## 2 Experimental Setup and Methods
### Error Estimation  
Various influencing factors contribute to error in the measurement of the film thickness. Especially during the transition of the laser beam from one medium to another, reflections lead to falsify the measurement. During measurements on the test rig, reflections occur at the interfaces of the glass and when entering the liquid film. Furthermore, the laser beam is diffusely back-reflected from the test rig wall. Figure 4 illustrates reflections of first order and diffuse laser reflections originating from surface roughness. Shown in green is the portion of the diffused laser beam that is not detected by the sensor. Figure 3: (a) Measurement section with location of film thickness measurement and thermocouples. (b) Film thickness sensor as a schematic view and mounted on top of the optical access of the SCR test rig. In particular, the portion r of the laser light that is reflected at the film surface has a large impact in the measurement error and is discussed in detail below. The intensity of the laser beam focused on the detector \(\mathrm{I_{x,total}}\) is composed of the intensity transmitted through the film \(\mathrm{I_{x}}\), which is diffusely reflected back, and the intensity reflected from the film surface \(\mathrm{I_{r}}\). Using Equation (3), the relative error due to the reflection on the film surface for both wavelength 1 and k can be calculated with Equation (4):  
\[\Delta\delta_{\mathrm{r,rel}}=\left|1-\frac{\kappa\ \cdot\ln\frac{\left( \mathrm{I_{x,l}}+\mathrm{I_{r,l}}\right)\cdot\mathrm{I_{0,k}}}{\left(\mathrm{I_ {x,k}}+\mathrm{I_{r,k}}\right)\cdot\mathrm{I_{0,l}}}+\mathrm{b}}{\kappa\cdot \ln\frac{\mathrm{I_{r,l}}\cdot\mathrm{I_{0}}}{\mathrm{I_{r,l}}\cdot\mathrm{I_ {0}}}+\mathrm{b}}\right| \tag{4}\]  
where \(\mathrm{I_{0}}\) indicates the intensity of the laser before it passes through the film and r denotes the proportion of the light that is reflected back by the film surface. Hence, \(\mathrm{I_{r}}\) is given in Equation (5). For angles of incidence up to 30\({}^{\circ}\), the proportion r of light reflected from the film is 2.6%. \[\mathrm{I_{r}}=\mathrm{r}\cdot\mathrm{I_{0}} \tag{5}\]  
Only a portion z of the diffuse radiation \(\mathrm{I_{x}}\) is focused by the bi-convex lens onto the detector; z is an important factor, since the error due to \(\mathrm{I_{r}}\) increases proportionally as z decreases. \(\mathrm{I_{x}}\) can be calculated according to Equation (6) with \(\tau\) describing the part of the light that is transmitted through the film and not the one which is absorbed; \(\tau\) is known from the spectra measured in [40]. \[\mathrm{I_{x}}=\mathrm{z}\cdot(1-\mathrm{r})\cdot\mathrm{r}\cdot\mathrm{I_{0}} \tag{6}\]  
With Equations (5) and (6) and the assumption for simplification that the offset factor b is zero and \(\mathrm{I_{0,l}}\) is equal to \(\mathrm{I_{0,k}}\), the error can be estimated with Equation (7). Figure 4: Different reflections from the laser beam when entering the channel and the diffuse reflection from the channel wall. \(\mathrm{I_{x,total}}\): intensity of the laser beam focused on the detector, \(\mathrm{I_{x}}\): intensity transmitted through the film, \(\mathrm{I_{r}}\): intensity reflected from the film surface, \(\mathrm{I_{0}}\): intensity before transmitting through the film, \(\mathrm{I_{w}}\): intensity reflected from the window surface, \(\mathrm{\tau}\): part of the transmitted and not absorbed light, \(\mathrm{z}\): portion of the diffuse radiation that is focused onto the detector. \[\Delta\delta_{\text{r,rel}}\approx\left|1-\frac{\ln\left(\frac{(1-r)\cdot\gamma_{ \text{r}}+\pi}{(1-r)\cdot\gamma_{\text{k}}+\pi}\right)}{\ln\left(\frac{\gamma_{ \text{r}}}{\gamma_{\text{k}}}\right)}\right| \tag{7}\]  
Further errors are caused by reflections on the window surface (I\({}_{w}\)), fluctuations in signal intensity resulting from instabilities in the laser intensity and an increase of the urea concentration in the film during the measurement. The influence of urea concentration on film measurement was investigated in [40].