Improved metrological capabilities for three-dimensional (3D) measurements of various complex micro- and nanoparts are increasingly in demand. This paper gives an overview of the research activities carried out by the Physikalisch-Technische Bundesanstalt (PTB), the national metrology institute of Germany, to meet this demand. Examples of recent research advances in the development of instrumentation and calibration standards are presented. An ultra-precision nanopositioning and nanomeasuring machine (NMM) has been upgraded with regard to its mirror corner, interferometers and angle sensors, as well as its weight compensation, its electronic controller, its vibration damping stage and its instrument chamber. Its positioning noise has been greatly reduced, e.g., from 1σ = 0.52 nm to 1σ = 0.13 nm for the z-axis. The well-known tactile-optical fibre probe has been further improved with regard to its 3D measurement capability, isotropic probing stiffness and dual-sphere probing styli. A 3D atomic force microscope (AFM) and assembled cantilever probes (ACPs) have been developed which allow full 3D measurements of smaller features with sizes from a few micrometres down to tens of nanometres. In addition, several measurement standards for force, geometry, contour and microgear measurements have been introduced. A type of geometry calibration artefact, referred to as the “3D Aztec artefact”, has been developed which applies wet-etched micro-pyramidal marks for defining reference coordinates in 3D space. Compared to conventional calibration artefacts, it has advantages such as a good surface quality, a well-defined geometry and cost-effective manufacturing. A task-specific micro-contour calibration standard has been further developed for ensuring the traceability of, e.g., high-precision optical measurements at microgeometries. A workpiece-like microgear standard embodying different gear geometries (modules ranging from 0.1 mm to 1 mm) has also been developed at the Physikalisch-Technische Bundesanstalt.

X-ray computed tomography (XCT) is a fast-growing technology for dimensional measurements in industrial applications. However, traceable and efficient methods to determine measurement uncertainties are not available. Guidelines like the VDI/VDE 2630 Part 2.1 suggest at least 20 repetitions of a specific measurement task, which is not feasible for industrial standards. Simulation-based approaches to determine task specific measurement uncertainties are promising, but require closely adjusted model parameters and an integration of error sources like geometrical deviations during a measurement. Unfortunately, the development of an automated process to parameterize and integrate geometrical deviations into XCT models is still an open issue. In this work, the whole processing chain of dimensional XCT measurements is taken into account with focus on the issues and requirements to determine suitable parameters of geometrical deviations. Starting off with baseline simulations of different XCT systems, two approaches are investigated to determine and integrate geometrical deviations of reference measurements. The first approach tries to iteratively estimate geometric deviation parameter values to match the characteristics of the missing error sources. The second approach estimates those values based on radiographs of a known calibrated reference object. In contrast to prior work both approaches only use a condensed set of parameters to map geometric deviations. In case of the iterative approach, some major issues regarding unhandled directional dependencies have been identified and discussed. Whereas the radiographic method resulted in task specific expanded measurements uncertainties below one micrometre even for bi-directional features, which is a step closer towards a true digital twin for uncertainty estimations in dimensional XCT.

A fast and highly precise method of determining the geometrical scale factor of computed tomography (CT) measurements has been validated successfully by Bundesanstalt für Materialforschung und -prüfung (BAM), the Federal Institute of Metrology (METAS) and Physikalisch-Technische Bundesanstalt (PTB) within the scope of AdvanCT (Advanced Computed Tomography for dimensional and surface measurements in industry), a project funded in the European Metrology Programme for Innovation and Research (EMPIR). The method has been developed by PTB and requires only two radiographic images of a calibrated thin 2D standard (hole grid standard) from two opposite directions. The mean grid distance is determined from both radiographs. From this and with the help of the calibration result, the radiographic scale and therefore the voxel size is determined. The procedure takes only a few minutes and avoids a time-consuming CT scan. To validate the method, the voxel sizes determined via this method were compared with voxel sizes determined from CT scans of calibrated objects. Relative deviations between the voxel sizes in the range of 10⁻⁵ were achieved with minimal effort using cone-beam CT systems at moderate magnifications.

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.

This paper provides an overview of some of the optical measurement techniques for dimensional measurements of surface topographies. These techniques are used in laboratories, as well as close to the production line. The principles of white light interferometry, focus variation, fringe projection, confocal microscopy, and image processing will be addressed. Examples of typical applications will be given and some of their benefits and limitations discussed.