A Global Fitting Approach For Doppler Broadening Thermometry
Very recently, a spectroscopic determination of the Boltzmann constant, kB, has been performed at the Second University of Naples by means of a rather sophisticated implementation of Doppler Broadening Thermometry (DBT)1. Performed on a 18O-enriched water sample, at a wavelength of 1.39 µm, the experiment has provided a value for kB with a combined uncertainty of 24 parts over 106, which is the best result obtained so far, by using an optical method. In the spectral analysis procedure, the partially correlated speed-dependent hard-collision (pC-SDHC) model was adopted. The uncertainty budget has clearly revealed that the major contributions come from the statistical uncertainty (type A) and from the uncertainty associated to the line-shape model (type B)2. In the present work, we present the first results of a theoretical and numerical work aimed at reducing these uncertainty components. It is well known that molecular line shapes exhibit clear deviations from the time honoured Voigt profile. Even in the case of a well isolated spectral line, under the influence of binary collisions, in the Doppler regime, the shape can be quite complicated by the joint occurrence of velocity-change collisions and speed-dependent effects.
The partially correlated speed-dependent Keilson-Storer profile (pC-SDKS) has been recently proposed as a very realistic model, capable of reproducing very accurately the absorption spectra for self-colliding water molecules, in the near infrared3. Unfortunately, the model is so complex that it cannot be implemented into a fitting routine for the analysis of experimental spectra. Therefore, we have developed a MATLAB code to simulate a variety of H218O spectra in thermodynamic conditions identical to the one of our DBT experiment, using the pC-SDKS model. The numerical calculations to determine such a profile have a very large computational cost, resulting from a very sophisticated iterative procedure. Hence, the numerically simulated spectra (with the addition of random noise) have been used to test the validity of simplified line shape models, such as the speed-dependent Galatry (SDG) profile and pC-SDHC model. In particular, we have used the global fitting procedure that is described in Amodio et al4.
Such a procedure is very effective in reducing the uncertainty resulting from statistical correlation among free parameters. Therefore, the analysis of large amounts of simulated spectra has allowed us to study the influence of the choice of the model and quantify the achievable precision and accuracy levels, at the present value of the signal-to-noise ratio.