The metrological structural resolution for dimensional x-ray CT: analysis of the comparability between the CEB and the PBS method

The metrological structural resolution (MSR) describes the size of the smallest surface feature that can be measured dimensionally with a given accuracy. Several methods to determine the MSR for dimensional x-ray CT (dXCT) have been proposed in the past, two of which are compared and related in this publication, i.e. the curved-edge based (CEB) and the profile-based spectral (PBS) method. Both methods consider the surface structure as being described by a single surface on the relevant local scale and are also suitable for the application to optical or tactile coordinate measurement systems (CMSs). The CEB method evaluates the radii of circular shapes to determine the width of the Gaussian filter that describes the filtering of the surface by the CMS. The PBS method evaluates the instrument transfer function (ITF) determined by means of the measurement of a surface profile with a broad-band spatial frequency spectrum with a finite cut-off frequency. The PBS method yields the threshold wavelength for which the amplitude of the ITF drops below a certain level. While the resulting quantities of the two methods are very different they evaluate the same characteristic of the CMS. In this publication an analytical relation between those results is derived and shown to exist which is used to define the MSR. Simulated CT scans as well as dXCT measurements are performed to verify this relation. The results for the MSR obtained from both methods are consistent and deviations to the expectations based on theory are within a reasonable range.