Geometry and axes are important for multigrain crystallography experiment. You need to know how is your experiment relative, how are you rotating, what are x, y, z axes ?

The figure below gives an outline of a typical definition of laboratory axes and angles

Fig. 1: Experimental setup

More precise and detailed calculations are available in this file, extracted from the fable project: fable_geometry_version_1.0.8.pdf.

Because of the way data is saved in image files, there are always confusions with the orientation of detector images. They can be flipped in any way you can think of.

Here is an example, taken from an old Fable manual (Note: one of the example is wrong, I did see that some times ago, seb)

Fig. 2: Example for the 8 possible orientations of a 2D image.

Again, more precise definitions and calculations can be found in a former Fable manual: fableimageorientdoc_0.5.pdf

Let's assume our sample is rotated from ω1 = -20° to ω2 = +20° during the acquisition. When you reach extreme ω values you can see a shadow on one side of the diffraction images. These shadows originate from the DAC which has a limited opening angle on the outside. The further you rotate, the less 2θ angles are visible.

It's logically that the shadow of ω1 is on the opposite side of the shadow of ω2. But how do we have to rotate the images so they express reality?

Let's do it for the image at ω1 = -20°

Ask the beamline scientist if the images are saved in a different orientation than the actual setup geometry.

If this is not the case and the diffraction image on the screen is the same as the one you would see when we had a photofilm, everything is fine. If this is the case, you have to keep it in mind for the following steps.

Have a look at the sample stage. In which orientation is the rotation taking place? Where is the rotation axis pointing?

I guess in most setups the rotation axis of ω is pointing to the top or to the bottom (see figure 1). Other directions just make no sense. From this you can conclude that the shadow in our diffraction image has to be either on the right or on the left side of the image. With this information you can already exclude 4 out of the 8 possible orientations.

Watch the sample stage carefully while it is rotating. Is it rotating clockwise or counterclockwise during the image acquisition?

Let's assume we observe that it is rotated counterclockwise when we look at it from top. This means that the image at ω1 = -20° should see a shadow on the left side. Think about it carefully and try to follow and understand this conclusion.

After excluding another two of the possible orientations, we are left with only two possibilities. To find out the right one, you can compare your image with a still image which you took before or afterwards. Are there any features which are remarkable, such as a broken pixel on the detector or any other feature which you can see in every image? You can also compare the image at ω = 0° to see if there are recognizable diamond spots.

If you find something like this, you are lucky. In the example