*3.1. Pre-Sandblasting Measurements*

During the non-contact measurement of the spheres in their original state (pre-sandblasting) reflections caused by the brightness of the base plate were observed (Figure 3b). These reflections added glare and reduced the quality of the point cloud captured by the laser sensor. This made it necessary to sandblast the base plate (Figures 3c and 4a), prior to the insertion of the pre-blasted spheres. Once the pre-blasted spheres had been measured by contact (CMM) and non-contact (laser), the spheres were sandblasted. A uniform and completely matt finish was obtained in the three sets (Figure 4b,c).

**Figure 4.** Sphere sets: (**a**) plate of 10 pre-sandblasted spheres (only the support plate has been sandblasted to avoid reflections); (**b**) general view of the 3 plates of 10, 18 and 25 mm diameter spheres; (**c**) detail of the plate with 25 mm post-sandblasting spheres.

Contact measurements were carried out with the SP25 head with a Ø 1.5 mm diameter ruby tip. The laboratory has an air conditioning system that maintains the temperature within 20 ± 1 ◦C. Measurements were performed on the three sets of spheres with a minimum scanning density of 1 point/mm<sup>2</sup> for each of the hemispheres (only the upper half of each sphere is measured) of diameters of 10, 18 and 25 mm, respectively.

Table 1 shows the results of the contact measurements of the spheres in their original surface state before the sandblasting process. These data constitute the reference values for the subsequent comparative analysis that will be carried out with the measurements after sandblasting. Regarding contact measurements, the dimensions evaluated are the diameters of the spheres, the form error, and the standard deviation of the point cloud regarding the best-fit sphere. The average diameter values were 10.0026 mm for the Ø 10 mm spheres, 17.9977 mm for the Ø 18 mm spheres, and 25.0049 mm for the Ø 25 mm spheres, while the average form deviation was 0.0035 mm, 0.0023 mm, and 0.0028 mm, respectively. In contact measurement, the standard deviation parameter (Std. Dev.) tends to be close to 0 (in the higher case, it is lower than the CMM probing error: 0.002 mm). In general terms, these results correspond correctly to the estimated accuracy G100 for stainless steel spheres.


**Table 1.** Measurement results of the original (pre-sandblasted) spheres.

The spheres were then measured using a laser triangulation sensor (HP-L-10.6 from Hexagon Metrology) assembled in the CMM (Figure 5b). To obtain a real and accurate comparison with the contact measurements, all measurements have been carried out under the same environmental conditions (light and temperature) and with the same procedure of alignment and sequence of the spheres. For the sphere captures, five orientations were used (four at 45◦ from the cardinal points and one from the vertical position, at 0◦). These orientations were sufficient to capture at least the upper hemisphere of each sphere. The software used to capture the point clouds is the same PC-DMIS that controls the CMM, although Geomagic Control X software was preferred for point cloud processing, which involved the removal of points belonging to the base plate and those located below the equator of the spheres. Finally, a standard "2·Sigma" filter was applied to this trimmed cloud (hemisphere) to remove spurious points, clearly far from the spheres, which would distort all measurements.

**Figure 5.** Laser scanning of the spheres: (**a**) point clouds captured at normal gain (red) and high gain (blue), both in pre-sanded state; (**b**) general view of the HP-L-10.6 laser sensor scanning at 45◦.

The results obtained are also shown in the central area of Table 1. In addition to the diameter and the form deviation, the value of the standard deviation has been obtained when the cloud is fitted to a best-fit sphere (Least-Squares fitting). The average standard deviations are significantly larger than in the case of contact measurement, which corroborates the idea that a bright surface finish (these are "mirror polished" spheres) is not suitable for being captured with optical equipment. Note (Table 1) that both diameter and form deviation values are far from the reference values (even up to −0.144 mm for Ø 25 mm spheres or 0.187 mm for Ø 10 mm spheres).

On the other hand, the standard deviation of the values obtained by non-contact measurement on polished spheres (original state) reaches high values, on the order of 0.031 mm, regardless of the diameter value. These data show the problems that arise when non-contact measurement systems are used on polished parts because the surface brightness causes the generation of point clouds with poor metrological quality (Figure 5a).

Furthermore, laser measurements on the original spheres had to be carried out in high-gain mode (less sensitivity), because in normal-gain mode (high sensitivity), the sensor was not able to capture enough points, generating very poor clouds. As shown in Figure 5, due to the high brightness of the pre-sanded spheres, point clouds captured with normal gain (red cloud) cover the spheres very poorly, while the coverage is much higher with high gain (blue cloud). This effect is accentuated for the smaller spheres. In fact, in the case of 10 mm spheres, it was not possible to obtain accurate diameter values due to insufficient data. Thus, this high-gain mode allows the comparison between the pre- and post-sandblasting states.
