Absorption-line-shape recovery beyond the detection-bandwidth limit: Application to the precision spectroscopic measurement of the Boltzmann constant

Abstract

A theoretical model of the influence of detection bandwidth properties on observed line shapes in laser absorption spectroscopy is described. The model predicts artificial frequency shifts, extra broadenings and line asymmetries which must be taken into account in order to obtain accurate central frequencies and other spectroscopic parameters. This reveals sources of systematic effects most probably underestimated so far potentially affecting spectroscopic measurements. This may impact many fields of research, from atmospheric and interstellar physics to precision spectroscopic measurements devoted to metrological applications, tests of quantum electrodynamics or other fundamental laws of nature. Our theoretical model is validated by linear absorption experiments performed on H 2 O and NH 3 molecular lines recorded by precision laser spectroscopy in two distinct spectral regions, nearand mid-infrared. Possible means of recovering original line shape parameters or experimental conditions under which the detection bandwidth has a negligible impact, given a targeted accuracy, are proposed. Particular emphasis is put on the detection bandwidth adjustments required to use such high-quality molecular spectra for a spectroscopic determination of the Boltzmann constant at the 1 ppm level of accuracy.

Molecular dynamic simulations of N2-broadened methane line shapes and comparison with experiments

“…As shown in Ref. 31, time constant effects must be carefully accounted for in line profile analysis. In the present experiments, the frequency scans are typically 1 cm 1 wide, scan speed is 0.01 cm 1 /s, and detection time constant is 10 ms at 6 db/oct roll-off.…”

“…7 where detailed descriptions of the spectrometer, the experimental setup, and material supplies can be found. Note that, the influence of the small but asymmetric instrumental distortion which could be due to the detection time constant 31 was modelled by an asymmetric Lorentzian apparatus function as done in Ref. 7.…”

A determination of the molar gas constantRby acoustic thermometry in helium

“…These have been performed by (i) the measurement of a thermodynamic or electromagnetic intensive property of a macroscopic sample of gas, or (ii) the measurement of the electrical noise in a sense resistor, or (iii) the optical measurement of the absorption spectra of simple molecules. Remarkably, developments in all these methods has achieved a significant reduction of uncertainties: acoustic gas thermometry (AGT) now stands at the relative uncertainty level of 1 ppm or below [2,3,4,5,6], while dielectric constant gas thermometry (DCGT), refractive index gas thermometry (RIGT), Johnson noise thermometry (JNT) demonstrated overall uncertainties at the level of a few ppm [7,8,9], and Doppler broadening thermometry (DBT), shows a potential accuracy at the level of a few ppm or below [10,11]. This outstanding progress in several different primary thermometry techniques is important in view of their possible future application to the practical realization of the newly defined kelvin [12], allowing metrological laboratories across the world to realize a thermodynamic temperature standard by choosing the method which is best suited to the particular facilities, experience and knowledge available in the host institution.…”

Doppler Broadening Thermometry Based on Cavity Ring-Down Spectroscopy

“…By using more sophisticated line profiles and extrapolating the results obtained at different pressures to the zero-pressure limit [16,37,38,39,40,41], the uncertainty could be reduced to 1 ppm or less. …”

“…As have been intensively studied in Refs. [16,37,38,39,40,41], Table 1. Gaussian widths (FWHM, in MHz) and corresponding spectroscopy temperatures (in K) derived from the fitting of the spectra using different line profile models and parameters.…”