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Error Analysis in Optimization Problems Relevant for Calibration-Free Laser-Induced Breakdown Spectroscopy
Maali, Jenaan Jamileh
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The calibration-free laser-induced breakdown spectroscopy (CF LIBS) exploits model relations between the spectral parameters of the emitted light (line positions, width, and optical depth) and the physical parameters of plasma (particle number densities and temperature) to determine the latter from the plasma spectra. In turn, the spec- tral parameters are extracted from the measured optical data using the solution to the radiative transfer equation along a line of sight. In the present study, an error analysis is carried for optimization processes used to solve the latter problem. It is shown that, even with ideal optical data (homogeneous uniform plasma, no noise, summa spectral resolution), there are significant variations in relative errors of the line optical depth and width under which an optimization error has no significant change. For example, a least square fit of the data into a theoretical line profile with a relative error of under a fraction of per cent may yield relative errors in the line optical depth and width over a hundred per cent. The same holds for costs functions used in Monte Carlo LIBS meth- ods. The analysis is carried for the entire range of optical depth used in LIBS (from 10−4 to 100). This feature is shown to be a direct consequence of the very structure of the solution of the radiative transfer equation along a line of sight. A new method that is free of the noted uncertainties is proposed to determine the spectral parameters. It is applicable for optically thin and thick lines on the same footing. ( en )
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Awarded Bachelor of Science, summa cum laude, on May 8, 2018. Major: Mathematics. Emphasis/Concentration: Bachelor of Science
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College or School: College of Liberal Arts and Sciences
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Advisor: Sergei Shabanov. Advisor Department or School: Mathematics

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University of Florida
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University of Florida
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Copyright Jenaan Jamileh Maali. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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