Deconvolution angular

In the presented form Eq. (8.13) is only valid, if Hj (s) is, indeed, constant over the whole angular range required for analysis. If this is not the case and numerical deconvolution is aimed at, the standard algorithm may be adapted by consideration of the fact that, in any case, the broadening is a slowly varying function of 29. 

Many real angular intensity distribution functions have been found to closely approximate a Gaussian and for the remainder of this paper a Gaussian distribution will be used. It should be noted, however, that the angular deconvolution can be used on patterns from specimens with any form of disorientation function. For a Gaussian distribution, equation (2) becomes... 

Figure 2. Intensities (bottom) and positions (top) on the equator and layer lines I and 2 as measured by the fitting of nonlinear terms during angular deconvolution.

Multiangle Measurements. More information is potentially available from multiangle measurements. Zero-angle extrapolated data are more amenable to proper data transformation. Separation of translational and rotational motion of highly acicular particles is possible. Verification of peaks at more than one angle lends credence to their existence. Simultaneous deconvolution of angular data may provide a useful constraint. 

Data Transformations. The deconvolution of correlation functions yields the intensity-weighted diffusion coefficient distribution. Transformation to a size distribution requires division by the diameter raised to a high power and by an angular dependent function which oscillates over several orders of magnitude for particles larger than a half a micron. Given the artifacts from the primary deconvolution, extreme caution is advised when transforming data. 

Figure 24 TOF distributions for N2 and N2O formed by reaction of NO on Pd(l 1 0) from [79]. The velocity distributions were recorded at the peak of the angular distributions, 41° for N2 (closed circles) and 0° for N2O (open circles). The curve through the N2 TOF (full line) was obtained by deconvolution using two modified Maxwellian forms (broken lines).

Amongst the non-medical applications, an early paper is that of Lothian and ChappeP. The next step forward is the work of Sliepcevich and coworkers who were originally motivated by studies on sprays. They developed the theoreticad basis to relate the angular distribution of diffracted light to a particle size distribution and used it to deconvolute experimental data. 

For evaluating the angular dependence of line positions, the spectra have been deconvoluted by a computer program which was described previously [ll, 25j. Thereby frequency positions, widths and intensities of the strongly overlapping lines were obtained. 

In general, molecular motion is a combination of translation, rotation, and vibration. If one is interested only in vibration, the translational and rotational components of motion must be deconvoluted out, and that requires a change in coordinates. Translation could be screened out by using a reference system with its origin at the center of mass, but that would still leave a mixture of rotation and vibration. What is needed in order to have pure vibrations is a set of coordinates that vary in time in such a way that there is no net angular velocity around the three inertial axes. 

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