## 4 Conclusions  
The inspection system presented in this paper combines the use of a line scan camera with deflectometry techniques, allowing the extraction of three-dimensional surface information from cylindrical specular surfaces and subsequently reconstructing them with high accuracy. In addition, the reconstruction directly provides the absolute depth of defect locations. This additional information can then be evaluated depending on the specific application. The computing times of the system suggest that its use as an inline inspection system would be quite conceivable. It is possible to measure defects such as dents or scratches down to a depth of \(15\,\mathrm{\SIUnitSymbolMicro m}\). It is also possible to track surface deformations, which allows the system to be used for a wide range of problems. Comparing the system with existing inspection systems, it distinguishes itself by its high accuracy and reconstruction speed. There are significantly faster methods, such as eddy current inspection or two-dimensional optical inspection. However, these do not provide depth information on the surface. In terms of accuracy, better systems can be found in the literature, such as stylus methods or interferometric methods. However, due to the long acquisition times, these systems can only be used as inline systems to a limited extent. In addition, the presented system specializes in recording cylindrical reflective surfaces, which is not possible with methods such as PMD or FTP. Since the existing deflectometric methods are limited to the analysis of objects using a matrix camera and cannot accurately inspect the mantle surface of a cylindrical object [35], the presented system fills a gap in the literature by combining a deflectometric method with the use of a line scan camera. Thus, the system enables accurate and fast measurement of reflective cylindrical surfaces using deflectometric techniques. Even though the system gives promising results, this work should be seen only as an investigation of possibilities. Therefore, further validation of system-relevant parameters should take place in the future. For example, a correlation between screen size and angular resolution should be established. The maximum surface tilt at the system can provide valid information should also be investigated. In future studies, the illumination should be adjusted so that even very sharp-edged defect locations can be sufficiently illuminated. Here, it would be conceivable to set up the illumination spherically around the test object, as shown in [27]. To increase the application range of the system, a miniaturization of the component could be made to make the recording system as compact as possible. For the system to be used as an automatic inspection system, future work must develop a suitable evaluation of the data produced. Segmentation with the use of a two-dimensional image and subsequent three-dimensional evaluation of the defect locations found can be imagined here. In addition, the computation and evaluation times must be optimized. The aim should be to achieve an inspection time of around one second per part. It is uncertain if the system will be able to establish itself as an inspection system for rolling elements, since the benefit compared to two-dimensional inspection is not very high. Defects on a rolling element are unacceptable regardless, and therefore lead to exclusion of the defective part. However, an application in sleeve inspection or the production of linear guide rails, for example, would be conceivable. Project administration, S.G. and G.B. ; resources, A.L. ; software, S.G. and F.D. ; writing--original draft, S.G.; writing--review and editing, G.B., F.D. and A.L. All authors have read and agreed to the published version of the manuscript. This research was funded by Fertigungsgeritebau Adolf Steinbach GmbH & Co. KG, 97616 Salz, Germany, grant number IUK514/002.