Optimization of the parameters of a laser induced breakdown spectrometer (LIBS) using probabilistic-deterministic design of experiment

Abstract

A method for optimizing the settings of a LIBS device aimed at achieving the maximum intensity of analytical lines of the analyte of constant composition is considered using probabilistic-deterministic design of experiments (PDDE). A mixture of Cr, Mn, Fe, Co, and Ni oxides homogenized and diluted by fusion with a lead-phosphate mixture is used as an analyte. It is shown that data of mathematical processing of 25 spectra by the PDDE method can be used to develop mathematical models which relate the line intensity with the energy of the laser pumping lamp, the lag time of the first and second Q-switches, the time delay of the exposure onset, and the total exposure time. The use of the geometric mean and mathematical model in the form of the product of the partial dependences leads to a good correlation between the calculated and experimental values of the intensity for all the considered spectral lines. The simulation results presented for 16 analytical lines of Cr, Mn, Co, and Ni illustrate the applicability of the method under consideration. The experimentally achieved maximum intensities of analytical lines in the matrix of lead-phosphate glass differ from those calculated using the obtained models by 7 – 12 %. There is a linear correlation between the experimental and calculated values of the intensity at R2 = 0.99 and an inclination angle close to 45°. The spectra recorded during the experiment can be used for optimization of other parameters, e.g., the signal-to-noise ratio. The simplicity of calculations and relatively small number of tests in the optimization experiment make the PDDE a promising method for optimizing the LIBS parameters.