## 4 Conclusions  
In this paper, we presented a novel approach of combining the techniques of acoustic levitation and direct tunable diode laser absorption spectroscopy (TDLAS) in order to investigate the drying process of single droplets of pure water and protein solutions. To that end, we developed a non-invasive, calibration-free TDLAS-based hygrometer in order to determine absolute water mole fractions in the exhaust gas of the acoustic levitator. From this, the evaporation rate can be calculated in the form of the mass flow. Using a 1.37 \(\upmu\)m NIR diode laser and a Herriot-type multipass cell to achieve an absorption length of 18 m, it is possible to increase the detection range of the system and follow the complete drying process of droplets from protein solutions even after the critical point of drying. The validation of the designed setup was performed by drying droplets of pure water, leading to an optimal single scan H\({}_{2}\)O mole fraction resolution of 1.7 ppm in the range between 73 ppm and 1314 ppm. The drying of protein solutions was then successfully carried out. Analogous to the drying of water, the results were compared with the images of the drying droplet. Based on this comparison, it was possible to characterize the different phases of the particle formation, including the critical point of drying. Furthermore, by calculating the normalized squared equivalent radius based on the measured droplet volume and its change over time, it could be shown that the drying experiments carried out for pure water droplets over the complete evaporation process and for protein solution droplets up to the critical point can be adequately qualitatively described by the \(d^{2}\) law. This drying behavior was also shown in the drying of identical protein solutions at other drying temperatures as well as for multiple droplets at the same drying temperature. To the best of the authors' knowledge, for the first time, it was possible to observe the complete drying behavior of levitated single droplets from protein solutions using tunable diode laser absorption spectroscopy. This, compared to conventional imaging methods, makes it possible to reproducibly follow the drying process even beyond the critical point.  
In conclusion, the combination of acoustic levitation and TDLAS is very well suited for examining the drying of single droplets. This new approach is particularly useful for the investigation of the drying process of protein solutions even beyond the critical point, but might also be used for all other applications in process engineering where the detection of small changes in concentration is of interest.  
Conceptualization, J.F.A.P., H.B. and S.W.; methodology, J.F.A.P., H.B. and S.W.; software, J.F.A.P. and H.B.; validation, J.F.A.P. and H.B.; formal analysis, J.F.A.P. and H.B.; investigation, J.F.A.P. and H.B.; writing--original draft preparation, J.F.A.P.; writing--review and editing, J.F.A.P., H.B. and S.W.; visualization, J.F.A.P. and H.B.; supervision, S.W.; project administration, S.W.; funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript. This research was funded by the German Research Foundation, DFG WI 1602/13-2.  
Informed Consent Statement: Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the authors.  
This paper is dedicated to the memory of our esteemed colleague [PERSON], who initiated the collaborative work on the study of protein solutions. The authors are grateful for fruitful discussion with [PERSON] and [PERSON] from the Institute of Applied Mathematics 3 at the FAU. The authors gratefully acknowledge funding of the SAOT by the Bavarian State Ministry for Science and Art.  
The authors declare no conflict of interest.