# Application of Areal Topography Parameters in Surface Characterization
## 4 Conclusions  
This study extends the current understanding of surface topography evaluation by analyzing the behavior of five selected 3D areal surface texture parameters--\(Sa\), \(Sz\), \(Sq\), \(Sdq\), and \(Sdr\)--within the context of atomic force microscopy (AFM) measurements. The parameters were assessed through both simulation and experimental validation using a certified step height standard, with a particular focus on the influence of controlled geometric variations and instrumental factors.  
Simulations using idealized rectangular profiles demonstrated that even small deviations in step pitch, width, slope, or lateral positioning can significantly affect certain parameters. The results confirmed the sensitivity of \(Sa\) and \(Sq\) to lateral components, as well as the robustness of \(Sz\) as an extreme value parameter, and highlighted the need for further investigation into \(Sdq\) and \(Sdr\) under more complex topographies. The experimental AFM measurements aligned well with simulated values, providing empirical validation of the model. The 7 nm deviation in the \(Sz\) parameter value was attributed to unavoidable surface noise and microstructural irregularities present in physical standards.  
These findings emphasize the importance of rigorous calibration and comprehensive uncertainty evaluation for the accurate application of surface parameters. Without proper traceability, the use of certain amplitude or hybrid parameters, particularly \(Sa\) and \(Sq\), may lead to inconsistent or misleading conclusions. The use of Monte Carlo simulation, in accordance with the GUM and JCGM 101 guidelines, proved effective in quantifying uncertainty and supporting metrological reliability.  
Looking ahead, future work should focus on the development of integrated tools for automated uncertainty evaluation within AFM software ([[https://afm.oxinst.com/](https://afm.oxinst.com/)]([https://afm.oxinst.com/](https://afm.oxinst.com/)), accessed on 30 May 2022) environments, particularly using Bayesian and Monte Carlo approaches. Further research could also include systematic comparisons between AFM results and those obtained using other high-resolution measurement techniques, such as optical profilometry, confocal microscopy, or interferometry, in order to validate parameter  
\begin{table}
\begin{tabular}{l l l l l l} \hline  & \(Sa\) **(nm)** & \(Sq\) **(nm)** & \(Sz\) **(nm)** & \(Sdq\) & \(Sdr\) **(\%)** \\ \hline  & 15.60 & 28.72 & 117.02 & 0.17 & 1.76 \\ \hline Measurement uncertainty \(U\); \(k\) = 2; \(p\) = 95\% & 4.5 & 4.5 & 7 & 0.4 & 0.6 \\ \hline \end{tabular}
\end{table}
Table 6: AFM measurement results for reference step height standard.  
values across a broader range of instruments. In this regard, it is essential to further develop calibration methods for these instruments and ensure the reliable estimation of associated measurement uncertainties.  
Conceptualization, A.R., B.R. and V.A.; methodology, A.R., B.R. and V.A.; writing--original draft preparation, A.R., B.R. and B.S.; validation, B.S., I.S. and M.K.; writing--review and editing, I.S., M.K. and B.S.; formal analysis, V.A., M.K. and I.S.; investigation, A.R. and B.R. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflicts of interest.