measured pole figure intensities with their crystal and specimen directions
Syntax
pf = PoleFigure(h, r, I)
pf = PoleFigure([h1, h23], [r1, r2], [I1, I2])
pf = PoleFigure(h, r, I, cs, ss, superposition=c, complete=True)
Description
Each pole figure records intensities for one crystal direction, or for several superposed reflections, at a set of specimen directions. Store several pole figures as parallel lists of crystal directions, specimen directions and intensity arrays. An intensity array must have one value per specimen direction; all pole figures share their crystal and specimen frames.
By default specimen directions are antipodal axes because diffraction does not distinguish r and -r. Use complete=True for directional measurements that do distinguish them. Index by a pole-figure number to select a reflection, or use a measurement mask to filter its measured directions. Angles and corrections use radians unless stated otherwise.
Input
h |
Miller crystal direction or directions contributing to one pole figure; a list supplies one direction set per pole figure |
r |
vector3d specimen directions, or a list of direction sets |
intensities |
numeric intensity array, or a list with one array per pole figure |
frames |
optional crystalFrame and specimenFrame overriding the direction frames |
Keywords
| keyword | default | description |
|---|---|---|
superposition |
coefficients for superposed crystal directions, or one coefficient array per pole figure; default equal coefficients summing to one within each figure | |
complete |
keep specimen directions oriented rather than antipodal; default False |
Output
pf |
PoleFigure data set |
Properties
allH |
list of Miller direction sets, one per pole figure |
allR |
list of specimen direction sets |
allI |
list of intensity arrays matching allR |
c |
superposition coefficients for each entry of allH |
CS, SS |
crystal and specimen reference frames |
numPF |
number of pole figures |
antipodal |
whether specimen directions identify r with -r |
See also
loadPoleFigure, calcODF, PoleFigure.normalize, PoleFigure.correct
Members
| antipodal | whether the specimen directions are axes, r not told from -r |
| calcError | the mean deviation, one number per pole figure, from a recalculation by an ODF or from other pole figures on the same directions |
| calcErrorPF | the pole figures of the deviation from a recalculation: the difference between measured intensities and those an ODF predicts, or another pole figure on the same directions |
| calcNormalization | find intensity scale factors matching a recalculation to the measured pole figures |
| calcODF | calcODF(pf, …): an ODF reconstructed from the pole figure intensities, an SO3FunRBF |
| calcODFIterative | calcODFIterative(pf, …): the reconstruction refined successively over a ladder of halfwidths |
| calcPoleFigure | recalculate this data set’s pole figures from an orientation distribution |
| cat | the pole figures of several data sets in one, in order |
| correct | the pole figures corrected for background and defocusing |
| CS | the crystal frame, that of the crystal directions allH |
| export | write every pole figure of a data set to its own three column table |
| findOutlier | the measurements whose intensity deviates from the mean of their neighbours by more than alpha standard deviations |
| frame | the frame of the specimen directions, pf.SS |
| h | the crystal directions of all pole figures in one vector |
| how2plot | the plotting convention of the specimen directions, the session’s for frame-free ones |
| intensities | the intensities of all pole figures in one array, in the order of pf.r |
| isempty | whether the pole figures hold no measurement |
| isOutlier | the measurements whose intensity deviates from the mean of their neighbours by more than alpha standard deviations |
| load | the pole figures a file holds, or the files of a list, read by their format |
| max | the largest intensity of each pole figure, or the pointwise maximum with a number or another pole figure |
| mean | the mean intensity of each pole figure, the integral over the sphere |
| min | the smallest intensity of each pole figure, or the pointwise minimum with a number or another pole figure |
| minus | |
| mrdivide | |
| mtimes | |
| noisepf | simulated diffraction counts: Poisson counts of factor * I + background, the background subtracted again |
| normalize | the pole figures scaled to mean one, or to the pole figures an ODF predicts |
| numPF | the number of pole figures |
| plot | measured pole figures in a row, the specimen directions as markers coloured by intensity |
| plotDiff | the difference between measured pole figures and recalculated ones, or two measurements, drawn as pole figures of the error |
| plus | |
| PoleFigure | measured pole figure intensities with their crystal and specimen directions |
| r | the specimen directions of all pole figures in one vector |
| rdivide | |
| resolution | the resolution of the measurement, the finest over the pole figures |
| rotate | the specimen directions turned |
| scale | the intensities multiplied by alpha, one number or one per pole figure |
| select | the pole figures of the index or indices i, a data set of their own |
| SS | the specimen frame, that of the specimen directions allR |
| subsref | |
| times | |
| uminus | |
| union | the pole figures of several data sets in one |
| unique | the duplicated directions removed: equivalent specimen directions under the specimen group carry the same pole density, so they are merged and their intensities averaged |
MATLAB’s PoleFigure_index
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/PoleFigure_index_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.