## 2 Materials and Methods  
In this study, the metrological behavior of alumina is investigated as a high-performance technical material, based on parts produced by stereolithography. Through this additive manufacturing technique, parts are obtained and measured via contact to record the reference parameters. Subsequently, these parts are scanned and mathematically processed to derive parameters that can be compared with the reference values. The research methodology is schematically presented in Figure 1, where the different phases undertaken can be clearly observed. First, the parts under study were manufactured using the ultraviolet laser stereolithography process with Al\({}_{2}\)O\({}_{3}\). These parts, spherical objects with a diameter of 20 mm, were initially measured via contact using a coordinate measuring machine (CMM). Then, they were scanned with a conoscopic holography system. The point clouds obtained from the second system enabled the evaluation of parameters such as diameter and form error, using specific scripts and available software for metrology and reverse engineering. Prior to this, spurious points that distorted the scanned geometry were removed through a filtering process. Additionally, a standard deviation-based filter, validated in previous research [26], was applied to the point clouds. In the final phase, the values obtained through contact (CMM) and non-contact (CH) methods were compared and analyzed. The ultraviolet laser stereolithography manufacturing process for alumina ceramic parts involved the use of three pieces of equipment as follows [11]:  
* The C900 Flex printer (3 DCeram, Bonnac-la-Cote, France): This device allows for the fabrication of parts with a layer thickness of 50 \(\upmu\)m and a maximum working volume of 300 mm \(\times\) 300 mm \(\times\) 100 mm. Figure 1: Methodology. The left branch shows the reference measurement of the manufactured artifacts. The right branch shows the measurement with CH. The Ceradel PTF 16/130/610 furnace (3 DCeram, Bonnac-la-Cote, France): This furnace reaches a maximum temperature of 1300 \({}^{\circ}\)C in a nitrogen atmosphere and is primarily used for the debinding phase (removal of the binder from the ceramic paste). The HTL 20/17 sintering furnace (Thermoconcept, Merignac, France): This furnace is capable of achieving a maximum temperature of 1750 \({}^{\circ}\)C in a working chamber of 200 mm \(\times\) 250 mm \(\times\) 200 mm. To ensure reliable results, 18 spheres were manufactured using SLA technology from 3 DMIX ALUMINA AL-F02 paste (3 DCeram, Bonnac-la-Cote, France), supplied by the manufacturer of the printing equipment. The process was completed with the cleaning, debinding, and sintering phases [11]. For the measurement stage, the DEA Global Image 09158 coordinate measuring machine (Hexagon) was used to obtain reference measurements. It was equipped with a PH10 MQ indexing head and a ceramic stylus with a O4 mm ruby sphere end. Its maximum permissible error is 2.2 + 0.003 L \(\upmu\)m (L in mm), and its maximum radial error is 2.2 \(\upmu\)m (in repeatability). The data generated by this CMM were processed using the machine's proprietary control software, PC-DMIS 2019 R2. Over 100 contact points were recorded for each sphere, adhering to the criteria defined in ISO 10360-5 [27]. The evaluation of the point clouds to determine the diameter and form error values was conducted using routines specifically developed in MATLAB 2024b for this study. These routines provided the reference values used in the comparative analysis. On the other hand, the measurements analyzed in this study were obtained using the Conoscan 4000 3D conoscopic holography system (Optimet, Jerusalem, Israel), which integrates the Conopoint-10 sensor (Figure 2). For the study, the 25 Gold lens (25 mm) was used, featuring a depth of field (DOF) of 1.8 mm and a stand-off distance of 1.4 mm.