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Figure 2: Different versions of the multi-material gap standard: rejected first design version with general dimensions (a), accepted second design version with general dimensions and highlighted reference features shown by a red star (*) (b) 4.2 Calibration Reference measurements of the multi-material gap standards were performed using a high-precision tactile micro-CMS Zeiss F25 with the maximum permissible error (MPE) equal to (0.25 + L/666) um (where L = measuring length in mm). A complete calibration could not be performed in the assembled state as it would be impossible to measure the smallest gaps (the size goes down to 10 um) with the used touch probe with a diameter of 120 um. It was therefore necessary to follow an alternative calibration procedure composed of measurements in the mounted and dismounted state and subsequent correction of reference values described by the following four steps:

Figure 2 Different versions of the multi-material gap standard: rejected first design version with general dimensions (a), accepted second design version with general dimensions and highlighted reference features shown by a red star (*) (b) 4.2 Calibration Reference measurements of the multi-material gap standards were performed using a high-precision tactile micro-CMS Zeiss F25 with the maximum permissible error (MPE) equal to (0.25 + L/666) um (where L = measuring length in mm). A complete calibration could not be performed in the assembled state as it would be impossible to measure the smallest gaps (the size goes down to 10 um) with the used touch probe with a diameter of 120 um. It was therefore necessary to follow an alternative calibration procedure composed of measurements in the mounted and dismounted state and subsequent correction of reference values described by the following four steps:

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In order to thoroughly investigate single effects of each scenario, it is necessary to isolate different configurations (or at least group them in several sub-groups) and analyse them individually. As a general approach, it was decided to proceed systematically from the cases that are most frequent in industry. While multi-material scenarios including inter-material, in- material and mono-material measurements for testing length measurement errors (E-test) and probing error tests (P-test) are addressed by the authors of this publication simultaneously in other ongoing research works, this paper is aimed at the multi- material gap case. More specifically, the configurations with micro-gaps that tackle the CT limits are discussed here. 3 Multi-material gap test for CT
In order to thoroughly investigate single effects of each scenario, it is necessary to isolate different configurations (or at least group them in several sub-groups) and analyse them individually. As a general approach, it was decided to proceed systematically from the cases that are most frequent in industry. While multi-material scenarios including inter-material, in- material and mono-material measurements for testing length measurement errors (E-test) and probing error tests (P-test) are addressed by the authors of this publication simultaneously in other ongoing research works, this paper is aimed at the multi- material gap case. More specifically, the configurations with micro-gaps that tackle the CT limits are discussed here. 3 Multi-material gap test for CT
* lower part stands for the part that is in the first place of the assembly name Table 2: CNRs and scanning parameters for the five scanned sampl
* lower part stands for the part that is in the first place of the assembly name Table 2: CNRs and scanning parameters for the five scanned sampl
where “Wm and jp are the mean grey values (GV) of the material and background respectively, and o» is the standard deviation of the background GV. The values of tim were calculated based on the regions of interest (ROI) defined in the material (lower or top) and the values of wu» and o» based on the ROI inside the two biggest gaps as shown in Figure 3-b. The CNR values and CT scanning parameters are reported in Table 2. Figure 3: Orientation and position of the reference standard during scanning (a). Definition of regions selected for the calculation of CNR: (b)
where “Wm and jp are the mean grey values (GV) of the material and background respectively, and o» is the standard deviation of the background GV. The values of tim were calculated based on the regions of interest (ROI) defined in the material (lower or top) and the values of wu» and o» based on the ROI inside the two biggest gaps as shown in Figure 3-b. The CNR values and CT scanning parameters are reported in Table 2. Figure 3: Orientation and position of the reference standard during scanning (a). Definition of regions selected for the calculation of CNR: (b)
Figure 4: Different alignments for the evaluation of CT data. Alignment to the lower part (a) and alignment to the top part (b) The gaps were measured as the distance between two opposite points defined on the surfaces of the corresponding steps/tempered planes at certain x coordinates in the case of the tempered surface on both halves of the object (see Figure 5-a, b). Slightly different approaches were applied to measurements of single steps and the continuous gap created by the tempered planes. 5.2 Evaluation methods The points in the case of steps were constructed using a patch-based strategy. This strategy is based on the collection of c priori defined fitting points forming a 1x2 mm grid including 55 points (see Figure 5-c). A representative point defined as < centre of mass of the fitted points is used for the final evaluation.
Figure 4: Different alignments for the evaluation of CT data. Alignment to the lower part (a) and alignment to the top part (b) The gaps were measured as the distance between two opposite points defined on the surfaces of the corresponding steps/tempered planes at certain x coordinates in the case of the tempered surface on both halves of the object (see Figure 5-a, b). Slightly different approaches were applied to measurements of single steps and the continuous gap created by the tempered planes. 5.2 Evaluation methods The points in the case of steps were constructed using a patch-based strategy. This strategy is based on the collection of c priori defined fitting points forming a 1x2 mm grid including 55 points (see Figure 5-c). A representative point defined as < centre of mass of the fitted points is used for the final evaluation.
Figure 5: Description of the measurement procedure: two-point measurement of the gap between two steps (a) and two tempered planes (b). Principle of the patch-based construction of measurement points: grid-shaped patches on steps (c) and line-shaped patches on tempered planes (d) 7th Conference on Industrial Computed Tomography, Leuven, Belgium (iCT 2017)
Figure 5: Description of the measurement procedure: two-point measurement of the gap between two steps (a) and two tempered planes (b). Principle of the patch-based construction of measurement points: grid-shaped patches on steps (c) and line-shaped patches on tempered planes (d) 7th Conference on Industrial Computed Tomography, Leuven, Belgium (iCT 2017)
Figure 6: Histogram-based definition of the surface threshold value: mono-material case with automatic calculation of ISO-50% threshold value (a), multi-material sample with the automatic selection of low-attenuating material peak (b) and histogram of a multi-material sample, where the material line was dragged towards the high-attenuating material peak
Figure 6: Histogram-based definition of the surface threshold value: mono-material case with automatic calculation of ISO-50% threshold value (a), multi-material sample with the automatic selection of low-attenuating material peak (b) and histogram of a multi-material sample, where the material line was dragged towards the high-attenuating material peak
Figure 7: Results of CT scans performed on mono- and multi-material gap standards represented by measurement errors for different evaluation procedures: measurement errors evaluated on gaps between two tempered planes with data processed according to ISO and ISO- double procedure (a), and ISO-adv and ISO-double-adv procedure (b); measurement errors evaluated on gaps between two steps with data processed according to ISO and ISO-double procedure (c), and ISO-adv and ISO-double-adv procedure (d).
Figure 7: Results of CT scans performed on mono- and multi-material gap standards represented by measurement errors for different evaluation procedures: measurement errors evaluated on gaps between two tempered planes with data processed according to ISO and ISO- double procedure (a), and ISO-adv and ISO-double-adv procedure (b); measurement errors evaluated on gaps between two steps with data processed according to ISO and ISO-double procedure (c), and ISO-adv and ISO-double-adv procedure (d).
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