## 1 Introduction
proposed a novel approach known as surface-assisted thin-film LIBS (SA-TF-LIBS), where samples are deposited as thin films on substrates to minimize bulk matrix interference, enabling high-sensitivity and matrix-free detection [16]. Numerous other approaches have also been reported, such as internal standardization, chemometric calibration, and the use of buffer gases. However, many of these methods face practical limitations such as complex instrumentation, time-consuming pretreatment, and restrictions on applicable sample types, which hinder their scalability in industrial monitoring environments [17; 18; 19]. In laser-induced breakdown spectroscopy (LIBS), the matrix effect refers to variations in the emission signal intensity caused by differences in the physical or chemical properties of the sample matrix, even when the concentration of the target element is the same. Such effects can arise from factors such as thermal conductivity, density, surface roughness, and ablation behavior of the material. These matrix-dependent influences often reduce the accuracy and reproducibility of quantitative LIBS measurements. Cemented carbide is an alloy made by powder metallurgy with one or several refractory carbide (tungsten carbide, titanium carbide, etc.) powder as the main component and metal powder (Cobalt, nickel, etc.) as the bonding agent. It is mainly used in the manufacture of high-speed cutting tools and cutting tools for hard and tough materials, as well as the production of cold work molds, gauges, and high wear-resistant parts that are not subject to shock and vibration. Tungsten carbide is an important raw material for the production of cemented carbide, with the characteristics of wear resistance, corrosion resistance, and high temperature resistance. Tungsten carbide is suitable for machining at high temperatures, can make cutting tools, structural materials for kilns, jet engines, gas turbines, nozzles, etc., using the GB/T 4295 [20]. Cobalt powder, one of the key raw materials used in cemented carbide materials (such as cemented carbide and synthetic diamond tools), whose properties determine the bonding performance, strength, and toughness of cemented carbide materials and are essential to the performance of cemented carbide materials, adopts the standard GB/T 685-010 [21]. Previous LIBS studies have primarily focused on the qualitative analysis of ablation crater morphology, using it mainly as a diagnostic tool after laser ablation. In contrast, our work advances this by quantitatively extracting multiple morphology parameters--such as depth, radius, and volume--using depth-from-focus imaging, and integrating them directly into a nonlinear calibration model for matrix effect correction. This approach operationalizes crater morphology as a real-time, quantitative input for improving LIBS accuracy, rather than relying on post hoc qualitative inference. To the best of our knowledge, this is the first study to employ depth-of-focus-based 3D morphological reconstruction for micro-scale LIBS quantitative analysis and matrix effect calibration, representing a significant step forward in both methodology and application scope. To address these challenges, this study proposes an innovative matrix effect correction method based on the morphological characterization of laser ablation craters. A depth-of-focus (DOF) imaging approach is employed to enable the high-precision three-dimensional (3D) reconstruction of ablation morphology. This allows for the accurate calculation of the ablation volume, which directly reflects the energy coupling efficiency between the laser and the sample. Focusing on the detection of trace elements in high-performance cutting tools, this study investigates the complex interrelationships between ablation morphology, laser parameters (such as energy and pulse width), plasma characteristics (including temperature and electron density), and the physical properties of the target material.