A rational approximation for efficient computation of the Voigt function in quantitative spectroscopy

TL;DR

This paper introduces a fast, highly accurate rational approximation for computing the Voigt function, significantly improving efficiency over existing methods while maintaining high precision across practical parameter ranges.

Contribution

A new rational approximation method for the Voigt function using residue calculus that is faster and equally or more accurate than previous approaches.

Findings

Achieves average accuracy of 10^{-14} with 16 terms

Reduces computation time by over 50% compared to Weideman's method

Maintains stability without poles for all relevant parameters

Abstract

We present a rational approximation for rapid and accurate computation of the Voigt function, obtained by 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's rational approximation. Algorithmic stability is achieved due to absence of the poles at $y \geqslant 0$ and $ - \infty < x < \infty $.