Christina Kwade, Winter Semester 2019/20


Computed Tomography (CT) offers the possibility to create a holistic volume image, with which one can observe the interior of the examined part. The obtained volume can also be used to compare dimensions (e.g. lengths and distances) of the actual part measured by CT with the previously specified nominal values. For instance, one can analyse and measure wall thicknesses or check if a part adheres to its tolerances.


Definition of Metrology and Computed Tomography

Metrology is defined in the International vocabulary of metrology as the “science of measurement and its application”. They go on to specify that “metrology includes all theoretical and practical aspects of measurement, whatever the measurement uncertainty and field of application”. [1]

Computed Tomography is defined by the Verein Deutscher Ingenieure (VDI) as “imaging method in which the object is irradiated from different directions and mathematical algorithms are used to determine the distribution of the specific material properties of the tomographic object in the determined volume”. [2]

Motivation and Advantages of Computed Tomography as a Metrological Tool

CT offers a view into the interior of components and of the outer geometry in a non-destructive way. This is particularly advantageous for additive manufactured parts or such where there is otherwise no access to the inside. It is possible to check the dimensions of the part and material quality at the same time. Another major advantage is that almost all materials, surfaces and colours can be examined. It is also possible to examine a part that consists of two or more different materials. This also applies to parts that are already assembled, because in the assembled state the dimensions can be different. Therefore, there are a high number of possible applications. The test specimen also requires almost no special preparation. In addition, the method is contactless. It works for both, small and large parts. A further advantage is that it is a very visual method. To be able to evaluate and interpret the result, only a short training session is necessary. For typical installations, the achievable accuracy is usually in the micrometer range. [3] [4]

Physical Basis

Computed tomography is based on the attenuation of X-rays by matter, which can be described by the Lambert-Beer law. X-ray beams are emitted by an X-ray generator (e.g. an X-ray tube), hit the object to be measured and are then picked up by a detector. To be more precise, the residual intensity of the beam is measured when it hits the detector. Due to the different materials and pathlengths present in the part, the X-ray beam is attenuated. This is explained in detail in the article on X-ray tomography. The object can be rotated so that multiple images can be taken from different angles. There are different scanning strategies. One can scan the entire circle (i.e. 360°), or only 180°, or even smaller parts. Additionally, different trajectories are feasible (e.g. circular, helix, laminography). The process of combining these projections in order to gain the original image is called reconstruction. The article Bildrekonstruktion in der Computertomographie explains how this works mathematically. [4] [5]

Figure 1 serves as an illustration of the principle of Computed Tomography.

Figure 1: Principle of Computed Tomography


To get an representation of the inspected part that can be used for further investigations, one needs to separate the object from surrounding air or irrelevant parts: this procedure is called segmentation. This is often done with the ISO-50 % value approach. At a 50 % threshold, one makes a histogram of the number of voxels and their corresponding attenuation value, which is expressed as gray value; 0 % is set to be at the peak of the background, 100 % is at the peak of the material, and so 50 % is set to be the threshold. Voxels with an attenuation value above this ISO-50 % value are considered to be material and belong to the investigated part, while values lower are ignored. However, the most suitable percentage for the split value may vary depending on the material. This way it is possible distinguish the sample from the background in the image. [4] [6]

Figure 2 visualizes this method.

Figure 2: ISO 50 % Threshold

The length unit meter (International System of Units) is used here.

Application Examples

One of the many uses for CT is quality control. CT can be used to determine the geometry and dimension of a wide variety of objects, ranging from small plastic parts to workpieces made of aluminum or ceramics. Industry sectors that employ this method are, for example, the medical technology industry or the aerospace industry, which aim to reduce weight using hybrid construction. [5]

CT is also used in the manufacturing industry. For additively manufactured parts, for which internal access is not possible, CT is the only currently available non-destructive method for quality control. One example of this is a racing car oil manifold. The part has not only many internal holes that cannot be reached, but the position and orientation of the individual struts are critically important. [3]
Another example is the laser-sintered compressor wheel. Figure 3 shows a cross-section of such a wheel and the CAD alignment to visualize the dimensional deviations in false colour. [7]

Figure 3: Laser-sintered compressor wheel © SKZ - Das Kunststoff-Zentrum [7]

Cracks also can be detected non-destructively (Micro-CT for crack detection in concrete).
Another example is the food industry, where CT can be used to check the contents of cans. [8]

In summary, CT is applicable in many fields – more than shown here – and the number of applications is increasing. More applications can be found in [8].

Examples for Manufacturers

There are several CT manufacturers depending on the desired application. Some examples are:

Measurement Inaccuracy and Standards

In order to be able to interpret the significance of the measurement result, one must always consider the measurement uncertainty. This factor also reflects the quality of the result.

Influences on the measurement uncertainty can include the person performing the experiment, the environment, the sample, the process, the measurement itself or the measuring equipment. A possible and informative solution to the issues created by these factors could be a simulation. Partly due to their sheer number, it is not easy to determine all influences for use in mathematical formulas and simulations. Additionally, the process costs a lot of time. [5]

Variables for the image quality and the measurement accuracy include the distance of the object to the X-ray source or the distance between the angles, and thus the number of projections. The more images one combines, the better the result, but the longer it takes to acquire all projections (i.e. the scan duration increases). Other influences can also be the magnification, pixel size of the detector, or scattering. These are only the most important examples, however, there can be many more influences.
It is possible to reduce the measurement uncertainty by placing the radiation source and detector as close together as possible, thereby an enlargement is possible. [3] [5]

Another way to improve accuracy is a so-called data fusion, in which data from measurements with different magnifications, positions, or using other modalities can be combined. [3]

The measurement uncertainty of a common CT for typical industrial items was found to be in the range of 6-53 micrometers. However, it is quite difficult to determine the measurement uncertainty quantitatively because comparisons, simulations, or an analytical evaluation are needed. This information is therefore only a guide value. [9]

Another difficulty is that there are barely any standards that describe the procedure and evaluation of measurements with CT. The VDI/VDE 2630 guideline describes the principles and measurement uncertainties of computed tomography. In contrast, there are several standards and guidelines concerning coordinate measuring machines. For example, there are the VDI/VDE 2617 or standard ISO 10360, which describe tests with coordinate measuring machines. [2]

Linked Articles

Bildrekonstruktion in der Computertomographie

Micro-CT for Crack Detection in Concrete

X-Radiation and Computed Tomography

X-Ray Tomography

Literature

[1] Joint Committee for Guides in Metrology (Ed.): International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM). 3rd Edition, 2012, p. 16.

[2] VDI/VDE-Gesellschaft Mess- und Automatisierungstechnik (Ed.): Computed Tomography in Dimensional Measurement - Fundamentals and Definitions. VDI/VDE 2630 Part 1.1. Beuth Verlag GmbH, Düsseldorf (2016), p. 6.

[3] Kruth, J.P, Bartscher, M., Carmignato, S., Schmitt, R., De Chiffre, L., Weckenmann, A.: Computed Tomography for Dimensional Metrology. CIRP Annals (2011) 60, 2, p. 821-842.

[4] Weckenmann, A., Krämer, P.: Application of Computed Tomography in Manufacturing Metrology. Technisches Messen, Oldenburg Wissenschaftsverlag (2009) 76, 7-8, p.340-346.

[5] Weckenmann, A., Krämer, P.: Computed Tomography in Quality Control: Chances and Challenges. Journal of Engineering Manufacture. (2013) 227, 5, p. 634-642.

[6] Tretiak, I., Smith, R. A.: A Parametric Study of Segmentation Thresholds for X-ray CT Poriosity Characterisation in Composite Materials. Composites Part A: Applied Science and Manufacturing (2019) 123, p. 10-14.

[7] Leicht, Heinrich: Computertomographie gibt Einblicke in additiv gefertigte Bauteile. Bestimmung von Maßabweichungen und Porosität, 2017, https://www.skz.de/de/informationen/presse/pressearchiv-2017/8173.Computertomographie-gibt-Einblicke-in-additiv-gefertigte-Bauteile.html (Accessed on 16.01.2020).

[8] De Chriffre, L., Camignato, S., Kruth, J. P., Schmitt, R., Weckenmann, A.: Industrial Applications of Computed Tomography. CIRP Annals – Manufacturing Technology (2014) 63, p. 655-677.

[9] Angel, J. A. B., De Chiffre, L.: Comparison on Computed Tomography using Industrial Items. CIRP Annals (2014) 63, p. 473–476.

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