Direct assessment of the influence of pose repeatability on the accuracy of dimensional measurements for computed tomography systems with high degrees of freedom

<jats:title>Abstract</jats:title> <jats:p>Industrial x-ray computed tomography (CT) systems with high geometric flexibility are increasingly utilized for large-scale measurement objects or challenging measurement tasks. To maintain high accuracy when deviating from the established circular scan trajectory, trajectory calibration methods using multi-sphere reference objects with known marker positions are commonly employed. These multi-sphere objects can either be scanned together with the measurement object (online trajectory calibration) or in a separate scan (offline trajectory calibration). While offline calibration increases machine time, it generally results in higher scan quality. However, a sufficient pose repeatability is necessary to ensure comparable or even superior accuracy to online calibration. In this contribution, we present a straightforward procedure to compare both types of trajectory calibration in a way that the differences of the results can directly be traced back to the influence of the pose repeatability. The multi-sphere reference object is not only used for trajectory calibration, but simultaneously as a measurement object for repeated measurements. The methodology is tested on both a twin robotic CT system and a conventional CT system that is additionally equipped with a hexapod manipulator for adaptive object tilting. Results showed, independent from the type of trajectory calibration, systematic measurement errors in the order of 10<jats:sup>−5</jats:sup>–10<jats:sup>−4</jats:sup> of measured sphere distances and sphericity values below 50 <jats:inline-formula> <jats:tex-math/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mtext>μ</mml:mtext> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> </mml:math> </jats:inline-formula>. For sphere distances, random errors were increased by a factor of 5 due to the offline trajectory calibration, but were still low (<jats:inline-formula> <jats:tex-math/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:mtext>μ</mml:mtext> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> </mml:math> </jats:inline-formula>) in comparison to systematic errors and the spread of different measurement features. Overall, both investigated systems demonstrated sufficient positioning repeatability for offline trajectory calibration. The method is in general also applicable to any other types of manipulator systems used for CT devices. It provides a workflow for the decision which type of trajectory calibration is preferable for a given CT system.</jats:p>