## 2 Materials and Methods
The remaining specifications of the equipment are listed in Table 1.  
To obtain the diameter and form error values from the point clouds generated by the HC sensor, the Geomagic Control (v.X) software was initially used to manually remove spurious points. Subsequently, specific MATLAB scripts were employed to fit the point cloud to a sphere (the best-fit sphere) using the least squares method [28]. These routines also  
Figure 2: O18 mm sphere scanned with Conoscan 4000.  
allowed for the application of two filters: a filter to exclude points outside the sensor's maximum angle coverage (152\({}^{\circ}\)) and a coverage-based filter (k) to eliminate outlier points using a factor applied to the standard deviation (k\(\cdot\)\(\sigma\)) [6], a method commonly used in reverse engineering software. Both contact measurements (CMM) and non-contact measurements (CH) were conducted under controlled temperature conditions (20 \(\pm\) 0.5 \({}^{\circ}\)C). The measurement procedure using the CH sensor required the consideration of two parameters: the laser beam's power or energy level and the operating frequency, which indicates the data acquisition speed. Based on these two parameters, the goal is to ensure signal quality through the \"SNR\" (signal-to-noise ratio) metric, which can range from 0 to 1024 (0% to 100%) and is calculated from the signal power and the noise power of the signal. The higher the value, the better the signal, with it being advisable to achieve signals exceeding 50% [29]. Additionally, the \"Total\" parameter, representing the amount of light detected by the sensor in each measurement, must have acceptable values within the range of 1200 to 21,000. On the other hand, Table 3 presents the diameter and form error values obtained using the conoscopic holography sensor after applying both filters. Although, in this case, the recorded data exhibit greater deviation from the nominal value, at around 50 \(\upmu\)m, the same trend observed with contact measurements is also evident, as the differences between values do not exceed 3 \(\upmu\)m in any case. Additionally, it can be noted that the form error clearly depends on the applied filter, decreasing as the level of filtering increases (i.e., as the factor k decreases). It is worth mentioning that as the coverage factor increases, the number of filtered points decreases. Figure 3: Two-dimensional and 3D views of the distribution of points on sphere no. 6 for k = 1 and the angle covered of **(a)**\(151.9^{\circ}\) with CMM and **(b)**\(147.6^{\circ}\) with Conoscan. According to Table 5, the measurement ranges for form error deviations differ substantially depending on the applied filter. This difference is most pronounced when no filter is applied to the point cloud (k = 0). While the ranges for k = 1, k = 2, and k = 3 are 38 \(\upmu\)m, 74 \(\upmu\)m, and 95 \(\upmu\)m, respectively, the difference between the minimum and maximum deviation without filtering rises to 242 \(\upmu\)m.  
Regarding the form error, Figure 5 clearly illustrates the influence of applying a coverage filter to the standard deviation in improving the geometric quality of the point cloud. The form error deviations without filter application (green plot) are substantially higher compared to the rest. In summary, Table 6 presents the mean deviation values for diameter and form error alongside the number of points comprising the point cloud for each applied filter. It is observed that the dimensional quality of the point cloud, defined by the diameter (\(\O\)), is unaffected, as previously mentioned, while the geometric quality, defined by the form error  
Figure 4: Deviation of the diameters measured with the CH sensor with respect to the diameters measured with the CMM according to the different k filters. Figure 5: Deviation of the form error measured with the CH sensor with respect to the form error measured with the CMM according to the different k filters. (Fe), improves with k = 1, despite a more notable reduction in the number of points.