## 3 Results and Discussion
### Selection of Spectral Ranges for MLR and PLS Models  
During the first phase of the yeast fermentation, the carbon source glucose is mainly converted into ethanol and biomass. In the second phase, the product ethanol is consumed for biomass production [29; 30]. Strong and characteristic MIR absorption bands for the detection of glucose and ethanol can be observed in a spectral range between approximately 800 cm\({}^{-1}\) and 1400 cm\({}^{-1}\)[20; 21]. MIR-ATR spectra obtained during a yeast fermentation are shown in Figure 2 at selected times: 0 h: beginning of fermentation, 1.5 h: medium concentrations of glucose and ethanol, 3 h: complete consumption of glucose, maximum concentration of ethanol, and 10 h: end of fermentation, complete consumption of ethanol, maximum concentration of biomass. The MIR-ATR spectra of glucose and ethanol at their maximum concentrations (30 g L\({}^{-1}\) and 10 g L\({}^{-1}\), respectively) in deionized water are plotted in the upper right of Figure 2 for comparison. Glucose exhibits an intense peak at about 1030 cm\({}^{-1}\), as well as four lower absorption maxima at approximately 990 cm\({}^{-1}\), 1080 cm\({}^{-1}\), 1100 cm\({}^{-1}\), and 1150 cm\({}^{-1}\), primarily originating from C-O stretching vibrations [22; 31]. Ethanol shows two distinct peaks at approximately 1040 cm\({}^{-1}\) and 1090 cm\({}^{-1}\), originating from C-Ostretching vibrations, and furthermore, a C-C stretch signal at about 880 cm\({}^{-1}\)[22]. The partial spectral overlap of these analytes is caused by the alcoholic functional groups in glucose and ethanol [21]. Due to the spectral positions of the absorption bands of glucose and ethanol, the spectral region for the PLS evaluation of the MIR-ATR spectra has been restricted to a range from 850-1250 cm\({}^{-1}\) without loss of information. In the case of MLR models, the signal intensities in selected optical channels (S1-S4) were chosen. The bandwidth of the used spectral ranges was set to 20 cm\({}^{-1}\), a value that is typical for many commercially available optical filters in the MIR region [10]. For the determination of the glucose concentration, the spectral range from 1140-1160 cm\({}^{-1}\) has been taken as a measurement channel (S1), since only glucose absorbs in this range without spectral overlap with the MIR spectrum of ethanol. As a reference channel (S2), the spectral range from 1213-1233 cm\({}^{-1}\) has been used, where neither glucose, nor ethanol exhibits absorption bands. Since the only specific absorption band of ethanol at 880 cm\({}^{-1}\) was too small for an accurate quantitative analysis, the strong absorption band from 1040-1060 cm\({}^{-1}\) was taken as a measurement channel (S3) for ethanol despite the spectral overlap with glucose. Setting the reference channel (S4) in the direct spectral neighborhood (1060-1080 cm\({}^{-1}\)) to the measurement channel (S3), the cross-sensitivity to glucose could largely be compensated. In the recorded MIR-ATR spectra of the fermentation broth, no characteristic absorption bands for biomass could be identified. Therefore, the biomass concentration was correlated to the temporal concentration courses of glucose and ethanol. For this purpose, the measurement channel for glucose (S1) and ethanol (S3) were used in the 2D MLR model for the determination of biomass. Even in the case of Raman spectroscopy, most of the ethanol and glucose bands were located in the spectral range from 800-1400 cm\({}^{-1}\)[20; 32] (see Figure 3). Figure 2: FT-MIR-ATR spectra obtained during yeast fermentation and selected spectral regions (S1–S4) used for the MLR models. The spectra were corrected against the culture medium and inoculum without the initial carbon source glucose and offset-corrected by subtraction of a straight line. Top right: FT-MIR-ATR spectra of 30 g L\({}^{-1}\) glucose and 10 g L\({}^{-1}\) ethanol in deionized water for comparison (background against deionized water).