## 2 Materials and Methods
### Processing of RGB Color Sensors
#### 2.2.2 Determination of the Spectral Sensitivity Curves of an RGB Color Sensor  
An accurate and precise measurement of the RGB color sensor's spectral sensitivity functions \(R(\lambda)\), \(G(\lambda)\), and \(B(\lambda)\) is necessary to guarantee an adequate sensor processing for the proper monitoring of the relevant lighting control parameters in mixed lighting conditions as sketched in the Introduction. The literature usually suggests to use a monochromator for this purpose [113; 114; 115; 116; 117; 118]. An exemplary illustration of the experimental setup is given in Figure 3. As can be seen, a bright white light source of broad spectral composition, e.g., a xenon arc lamp or a Planckian emitter, provides the input to the monochromator. Within the monochromator, the light passing its entrance slit is projected onto an optical diffraction grating. Depending on its pre-selected rotation position, only light of a certain peak wavelength \(\lambda\) is thus projected onto the monochromator's exit slit. The resulting narrowband light output is eventually collected by an integrating sphere for spatial and angular homogenization of its corresponding light distribution [119]. At the same time, it holds both the (temperature-stabilized) color sensor that needs to be characterized and the spectroradiometer used to determine the spectral irradiance of the color stimulus registered by the color sensor. Based on this setup, the spectral sensitivity \(s_{k}(\lambda)\) of the \(k\)th sensor channel can be determined from the sensor responses \(c_{k}(\phi(\lambda))\) obtained for a set of selected color stimuli  
Figure 3: Schematic illustration of a monochromator setup used for determining the spectral sensitivity curves \(R(\lambda)\), \(G(\lambda)\), and \(B(\lambda)\) of an RGB color sensor. Figure 2: Structural components and functions of the six structural layers of an RGB color sensor. \(\phi(\lambda)\) provided by the monochromator. According to [PERSON] et al. [42], \(s_{k}(\lambda)\) can be approximated as follows:  
\[s_{k}(\lambda)\approx\frac{c_{k}(\phi(\lambda))-\overline{n}_{k}}{\delta\cdot \overline{\Delta}\phi(\lambda)\Delta\lambda}, \tag{2}\]  
where \(\overline{n}_{k}\) is the mean value of random noise observed for a no-light condition, i.e., when the monochromator output is closed and \(\delta\) is a constant factor representing the sensor's gain and integration time settings. In the present work, an RGB color sensor prototype, which had been developed as part of the INNOSYS project [120] funded by the German Federal Ministry of Education and Research, served as the corresponding test device. Its spectral sensitivities were measured as described above using Equation (2) with a step size of \(\Delta\lambda=1\,\mathrm{nm}\), where each of the color stimuli used for probing exhibited a full-width at half-maximum (FWHM) of approximately \(2\,\mathrm{nm}\). The corresponding laboratory setting is shown in Figure 4. The measurements were performed using a six-inch integrating sphere (Labsphere Inc., North Sutton, NH, USA) with a highly reflective white PTFE coating, a \(300\,\mathrm{W}\) xenon arc lamp connected to an MSH \(300\) monochromator (Quantum Design GmbH, Darmstadt, Germany), and a Spectro \(320\)D R5 spectroradiometer (Instrument Systems GmbH, Munich, Germany), which was directly attached to the north-pole port of the integrating sphere via a fiber-optic light guide. The main exit port of the integrating sphere at \(90^{\circ}/0^{\circ}\) concomitantly served as the sensor mount to ensure a homogeneous light distribution in the color sensor's field of view. Due to random errors and systematic uncertainties in the measurement process of the spectral sensitivities, e.g., caused by measurement noise and the finite spectral bandwidth of the color stimuli, discrepancies between model-calculated virtual sensor responses and real sensor measurements must be expected.