## 4 Discussion  
From the extracted RF conductivity data summarized in Table 5, the powder areal weight plays a role in the change of the RF conductivity. These values are instructive for the optimization of the deposition process. In particular, conductive nano-powders added on a conductive composite built up with micro-fibers is a sensitive process. The extracted RF conductivity is a direct signature of the surface conductivity and depends on (i) the spatial distribution of the nano-powders, (ii) their interactions with the hosting material, and (iii) the powder areal weight. In addition, it is demonstrated that the hosting material consisting of conductive fibers, presents a dispersion in the measured RF conductive values (T1.1 and T1.2 that are not doped with nano-powders). These findings are attributed to the material characteristics and not to the measurement set-up. Indeed, calibration has been performed by checking the measurement reproducibility considering metallic standard metallic materials. Surprisingly, the last line of the table that gives an estimation of the reproducibility of the microwave measurement presents a large deviation for materials references T1.1 and T3.2 and needs further investigation. The following hypothesis are considered for the resolution of the inverse problem:  
* Only the reflected wave at the surface material contributes to the determination of the conductivity. Further development assuming microwave absorption within the materials will be considered. * During the measurement campaign, we observed a temperature variation around 0.4 \({}^{\circ}\)C. Together with drift of the electronic system, the vector calibration is affected as the calibration error terms are determined for fixed environmental conditions. For example, the calibration standard, i.e., aluminium metallic plate (at 24.4 mm for the antenna aperture) considered as ideal in the calibration process (\(\sigma_{RF}\rightarrow\infty\)) yields to a value around 14 \(\times\) 10\({}^{4}\) S/m when measured after the measurement campaign. * Errors induced by the distance control between the material surface and the antenna aperture impact the measurement accuracy. The reasons given above yields to measurement uncertainties. These results are instructive as they suggest that a real-time calibration procedure (including temperature and distance measurement) would be beneficial to enhance the measurement accuracy. This work contributes to the penetration of microwave free-space measuring techniques developed by several research groups [12; 13; 14; 15; 16]. Conceptualization, G.K., I.A., A.V., F.K., and K.H. ; methodology, G.K., I.A., A.V., F.K., and K.H. ; validation, G.K., I.A., A.V., F.K., and K.H. ; investigation, G.K, I.A., A.V., F.K., and K.H. ; resources, G.K., I.A., A.V., F.K., and K.H. ; data curation, G.K., I.A., A.V., F.K., and K.H. ; \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **T1.1** & **T1.2** & **T2.1** & **T2.2** & **T3.1** & **T3.2** & **T4.1** & **T4.2** \\ \hline Thickness (\(\mathrm{\SIUnitSymbolMicro m}\)) & 350 & 370 & 450 & 400 & 460 & 370 & 470 & 440 \\ Powder areal weight (g/m\({}^{2}\)) & 0 & 0 & 25.11 & 26.00 & 14.56 & 19.00 & 32.33 & 35.67 \\ \(e_{r}^{\prime}\)(F/m) & 8917 & 1417 & 1966 & 1053 & 864 & 511 & 21,943 & 6150 \\ \(-e_{r}^{\prime}\) (F/m) & 4848 & 1908 & 2668 & 3949 & 8174 & 10314 & 11,527 & 5124 \\ \(\sigma_{RF}\) (S/m) & 2697 & 1061 & 1484 & 2197 & 4547 & 5738 & 6413 & 2851 \\ \(\Delta\sigma_{RF}^{\prime}/\sigma_{RF}\) (\(\%\)) & 51.7 & 0.02 & 10.8 & 6.15 & 13.9 & 25.4 & 12.8 & 1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Extracted complex permittivity and conductivity as a function of the powder areal weight—f = 10 GHz. writing--original draft preparation, K.H. ; writing--review and editing, G.K., I.A., A.V., F.K., and K.H. ; supervision, A.V., F.K., and K.H. ; project administration, K.H. ; funding acquisition, A.V., F.K., and K.H. All authors have read and agreed to the published version of the manuscript.