Distortion parameters

To describe the X-ray imaging system the projection of 3D object points onto the 2D image plane, and nonlinear distortions inherent in the image detector system have to, be modelled. A parametric camera model based on a simple pinhole model to describe the projection in combination with a polynomal model of the nonlinear distortions is used to describe the X-ray imaging system. The parameters of the model are estimated using a two step approach. First the distortion parameters for fixed source and detector positions are calculated without any knowledge of the projection parameters. In a second step, the projection parameters are calculated for each image taken with the same source and detector positions but with different sample positions. 

The camera model has a high number of parameters with a high correlation between several parameters. Therefore, the calibration problem is a difficult nonlinear optimization problem with the well known problems of instable behaviour and local minima. In out work, an approach to separate the calibration of the distortion parameters and the calibration of the projection parameters is used to solve this problem. 

Based on the camera model the distortion parameters are calculated for fixed source and detector positions without any knowledge of the projection parameters. 

A planar calibration pattern is placed in front of the image intensiher tube to calculate the distortion parameters. The calibration marks are arranged in a regular, right angled... 

Once the distortion parameters are calibrated, undistorted images are used to estimate the projection parameters. The. sample under investigation is recorded together with a calibration body. Although a 3D calibration body in general provides higher accuracy, a planar calibration body is used, because it is much easier to handle. To overcome... 

There is no reason why the distortion parameter should not contain an entropy as well as an energy component, and one may therefore write 0 = 0q-sT. The entropy of adsorption, relative to bulk liquid, becomes A5fi = sexp(-ca). A critical temperature is now implied, Tc = 0o/s, at which the contact angle goes to zero [151]. For example, Tc was calculated to be 174°C by fitting adsorption and contact angle data for the -octane-PTFE system. 

Figure 3. The temperature dependence of the crystal distortion for VjSi, (0), derived from the data in Figure 2 [curves (a) and (c)], as discussed in reference 5. The dot-dashed curve shows the same distortion parameter for In-26.5 at%Tl derived from the data in Figure 1. The inset shows in detail the data below the super-c-nducting critical temperature, Tc. (From reference 5)...

Disorder of Nanocomposites and Common Polymers. If one compares the distortion parameters of particular nanocomposites with those of common polymer materials, the relative standard deviations are generally smaller by 1 order of magnitude. More than 30 layers are correlated to each other, whereas the correlation in commercial polymer materials is generally ranging shorter than 4 layers. 

In interpreting the experimentally determined moments however (which with the sole exception of Fe(Cp)2+ relate only to average moments), the part played by two parameters is of great importance, namely the distortion parameter, A, and the orbital reduction factor,... 

For the d5, 2A (a2 53) system an identical approach is adopted (68). In the adiabatic situation the distortion parameter is given by /A = 2 cs/(c2 - s2), again withe2 + s2 = 1, and carrying through the vibronic treatment as before yields... 

V 0.48), Ammeter and Swalen also calculated the adiabatic distortion parameter for the Co(Cp)2/Fe(Cp)2 system, finding A = 528 cm 1. In both cases however calculations were carried out to determine the value of the purely static distortion which would reproduce, via the vibronic coupling mechanism, the results for c and 45- For the Ru(Cp)2 host the corrected value of A proved to be 200 cm 1 and for the Fe(Cp)2 host 840 cm-1. Thus in the Ru(Cp)2 host, with a rather long metal to carbon distance, the vibronic effect... 

The esr data of Prins and Reinders 144) were also used by Sohn, Hendrickson, and Gray 146) in a preliminary interpretation of their magnetic susceptibility measurements 99). Thus the g values reported were found to lead to the prediction of a substantial temperature dependence of the moment over the range studied, which was not in fact observed however, the data could be accommodated by assuming either that the distortion parameter, A, increased from about 300 to around 700 cm-1 between 4.2 K and 300 K, or that the 22+(ct 54) state lay only some 350 cm-1 above the ground level. 

They recorded a spectrum very similar to that reported by Horse field and Wasserman, find-ingg = 3.21 andgL = 1.83, from which they calculated A to be 2086 cm-1 at 20 K, compared with 526 cm-1 estimated from the room temperature MCD measurements. Thus, in this work, the distortion parameter was thought to decrease with increasing temperature, in direct contradiction of the trend postulated by Sohn, Hendrickson, and Gray 99). 

There are though a number of other reasons for believing that the results of Prins et al. do correspond to those for the Fe(Cp)2+ system. Thus, it is hard to understand the wide range of g values found for the various substituted ferricenium complexes if these are all to be ascribed to Fe3+, and in addition the distortion parameters deduced by Prins et al. are very much of the same order of magnitude as those determined for the carborane and... 

TABLE 6.4. Comparison of Thin-Film and Single-Crystal CuGaS2 Lattice Parameters (a and c), c/a, and the Distortion Parameter x ... 

Hawthorne (1976) showed that the distortion parameter of site M2 is a function of the formal charge on site M4. Because site Ml shows the most severe distortion, the simple relationships connecting site M4 occupancy and cell edges may be complicated to some extent by the distortion induced on site Ml. 

Table 5.47 Polyhedral distortion parameters for C2lm amphiboles (from Flawthome, 1981a). ...

Amide distortion parameters defined in accordance with Winkler-Dunitz . 

Angle subtended by the axes of the nitrogen lone pair and the carbonyl carbon 2p orbital. Amide distortion parameters defined in accordance with Winkler-Dunitz . 

Friend et al. 469,4 70) have reported X-ray diffraction studies of highly drawn films prepared from Durham polyacetylene. They analysed the width of the diffraction peaks to obtain a crystallite size perpendicular to the chains of 5 nm in Durham polyacetylene compared to 10 nm in Shirakawa polyacetylene and distortion parameters... 

After introducing the relative axial distortion parameter v = Aax/A.sf, the Hamiltonian becomes... 

Figure 13. Cell dimensions plotted against the lattice distortion parameter of polyethylene (40) ((O) melt crystallized, A (9) melt crystallized, B (Is) single crystal ( ) cast film high pressure crystallized, C)...

Size and distortion parameters for 001 diffraction profiles from high modulus carbon fibres... 

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