A method for merging the results of separate least-squares fits and testing for systematic errors

Abstract

A method is presented for merging the results of separate least-squares fits to obtain the most precise, single values for each of the molecular constants of a spectroscopic system. The output molecular constants and accompanying variance-covariance matrices from each of the separate fits are taken together as input to a correlated least-squares fit, which then yields the desired merged single values. The method is applied to a X-r8 diatomic model band system using well-defined synthetic data as an example. Other currently used, multistate methods of obtaining molecular constants for a spectroscopic system are special cases of the method described here. For the nonlinear least-squares fits required for multiplet states, the merge method is particularly advantageous. The properties of the merged values of the molecular constants and their standard errors are examined with regard to forming confidence limits for these estimates and it is shown that, in most spectroscopic applications, the confidence limits have their usual meaning. Furthermore, it is similarly shown that the confidence limits for the variance of the merged fit provide a simple and convenient test for the presence of relative systematic errors between the separate least-squares results being merged. Although the method is illustrated here by merged separate band-by-band results, it also can be applied to any type of spectroscopic results.

High-Resolution Laser Spectroscopy of YbCl: The A2Π–X2Σ+ Transition

“…, which has been described elsewhere (19,20), takes advantage of redundancies in the fitted parameters. The ground state constants follow a regular trend with vibrational quantum number, and it was possible to calculate equilibrium values in the merge of the constants from the five bands.…”

Reanalysis of the Ångström System (B1Σ+- A1Π) in the13C16O Isotopic Molecule

“…In the frame of the body of this t the calculated (unperturbed) T (v, J) calc rotational term values of the A 1 Π v = 1 and 2 state were derived. The nal values of the rotational structure parameters of the studied B 1 Σ + state were achieved at the third stage of the calculations, as a result of the least squares merge ttings of all bands analysed in this work, according to the procedure proposed by Albritton et al [48] and Coxon [49]. In this method, the tted bands have to have the common upper vibrational level.…”

Emission Spectroscopy of AlH: the X¹Σ⁺, A¹Π and C¹Σ⁺ States Characteristics

“…The calculations of the final molecular parameters, bands origins and vibration terms values for the observed levels were performed by the least-squares merge fit described by Albritton et al [19] and by Coxon [20]. Such merging is equivalent to a global fit of all data parameters sets for all states but it is more careful and makes it possible to find prospective strong correlations between molecular parameters or systematic errors of wave numbers measurements.…”