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Basics of EBSD
Automated indexing and orientation measurement
The crystal orientation is calculated from the Kikuchi band positions by the computer processing the digitised diffraction pattern collected by the CCD camera. The Kikuchi band positions are found using the Hough transform. The transform between the coordinates (x,y) of the diffraction pattern and the coordinates (ρ, θ) of Hough space is given by (Figure 8):
A straight line is characterised by ρ, the perpendicular distance from the origin and θ the angle made with the x-axis and so is represented by a single point (ρ, θ)in Hough space. Kikuchi bands transform to bright regions in Hough space which can be detected and used to calculate the original positions of the bands (Figure 9).
Using the system calibration, the angles between the planes producing the detected Kikuchi bands can be calculated. These are compared with a list of inter-planar angles for the analysed crystal structure to allocate Miller indices to each plane. The final step is to calculate the orientation of the crystal lattice with respect to coordinates fixed in the sample. This whole process takes less than a few milliseconds with modern computers.
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