Characterization of the effects of detector angular misalignments and accuracy enhancement of X-ray CT dimensional measurements
Authors:   North Star Imaging, Inc. (NSI), Aloisi Valentina ,   North Star Imaging, Inc. (NSI), Schlecht Joseph ,   North Star Imaging, Inc. (NSI), Ferley Eric ,   University of Padova (UNIPD), Carmignato Simone 
Published: April 2023

Fundamental requirements for using X-ray computed tomography (CT) systems as coordinate measuring systems (CMSs) for traceable coordinate metrology are the study of measurement accuracy and the establishment of traceability to the unit of length, the meter.

Due to their complex nature, CT scanning technology and thus CT measurements are affected by multiple error sources that complexly interact in the measurement chain. The German guideline VDI/VDE 2630-part 1.2 [1] provides a detailed description of the factors influencing CT dimensional measurements. Examples of these influence factors are CT scanning parameters, work-piece properties (e.g. material, size, surface roughness), geometrical errors, software and data processing etc. Because of the multitude of these influencing quantities and the complexity and non-linearity of their interaction, CT measurements traceability is a major challenge for metrological applications. In particular, the assessment of measurement uncertainty, which is essential for traceability establishment, is one of the most critical tasks.

Among the influence factors affecting CT measurement chain, the study and analysis of CT system geometrical errors is of primary importance [2-6]. As for most precision measuring instruments, the design of a CT system involves the assembly of several components, the most important of which are the X-ray source, the rotary table and the detector.

The determination of the CT system geometry is a crucial step on which all the following steps in the measurement chain rely on. In fact, the system geometry provides the necessary information to fully describe the geometry of data acquisition and performing the tomographic reconstruction on which all the dimensional analyses are based. An error in the determination of the CT system geometry (i.e. geometric set-up) or the presence of geometrical errors not accounted for during the reconstruction affect all the subsequent steps in the measurement chain and could lead to artifacts, distortions and measurement errors in the reconstructed volume [2]. It is evident, therefore, that it is extremely important to investigate and quantify the influence of CT system geometrical errors on CT measurements.

In general, no coordinate measuring system is constructed and aligned perfectly. In an ideal perfectly aligned CT system (see Figure 1), the X-ray focal spot center (the vertex of X-ray cone), the center of rotation and the detector center are positioned on a straight line. This line is perpendicular to the detector surface on its center and coincides with the central ray (i.e. the X-ray path on the central plane of the cone that goes perpendicularly from the focal spot center to the center of the detector). Moreover, the rotation axis is perpendicular to the line containing the center of rotation, the X-ray focal spot and the detector center, while its projection is parallel to the detector columns [2]. In real practice, however, it is not possible to reach the perfect alignment conditions described above and some residual errors between the three components will be present in the system geometry [2].

In a real CT system, the actual geometry therefore will be affected by the presence of geometrical misalignments. Any discrepancy between the actual system geometry and the geometry used in the reconstruction phase (i.e. the use of an incorrect CT system geometry for reconstruction) will lead to the presence of artifacts, distortions and measurement errors. Therefore, the presence of geometrical misalignments and/or the wrong estimation of the system geometry could have a strong impact on the reconstructed volume leading to artifacts and distortions, and to measurement errors for metrological applications [2, 6]. Thus, it is of fundamental importance to study the effects of geometrical misalignments on CT measurements and to determine the sensitivity of measurements to the different misalignments.

In reference [4], Kumar et al. investigated the influence of specific geometrical errors on simulated ball bars showing that they can have significant impact on CT data. In reference [5], Ferrucci et al. studied different simulated detector angular misalignments of 1°, 2°, 5° and 10°, showing that – depending on the kind of misalignments – significant distortions might be present in the CT volume.

In this work, different sets of CT experimental investigations, performed with CMM calibrated reference objects, were specifically designed to investigate the effects of CT system detector angular misalignments on CT measurement results. Different detector angular misalignments were purposefully induced on a flat panel detector in order to determine the effects of detector pitch, yaw and roll on CT measurements (i.e. respectively θ, γ, η in Figure 1). Repeated CT scans of CMM calibrated reference objects were acquired with a NSI metrological CT system in both the aligned and purposefully misaligned configurations. For each detector misalignment (i.e. pitch, yaw and roll), three amplitudes of the misalignment were physically induced on the flat-panel detector in order to study the sensitivity of CT measurement errors to the particular type of detector misalignment. For each of the nine misaligned configurations considered in the study, sphere center-to-center distance errors, sphere diameter errors and sphere form errors were calculated and compared to the reference CMM measurements. The influence of the object positioning and measurement direction on the CT measurement errors caused by a misaligned detector were also studied in order to fully characterize the measurement errors in presence of a purposefully misaligned detector. This is of primary importance to enhance CT measurement accuracy.

After characterizing and providing a description of the effects produced by each detector angular misalignment on CT measurement results, the paper shows results from an automatic method that effectively corrects for detector misalignments physically present on the CT system hardware. NSI proprietary reconstruction software efX CT, featuring an in house developed algorithm capable of correcting for detector misalignments, was used for the reconstruction of CT scans and it is demonstrated how a significant enhancement of CT measurement accuracy is obtained.