Fitting LIBS Spectra using Gradient Descent

Laser-induced breakdown spectroscopy (LIBS) is a non-contact analytical technique that allows for the elemental analysis of a sample by analyzing the light emitted from a plasma generated by a focused laser pulse. It has been employed in planetary in-situ missions, such as the ChemCam instrument on the Mars Science Laboratory rover [1] and the SuperCam instrument on the Mars 2020 Perseverance rover [2]. Usually the analysis of LIBS spectra relies on the use of calibration data, which is obtained by measuring the spectra of reference samples with known compositions. In the above stated missions calibration data was obtained by measuring the spectra of reference samples in the laboratory with the space- as well as the replica instruments
and by using onboard calibration targets [3].

Figure 1: General scheme of the spectra fitting approach

 

 

The calibration-free LIBS (CF-LIBS) method enables the determination of quantitative plasma parameters without the need for such calibration data @ciucci99. Usually CF-LIBS is based on the (Saha-)Boltzmann plot method, which relies on the assumption of a local thermal equilibrium (LTE) and the selection of suitable transitions.

Another class of methods consists of the direct fitting of a plasma model producing a synthetic spectrum to the experimentally obtained spectrum. This method is more flexible and can be applied to more complex plasma models, such as non-LTE plasmas, but it is also computationally more expensive @demidov16 @gornushkin22a.

In this work we present a fitting scheme that utilizes gradient descent to find the optimal plasma parameters.

Based on the homogeneous 1D plasma model at LTE, we show that the gradient descent approach is able to find the optimal solution fast and consistently.

We emphasize that this approach is generic and can be extended to more involved plasma models, such as non-LTE plasmas, which are relevant for the analysis of LIBS spectra obtained in planetary in-situ missions.

 

References
[1] R. C. Wiens et al., “The ChemCam Instrument Suite on the Mars Science Laboratory (MSL) Rover: Body Unit and Combined System Tests,” Space Science Reviews, vol. 170, no. 1, pp. 167–227, Sept. 2012, doi: 10.1007/s11214-012-9902-4.
[2] S. Maurice et al., “The SuperCam Instrument Suite on the Mars 2020 Rover: Science Objectives and Mast-Unit Description,” Space Science Reviews, vol. 217, no. 3, p. 47, Apr. 2021, doi: 10.1007/s11214-021-00807-w.
[3] S. M. Clegg et al., “Recalibration of the Mars Science Laboratory ChemCam Instrument with an Expanded Geochemical Database,” Spectrochimica Acta Part B: Atomic Spectroscopy, vol. 129, pp. 64–85, Mar. 2017, doi: 10.1016/j.sab.2016.12.003.
[4] A. Ciucci, M. Corsi, V. Palleschi, S. Rastelli, A. Salvetti, and E. Tognoni, “New Procedure for Quantitative Elemental Analysis by Laser-Induced Plasma Spectroscopy,” Applied Spectroscopy, vol. 53, no. 8, pp. 960–964, Aug. 1999, doi: 10.1366/0003702991947612.
[5] A. Demidov et al., “Monte Carlo Standardless Approach for Laser Induced Breakdown Spectroscopy Based on Massive Parallel Graphic Processing Unit Computing,” Spectrochimica Acta Part B: Atomic Spectroscopy, vol. 125, pp. 97–102, Nov. 2016, doi: 10.1016/j.sab.2016.09.016.
[6] I. Gornushkin, “Calibration-Free Quantitative Analysis,” Laser-Induced Breakdown Spectroscopy in Biological, Forensic and Materials Sciences. Springer International Publishing, Cham, pp. 67–99, 2022. doi: 10.1007/978-3-031-14502-5_3.