# Additive Manufacturing of Ceramic Reference Spheres by Stereolithography (SLA)
## 1 Introduction
Sintering conducted in ambient air typically yields material densities ranging from 95% to 99% of the theoretical maximum; however, sintering under vacuum or pressure conditions further reduces porosity levels. Studies have demonstrated that ceramic density and bending strength exhibit enhancement with increasing sintering temperature [11; 12]. Alumina is a very versatile ceramic material, and its properties make it especially suitable for applications where temperature or biocompatibility are critical factors [13]. Due to its high hardness and stability, it serves as an abrasive, as a protective oxide on metal surfaces, as a refractory for furnaces and as a high-quality electrical insulator due to its high electrical resistance over a wide temperature range. Due to its excellent biocompatibility, it is used in biomedical applications. The white color, the dimensional stability with temperature, and the lightness of alumina has also aroused interest in the field of optical measuring equipment calibration [14], where reduction of weight for large-range master gauges and calibration devices makes the use of lightweight ceramics even more interesting [15]. Indeed, it is common to find research studies examining the metrological behaviors of ceramic reference elements, such as those made from alumina [16; 17; 18]. However, ceramic artifacts produced by conventional methods are solid and therefore heavy. Additionally, precision ceramic spheres typically have excellent dimensional qualities and surface finishes. They often use G5, G10 grades [19], which require very low roughness (Ra < 0.02 \(\upmu\)m), resulting in shiny finishes that are unsuitable for use with many optical sensors (e.g., laser 3D scanners) [20]. To address this issue, it is beneficial to fabricate lightweight reference elements with high thermal stability and a matte finish that make them suitable for 3D scanners used in optical metrology and reverse engineering. The additive manufacturing processes for alumina spheres are promising candidates for producing these elements. This technique enables the creation of hollow, matte white spheres with relatively large diameters (up to 50 mm or more), reducing their weight and thus minimizing their impact on the deformation of the supporting structures, which is particularly advantageous for the calibration of medium- and high-range scanners. However, there is a lack of research focused on this field using alumina parts fabricated through additive manufacturing processes involving ultraviolet laser photopolymerization. The chosen design for manufacturing the artifacts is based on a canonical sphere geometry, widely used as a reference element for equipment calibration. It is noteworthy that spheres represent a geometry that is straightforwardly definable in measurement software and ensures traceability of comparisons between measurements obtained by contact from a coordinate measuring machine (CMM). In this work, artifacts based on hemispheres are designed and manufactured using four design variables (wall thickness, support shape, fill type, and orientation) and one manufacturing variable (arrangement of spheres on the printing tray) in order to analyze the influence of each on the achieved dimensional and geometric quality. For this purpose, diameters, shape errors, and the distribution of these errors on the surface of the spheres will be considered. The following sections describe the equipment used for both the fabrication and measurement of the artifacts, the research methodology, the experimentation conducted, the results obtained, and the conclusions reached. Specifically, Section 2 is dedicated to presenting the equipment used and the methodology followed, from the initial step of proposing different designs to the final phase of analysis, including the fabrication of the parts and contact measurement using high-precision equipment. Section 3 details the experimentation, providing comprehensive information on the part designs, the parameters of the manufacturing stages, and the measurement processes.