About the use of inverse calibration in laser-induced breakdown spectroscopy quantitative analysis

Many of the current analytical application of LIBS are based on the build of a 'simple' univariate and linear calibration curve, where the signal is plotted as a function of the concentration of the analyte in the calibration standards. Recently, it has been proposed to consider also in LIBS, as was done in other spectroanalytical techniques, the use an inverted calibration curve, obtained by plotting the standard concentration as a function of the corresponding LIBS signals. The purpose of this communication is evidencing that some peculiar characteristics of the LIBS signal, including the non-homoscedasticity of the data used for building the calibration curve, in most of the cases make the application of inverse methods less convenient than the classical direct approach. An example is given using real spectral signals acquired on brass samples for the measure of the composition of the alloy, showing that, in that specific case, the use of inverse calibration leads to analytical results less precise than the direct one, at the same time giving a severe underestimation of the limits of confidence of the corresponding calibration curve. Based on these findings, a general method for obtaining a symmetrical calibration curve, which takes correctly into account the indetermination on both the standards' concentration and the LIBS signal, is proposed.