EBSD.gradient

A method of EBSD.

the derivative of the orientation along the two axes of the plane of the map, per unit length, as a pair of framed vectors; or along a direction of the specimen; MATLAB’s EBSD.gradient

Syntax

gX, gY = gradient(ebsd)

gX, gY = gradient(ebsd, stencil='lattice') # least squares over the stencil of the lattice

gX, gY = gradient(ebsd, stencil='full')

gD = gradient(ebsd, xvector)

Description

The derivative at a pixel is the rotation vector of the step to its neighbour divided by the step length, a vector of the left tangent space, fitted over several neighbours. Only comparable neighbours count: inside the map, indexed, of the same phase and, where the map carries grain ids, of the same grain. A pixel whose neighbours do not span two directions gets NaN, as does every pixel of a map of a single row.

The stencil chooses the neighbours:

• ‘oneSided’, the default: the next pixel along each of the two lattice directions, the previous one only where the map ends; NaN where a neighbour inside the map is missing or not comparable.
• ‘lattice’ (MATLAB’s ‘1hop’): a least squares fit over the axial neighbours, four on a square grid and six on a hexagonal one, the central difference in the interior.
• ‘full’: a least squares fit over all eight neighbours, which leaves the fewest pixels NaN.

MATLAB returns the derivatives along the lattice directions with the basis as second output; the port returns them along the axes of the plane of the map. A direction off the plane of the map gives NaN.

Input

Keywords

Output

See also

gradientX, gradientY, curvature, calcGND, weightedBurgersVec

MATLAB’s EBSD.gradient

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}