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This paper describes the optimisation theory on which VPFIT, a non-linear least-squares program for modelling absorption spectra, is based. Particular attention is paid to precision. Voigt function derivatives have previously been calculated using numerical finite difference approximations. We show how these can instead be computed analytically using Taylor series expansions and look-up tables. We introduce a new optimisation method for an efficient descent path to the best-fit, combining the principles used in both the Gauss-Newton and Levenberg-Marquardt algorithms. A simple practical fix for ill-conditioning is described, a common problem when modelling quasar absorption systems. We also summarise how unbiased modelling depends on using an appropriate information criterion to guard against over- or under-fitting. The methods and the new implementations introduced in this paper are aimed at optimal usage of future data from facilities such as ESPRESSO/VLT and HIRES/ELT, particularly for the most demanding applications such as searches for spacetime variations in fundamental constants and attempts to detect cosmological redshift drift., 15 pages, 7 figures, to appear in MNRAS

The absorption spectra of a water molecule perturbed by argon pressure were measured in the 6700–7650 cm−1 region. The spectra were recorded at an IFS 125HR Fourier spectrometer with a high signal-to-noise ratio at a room temperature with a spectral resolution of 0.01 cm−1. The argon pressure was varied from 0 to 0.9 atm. Using three line profile models (the traditional Voigt profile; the quadratic Voigt profile, which depends on the speed of an absorbing molecule; and the Hartmann–Tran profile), the parameters of the absorption lines of the water molecule were calculated. A better agreement with the experimental data is provided by the Hartmann–Tran profile. It is suggested to use a relatively simple Voigt profile for mass measurements at pressures above 300 mbar.

H2O absorption lines broadened by air pressure were recorded in the 5900–6100-cm−1 spectral region with the use of a Bruker IFS 125 HR spectrometer. The intensities and broadening and shift coefficients of H2O absorption lines are determined for the Voigt profile and the modified Voigt profile which takes into account the dependence of the broadening on the speed of the colliding molecules. The atmospheric transmission is calculated with the use of H2O line parameters from different versions of the HITRAN and GEISA spectroscopic databases and our new data. Model spectra are compared with atmospheric solar spectra measured with a ground-based Fourier spectrometer. It is shown that the use of our new data on H2O absorption line parameters improves the agreement between the model and measured atmospheric spectra.

The analytical expression for the Voigt profile, along with its simplified forms for the Gaussian and Lorentzian dominance, is presented. The applicability of the Voigt profile in the description of anomalous diffusion phenomena, ubiquitous in different fields of science including protein folding, is discussed. It is shown that the Voigt profile is a good descriptor of the processes occurring in protein folding and in the native state. The usefulness of the Voigt profile in deriving important information of the diffusive motions in proteins from a quasielastic incoherent neutron scattering experiments is illustrated.

Dual-comb spectroscopy has become a topic of growing interest in recent years due to the advantages it offers in terms of frequency resolution, accuracy, acquisition speed, and signal-to-noise ratio, with respect to other existing spectroscopic techniques. In addition, its characteristic of mapping the optical frequencies into radio-frequency ranges opens up the possibility of using non-demanding digitizers. In this paper, we show that a low-cost software defined radio platform can be used as a receiver to obtain such signals accurately using a dual-comb spectrometer based on gain-switched semiconductor lasers. We compare its performance with that of a real-time digital oscilloscope, finding similar results for both digitizers. We measure an absorption line of a H13C14N cell and obtain that for an integration time of 1 s, the deviation obtained between the experimental data and the Voigt profile fitted to these data is around 0.97% using the low-cost digitizer while it is around 0.84% when using the high-end digitizer. The use of both technologies, semiconductor lasers and low-cost software defined radio platforms, can pave the way towards the development of cost-efficient dual-comb spectrometers.

As a rule, the width of a spectral line in atomic emission spectral analysis with arc sources is much smaller than the hardware function of the spectral device. Thus, the spectral line contour is determined by the hardware function of the device and can be approximated, e.g., by the Voigt function. However, when reference samples with a wide range of element concentrations are analyzed, there is a frequent problem of self-absorption that causes one to change the analytical line, which is not always possible. It is proposed to modify the Voigt function by adding a factor that describes self-absorption, by analogy with the Bouguer–Lambert law. The possibility of using the proposed function is evaluated during the analysis of reference samples of rocks, ores, and sandstones in a Grand-Potok spectral system with a MAES analyzer and BLPP-2000 photodetector arrays. The use of the proposed approximating function has provided an increase in the working range of the calibration curves of Cu 327.3954 nm, Cu 324.7532 nm, Pb 287.3311 nm, Ni 305.0818 nm, and Mo 313.2594 nm by 1–3 orders of magnitude.

Terahertz time-domain spectroscopy (THz-TDS) has been used to analyze mixtures of imidacloprid, carbendazim, and flour substrate. A multiple spectra baseline correction (MSBC) method was adopted to...

In this paper, by using the confluent hypergeometric function of the first kind, we propose a further extension of the Voigt function and obtain its useful properties as (for example) explicit representation and partly bilateral and partly unilateral representation. By means of the present representations, we derive several (presumably new) generating functions which are partly bilateral and partly unilateral. Some interesting recurrence relations of the Voigt function introduced here are also indicated.

Direct-comb spectroscopy techniques uses optical frequency combs (OFCs) as spectroscopic light source. They deliver high sensitivity, high frequency resolution and precision in a broad spectral range. Due to these features, the field has burgeoned in recent years. In this work we constructed an OFC-based cavity-enhanced Fourier-transform spectrometer in the near-infrared region and used it for a line-shape study of rovibrational transitions of CO perturbed by Ar. The highly sensitive measurements spanned the wavenumber range from 6270 cm $^{-1}$ to 6410 cm $^{-1}$ , which covered both P and R branch of the second overtone band of CO. The spectrometer delivers high-resolution surpassing the Fourier-transform resolution limit determined by interferogram length, successfully removing ringing and broadening effects caused by instrumental line shape function. The instrumental-line-shape-free method and high signal-to-noise ratio in the measurement allowed us to observe collisional effects beyond those described by the Voigt profile. We retrieved collisional line-shape parameters by fitting the speed-dependent Voigt profile and found good agreement with the values given by precise cavity ring-down spectroscopy measurements that used a continuous-wave laser referenced to a stabilized OFC. The results demonstrate that OFC-based cavity-enhanced Fourier-transform spectroscopy is a strong tool for accurate line-shape studies that will be crucial for future spectral databases.

BACKGROUND: Chemical exchange saturation transfer (CEST) MRI is a promising approach for detecting biochemical alterations in cancers and neurological diseases, but the quantification can be challenging. Among numerous quantification methods, Lorentzian difference (LD) is relatively simple and widely used, which employs Lorentzian line-shape as a reference to describe the direct saturation (DS) of water and takes account of difference against experimental CEST spectra data. However, LD often overestimates CEST and nuclear overhauser enhancement (NOE) effects. Specifically, for fast-exchanging CEST species require higher saturation power (B(1_sat)) or in the presence of strong magnetization transfer (MT) contrast, Z-spectrum appears more like a Gaussian line-shape rather than a Lorentzian line-shape. METHODS: To improve the conventional LD analysis, the present study developed and validated a novel fitting algorithm through a linear combination of Gaussian and Lorentzian function as the reference spectra, namely, Voxel-wise Optimization of Pseudo Voigt Profile (VOPVP). The experimental Z-spectra were pre-fitted with Gaussian and Lorentzian method independently, in order to determine Lorentzian proportionality coefficient (a). To further compensate for the line-shape changes under different B(1_sat)’s, a B(1)-dependent adjustment was applied to the experimental Z-spectra (Z(_exp)) according to the prior knowledge learned from 5-pool Bloch equation-based simulations at a range of B(1_sat)’s. Then, the obtained Z-spectra (Z(_B1adj)) was fitted by the previously defined VOPVP function. Considering the asymmetric component of MT, the positive- and negative-side of Z-spectra were fitted separately, while the middle part (−0.6 to 0.6 ppm, consisted primarily of DS) was fitted using Lorentzian function. Finally, the difference between Z(_VOPVP) and Z(_exp) was defined as the CEST and NOE contrast. To validate our VOPVP method, an extensive simulation of CEST Z-spectra was performed using 5-pool model and 6-pool model with greater MT component. RESULTS: In comparison with LD approach, VOPVP exhibited lower sum of squares due to error (SSE) and higher goodness of fit (R-square) for the experimental Z-spectra at all B(1_sat). Moreover, the results indicated that VOPVP fitting improved the overestimated contributions from amide proton transfer (APT) and NOE through LD at all B(1_sat). Despite that the relationship for B(1)-dependent adjustment was pre-determined using a single 5-pool model, the VOPVP fittings obtained accurate quantification for multiple 6-pool models with a range of T(1)w’s and T(2)w’s. The robustness of VOPVP fitting was also proved by simulations using 3T parameters. Furthermore, we assessed VOPVP in vivo in a glioblastoma-bearing mouse. Compared to LD maps, VOPVP quantification maps displayed higher contrast-to-noise ratio between tumor and normal contralateral tissue for APT, glutamate and nuclear overhauser effect (NOE), when B(1_sat) >1 µT. CONCLUSIONS: As an improvement of LD method, VOPVP fitting can serve as a simple, robust and more accurate approach for quantifying CEST and NOE contrast.

The weak low frequency tail of the ozone Wulf band is newly studied by high sensitivity cavity ring down spectroscopy (CRDS) in the 7920–8700 cm−1 range. Although strongly obscured by impurity lines, the ozone absorption signature shows up in the recorded spectra as two mostly unresolved absorption bands. These two bands with maximum near 8154 and 8450 cm−1 are hot bands from the (020) and (100) ground state vibrational levels reaching the same predissociated 3A2(000) upper state of 16O3. The observed bands include a mostly structureless continuum and lines exhibiting a clear broadening due to the predissociation of the 3A2(000) upper state. On the basis of assignments of the rotational structure available in the literature for the 3A2(000)-X1A1(000) cold band centered near 9553 cm−1, seventy-four relatively narrow lines could be rotationally assigned to the 3A2(000)-X1A1(020) and 3A2(000)-X1A1(100) hot bands. A line shape analysis, performed using a Voigt profile, provided the width of the Lorentzian component. Additional recordings performed at various pressures for 18 lines allowed to disentangle the pressure and predissociation contributions to the fitted Lorentzian widths. As a result, the newly derived pressure broadening coefficients of the considered rovibronic transitions are found to be similar to those of the rovibrational infrared bands. All the lines studied are affected by significant predissociation due the spin-orbit coupling between the 3A2(000) level and high lying dissociative vibrational levels of the X1A1 electronic ground state. The resulting set of predissociation widths for sixty lines ranges between 9 × 10−3 and 0.2 cm−1 corresponding to upper state lifetime of 560 and 25 ps, respectively. The reported results are discussed in relation with previous experimental and theoretical studies.

We present redshift space two-point ($\xi$), three-point ($\zeta$) and reduced three-point (Q) correlations of Ly$\alpha$ absorbers (Voigt profile components having HI column density, $N_{\rm HI}>10^{13.5}$cm$^{-2}$) over three redshift bins spanning $1.7< z, Comment: 25 pages, 17 figures; Accepted in MNRAS; Comments welcomed

In this paper, we used requantized Classical Molecular Dynamics Simulations (rCMDS), corrected by the room temperature air-broadening coefficients measured in the ν3 band of N2O, to predict line-shape parameters including the broadening coefficient, its speed dependence component, the Dicke narrowing and the line-mixing coefficients, associated with various line-shape models for air-broadened N2O absorption lines. For that, we first computed the auto-correlation functions of the N2O dipole moment, responsible for the absorption transitions. The Fourier-Laplace transform of these functions directly yields the absorption spectra. Calculations were made for three temperatures 200, 250 and 296 K and 1 atm of N2O/air mixtures and for a large range of values of the ratio between the Doppler and Lorentzian widths. The obtained spectra were then fitted with the quadratic speed-dependent Voigt profile including the first-order line mixing using a multi-spectrum fitting procedure. Comparisons with values determined from room temperature high-precision measurements in the ν3 band of N2O by using the same profile [Loos et al, J. Quant. Spectrosc. Rad. Transf., 151, 2015, 300-309] show that our retrieved line broadening coefficients are overestimated by about 4%. The difference between the measured and predicted line broadening coefficients was used to empirically correct the rCMDS auto-correlation functions and thus the corresponding absorption spectra. These latter were then fitted with the Voigt, the speed-dependent Voigt, and the speed-dependent Nelkin-Ghatak profiles, all of them being associated with the first-order line-mixing approximation, providing the corresponding line-shape parameters for lines up to J′′ ≤ 59. The temperature dependences of various line-shape parameters were also deduced. The results show a very good agreement with available experimental data for all the considered parameters.

Accurate and rapid spectrum fitting is very important for quantitatively analyzing laser-induced breakdown spectroscopy (LIBS). The Voigt function is often used to fit LIBS spectral lines. We propose a new approximate Voigt function formula. Based on the classic Lorentz–Gauss linear combination formula, a summation term was added that contained a specific convolution operation to improve the Voigt function’s calculation and fitting accuracy. This formula can be used for the approximate calculation of the Voigt function with an overall accuracy of 0.31% and a full width at half-maximum internal accuracy of 0.25% when the ratio of Lorentzian linewidth to Gaussian linewidth is 1:1. The formula was then applied to LIBS data processing to fit four element spectral lines of calcium (Ca-393.37, 396.85, and 422.67 nm) and potassium (K-766.49 nm). The fitting results showed that this new approximate formula could fit at least seven data points, and compared with the complex plane partition method and the classic linear combination formula, the new formula had better fitting speed and accuracy.

Nuclear magnetic resonance (NMR) spectroscopy is well-established to address questions in large-scale untargeted metabolomics. Although several approaches in data processing and analysis are available, significant issues remain. NMR spectroscopy of urine generates information-rich but complex spectra in which signals often overlap. Furthermore, slight changes in pH and salt concentrations cause peak shifting, which introduces, in combination with baseline irregularities, un-informative noise in statistical analysis. Within this work, a straight-forward data processing tool addresses these problems by applying a non-linear curve fitting model based on Voigt function line shape and integration of the underlying peak areas. This method allows a rapid untargeted analysis of urine metabolomics datasets without relying on time-consuming 2D-spectra based deconvolution or information from spectral libraries. The approach is validated with spiking experiments and tested on a human urine 1H dataset compared to conventionally used methods and aims to facilitate metabolomics data analysis.

The broadening and shift coefficients of H2O absorption lines are compared for Ar, He, H2, and N2 buffer gases. The broadening and shift coefficients were derived from the analysis of the absorption spectra recorded with an FTIR spectrometer in the spectral region 8650–9020 cm−1 with a spectral resolution of 0.01 cm–1. Using two model line profiles (Voigt and speed-dependent Voigt profiles) the parameters of the H2O absorption lines were calculated. It is shown that the speed-dependent Voigt profile provides better agreement with experimental data.

An algorithm is proposed for mathematical processing of Mossbauer spectra of solid solutions by the Tikhonov regularization method using the Voigt function as an elementary line. Spectra of solid solutions Fe100–xGex (x = 5–25 at.%) and Fe75Si15Al10 were processed as examples to show that the algorithm can produce a physically reasonable solution, improve significantly the quality of the processed spectra, and expand the possibilities of Mossbauer spectroscopy. The Voigt function was shown to be a satisfactory approximation for describing the statistical ensemble of nonequivalent local Fe configurations in disordered solid solutions.

The present work is dedicated to the ν6 band of 12CH3I with the aim of generating a complete line list for databases. High resolution Fourier transform spectra have been recorded in MONARIS and a multispectrum fitting procedure using Voigt profile has been applied to retrieve line positions, intensities, and self-broadening coefficients for around 1200 transitions of the ν6 band between 854 and 963 cm−1. Rotational dependences of transition dipole moment squared and self-widths have been studied and empirically modeled. Line positions are retrieved with accuracy equal to 4.10−4 cm−1. The accuracy of line intensities and self-widths measurements is estimated between 5 and 10 %. Theoretical estimates of CH3I self-broadening coefficients for large ranges of rotational quantum numbers (0 ≤ J ≤ 70, 0 ≤ K ≤ 20) are also provided in the frame of a semi-classical approach with exact trajectories and of a semi-empirical method including a correction factor to the Anderson-type line-width expression. Comparisons of our results with the data previously published in the literature are presented and discussed. A complete line list of 5787 transitions is generated. Available as supplementary material, this line list can be used for spectroscopic databases and atmospheric or industrial detection of CH3I.

Ro-vibrational transitions of the 00°3–00°0 band around 1.52 µm with line intensities in the order of 10−24 to 10−23 cm−1/(molecule·cm−2) have been recorded using a comb-assisted laser-locked cavity ring-down spectrometer with high sensitivity as well as high precision. In total, 88 line positions were determined with a sub-MHz uncertainty (1-σ), better than previous experimental results by 1–2 order of magnitude. N2-induced line shape parameters of 20 isolated transitions were derived by using the Voigt profile and the quadratic Speed-Dependent Voigt profile with relative uncertainties of 1–2% (1-σ). Comparisons of the line parameters determined in this work with literature experimental values are given.

A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and Gauss function known as the Voigt function. First, a compact review of several approximations using a consistent notation is presented. The comparison with accurate reference values indicates relative errors as large as some percent., Comment: 7 pages and 2 supplementary pages, 5 figures

Using Fourier transform spectrometer, He-broadening coefficients have been measured for the first time in the P and R branches of the 2ν1 parallel band of carbonyl sulfide (OCS). The measurements have been performed at room temperature for rotational quantum number up to J = 70. A total of 131 lines were measured using a nonlinear least squares multi-pressure spectrum fitting procedure. Since the measurements have been performed using different values of OCS pressures, we have also retrieved line intensities of the ro-vibrational lines of the same branches. The fits were performed using the Voigt profile which leads to a precise determination of these spectroscopic parameters. From line intensities, we have determined vibrational transition moment, band intensity as well as Herman-Wallis parameters for the 2ν1 band. The results have been discussed as a function of the rotational quantum number and compared to previous data. The line-mixing effect on broadening coefficients was also analyzed showing a negligible influence.

Here we indicate how a particular version of the trapezoidal integration with residue correction for the evaluation of the Voigt functions indicated by us previously can be easily extended to serve the purpose of reference value generation. Specifically by resorting to quadruple precision, we demonstrate a reliable computation with a minimum of 30 digit accuracy for the Voigt functions H(x, a) and G(x, a). Compared to the prescription of Boyer et al., this method reduces the computational cost several fold when very high reference accuracy is the aim. In addition we show that when both the parameters x and a are less than unity, the series of Faddeeva et al. can be profitably used for the required evaluation instead of this quadrature.

For the ordinary and the generalised Voigt functions, we indicate an accurate and efficient sinc function based numerical integration method. This involves a trapezoidal integration with residue correction for the poles of the integrand. We provide a rough saddle point estimate of the discretisation error. We also indicate how to reduce the numerical oscillations by symmetrising the quadrature nodes around the real part of the singularity. By a suitable step size choice, a minimum of 14 digit accuracy (with respect to published reference values) is guaranteed for the generalised Voigt function evaluation for all values of the dependent parameters.

Linestrengths, self-broadening and narrowing coefficients for 8 absorption transitions of CO2 near 1.43 µm were measured using the wavelength modulation direct absorption spectroscopy (WM-DAS) at 300–1000 K and 5–20 kPa. The SNR was enhanced to 1500 for the peak absorbance around 5% at room temperature and remains at 550 for the peak absorbance around 1% at high temperatures by use of the WM-DAS method. The Voigt, Rautian, Galatry and quadratic speed-dependent Voigt profiles were used to recover the absorbance and retrieve the best-fit spectroscopic parameters and their temperature dependence. The quadratic speed-dependent Voigt profile was found to give the best combination of accuracy and robust lineshape parameters. The measured linestrengths and self-broadening coefficients compare well with the available values listed in the HITRAN/HITEMP database. The self-narrowing coefficients were also determined for GP, RP and qSDVP with analyses of the uncertainties in these spectroscopic parameters.

Graphene has many unique properties which make it an attractive material for many applications. Analytical methods to differentiate graphene from graphite, like the optical contrast technique, atomic force microscopy or conventional Raman analysis based on intensity ratios, require a specific sample preparation and substrate. Here we report a method to distinguish between few-layer graphene (with less than 10 layers) and graphite that is independent of a specific sample preparation or substrate. Our approach is based on the symmetry of the Raman 2D peak in graphene and its asymmetry in graphite. By evaluating the coefficient of determination R2 of a Voigt profile fit we can establish a benchmark that discerns graphene from graphite. We found values above 0.985 to be characteristic of graphene. The results were confirmed by thickness measurements with atomic force microscopy. We applied this analysis to both individual graphene flakes and graphene flakes as a thick film. This method allows for fast characterisation of large quantities, a feature that is needed for industrial application. It can be used to determine the graphene content of flakes produced from graphite exfoliation and the efficiency of various production methods.

In this work, contribution of all the broadenings in the emission line broadening in atmospheric pressure plasma jets (APPJs) have been determined for the cases of 667 nm and 728 nm lines. By fitting the experimental data with Voigt function, the experimental broadening have been obtained. By calculating Instrumental, Doppler, Resonance and Van Der Waals broadenings, and using experimental broadening, Stark broadening have been obtained. Finally, by using Griem's formula, the electron density and temperature have been determined and the effect of supply power parameters, voltage amplitude, frequency and pulse width, on the lines intensities and Stark broadening and the electron density and temperature have been investigated.

Gas line shape is determined by the Voigt profile, which is the convolution of Lorentz and Doppler profiles. The calculation amount in the Voigt profile is much larger than that in the two other profiles, and an approximate Lorentz or Doppler profile is generally used in gas concentration detection via tunable laser absorption spectroscopy. The normalized peak ratio and error function are introduced to compare the approximating effect of the two profiles. The normalized peak ratio value is simulated for Doppler profile and Lorentz profiles over a variable temperature and pressure, respectively. The 10%, 5% and 2.5% error functions for pressure versus temperature are obtained for the two profiles. Oxygen at a wavelength of 760 nm is used to demonstrate the simulation results. The presented method of investigating line shapes can be applied to other gas spectrum lines.

Absolute line intensities and a first determination of self-broadening and shift coefficients are presented here, deduced from room temperature measurements for 302 rovibrational lines of NH 3 in the 2ν 4 band, using Fourier transform infrared spectroscopy. These lines, ranging from 1 ≤ J ≤ 11 to 0 ≤ K ≤ 11, are located in the 3060–3580 cm −1 spectral range. The lines were fitted with a single spectrum non-linear least squares fitting procedure. The absence of signature in the residuals suggests that the Voigt profile is well suited to fit the experimental line shapes without the need of taking into account line mixing effects, in the pressure range used. Average absolute accuracies of the measurements are estimated to ±4% for line intensities and self-broadening coefficients and to ±13% for self-shift coefficients. The J and K dependences of the self-broadening coefficients have been observed and modeled using an empirical polynomial expression. The results are compared with previous experimental and calculated data. Our absolute line intensities, S 0 , are in good agreement with previous work and HITRAN2016 database, but with a reduced uncertainty. The self-broadening coefficients, γ 0 , as well as the pressure shift coefficients, δ 0 , are in reasonable agreement with those reported for various vibrational bands in the 3 µm spectral region, which indicates that no obvious vibrational dependence was observed. For shift coefficients, it should be noted that this is not the case in many studies which put in evidence a large dependence with vibrational excitation. This study complements the existing line parameters in the 3 µm spectral region, essential for the analysis of atmospheric spectra. For this purpose, the complete list of measurements is provided as supplementary material.

The absorption spectra of a mixture of CO with CO2 at different partial pressures of CO2 have been recorded at room temperature in the 2000–2300 cm−1 region using a Bruker IFS 125 HR FTIR spectrometer. To obtain the spectral line parameters for the fundamental band of CO molecule, the quadratic speed-dependent Voigt profile was used for the first time. The CO2 pressure induced broadening and shift coefficients for 49 spectral lines have been measured. A comparison with the published data is discussed.

International audience; The room temperature spectrum of the very weak third overtone band of carbon monoxide in natural isotopic abundance is recorded by cavity ring down spectroscopy (CRDS) referenced to a frequency comb, between 8206 and 8465 cm-1. The sensitivity of the recordings (noise equivalent absorption on the order of min~ 5×10-12 cm-1) allowed for measuring lines with intensity as weak as 1×10-30 cm/molecule at a recording pressure limited to 10.0 Torr. The use of low pressure values (1.0 and 10.0 Torr) helped to minimize the impact of profile effects on the derived line positions and line intensities. The line profile analysis was performed using the speed dependent Nelkin-Ghatak model for the 10 Torr recordings while the Voigt profile was found sufficient to account for the line shapes recorded at 1.0 Torr. Overall, line parameters of 227 transitions are derived. The observed transitions belong to the 4-0 band of the 12C16O, 13C16O, 12C18O and 12C17O isotopologues present in natural abundance in the sample and to the 5-1 hot band of 12C16O. For a large part of the observations, line positions are reported with accuracy as good as 4×10-6 cm-1 (~120 kHz). The selfinduced line shift of the 4-0 band is reported for the first time from the position values at 1 and 10 Torr. Using literature values of the 1-0, 2-0 and 3-0 bands, the vibrational dependence of the self-induced pressure shift in CO is discussed. The experimental values of the 12C16O v= 4 energy levels J < 26 are reproduced with a standard deviation of 2.5×10-6 cm-1 (75 kHz). The intensities of the 12C16O lines reported with an accuracy better than 1% show an overall good agreement with literature values in particular with those included in the HITRAN database.

Collisional broadening and shift coefficients as well as Dicke narrowing parameters have been measured at room temperature in the 2ν4 band of NH3 perturbed by O2 and N2 for 310 rovibrational lines with rotational quantum numbers 1 ≤ J ≤ 11 and 0 ≤ K ≤ 11. The experiments were performed at room temperature with ammonia mixtures in nitrogen and oxygen at different pressures using a high-resolution Fourier transform spectrometer and a mono-spectrum non-linear least squares fitting of Voigt and soft-collision Galatry profiles. Because of Dicke narrowing effect, departure from the Voigt profile is observed that allowed measurement of narrowing parameters for about 100 transitions of the 2ν4 band. The collisional broadening coefficients obtained with Galatry profile are larger by about 5% than those derived from Voigt profile. Average absolute accuracies of the measurements are estimated to be 5%, 10% and 14% for broadening, shift and narrowing coefficients, respectively. Air-broadening coefficients were retrieved from the linear combination of O2- and N2-broadening coefficients. The results are in good agreement with previous experimental data available in the literature. The whole set of results is given as supplementary material for a possible use in spectroscopic databases.

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 $w(i z_-)-w(i z_+)$ of two complex error functions (essentially Voigt functions) has to be evaluated where the function arguments $z_\pm$ are given by the sum and difference of two square roots. These two terms describing $z_\pm$ 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 Humlicek, 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., Comment: 12 pages, 7 figures, 4 tables; Article published in J. Quant. Spectros. & Rad. Transfer (missing title in original arxiv submission from October 2020 added)

We introduce a Bayesian approach coupled with a Markov Chain Monte Carlo (MCMC) method and the maximum likelihood statistic for fitting the profiles of narrow absorption lines (NALs) in quasar spectra. This method also incorporates overlap between different absorbers. We illustrate and test this method by fitting models to a "mini-broad" (mini-BAL) and six NAL profiles in four spectra of the quasar UM675 taken over a rest-frame interval of 4.24 years. Our fitting results are consistent with past results for the mini-BAL system in this quasar by Hamann et al. (1997b). We also measure covering factors ($C_{\rm f}$) for two narrow components in the CIV and NV mini-BALs and their overlap covering factor with the broad component. We find that $C_{\rm f}$(NV) is always larger than $C_{\rm f}$(CIV) for the broad component, while the opposite is true for the narrow components in the mini-BAL system. This could be explained if the broad and narrow components originated in gas at different radial distances, but it seems more likely to be due to them produced by gas at the same distance but with different gas densities (i.e., ionization states). The variability detected only in the broad absorption component in the mini-BAL system is probably due to gas motion since both $C_{\rm f}$(CIV) and $C_{\rm f}$(NV) vary. We determine for the first time that multiple absorbing clouds (i.e., a broad and two narrow components) overlap along our line of sight. We conclude that the new method improves fitting results considerably compared to previous methods., Comment: 18 pages, 12 figures, accepted for publication in ApJ

Topic of this chapter is the evaluation of the error function, the Fresnel functions, and some related functions, like the Dawson integral and the Voigt profile functions in the complex domain. The computation is based on the incomplete gamma function, and thus various numerical techniques are used in dependence of the function arguments. The corresponding programming code is freely available.