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Journal for Geometry and Graphics 17 (2013), No. 2, 205--211
Copyright Heldermann Verlag 2013

Application of Focal Curves for X-ray Microdiffraction Methods

Frank Henschel
Faculty of Informatics and Mathematics, University of Applied Sciences, 01069 Dresden, Germany

Jürgen Bauch
Institute for Material Science, University of Technology, 01062 Dresden, Germany

In order to harness the full potential of X-ray diffraction methods, in particular the Kossel and X-ray Rotation Tilt technique, it is necessary to implement a fast and automatic detection and evaluation process for digital recordings or digitized film. Due to the registration of the reflection fine structure, the individual data can be used, e.g., for calculating the precision residual stress tensors directly. For this application it is necessary to know the complete recording geometry. In our method we pay attention to the focal curves: As all the diffraction cones have the same apex, the orientation can be determined solely by the reflection lines, which result as intersection with the image plane. The apex of the cones is the source of X-ray radiation in the investigated sample area. In addition to the principal point, the distance from the image plane to the sample can be determined by the respective focal curves of reflection lines without use of a scaling factor.

Keywords: Conic section, focal conics, orientation, X-ray microdiffraction, Kossel technique.

MSC: 51N05; 51N20, 68U10

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