AHELP for CIAO 4.13 Sherpa v1

# 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 [1] , [2] . 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 [2] , 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 [3] 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 [2] , is

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

### References

• [2] https://en.wikipedia.org/wiki/Voigt_profile