voigt1d

Context: models

Synopsis

One dimensional Voigt profile.

Syntax

voigt1d

Description

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.

Examples

Example 1

>>> 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

Example 2

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

Added in CIAO 4.13

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

Bugs

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