Geometrical effects in data collection and processing for calibration-free laser-induced breakdown spectroscopy

- Data processing in CF LIBS is developed for a general ray tracing geometry in spectral data collection.
- An analysis of uncertainties in the determined values of spectral and physical parameters of LIPs due to an incorrect ray geometry in the data processing is given.
- Any CF LIBS method based on fitting the spectral data is shown to give the values of spectral parameters with relative errors 25% and higher if a proper geometry of ray tracing is ignored.
- Safe for a few found exceptions, the geometrical uncertainties cannot be eliminated from CF LIBS data processing, unless a correct geometry of ray tracing is accounted for.

Data processing in the calibration-free laser-induced breakdown spectroscopy (LIBS) is usually based on the solution of the radiative transfer equation along a particular line of sight through a plasma plume. The LIBS data processing is generalized to the case when the spectral data are collected from large portions of the plume. It is shown that by adjusting the optical depth and width of the lines the spectra obtained by collecting light from an entire spherical homogeneous plasma plume can be least-square fitted to a spectrum obtained by collecting the radiation just along a plume diameter with a relative error of 10−11 or smaller (for the optical depth not exceeding 0.3) so that a mismatch of geometries of data processing and data collection cannot be detected by fitting. Despite the existence of such a perfect least-square fit, the errors in the line optical depth and width found by a data processing with an inappropriate geometry can be large. It is shown with analytic and numerical examples that the corresponding relative errors in the found elemental number densities and concentrations may be as high as 50% and 20%, respectively. Safe for a few found exceptions, these errors are impossible to eliminate from LIBS data processing unless a proper solution of the radiative transfer equation corresponding to the ray tracing in the spectral data collection is used.