High but Imperfect Orientation

Introduction. The following two chapters are devoted to the evaluation of the orientation of structural entities in the studied material, not to the analysis of the inner structure (topology) of these entities. First discussions of the problem of orientation smearing go back to Kratky [248,249], Unfortunately, the corresponding mathematical concepts are quite involved, and a traceable presentation would require mathematical reasoning that is beyond the scope of this textbook. Thus only ideas, results and references are presented. 

Whenever we are considering orientation, we are dealing with anisotropic scattering data. Orientation is most frequently analyzed in 2D scattering data with fiber symmetry or in pole-figure data recorded by means of a texture goniometer. 

The aim of orientation analysis is not only the quantitative description of orientation, but also the separation of orientational effects from topological ones - ultimately meaning the desmearing of imperfect orientation in order to reconstruct the scattering pattern of the perfectly oriented structural entities. 

In the present chapter we assume that rigid and well-defined structural entities are present but not perfectly oriented -similar to a bundle of jackstraws (Fig. 9.1). 

Moreover, we assume that there is no coupling between the orientation of a structural entity and its structure. Two general topics are addressed 

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