## 3 Results
### Matrix Effect Calibration of Laser-Induced Breakdown Spectroscopy Based on Ablation Morphology  
According to the above method, the spectra and ablation morphologies of these samples were obtained, and the ablation morphology characteristic information was extracted for spectral correction. To avoid spectral interference, the spectral line at 340.512 nm was selected as the analysis line of Co. Part of the spectrum is shown in Figure 13.  
Under the matrix effect caused by the degree of compression, after normalizing the spectral line intensity using the radius and volume information of the ablation morphology, as shown in Figure 14, the \(\mathbf{R}^{2}\) and \(\mathbf{R}_{MSECV}\) of the calibration curve have been greatly improved. Because the degree of compression is different, without calibration, for Co, the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Co Concentration (\%)** & \
\begin{tabular}{c} **LIBS Signal** \\ **Intensity (a.u.)** \\ \end{tabular} & **Coater Depth (\(\mu\)m)** &
\begin{tabular}{c} **Surface** \\ **Roughness Ra (nm)** \\ \end{tabular} \\ \hline Sample A & 0.85 & 1200 & 5.2 & 150 \\ \hline Sample B & 0.87 & 935 & 8.4 & 320 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Effect of Crater Morphology on the Co LIBS Signal at Similar Concentrations.  
Figure 13: Influence of different ablations of the same content element on spectral intensity. (**a**) Spectral differences caused by the absence of a label during ablation. (**b**) Three-dimensional ablation morphologies reconstructed under different labels.  
\(R^{2}\) value of the 340.512 nm spectral line increased from 0.726 to 0.95, and the ARE value of the 340.512 spectral line decreased from 294.52% to 47.25%; it is worth noting that the data points of different matrix samples all fall on the same calibration curve, so the spectrum corrected by the ablation morphology effectively overcomes the matrix effect of different pressures on the sample.  
Under the matrix effect caused by different laser energies, after normalizing the spectral line intensity using the radius and volume information of the ablation morphology, as shown in Figure 15a, the \(R^{2}\) and \(R_{\text{MSECV}}\) of the calibration curve have been greatly improved. Because the laser energy is different, without calibration, as shown in Figure 15b, for Co, the \(R^{2}\) value of the 340.512 nm spectrum line increased from 0.82 to 0.98, and the ARE value of the 340.512 spectrum line decreased from 140.31% to 12.09%; it is worth noting that the data points of different matrix samples all fall on the same calibration curve, so the spectrum after ablation morphology correction effectively overcomes the matrix effect brought by laser energy to the sample.  
To demonstrate the superiority of the proposed method, we conducted a comparative analysis against several typical calibration approaches, including traditional univariate calibration without morphology correction, linear multivariate calibration, and morphology-only correction models without nonlinear fitting. The results show that our nonlinear calibration model integrating three-dimensional ablation crater morphology significantly outperforms these methods in terms of accuracy and stability, achieving an R\({}^{2}\) of 0.987 and RMSE of 0.1. This confirms that incorporating detailed 3D morphological parameters and  
Figure 14: Calibration curve of Co. (**a**) Calibration curve constructed using raw spectral data at 340.512 nm; (**b**) calibration curve constructed using corrected data after nonlinear matrix effect compensation.  
Figure 15: (**a**) Calibration curve obtained using raw spectral data at 340.512 nm; (**b**) calibration curve obtained using corrected data after nonlinear matrix effect compensation.  
nonlinear regression effectively mitigates matrix effects, enhancing the precision of LIBS quantitative analysis beyond conventional techniques.