Abstract 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.

中文翻译：

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硅酸盐岩激光诱导击穿光谱分析中非线性多变量校准的新方法

摘要 本文提出了一种对硅酸盐岩石进行定量激光诱导击穿光谱 (LIBS) 分析的新方法。该方法改编自 Franzini 和 Leoni 算法，这是一种广泛用于 X 射线荧光分析的方法，用于校正确定地质材料成分中的基体效应。为了说明所提出的新方法的特点，通过构建线性单变量校准曲线、线性多变量校准表面 (PLS) 和使用人工神经网络，对 19 个地质标准中的 9 个元素进行了量化。然后将结果与从这里提出的算法的应用得出的预测进行比较。发现 Franzini 和 Leoni 方法给出的结果比线性单变量和多变量方法更精确，并与人工神经网络的应用相媲美。所提出方法的一个明显优势是可以使用线性优化算法构建多元非线性校准表面，这一特征使得 Franzini 和 Leoni 方法在 LIBS 分析中的应用相对于基于算法的算法而言更加简单（和可控）。关于人工神经网络。