## 5 Conclusions  
In this work, we introduced a novel method for determining the dust particle size and dust density in a low-pressure nanodusty Ar-HMDSO plasma, derived from measurements of the free electron density and laser light extinction. Comparing the measured values of the decrease of the electron density and the transmittance to those predicted by OML theory and the Lambert-Beer law, respectively, the combined error can be minimized such that the best-fitting values of the dust particle size and dust density can be determined.  
As expected from the raw data and literature, the dust growth in the first growth cycle  
Figure 8: Overview of the results of the fitting procedure for the plasma power scan. The dust particle radius \(a\) (in blue circles) and the dust density \(n_{\mathrm{d}}\), both at the moment of formation of the void, are plotted as a function of plasma power. The error bars are the result of the errors in the measured electron density \(\hat{n}_{\mathrm{e}}\) and transmittance \(\hat{T}\), as propagated through the fitting procedure. Again, a constant value of the electron temperature \(T_{\mathrm{e}}=3\,\mathrm{eV}\) and the negative ion density \(n_{\mathrm{i-}}=4n_{\mathrm{e,initial}}\) are assumed.  
is found to be linear, with a typical dust particle size of \(\sim\)140 nm right before the appearance of the void. The dust density is usually in the order of \(\sim\)10\({}^{14}\) m\({}^{-3}\). Furthermore, it was observed that the interpretation of the data can become obscured by the appearance of the void region and the growth of a successive generation of dust particles. Generally, the dust particle size and dust density show opposite trends: When the dust particle size increases, the dust density decreases. The fitting procedure relies on assumptions of the electron temperature and the negative ion density; two quantities that are difficult to estimate or experimentally determine. The sensitivity of the fitting procedure to these parameters was investigated, which yielded similar trends in both dust particle size and density, while only the absolute values shifted. Finally, the method was used to investigate the dependence of the dust particle size and dust density on the plasma power. Interestingly, a lower plasma power yielded larger dust particle sizes, which is a direct consequence of the slower dust growth cycle, i.e., the longer residence time in the plasma.  
The proposed fitting procedure shows that the time-synchronized measurement of the free electron density of the plasma and the laser light extinction by the dust cloud can reveal information about the dust particle size and dust density. This novel, experimentally convenient and non-intrusive method provides more insight into the fundamentals of nanodusty plasma physics.  
Conceptualization, J.B.; Data curation, T.D.; Formal analysis, T.D. and T.S.; Funding acquisition, J.B.; Investigation, T.D. and T.S.; Methodology, T.D.; Software, T.D.; Supervision, J.B.; Writing--Original draft, T.D. and T.S. All authors have read and agreed to the published version of the manuscript.  
This work has been financed by the Dutch Research Council (NWO) of the Netherlands, proj. 17-24 Synoptics n. 2.  
Not applicable.  
The measurement data is available from the corresponding author upon reasonable request. The computer code used for the data analysis and interpretation is available from the corresponding author upon reasonable request.  
The authors would like to thank [PERSON] and [PERSON] for their skillful technical support.  
Author [PERSON] was employed by Prodrive Technologies B.V. The other authors declare no competing interests.  
The following abbreviations are used in this manuscript:  
HMDSO Hexamethyldisiloxane  
LES Light Extinction Spectroscopy  
LIP Laser-induced Photodetachment  
MCRS Microwave Cavity Resonance Spectroscopy  
OML Orbital Motion Limited  
SEM Scanning Electron Microscope  
TIRE-LII Time-resolved Laser-induced Incandescence  
VNA Vector Network Analyzer