## 3 Results
### Automotive Multi-Layer System on Plastic Substrate
#### 3.2.1 Substrate Characterization  
The plastic substrate shown here is a SABIC(r) PP compound 8500 elastomer-modified mineral filled polypropylene for automotive painted exterior applications. In contrast to metallic substrates, plastic substrates are transparent in the terahertz region, so backside reflections together with transmission properties can give additional information (see Figure 2). Figure 7 shows the time-domain signal, which was measured with THz TDS reflectometry at \(8^{\circ}\) angle of incidence. At a delay time of about 33 ps, a backside reflection signal appears. The oscillations towards longer delay times are caused by a sharp absorption band in the PP material. If the time-domain signal is set to zero outside the green box in Figure 7, the backside reflection can be ignored. This results in the THz spectra shown in Figure 8a, with no indication of an absorption feature in the PP material. If the complete pulse trace inside  
Figure 6: Reflection measurement (black) and fitted model (red) of the full three-layer stack on a metal substrate. Figure 7: THz TDS measurement in reflection geometry on a plastic substrate. For evaluation without backside reflection, the signal outside the green box was set to zero. For evaluation with backside reflection, the signal outside the blue box was set to zero. the blue box of Figure 7 is used, the spectra shown in Figure 8b are obtained. The time interval between the front and backside reflection pulses is responsible for the oscillations in the reflection signal (see Figure 8b) and enables us to determine the thickness of the PP substrate. The shape of the backside reflection pulse at a delay time of about 33 ps contains information about the complex refractive index of the PP, especially about the spectral absorption, which can be clearly seen around 1.1 THz in Figure 8b. Note that this feature is not visible in Figure 8a. Since the THz radiation that was reflected on the backside travelled twice through the PP substrate, this backside reflection contains much more information about any absorption features inside the PP than the front side reflection. If the reflection measurement is additionally combined with the results of a transmission measurement, another small absorption feature appears around 3.3 THz, which is not visible in the reflection measurements (see Figure 8c). The transmission measurement was made with the ellipsometer set up at 0\({}^{\circ}\) angle of incidence, with a collimated beam and a beam diameter of 16 mm. For these measurements we align a metallic mirror on the sample stage. First, a reference measurement is acquired. Afterwards, the measured sample is put between the aperture and the polarizer for the transmission measurement. By fitting all measurements simultaneously using the same optical parameters, the substrate thickness and the frequency dependent complex refractive index can be determined with high accuracy and with very good agreement between measurement and model (see Figures 7 and 8). The resulting dispersion is shown in Figure  
Figure 8: Substrate calibration: (**a**) Reflectometric measurement and theoretical model at 8\({}^{\circ}\) angle of incidence without accounting for the backside reflection in s-polarization; (**b**) Reflectometric measurement and theory at 8\({}^{\circ}\) angle of incidence with backside reflection for s-polarization; (**c**) Transmission measurement and theory at 0\({}^{\circ}\) angle of incidence. Figure 9: Substrate calibration: (**a**) Ellipsometric measurement (black) and theoretical model (red) at 70\({}^{\circ}\) angle of incidence with backside reflection; (**b**) Resulting in-plane n\({}_{xy}\) and out-of-plane n\({}_{x}\) dispersion. In analogy to reflection measurements, ellipsometric measurements that do not account for backside reflections are insensitive to weak absorption features. However, if the backside reflection is included in the ellipsometric measurement (see Figure 9a), additional optical properties can be obtained.