apeaks: Calculate absorption spectra
In AlexCast/rho: R Hydrology Optics

Description Usage Arguments Details Value References See Also Examples

This function evaluates an absorption band model at the desired reference positions.

apeaks(
  center,
  sigma,
  hwhm,
  scale,
  sr,
  model = c("Gauss", "Lorentz", "Voigt"),
  peaks = FALSE
)

`center`	Center position reference of each absorption band.
`sigma`	Standard deviation for the Gaussian model.
`hwhm`	Half width at half maximum for the Lorentzian model.
`scale`	Scale height at the center of each absorption band.
`sr`	Position reference at which the absorption models should be evaluated in any suitable scale (energy, frequency, wavelength).
`model`	One of 'Gauss', 'Lorentz' or 'Voigt'. See details.
`peaks`	Logical. Should the peak curves for each absorption band be returned?

Observed absorption bands are not sharp due to several line broadening process grouped into homogeneous processes represented by a Lorentzian profile and inhomogeneous processes represented by a Gaussian profile. The Voigt profile combine both processes.

The line width parameters for each profile are requested in their most common formats, standard deviation for the Gaussian model and half width at half maximum (HWHM) for the Lorentzian model. The HWHM is related to the standard deviation for the Gaussian function by: HWHM = sqrt(2*log(2)) * sigma

The Voigt profile is calculated with the analytical approximation of Liu et al. (2001) and the empirical approximation of Olivero & Longbothum (1977) for the HWHM of the Voigt profile.

Units for the parameters depend on the scale used to represent the absorption process (e.g., energy, frequency, wavenumber, wavelength).

If peaks is FALSE, a numeric vector with the summed peaks. If peaks is true, a matrix is returned, with peaks per row.

Liu, Y.; Lin, J.; Huang, G.; Guo, Y.; Duan, C. 2001. Simple empirical analytical approximation to the Voigt profile. Journal of the Optical Society of America B 18, 5, 666-672. DOI: 10.1364/JOSAB.18.000666

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. DOI: 10.1016/0022-4073(77)90161-3

adeconv

sr <- seq(-10, 10, 0.01)
pg <- apeaks(0, 1, 0, 1, sr = sr, 'Gauss')
pl <- apeaks(0, 0, sqrt(2*log(2)), 1, sr = sr, 'Lorentz')
pv <- apeaks(0, 0.7638, 0.4 * sqrt(2*log(2)), 1, sr = sr, 'Voigt')
plot(sr, pg, type = 'l', col = 2, ylab = 'Height')
lines(sr, pl, col = 3)
lines(sr, pv, col = 4)
legend('topright', c('Gauss', 'Lorentz', 'Voigt'), col = 2:4, lty = 1, bty = 'n')
legend('topright', expression(HWHM == sqrt(2*log(2))), bty = 'n')