Line profile Gauss

Figure 2.3 Comparison of Gauss (blue line) and Lorentz (green line) curves of equal area and same FWHM, and a Voigt (red line) profile produced by convoluting the other two curves...

Another typical problem met in this kind of analysis is known as the hook effect . It is due to an overestimation of the background line to the detriment of the peak tails. As a consequence, the low order Fourier coefficients of the profile are underestimated. In the fitting procedure by pseudo-Voigt functions, this problem occurs if the Gauss content is so high that the second derivative of the Fourier coefficients is negative this is obviously physically impossible because it represents a probability density. 

Figure 6.1 Comparison of 26 — 6 scan profiles obtained by a monochromatized (pure Cu kal) parallel beam configuration (hybrid x-ray mirror) and a conventional parallel beam configuration achieved by divergence slit (ds) module measured at 001/100 (a), 002/200 (b), 003/300 (c), 004/400 (d) of 500nm-thick Pb(Zro.B4Tio.46)03 thin film. Dotted lines represent the second derivative of the profiles, indicating the peak positions. Note that the profiles are simulated fitted profiles for obtained spectrum using pseudo-Voight function (mixed Lorentz and Gauss function).

Figure 9 The emission spectrum of a tetracene film evaporated onto a glass substrate kept at 89 K and the emission monitored at 180 K (full circles). Its decomposition into Gauss profiles (II, III, IV, V) is shown by solid lines. The dashed curve is the sum of the gaussians. The lacking band I (=540 nm) is characteristic of the monomer emission from crystalline films formed at T > 140 K. Adapted from Ref. 72.

By periodic measurements of the profile detail points we can use the same photo-theodolite base stations and also the same orientation points. All this can simplify the field measurements and so the photogrammetrical measurements were also more economical. The cost also depends on automatic registration of the stereo-model coordinates and further on-line transformation to Gauss-Kriiger and profile coordinates. 

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. 

The line-shape of an experimental spectrum can in principle be determined by the procedure illustrated in Fig, 9.2. The 2nd derivative of the resonance line is then recorded. For a Gauss line the ratio hi/h2 between the minimum and maximum amplitudes of the 2nd derivative (Fig. 9.2(a)) equals 2.24 [18], while for a Lorentz shape it approaches the value 4. The hi/h2 ratio for a Voigt profile varies... 

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... 

Figure 2.3 shows Gauss and Lorentz profiles of equal area and FWHM as well as the resulting Voigt distribution. While the Lorentz portion dominates at the line wings, the Gauss portion determines the shape in the line core. 

ELIAS II (LTB Lasertechnik Berlin GmbH, Berlin, Germany), having an instrument profile width of 0.13 pm (FWHM), which is negligible compared to the line width. The measured profiles were used to determine the line positions and intensities of the Cu doublet. For these values Gauss profiles with 1.4 pm FWHM were calculated, representing the Doppler broadening for Cu at 2600 K. 

Figure 2.14 Normalized, shot-noise determined, minimnm detectable absorbance for Gauss- and Lorentz-shaped absorption lines as function of AAinst rectangular instrument profile assumed...

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