Voigt line width

It is essential to correctly evaluate the absorption cross-section a relative to the laser line profile, the spectral resolution of the light collection optics, and the natural HO line width as influenced by Doppler, Voigt, or collisional broadening. The principles governing absorption measurements of HO over a distance through the atmosphere are discussed by Hiibler et al. (38). 

Gaussian Laser Profile-Voigt Atom Profile. This case turns out to be a better approximation of our experimental situation, i.e., the laser FWHM is fairly broad compared to the absorption line width and the absorption profile of atoms in an atmospheric combustion flame is described by a Voigt profile. Here the laser is assumed to have a Gaussian spectral profile as well as a Gaussian atomic absorption profile. In this case, convolution of two Gaussian functions is still a Gaussian function. Evaluation of the ratio n2/nT, and the fluorescence radiance. Bp, allows determination of the half width of the fluorescence excitation profile, 6X... 

Fig. 11. (Upper) Splitting of pHe+ states due to magnetic interactions, and observable laser transitions between the F+ and F states according to Bakalov and Korobov [33]. (Lower) Observed hyperfine splitting of the unfavoured laser transition (n, L) = (38,34) —> (37, 35) [16]. The laser bandwidth is 1.2 GHz. The solid line is the result of a fit of two Voigt functions (a Gaussian fixed to the laser bandwidth convoluted with a Lorentzian to describe the intrinsic line width) to the spectrum. The intrinsic width of each lines was found to 0.4 0.1 GHz. From Widmann et al. [16]...

The line shapes are described by Voigt functions, which reflect the Lorentzian line profiles due to natural line width and Gaussian profiles due to Doppler broadening. The instrumental broadening by the rocking curve of the crystal, de-focusing and the finite resolution of the detector is described well by a Voigt profile shape too [3[. 

ESR lines in solution can almost always be approximated by a Lorentz function. In the solid state the line-shape can in general be reproduced by a Gauss curve. In some instances a so-called Voigt profile can give a better approximation to the experimental line-shape. A Voigt line is a convolution of a Lorentz and a Gauss line. The shape is determined by the ratio ABi/ABg of the respective line-widths. The shapes of the 1st derivative lines of these types are given in Fig. 9.1. 

Fig. 9.13 Schematic shapes of saturation curves for homogeneous, inhomogeneous and Voigt ESR-lines. A homogeneous line has the Lorentz shape usually occurring in liquids. An inhomogeneous line is an envelope of narrow homogeneous lines, with the envelope usutilly approximated by a Gaussian, wWle the Voigt line is an envelope of homogeneous lines with an appreciable line-width...

The formulae were incorporated in a computer program [82], The input is an experimental array of the 1st derivative peak-to-peak ESR amplitude against the microwave power that is read from a previously prepared file and initial trial parameter values for the Lorentzian and Gaussian line-widths and the microwave power Po) at saturation that are provided interactively. The corresponding theoretical amplitudes were obtained by numerical differentiation of the Voigt function (1). A non-linear least squares fit of the calculated saturation curve to the experimental data is performed. Output data consist of a graph of the experimental data and the... 

Another approach for data processing involves simulation of pure spectra. These model spectra are then taken for a quantitative description of the mixture spectra. This procedure is referred to as indirect hard modelling (IHM). Obviously, changes in line shape, line width, and chemical shift may occur as function of concentration and due to system imperfections which are taken into account by IHM. The peaks are modelled by Voigt-functions with variable Gaussian to exponential ratio. The main advantage of IHM is that it allows a limited physical interpretation of the models. Further, unlike PLS based methods, IHM only requires reference spectra of the pure compounds, reducing the calibration effort drastically. 

Empirical fits to the Voigt line width a brief review. /. Quant. Spectrosc. Radiat. Transfer, 17 (2), 233-236. 

The FWHM of the Voigt profile, the so-called Voigt line width AAy, cannot be obtained by simple addition of the Doppler and Lorentz widths, but can be approximated by an empirical formula ... 

Fig. 1. The Voigt lineshape is plotted for three different values of the Voigt parameter, a - WL/WG, namely a = 0 (Gaussian, dotted line), a = 1 (solid line, with the component Lorentzian and Gaussian lineshapes having an equal width given by tl/(, W 0.6107 H-) and a x (Lorentzian, dashed line). The frequency scale is given in units of the FWHM of the Voigt lineshape, W.

Figure J. 23. Lorentzian, Doppler, and Voigt spectral line profiles for approximately equal half widths and intensities. (From Andrews et al.., 1987).

Doppler broadening has a Gaussian lineshape, and its convolution with the Lorentzian natural lineshape yields a Voigt profile. In typical experiments, this effect can be neglected since the Doppler width is usually much smaller than the resolution of the apparatus. Collisional line broadening is also Lorentzian, and the Lorentzian component of measured lines must be carefully extrapolated to zero pressure. 

This represents a Voigt profile, that is, a convolution product of a Lorentzian function with halfwidth y and a Doppler function. A comparison with Vol. 1, (3.33) shows, however, that the Doppler width is reduced by the factor sine = Vx/v = b jld, which equals the collimation ratio of the beam. The collimation of the molecular beam therefore reduces the Doppler width Aa>o of the absorption lines to the width... 

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