Projection center PC

The projection center enables the reverse transformation of a projection image into its original 3-dimensional translation-periodic lattice.
From this becomes clear that the more accurately this projection point is determined, the more trustful the resulting reverse transformation can be.

PC is described by a coordinate triple [PC_x,PC_y,PC_z].

Projection center as defined in CALM describes the point where the primary electron beam hits the sample surface. The vertical projection onto the detector screen defines the pattern center.
Any eucentric tilt of the sample does not change PC but any tilt of the detector does.

Pattern center: In the past, often this term is used describing only [PC_x,PC_y]. Then, PC_z is either ignored or referred to as detector distance (DD).

Please note: Each commercial EBSD supplier uses his own definition. CALM uses an “aspect-ratio free” input in the user interface matching to DynamicS (Bruker).
Aztec (Oxford Instr.) stores the projection center in the exported tiff-file at the end. It is readable by any ASCII editor, e.g. Notepad++. The coordinate [pc_y,pc_y,dd] can be transferred into CALM data using the following equations. F represents the form factor of the image, i.e., horizontal numer divided by vertical number of pixels.
OIM (EDAX-TSL) displays the projection center as [x*,y*,z*]. The transformation is identical since for a circular image F=1. ·

			PC_x	PC_y	PC_z
Aztec	[pc_y,pc_y,dd]	F = 1244/1024	pc_x	1 ‒ (pc_y· F)	dd · F
OIM	[x,y,z*]		x*	1 ‒ y*	z*

[PC_x,PC_y,PC_z] should be preferably entered in CALM before trace and bandwith definition since PC affects both..

The use of a reference pattern

For very precise measurements the exact PC is requested for each individual Kikuchi pattern seperately, i.e. collect for each pattern an additional pattern, preferably from a cubic or a very well-known phase. The acquisition conditions have to be exactly the same.

This means…
Either: Don’t move the beam to the diffracting particle but shift the stage until the particle is in the center of the SEM image.
Or: Collect the pattern at very high magnifaction. Then any movement of the beam is comparatively small compared to the size of an image pixel.

Example: For a detector screen of 38×28 mm (what is slightly bigger than the really captured image size) and a resolution of 1342×1024 pixels the effective distance between two adjacent image pixels is approximately 28µm. This means, if two measurement positions (between reference and interesting phase) have a distance of 28µm, their pattern centers are shifted by one pixel against each other. For the hypothetically used pattern this difference changes PC by about ±0.001.

Please note: Possible charging unpredictably shifts the beam position and so the projection center PC.