The Index of EBSD data

The Index of EBSD data edit page

In previous chapters we have discussed how to select EBSD data by properties. In this chapter we discus the ordering of EBSD pixels within MTEX. Lets start by importing some sample data

plottingConvention.default('y↑→x');
mtexdata twins

ebsd = EBSDsquare (y↑→x, row↑→col)
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
     0     46 (0.2%)  notIndexed          none                                   
     1  22833 (100%)   Magnesium  LightSkyBlue     6/mmm        X||a*, Y||b, Z||c
 
 Properties: bands, bc, bs, error, mad, oldId
 Scan unit : um
 X x Y x Z : [0 → 50] x [0 → 41] x [0 → 0]
 Normal vector: (0,0,1)
 Square grid  :137 x 167

The imported map is an EBSDsquare, i.e. it is already stored as a matrix - see Square and Hex Grids. Restricting it to a very small rectangular subset gives back a plain list of pixels, since the selection is in general not a rectangle

poly = [44 0 4 2];
ebsd = ebsd(inpolygon(ebsd,poly))

plot(ebsd,ebsd.orientations,'micronbar','off','edgecolor','k','backend','patch')

ebsd = EBSD (y↑→x)
 
 Phase  Orientations    Mineral         Color  Symmetry  Crystal reference frame
     1     98 (100%)  Magnesium  LightSkyBlue     6/mmm        X||a*, Y||b, Z||c
 
 Properties: bands, bc, bs, error, mad, oldId
 Scan unit : um
 X x Y x Z : [44 → 48] x [0 → 1.8] x [0 → 0]
 Normal vector: (0,0,1)

In the above plot each square corresponds to one entry in the variable ebsd which as an index from 1 to 98. Let us visualize this index

text(ebsd,1:length(ebsd))

We may easily select specific pixels by specifying their indices

hold on
plot(ebsd(16:18),'edgeColor','red','facecolor','none','linewidth',4,'backend','patch')
legend off
hold off

Whether lines or columns run first is inherited from the order of the data the subset was taken from. Here that is the gridded map, whose linear index runs down a matrix column, i.e. along y - which is why the numbers above count downwards rather than across. Had the map been imported as a plain list, they would follow the order of the lines in the file instead.

Since we have restricted our large EBSD map to the small subset, the indices of the restricted data do not coincide with the indices of the imported data anymore. However, the original indices are still stored in ebsd.id. Lets visualize those

plot(ebsd,ebsd.orientations,'micronbar','off','edgecolor','k','backend','patch')
text(ebsd,ebsd.id)

In order to select EBSD data according to their original id use the option 'id', i.e., the three pixels highlighted above are

hold on
plot(ebsd('id',ebsd.id(16:18)),'edgeColor','red','facecolor','none','linewidth',4,'backend','patch')
legend off
hold off

A pixel may also be addressed by where it sits in the map, using the option 'xy'

ebsd('xy',44.5,1)

ans = EBSD (y↑→x)
 
 Phase  Orientations    Mineral         Color  Symmetry  Crystal reference frame
     1      1 (100%)  Magnesium  LightSkyBlue     6/mmm        X||a*, Y||b, Z||c
 
    Id   Phase              orientation   bands    bc    bs   error   mad   oldId
 20280       1   (176.5°,104.1°,182.9°)      10   139   245       0   0.5     650
 Scan unit : um
 X x Y x Z : [44 → 44] x [0.9 → 0.9] x [0 → 0]
 Normal vector: (0,0,1)

Note that ebsd(x,y) does NOT do this - it is an error. On a gridded map the very same expression is the pixel in row x and column y, see below, so one and the same line would mean two different pixels depending on whether the map happens to be stored as a matrix or as a list. 'xy' means the same in both cases.

Square Grids

Our subset is a list, but the pixels in it do sit on a grid, so we may put it back into matrix form with gridify.

ebsd = ebsd.gridify;

plot(ebsd,ebsd.orientations,'micronbar','off','edgeColor','black','backend','patch')

[i,j] = ndgrid(1:size(ebsd,1),1:size(ebsd,2));
str = arrayfun(@(a,b) ['(' int2str(a) ',' int2str(b) ')'],i,j,'UniformOutput',false);
text(ebsd,str)

This allows to select EBSD data simply by their coordinates within the grid, e.g., by

hold on
plot(ebsd(2,2:4),'edgeColor','red','facecolor','none','linewidth',4,'backend','patch')
legend off
hold off

Note that the gridify command changes the order of measurements. They are now sorted such that rows run first and columns second, as this is the default convention how Matlab indexes matrices. This is unavoidable and the reason why an imported map is put on its grid right away - see Square and Hex Grids.

plot(ebsd,ebsd.orientations,'micronbar','off','edgeColor','black','backend','patch')
text(ebsd,1:length(ebsd))

Hexagonal Grid

Everything above applies to EBSD data measured on a hexagonal grid as well. Such data is imported as an EBSDhex, i.e. it already is in matrix form

plottingConvention.default('y↓→x');
mtexdata titanium

ebsd = EBSDhex (y↓→x)
 
 Phase  Orientations           Mineral         Color  Symmetry  Crystal reference frame
     0    8100 (99%)  Titanium (Alpha)  LightSkyBlue       622        X||a, Y||b*, Z||c
 
 Properties: ci, grainid, iq, sem_signal, oldId
 Scan unit : um
 X x Y x Z : [0 → 996] x [0 → 998] x [0 → 0]
 Normal vector: (0,0,1)
 Hex grid     :97 x 84

and can be indexed similarly as in the square case.

ebsd = ebsd(10:16,68:79);

Lets visualize the matrix coordinates for the hexagonal grid

plot(ebsd,ebsd.orientations,'edgeColor','k','micronbar','off','unitcell')
axis off

[i,j] = ndgrid(1:size(ebsd,1),1:size(ebsd,2));
str = arrayfun(@(a,b) ['(' int2str(a) ',' int2str(b) ')'],i,j,'UniformOutput',false);
text(ebsd,str)

Cube Coordinates

In hexagonal grids it is sometimes advantageous to use three digit cube coordinates to index the cell. This can be done using the commands hex2cube and cube2hex. Much more details on indexing hex grids can be found at here.

plot(ebsd,ebsd.orientations,'edgeColor','k','micronbar','off','unitcell')
axis off

[i,j] = ndgrid(1:size(ebsd,1),1:size(ebsd,2));
[x,y,z] = ebsd.hex2cube(i,j);
str = arrayfun(@(a,b,c) ['(' int2str(a) ',' int2str(b) ',' int2str(c) ')'],x,y,z,'UniformOutput',false);
text(ebsd,str)