1. Electron backscatter diffraction (EBSD) is a common laboratory based tool used to measure crystal
orientations from crystalline sam-ples.
The emergence of the technique can be traced to rapidimage anal-ysis (or) patternanalysis routines
to produce extremely richdata sets that can be interro- gated for
1. crystallographic texture,
2. grain orientation,
3. grain shape, and
4. local deformationstructure.
Frames of reference
Establishing a consistent coordinate frame, with appropriate trans- formations between the sample,
the crystal structure, and the diffrac- tion pattern is at the heart of successful and confident use of
EBSD orientation data.
A natural choice of coordinate system is based upon the gnomonic projection used to
capture the angular diffraction data on a flat phos- phor screen, starting with the source
point at the electron beam position on the sample, and the central Z-axis of the gnomonic
projection meet- ing the detector plane at the point that is called the “pattern centre” (PC).
The gnomonic projection transforms polar angles θ into radial dis- tances ρ = tan (θ)
measured from the pattern centre. This is why, for the detector plane, we define a gnomonic,
two-dimensional (Xg, Yg) coordi- nate system with (0 The gnomonic coordinate system is
defined on the two-dimensional (Xd, Yd) detection plane in the three-dimensional detector
coordinate system (Xd, Yd, Zd) in which we measure all distances on a common length
scale (pixels, mm, or fractions of the pattern size). The Zd-axis points from a position on
the sample towards the screen and calibrates the gnomonic coordinates via xg = xd/zd and
yg = yd/zd.
2. , 0) at the pattern centre, where (xg,yg) are the re- spective components of the radial distance ρ.
