A novel pole figure inversion method: specification of the MTEX algorithm

A novel algorithm for ODF (orientation density function) estimation from diffraction pole figures is presented which is especially well suited for sharp textures and high-resolution pole figures measured with respect to arbitrarily scattered specimen directions, e.g. by area detectors. The estimated ODF is computed as the solution of a minimization problem which is based on a model of the diffraction counts as a Poisson process. The algorithm applies discretization by radially symmetric functions and fast Fourier techniques to guarantee smooth approximation and high performance. An implementation of the algorithm is freely available as part of the texture analysis software MTEX.

[1]  H. Schaeben.  Texture Approximation or Texture Modelling with Components Represented by the von Mises–Fisher Matrix Distribution on SO(3) and the Bingham Distribution on S4++ , 1996 .

[2]  Stefan Kunis,et al.  Efficient Reconstruction of Functions on the Sphere from Scattered Data , 2007 .

[3]  Anil K. Jain,et al.  Texture Analysis , 2018, Handbook of Image Processing and Computer Vision.

[4]  J. Pośpiech,et al.  The Feasibility of the Reproduction of the Texture Function by the Vector Method , 1981 .

[5]  Kurt Jetter,et al.  Recent Progress in Multivariate Approximation , 2001 .

[6]  K. Gerald van den Boogaart,et al.  Spherical harmonics in texture analysis , 2003 .

[7]  J. Pośpiech,et al.  Demonstration of the Ghost Effect in the Presentation of the Orientation Distribution of Texturized Materials , 1980 .

[8]  H. Wenk.  Preferred orientation in deformed metals and rocks : an introduction to modern texture analysis , 1985 .

[9]  R. Carlton.  Z. , 1904, Industrial and Labor Relations Terms.

[10]  D. Ruer.  Méthode vectorielle d'analyse de la texture , 1976 .

[11]  H. Bunge.  Texture Analysis in Materials Science , 1982 .

[12]  Daniel Potts,et al.  Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers , 2007 .

[13]  H. Schaeben,et al.  Entropy optimization in quantitative texture analysis , 1988 .

[14]  Martin D. Buhmann,et al.  Radial Basis Functions: Theory and Implementations: Preface , 2003 .

[15]  E. Rybacki,et al.  Glide systems of hematite single crystals in deformation experiments , 2008 .

[16]  Christopher Hammond.  The Basics of Crystallography and Diffraction , 1997 .

[17]  Helmut Schaeben,et al.  Kernel-based methods for inversion of the Radon transform on SO(3) and their applications to texture analysis , 2007 .

[18]  Stefan Kunis,et al.  Fast spherical Fourier algorithms , 2003 .

[19]  V. Schulze,et al.  Crystallographic texture approximation by quadratic programming , 2006 .

[20]  W. Schäfer,et al.  The Jülich neutron diffractometer and data processing in rock texture investigations , 2000 .

[21]  H. Schaeben,et al.  A Simple Standard Orientation Density Function: The Hyperspherical de la Vallée Poussin Kernel , 1997 .

[22]  N. Morimoto,et al.  Microstructure and crystallographic-texture of giant barnacle (Austromegabalanus psittacus) shell. , 2006, Journal of structural biology.

[23]  Philip Crotwell.  Constructive Approximation on the Sphere , 2000 .

[24]  R. Roe.  Description of Crystallite Orientation in Polycrystalline Materials. III. General Solution to Pole Figure Inversion , 1965 .

[25]  M. Miller,et al.  A novel optimization-based pole-figure inversion method: comparison with WIMV and maximum entropy methods , 2006 .

[26]  D. Varshalovich,et al.  Quantum Theory of Angular Momentum , 1988 .