## 1 Introduction  
Additive manufacturing (AM) offers numerous advantages for the production of parts with complex geometries and those made of materials other from traditional polymers, such as ceramics, metals, or composites. Furthermore, advancements in the development of these technologies are enabling the elimination of molds and tools required by traditional methods, allowing parts to be manufactured layer by layer with these materials [1, 2, 3, 4, 5]. However, many challenges remain, and improvements are needed; mechanical properties and the precision of parts produced by additive manufacturing are two key areas under current intensive research [6, 7, 8, 9, 10, 11, 12]. Among the materials most actively studied in additive manufacturing (AM) are ceramics [9, 13, 14, 15], with alumina being a notable example. This material is ideal for applications where temperature resistance and biocompatibility are critical factors. Its characteristics--such as resistance, wear, hardness, stability, and lightness--are also leveraged in other fields, such as precision metrology. One AM technology under investigation employs the ultraviolet laser photopolymerization of alumina paste. Commonly known as stereolithography (SLA) [15; 16; 17], this process is referred to by the acronym VPP-UVL/C, according to ISO 52900:2021 [18]. The manufacturing process involves four distinct stages: the 3D printing of the parts, cleaning of unpolymerized material, removal of the substrate or binder, and sintering of the part. The final product is thermally stable and lightweight, making it attractive, as noted, in the field of precision metrology. In this domain, it is essential to validate the capability of optical inspection systems to generate data (point clouds) that can be used to assess whether the measured dimensions deviate from nominal or reference values and to determine the magnitude of such deviations, typically obtained using coordinate measuring machines (CMMs). Conoscopic holography (CH), as an optical inspection system, offers certain advantages compared to other technologies, such as simplicity, stability, and precision [19; 20; 21]. In 1985, [PERSON] and [PERSON] developed this interferometric technique using incoherent light based on the birefringence properties of uniaxial crystals. With appropriate calibration, this method calculates the original distance to the light-emitting point by analyzing the frequency of one of the signal lines. This technology enables the recording of three-dimensional information about the inspected object, which, when properly processed, allows for the evaluation of measurement accuracy. There is no doubt that other metrological evaluation techniques exist that offer effective solutions for measuring complex parts, such as those produced by additive manufacturing--especially when internal or hard-to-access geometries need to be characterized. Computed tomography (CT) is one such technique, capable of providing both dimensional and geometrical data simultaneously while also offering insight into potential internal defects within the parts' structure [22; 23]. Studies on this technology have focused on surface determination in order to achieve sub-voxel accuracy (i.e., below tenths of a millimeter) in the identification of both internal and surface points [23; 24]. However, the high cost of CT systems compared to CH limits their accessibility, particularly when research requirements are restricted to surface data rather than internal features. Numerous studies support the effectiveness of conoscopic holography as an optical measurement system in various industrial settings [20] and across different materials. However, the emergence of new manufacturing technologies, such as ultraviolet light stereolithography applied to the production of alumina parts, necessitates the validation of this system given the distinct structural configuration of the final part (density, porosity, roughness, etc.).