Alignment: Camera tilt and rotation axis centering

On the importance of a good alignment

The relative alignment between the sample rotation axis and the X-ray detection system is of crucial importance for the reconstruction of tomographic image data.

The centering problem is illustrated schematically in fig_axis_alignment. In the following paragraphs, the principles behind the automatic alignment procedure will be discussed.

- Schematic showing the usual unaligned situation at the left, and the perfectly aligned configuration at the right.

Preparing the alignment sample

The alignment sample consists of a simple long and thin vertical piece of wire made from some heavily absorbing material (tungsten) to produce a well visible attenuation contrast over a wide energy range. One such sample is shown in fig_alignment_wire (left).

- The alignment sample used for the camera tilt and centering alignment (left) and the X-ray absorption images produced by the sample at a rotation angle of zero and 180 degrees (right, top and bottom).

When placing the sample, two conditions must be fulfilled in order to enable an automatic measurement of the alignment:

1. The wire must be ideally visible over the entire height of the detector. No other parts of the sample holder (e.g.: it’s base, etc.) must be visible in the field of view.

2. The entirety of the wire diameter must be within the field of view at all visible heights for both a projection image at zero degrees and one at 180 degrees.

Two representative projection images meeting these conditions are shown in fig_alignment_wire (right).

Measuring the alignment

To measure the alignment, the corresponding functions of the alignment module are used.

To determine the alignment of a given configuration of the setup, a flat-field image without the alignment sample is acquired first, followed by the two projection images of the wire sample at a sample rotation angle of zero and 180 degrees. The data processing then follows these steps, the results of which are illustrated in fig_alignment_calculation.

- The calculation of the projected rotation axis on the detector from the two measured projection images at zero and 180 degrees.

Automatic alignment procedure

During the automatic alignement procedure (scripts/auto_align:Script ``auto_align.py`` or run_auto_align()), the above alignment measurement is performed multiple times, and the alignment is automatically adjusted by moving the camera rotation motor (tilt) and transverse sample translation motion (centering offset) each time to approach the ideal alignment in an iterative manner. Typically, a few iterations are required to achieve satisfactory results. The residual misalignment is normally well below a pixel in the centering position, and well below a pixel over the full detector field of view in terms of the tilt, as shown in fig_alignment_iteration.

- The iterative improvement of the camera tilt and centering alignment. Note how the algorithm initially corrected the tilt in the wrong direction, but then detected the error in the sign and compensated for it in the next step. Also, the line fit in the second iteration is rejecting a set of anomalous data points near the bottom edge of the detector (red data points) which are marked as outliers by the RANSAC algorithm.