Center of Rotation and Tilt

Center of Rotation (COR) and Tilt usage

The correct center of rotation is required for a good reconstruction. We provide two automatic ways of getting a center of rotation. However, sometimes the values they find are not accurate, so there is also a manual way to adjust the center of rotation.

The algorithms used for reconstruction require a COR for each sinogram, i.e. a list of CORs equal to the number of sinograms (also equal to the number of rows in a projection). This is abstracted away and the two final values that are used are: center of rotation and tilt.

In that case the COR refers to the value at sinogram 0 (also referred to as slice 0). Using the tilt we then use a linear regression to calculate the COR for each sinogram in the data.

Entering known COR and tilt

If the COR and tilt are already known you can enter them in the “Enter known COR/Tilt manually here” section and press “Use COR/Tilt values from above”. In this case you can go immediately to reconstruction.

Correlate 0 and 180

This automatic COR algorithm finds the shift between the projections at 0 and 180 degrees. The projection exactly at 180 degrees is necessary for the best result. We provide the option of loading a 180 degree projection in the load dialog.

The algorithm will not run unless a 180 degree projection has been loaded.

This is not a problem and could be rectified either by adding a manual COR or using the minimisation algorithm.

Minimise error

This automatic COR algorithm uses the square sum of the projection as a noise heuristic. It minimises the noise in order to find the best COR for that sinogram.

It does so for a number of sinograms (slices) and adds the result in the COR table.

This algorithm may not work well on noisy data or with very bright outliers, as the minimisation can get lost in a local minima and not find the best reconstructed slice. As the same heuristic is also used in the manual “Refine” window, to highlight one of the choices as the best, the behaviour can also be seen there.

In this case the best action is to use the correlate as a starting point, and go immediately to manual COR correction.

Manual COR correction

Due to the limitations of the algorithms above there is also a manual way of calculating the COR - using the “COR Table - refine manually” part of the GUI.

In that table you can click Add to add a new COR for the currently selected slice. Once added you can click the row and then “Refine” which will take you to a window that reconstructs the sinogram with multiple CORs simultaneously, and allows you to visually pick the best one.

After you have two or more CORs in the table, a fit will be performed in order to find the COR and tilt using the data from the table rows.

It is sometimes good enough to add a COR at the top of your data and the bottom. Once the best CORs for those are found, the resulting tilt should be accurate. To increase the accuracy further add more COR rows.

To reconstruction

Once you have a satisfactory value of COR or tilt, you are ready to proceed to the “Reconstruct” tab.

Information about the filters and algorithms can be found in the other pages of the Reconstruction Help page.