Comparison of different voxel size calibration strategies

Coordinate measuring machines (CMM) are traditionally used in industry for verifying geometric dimensions and tolerances of parts. In the last decade X-ray computed tomography (CT) is being increasingly used in industry for dimensional analysis purposes as well. Tactile CMM is based on point-to-point collection of measurement data, while CT scans entire workpiece and generates a volumetric point cloud of measurement data. The influence of different approaches in gathering of data when using CMM and CT on calculation of voxel size is experimentally tested and discussed in this work and compared with other standard voxel size calibration options like use of reference standards and calibration of magnification axis. Several typical industrial workpieces are used to demonstrate the differences that arise because of different voxel size calibration strategies.


Introduction
Voxel size directly influences all dimensional information evaluated from a CT volume.Therefore, it is of outmost importance to accurately determine voxel size [1].There are several approaches for determination of voxel size: 1. Use of magnification axis value to determine the source-to-object distance.
2. Scan of a reference standard under the same conditions as the workpiece.
3. Externall calibration of a suitable measurand on the workpiece.Due to various influences, such as positioning / straightness errors and difficult determination of source-to-detector distance, the first approach is usually the least accurate option.Recent developments, using calibrated 2D grids and appropriate error revesal techniques, indicate that good results can be achieved [2].The second approach relies on various types of standards suitable for CT metrology, which can be accurately calibrated using classical traceable methods.Multiple designs are commercially available (e.g.multi-sphere standards, ball-bars etc.) and can be traceably calibrated.Ideally, a standard is placed alongside the measured workpiece; if that is not possible then an additional scan needs to be made.Another difficulty most often arises due to different materials of workpiece and standard, which leads to differences in reconstruction / segmentation parameters and consequently introduces errors in voxel size calibration.For the third approach a feature on the workpiece itself is calibrated externally, usually with a tactile CMM, and used as a reference for voxel size calibration.Work in this research concentrates on comparison of results of second and third approach.For aforementioned reasons, external calibration is sometimes preferred to use of reference standards, but due to difference in acquisition of measurement data between CMM and CT we also investigated possible differences in definition of measurands in CT data.Tactile CMMs operate by positioning the tip of a probing system in contact with the surface of a workpiece and measuring the spatial position of a point location on the surface, yielding high accuracy but low density data.In contrast, when using CT a workpiece is scanned without actually touching the part.A high density volumetric cloud of measurement points is generated, from which a dimensional characterization of the workpiece can be constructed.Considering the above, the advantage of CT compared to other measuring techniques-the high density of points acquired on the scanned part-could present a possible source of error when using sparse CMM data to calibrate it [3].Additionally, morphological filtering is very different for CMM and CT.For that reason, we decided to also investigate different definitions of measurands in CT scanned data: one definition uses all the data points in a selected feature, and another where measurand is defined in the same manner as on the CMM-using same number and position of data points.

Measurements
In order to analyse the influence of two different external calibration strategies, as well as other mentioned voxel size calibration approaches, a similar datum reference frame (DRF) was defined for both CT and CMM measurements of a typical industrial workpiece (Figure 2).Distance between cylinders C2 and C3 was chosen as a suitable feature to be used for calculation of voxel size.Reference workpiece (ball bar standard) was scanned using the same conditions as the workpiece, and magnification axis was calibrated by the CT manufacturer using several ball bars at different magnification axis positions.Voxel size was calculated using three different strategies: 1.Using magnification axis position to calculate voxel size; 2. Using reference value of a ball bar standard (distance between sphere centres); 3. Axial distance C2-C3, cylinders C2 and C3 defined using high density data points (VG Studio Max Autofit/Auto expand algorithm, yielding 1000 data points per each cylinder); 4. Axial distance C2-C3, cylinders C2 and C3 defined using data points that correspond to CMM data points (3 circle sections with 4 points per section, for each cylinder).
After calibration of voxel size was performed, all of the selected measurands were measured according to standard practice, i.e. using full surface to determine each feature (VG Studio Max Autofit/Auto expand algorithm).Table 1 shows deviations of these measurands from CMM values.A similar approach was repeated for another workpiece, shown in Figure 3.The main difference between these workpieces is in the manufacturing technology; while the first workpiece is casted, the second workpiece is machined.Both workpieces were made of aluminium, and similar XCT parameters were used to acquire XCT scans.Due to different geometry, different features were used to calibrate voxel size on the second workpiece: 1.Using magnification axis position to calculate voxel size; 2. Using reference value of a ball bar standard (distance between sphere centres); C1 C2 C3 D1 3. Axial distance C1-C2, cylinders C1 and C2 defined using high density data points (VG Studio Max Autofit/Auto expand algorithm, yielding 1000 data points per each cylinder); 4. Axial distance C1-C2, cylinders C1 and C2 defined using data points that correspond to CMM data points (4 circle sections with 4 points per section for cylinder C1, 3 circle sections with 4 points per section for cylinder C2).

Discussion
Before we analyse the measurement results, it is useful to discuss the quality of standards which were used to calibrate the voxel sizes in different scenarios.Since the focal spot is positioned behind a protective window (and can be moved when changing target material [4]) and actual detector plane lies beneath the front surface of the detector, it is not possible to measure sourceto-detector distance directly.Because of this, magnification axis was calibrated using ball bars of two sizes, 30 mm and 60 mm, at 3 positions along the magnification axis length.The same ball bar (30 mm) was later used to directly calibrate the voxel sizes of each workpiece.Measurement uncertainty of ball bar calibration (distance between two spheres) was U = 1,5 µm, k = 2. CMM which was used to measure selected features on both workpieces had measurement uncertainty of U = 4 µm, k = 2. Number and position of points taken on a feature during CMM measurement is directly related to the shape deviation of that feature; while for a perfect feature the mathematical minimum of measured points would be sufficient, for increasing shape deviations the necessary number of measured points also increases.This is compounded by the fact that CMM measurement always performs C1 C2

C5 C3 C4
morphological filtering on the measured surface, changing the measurement result as a function of selected tip diameter.Workpieces selected for this research had very different shape deviations, caused by different manufacturing processes (Table 3).It is obvious from data in Table 3 that when large shape deviations are present (workpiece 1) XCT results are 2-3 times larger than CMM results.This effect is even more pronounced for small shape deviations (workpiece 2) when XCT results are up to 13 times larger than results obtained with CMM.While it could be reasonably expected that more measurement points should increase shape deviation because of more information about the measured surface, it is likely that in the second case XCT errors in surface determination contributed to increased shape deviation.
If it is assumed that all deviations are random (which should be valid for axial distance measurements), a simple sum-ofdifference analysis indicates that for object with large shape deviations scanning a reference artefact (e.g. a ball bar) with the workpiece is preferable to external calibration with a CMM.For objects with small shape deviations, external calibration is preferable.In this case, point-to-point comparison between CMM and XCT measurements seems to provide better calibration data.While it could be expected that differences between point-to-point and full surface XCT data would be negligible for welldefined geometry, it is likely that using point-to-point approach minimises the contribution of XCT surface determination errors.

Conclusion
Several typical approaches to voxel size calibration in XCT metrology were compared in an attempt to determine the optimum approach.Two workpieces with extreme differences in shape deviations were chosen as test objects.
First approach to calibration of voxel sizecalibration of the source-to-object distancewas performed by measuring two calibrated ball bars along the length of the magnification axis, as recommended by the XCT scanner manufacturer.The second approach was to use the distance between sphere centres of a ball bar as a reference standard by placing it in the measured volume together with the workpieces.Third and fourth approach were based on external calibration of several features on each workpiece using a CMM; the difference being whether XCT features were defined with points that correspond to CMM measurement or by using entire available surface.
Results show that for objects with large shape deviations, the use of reference standard is preferable to external calibration on CMM.On the other hand, external calibration of voxel size for object with very small shape deviations resulted with the smallest deviations between XCT and CMM data.In this case, using point-to-point definition of XCT features yielded the best results, likely because it also minimised XCT surface determination errors.Future research will be focused on better determination of this effect, by using a larger number of measurement objects and measurands.In addition, other approaches to calibration of source-to-object distance should also be investigated, as the approach used in this research resulted with largest deviations from CMM data.

Figure 1 :
Figure 1: Approaches for calculating voxel size value.
Figure 2: Measurands on the second workpiece.

Table 3 :
Shape deviations for selected featurs.All values in µm.