Scattering image pattern

In oriented systems (fibres or stretched films), the scattered image often appears as a two-bar or a four-point pattern with the scattering maximum at or near the meridian (fibre axis). The one-dimensional scattered intensity along the meridian must be calculated by the projection method using the following fonnalism... 

A shortcut solution for the analysis of anisotropic data is found by mapping scattering images to scattering curves as has been devised by Bonart in 1966 [16]. Founded on Fourier transformation theory he has clarified that information on the structure in a chosen direction is not related to an intensity curve sliced from the pattern, but to a projection (cf. p. 23) of the pattern on the direction of interest. 

Thus every reflection in the fiber diagram is defined by one function fj (u, uoj, uwj) and four quadrant functions. If the model shall be fitted to a scattering pattern in which the fiber is tilted with respect to the primary beam, weighting factors are attached to each of the quadrant functions. After the fit of an experimental scattering image, the found factors quantify the tilt, and the corresponding distortion of the scattering pattern can be eliminated. 

Patterns can be collected with meaningful statistics within fractions of seconds, if strong scatterers are studied, or they can be built up in repetitive measurements if reversible changes are studied. As a consequence, complete one-dimensional or two-dimensional image patterns can be collected in consecutive time intervals or time frames. The image information of each consecutive time frame has to be accumulated in separate memory segments. Thus time is added as another dimension to the one-or two- dimensional position information. 

Figure 16.5. (a) Fiber cross-section irradiated by an X-ray beam at an offset x from its center. The structure p pf) shows fiber symmetry. From all structures along the beam path a superposition is probed. y is the variable of the integration, (b) One-dimensional tomographic reconstruction turns the measured series of projected scattering patterns that carry the accumulated structure information passed by the beam (vertical bars) into the image patterns from voxels (quadratic boxes) residing on the fiber radius... 

This chapter presents an overview of work that has been performed by the author aiming to develop adapted (i. e. a structural model is chosen as late as possible) evaluation methods for SAXS diagrams with fiber symmetry and the results obtained so far [I ]. The basic principle of the methods to be presented is the extraction of curves from the 2D data in the scattering patterns by catain kinds of integ tions ( projections ). The importance of such projections has early been recognized (5]. Novel is the analysis of the extracted curves in terms of ID and 2D structural models. Applicability is assessed by comparison of the results with the obvious features of the scattering images. 

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