Methodology for fast curve fitting to modulated Voigt dispersion lineshape functions

摘要

Faraday rotation spectroscopy (FAMOS) as well as other modulated techniques that rely on dispersion produce lock-in signals that are proportional to various Fourier coefficients of modulated dispersion lineshape functions of the molecular transition targeted. In order to enable real-time curve fitting to such signals a fast methodology for calculating the Fourier coefficients of modulated lineshape functions is needed. Although there exist an analytical expression for such Fourier coefficients of modulated Lorentzian absorption and dispersion lineshape functions, there is no corresponding expression for a modulated Voigt dispersion function. The conventional computational route of such Fourier coefficients has therefore so far either consisted of using various approximations to the modulated Voigt lineshape function or solving time-consuming integrals, which has precluded accurate real-time curve fitting. Here we present a new methodology to calculate Fourier coefficients of modulated Voigt dispersion lineshape functions that is significantly faster (several orders of magnitude) and more accurate than previous approximative calculation procedures, which allows for real-time curve fitting to FAMOS signals also in the Voigt regime.