Hartmann-Tran Profile Research Articles

High-precision HD spectroscopy near 1.53 μm

In this study, we report highly precise and accurate measurements of the P(5), P(6), and O(3) transitions of the 2–0 band of HD occurring at approximately 1.5 μm. HD spectra were acquired in the pressure range of 100–900 Torr using a cavity ring-down spectrometer linked to an optical frequency comb. The line-shape analysis was performed using the Hartmann–Tran profile in the so-called β-corrected version. For the P(5) transition, we improved the accuracy of previous line center frequency determinations by more than two orders of magnitude. Moreover, for the P(5) and P(6) line centers, the total standard uncertainty is below 3 MHz, similar to those provided by quantum electrodynamics predictions, making them useful for direct comparisons that might foster future improvements of the theoretical model.

Spectral profile of ro-vibrational transitions of HCl broadened by He, Ar and SF6: Testing the β-correction to the Hartmann-Tran profile and the speed dependent (complex) hard collision model

The β-correction to the Hartmann-Tran (HT) profile, recently introduced to model the spectral shape of a molecular transition strongly affected by the Dicke narrowing effect (Konefal et al., JQSRT 242 (2020) 106,784), the HT profile (Ngo et al., JQSRT 129 (2013) 89), and the speed dependent (complex) hard collision model (SDcHC, in which the velocity changing collision rate is characterized by a complex number) are tested using spectra of two rovibrational lines of HCl. The R(5) and R(9) lines of the fundamental band of HCl broadened by He, Ar and SF6 have been recorded with a difference-frequency laser spectrometer for total pressures ranging from 12 to 930 mbar. These lines, measured in large pressure ranges with different collision-partners provide a meaningful test of the above-mentioned line-shape models. The results confirm that non-Voigt effects are significant for HCl broadened by Ar and SF6 and mainly due to the large influence of the Dicke narrowing effect. For HCl-SF6 and HCl-Ar, especially for the R(9) line, using the β-correction together with the HT profile (and with the speed-dependent hard collision model, SDHC) significantly improves the fit residuals while it has no effect on (or tends to deteriorate) the quality of the fit for HCl-He and for the R(5) line of HCl-SF6, for which the influence of velocity changing collisions is smaller. Except for HCl-He, the SDcHC model leads to better quality of fit compared to the HT profile. The results also show that numerical correlations between refined line-shape parameters of the HT profile are important and can lead to ill-determined parameters while they are more properly determined with the SDcHC model.

Comparative line position and line strength analysis of the [formula omitted] dyad of [formula omitted] and [formula omitted

A highly accurate ro-vibrational analysis of FTIR spectra (line positions of 13CD4 and line strengths of both the 12CD4 and 13CD4 species) is presented. The high-resolution infrared spectra of both molecules were measured with a Bruker IFS125 HR Fourier transform infrared spectrometer at an optical resolution of 0.003 cm−1 and analyzed in the regions of 800–1400 cm−1 where the ν2/ν4 dyad is located. The number of 901 transitions with Jmax=23 were assigned to the ν4 and ν2 bands of 13CD4 (this number is about 5.3 times higher in comparison with the number of known assigned transitions for 13CD4). The weighted fit of experimental line positions was made using the Hamiltonian model which takes into account the resonance interactions between the (0001,F2) and (0100,E) vibrational states. As a result, set of 18 fitted parameters of the (0001,F2)/(0100,E) vibrational states of 13CD4 was determined which reproduce the initial 901 experimental ro–vibrational line positions with the drms=2.59×10−4 cm−1, which is close to the experimental uncertainty of the recorded spectra and about 1330 times better in comparison with the reproduction of the same line position values by the use of parameters from Loëte et al. (1983). The analysis of 1557 experimental lines of the dyad of 12CD4 and 131 lines of the dyad of 13CD4 was fulfilled with the Hartmann–Tran profile to simulate the measured line shape and to determine experimental line intensities. Sets of 6/1 varied effective dipole moment parameters of 12CD4/13CD4 are determined which reproduce the initial 1557/131 line strengths with the drms=4.80% and 4.21%. Lists of the assigned line positions and strengths in the studied region are presented as the Supplementary data to this paper.

Revising the H2 16O line-shape parameters around 1.1 μm based on the speed-dependent Nelkin–Ghatak profile andthe Hartmann–Tran profile

Accurate spectroscopic data for H2 16O in the 1.1 μm region are particularly important for the study of Earth’s atmosphere. The pure water vapor molecular spectra were measured based on direct laser absorption spectroscopy using a narrow line-width external cavity diode laser combined with a high-precision Fabry–Pérot etalon. A total of 31 H2 16O transitions were studied for the first time by using the speed-dependent Nelkin–Ghatak profile and the Hartmann–Tran profile. From an accurate line-shape analysis, we obtained the line intensities and the self-broadening coefficients, and they are compared with the available data reported in the HITRAN 2016 database and the HITRAN 2020 database. Finally, we obtained information on the influence of Dicke narrowing, as well as the correlations between Dicke narrowing and speed dependence, and of speed-dependent effects.

Line-shape parameters and line mixing for the low-intensity high-J oxygen transitions

We present the results of investigations of the oxygen B-band R-branch transitions with intensities in the range from 1.5×10−26 to 2.5×10−28 cm−1/(molecule/cm2) and the total angular momentum quantum number for the lower state, J”, up to 38. High resolution CRDS laboratory spectra were fitted with the Voigt profile as well as with advanced line-shape functions consistent with the Hartmann–Tran profile, that is the speed-dependent Voigt profile and speed-dependent Nelkin–Ghatak profile using the multispectrum fitting technique. The line positions, line intensities and other line-shape parameters, together with our previous data, were collated to show trends for the whole R branch. Using the determined frequencies of the B-band transitions, the Dunham fit was performed to obtain spectroscopic parameters for both ground and excited states. Newly recorded spectra at the band head, with the signal-to-noise ratio above 20000, were analyzed with line profiles including also the line mixing. First-order line mixing determined directly from the line shape fitting at relatively low pressure (32 Torr) is in good agreement with values calculated by Sung et al. [1].

The effects of advanced spectral line shapes on atmospheric carbon dioxide retrievals

Line shape effects such as speed-dependence and collisional (Dicke) narrowing are manifest in high signal-to-noise ratio laboratory spectra for a wide range of molecular species and sample conditions. However, these effects are usually neglected in spectroscopic models used in remote sensing of atmospheric greenhouse gases. Here we examine the effects of line profile choice on laboratory spectra and XCO2 values retrieved from Total Carbon Column Observing Network (TCCON) spectra. To this end, we utilize limiting cases of the Hartmann-Tran profile (HTP) with shape parameters recently measured by cavity ring-down spectroscopy. Significant differences highlighting the importance of including speed-dependence effects in forward models were observed both in scaling retrievals as well as profile retrievals. However, because of uncertainties associated with the atmospheric temperature gradient, it was not possible to extract accurate carbon column profiles even with inclusion of these new line shape parameters and advanced line profiles.

Assessment of the precision, bias and numerical correlation of fitted parameters obtained by multi-spectrum fits of the Hartmann-Tran line profile to simulated absorption spectra

Although the Voigt profile has long been used to analyze absorption spectra, the quest for increased precision, accuracy and generality drives the application of advanced models of atomic and molecular line shapes. To this end, the Hartmann-Tran profile is now recommended as a standard for high-resolution spectroscopy because it parameterizes relevant higher-order physical effects, is computationally efficient, and reduces to other widely used profiles as limiting cases. This work explores the uncertainty with which line shape parameters can be obtained from constrained multi-spectrum fits of spectra simulated with this standard profile, varying uncertainty levels in the spectrum detuning and absorption axes, and spanning a range of sampling density, pressure, and line shape parameter values. The analysis focuses on how noise-limited measurement precision of frequency detuning and absorption drive statistical uncertainties in fitted parameters and numerical correlations between these quantities. Also, we quantify the degree of equivalence between the full Hartmann-Tran profile and those derived from it in terms of fitted peak areas and line shape parameters. Finally, we introduce a new open-source software package named Multi-spectrum Analysis Tool for Spectroscopy (MATS), which allows users to fit the HTP and its derived profiles to experimental or simulated absorption spectra to explore the limits of the HTP under actual experimental or user-defined conditions.

Simultaneous measurement of H2O concentration and effective absorption optical path length under unknown optical path length condition based on a single spectral line

Quantitative gas measurement under the condition of unknown optical path length is a challenge in laser absorption spectroscopy technology field. In this paper, we proposed a tunable diode laser absorption spectroscopy line shape analysis (TDLAS-LSA) method for simultaneous measurement of water vapor concentration and effective optical path length (EOPL) under unknown optical path conditions. A single H2O absorption line near 1383.9 nm (7226.02 cm−1) was selected, and its line strength, self-broadening coefficient and temperature-dependence coefficient were measured experimentally to improve the HITRAN databases. The Lorentz broadening and line area were accurately extracted by Hartmann-Tran profile (HTP) fitting, and the gas concentration and EOPL were calculated based on the spectral line shape analysis method. Eight concentrations of water vapor in the range of 146 ppm ∼ 4.39% were measured experimentally, and the maximum average deviation between the TDLAS-LSA method and the commercial sensor was less than 7.1%. Comparing the EOPL with mechanical measurement, the maximum deviation of multiple measurements is less than 5.7%. The results showed that the TDLAS-LSA method can effectively perform gas sensing under unknown optical path conditions, and has great application potential in low-cost, in-situ and multi-parameter simultaneous measurement.

High accuracy CO2 Fourier transform measurements in the range 6000–7000 cm−1

A Bruker IFS 125HR Fourier-transform spectrometer has been used to measure pure carbon dioxide transmittance spectra in the spectral range 6000–7000 cm−1, including the bands 30011-00001, 30012-00001, 30013-00001, 30014-00001, and 00031-00001. A total of 10 measurements with absorption path lengths between 14.6 and 59.4 m and sample pressures from 3 to 80 mbar were performed at 295 K. A multispectrum fitting approach was used applying the Hartmann-Tran profile extended to account for line mixing in the Rosenkranz first order perturbation approximation. Line positions, self-shifts, intensities, self-broadened widths, their speed dependence and in some cases line mixing were adjusted for fitting the measurements. A rigorous error analysis has been performed. The primary goal of this work was to investigate whether Fourier transform spectroscopy can deliver line intensity accuracy down to the 0.1% level. In this work, a combined systematic standard uncertainty of 0.15% has been achieved, further improvements down to the 0.1% level are feasible. The achieved level of combined standard uncertainty has, to our knowledge, not been reached by Fourier-transform spectroscopy before. Comparisons with most recent work are presented for line positions, line intensities, self-broadening and its speed dependence, and self-shifts. Measurement and line parameter databases are provided on Zenodo (doi:10.5281/zenodo.4525272).

Absorption line asymmetry: Speed-dependent effects observed from coherent transients on the 86 GHz line of HC15N in collision with polar and diatomic molecules and with rare gases

The shape of the J = 0→1 rotational line of HC15N at 86 GHz has been recorded in collision with various polar and diatomic molecules and with all rare gases within the 135-300 kelvin temperature range. The coherent transient technique employed, optical precession in the time domain, has revealed as very propitious to analyze departures observed from the Voigt profile. First, a detailed analysis of frequency-instabilities of the electromagnetic source has been done and their consequences on observed signals are discussed in details. Then, it has been clearly evidenced that Voigt profile departures result from the speed-dependence (SD) of collisional broadening and frequency-shifting rates, a feature responsible of narrowing and asymmetry of lineshapes, respectively, in the frequency domain. In contrast, it appears that velocity/speed changing collisions have a negligible influence. From a comparison of the hypergeometric SD-Voigt profile with the quadratic SD-Voigt profile, it is shown the latter could be inappropriate in case of SD-frequency-shifts. So, experimental records have been fitted using the asymmetric hypergeometric SD-Voigt profile and temperature dependences have been analyzed. Finally and as required for inclusion in databases, results are also given using Hartmann-Tran profile parameters.

Spectral line-shape analysis of CO2 transition using Hartmann-Tran profile and its asymptotic limits

In this paper, the Hartmann-Tran profile (HTP) and its asymptotic limits are employed to analyze the experimentally-measured absorption spectra of CO2 gas. The fitted results by multi-spectrum fitting are compared to those from the ordinary line-shape models. The equivalence and computational efficiency of the asymptotic limits of HTP to their ordinary counterparts are studied. The research shows that the parameters of line position ω0, intensity S, pressure broadening coefficient Γ0/p and shifting coefficient Δ0/p by HTP agree well with those from the speed-dependent hard-collision line-shapes. In comparison, the poorly-determined partial-correlation parameter η makes the fitted line-narrowing parameters less reliable.

Line strength analysis of the second overtone [formula omitted] band of D[formula omitted

The high resolution infrared spectrum of di–deuterated hydrogen sulfide D2S was recorded with a Bruker IFS 125HR Fourier transform infrared spectrometer and analyzed in the region of 2400–2900 cm−1 where ro–vibrational bands of the so–called second triad of D2S are located. The present study is focused on the line strength analysis of the weak 3ν2 band which is made for the first time. The strength analysis comprise 300 lines (376 transitions) with maximum values of the quantum numbers Jmax = 18 and Kamax = 9 and was performed by the fit of the experimental line shapes with a Hartmann–Tran profile. The six effective dipole moment parameters of the 3ν2 band were obtained from the weighted fit which reproduce the initial experimental line strengths with the drms=3.1%.

Line strengths, widths and shifts analysis of the [formula omitted][formula omitted] and [formula omitted] bands in [formula omitted]SiH[formula omitted][formula omitted]SiH[formula omitted] and [formula omitted]SiH[formula omitted

The high resolution infrared spectra of SiH4 in its natural abundance were recorded with a Bruker IFS125 HR Fourier transform infrared spectrometer at an optical resolution of 0.003 cm−1 and analyzed in the region of 1600–2100 cm−1 where the first bending overtone 2ν2,2ν4 and combinational ν2+ν4 bands are located. A line strength analysis of the 2018 (1636/211/171) experimentally recorded transitions of the 28SiH4,29SiH4, and 30SiH4 species was made by the fit of their line shapes with the Hartmann-Tran profile and 9 effective dipole moment parameters (7/1/1 fitted parameters for the 28SiH4,29SiH4 and 30SiH4 species, respectively) were obtained from the weighted fit which reproduce initial experimental line strengths of 28SiH4,29SiH4 and 30SiH4 with the drms=3.65%,3.77% and 3.46%. Self–broadening coefficients of 1064 lines (typically lying between (8 and 10)×10−2 cm−1·atm−1) and self–shift coefficients of 785 lines (typically lying between (5 and 10)×10−3 cm−1·atm−1) of all three isotopologues of silane were determined from the multi–spectrum analysis of these lines.

Comprehensive study of the pentad bending triad region of germane: Positions, strengths, widths and shifts of lines in the [formula omitted][formula omitted] and [formula omitted] bands of [formula omitted]GeH[formula omitted][formula omitted]GeH[formula omitted][formula omitted]GeH[formula omitted][formula omitted]GeH[formula omitted][formula omitted]GeH[formula omitted

The high resolution infrared spectra of GeH4 in its natural abundance were recorded with a Bruker IFS125 HR Fourier transform infrared spectrometer at an optical resolution of 0.003 cm−1 and analyzed in the region of 1400–2000 cm−1 where the first bending overtone 2ν2,2ν4 and combinational ν2+ν4 bands are located. Ro–vibrational line positions and energies of the 70GeH4 species were analysed for the first time and line positions and energies of the 72GeH4 and 74GeH4 species were improved considerably in comparison with the preceding studies. The numbers of 2316/2406/873/3007/2257 transitions with Jmax = 21/23/18/22/19 of the 2ν2 (A1− and E−type sub–bands), 2ν4 (A1−,E− and F2−type sub–bands) and ν2+ν4 (F1− and F2−type sub–bands) bands of the 70GeH4,72GeH4,73GeH4,74GeH4, and 76GeH4 molecules were used in the joint weighted fit of experimentally assigned transitions with the Hamiltonian model which takes the resonance interactions between the seven, (0200,A1),(0200,E),(0101,F1),(0101,F2),(0002,A1),(0002,E) and (0002,F2), vibrational states into account. From our preceding studies 5563 hot band transitions were also taken into account. As the result of a joint fit, a set of 129 fitted parameters was obtained which reproduce the initial 16422 experimental (including “hot”) transitions of five isotopologues with the drms=3.26×10−4 cm−1. A line strength analysis of the 1697 experimentally recorded transitions of all species was made by the fit of their line shapes with the Hartmann-Tran profile and 13 effective dipole moment parameters were obtained from the weighted fit which reproduce the initial experimental line strengths with the drms=3.4%. Self–broadening coefficients of 993 lines and self–shift coefficients of 674 lines were determined from the multi–spectrum analysis of these lines.

Quantitative analysis of ro–vibrational spectra of ethylene: Line strengths of the [formula omitted] and [formula omitted] bands of [formula omitted]C[formula omitted]H[formula omitted]D[formula omitted]-cis

For the 12C2H2D2-cis molecule a line strength analysis of 1473/400 transitions of the ν12/ν3 bands was performed by the fit of their line shapes with the Hartmann–Tran profile. Ten effective dipole moment parameters (six parameters for the ν12 band and four parameters for the ν3 band) were obtained from the weighted fit which reproduce the initial experimental 1473 transition strengths of the ν12 band with the drms=3.11%. For the very weak ν3 band 400 experimental transitions are reproduced with the drms=7.72%. The results of the analysis are presented as the Supplementary material to this paper.

Computational aspects of speed-dependent Voigt and Rautian profiles

For accurate line-by-line modeling of molecular cross sections several physical processes “beyond Voigt” have to be considered. For the speed-dependent Voigt and Rautian profiles (SDV, SDR) and the Hartmann-Tran profile the difference w(iz−)−w(iz+) of two complex error functions (essentially Voigt functions) has to be evaluated where the function arguments z ± are given by the sum and difference of two square roots. These two terms describing z ± can be huge and the default implementation of the difference can lead to large cancellation errors. First we demonstrate that these problems can be avoided by a simple reformulation of z−. Furthermore we show that a single rational approximation of the complex error function valid in the whole complex plane (e.g. by Humlíček, 1979 or Weideman, 1994) enables computation of the SDV and SDR with four significant digits or better. Our benchmarks indicate that the SDV and SDR functions are about a factor 2.2 slower compared to the Voigt function, but for evaluation of molecular cross sections this time lag does not significantly prolong the overall program execution because speed-dependent parameters are available only for a fraction of strong lines.

Ro–vibrational analysis of the first hexad of hydrogen sulfide: Line position and strength analysis of the 4ν2 band of H232S and H234S for HITRAN applications

The high resolution infrared spectrum of hydrogen sulfide H232S was recorded with a Bruker IFS 125HR Fourier transform infrared spectrometer and analyzed in the region of 4400–5400 cm−1 where ro–vibrational bands of the so–called first hexad of hydrogen sulfide are located. The present study is focused on the weak 4ν2 band. The 505 transitions with maximum values of the quantum numbers Jmax=17 and Kamax=8 (Jmax = 9 and Kamax=7 in the preceding studies) were assigned in the experimental spectrum. On this basis, 132 upper ro–vibrational energies (which is 2.5 times as high as in the preceding studies) were obtained. These data were used in the weighted fit of the Watson Hamiltonian parameters. The 28 varied parameters reproduce the 132 initial energy values with the root mean square deviation drms=3.5×10−4 cm−1. Strength analysis of the 287 strongest experimentally recorded transitions was made by the fit of their line shapes with the Hartmann-Tran profile. The eight effective dipole moment parameters of the 4ν2 band were obtained from the weighted fit which reproduce the initial experimental line strengths with the drms=3.1%. A comparison of the obtained results with the results of variational calculations and HITRAN data is presented. For the first time, transitions of the 4ν2 band of H234S were assigned in the experimental spectrum.

Investigation of the Spectral Line Intensities of the ν9 Band of the Trans-Conformer of Ethylene

The intensities of 740 vibrational-rotational lines of the ν9 fundamental band in the IR spectrum of the trans-C2H2D2 molecule are first analyzed. The Hartmann–Tran profile is used to fit the line contour. More than 2700 spectral transitions are assigned using the ground state combination difference method and the isotopic substitution theory. The special features of the spectral line broadening and the influence of the parameters of the Hartmann–Tran line profile on the accuracy of line contour reconstruction are considered.

Accurate deuterium spectroscopy and comparison with ab initio calculations

We present accurate measurements of the quadrupole S(3) and S(4) transitions of the ${\mathrm{D}}_{2}\phantom{\rule{4pt}{0ex}}2\ensuremath{-}0$ band. Self-perturbed spectra were collected in a wide pressure range with a cavity ring-down spectrometer linked to an optical frequency comb. The results of ab initio quantum scattering calculations were incorporated into the line-shape analysis which was performed using the Hartmann-Tran profile. This approach allowed us to mitigate the collisional systematics and to reach a 900-kHz accuracy of the transition frequencies, which represents a 30-fold improvement compared to previously available data. We also compare our findings with newly calculated transition frequencies that include relativistic and quantum electrodynamics corrections up to ${\ensuremath{\alpha}}^{7}$. The differences between theoretical and experimental values for the transition frequencies are 2.2 MHz and 3.3 MHz for the S(3) and S(4) transitions, respectively.

Spectral Line Shape Analysis Using Hartmann‐Tran Profile for Tunable Diode Laser Absorption Spectroscopy of Water Vapor at 1.39 μm

In this study, spectral line shape analysis was conducted for water vapor absorption at 1.39 μm with a Hartmann‐Tran profile (HTP), which is capable of being efficiently and accurately reduced to (speed dependent) Voigt and (speed dependent) Rautian profiles. The near‐IR absorption lines of water vapor were measured using tunable diode laser absorption spectroscopy (TDLAS). The spectrum fitting code was home‐written based on the Trust region reflective algorithm and the HTP. Voigt profile (VP), Rautian profile (RP), speed‐dependent VP (SDVP), and speed‐dependent Rautian profile (SDRP), which were reduced from the HTP, were used as model functions to test the validity of the near‐IR absorption lines of water vapor in terms of line shape profile. With the SDVP, the standard deviation of the fitting residuals was at a 10−3 level relative to the most intense peak height in a range of 1.39 μm at 2.5 Torr and room temperature, while the global standard deviation was less than 0.5 × 10−3, thus showing the best result among them. This suggests the need to consider the speed‐dependent collision width in the self‐broadening of water vapor.