Gaussian curves effects

Finite resolution and partial volume effects. Although this can occur in other areas of imaging such as MRS, it is particularly an issue for SPECT and PET because of the finite resolution of the imaging instruments. Resolution is typically imaged as the response of the detector crystal and associated electron to the point or line source. These peak in the center and fall off from a point source, for example, in shapes that simulate Gaussian curves. These are measures of the ability to resolve two points, e.g. two structures in a brain. Because brain structures, in particular, are often smaller than the FWHM for PET or SPECT, the radioactivity measured in these areas is underestimated both by its small size (known as the partial volume effect), but also spillover from adjacent radioactivity... 

Fig. 12.25 The Cotton effect (a) positive Cotton effect (b) negative Cotton effect. The absorption band is not shown it would be a positive Gaussian curve centered on Am, but o scale. The dashed line represents the ORD curve (and relates to the refractive index scale on left. The solid line represents the CD curve ( ( — scale on right). The maximum absorption, zero values of DRD. and maxima and minima of CD values occur at The...

In this system the bands (zones) broaden because of diffusion effects and nonequilibrium. This broadening mechanism is fairly symmetrical and the resulting elution bands approach the shape of a Gaussian curve. This system best explains liquid or gas partition chromatography. The system may be viewed in two ways ... 

A numerical calculation of the line profiles due to the combined effect of the natural lifetime, the light-shift and the saturation has been performed taking into account all possible trajectories of atoms inside the metastable beam. Actually, the study of experimental linewidths shows there are some other stray effects responsible for the broadening of the lines. He have considered their contribution by making a convolution of the line profile with a gaussian curve. 

FIGURE 4-24 Cross sections of pollutant concentrations at two locations downwind of a smokestack. Note that physical height of the stack is typically less than the effective height of the stack, which takes plume rise into account. The total flux of pollutant is identical at each downwind location, although concentration decreases as the plume widens. The shape of each concentration versus distance plot is a normal, or Gaussian, curve hence, this is often called a Gaussian plume (adapted from Boubel et al, 1994). 

Stoichiometry fluctuations are also responsible for a line broadening effect that, with the exception of cubic phases, is also hkl) dependent. The effect on the line profile is directly related to the nature of the fluctuation if the compositional variation is described by a suitable function, e.g. a Gaussian curve, then the resulting peak profile component is also Gaussian and the FT for this effect can be written as ... 

Analysis of the data with a sum of two gaussian curves or by the Log-normal analysis indicates clearly that binding of calcofluor at high concentrations induces a disruption in the structure of ai-acid glycoprotein. Apparently, calcofluor induces a pressure at the surface of the protein that denatures it partially. This effect is identical to that observed when hydrostatic pressure is applied on proteins (Ruan and Weber, 1993 Ruan and Baliiy, 2002). 

It is possible, by identifying each desorption curve with a Gaussian curve, to decompose each spectrum and evaluate the effect of each species as a function of time and temperature of adsorption Ta. 

Figure 4-3 Gaussian curves showing the effect of doubling the standard deviation. The number of observations for each curve, which is the area beneath the curve, is the same.

Stephens PJ, Harada N. ECD cotton effect approximated by the Gaussian curve and other methods. Chirality 2010 22 229-233. 

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