## 1 Introduction  
Optical metrology is an important part of modern production [1, 2], since light can be most easily and quickly tailored according to measurement requirements, is contact-free and can usually be employed as non-damaging. Concerning the setting of the measurement with respect to the production environment, there seems to be no generally accepted terminology on the definition of terms such as in-process or in situ metrology [3] and the like [4]. Recently, [PERSON] et al. gave an extensive overview on surface metrology for precision manufacturing [1]. In their paper, the authors classify the related terms \"so that they can be used distinguishably and properly [...] in the manufacturing community\". The following items show their classification:  
* In situ surface metrology: Measurement of the workpiece surface is carried out on the same work floor and in the same manufacturing environment, without isolating the workpiece from the manufacturing environment. * In-line/On-line surface metrology: Measurement of the workpiece surface is carried out on a production line without moving the workpiece outside the production line. * On-machine surface metrology: Measurement of the workpiece surface is carried out on a manufacturing machine where the workpiece is manufactured. * In-process surface metrology: The on-machine measurement of the workpiece surface is carried out while the manufacturing process is taking place. The classification given above will be used in the present paper as well. The authors of [1] further distinguish \" \"pre-process\" on-machine surface metrology \(\approx\) conducted before the manufacturing process and \" \"post-process\" on-machine surface metrology \(\approx\) conducted after the manufacturing process. These terms, especially the last one, will not be used here, since it is easily confused with the common understanding of [3]. * Post-process measurement: The measurement occurs after the finished workpiece is removed from the machine. A typical scenario is a measurement using a coordinate measuring machine to inspect the finished workpiece. Post-process measurements usually can afford time-consuming procedures and dedicated inspection areas, e.g., with vibration isolation, constant temperature or the like and is thus often used for high precision metrology that is not applicable in a production environment. The challenge for modern optical metrology is how to create techniques that are simultaneously precise, fast, robust and capable of handling geometrical complexity in order to be useful as in-process or in situ measurement. Figure 1 shows the \"Tetrahedron of Optical Metrology\" for the characterization of measurement tasks and measurement systems [5]. It describes the measurement speed (S), the measurement uncertainty, named precision (P) here for short, the tolerance with respect to disturbances, such as mechanical vibrations, described as robustness (R), and the influence of the geometrical properties of the measurement object or the measurement situation, described as geometrical complexity (C). For every combination of S, P, R and C, there is a characteristic filling of the tetrahedron. Most measurement systems have their strengths in one or two of these properties, but the challenge lies in the combination of these properties. Requirements for measuring systems result from the respective measuring task. For example, the measurement of a component with a component tolerance of 0.5 \(\upmu\)m requires a measurement uncertainty of \(\leq\)50 nm, the scanning of an area of 1 cm\({}^{2}\) in steps of 1 \(\upmu\)m in 1 s requires a data rate of 100 million points/s, and with a vibration amplitude of approximately 2 mm at 10 Hz, there is an acceleration of approximately 1 g. The geometric complexity of the object increases from spheres to aspheres to freeform surfaces deviating strongly from aspheres up to complex free forms, which may contain poorly accessible areas, holes or cavities.