10 0 3.40282e+38 mdl.pos thawed 0 -3.40282e+38 3.40282e+38 mdl.ampl thawed 1 -3.40282e+38 3.40282e+38

Force the widths of the Gaussian and Lorentzian components to be the same:

>>> mdl = Voigt1D() >>> mdl.fwhm_l = mdl.fwhm_g / np.sqrt(2 * np.log(2))

ATTRIBUTES

The attributes for this object are:

Attribute
Definition
fwhm_g
The full-width half-maximum (FWHM) of the Gaussian distribution.
fwhm_l
The full-width half-maximum of the Lorentzian distribution.
pos
The center of the profile.
ampl
The amplitude of the profile.

Notes

Following [wiki_voigt] , the Voigt profile can be written as:

f(x) = ampl * Re[w(z)] / (sqrt(2 * PI) * sigma)

where Re[w(z)] is the real part of the Faddeeva function [wiki_faddeeva]

and sigma and gamma are parameters of the Gaussian and Lorentzian model respectively:

z = (x - pos + i * gamma) / (sqrt(2) * sigma) sigma = fhwm_g / sqrt(8 * log(2)) gamma = fwhm_l / 2

One common simplification is to tie the sigma and gamma parameters together, which can be achieved by linking the fwhm_l parameter to fwhm_g with the following equation:

fwhm_l = fwhm_g / sqrt(2 * log(2))

An approximation for the FWHM of the profile, taken from [wiki_voigt] , is

0.5346 fwhm_l + sqrt(0.2166 fwhm_l^2 + fwhm_g^2)

References

[Voigt_1912] https://publikationen.badw.de/de/003395768
[wiki_voigt] https://en.wikipedia.org/wiki/Voigt_profile
[wiki_faddeeva] https://en.wikipedia.org/wiki/Faddeeva_function

Changes in CIAO

The pseudovoigt1d and voigt1d models were added in CIAO 4.13 and replace the absorptionvoigt and emissionvoigt models.

See the bugs pages on the Sherpa website for an up-to-date listing of known bugs.

December 2023