Precise Measurement with Computer Tomography

To be able to measure the shape and position of a measured object with sufficient precision, it is necessary to correct systematic errors in tomography. Several process-related effects lead to these systematic deviations. Common to all of them is the dependence on various parameters, such as cathode voltage of the X-ray tubes, the radiation spectrum that depends on it, as well as material and geometry of the measured object itself.

An example of this is beam hardening. This effect can be traced to the fact that the radiation spectrum of an X-ray tube is made up of various frequencies. Due to their higher energy, high-frequency radiation components are absorbed by the irradiated material at a lower proportion than the low-frequency ones. As shown in Figure 41, this has the effect that for a large material thickness, low-energy sections of the X-ray spectrum can even be completely absorbed, and thus only high-energy radiation impinges on the detector. Since the mathematical algorithm for 3-D reconstruction is based on the thickness dependent absorption of the entire X-ray spectrum, material areas with large radiographic length will systematically be measured as too large. This effect is known as a beam hardening artifact.

Fig. 41: Filtering out soft radiation: Portions of the radiation spectrum are absorbed differently, due to material and geometric influences.

Other geometric artifacts arise from scattered radiation, the orientation of the rotary axis in the image, and other effects (Fig. 42).

Analytical capture and correction of these complex interrelationships is barely possible at the moment, considering that the associated parameters are only partially known or completely unknown. This also applies to the part geometry, the material density, and the exact X-ray spectrum. Through integration of additional tactile or optical sensors, these systematic measurement deviations can be measured with sufficient precision and corrected. This measurement must be carried out only once for each type of measured object and only at a few relevant points. The correction data are stored in the measurement program and are used again for new measurements of the same object type.

Fig. 42: Geometry artifact: In the area of the sidewall of the measured object (see arrow), a geometric deviation is visible that does not exist in reality.

Figure 43 illustrates the principle of the described correction method. The geometric artifact arises because, when rotating the rectangular measured object, shorter radiographic lengths occur at the corners than in the middle. This leads to an apparent spherical shape during measurement. Using, for example, tactile measurement of calibration points, these deviations are captured precisely. Building on these reference points, the tomographic point cloud is corrected geometrically as an entire entity. Due to the constant nature of the error curve, relatively few calibration points are sufficient. In Figure 36 (see p. 56), these process steps are represented. Using the “autocorrection” feature, traceable measurement results with specified measurement uncertainties are obtainable when using computer tomography.

Fig. 43: Autocorrection; a) Measured object in X-ray path; b) Object rotated in X-ray path – artifact generation; c) Workpiece; d) Tomography result with apparent bulge; e) Calibration points on the measured object; f) Calibration points with the tomography result; g) Corrected tomography result; h) Final measurement result.

Independent of the tomography process, it is possible to use these devices to measure important dimensions directly by using optical or tactile sensors. This can also be used for measurement of very small features with tight tolerances.