The most important difference between MTEX and many other EBSD software is that in MTEX the Euler angle reference is always the map reference frame. This mean the \(x\) and \(z\) axes of the map are exactly the rotation axes of the Euler angles.

In case the map coordinates and the Euler angles in your data are with respect to different reference frames it is highly recommended to correct for this while importing the data into MTEX. This section explains in detail how to do this.

## On Sreen Orientation of the EBSD Map

Many people are concerned when the images produced by MTEX are not aligned exactly as they are in their commercial software. It is indeed very important to understand exactly the alignment of your data. However, the important point is not whether a map is upside down on your screen or not. The important point is how your map aligns with the specimen, as we want to use the map to describe properties of the specimen.

There are basically two components in an EBSD data set that refer to the specimen reference frame: the spatial coordinates \(x\), \(y\) and the Euler angles \(\phi_1\), \(\Phi\), \(\phi_2\). To explain the difference have a look at the EDAX export dialog

Here we have the axes \(x\) and \(y\) which describe how the map coordinates needs to be interpreted and the axes \(A_1\), \(A_2\), \(A_3\) which describe how the Euler angles, and in consequence, the pole figures needs to be interpreted. We see that in none of these settings the map reference system coincides with the Euler angle reference frame.

This situation is not specific to EDAX but occurs as well with EBSD data from Oxford or Bruker, all of them using different reference system alignments. For that reason MTEX strongly recommends to transform the data such that both map coordinates and Euler angles refer to the same coordinate system.

Doing this we have two choices:

- transform everything to the reference system \(x\), \(y\) using the option
`'convertEuler2SpatialReferenceFrame'`

. This will keep the map coordinates while changing the Euler angles - transform everything to the reference system \(A_1\), \(A_2\), \(A_3\) using the option
`'convertSpatial2EulerReferenceFrame'`

. This will keep the Euler angles while changing the map coordinates.

In the case of EDAX data imported from an `*.ang`

file we still need to specify the export option used by the EDAX software. This is done by the options `'setting 1'`

, `'setting 2'`

, `'setting 3'`

or `'setting 4'`

.

Since setting 2 is default for most EDAX exports a typical command for importing data from an ang file would look like this

The plot does not yet fit the alignment of the map in the EDAX software as it plots the x-axis be default to east and the z-axis into the plane. This is only a plotting convention and can be set in MTEX by

Other plotting conventions are `plotx2north`

, `plotx2west`

, `plotx2south`

and `plotzOutOfPlane`

. Note that these options only alter the orientation of the EBSD map and the pole figures on the screen but does not change any data.

## Verify the reference system

One way of verifying the reference systems is to visualize crystal shapes on top of the orientation map. To do this we proceed as follows

It may also be helpful to inspect pole figures

As pole figures display data relative to the specimen reference frame MTEX automatically aligns them on the screen exactly as the spatial map above, i.e., according to our last definition with x pointing towards east and y to the south.

## Change the map reference system

In order to manually change the map reference frame one may apply a rotation to the map coordinates only. E.g. to flip the map left to right while preserving the Euler angles one can do

## Change the Euler angle reference system

Analogously we may change the Euler angle reference frame while keeping the map coordinates

## Changing both reference system simultaneously

Sometimes it is necessary to relate the EBSD data to a different external reference frame, or to change the external reference frame from one to the other, e.g. if one wants to concatenate several ebsd data sets where the mounting was not done in perfect coincidence. In these cases the data has to be rotated or shifted by the commands rotate and shift. The following commands rotate both reference frames of the entire data set by 5 degree about the z-axis.