Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC Technical Report)

The report of an IUPAC Task Group, formed in 2011 on "Intensities and line shapes in high-resolution spectra of water isotopologues from experiment and theory" (Project No. 2011-022-2-100), on line profiles of isolated high-resolution rotational-vibrational transitions perturbed by neutral gas-phase molecules is presented. The well-documented inadequacies of the Voigt profile (VP), used almost universally by databases and radiative-transfer codes, to represent pressure effects and Doppler broadening in isolated vibrational-rotational and pure rotational transitions of the water molecule have resulted in the development of a variety of alternative line-profile models. These models capture more of the physics of the influence of pressure on line shapes but, in general, at the price of greater complexity. The Task Group recommends that the partially Correlated quadratic-Speed-Dependent Hard-Collision profile should be adopted as the appropriate model for high-resolution spectroscopy. For simplicity this should be called the Hartmann--Tran profile (HTP). The HTP is sophisticated enough to capture the various collisional contributions to the isolated line shape, can be computed in a straightforward and rapid manner, and reduces to simpler profiles, including the Voigt profile, under certain simplifying assumptions.Comment: Accepted for publication in Pure and Applied Chemistr

Hyperfine structure effects in Doppler-broadening thermometry on water vapor at 1.4 μm

This article builds upon a previous work dealing with the budget of uncertainties associated to our recent determination of the Boltzmann constant by means of Doppler broadening thermometry. We report on the outcomes of theoretical calculations and numerical simulations aimed to precisely quantify the influence of the unresolved hyperfine structure of a given ortho component of the H218O spectrum at 1.4 μm on the measurement of the Doppler width of the line itself. We have found that, if the hyperfine structure 44,1 → 44,0 of the line of the ν1ν3 band was ignored, the spectroscopic measurement of the Boltzmann constant would be affected by a relative systematical deviation of 4·10-8

Investigating the ultimate accuracy of Doppler-broadening thermometry by means of a global fitting procedure

Doppler-limited, high-precision, molecular spectroscopy in the linear regime of interaction may refine our knowledge of the Boltzmann constant. To this end, the global uncertainty in the retrieval of the Doppler width should be reduced down to 1 part over 10^6, which is a rather challenging target. So far, Doppler-broadening thermometry has been mostly limited by the uncertainty associated to the line shape model that is adopted for the nonlinear least-squares fits of experimental spectra. In this paper, we deeply investigate this issue by using a very realistic and sophisticated model, known as partially correlated speed-dependent Keilson-Storer profile, to reproduce near-infrared water spectra. A global approach has been developed to fit a large number of numerically simulated spectra, testing a variety of simplified line-shape models. It turns out that the most appropriate model is the speed-dependent hard-collision profile. We demonstrate that the Doppler width can be determined with relative precision and accuracy, respectively, of 0.42 and 0.75 part per million

The Boltzmann constant from the H2(18)O vibration–rotation spectrum: complementary tests and revised uncertainty budget

We report on complementary tests and measurements regarding our recent determination of the Boltzmann constant, kB, by means of Doppler broadening thermometry, also providing additional information as compared to previous articles. A revised uncertainty budget is illustrated, including some new components that were ignored in previous spectroscopic experiments, and better quantifying other components that were estimated to be negligible. In particular, we consider the relativistic Doppler effect, the perturbation caused by the finite bandwidth of the detection system and the influence of the spontaneous emission content of the probe laser. These new components do not increase the global uncertainty which still amounts to 24 ppm. Our value for the Boltzmann constant is 1.380 631 (33)  ×  10−23 J K−1, which is the best determination reported so far by using an optical method

Frequency-comb-calibrated Doppler broadening thermometry

We describe an implementation of Doppler broadening thermometry based upon a room-temperature continuous-wave quantum cascade laser at 9.07 mu m, coherently phase locked to a thulium optical frequency comb centered at 2 mu m. The thermodynamic temperature is retrieved from the analysis of multiple-line absorption spectra of the NH3 nu(2) band, adopting semiclassical line-shape models and taking into full account the speed dependence of collisional broadening. We demonstrate that a precision of approximately five parts over 10(5) can be reached as a result of the analysis of only 90 absorption spectra, as acquired as a function of the gas pressure

Narrowing Effects in the H₂¹⁸O Near-IR Spectrum: Experimental Test of the Partially-Correlated Quadratic-Speed-Dependent Hard-Collision Profile

<p>We present the outcomes of a specific study on the quadratic approximation in the partially-Correlated Speed-Dependent Hard-Collision profile (pC-SDHC), which is currently the recommended profile to replace the Voigt convolution for the shape of isolated high-resolution rotational-vibrational transitions, when perturbed by neutral gas-phase molecules. It includes the main effects occurring in the line formation, in particular the Dicke narrowing and the speed-dependent effects, as well as the possible correlation between them. We tested the quadratic (q-) and hypergeometric (hg-) versions for the speed dependence of the pC-SDHC on high quality H₂¹⁸O absorption spectra, in coincidence with three vibration-rotation transitions of the <em>ν</em>₁+ <em>ν</em>₃band, at 1<em>.</em>39<em>µm</em>, looking for possible differences in the retrieved parameters. The absorption spectra were observed in the Doppler regime, with unprecedented spectral fidelity, by using a dual-laser absorption spectrometer, recently developed for the aim of a spectroscopic determination of the Boltzmann constant. The investigated transitions were: 2_2<em>,</em>1→ 2_2<em>,</em>0 , 4_4<em>,</em>1→ 4_4<em>,</em>0and 3_0<em>,</em>3→ 2_0<em>,</em>2. The pC-SDHC profile is found to be quite robust, regardless of the choice of the particular speed dependence, provided that the velocity-changing collision frequency is considered as a free parameter. In particular, the pressure broadening and shifting parameters, retrieved by using the quadratic and hypergeometric versions, were found to be fully consistent. Similarly, the integrated absorbance was found to be completely unaffected by the choice of the speed-dependence, in the whole pressure range that we have explored. It should be said, however, that the velocity-changing collision frequency resulted to be physically meaningful only for the hg-version, but not for the q-version. Therefore, in the quadratic approximation, the collision frequency must be considered just as an indispensable parameter to be included in the fitting procedure for the aims of a successful fit.</p

COMB-ASSISTED QCL DOPPLER-BROADENED THERMOMETRY IN NH3_3 SAMPLES

Author Institution: IMRA America, Ann Arbor, MI; Dipartimento di Fisica del Politecnico di Milano, Milano, Italy; Seconda Universita Di Napoli, Caserta, Italy; Deutsches Eleketronen-Synchrotron, Hamburg, Germany; IMRA America, Ann Arbor, MIThe thermodynamic temperature of a gaseous medium at thermodynamic equilibrium can be extracted from molecular spectra by examining: the relative intensities of rotational structures, the relative intensity of vibrational satellites, or the Doppler width of individual rovibrational lines. Of these methods, Doppler broadening thermometry (DBT), measuring the Doppler width of a single, well-isolated absorption profile, represents a primary method providing the most accurate optical determinations. DBT requires highly precise, accurate and repeatable frequency scanning of a narrow-linewidth probe laser around a given center frequency. This requirement often calls for complicated sideband-based approaches or frequency-locking techniques. We describe here an elegant implementation of Doppler broadening thermometry in which a room-temperature continuous-wave quantum cascade laser at 9.07 $\mu$m is coherently phase-locked to a thulium frequency comb centered at 2 $\mu$m. Repeated tuning of the repetition-rate enables wide and highly accurate frequency scans throughout multiple rovibrational lines of ammonia. Hence, the thermodynamic temperature is retrieved from a manifold of profiles, rather than from a single, isolated line, taking advantage of the simple scaling law that relates Doppler width and line-center frequency. This is realized, regardless of the complexity of the adopted lineshape model, by implementing a multiple-line fitting procedure with some relevant physical constraints. The precision attained for the retrieved gas temperature, even in the absence of an accurate control of the thermodynamic conditions of the ammonia sample, is as high as 50 ppm, even from an analysis of a restricted number of spectra ($\sim$100), acquired at different gas pressures. This represents a particularly relevant result as compared to previous DBT based upon Doppler-width retrievals from an isolated spectral line