the Radon transform of a Bingham distribution: its pole figure, in closed form, its inverse pole figure, or their values

Syntax

pdf = odf.radon(h)

The pole figure of the crystal direction h.

ipdf = odf.radon(r=r)

The inverse pole figure of the specimen direction r.

val = odf.radon(h, r)

The pole figure at the directions r.

pdf = odf.radon([h1, h2], superposition=[0.5, 0.5])

The superposed pole figure of several directions.

pdf = odf.radon(h, bandwidth=32)

A harmonic expansion of another bandwidth.

Description

The pole figure of h at r is the mean of the density over the orientations taking h to r, a great circle in the quaternions; for a Bingham distribution it is a closed form in a Bessel function, Kunze and Schaeben’s formula, which is expanded into spherical harmonics. The inverse pole figure goes through the harmonic form of the distribution. Several crystal directions give the weighted sum of their pole figures, the pole figure of superposed reflections, equally weighted unless superposition is given.

Input

odf SO3FunBingham

Keywords

keyword	default	description
`h`	`None`	Miller or vector3d, the crystal direction, or a list of them
`r`	`None`	vector3d, the specimen direction
`superposition`	`None`	the weights of several crystal directions
`bandwidth`	`None`	the bandwidth of the harmonic expansion; 64 or the preference maxS2Bandwidth, the smaller, for the pole figure

Output

`pdf`	S2FunHarmonic, the pole figure in the specimen frame, or the inverse pole figure in the crystal frame
`val`	the values of the pole figure at r

References

K. Kunze, H. Schaeben, The Bingham distribution of quaternions and its spherical Radon transform in texture analysis, Mathematical Geology 36 (2004) 917-943

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/SO3FunBingham.radon_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.

SO3FunBingham.radon