Voigt Profile Research Articles

Collisional broadening and pressure shift of the potassium resonance doublets by nitrogen, helium, and hydrogen at high temperatures

This paper presents measurements of collisional broadening and pressure shift parameters for the potassium D1 and D2 transitions near 0.77 μm with the collisional partners of molecular nitrogen, helium, and molecular hydrogen. Experiments were conducted in a shock tube at temperatures from 1100 K up to 1900 K, using tunable diode laser absorption spectroscopy and KCl salts as precursors of atomic potassium. In many of the experiments, the target gas was blended with argon to increase the ratio of the driver to driven gas speed of sound. This approach was employed to generate strong incident and reflected shock waves with sufficient temperature rises to produce optimal potassium concentrations (1–10 ppb) in the test gas for high signal-to-noise ratio absorption line shape measurements. The well-resolved absorption line shapes were modeled as Voigt profiles and a least-squares fitting algorithm yielded multiple variables, including the potassium concentration, the collisional full half-widths, and the pressure-induced shifts. Any broadening and shift contributions from the argon dilution were subtracted from the measurements using previous correlations. The pressure-normalized results, i.e., collisional broadening coefficients and pressure shift coefficients, are presented as temperature-dependent power-law relations for the species of interest. The helium and hydrogen results show good agreement with lower-temperature experimental data within 15–20%, and high-temperature theoretical predictions within 10–30%. However, larger discrepancies are observed between the nitrogen results and existing low-temperature experimental data and simplified impact theory predictions. These results may suggest that a more detailed model for the nitrogen collisional broadening of potassium is warranted. The presented correlations may also be useful for the development of potassium-based sensing methods with application to combustion, hypersonics, and astrophysics.

Measurement of Secondary Structure Changes in Poly-L-lysine and Lysozyme during Acoustically Levitated Single Droplet Drying Experiments by In Situ Raman Spectroscopy.

Drying processes such as spray drying, as commonly used in the pharmaceutical industry to convert protein-based drugs into their particulate form, can lead to an irreversible loss of protein activity caused by protein secondary structure changes. Due to the nature of these processes (high droplet number, short drying time), an in situ investigation of the structural changes occurring during a real drying process is hardly possible. Therefore, an approach for the in situ investigation of the expected secondary structural changes during single droplet protein drying in an acoustic levitator by time-resolved Raman spectroscopy was developed and is demonstrated in this paper. For that purpose, a self-developed NIR–Raman sensor generates and detects the Raman signal from the levitated solution droplet. A mathematical spectral reconstruction by multiple Voigt functions is used to quantify the relative secondary structure changes occurring during the drying process. With the developed setup, it was possible to detect and quantify the relative secondary structure changes occurring during single droplet drying experiments for the two chosen model substances: poly-L-lysine, a homopolypeptide widely used as a protein mimic, and lysozyme. Throughout drying, an increase in the β-sheet structure and a decrease in the other two structural elements, α-helix, and random coil, could be identified. In addition, it was observed that the degree of structural changes increased with increasing temperature.

Simple Analytical Expression of the Voigt Profile

This work examines several analytical evaluations of the Voigt profile, which is a convolution of the Gaussian and Lorentzian profiles, theoretically and numerically. Mathematical derivations are performed concisely to illustrate some closed forms of the considered profile. A representation in terms of special function and a simple and interesting approximation of the Voigt function are well demonstrated, which could have promising applications in several fields of physics, e.g., atmospheric radiative transfer, neutron reactions, molecular spectroscopy, plasma waves, and astrophysical spectroscopy.

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.

Super-Accuracy Calculation for the Half Width of a Voigt Profile

A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10−17 for arbitrary αL/αG ratios. In particular, the accuracy reaches an astonishing 10−34 (quadruple precision) in the domain 0 ≤ αL/αG ≤ 0.2371 ∪ αL/αG ≥ 33.8786.

Addendum: Precision in high resolution absorption line modelling, analytic Voigt derivatives, and optimization methods

ABSTRACT The parent paper to this Addendum describes the optimization theory on which vpfit, a non-linear least-squares program for modelling absorption spectra, is based. In that paper, we show that Voigt function derivatives can be calculated analytically using Taylor series expansions and look-up tables, for the specific case of one column density parameter for each absorption component. However, in many situations, modelling requires more complex parameterization, such as summed column densities over a whole absorption complex, or common pattern relative ion abundances. This Addendum provides those analytic derivatives.

CO<sub>2</sub>-broadened coefficients of water vapor molecule in 1.1 μm band

The absorption spectral parameters of water vapor molecules are the key basic scientific data for the remote sensing detection and the planetary observation applications. Based on a narrow line-width external cavity diode laser and a long-path absorption cell, 18 absorption spectral lines of CO<sub>2</sub>-broadened water vapor molecules in a 9332–9722 cm<sup>–1</sup> range at room temperature are measured. To obtain the CO<sub>2</sub>-broadened water vapor molecule coefficients, the Voigt profile and the quadratic speed-dependent Voigt profile are used to fit the absorption spectrum data. The quadratic speed-dependent Voigt profile shows better fitting capability. Comparing with the air-broadened coefficients of the corresponding region from the HITRAN2020 database, the mean ratios of the CO<sub>2</sub>-broadened coefficients of water vapor molecules and the air-broadened coefficients obtained from the two models of the line shape are 1.327 and 1.454, respectively, which verifies that the method of estimating the CO<sub>2</sub>-broadened coefficient by the air-broadened coefficient of water vapor molecules has certain reliability. This study can provide reference data of measured spectral parameters for the detection technology and related research of atmospheric structures of Mars and Venus in the near-infrared region.

Obtaining Voigt Functions Via Quadrature Formula for the Fractional in Time Diffusion and Wave Problem

In many given physical problems and in the course of dispersion curve through a spectral line under the influence of the Doppler-effect and in collision damping, the Voigt functions have been widely utilized. By taking advantage of the fractional calculus in spectral theory and the Sturm-Liouville problems, in this paper, we obtain the Voigt functions via the quadrature formulae of one dimensional fractional in time evolution diffusion and wave problems consisting of different initial and inhomogeneous boundary conditions.

Critical Evaluation of Spectral Resolution Enhancement Methods for Raman Hyperspectra.

Overlapping peaks in Raman spectra complicate the presentation, interpretation, and analyses of complex samples. This is particularly problematic for methods dependent on sparsity such as multivariate curve resolution and other spectral demixing as well as for two-dimensional correlation spectroscopy (2D-COS), multisource correlation analysis, and principal component analysis. Though software-based resolution enhancement methods can be used to counter such problems, their performances often differ, thereby rendering some more suitable than others for specific tasks. Furthermore, there is a need for automated methods to apply to large numbers of varied hyperspectral data sets containing multiple overlapping peaks, and thus methods ideally suitable for diverse tasks. To investigate these issues, we implemented three novel resolution enhancement methods based on pseudospectra, over-deconvolution, and peak fitting to evaluate them along with three extant methods: node narrowing, blind deconvolution, and the general-purpose peak fitting program Fityk. We first applied the methods to varied synthetic spectra, each consisting of nine overlapping Voigt profile peaks. Improved spectral resolution was evaluated based on several criteria including the separation of overlapping peaks and the preservation of true peak intensities in resolution-enhanced spectra. We then investigated the efficacy of these methods to improve the resolution of measured Raman spectra. High resolution spectra of glucose acquired with a narrow spectrometer slit were compared to ones using a wide slit that degraded the spectral resolution. We also determined the effects of the different resolution enhancement methods on 2D-COS and on chemical contrast image generation from mammalian cell spectra. We conclude with a discussion of the particular benefits, drawbacks, and potential of these methods. Our efforts provided insight into the need for effective resolution enhancement approaches, the feasibility of these methods for automation, the nature of the problems currently limiting their use, and in particular those aspects that need improvement.

Spectral analysis of H2O near 7180 cm–1 to accurately measure trace moisture in N2 gas: evaluation of line shape profiles using Akaike Information Criterion

The absorption spectra of H2O in N2 gas were measured at atmospheric pressure and room temperature near 7180 cm–1 in the moisture range of 9.7–148.7 nmol mol−1 in mole fraction using cavity ring-down spectroscopy. The line shape profiles used for the spectral analysis for the trace moisture measurement were evaluated based on the Akaike Information Criterion as well as the fitting residuals. The optimal line shape profile in this study was the speed-dependent asymmetric Voigt profile (SDAVP). From the comparison of the fitting results calculated using the Lorentzian profile (LP) with those calculated using the SDAVP, the relative difference in the integrated line area between the two line shape profiles was found to be systematic and constant. The measurement error due to the use of the LP could be corrected using a correction factor of 1.00479 ± 0.00077.

A detailed view of the Gaussian–Lorentzian sum and product functions and their comparison with the Voigt function

The Gaussian–Lorentzian sum (GLS) and product (GLP) functions remain important in X‐ray photoelectron spectroscopy (XPS) peak fitting. Here, we present a detailed view of these functions, comparing them with each other and with the Voigt function (the “LA(m)” function). First, we show the GLS, GLP, and LA(m) functions as a function of their mixing parameters, m, which reveals differences between them. We then illustrate the use of these functions to fit a series of spectra acquired at different pass energies (resolutions). Next, we show the underlying Gaussian and Lorentzian components of a series of GLS and GLP functions as a function of m, which confirms that the GLS is a simple linear combination of Gaussian and Lorentzian functions. However, one of the two functions used to make the GLP can be very wide, that is, at its extremes, one of these functions has infinite width. We then discuss a plot of the areas of the GLS, GLP, and LA(m) functions as a function of m, which reveals the expected, linear increase in area of the GLS, but nonlinear changes in the areas of the other two functions. Finally, to better understand them, we fit these functions to each other. These results indicate that the GLS and GLP better match the LA(m) function at lower and higher values of the mixing parameter, respectively.

Molecular dynamics simulations of pressure-broadened symmetric-top gas spectra. Application to CH3F-Ar and CH3F-He mixtures

We present a new approach, based on requantized classical molecular dynamics simulations (rCMDS), to calculate pressure-broadened absorption spectra of symmetric-top molecules. We test it in the cases of CH3F-He and CH3F-Ar gas mixtures at room temperature for which predictions are made, without use of any adjusted parameter, based on input inter-molecular potentials from the literature. The results show that the Lorentz pressure-broadenings, deduced from fits of the computed spectra, are in good agreement with available measured values. Furthermore, the predicted effects of line-mixing at high pressure are also very consistent with observations. In addition, the study of the influence of the speed dependence of the pressure-broadening coefficient is promising but needs to be confirmed, since based on only one experimental result available. This opens renewed perspectives for predictions of symmetric-top molecules line shapes beyond the Voigt profile.

Line intensity parameters, He-broadening and line shift coefficients in the 2v 2 0 and 3v 2 1 − v 2 1 bands of OCS

Using Fourier transform spectrometer, He-broadening coefficients in the and bands of carbonyl sulfide (16O12C32S) have been measured for the first time in the P- and R-branches. Measurements have been performed at room temperature (295 K) for 200 ro-vibrational lines with rotational quantum number ranging from 1 ≤ J ≤ 64, using a mono-spectrum non-linear least squares fitting of Voigt profiles. The measured values were discussed as a function of the rotational quantum number and compared to previous data. These broadening coefficients were also calculated on the basis of Robert and Bonamy's formalism using an ab-initio potential energy surface (PES). In addition, we have measured pressure shift coefficients for 92 transitions in both bands, these results were compared with those of the 2ν3 band. The line intensities in the and bands were also retrieved using the same spectra. The analysis of these intensities allows us to derive a consistent set of line intensity parameters such as vibrational transition moments, band intensities as well as Herman-Wallis (HW) coefficients.

The H i Column Density Distribution of the Galactic Disk and Halo

Abstract We present a census of neutral gas in the Milky Way disk and halo down to limiting column densities of N(H i) ∼ 1014 cm−2 using measurements of H i Lyman series absorption from the Far Ultraviolet Spectroscopic Explorer. Our results are drawn from an analysis of 25 AGN sight lines spread evenly across the sky with Galactic latitude ∣b∣ ≳ 20°. By simultaneously fitting multi-component Voigt profiles to 11 Lyman series absorption transitions covered by FUSE (Lyβ–Lyμ) plus HST measurements of Lyα, we derive the kinematics and column densities of a sample of 152 H i absorption components. While saturation prevents accurate measurements of many components with column densities 17 ≲ log N(H i) ≲ 19, we derive robust measurements at log N(H i) ≲ 17 and log N(H i) ≳ 19. We derive the first ultraviolet H i column density distribution function (CDDF) of the Milky Way, both globally and for low-velocity (ISM), intermediate-velocity clouds (IVCs), and high-velocity clouds (HVCs). We find that IVCs and HVCs show statistically indistinguishable CDDF slopes, with β IVC = − 1.01 − 0.14 + 0.15 and β HVC = − 1.05 − 0.06 + 0.07 . Overall, the CDDF of the Galactic disk and halo appears shallower than that found by comparable extragalactic surveys, suggesting a relative abundance of high column density gas in the Galactic halo. We derive the sky-covering fractions as a function of H i column density, finding an enhancement of IVC gas in the northern hemisphere compared to the south. We also find evidence for an excess of inflowing H i over outflowing H i, with −0.88 ± 0.40 M ⊙ yr−1 of HVC inflow versus ≈0.20 ± 0.10 M ⊙ yr−1 of HVC outflow, confirming an excess of inflowing HVCs seen in UV metal lines.

Diode laser measurements of high-temperature line strength and self-broadening coefficient of carbon dioxide near 2.0 μm

A tunable diode laser combined with a self-made heated static cell was used to measure the high-resolution absorption spectra of ten strong lines of carbon dioxide belonging to the 20012 ← 00001 band near 2.0 μm in the temperature range of 296 K to 1100 K. Using the Voigt profile of the measured direct absorption spectrum and the line strength, self-broadening coefficient and temperature dependent exponent of the ten lines were determined. The measured spectral line strength and self-broadening coefficients of 12C16O2 were compared well with the available values listed in the HITEMP/HITRAN database. The uncertainties and primary error sources in the determination of those parameters were discussed respectively. The temperature dependence exponents of self-broadening coefficients were compared with the calculated values obtained from HITEMP2010. We found that there was not a monotonic relationbetween the temperature exponent n and the J values, which was different with the result reported in the previous papers.

Redshift space three-point correlation function of IGM at z < 0.48

ABSTRACT Ly α forest decomposed into Voigt profile components allows us to study clustering properties of the intergalactic-medium and its dependence on various physical quantities. Here, we report the first detections of probability excess of low-z (i.e z < 0.48) Ly α absorber triplets over redshift-space scale of r∥ ≤ 8 pMpc (Mpc in physical units) with maximum amplitude of $8.76^{+1.96}_{-1.65}$ at a longitudinal separation of 1–2 pMpc. We measure non-zero three-point correlation ($\zeta = 4.76^{+1.98}_{-1.67}$) only at this scale with reduced three-point correlation Q = $0.95^{+0.39}_{-0.38}$. The measured ζ shows an increasing trend with increasing minimum H i column density (NH i) threshold while Q does not show any NH i dependence. About 88 per cent of the triplets contributing to ζ (at z ≤ 0.2) have nearby galaxies (whose distribution is known to be complete for ∼0.1L* at z < 0.1 and for ∼L* at z ∼ 0.25 within 20 arcsec to the quasar sightlines) within velocity separation of 500 km s−1 and median impact parameter of 405 pkpc. The measured impact parameters are consistent with majority of the identified triplets not originating from individual galaxies but tracing the underlying galaxy distribution. Frequency of occurrence of Broad-Ly α absorbers (b > 40 km s−1) in triplets (∼85 per cent) is factor ∼3 higher than that found among the full sample (∼32 per cent). Using four different cosmological simulations, we quantify the effect of peculiar velocities and feedback and show that most of the observed trends are broadly reproduced. However, ζ at small scales (r∥ < 1 pMpc) and its b-dependence found in simulations are inconsistent with observations. This could either be related to the failure of these simulations to reproduce the observed b and NH i distributions for NH i > 1014 cm−2 self-consistently or to the wide spread of signal-to-noise ratio in the observed data.

MCMC-based Voigt Profile Fitting to a Mini-BAL System in the Quasar UM 675* †

Abstract We introduce a Bayesian approach coupled with a Markov Chain Monte Carlo method and the maximum-likelihood statistic for fitting the profiles of narrow absorption lines (NALs) in quasar spectra. This method also incorporates the 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 UM 675 taken over a rest-frame interval of 4.24 yr. Our fitting results are consistent with past results for the mini-BAL system in this quasar by Hamann et al. We also measure covering factors (C f) for two narrow components in the C iv and N v mini-BALs and their overlap covering factor with the broad component. We find that C f (N v) is always larger than C f (C iv) 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 being 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 f (C iv) and C f (N v) 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.

Magnetic Field Effects of Charge Transfer Excitons in Organic Semiconductor Devices

AbstractThe topic of this review is the effect of magnetic field on photo‐current (PC) in organic semiconductor devices. Magnetic field modifies the fraction of the singlet/triplet population in the charge transfer excitons (CTE) whose lifetime is spin configuration dependent yielding magneto‐PC (MPC). We review MPC in the framework of the polaron pair model and emphasize the effect of CTE lifetime on MPC. In addition to a detailed calculation of the MPC response we find a range of physical parameters in which the response follows a simple ′fit function′. For example, a sum of wide and narrow Lorentzian functions, MPC(B)=cwB2/(B2+bw2)+cnB2/(B2+bn2), in the case of hyperfine interaction; or a Voigt profile V=L*G, where the sign * stands for the convolution operation between a Lorentzian (L) and a Gaussian (G) functions, in the case of thermal spin polarization. We provide expressions for the fit parameters in terms of physical parameters.

Measurement of redshift-space two- and three-point correlation of Lyα absorbers at 1.7 < z < 3.5: implications on evolution of the physical properties of IGM

ABSTRACT We present redshift-space two-point (ξ), three-point (ζ), and reduced three-point (Q) correlation of Lyα absorbers (Voigt profile components having H i column density, NH i > 1013.5 cm−2) over three redshift bins spanning 1.7 < z < 3.5 using high-resolution spectra of 292 quasars. We detect positive ξ up to 8 h−1 cMpc in all three redshift bins. The strongest detection of ζ = 1.81 ± 0.59 (with Q = 0.68 ± 0.23) is in $z$ = 1.7–2.3 bin at 1–2 h−1 cMpc. The measured ξ and ζ values show an increasing trend with NH i, while Q remains relatively independent of NH i. We find ξ and ζ to evolve strongly with redshift. Using simulations, we find that ξ and ζ seen in real space may be strongly amplified by peculiar velocities in redshift space. Simulations suggest that while feedback, thermal and pressure smoothing effects influence the clustering of Lyα absorbers at small scales, i.e. <0.5 h−1 cMpc, the H i photoionization rate (ΓH i) has a strong influence at all scales. The strong redshift evolution of ξ and ζ (for a fixed NH i cut-off) is driven by the redshift evolution of the relationship between NH i and baryon overdensity. Our simulation using best-fitting ΓH i($z$) measurements produces consistent clustering signals with observations at $z$ ∼ 2 but underpredicts the clustering at higher redshifts. One possible remedy is to have higher values of ΓH i at higher redshifts. Alternatively the discrepancy could be related to non-equilibrium and inhomogeneous conditions prevailing during He ii reionization not captured by our simulations.

Precision in high resolution absorption line modelling, analytic Voigt derivatives, and optimization methods

ABSTRACT This paper describes the optimization 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 optimization 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 summarize how unbiased modelling depends on using an appropriate information criterion to guard against overfitting or underfitting. 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 space–time variations in fundamental constants and attempts to detect cosmological redshift drift.