The most important difference between MTEX and many other EBSD software is that in MTEX the Euler angle reference is always the map reference frame. This mean the \(x\) and \(z\) axes of the map are exactly the rotation axes of the Euler angles.
In case the map coordinates and the Euler angles in your data are with respect to different reference frames it is highly recommended to correct for this while importing the data into MTEX. This section explains in detail how to do this.
On Screen Orientation of the EBSD Map
Many people are concerned when the images produced by MTEX are not aligned exactly as they are in their commercial software. It is indeed very important to understand exactly the alignment of your data. However, the important point is not whether a map is upside down on your screen or not. The important point is how your map aligns with the specimen, as we want to use the map to describe properties of the specimen.
There are basically two components in an EBSD data set that refer to the specimen reference frame: the spatial coordinates \(x\), \(y\) and the Euler angles \(\phi_1\), \(\Phi\), \(\phi_2\). To explain the difference have a look at the EDAX export dialog
Here we have the axes \(x\) and \(y\) which describe how the map coordinates needs to be interpreted and the axes \(A_1\), \(A_2\), \(A_3\) which describe how the Euler angles, and in consequence, the pole figures needs to be interpreted. We see that in none of these settings the map reference system coincides with the Euler angle reference frame.
This situation is not specific to EDAX but occurs as well with EBSD data from Oxford or Bruker, all of them using different reference system alignments. For that reason MTEX strongly recommends to transform the data such that both map coordinates and Euler angles refer to the same coordinate system.
The best way to do this is to rotate the Euler angles such that the Euler angle reference frame and the map reference frame coincide. For general formats this is done by the options 'EulerCorrection' followed by the rotation that aligns the Euler reference frame with the map reference frame.
In EDAX software one can choose between several alignments between those coordinate system. They are numbered 1 to 4, with setting 2 being the most used. As the setting is not stored within the file MTEX assumes setting 2 and reminds you about it when importing the data. If your data was exported with a different alignment specify it explicitly, and use 'setting',0 to switch the correction off. Hence a typical command for importing data from an .ang file would look like
plottingConvention.default('y↓→x');
ebsd = EBSD.load([mtexEBSDPath filesep 'olivineopticalmap.ang'],'setting',2)
plot(ebsd('olivine'),ebsd('olivine').orientations,'refFrame','on')ebsd = EBSDsquare (y↓→x, row↓→col)
Phase Orientations Mineral Color Symmetry Crystal reference frame
1 44953 (90%) olivine LightSkyBlue mmm
2 1370 (2.8%) Dolomite DarkSeaGreen -3 X||a, Y||b*, Z||c
3 2311 (4.6%) Enstatite Goldenrod mmm
4 1095 (2.2%) Chalcopyrite LightCoral 4/mmm
Properties: ci, fit, iq, sem_signal, unknown1, unknown2, unknown3, unknown4, oldId
Scan unit : um
X x Y x Z : [0 → 888] x [0 → 888] x [0 → 0]
Normal vector: (0,0,1)
Square grid :223 x 223
The plot should already fit the alignment of the map in the EDAX software as MTEX by default plots the x-axis to east and the y-axis to the south. However, if a different alignment with respect to the screen is more useful we can pass the plottingConvention we want to the plot. This affects only that plot - to change the alignment of the whole session use plottingConvention.default instead.
% assume we want x pointing down and y pointing towards east
plot(ebsd('olivine'),ebsd('olivine').orientations,'how2plot','x↓→y','refFrame','on')
Note that these options only alter the orientation of the EBSD map and the pole figures on the screen but does not change any data.
Verify the reference system
One way of verifying the reference systems is to visualize crystal shapes on top of the orientation map. To do this we proceed as follows
% reconstruct grains
grains = calcGrains(ebsd);
% chose the correct crystal shape (cubic, hex are generic forms)
cS = crystalShape.olivine;
% select only large grains
largeGrains = grains(grains.numPixel>500)
% and plot the crystal shapes
plot(ebsd('olivine'),ebsd('olivine').orientations,'refFrame','on','location','se')
hold on
plot(largeGrains,cS,'colored')
hold off
legend offlargeGrains = grain2d (y↓→x)
Phase Grains Pixels Mineral Symmetry Color
1 8 9556 olivine mmm LightSkyBlue
boundary segments: 1980 (7920 µm)
inner boundary segments: 2 (8 µm)
triple points: 582
Id Phase Pixels meanRotation GOS
1058 1 508 (191°,63°,138°) 0.0045
1473 1 502 (108°,120°,182°) 0.0028
2203 1 708 (48°,66°,193°) 0.046
3177 1 510 (21°,69°,143°) 0.0058
3507 1 1463 (26°,53°,23°) 0.088
4216 1 1475 (26°,53°,199°) 0.091
5239 1 1191 (25°,58°,11°) 0.056
9773 1 3199 (133°,6°,322°) 0.05
It may also be helpful to inspect pole figures
h = Miller({1,0,0},{0,1,0},{0,0,1},ebsd('O').CS);
plotPDF(ebsd('O').orientations,h,'contourf')
As pole figures display data relative to the specimen reference frame MTEX automatically aligns them on the screen exactly as the spatial map above, i.e., according to our last definition with x pointing towards south and y to the east.
Change the map reference system
In order to change the map coordinates one may apply a rotation to the map coordinates only. E.g. to flip the map left to right while preserving the Euler angles one can do
rot = rotation.byAxisAngle(yvector,180*degree);
ebsd_rot = rotate(ebsd,rot,'keepEuler');
% reconstruct grains
grains = calcGrains(ebsd_rot('indexed'));
% select only large grains
largeGrains = grains(grains.numPixel>500);
% the crystal shapes are drawn on top of the map - put the reference frame
% box into a corner where none of them covers it
plot(ebsd_rot('olivine'),ebsd_rot('olivine').orientations,...
'refFrame','on','Location','ne')
% and plot the crystal shapes
hold on
plot(largeGrains,cS,'colored')
legend off
hold off
Change the Euler angle reference system
Analogously we may change the Euler angle reference frame while keeping the map coordinates
ebsd_rot = rotate(ebsd,rot,'keepXY');
% reconstruct grains
grains = calcGrains(ebsd_rot('indexed'));
% select only large grains
largeGrains = grains(grains.numPixel>500);
plot(ebsd_rot('olivine'),ebsd_rot('olivine').orientations,...
'refFrame','on','Location','se')
% and plot the crystal shapes
hold on
plot(largeGrains,cS,'colored')
legend off
hold off
Changing both reference system simultaneously
Sometimes it is necessary to relate the EBSD data to a different external reference frame, or to change the external reference frame from one to the other, e.g. if one wants to concatenate several ebsd data sets where the mounting was not done in perfect coincidence. In these cases the data has to be rotated or shifted by the commands rotate and shift. The following commands rotate both reference frames of the entire data set by 5 degree about the z-axis.
% define a rotation
rot = rotation.byAxisAngle(zvector,5*degree);
% rotate the EBSD data
ebsd_rot = rotate(ebsd,rot);
% reconstruct grains
grains = calcGrains(ebsd_rot('indexed'));
% select only large grains
largeGrains = grains(grains.numPixel>500);
plot(ebsd_rot('olivine'),ebsd_rot('olivine').orientations,...
'refFrame','on','Location','se')
% and plot the crystal shapes
hold on
plot(largeGrains,cS,'colored')
legend off
hold off