## 1 Introduction  
In the automotive industry, quality control is a key step for every production stage. The multi-layer coating on the car body is important for the durability and appearance of the car. The functionality of the coating essentially depends on the correct thickness of the individual coating layers, which requires a thickness measuring system with high accuracy of at least \(\pm 1\)\(\upmu\)m. Commonly used methods are eddy current techniques and magnetic gauges (that only measure total thickness), microsection (which is destructive), and ultrasonic measurements (that require a coupling medium). Since most paints used in the automotive industry are transparent in the terahertz spectral range, terahertz time-domain spectroscopy (THz TDS) in reflection geometry is a promising tool for measuring the thicknesses of each layer of a multi-layer stack. Furthermore, THz TDS measurements are not only limited to metal substrates but are applicable to many different substrate materials. This includes plastics like polypropylene (PP), which are commonly used in the automotive industry, too. Rapid progress in system performance in recent years allows for accurate, fast, non-contact and nondestructive inline terahertz measurements in production environments, making THz TDS in reflection geometry the ideal tool for automotive quality control [1, 2, 3, 4, 5, 6, 7, 8]. For precise inline thickness measurements of dielectric layers, the exact frequency dependent complex refractive indices of each layer must be known in advance. Thus, there is a lot of research activity regarding the determination of optical properties of unknown materials in the THz frequency range [9; 10; 11; 12; 13; 14; 15; 16]. Spectroscopic ellipsometry is a well-established technique for the characterization of a plurality of isotropic and anisotropic materials and for thickness measurements in a broad range from the VUV to the IR spectral range [17; 18; 19; 20; 21]. In contrast to pure reflectometry measurements [22; 23], no reference measurements are needed for ellipsometric measurements. In combination with its high sensitivity to material properties and film thicknesses, ellipsometry is the ideal tool for material characterization. Recently, ellipsometry has also gained importance for the measurement of optical constants in the terahertz frequency range [24; 25; 26; 27; 28; 29; 30; 31]. In contrast to transmission measurements, ellipsometry is applicable to highly absorbing substrates and thin films on non-transparent substrates. In contrast to reflectometry measurements, ellipsometry does not need any reference measurement and avoids the problems of phase detection due to misplacement errors [32; 33; 34]. This makes THz TDS-ellipsometry the ideal tool for characterizing the optical properties of thin films and complex substrates in the terahertz frequency range. In this work, we apply THz TDS ellipsometry with more than 5 THz bandwidth to multi-layer systems of automotive car body paint on different substrates. This type of measurement is planned to become a central part of the quality control of automotive paints: THz-TDS ellipsometry is used in the laboratory to accurately determine the material properties of the paint layers in the THz range. These data are then used as a fixed calibration for inline thickness measurements with THz-TDS reflectometry, which can be conducted at higher measurement speeds. The goal of this study is to validate the feasibility of THz ellipsometry measurements for the calibration parameter determination for THz TDS inline quality control. This process is presented with the first sample, which is a three-layer stack on a metal substrate. Firstly, each individual layer was characterized by THz TDS ellipsometry. Secondly, a THz TDS reflectometry measurement is performed and compared with the results from the ellipsometric measurement. A second example demonstrates the material characterization of a plastic substrate with an anisotropy in the refractive index.