## 4 Conclusions  
We have demonstrated the potential of THz TDS ellipsometry for determining the optical parameters of typical automotive pains on both metal and plastic substrates. Ellipsometry is self-referencing and provides the possibility of evaluating the complex refractive index and the layer thickness at the same time. The resulting dispersion curves can be used in the evaluation of thickness measurements with THz time-domain reflectometry on multi-layer car body pains with high accuracy. Thus, the combination of both measurement techniques allows for fast and precise quality control of paint thicknesses in production environments.  
In addition, we have demonstrated that anisotropic materials can be fully analyzed with THz ellipsometry. Up to now, thickness measurements of car body pains on anisotropic substrates were based on THz reflectometry only, which is unable to measure the out-of-plane refractive index. However, the out-of-plane refractive index is important in many cases: First, if the substrate thickness has to be measured simultaneously with the thickness of all paint layers. Second, if the absolute transmission and/or reflection values for different angles of incidences and polarizations are of interest. This information is extremely important for radar transmission/reflection, which becomes even more relevant in the context of autonomous driving.  
Figure 12: Characterization of the three-layer paint stack on an anisotropic plastic substrate in reflection geometry: (**a**) Reflectometric measurement and theory at 8\({}^{\circ}\) angle of incidence without backside reflection; (**b**) Reflectometric measurement and theory at 8\({}^{\circ}\) angle of incidence with backside reflection allowing the determination of all layer thicknesses and the substrate thickness.  
Furthermore, the presented methodology can also be used for characterizing complex, unknown materials in research and development applications. The combination of THz TDS ellipsometry with THz TDS transmission and reflectometry measurements enable material characterization with extremely high accuracy.  
Nevertheless, the thickness and dispersion results of the proposed methodology have to be verified with other measurement methods, if the optical constants of the material under test are not precisely known. Because THz TDS measurements are indirect measurements, the results depend strongly on the choice of a suitable model. After verifying the correctness of the model with complementary techniques, the proposed methodology allows high precision sample characterizations.  
Outlook:  
In future, we are planning to reduce the spot size of the ellipsometer to a value comparable to standard THz TDS reflectometers (~1 mm) by adding additional focusing optics. Moreover, we would like to introduce a variable angle of incidence. The highest sensitivity of ellipsometric measurements is obtained close to the Brewster angle, which is material dependent. Therefore, multi-layer samples should be characterized under different angles of incidence, in order to further increase the accuracy of the measurement.  
Conceptualization, H.K. and R.M.; Development of THz components: L.L. and R.K., Methodology, H.K.; Software, H.K.; Validation, H.K., Formal analysis, H.K.; Investigation, H.K.; Resources, R.M.; Data curation, H.K.; Writing--original draft preparation, H.K.; Writing--review and editing, H.K., B.G., L.L., R.K. and R.M.; Visualization, H.K.; Supervision, R.M., B.G.; Funding acquisition, B.G. All authors have read and agreed to the published version of the manuscript.  
This work was funded by Deutsche Forschungsgesellschaft (DFG) under Grant Nos. GL 958/1-2.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflict of interest.