Explains EBSD color coding.

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Colorcoding of orientations |

Assigning the Euler angles to the RGB values |

Colorcoding according to inverse pole figure |

EBSD/plotspatial, grain/plotGrains, ebsdColorbar, orientation2color

In order to visualize orientation maps as they are measured by EBSD one has to assign a color to each possible orientation. As an example, one may think of representing an orientation by its Euler angles ph1, Phi, phi2 and taking these as the RGB values of a color. Of course, there are many other ways to do this. Before presenting all the possibilities MTEX offers to assign a color to each orientation let us shortly summarize what properties we expect from such an assignment.

- crystallographic equivalent orientations should have the same color
- similar orientations should have similar colors
- different orientations should have different colors
- the whole colorspace should be used for full contrast
- if the orientations are concentrated in a small region of the orientation space, the colorspace should be exhaust by this region

It should be noted that it is impossible to have all the 4 points mentioned above represented by a single colorcoding. This is mainly due the fact that the orientation space is three dimensional and the colorspace is only two dimensional, i.e., there are too few colors to cover the whole orientation space in an unambiguous way. Hence, some compromises have to be accepted and some assumptions have to be made.

Using the Euler angles as the RGB values is probably the simplest way of mapping an orientation to a color. In MTEX such a color map is defined as a variable of type orientatiomMapping

% we have to set up a crystal symmetry first, as it defines the fundamental % region for the Euler angles cs = crystalSymmetry('432') % thise defins the orientation map oM = BungeRGBOrientationMapping(cs)

cs = crystalSymmetry symmetry: 432 a, b, c : 1, 1, 1 oM = BungeRGBOrientationMapping with properties: center: [1×1 quaternion] phi1Range: [0 6.2832] phi2Range: [0 1.5708] PhiRange: [0 1.5708] CS1: [6×4 crystalSymmetry] CS2: [1×1 specimenSymmetry] antipodal: 0

Given an arbitrary orientation

`ori = orientation('Euler',10*degree,20*degree,0*degree)`

ori = orientation size: 1 x 1 crystal symmetry : 1, X||a, Y||b, Z||c specimen symmetry: 1 Bunge Euler angles in degree phi1 Phi phi2 Inv. 10 20 0 0

we can compute the corresponding color as rgb values by

rgb = oM.orientation2color(ori)

rgb = 0.0278 0.2222 0

Lets visualize the orientation map by plotting it in orientation space as phi_2 sections

plot(oM,'sections',6,'phi2')

Although this visualization looks very smooth, the orientation map using Euler angles introduces lots of color jumps, i.e., the point 2 of our requirement list is not satisfied. This becomes obvious when plotting the colors as sigma sections, i.e., when section according to phi_1 - phi_2

plot(oM,'sections',6,'sigma')

The standard way of mapping orientations to colors is based on inverse pole figures. The following orientation map assigns a color to each direction of the fundamental sector of the inverse pole figure

oM = ipdfHSVOrientationMapping(cs) plot(oM)

oM = ipdfHSVOrientationMapping with properties: inversePoleFigureDirection: [1×1 vector3d] CS1: [6×4 crystalSymmetry] CS2: [1×1 specimenSymmetry] antipodal: 0 colorPostRotation: [1×1 rotation] colorStretching: 1 whiteCenter: [1×1 vector3d] grayValue: [0.2000 0.5000] grayGradient: 0.5000 maxAngle: Inf sR: [1×1 sphericalRegion] refl: [1×1 vector3d] rot: [1×1 rotation] alpha: 0

We may also look at the inverse pole figure sphere in 3d. One can nicely observe how the color map follows the given symmetry group.

close all plot(oM,'3d')

Alternatively, we may plot the color mapping in 2d on the entire sphere together with the symmetry elements

plot(oM,'complete') hold on plot(cs) hold off

The orientation map provides several options to alter the alignment of the colors. Lets give some examples

```
% we may interchange green and blue by setting
oM.colorPostRotation = reflection(yvector);
plot(oM)
```

or shift the cycle of colors red, green, blue by

oM.colorPostRotation = rotation('axis',zvector,'angle',120*degree); plot(oM)

Lets now consider an EBSD map

```
mtexdata forsterite
plot(ebsd)
```

and assume we want to colorize the Forsterite phase according to its orientation. Then we first define the orientation mapping. Note that we can pass the phase we want to color instead of the crysta symmetry

`oM = ipdfHSVOrientationMapping(ebsd('Forsterite'))`

oM = ipdfHSVOrientationMapping with properties: inversePoleFigureDirection: [1×1 vector3d] CS1: [4×2 crystalSymmetry] CS2: [1×1 specimenSymmetry] antipodal: 0 colorPostRotation: [1×1 rotation] colorStretching: 1 whiteCenter: [1×1 vector3d] grayValue: [0.2000 0.5000] grayGradient: 0.5000 maxAngle: Inf sR: [1×1 sphericalRegion] refl: [] rot: [1×1 rotation] alpha: 0

We may also want to set the inverse pole figure direction. This is done by

oM.inversePoleFigureDirection = zvector;

Next we compute the color corresponding to each orientation we want to plot.

`color = oM.orientation2color(ebsd('Forsterite').orientations);`

Finally, we can use these colors to visualize the orientations of the Forsterite phase

`plot(ebsd('Forsterite'),color)`

We can visualize the orientations of the forsterite phase also the other way round by plotting them into the inverse pole figure map.

plot(oM) hold on plotIPDF(ebsd('Forsterite').orientations,oM.inversePoleFigureDirection,... 'MarkerSize',4,'MarkerFaceColor','none','MarkerEdgeColor','k') hold off

I'm plotting 12500 random orientations out of 152345 given orientations

Since orientations measured by EBSD devices are pure rotations specified by its Euler angles, we may restrict the crystal symmetry group to pure rotations as well. As this group is smaller, in general, the corresponding fundamental sector is larger, which allows distinguishing more rotations

% this restricts the crystal symmetries used for visualization % to proper rotations ebsd('Forsterite').CS = ebsd('Forsterite').CS.properGroup; oM = ipdfHSVOrientationMapping(ebsd('Forsterite')) % plot(oM)

oM = ipdfHSVOrientationMapping with properties: inversePoleFigureDirection: [1×1 vector3d] CS1: [4×1 crystalSymmetry] CS2: [1×1 specimenSymmetry] antipodal: 0 colorPostRotation: [1×1 rotation] colorStretching: 1 whiteCenter: [1×1 vector3d] grayValue: [0.2000 0.5000] grayGradient: 0.5000 maxAngle: Inf sR: [1×1 sphericalRegion] refl: [1×1 vector3d] rot: [1×1 rotation] alpha: 0

We observe that the fundamental sector is twice as large as for the original crystal symmetry. Furthermore, the measured Euler angles are not symmetric within this enlarged fundamental sector

hold on plotIPDF(ebsd('Forsterite').orientations,oM.inversePoleFigureDirection,... 'MarkerSize',4,'MarkerFaceColor','none','MarkerEdgeColor','k') hold off

I'm plotting 25000 random orientations out of 152345 given orientations

Lets finish this example by plotting the ebsd map of the Forsterite orientations color mapped according to this restricted symmetry group. The advantage of restricting the symmetry group is that we can distinguish more grains.

color = oM.orientation2color(ebsd('Forsterite').orientations); plot(ebsd('Forsterite'),color)

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