Interpolating EBSD Data edit page

In the section Denoising and Filling Missing Data we have discussed how to work with noisy EBSD data the contained non indexed pixels. Hereby, we made the assumption that the grid before and after the operations is the same.

In this section we explain how to interpolate an EBSD map at positions that do not belong to the grid. Lets us consider a simple example

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

[grains, ebsd] = calcGrains(ebsd);

% this command here is important :)
ebsd = ebsd.project2FundamentalRegion(grains);

plot(ebsd,ebsd.orientations)
ebsd = EBSDsquare (y↑→x)
 
 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 command interp interpolates the orientation at arbitrary coordinates x and y. It does not require the data to be on a grid - a plain EBSD, a phase subset and a rotated or sheared map work just as well - but our map is an EBSDsquare anyway, since that is how it was imported, see Square and Hex Grids.

x = 30.5; y = 5.5;
e1 = interp(ebsd,x,y)
e1 = 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   grainId
  1       1   (162.8°,112.1°,186.1°)      10   160   255       0   0.4    3109       110
 Scan unit : um
 X x Y x Z : [30 → 30] x [5.5 → 5.5] x [0 → 0]
 Normal vector: (0,0,1)

By default the command interp performs inverse distance interpolation. This is different to

e2 = ebsd('xy',x,y)
e2 = 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   grainId
 13993       1   (162.8°,112.1°,186.1°)      10   160   255       0   0.4    3109       110
 Scan unit : um
 X x Y x Z : [31 → 31] x [5.4 → 5.4] x [0 → 0]
 Normal vector: (0,0,1)

which returns the nearest neighbor EBSD measurement. Lets have a look at the difference

angle(e1.orientations,e2.orientations)./degree
ans =
     0

Change of the measurement grid

The command interp can be used to evaluate the EBSD map on a different grid, which might have higher or lower resolution or might even be rotated. Lets demonstrate this

% unit cell of twice the size, rotated by 45 degree
uC = rotate(2*ebsd.unitCell,45*degree);

% define the EBSD data set on this new grid
ebsdNewGrid = gridify(ebsd,'unitCell',uC)

% plot the regridded EBSD data set
plot(ebsdNewGrid('indexed'),ebsdNewGrid('indexed').orientations)

xlim(ebsd.extent(1:2)), ylim(ebsd.extent(3:4))
ebsdNewGrid = EBSDsquare (y↑→x)
 
 Phase  Orientations     Mineral         Color  Symmetry  Crystal reference frame
     0    6059 (51%)  notIndexed          none                                   
     1    5713 (49%)   Magnesium  LightSkyBlue     6/mmm        X||a*, Y||b, Z||c
 
 Properties: bands, bc, bs, error, mad, oldId, grainId
 Scan unit : um
 X x Y x Z : [-21 → 70] x [-25 → 66] x [0 → 0]
 Normal vector: (0,0,1)
 Square grid  :108 x 109

Note, that we have not rotated the EBSD data but only the grid. All orientations as well as the position of all grains remains unchanged.

The new grid is generated from the cell to cell translations of the given unit cell, i.e. it is rotated by 45 degree as well. Since such a rotated grid can not fill a rectangular matrix, the corners of ebsdNewGrid stick out of the map and contain no data - this is why we have restricted the plot above to the indexed measurements.

Another example is the change from a square to an hexagonal grid or vice versa. In this case the command interp is implicitly called by the command gridify. In order to demonstrate this functionality we start by EBSD data on a hex grid

plottingConvention.default('y↓→x');
mtexdata ferrite silent
plot(ebsd(1:50,1:100),ebsd(1:50,1:100).orientations)

and resample the data on a square grid. To do so we first define a smaller square unit cell corresponding to the hexagonal unit cell

% define a square unit cell
squnitCell = ebsd.dPos / 4 * vector3d([-1 -1 1 1],[-1 1 1 -1],0).';

% use the square unit cell for gridify

ebsdS = ebsd.gridify('unitCell',squnitCell);

plot(ebsdS(1:150,1:350),ebsdS(1:150,1:350).orientations)