## 1 Introduction  
Laser-induced breakdown spectroscopy (LIBS) is a powerful atomic emission spectroscopy (AES) technique that employs a highly energetic, short-duration laser pulse as the excitation source [1]. When the laser pulse is tightly focused onto the surface of a solid, liquid, or gaseous sample, it generates high-temperature microplasma through rapid ablation. This plasma contains atoms, ions, and electrons derived from the sample material, which are excited to higher energy levels and subsequently emit characteristic spectral lines as they return to lower energy states. By analyzing the wavelengths and intensities of these emitted spectral lines, the elemental composition of the sample can be determined with high sensitivity and specificity. One of the major advantages of LIBS is its rapid analysis capability, enabling real-time, in situ, and on-line detection without the need for complex sample preparation [2]. Additionally, LIBS is minimally destructive, requires little to no contact with the sample, and can be applied in remote or hazardous environments using fiber optics or robotic systems. These features make LIBS a highly versatile tool, suitable for a wide range of application scenarios. Over the past two decades, LIBS has gained significant attention and has been widely applied in various domains of scientific research and industrial inspection, including metallurgy, geological prospecting, food safety analysis, energy production, biomedicine, cultural heritage conservation, environmental monitoring, and defense-related fields [3; 4; 5; 6]. Despite its many advantages, LIBS is still constrained by several challenges, among which matrix effects are particularly prominent and problematic. Matrix effects refer to the influence of the surrounding material composition and properties on the spectral emission intensity of the target analyte elements [7]. These effects manifest in different forms. Spectral matrix effects arise when the emission lines of matrix elements overlap or interfere with the weak emission lines of analyte elements, potentially obscuring detection; this can be mitigated to some extent by the careful selection of spectral lines. Physical matrix effects result from variations in sample physical properties such as thermal conductivity, heat capacity, absorption coefficient, density, and water content [8; 9]. These properties influence the laser-sample interaction process, affecting the amount of material ablated and the energy transferred to the plasma [10]. Chemical matrix effects, on the other hand, are related to chemical interactions within the sample, such as the formation of stable compounds or differences in ionization potentials, which can alter the excitation and emission behavior of analytes [11]. Furthermore, the overall plasma dynamics and the ablation process are highly nonlinear and complex, involving rapid heating, phase transitions, material removal, and plasma expansion. These factors together lead to signal instability and inaccuracy in quantitative analysis, which poses a significant barrier to LIBS being deployed in high-precision or industrial-level applications [12]. To address matrix effects, a variety of correction and compensation techniques have been proposed in the literature. For instance, [PERSON] et al. developed a method based on the physical modeling of spectral emission, in which matrix effects were corrected by estimating both the vaporized mass and plasma temperature [13]. The vaporized mass was measured using ultrasonic signals, while plasma temperature was determined through a two-line Boltzmann plot method [14]. [PERSON], [PERSON] introduced a dual-laser system, in which the primary laser creates a plasma plume and the secondary laser re-excites the plume in a controlled chamber, thereby reducing matrix interferences and improving spectral repeatability [15]. [PERSON] et al.