Fast high-precision determination of geometrical magnification in industrial computed tomography

Industrial computed tomography (iCT) is used to measure the geometry of workpieces. The dimensions obtained in this way are used for quality assurance and must therefore be extremely reliable. The first step consists in calibrating the CT scanners’ geometric image magnification. The method used so far of performing full reference measurements with 3D material measures is increasingly reaching its limits: It is, in particular, not possible to trace back small dimensions with sufficient accuracy. Furthermore, this conventional method is time-consuming and requires very sensitive and expensive material measures.

Provided that high-accuracy rotary stages are used in iCT (which is usually the case), it is sufficient to use 2D material measures [1] to ensure the traceability of coordinate measuring systems. For this purpose, material measures were realized in the form of, e.g., etched Invar metal foils with a hole pattern arranged in the form of a lattice in various sizes [2] (Fig. 1). In the course of this development, their traceability was proven at PTB by means of existing optical coordinate measuring machines with a relative uncertainty already as small as 2 × 10^-6 in the average hole spacing as a reference, and the transferability to iCT was demonstrated [3].

Further measures for the correction of real iCT measurements are necessary as the use of X-rays and their interaction with the workpiece, the source and the detector are highly complex. Among these complex interactions, the depth of penetration into the detector material which depends on the spectrum [4], the so-called beam hardening through the object, scattered radiation, and diffraction, for example, are worth mentioning. Since the new method proposed here is time-efficient, it represents a considerable contribution to the systematic investigation of the influence of such effects on coordinate measurement.

The AdvanCT EMPIR project, which was launched in mid-2018 [5], was initiated and has been coordinated by PTB. Industrial partners, research institutes and national metrology institutes (such as PTB) are part of this project. Within the scope of AdvanCT, the application of the standards and the evaluation of the measurements were tested with our partners in 2020 (Fig. 2), and validation by means of the known measurement strategies was carried out. Upon completion of these tests, which have been very promising so far, it is planned to transfer the procedure to industry and science next year for practical application.

[1] J. Illemann et al., “An efficient procedure for traceable dimensional measurements and the characterization of industrial CT systems”, Proc. of DIR 2015, http://www.ndt.net/events/DIR2015/app/content/Paper/46_Illemann.pdf
[2] J. Illemann et al., “Determining spectrum-dependent source and detector positions in cone-beam CT”, Proc. of ICT2018, http://www.ndt.net/article/ctc2018/papers/ICT2018_paper_id163.pdf
[3] J. Illemann et al., “Traceable radiographic scale calibration of dimensional CT”, Proc. of ECNDT 2018, https://www.ndt.net/article/ecndt2018/papers/ecndt-0175-2018.pdf
[4] J. Illemann, M. Bartscher, “X-ray spectrum dependence of the magnification of cone-beam CT”, Proc. of ICT 2017, http://www.ndt.net/events/iCT2017/app/content/Paper/34_Illemann.pdf
[5] https://www.ptb.de/empir2018/advanct/home/



Fig. 1: Picture of a 50 µm etched Invar metal foil with a 30 mm lattice as a standard material measure, and microscopic magnifications of a single etched hole. The bevel of the edges of a few 10 µm due to the cost-effective fabrication process is tolerable to determine the position of the center of the holes.



Fig. 2. Left: Framed material measures used in the AdvanCT project. Center: optically calibrated positions of the hole centers – 250-fold magnification of the errors. The mean horizontal grid dimension is 750.019 µm; the errors due to the fabrication process amount to up to 3 µm. Right: X-ray image of the grid (the inscription below is not etched through). Nine holes in the pattern are not etched, so that the position and the orientation are distinct, even if the foil is not fully detected.