## 4 Discussion  
The following discussion describes some highlights on the conceptional progress to achieve fast, precise and rugged optical metrology for complex samples or measurement situations as discussed in the context of Figure 1. Speed (S) and Precision (P) have been continuously enhanced in the past until they meet physical or economic limits. In general, short illumination times and/or single shot measurements are not only beneficial for measurement speed but also for an increase in Robustness (R). We have concentrated here on _intrinsically_ robust methods that lend themselves also to complex geometries (C). Gradient- or differential-based measuring principles are a clue to obtaining rugged measurement systems. Table 1 thus describes successful concepts discussed in this paper with respect to robustness and complexity. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Requirement** & **Method** & **Principle Feature** & **Benefits** \\ \hline Robustness (R) & Computational Shear Interferometry (CoSi) & measures finite phase differences (defined by shear) & (i) enables interferometry using low coherent light, (ii) intrinsically robust against vibration \\ \cline{2-4}  & Deflectometry & differential measurement & intrinsically robust against vibration \\ \cline{2-4}  & Fringe Projection & triangulation & robust against ambient conditions \\ \hline Complexity (C) & Multiple Viewing Directions for digital holography (MuVie) & multiple illumination and observation directions & enables 360\({}^{\circ}\)-view \\ \cline{2-4}  & Computational Shear Interferometry (CoSI) & measures coherence function & (i) measures extended curvature due to variable shear, (ii) enables use of MArS \\ \cline{2-4}  & Multiple Aperture Shear Interferometry (MArS) & simultaneous use of multiple light sources & (i) enables measurement of aspheres, (ii) solves aperture problem \\ \cline{2-4}  & Fringe Projection & triangulation & suitable for complex sample geometry \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview over measurement methods discussed in this paper and their impact on robustness (R) and the ability to deal with complex measurement situations (C). Compare to the tetrahedron of optical metrology, as shown in Figure 1.  
Figure 17: Multidirectional determined structure functions of area 1 (red) and area 2 (black). In the higher spatial frequency range up to about the separation n = 100, the amplitude of both SFs is almost identical. This clearly confirms the very similar roughness values. For further explanation, see text. For interferometry, vibrations are a major concern, since they disrupt phase measurements [7]. This problem is often targeted, e.g., by compensation measures [61] or fast data acquisition [62]. In contrast to such approaches, we are concentrating on intrinsically robust interferometry approaches, especially based on CoSI. Additional degrees of freedoms are gained from CoSI, as it allows for a better adaption to surface gradients by a proper choice of the shear. In terms of geometrical complexity, we have demonstrated approaches that not only concentrate on the geometrical complexity as such but also use the tailoring of the coherence of light to approach difficult geometric conditions as tackled by MuVie and MarS. A substantial further benefit results from MarS that solves the aperture problem by simultaneously using multiple light sources. For geometrical methods, the situation appears a bit different. Deflectometry, being a differential measurement technique, is intrinsically robust against rigid body motion. It does not need vibration isolation and usually copes with ordinary in-door illumination. Due to its dependence on specular reflection, an aperture problem may, however, easily arise for free form surfaces. Fringe projection requires diffusely scattering surfaces and is thus less dependent on the curvature or aspect ratio or complexity of the test surface.