Line width at half maximum of the Voigt profile in terms of Gaussian and Lorentzian widths: Normalization, asymptotic expansion, and chebyshev approximation

摘要

Normalization by the Voigt width was applied to both the Lorentz and Gaussian widths in the half width at half maximum (HWHM) equation. The normalization simplified the HWHM equation into a univariate relation for the normalized Lorentz width eta(L) = Lambda(eta(G)) as a function of the normalized Gaussian width with a finite domain eta(G) is an element of [0, 1]. The asymptotic expansion of the last function provided local analytical approximations with limited accuracy at both ends of the Lorentz and Gaussian limits. Chebyshev approximations resulted in far better accuracies with a greatly improved range span. The rational Chebyshev approximation provided the highest accuracies and was implemented for deriving polynomial equations for the Voigt width gamma(V) in terms of both the Lorentz width gamma(L) and the Gaussian width gamma(G). Seventh-order and ninth-order polynomial approximations provided up to a ten-digit accuracy. Quartic and segmented closed-form analytical approximations provided a five-digit accuracy. All of these approximations were more accurate than the four-digit maximum accuracy approximations reported in earlier studies.