Lorenz Butzhammer

As industrial computed tomography (CT) systems evolve toward robotic CT and freely selectable three-dimensional acquisition trajectories, spatial resolution must be evaluated not only globally but also with respect to position and direction within the three-dimensional measuring volume. The modulation transfer function (MTF) is a key metric for spatial resolution, yet the widely used ASTM E1695−20 method, based on edge response analysis of cylindrical objects, provides only averaged axial-plane values and lacks directional information. To overcome these limitations, this contribution proposes an extended MTF evaluation approach suitable for advanced 3D trajectories. The method analyzes individual gray value profiles along lines perpendicular to object surfaces and applies local averaging to improve robustness against voxel grid effects and noise. While a cylindrical object is used for comparability with ASTM E1695−20, a spherical object enables full 3D directional MTF assessment.

Digital models using computer simulation for the acquisition of X-ray projections offer the possibility to virtually perform a X-ray computed tomography (CT) measurement. Virtual CT scans benefit research and development of X-ray computed tomography, serving various purposes while reducing physical scan time and therefore cost. The accuracy of a digital model determines its utility. Suitable test procedures of digital models can assure the sufficient accuracy of a digital model regarding a specific task. For the use of digital models in dimensional metrology an agreement of dimensional measurands compared to a physical counterpart is important. In this contribution, a physical and virtual CT measurements of a calibrated Multi Feature Check mini specimen are evaluated regarding surface transition metrics of the volume data and its metrological compatibility of dimensional measurands. For the evaluation of the gray value response at the surface transition, a methodology that uses local sampling patterns to generate a locally averaged edge response is presented. The digital model shows promising results to serve as a basis for further extension to determine the measurement uncertainty of dimensional CT measurements using the Monte-Carlo method in the future.

Selecting scan angles such that surface segments are aligned with straight X-ray paths (i.e., rays are tangential to the surface and therefore perpendicular to the local surface normal) is known to produce sharper transitions of those surface segments in the reconstructed volume. This enhances dimensional accuracy in sparse-view computed tomography (CT). However, existing approaches offer no direct means to exploit this criterion for automatic scan-angle optimization. We propose a method that uses a virtual representation of the CT setup, including an STL surface model of the inspected part, to automatically identify taskspecific scan angles. Using elementary vector calculus, the algorithm determines projection directions that generate tangential X-rays for targeted surface segments. To support different levels of geometric complexity, we introduce two variants of the angle-selection procedure. The methods were experimentally validated on two objects with distinct absorption and geometric characteristics. For a steel gauge block, employing the minimum number of task-specific projections required for surface-data completeness substantially outperformed a conventional high-projection scan. For a geometrically more complex test object, surface-related errors were still reduced within the region of interest. The proposed approach – particularly suited for flat surface structures and not accounting for image-degrading factors other than cone-beam artifacts – shows promise for high-throughput dimensional metrology of mono-material parts.

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 10⁻⁵–10⁻⁴ of measured sphere distances and sphericity values below 50 μ m . For sphere distances, random errors were increased by a factor of 5 due to the offline trajectory calibration, but were still low ( < 1 μ m ) 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.

Zusammenfassung: Eine Erweiterung der Scantrajektorie für die industrielle Röntgen-Computertomographie von einer kreisförmigen Form (entsprechend einer 360°-Rotation des Messobjekts) hin zu frei wählbaren Aufnahmeposen hat das Potenzial, durch eine geeignete Trajektorienanpassung Messabweichungen zu reduzieren. In diesem Beitrag wird eine solche Trajektorienanpassung durch einen Hexapoden als Messobjektmanipulator und eine güteparameterbasierte Methodik zur Wahl einzelner Trajektorienpunkte erreicht. Die Ergebnisse zeigen, dass sich vor allem für eine geringe Projektionszahl signifikante Vorteile ergeben, was vor allem im Hinblick auf Inline-CT mit hohem Durchsatz von Relevanz ist.

Systematic and random measurement errors are the cause of uncertain conformance and non-conformance statements. A wrong conformance statement occurs if the workpiece is accepted and is a reject part (type II error or false-negative) and a wrong non-conformance statement if the workpiece is rejected and is an in-spec part (type I error or false-positive). In order to avoid type I and type II errors, measurement uncertainty must be taken into account in the conformance and non-conformance testing. In practice, some procedures are used to consider measurement errors or the uncertainty that deviate from the state-of-the-art in research and technology. As these methods have become established over many years, they are still widely used despite better theoretical knowledge. The standard ISO 14253-1:2017 specifies a procedure based on probability and measurement uncertainty that is in accordance to the internationally accepted “Guide to the expression of uncertainty in measurement” and its supplements but is often not used due to the complexity of the evaluation of measurement uncertainty. In this contribution we give an overview and comparison of the different existing methods and provide an suggestion for supplementing the standard ISO 14253-1:2017, as Monte Carlo simulations enable a direct probability-based conformance and non-conformance testing even for complex measurement processes.

CT systems with high degrees of freedom such as robot-guided setups allow CT scanning with arbitrary 3D trajectories. However, many existing systems require an additional calibration scan to determine the exact source/detector poses of new trajectories. I....

Industrial x-ray computed tomography (CT) represents an established measurement technique in the field of nondestructive testing and dimensional metrology. However, the measurement accuracy is sometimes limited by measurement artifacts that cannot be avoided using a standard circular scan trajectory. This problem can be addressed with the aid of flexible 3D trajectories, but up to date, the application of these is mainly restricted to special CT devices using robot arms. In this paper, we present results using a hexapod as an additional positioning system in a commercial industrial CT scanner. In addition to the 360^∘rotation, task-specific tilting of the part during the scan is possible in this way. We used and adapted geometry calibration procedures based on a multi-sphere reference object to enable reconstruction with high accuracy. Using a demonstrator test fixture with high absorbing elements, we show that severe metal and truncation artifacts can be avoided for a region-of-interest scan. Furthermore, cone-beam artifacts, which are inherent to circular scan trajectories, can be reduced significantly. Using measurement objects that can be measured well with a circular trajectory, we found that applying a 3D trajectory leads to dimensional measurement deviations in the same range or even lower than those of a circular trajectory. This suggests that the pose repeatability of the hexapod is sufficient to perform complex scan paths without general loss of accuracy. The obtained results could be relevant for end users of conventional CT scanners, as upgrading existing devices is in principle possible. The presented investigations form the basis for the application of trajectory optimization algorithms.