Assessment of the precision, bias and numerical correlation of fitted parameters obtained by multi-spectrum fits of the Hartmann-Tran line profile to simulated absorption spectra

Abstract

Although the Voigt profile has long been used to analyze absorption spectra, the quest for increased precision, accuracy and generality drives the application of advanced models of atomic and molecular line shapes. To this end, the Hartmann-Tran profile is now recommended as a standard for high-resolution spectroscopy because it parameterizes relevant higher-order physical effects, is computationally efficient, and reduces to other widely used profiles as limiting cases. This work explores the uncertainty with which line shape parameters can be obtained from constrained multi-spectrum fits of spectra simulated with this standard profile, varying uncertainty levels in the spectrum detuning and absorption axes, and spanning a range of sampling density, pressure, and line shape parameter values. The analysis focuses on how noise-limited measurement precision of frequency detuning and absorption drive statistical uncertainties in fitted parameters and numerical correlations between these quantities. Also, we quantify the degree of equivalence between the full Hartmann-Tran profile and those derived from it in terms of fitted peak areas and line shape parameters. Finally, we introduce a new open-source software package named Multi-spectrum Analysis Tool for Spectroscopy (MATS), which allows users to fit the HTP and its derived profiles to experimental or simulated absorption spectra to explore the limits of the HTP under actual experimental or user-defined conditions.