## 3 Results
### Repeatability and Stability Verification Experiment  
A homogeneous standard sample with a known Co content was selected to assess the repeatability and stability of the LIBS signal and ablation morphology parameters, as well as to evaluate whether including morphological parameters improves prediction robustness by reducing signal fluctuations. On the same polished surface, 15 independent single-shot LIBS measurements were conducted at spatially distinct locations under identical laser energy and focusing conditions. The LIBS spectral intensity of Co I (340.512 nm) was recorded. The ablation crater morphology (depth, diameter, roughness) was measured via DOF. To quantify measurement dispersion, the coefficient of variation (CV) was calculated for both LIBS intensity and morphological parameters  
\[\text{CV}=\frac{\sigma}{\mu} \tag{22}\]  
where \(\sigma\) is the standard deviation and \(\mu\) is the mean value. We conducted a comparative analysis of the standard deviations of predicted concentrations derived from two distinct models: a conventional model relying exclusively on LIBS intensity, and an enhanced model integrating morphological parameters through multivariate regression. This approach allows for the evaluation of the impact of morphological information on prediction precision. As presented in Table 3, the LIBS signal intensity showed a moderate degree of variability, even under identical laser and surface conditions. Specifically, the coefficient of variation (CV) for the Co I (340.512 nm) spectral lines were 11.8% and 13.2%, respectively, across 15 spatially distinct measurements on the same sample. This level of fluctuation indicates that signal stability is affected by local surface heterogeneities and possibly subtle plasma-material interactions. The corresponding ablation morphology parameters also demonstrated measurable variation: crater depth: CV = 9.5%, crater diameter: CV = 5.2%, surface roughness (Ra): CV = 7.8%. These results suggest that morphology-induced variability is a non-negligible factor contributing to LIBS signal fluctuations. Importantly, the magnitude of morphological CVs was generally comparable to, or slightly lower than, that of spectral intensities, highlighting a potential causal relationship between ablation morphology and signal repeatability. It indicates that both signal and ablation morphology show non-negligible spatial fluctuation, even on a uniform sample. To evaluate the impact of incorporating ablation morphology on the robustness of quantitative predictions, we compared the standard deviation of predicted Co concentrations using two different calibration models. Using the conventional model, which relies solely on the raw LIBS intensity of Co I (340.512 nm), the predicted Co concentration exhibited a standard deviation of \(\pm\)0.084 wt% across 15 measurement points on the same sample. In contrast, the corrected model, which \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Mean Value** & **Standard Deviation (\(\sigma\))** &
\begin{tabular}{c} **Coefficient** \\ **of Variation (CV, \%)** \\ \end{tabular} \\ \hline Co I Intensity (340.512 nm) & 8240 a.u. & 1030 a.u. & 12.5\% \\ \hline Crater Depth & 18.7 μm & 1.75 μm & 9.4\% \\ \hline Crater Diameter & 42.3 μm & 2.1 μm & 5.0\% \\ \hline Surface Roughness (Ra) & 0.94 μm & 0.078 μm & 8.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis of Signal Repeatability and Morphological Fluctuations in Uniform Samples. integrated morphological parameters--specifically crater depth and surface roughness (Ra)--via a multivariate linear regression framework, reduced the prediction standard deviation to \(\pm\)0.047%. As shown in Figure 16, the comparative bar chart of standard deviations visually highlights the significant reduction in uncertainty achieved through morphology correction.