## 2 Materials and Methods  
As the basic principle of TDLAS has been explained in the literature in detail [15; 16; 18; 20; 23], only the basics of this technique will be briefly reviewed here. TDLAS is based on the detection of the molecule-specific attenuation of a fast and continuously tunable, spectral narrowband laser beam as it passes through the measurement volume to be investigated. The laser wavelength is thereby tuned by the periodic modulation of the operating current over an isolated molecular absorption line [24]. In our case, for measuring the amount of water in our drying gas from a levitated droplet, we have chosen the \(110\to 211\) transition at 1396.97 nm (7299.43 cm\({}^{-1}\)) in the 1.4 \(\upmu\)m (7140 cm\({}^{-1}\)) overtone band. This well-described transition has already been used previously in several publications [20; 21; 25] and is free from possible spectral interference, especially by other water lines or CO2. To describe the attenuation of the laser light caused by the water molecules, an extended version of the Lambert-Beer law can be used [23]:  
\[I(\
u,t)=I_{0}(\
u)\cdot\exp(-S(T)\cdot\varphi(\
u-\
u_{0})\cdot N_{V}\cdot L) \cdot Tr(t)+E(t). \tag{1}\]  
Here, \(I_{0}(\
u)\) is the initial intensity, \(I(\
u,t)\) the detected intensity after passing the absorbing medium of absorption length \(L\), and \(N_{V}\) the number density of absorbing molecules. The absorption line is characterized by the temperature-dependent line strength \(S(T)\) and the area-normalized shape function \(\varphi(\
u-v_{0})\), which is centered at the wavelength of \(v_{0}\). Furthermore, \(Tr(t)\) and \(E(t)\) consider spectrally broadband transmission losses and possible background radiation hitting the detector, respectively. By resolving equation (1) for the absorber number density \(N_{V}\) and spectrally integrating over the absorption line profile, the absorber density can be calculated by [18]:  
\[N_{V}=\frac{1}{S(T)\cdot L}\int\ln\biggl{(}\frac{I(\
u,t)-E(t)}{I_{0}(\
u) \cdot Tr(t)}\biggr{)}\frac{\mathrm{d}\
u}{\mathrm{d}t}\mathrm{d}t. \tag{2}\]  
When looking at Equation (2), it can be seen that no calibration of the measurement system with a reference gas is necessary, since all quantities are either measured by the detector (\(I(\
u,t),\ I_{0}(\
u),\ Tr(t),\ E(t)\)), come from a spectroscopic database (\(S(T)\)) such as HITRAN16 [26], or are derived from the experimental conditions or supporting measurements (\(L,\ \frac{\mathrm{d}\
u}{\mathrm{d}t}\)). In particular, the dynamic tuning coefficient of the laser \(\frac{\mathrm{d}\
u}{\mathrm{d}t}\) is of great importance as normalization of the line area is only valid in the wavelength domain. Thus, the absorption signal has to be transferred from the time domain to the wavelength domain while considering the dynamic tuning behavior \(\frac{\mathrm{d}\
u}{\mathrm{d}t}\) of the diode laser [27]. In our case, the dynamic tuning coefficient is determined continuously by evaluating the wavelength-dependent transmission through a Fabry-Perot etalon [20]. Based on the absorber number density \(N_{V}\), the water mole fraction \(x_{\mathrm{H2O}}\) can be calculated by applying the ideal gas law. Additionally, the water mass flow \(\dot{m}\) in the exhaust gas can be derived by taking the nitrogen volume flow into account [23]. The initial volume \(V\) of the injected droplet can be calculated by integrating the measured mass flow over the entire evaporation process. Using this principle, we developed our TDLAS-based hygrometer for the investigation of the drying process of acoustically levitated droplets. The general setup of the hygrometer applied to the acoustic levitator is depicted in Figure 1. In order to carry out the evaporation experiments of the microdroplets under defined conditions, the acoustic levitator (Borosa Acoustic Levitation L200, Bochum, Germany) is surrounded by a heating chamber consisting of eight heating cartridges and two type-K thermocouples to adjust a constant drying temperature.