Papers by Author: Ralf Hielscher

Paper TitlePage

Authors: Swanhild Bernstein, Ralf Hielscher, Helmut Schaeben
277
Authors: K.Gerald van den Boogaart, Ralf Hielscher
Abstract: A long time has past since the introduction of the harmonic method for the reconstruction of the ODF from polefigure measurements, and it has been replaced by discrete methods of inversion, because of its incapability with respect to ghost effects. The harmonic method is still not in its best possible state: it disregards the high order harmonics; it disregards measurement errors and therefore gives suboptimal results; it does not provide standard errors, neither for the C-coefficients nor for the ODF; and there are the ghost effects. However, the harmonic method is a well established inversion method and it can improved at these points. Statistical considerations based on geostatistics and a model of the unknown ODF as a random function in a Baysian approach yields an inversion method, which can be characterized as a smoothing spline method. This new method is statistically optimal among all linear methods and resembles favorable features of the harmonic method in an improved way. It provides an optimal linear reconstruction of the even part of the ODF. It does not truncate the harmonic series expansion at a fixed level, but accounts for every even harmonic space in an optimal way with respect to its signal to noise ratio in the polefigure measurements. The method applies for irregularly sampled and incomplete pole figures. The method accomplishes standard errors for the ODF and the C-coefficients. Discrete inversion methods, explicitly or not, reconstruct the odd harmonic part of the function based on the principle of maximum entropy. Based on the theory of exponential families a continuous odd part (and the truncated even part) can be computed based on the entropy principle and the C-coefficients estimated by the spline method.
267
Authors: Helmut Schaeben, Swanhild Bernstein, Ralf Hielscher, Judith Beckmann, Jens Keiner, Jürgen Prestin
245
Authors: Ralf Hielscher, Swanhild Bernstein, Helmut Schaeben, K.Gerald van den Boogaart, Judith Beckmann, Jürgen Prestin
313
Authors: F. Bachmann, Ralf Hielscher, Helmut Schaeben
Abstract: The MATLAB™ toolbox MTEX provides a unique way to represent, analyse and interpret crystallographic preferred orientation, i.e. texture, based on integral (“pole figure”) or individual orientation (“EBSD”) measurements. In particular, MTEX comprises functions to import, analyse and visualize diffraction pole figure data as well as EBSD data, to estimate an orientation density function from either kind of data, to compute texture characteristics, to model orientation density functions in terms of model functions or Fourier coefficients, to simulate pole figure or EBSD data, to create publication ready plots, to write scripts for multiple use, and others. Thus MTEX is a versatile free and open-source software toolbox for texture analysis and modeling.
63
Showing 1 to 5 of 5 Paper Titles