A new approach to non-linear multivariate calibration in laser-induced breakdown spectroscopy analysis of silicate rocks

In this paper a new approach to quantitative Laser-Induced Breakdown Spectroscopy (LIBS) analysis of silicate rocks is presented. The method is adapted from the Franzini and Leoni algorithm, a method widely used in X-Ray Fluorescence analysis for correcting the matrix effects in the determination of the composition of geological materials. To illustrate the features of the new method proposed, nine elements were quantified in 19 geological standards by building linear univariate calibration curves, linear multivariate calibration surfaces (PLS) and using Artificial Neural Networks. The results were then compared with the predictions derived from the application of the algorithm here proposed. It was found that the Franzini and Leoni approach gives results much more precise than linear uni- and multivariate approaches, and comparable with the ones derived from the application of Artificial Neural Networks. A definite advantage of the proposed approach is the possibility of building multivariate non-linear calibration surfaces using linear optimization algorithms, a feature which makes the application of the Franzini and Leoni method in LIBS analysis much simpler (and controllable) with respect to the algorithms based on Artificial Neural Networks.