Voigt-profile

The observable profile of a spectral line is, in general, neither a pure Lorentz nor a pure Gauss distribution but a combination of both, known as a Voigt profile. If it is assumed that Doppler and collision broadening are independent processes, the Voigt profile is the result of the convolution of the Lorentz distribution with AAc and the Gauss distribution with AAd. Since the Voigt profile cannot be obtained analytically, numerical convolution procedures have to be applied. A parameter often used for profile characterization is the 

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  

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It is common, however, for liquid-phase systems to include many specific absorbing species. Such species could include isotopic variations, conformational isomers, and solvent-solute interactions resulting in varied-lifetime transient associations between molecules. Distributions resulting from these effects give the Voigt profile utility in studying liquid spectra. We must understand, however, that the functions introduced here are only rough approximations when applied to the spectra of liquids because of the complexities just mentioned and others beyond the scope of this work. 

Fig. 28 Pure rotational spectrum of C>2. Trace (a) is the S3 transition recorded at a pressure of 1.0 atm. Trace (b) is the result of deconvolving the S3 profile with a Voigt profile to remove most of the pressure broadening, Doppler broadening, and instrument effects. Trace (c) was calculated using a 0.035-cm-1 Gaussian profile and calculated spin splittings. The traces are scaled to the same height.

Figure 2.8 Several energy-distribution functions, all normalized to the same height. The Lorentzian and Gaussian distributions are shown for equal fwhm values. The Voigt profile results from the convolution of the shown Lorentzian and Gaussian functions.

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... 

The lineshape function g(V-Vc) is defined assuming a Voigt profile ( 7) which allows for a combination of Doppler and collision... 

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[. 

The energy values have been obtained by unfolding the spectra by a least-squares fit using Voigt profiles, the main criterium being the minimization of the number of profiles. 

The XANES spectrum for P409 80,140) shows a preedge absorption band at 2148.2 eV, which is assigned to an electron transition from the P(III)-ls orbital into an unoccupied MO with main contributions from P(III) and 0. Above 2150 eV, two broad resonances have been observed, which could be fitted by three Voigt profiles of approximately... 

Similar to a Voigt profile, this line shape expression is a convolution of Equation (11) and a Gaussian distribution to account for inhomogeneous broadening [12,31]. This profile is the best profile currently employed for the analysis of spectra exhibiting significant overlap of modes of different phases. 

FIGURE2.9. VSFspectraoftightlypackedmonolayerscomposedofDLPC(n = 12),DMPC(n = 14),DPPC (n = 16) and DSPC in = 18) where n is the number of carbon atoms in the acyl chains, (a) The CCLi/water interface, (b) The air/water interface. Order parameters appear beneath the phosphochohne acronyms. Spectral features were fit with Voigt profiles, although the solid fines in the figures serve only as guides to the eye. From Ref. [49]. 

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