Direct-fitting approach to the analysis of high-resolution optical spectra: Monte Carlo and experimental studies of OH A(0)→X(0) spectra

Abstract

The traditional approach for analyzing high-resolution optical spectra involves locating and measuring line frequencies, then assigning and fitting these to an appropriate model for the molecular energy levels. The alternative approach of fitting the spectrum directly is particularly appealing in the case of congested spectra with many overlapped features. The capabilities and limitations of direct fitting are explored in application to the 0–0 band of the OH A→X transition, as recorded on a charge-coupled-device array using a high-pressure Tesla discharge source. Monte Carlo calculations confirm that for Poisson (counting) data, the parameter errors from the variance–covariance matrix are trustworthy, unless weights are neglected, in which case the error estimates can be wildly optimistic. In the fitting of actual spectra, a major barrier is the derivation of a suitable instrumental line-shape function. In particular, the often adopted triangular slit function is grossly inadequate. A systematic procedure has been devised for obtaining the line shape as a sum of Gaussian and Lorentzian components. This method has facilitated the analysis of experimental spectra spanning the region 3071–3103 Å. A model having 46 adjustable parameters determines the temperature (320 K) of the low-N′ levels of the A state with σ < 1 K and corroborates theoretical intensity branching ratios within 2%. It also determines within 10% the contribution to the emission from OD, which is present in natural abundance (H:D≈7000) in the source.