Broadening Voigt profile

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.

Blickensderfer et al. (119) have recently extended the Samson theory to include various vessel geometries under conditions of pure Doppler, pure Lorentz, and Voigt (a combination of Doppler, Lorentz, and natural broadening) line profiles. The quenching cross section can be obtained also by a dynamic method in which the decay of the fluorescence intensity is measured after the exciting light is cut off. If the initial fluorescence intensity is / and the intensity after a lime f is If, we obtain... 

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[. 

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. 

The combination of both types of profile functions (which is normally due to the predominance of both pressure and temperature broadening) results in a so-called Voigt profile, which can be described by ... 

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. 

Note that observed Une shapes may not be purely Lorentzian or Gaussian when more than one broadening mechanism contributes in the interaction. The combinations of Lorentzian and Gaussian line-shape functions can normally be approximated by a so-called 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... 

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