the pole figures an ODF predicts: simulated diffraction intensities, superposed pole figures and any specimen directions

Syntax

pf = calcPoleFigure(odf, h, r)

One pole figure per element of h.

pf = calcPoleFigure(odf, h, resolution=5*degree)

On a regular grid of the upper hemisphere.

pf = calcPoleFigure(odf, h, resolution=5*degree, complete=True)

On a regular grid of the whole sphere.

pf = calcPoleFigure(odf, [h1, h2], [r1, r2])

One set of specimen directions per pole figure.

pf = calcPoleFigure(odf, [h1, h23], r, superposition=[1, [0.2, 0.8]])

H23 two superposed directions.

pf = calcPoleFigure(odf, pfMeasured)

On the directions of a measurement.

Description

The intensity of the crystal direction h at the specimen direction r is the mean of the ODF over all orientations that take h to r, its radon transform. Where the specimen directions are axes, as on the default grid of the upper hemisphere, it is the mean of r and -r.

A Python list of crystal directions makes one pole figure per entry. An entry of several directions is their superposition, weighted by the superposition coefficients, as the overlapping reflections a diffractometer measures together.

Without specimen directions the pole figures are evaluated on regularS2Grid, which takes the remaining keywords. noisepf turns the intensities into counts.

Input

`odf`	SO3Fun
`h`	Miller or vector3d in the crystal frame of the ODF, or a list of them, one per pole figure

Keywords

keyword	default	description
`r`	`None`	vector3d, the specimen directions, or a list of them, one per pole figure; by default a regular grid
`superposition`	`None`	the weights of the superposed directions, a list with one entry per pole figure
`complete`	`False`	the whole sphere instead of the upper hemisphere, the directions without antipodal symmetry (MATLAB’s flag complete)

Output

`pf`	PoleFigure

Used on

ColorMaps, PlotTypes, PoleFigure2ODFAmbiguity, PoleFigure2ODFGhostCorrection, PoleFigureExport, PoleFigureRefinement, PoleFigureSantaFe, PoleFigureSimulation

MATLAB’s SO3Fun.calcPoleFigure

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/SO3Fun.calcPoleFigure_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.

SO3Fun.calcPoleFigure