an ODF reconstructed from pole figures by a ladder of kernel widths, from wide to the target, each step started from the last

Syntax

odf = calcODFIterative(pf)

The defaults.

odf = calcODFIterative(pf, halfwidth=5*degree)

The target halfwidth.

odf = calcODFIterative(pf, thinning=0)

Every node of every grid kept.

Description

Where the pole figures are sampled very irregularly, a coarse model fills the gaps with volume along the fibres it justifies, and finer models refine it. The method is an elaborate start for calcODF and acts as a regularisation.

The halfwidths run from sqrt(e)^(maxSteps-1) times the target down to the target, the steps whose grid would be coarser than 45 degree left out. Each step solves on an equispaced grid of its own resolution, starting from the previous ODF evaluated on that grid (MATLAB interpolates it), the first from the uniform ODF. Before every solve the nodes whose share is below thinning times the uniform one are removed.

MATLAB’s second output alpha is not returned; MATLAB’s flag nothinning is thinning=0. Further keywords go to MLSSolver.

Input

`pf`	PoleFigure

Keywords

keyword	default	description
`resolution`	`None`	the resolution of the finest grid, by default that of the pole figures
`halfwidth`	`None`	the target halfwidth of the ansatz functions, by default the resolution
`kernel`	`None`	SO3Kernel, whose type gives the ansatz functions and whose halfwidth the target, instead of the de la Vallee Poussin kernel
`maxSteps`	`5`	the number of halfwidths of the ladder
`thinning`	`0.025`	remove the nodes below this fraction of the uniform share; 0 keeps all
`verbose`	`False`	report the fit of every pole figure in every step

Output

odf SO3FunRBF

References

F. Bachmann, Texturbestimmung aus Beugungsbildern, in: Optimierung der Goniometrie zur Texturbestimmung aus Roentgenbeugungsbildern, Springer Spektrum, Wiesbaden (2016)

Used on

PoleFigureRefinement

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/calcODFIterative_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

calcODFIterative