A Rational Approximation for Efficient Computation of the Voigt Function in Quantitative Spectroscopy

Abstract

We present a rational approximation for rapid and accurate computation of the Voigt function, obtained by sampling and residue calculus. The computational test reveals that with only $16$ summation terms this approximation provides average accuracy ${10^{ - 14}}$ over a wide domain of practical interest  $0 < x < 40,000$ and ${10^{ - 4}} < y < {10^2}$ for applications using the HITRAN molecular spectroscopic database. The proposed rational approximation takes less than half the computation time of that required by Weideman\text{'}s rational approximation. Algorithmic stability is achieved due to absence of the poles at $y \geqslant 0$ and $ - \infty  < x < \infty $.