estimation of the ODF from the PDF

High resolution texture analysis
sponsored by DFG (Az. SCH 465/15-1, -2) from 2003 – 2005

Quantitatively crystallographic preferred orientations are described by the orientation density function (ODF) which is defined as the relatively frequency of crystal orientations by volume within the specimen.Using diffraction techniques so called pole figure intensities are measured that describe the relative frequency of certain crystal lattice planes within the specimen. A novel method for PDF-to-ODF reconstruction was designed to work with arbitrary pole figure layouts and to be fast enough for hight resolution pole figures. This could achieved using multi scale algorithms based on fast spherical Fourier techniques. In order to make the method robust we have found our method upon a statistical formulation of the reconstruction problem.



pole figure of a quartz sample

Team: Prof. Dr. J. Prestin, Univ. Lübeck, Prof. Dr. Helmut Schaeben, PD Dr. Swanhild Bernstein, Dr. Ralf Hielscher

MTEX, a MATLAB toolbox for quantitative texture analysis:

Boogaart, K.G.v.d., Hielscher, R., Prestin, J., Schaeben, H., 2007, Kernel-based methods for inversion of the Radon transform on SO(3) and their applications to texture analysis: Journal of Computational and Applied Mathematics 199, 122 - 140 pdf

Bernstein, S., Schaeben, H., 2005, A one-dimensional Radon transform on SO(3) and its application to texture goniometry: Mathematical Methods in the Applied Sciences 28, 1269-1289 pdf

Schaeben, H., 2006, Interpolation of Raster Images in Large Data Cubes: Proceedings IAMG'2006, Liège, Sep 3 - 8, 2006, CD S06_18, 4p pdf

Schaeben, H., Hielscher, R., 2006, Resolving the Inverse Radon Problem on SO(3) -- Special Cases: Proceedings IAMG'2006, Liège, Sep 3 - 8, 2006, CD S11_30, 4p pdf

Hielscher, R., Schaeben, H., 2006, A novel method to determine crystallographic preferred orientations from diffraction experiments: Proceedings IAMG'2006, Liège, Sep 3 - 8, 2006, CD S06_12, 1p pdf