Analytische Chemie
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Tomography of a laser-induced plasma in air is performed by inverse Radon transform of angle-resolved plasma images. Plasmas were induced by single laser pulses (SP), double pulses (DP) in collinear geometry, and by a combination of single laser pulses with pulsed arc discharges (SP-AD). Images of plasmas on metallurgical steel slags were taken at delay times suitable for calibration-free laser-induced breakdown spectroscopy (CFLIBS). Delays ranged from few microseconds for SP and DP up to tens of microseconds for SP-AD excitation. The white-light and the spectrally resolved emissivity ε(x,y,z) was reconstructed for the three plasma excitation schemes. The electron number density Ne(x,y,z) and plasma temperature Te(x,y,z) were determined from Mg and Mn emission lines in reconstructed spectra employing the Saha-Boltzmann plot method. The SP plasma revealed strongly inhomogeneous emissivity and plasma temperature. Re-excitation of plasma by a second laser pulse (DP) and by an arc discharge (SP-AD) homogenized the plasma and reduced the spatial variation of ε and Te. The homogenization of a plasma is a promising approach to increase the accuracy of calibration-free LIBS analysis of complex materials.
The performance of the Monte Carlo (MC) algorithm for calibration-free LIBS was studied on the example of a simulated spectrum that mimics a metallurgical slag sample. The underlying model is that of a uniform, isothermal, and stationary plasma in local thermodynamical equilibrium.
Based on the model, the algorithm generates from hundreds of thousands to several millions of simultaneous configurations of plasma parameters and the corresponding number of spectra. The parameters are temperature, plasma size, and concentrations of species. They are iterated until a cost function, which indicates a difference between synthetic and simulated slag spectra, reaches its minimum. After finding the minimum, the concentrations of species are read from the model and compared to the certified values. The algorithm is parallelized on a graphical processing unit (GPU) to reduce computational time. The minimization of the cost function takes several minutes on the GPU NVIDIA Tesla K40 card and depends on the number of elements to be iterated. The intrinsic accuracy of the MC calibration-free method is found to be around 1% for the eight elements tested. For a real experimental spectrum, however, the efficiency may turn out to be worse due to the idealistic nature of the model, as well as incorrectly chosen experimental conditions. Factors influencing the performance of the method are discussed.
In the LIBS literature, almost every second article reports the determination of the plasma temperature using the Boltzmann plot method or the determination of the electron density using the Stark line broadening relation. The first requires the measurement of the integrated intensities of the spectral lines, and the second requires the measurement of the linewidth, under the same assumption of optical thinness. It is taken for granted that this can be easily done either by working with the raw spectra or by fitting an appropriate function to the observed spectral lines. As a rule, reported data are not verified either by an alternative method (e.g., Thomson scattering) or by computer simulations using synthetic spectra.
However, the question of how to extract the necessary information from the raw spectral data is not as simple as it might seem. The quality of such an extraction will depend critically on the type of spectral instrument used, its resolution, and the noise superimposed on the data. The problem is that we do not see the spectrum emitted by the plasma, but the spectrum distorted by the measurement; an exaggerated example of such a distortion is shown in Fig. 1. The elimination of this distortion belongs to the class of inverse problems, the so-called ill-posed problems, whose successful solution crucially depends on the quality of the information available. When it comes to spectroscopy, quality of information primarily means high spectral resolution and low noise. Not all spectrometers used in LIBS can provide the quality needed to solve the inverse problem; this casts doubt on many published plasma measurements.
The current presentation will be devoted to general shortcomings in the processing of spectral data and inaccuracies in the determination of plasma parameters resulting from these shortcomings. The analysis is based on the use of synthetic spectra produced by plasma with known characteristics, i.e., temperature, species densities, and electron density. The estimation of errors caused by inadequate processing of spectral data is made by comparing the initial and reconstructed plasma parameters. Recipes will be given for which the analytic function best approximates the observed spectral lines, and how data processing errors affect accuracy of calibration-free LIBS will be discussed. These issues were only partially covered in previously published works, for example [1, 2, 3].
Many applications of LIBS require the measurement of plasma temperature and electron density, which in turn requires knowledge of the integrated line intensity and the shape of the spectral lines. While the integral intensity is preserved as light passes through the spectrometer, the shape emitted by an individual atom or ion is greatly distorted. This is due, firstly, to the transfer of light through the plasma (self-absorption), secondly, to the influence of the instrumental function of the spectrometer, and, thirdly, to the aberrations of the optical system. In addition, processing of spectral information, such as background removal, noise reduction, deconvolution, and line fitting, introduces additional errors in the reconstructed linewidth and line integral, which leads to erroneous temperature and electron density values.
This communication will be devoted to the general shortcomings of spectral data processing and the resulting inaccuracies in determining the plasma parameters. The analysis is based on the use of synthetic spectra generated by plasma with known temperature and particle density. The estimation of errors caused by inadequate processing of the spectral data is made by comparing the initial and determined plasma parameters. As a result, an improved data processing method will be proposed that takes into account the spectrum distortion by the instrumental function and integration on the pixel detector. The former is accounted for by convolution (instead of deconvolution) of the estimated line profile using a predetermined slit function, and the latter is achieved by piecewise integration of the line profile by the pixel detector, taking into account the pixel size and uniform or non-uniform pixel separation. Recommendations will be made for which analytic function best approximates the observed spectral lines and examples will be given for the application of this routine to calibration-free LIBS using both synthetic and experimental data.