## 2 Materials and Methods  
### State of the Art  
The most established systems for inspecting metallic surfaces rely on the approach of non-destructive eddy current technology [12; 13; 14]. These eddy current inspection systems induce a current into the metallic material via a magnetic field. Defects, such as scratches or air pockets near the surface, interfere with the current signal and can be detected. These systems can be used on all ferromagnetic components for quality assurance. They have a high inspection speed and good resolution. Furthermore, non-destructive testing methods that use ultrasonic to examine the entire body are presented in [15; 16; 17]. Since ultrasonic can penetrate into a test specimen, these methods are not limited to pure surface inspection, but also consider defects, such as air pockets in the material. Specifically for the inspection of rolling element surfaces, methods [18; 19] can be found in the literature which are limited to two-dimensional surface inspection. Non-destructive optical methods that do not specifically relate to the inspection of rolling elements are also presented. For example, [20; 21] point out an optical method that obtains and evaluates two-dimensional surface information via an optical approach. The problem of surface inspection is limited in many systems to the extraction and evaluation of two-dimensional surface information. Thus, in a potential test procedure, a distinction can only be made between good and bad parts. However, since large quantities of parts must be inspected and evaluated in rolling element inspection, the introduction of a tolerance limit would be desirable here to reduce scrap. Thus, an inspection system must also record and evaluate the depth, i.e., three-dimensional information of the defect location. Several approaches to surface inspection exist in the literature. Ideas, such as [22; 23] gather under the term of phase-measuring deflectometry (PMD). Here, a stripe-like pattern is observed through the reflective surface of the test object. Changes in this pattern can then be evaluated to conclude the surface condition. However, these approaches are difficult to transfer to the use of a line scan camera for cylindrical surfaces imaging. Other approaches such as [24; 25] use Fourier transform profilometry (FTP) to extract surface information. Again, a fringe pattern is used, but this time it is projected onto the surface. The image captured by a camera is then evaluated using this pattern. Two problems arise here. First, projection onto a reflective surface is not possible, and second, the use of a line scan camera to capture the cylindrical surface is not viable. Other ideas such as [26] use interferometry to scan the surface. These methods take a small sized area of the surface with a very accurate depth resolution. Depending on the sampling time of the system, high acquisition times preclude its application as an inline system. The method from work [27] uses different illumination patterns to determine the reflection direction between the camera and screen. This method requires a reflective surface and can also be applied using a line scan camera. A version adapted for line scan cameras will find its application in this work. To evaluate and display this information, the resulting gradient field has to be transformed into a height map, i.e., into a virtual surface. In the works [28; 29; 30; 31; 32; 33; 34] approaches can be found which make this possible.