Full Width at Half Maximum of a Voigt Profile

Computes the full width at half maximum (FWHM) of a Voigt profile from its Gaussian and Lorentzian widths, with the approximation of Olivero and Longbothum (1977), accurate to about 0.02%: $$f_V \approx 0.5346\,f_L + \sqrt{0.2166\,f_L^2 + f_G^2}$$

Usage

voigt_fwhm(wG, wL)

Arguments

wG, wL

The Gaussian and Lorentzian full widths at half maximum, for example the wG and wL parameters of a Voigt fit with peak_fit(). Vectors are recycled.

Value

A numeric vector of Voigt FWHM, in the units of wG and wL.

Details

The total width of a fitted line is often better determined than its split into Gaussian and Lorentzian parts, which trade off against each other when a line is noisy or sampled by few channels. It is the width to use for the H\(\alpha\) line in electron_density(), whose Stark profile is not Lorentzian.

References

• Olivero, J.J., Longbothum, R.L. (1977). Empirical fits to the Voigt line width: a brief review. Journal of Quantitative Spectroscopy and Radiative Transfer, 17(2):233-236.

See also

voigt_profile(), peak_fit(), electron_density()

Author

Christian L. Goueguel

Examples

voigt_fwhm(wG = 0.1, wL = 0)    # Gaussian limit
#> [1] 0.1
voigt_fwhm(wG = 0, wL = 0.1)    # Lorentzian limit
#> [1] 0.1000003
voigt_fwhm(wG = 0.1, wL = 0.1)
#> [1] 0.1637596