Gridded EBSD Data edit page

In this section we discuss specific operations that are available for EBSD data which are measured on a square or hexagonal grid.

By default MTEX ignores any gridding in the data. The reason for this is that when restricting to some subset, e.g. to a certain phase, the data will not form a regular grid anyway. For that reason, almost all functions in MTEX are implemented to work for arbitrarily aligned data.

On the other hand, there are certain functions that are only available or much faster for gridded data. Those functions include plotting, gradient computation and denoising. The key command to make MTEX aware of EBSD data on a hexagonal or square grid is gridify.

In order to explain the corresponding concept in more detail lets import some sample data.

plotx2east
mtexdata twins

plot(ebsd('Magnesium'),ebsd('Magnesium').orientations)
ebsd = EBSD
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
     0     46 (0.2%)  notIndexed                                                 
     1  22833 (100%)   Magnesium  LightSkyBlue     6/mmm       X||a*, Y||b, Z||c*
 
 Properties: bands, bc, bs, error, mad, x, y
 Scan unit : um

As we can see already from the phase plot above the data have been measured at an rectangular grid. A quick look at the unit cell verifies this

ebsd.unitCell
ans =
    0.1500    0.1500
   -0.1500    0.1500
   -0.1500   -0.1500
    0.1500   -0.1500

If we apply the command gridify to the data set

ebsd = ebsd.gridify
ebsd = EBSDsquare
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
     0     46 (0.2%)  notIndexed                                                 
     1  22833 (100%)   Magnesium  LightSkyBlue     6/mmm       X||a*, Y||b, Z||c*
 
 Properties: bands, bc, bs, error, mad, x, y, oldId
 Scan unit : um
 Grid size (square): 137 x 167

we data get aligned in a 137 x 167 matrix. In particular we may now apply standard matrix indexing to our EBSD data, e.g., to access the EBSD data at position 50,100 we can simply do

ebsd(50,100)
ans = EBSD
 
 Phase  Orientations    Mineral         Color  Symmetry  Crystal reference frame
     1      1 (100%)  Magnesium  LightSkyBlue     6/mmm       X||a*, Y||b, Z||c*
 
    Id   Phase   phi1   Phi   phi2   bands    bc    bs   error   mad      x      y   oldId
 13613       1    156   101    239      10   149   133       0   0.7   29.7   14.7    8283
 Scan unit : um

It is important to understand that the property of beeing shaped as a matrix is lost as soon as we select a subset of data

ebsdMg = ebsd('Magnesium')
ebsdMg = EBSD
 
 Phase  Orientations    Mineral         Color  Symmetry  Crystal reference frame
     1  22833 (100%)  Magnesium  LightSkyBlue     6/mmm       X||a*, Y||b, Z||c*
 
 Properties: bands, bc, bs, error, mad, x, y, oldId
 Scan unit : um

However, we may always force it into matrix form by reapplying the command gridify

ebsdMg = ebsd('Magnesium').gridify
ebsdMg = EBSDsquare
 
 Phase  Orientations    Mineral         Color  Symmetry  Crystal reference frame
     1  22833 (100%)  Magnesium  LightSkyBlue     6/mmm       X||a*, Y||b, Z||c*
 
 Properties: bands, bc, bs, error, mad, x, y, oldId
 Scan unit : um
 Grid size (square): 137 x 167

The difference between both matrix shapes EBSD variables ebsd and ebsdMg is that not indexed pixels in ebsd are stored as the seperate phase notIndexed while in ebsdMg all pixels have phase Magnesium but the Euler angles of the not indexed pixels are set to nan. This allows to select and plot subregions of the EBSD in a very intuitive way by

plot(ebsdMg(50:100,5:100),ebsdMg(50:100,5:100).orientations)

The Gradient

gradX = ebsdMg.gradientX;

plot(ebsdMg,norm(gradX))
caxis([0,4*degree])

Hexagonal Grids

Next lets import some data on a hexagonal grid

mtexdata copper

[grains, ebsd.grainId] = calcGrains(ebsd)
ebsd = ebsd.gridify

plot(ebsd,ebsd.orientations)
ebsd = EBSD
 
 Phase  Orientations  Mineral         Color  Symmetry  Crystal reference frame
     0  16116 (100%)   Copper  LightSkyBlue       432                         
 
 Properties: confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, x, y
 Scan unit : um
 
 
grains = grain2d
 
 Phase  Grains  Pixels  Mineral  Symmetry  Crystal reference frame
     0     751   16116   Copper       432                         
 
 boundary segments: 12326 (37010 µm)
 inner boundary segments: 4 (12 µm)
 triple points: 1266
 
 Properties: meanRotation, GOS
 
 
ebsd = EBSD
 
 Phase  Orientations  Mineral         Color  Symmetry  Crystal reference frame
     0  16116 (100%)   Copper  LightSkyBlue       432                         
 
 Properties: confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, x, y, grainId
 Scan unit : um
 
 
ebsd = EBSDhex
 
 Phase  Orientations  Mineral         Color  Symmetry  Crystal reference frame
     0  16116 (100%)   Copper  LightSkyBlue       432                         
 
 Properties: confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, x, y, grainId, oldId
 Scan unit : um
 Grid size (hex): 136 x 119

Indexing works here similarly as for square grids

plot(ebsd(1:10,:),ebsd(1:10,:).orientations,'micronbar','off')
plot(ebsd(:,1:10),ebsd(:,1:10).orientations,'micronbar','off')

Switching from Hexagonal to Square Grid

Sometimes it is required to resample EBSD data on a hex grid on a square grid. This can be accomplished by passing to the command gridify a square unit cell by the option unitCell.

% define a square unit cell
unitCell = [-2.5 -2.5; -2.5 2.5; 2.5 2.5; 2.5 -2.5];

% use the square unit cell for gridify
ebsdS = ebsd.gridify('unitCell',unitCell)

% visualize the result
plot(ebsdS, ebsdS.orientations)
ebsdS = EBSDsquare
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
    -1   135 (0.95%)  notIndexed                                                 
     0   14025 (99%)      Copper  LightSkyBlue       432                         
 
 Properties: x, y, confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, grainId, oldId
 Scan unit : um
 Grid size (square): 118 x 120

In the above example we have chosen the square unit cell to have approximately the same size as the hexgonal unit cell. This leads to quite some distortions as squares can not reproduces all the shapes of the hexagones. We can reduce this issue by chosing the quare unit cell significantly smaller then the hexagonal unit cell.

% a smaller unit cell
unitCell = [-1 -1; -1 1; 1 1; 1 -1];

% use the small square unit cell for gridify
ebsdS = ebsd.gridify('unitCell',unitCell)

plot(ebsdS,ebsdS.orientations)
hold on
plot(grains.boundary,'lineWidth',2)
hold off
ebsdS = EBSDsquare
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
    -1   442 (0.51%)  notIndexed                                                 
     0   86579 (99%)      Copper  LightSkyBlue       432                         
 
 Properties: x, y, confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, grainId, oldId
 Scan unit : um
 Grid size (square): 293 x 297

It is important to understand that the command gridify does not increase the number of data points. As a consquence, we end up with many white spots in the map which corresponds to orientations that have been set to NaN. In order to fill these white spots, we may either use the command fill which performs nearest neighbour interpolation or the command smooth which allows for more suffisticated interpolation methods.

% nearest neigbour interpolation
ebsdS1 = fill(ebsdS,grains)

plot(ebsdS1('indexed'),ebsdS1('indexed').orientations)
hold on
plot(grains.boundary,'lineWidth',2)
hold off
ebsdS1 = EBSDsquare
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
    -1   442 (0.51%)  notIndexed                                                 
     0   86579 (99%)      Copper  LightSkyBlue       432                         
 
 Properties: x, y, confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, grainId, oldId
 Scan unit : um
 Grid size (square): 293 x 297
% interpolation using a TV regularisation term
F = halfQuadraticFilter;
F.alpha = 0.5;
ebsdS2 = smooth(ebsdS,F,'fill',grains)

plot(ebsdS2('indexed'),ebsdS2('indexed').orientations)
hold on
plot(grains.boundary,'lineWidth',2)
hold off
ebsdS2 = EBSD
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
    -1   442 (0.51%)  notIndexed                                                 
     0   86579 (99%)      Copper  LightSkyBlue       432                         
 
 Properties: x, y, confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, grainId, oldId, quality
 Scan unit : um

Gridify on Rotated Maps

A similar situation occurs if gridify is applied to rotated data.

ebsd = rotate(ebsd,20*degree)

ebsdG = ebsd.gridify

plot(ebsdG,ebsdG.orientations)
ebsd = EBSDhex
 
 Phase  Orientations  Mineral         Color  Symmetry  Crystal reference frame
     0  16116 (100%)   Copper  LightSkyBlue       432                         
 
 Properties: confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, x, y, grainId, oldId
 Scan unit : um
 Grid size (hex): 136 x 119
 
 
ebsdG = EBSDhex
 
 Phase  Orientations  Mineral         Color  Symmetry  Crystal reference frame
     0   15300 (58%)   Copper  LightSkyBlue       432                         
 
 Properties: confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, x, y, grainId, oldId
 Scan unit : um
 Grid size (hex): 151 x 175

Again we may observe white spots within the map which we can easily fill with the fill command.

ebsdGF = fill(ebsdG)

plot(ebsdGF,ebsdGF.orientations)
ebsdGF = EBSDhex
 
 Phase  Orientations  Mineral         Color  Symmetry  Crystal reference frame
     0   16205 (61%)   Copper  LightSkyBlue       432                         
 
 Properties: confidenceindex, fit, imagequality, semsignal, unknown_11, unknown_12, unknown_13, unknown_14, x, y, grainId, oldId
 Scan unit : um
 Grid size (hex): 151 x 175