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Figure from:Measurement error due to self-absorption in calibration-free laser-induced breakdown spectroscopy

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Table 2: Uncertainties associated to the Ge-fraction measurement for two transitions and three measurement locations (labelled 11, 6 and 2): atomic fraction C, line-center optical depth to, weight factor 1 — e~*® (see eq 10), and line width error Awsq/wsq. The intensity measurement error A//T, the associated error growth factor g, and the errors of atomic number density An, /n, and atomic fraction AC/C are given for line-center (subscript 0) and line-integrated intensity (subscript ine) measurements (see details in SM 1.4 and SM 2.5).

Table 2 Uncertainties associated to the Ge-fraction measurement for two transitions and three measurement locations (labelled 11, 6 and 2): atomic fraction C, line-center optical depth to, weight factor 1 — e~*® (see eq 10), and line width error Awsq/wsq. The intensity measurement error A//T, the associated error growth factor g, and the errors of atomic number density An, /n, and atomic fraction AC/C are given for line-center (subscript 0) and line-integrated intensity (subscript ine) measurements (see details in SM 1.4 and SM 2.5).

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Figure 1: Intensity vs t9 computed according eq 1: line-center in- tensity (black curve) and line-integrated intensities (colored curves) for line profiles with different ratios of Gauss width wg over Lorentz width wy.
Figure 1: Intensity vs t9 computed according eq 1: line-center in- tensity (black curve) and line-integrated intensities (colored curves) for line profiles with different ratios of Gauss width wg over Lorentz width wy.
Figure 2: Error growth factor vs t9 computed according eq 11 for Jo- measurements (black curve) and Jj;,e-measurements of line profiles with different ratios of Gauss width wg over Lorentz width wz (col- ored curves).
Figure 2: Error growth factor vs t9 computed according eq 11 for Jo- measurements (black curve) and Jj;,e-measurements of line profiles with different ratios of Gauss width wg over Lorentz width wz (col- ored curves).
Table 1: Electron density n,, plasma temperature T, and plasma diam- eter along the line of sight L, deduced from the spectra analysis (see SM 2.2). The calculation of the spectral radiance according to eq | is implemented in an iterative measurement proce- dure that allows us to deduce the plasma properties in- cluding the elemental composition from the best agree- ment between measured and computed spectra [20].
Table 1: Electron density n,, plasma temperature T, and plasma diam- eter along the line of sight L, deduced from the spectra analysis (see SM 2.2). The calculation of the spectral radiance according to eq | is implemented in an iterative measurement proce- dure that allows us to deduce the plasma properties in- cluding the elemental composition from the best agree- ment between measured and computed spectra [20].
Figure 3: Measured and computed spectral radiance of weakly (a) and strongly (b) self-absorbed lines. The measurements were performed for different locations on the sample surface, corresponding to differ- ent Ge-fractions within the thin film.
Figure 3: Measured and computed spectral radiance of weakly (a) and strongly (b) self-absorbed lines. The measurements were performed for different locations on the sample surface, corresponding to differ- ent Ge-fractions within the thin film.
Figure 4: Line-center spectral radiance (a,b) and line-integrated radiance (c,d) as functions of the Ge atomic number density and to (secondary x-axis) for weakly (a,c) and stronly (b,d) self-absorbed lines. The blue and green curves are the line intensities computed for a uniform plasma in LTE considering and ignoring self-absorption, respectively. The analytical measurement error is indicated for an intensity measurement error of 5% (dashed lines).
Figure 4: Line-center spectral radiance (a,b) and line-integrated radiance (c,d) as functions of the Ge atomic number density and to (secondary x-axis) for weakly (a,c) and stronly (b,d) self-absorbed lines. The blue and green curves are the line intensities computed for a uniform plasma in LTE considering and ignoring self-absorption, respectively. The analytical measurement error is indicated for an intensity measurement error of 5% (dashed lines).