Matrix effects in laser-induced breakdown spectroscopy: A review from fundamental mechanisms to data-driven modeling strategies

The inherent paradox of laser-induced breakdown spectroscopy (LIBS) lies in its robustness for qualitative identification despite its historically limited quantitative precision. This discrepancy is rooted in the matrix effect , a complex coupling of physical and chemical interferences that disrupts the proportionality between emission intensity and analyte concentration. Critically examining the more than fifty-year evolution of the community’s response to this challenge, we trace a trajectory from early empirical recognition and physical modeling through calibration-free LIBS to multivariate chemometrics and the current rise of deep learning. We argue that progress toward more transferable and matrix-robust calibration may require a shift in modeling philosophy: from a paradigm of strictly controlling the physics to one of intelligent, physically constrained adaptation. To bridge this gap, we propose a physical state-space model as the organizing framework of this review: a latent-state formulation in which the LIBS spectrum is generated by an ordered chain of coarse-grained physical operators acting on a hidden sample state, with stage-resolved stochasticity entering throughout the chain and residual detector-level measurement noise. The operator chain comprises M for material removal, A for ablated-material transfer and initial speciation, P for plasma-state, R for radiation generation and transport to the acquisition-system entrance, and F for instrumental transfer and detection. By mapping specific interferences, such as surface hardness, moisture content, and easily ionizable elements (EIEs), to the operator or operators they primarily perturb, the review recasts matrix effects as structured physical perturbations rather than as undifferentiated black-box error. Building on this framework, we organize the emerging hybrid physics–artificial intelligence (AI) approaches – which constrain data-driven models with physical structure – into a graded taxonomy, ranging from light correction of physically derived estimates to architectures that embed physical laws directly into the model. We further address the largely neglected problem of uncertainty quantification for LIBS predictions, outlining a tiered protocol for producing calibrated and validated uncertainty estimates. We conclude that this state-space framework can provide a formal computational backbone for the development of autonomous LIBS sensors with calibrated uncertainty and more transferable, matrix-robust calibration for in situ applications.