Self-Absorption Coefficient from Line Widths

Estimates the self-absorption coefficient of an emission line from the ratio of its measured Stark width to the width it would have if it were optically thin (El Sherbini et al., 2005).

Usage

self_absorption(width, thin_width, alpha = -0.54)

Arguments

width: The measured Lorentzian full width at half maximum of the line, in nm.
thin_width: The width of the line if it were optically thin, in nm.
alpha: The exponent of the relation. Default is -0.54.

Value

A tibble with the self-absorption coefficient SA and the intensity_correction factor $1/SA$.

Details

Self-absorption flattens and broadens a line. The self-absorption coefficient, the ratio of the measured peak intensity to the intensity without absorption, is $$SA = \left(\frac{\Delta\lambda}{\Delta\lambda_0}\right)^{1/\alpha}, \quad \alpha = -0.54$$ where $\Delta\lambda$ is the measured Lorentzian (Stark) width and $\Delta\lambda_0$ the width of the optically thin line. The latter follows from the electron density measured on an optically thin line (such as H$\alpha$, see electron_density()) and the Stark width of the line at that density (stark_width()). $SA = 1$ means no self-absorption; the measured intensity divided by $SA$ corrects it.

References

El Sherbini, A.M., El Sherbini, Th.M., Hegazy, H., Cristoforetti, G., Legnaioli, S., Palleschi, V., Pardini, L., Salvetti, A., Tognoni, E. (2005). Evaluation of self-absorption coefficients of aluminum emission lines in laser-induced breakdown spectroscopy measurements. Spectrochimica Acta Part B, 60(12):1573-1579.

Examples

# a line twice as wide as expected from its Stark width
self_absorption(width = 0.04, thin_width = 0.02)
#> # A tibble: 1 × 4
#>   width thin_width    SA intensity_correction
#>   <dbl>      <dbl> <dbl>                <dbl>
#> 1  0.04       0.02 0.277                 3.61