CT scan trajectory calibration based on projected metal spheres: When and how should errors from elliptical distortion be corrected?

Abstract

The majority of geometry calibration procedures for industrial X-ray Computed Tomography (CT) are based on determining projected sphere centres in X-ray projections. The centres are typically derived from the elliptical contours that arise for cone beam setups. However, the ellipse centre is not identical with the projected sphere centre. A correction method (also known as Deng correction) exists, but is only used in some instances in literature. To this extent, it is an open question for which cases the correction leads to a significant improvement. For specific cases, it can even lead to larger errors. In this contribution, we therefore analyse the parameter range for which the correction is suitable. This is done by means of a simulation parameter study. Additionally, we propose an adapted correction formula that can be used for 3D scan trajectory calibration where the source-detector-distance is known. It is further proposed to keep the ellipse orientation in the ellipse fitting routine fixed. The results from simulation are selectively compared with experimental findings. Overall, the adapted correction leads to superior results compared with the original Deng correction. Whether a correction leads to an improvement at all strongly depends on the ratio between the axial source-object-distance and the sphere radius and on the position of the projected sphere centre on the detector. A theoretically derived decision criterion was largely confirmed. The presented results therefore can give a guidance for potential users who want to decide whether a correction is advantageous for a given sphere radius and CT system geometry.

Exact computation of projected sphere centres in cone beam x-ray projections

“…However, this correction is numerically unstable due to a division by zero close to the detector centre and therefore cannot be universally applied without precaution. An adapted correction formula was proposed by Butzhammer et al [6] based on an approximation that eliminates the numerical instability of the Deng method.…”