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Abstract
This work demonstrates the efficiency of machine learning in the correction of spectral intensity variations in laser-induced breakdown spectroscopy (LIBS) due to changes of the laser pulse energy, such changes can occur over a wide range, from 7.9 to 71.1 mJ in our experiment. The developed multivariate correction model led to a precise determination of the concentration of a minor element (magnesium for instance) in the samples (aluminum alloys in this work) with a precision of 6.3% (relative standard deviation, RSD) using the LIBS spectra affected by the laser pulse energy change. A comparison to the classical univariate corrections with laser pulse energy, total spectral intensity, ablation crater volume and plasma temperature, further highlights the significance of the developed method.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser spectroscopy relies on optical processes in materials excited directly or indirectly by laser radiation. It is especially the case of laser-induced breakdown spectroscopy (LIBS), where a laser pulse (ns duration in general) is focused on a sample to be analyzed inducing a plasma on its surface through ablation [1,2]. The constraint from the ambient gas on the plasma leads to the excitations of the elemental species inside, atoms, ions and molecules, through collisions [3,4]. The subsequent deexcitation generates optical radiation, providing thus the LIBS spectrum. The corresponding line intensity obviously depends on the laser fluence (or equivalently laser pulse energy for a constant beam focus spot), although such dependence can be far from a linear relationship. The study of LIBS spectrum fluctuation caused by laser fluence variation presents important interests, because of the attractive and unique features of LIBS for in situ and online detection and analysis in many application scenarios. In these applications, the laser fluences deposited onto the materials to be analyzed can become much less controllable as in the laboratory. Such situation is especially the case for online inspection and control of a production line of raw or recycling materials (minerals, plastics or metal spare pieces…), where the laser fluence can change because of variations of the working environment and/or the geometry of the laser materials interaction [5]. It is also the case for remote sensing with the well-known example of the ChemCam project, where the LIBS instrument onboard the Curiosity rover performed LIBS analyses of Mars rocks at various distances of about from 1 to 7 m [6]. The conservation of optical etendue leads to significant fluence changes for a constant laser pulse energy while the detection distance changes. Since the laser fluence represents the only energy source driving the whole LIBS process, its variation influences all the steps in LIBS, from laser ablation to plasma formation, evolution and emission [7]. Nonlinear dependence of the ablation rate on laser fluence [8] causes the ablated mass to vary with multiple threshold laws in several interaction regimes as laser fluence increases [9,10]. Plasma formation during the post-breakdown interaction [11] between the ablation vapor and the laser pulse results in a direct influence on the physical properties of the plasma by the laser fluence within different modes of laser-supported absorption wave [12,13].
Although there is still no complete physical model to quantitatively describe the dependence of plasma emission intensity on laser fluence, a generally accepted practice is, in a univariate correction method, to normalize the spectra by the laser fluence, or in an equivalent way by an experimentally observable quantity which is believed to be proportional to the laser fluence, such as the acoustic wave emitted as a consequence of the blast wave generated during laser ablation [14,15], the ablated mass [16], or the emission intensity from a proxy external standard [17]. In the cases where any additional measurement is not available, correction can be performed by normalizing with a suitable quantity extracted from the spectra [18], such as the continuum spectral background [19], the total spectral intensity (total area under the spectrum) [20,21], or the line intensity of an internal standard element [22,23], if a common element with known concentrations exists in all the samples to be analyzed. Beyond univariate correction methods, multivariate normalization methods were also applied to correct LIBS intensity fluctuations due to laser pulse energy changes [24]. Calibration-free laser-induced breakdown spectroscopy (CF-LIBS) has been introduced to correct LIBS intensity fluctuations due to the change of plasma property in a general way [25], it has however not been dedicated to correcting intensity variations due to laser pulse energy changes.
In this work, LIBS measurements were performed on a set of certified reference aluminum alloy samples with different laser pulse energies, varied over nearly an order of magnitude from 7.9 mJ to 71.1 mJ, while their focus on the sample surface was kept unchanged. The variations of the emission intensities from a minor element in the samples, magnesium for instance, with either atomic and ionic lines Mg I and Mg II, were observed and first corrected with a univariate correction method, by normalizing with the laser pulse energy and the total spectral intensity. The results of such normalization are discussed in terms of empirical multiple threshold logarithm laws of laser ablation. Spectral intensity fluctuation correction with a physical model involving the ablation crater volume and the plasma temperature was then implemented. A multivariate correction model based on a machine learning approach consisting of a spectral feature selection and a back-propagation neural network algorithms was then developed to further correct the fluctuation of LIBS spectrum line intensities. Calibration curves corresponding to the different normalization methods were built to assess the corresponding correction efficiencies.
2. Samples and experimental setup
In the experiment, eight certified reference aluminum alloy samples (purchased from NCS Testing Technology Co.) with a cylindrical form were used. Their flat surfaces were polished and cleaned before the measurements. The use of aluminum alloys for this experiment was motivated by the fact that the matrix element aluminum has a relatively simple LIBS spectrum, which avoided the spectral interference problem for a better focus on the correction of spectrum fluctuation induced by laser pulse energy variation. The elemental compositions of the samples are shown in Table 1. Magnesium contained in these samples as minor element was chosen as the test element, since it presents strong atomic and ionic emission lines in a narrow spectral window from 279 to 286 nm without interference with other elements. The Mg concentrations in the used sample varied from 23 to 1360 ppm as shown in Table 1. The use of a set of samples with a gradient of elemental concentration allowed performing statistics on the observed results and in the multivariate correction model, having enough samples for model training and model validation. The samples S4, S5 and S6, with their Mg concentrations in the middle of the concentration range, were used as the test samples. Pulses from a Nd:YAG laser operated in its fundamental of 1064 nm and at a repetition rate of 10 Hz were focused by a lens of 50 mm focal length slightly under the sample surface with an estimated laser spot of about 200 µm on the sample surface. Five laser pulse energies, 7.9, 23.7, 39.5, 55.3 and 71.1mJ measured before they hit the samples, were used in the experiment. Samples were mounted on a motorized X-Y-Z displacement stage. For each sample and a given laser pulse energy, twenty replicate measurements were performed. Each replicate spectrum was an accumulation of one hundred laser shots uniformly distributed over ten craters. A center-to-center distance of 0.5 mm between neighboring craters was left to avoid mutual influence between the laser impacted zones. The optical emission from the generated plasma was collected by a two-lens optical arrangement along a direction perpendicular to the incident laser beam and parallel to the sample surface, and was coupled via an optical fiber into a Mechelle spectrometer, equipped with an intensified charge coupled device (ICCD) camera (Mechelle 5000 and iStar CCD from Andor Technology). The detection system was calibrated for its spectral response with a deuterium halogen light source (Ocean Optics). The ICCD camera was synchronized to laser pulses with a delay of 1000 ns and a gate of 2000 ns after each laser shot. Such delay and detection gate were chosen for the detection of a plasma in the local thermodynamic equilibrium (LTE) with a relatively well defined temperature [26].
Table 1. Elemental compositions of the samples used in the experiment. The S4, S5 and S6 presented in italic in the table, were used as the test samples for the correction models.
3. Experimental results and discussion
3.1 Correction by normalizing with laser pulse energy and total spectral intensity
Figure 1(a) presents the replicate-averaged spectra from the sample S5 in the range from 278.75 nm to 286.00 nm acquired with different laser pulse energies, showing a large fluctuation of the Mg II 280.3 nm line (similar to the neighboring Mg II 279.6 nm line) with a relative standard deviation (RSD) of 60.2% and a smaller RSD of 28.2% for the Mg I 285.2 nm line. The larger variation for the ionic line compared to the atomic line can be explained by the fact that the first corresponds to a higher excited energy with a population more sensitive to the variation of the plasma temperature caused by a change of laser fluence. Without any correction, an atomic line is therefore more suitable for minimizing the effect of laser fluence change. Figure 1(b) shows the spectra normalized with laser pulse energy. A good result is obtained for the ionic line with a reduced intensity RSD of 11.0%. In contrast, the atomic line exhibits an enlarged RSD of 82.9% confirming the clear nonlinear variation behavior of this line with respect to the laser pulse energy. The same measurements were also applied to the other test samples S4 and S6, with the results shown in Table 2, confirming further the observations with S5. Table 2 presents also the RSDs of spectral intensity resulted from normalization with the total spectral intensity (defined as the total area under the whole spectrum), showing a similar correction effect, although somehow less efficient, as the laser pulse energy normalization. This result confirms the correlation between the laser pulse energy and the total spectral intensity reported previously [20,21].
Fig. 1. Detailed spectra of the Mg II 280.3 nm line and the Mg I 285.2 nm line from the sample S5 and for the 5 used laser pulse energies: (a) raw spectra and (b) spectra normalized by laser pulse energy.
Table 2. RSD values of the magnesium line intensities (Mg I 285.2 nm and Mg II 280.3 nm lines) for the 3 test samples S4, S5 and S6 with the raw, laser pulse energy-normalized and total intensity-normalized spectra.
In order to further understand the different efficiencies of normalization with laser pulse energy between the atomic and the ionic lines, the raw line intensities (defined as the count at its maximum minus the background around it) of these two lines from the sample S5 are plotted in Fig. 2 as a function of the laser pulse energy. Different behaviors can be observed for these lines. The atomic line exhibits a smaller intensity variation range with respect to the laser energy change, conforming the observation in Fig. 1(a), such change is however clearly nonlinear. The ionic line presents a larger variation range, the experimental points fit however better to a linear increase with the laser energy. We can empirically fit the experimental points with multiple threshold logarithmic laws in the form of [8]
Fig. 2. Raw spectral intensities of the 2 Mg lines from the sample S5 as a function of the laser pulse energy, and their fits with multiple threshold logarithm laws (dotted gray curves). The error bars in the figure correspond to the standard deviation (SD) of the replicate measurements.
The results shown above tell us that the fluctuation of the Mg II line due to laser pulse energy change can be corrected by normalizing with the laser energy in a relatively satisfactory way. Let us look at the effect of the normalization on the calibration curves established with this line. Such calibration curves are obtained by fitting the average raw line intensities and the average normalized line intensities as a function of the magnesium concentration (in the range covered by the 8 samples) for the different laser pulse energies as shown in Fig. 3. We can see in Fig. 3(a) that, for raw spectra, each specific laser energy leads to a well-defined linear model, with a determination coefficient ${R^2}$ larger than 0.97. This means a good repeatability of the measurements from a sample to another. The linearity of the calibration curves indicates also a negligible self-absorption of the Mg II 280.3 nm line in the used Mg concentration range. We can also remark small error bars of the averaged line intensities, indicating a good repeatability of the replicate measurements for a given sample. With different laser pulse energies, calibration curves with different slopes appear. Thus, laser fluence changes result in a dispersion of the line intensities with respect to a linear relation between the intensity and the concentration. Such dispersion can be quantified by the determination coefficient calculated for the intensities measured with all the laser pulse energies with respect to a unique linear regression of all the intensities. With our experimental data, such calculation results in a value of ${R^2} = $ 0.5144, indicating the importance of the dispersion. With the normalized intensities in Fig. 3(b), such determination coefficient increases to ${R^2} = $ 0.9613, showing an efficient correction of the line intensity fluctuation, while other indicators, the individual determination coefficients for a given laser energy and error bars, remain practically unchanged. The same assessment procedure was applied to the Mg I line, a different behavior was observed in confirmation to the results shown in Fig. 1. The determination coefficient for the raw intensities for all the laser energies was ${R^2} = 0.7911$, while it became ${R^2} = 0.3428$ for all the normalized intensities, indicating a degradation with the normalization.
Fig. 3. Calibration curves resulted from linear fittings of the average intensities of the raw spectra (a) and laser energy-normalized intensities (b) of the Mg II 280.3 nm line as a function of Mg concentration for different laser pulse energies. The error bars correspond to the standard deviation (SD) of the replicate measurements.
3.2 Correction with the crater volume and the plasma temperature
It is well known that under the LTE approximation, the spectrally integrated line intensity (corresponding to the area under an emission line) can be expressed as [27]
where $I_\lambda ^{ki}$ is the integral intensity of the line at a wavelength $\lambda $, such line is resulted from the transition from a up state k (energy of the level ${E_k}$) to a lower state i of a species s of an atom presenting in a plasma with particle density n and temperature T, ${A_{ki}}$ is the transition probability between the two states and ${U_s}(T )$ the partition function of the species at the plasma temperature T, and F represents an experimental parameter taking into account the optical efficiency of the collection system and the plasma geometrical form. For a given experimental arrangement and a given sample, when the laser pulse energy changes, the atomic and ionic spectral intensity can fluctuate through the two parameters: i) n, since the ablated mass is changed; ii) ${e^{ - ({{E_k}/{k_B}T} )}}/{U_s}(T )$, since the plasma temperature is changed. If we take a laser pulse energy (the smallest one in our experiment for example) as the reference, and denote the corresponding plasma density and temperature respectively as ${n_0}$ and ${T_0}$, then when the laser energy changes to a different value, the measured line intensity can be correct back to a normalized value $\overline {I_\lambda ^{ki}} $ with respect to the reference laser energy according toTable 3. Ablation crater volume, plasma electron density and temperature and the corresponding standard deviations (SD) determined for the different laser pulse energies used in the experiment.
The electron density ${n_e}$ of the plasmas was calculated with the Stark broadening of the ${H_\alpha }$ line. The temperature T of the plasmas was then extracted from the corresponding spectra using the Saha-Boltzmann plot [28]. A set of atomic and ionic lines from aluminum was used for the plot, which includes Al I lines (at 236.7 nm, 256.8 nm, 257.5 nm, 265.2 nm, 266.0 nm, 308.2 nm, 309.3 nm, 394.4 nm, and 396.2 nm) and Al II lines (at 281.6 nm, 466.3 nm and 704.2 nm). They were selected for a good correlation with a linear plot without significant perturbation from self-absorption. For a given laser pulse energy, the electron density and the temperature were calculated for all the samples. The averaged value over the samples is presented in the Table 3 as the mean together with the standard deviation, for all the laser pulse energies. With the electron densities shown in Table 3, we can especially verify the McWhirter criterion ${n_e}({\textrm{c}{\textrm{m}^{ - 3}}} )> 1.6\cdot {10^{12}}\sqrt T \Delta {E^3}$, as a necessary condition providing the lowest value of the electron density for a plasma in the LTE [1]. Using the largest energy difference, $\Delta E = $ 5.25 eV, for the above aluminum lines used for the temperature determination, and with the corresponding temperatures, the minimal electron densities were determined for the plasmas induced with the different laser pulse energies respectively at the values in $\textrm{c}{\textrm{m}^{ - 3}}$ of $2.5 \times {10^{16}} $ , $2.7 \times {10^{16}}\; $ , $2.8 \times {10^{16}} $ , $ 2.8 \times {10^{16}} $ , and $2.9 \times {10^{16}}$. A comparison with the experimentally determined values shown in Table 3 allows us confirming the satisfaction of the necessary condition of the LTE in our experiment. Knowing the plasma temperature, the partition function ${U_s}(T )$ was determined using the NIST Atomic Spectra Database Levels Data [29].
The above experimentally determined values of crater volume and plasma temperature were used to correct the two magnesium raw line intensities (defined as the count at its maximum minus the background around it) obtained from the test samples (S4, S5 and S6) according to Eq. (3) by using the smallest laser energy of 7.9 mJ as the reference. After the correction, the RSD values of the intensities are shown in Table 4. We can see that compared to the raw spectra (Table 2), the correction on the ionic line is much more efficient, especially with the simultaneous correction with the crater volume and the plasma temperature. The reduced mean RSD over the test sample of 7.4% is significantly improved compared to the normalization with laser pulse energy and the total spectral intensity. Figure 4 shows calibration curves constructed with intensities respectively normalized with the carter volume, the plasma temperature and the both factors. Comparing to the results in Fig. 3, improvements are observed. In particular, the result of simultaneous normalization with the two factors shows a ${R^2}$ of 0.9744 better than the normalization with laser pulse energy. We can however remark that in practice, the measurement of the crater volume is not always possible, especially for industrial applications. This would limit the implementation of the correction method in this section.
Fig. 4. Calibration curves resulted from linear fitting of average intensities of Mg II 280.3 nm line with crater volume-normalized spectrum (a), temperature-normalized spectra (b) and crater volume and temperature normalized spectra (c). The error bars correspond to the standard deviation (SD) of the replicate measurements.
Table 4. RSD values of the magnesium line intensities (Mg I 285.2 nm and Mg II 280.3 nm lines) for the 3 test samples S4, S5 and S6 after corrections respectively with the ablation crater volume, the plasma temperature, and the both factors.
3.3 Multivariate correction model based on machine learning
A multivariate model based on machine learning was developed to further correct spectral line intensity fluctuation. The algorithms developed in our previous research [30] were further adapted and optimized to better fit the specificity of the present work. Briefly, a feature selection procedure based on SelectKBest (SKB) algorithm [31] selected fifty of the most important pixel intensities among the 23825 intensities in a spectrum according to their score calculated by the covariance with the Mg concentrations of the samples. The criterion for such selection corresponds to a minimal Pearson’s correlation coefficient between the spectral intensities and the element concentrations of 0.60 for a strong correlation between them [32]. The selected intensities were used as the input variables of a back-propagation neural network (BPNN) to train and validate the correction model. The BPNN algorithm was chosen in this work because its wide and successful uses in many applications. The structure of the neural network consists of an input layer with fifty neurons corresponding to the selected pixel intensities, a first hidden layer with the same number of neurons, a second hidden layer with 5 neurons and an output layer with a single neuron. Such modified neural network structure compared to our previous work [30] ensured a better performance of correction as indicated by our tests. If the laser pulse energy or an equivalent observable is measured in the experiment, as it was the case in our work, a generalized spectrum [30] is formed by concatenating the selected pixel intensities with an additional variable. In our experiment, it corresponded to the laser pulse energy. Such supplementary information is provided through an additional neuron in the input layer (the 51st one), with corresponding modifications in the neural network structure (fifty-one neurons in the 1st hidden layer). The activation function used in the neural network was the relu function. The epochs of the final neural network were determined to be around 200 in order to minimize the mean absolute error in the training process.
For the model training, one of the test samples (S4, S5 and S6) was first excluded, the remaining set of seven samples was used to train the calibration model. As we mentioned in Section 2, for a given training sample, twenty replicate spectra were acquired for each of the five different laser pulse energies, resulting in $7 \times 5 \times 20 = 700$ individual training spectra. Once the model trained, in the validation procedure with the test sample, the calculation with its twenty replicate spectra for a given laser pulse energy using the model, resulted in twenty replicate Mg concentrations, which was further averaged to obtain a mean concentration corresponding to the laser pulse energy. The calculation was then repeated for the sets of replicate spectra for the other laser pulse energies, finally resulting in five mean predicted Mg concentrations. The SD of the mean predicted Mg concentrations was thus calculated to assess the residual fluctuation due to the laser pulse energy change. The same procedure was applied successively to the three test samples S4, S5 or S6. In this work, both the raw spectra and the spectra normalized with laser pulse energy were processed in an identical way.
Figure 5 shows the results of feature selection by the SKB algorithm with the raw training spectra, together with a replicate spectrum from the sample S5 ablated by a laser pulse energy of 7.9 mJ. We can see that high score pixels are concentrated in the spectral range from 279.0 nm to 286.5 nm due to the presence of Mg I and Mg II lines. A further detailed inspection shows that the pixels of the Mg I 285.2 nm line receive the highest scores despite its lower intensity compared to the Mg II lines (inset in Fig. 5(a)). Correspondingly, the Pearson’s correlation coefficient also shows high values for the pixels related to the Mg I (Fig. 5(b)). This corresponds to the observations above on the smaller fluctuations of the Mg I line than those of the Mg II line with respect to the same variation of laser pulse energy (Figs. 1 and 2).
Fig. 5. Results of feature selection with the SelectKBest algorithm: selected pixels in the spectrum (in red) with in the inset a detailed view on the spectral range from 279.0 nm to 286.5 nm from the sample S5 ablated by a laser pulse energy of 7.9 mJ and the SKB scores obtained by the pixels. (b) Pearson’s correlation coefficients for selected pixels in the spectral range from 279.0 nm to 286.5 nm.
Figure 6 shows the calibration models trained with the raw spectra together with the result of test with the sample S5. The selected features were used as the input variables in Fig. 6(a), and the generalized spectrum was used in Fig. 6(b). We can see that the ${R^2}$s for the both cases reach a value very close to the unity, and are significantly improved compared the univariate models presented above (All energies ${R^2}$ in Figs. 3 and 4). Concerning the fluctuation of the predicted Mg concentrations of the sample S5 (insets in Fig. 6), RSDs of 7.2% and 5.4% are respectively obtained for the cases of selected features and generalized spectrum, both improved compared to the univariate model. Although ${R^2}$ presents similar values for the two cases in Fig. 6, the RSD shows a smaller value for the generalized spectrum. This result means that the use of laser pulse energy in the generalized spectrum improves the prediction performance of the calibration model. The importance of laser energy as an additional dimension in the generalized spectrum can also be illustrated by calculating the ratio between the average connection weights of the additional neuron (the 51st one) in the input layer and of the five neurons in the same layer corresponding to the five features receiving the highest scores in the feature selection procedure. This ratio is actually 2.57, indicating the importance of laser pulse energy in the neural network.
Fig. 6. Multivariate correction models and their validations with the sample S5, with the selected features (a) and the generalized spectrum (b). The insets show the residual fluctuations of the predicted Mg concentration of the sample S5, together with the corresponding RDS values.
With the spectra normalized by laser pulse energy, the calculation of the fluctuation of the predicted Mg concentrations for the sample S5 resulted in RSDs of 11.9% and 10.9% respectively for the cases of selected features and generalized spectrum. These values are comparable to those obtained with the normalization by laser pulse energy (Table 2), and not improved compared to the normalization by the crater volume and plasma temperature (Table 4). We can also observe a smaller value of 1.25 for the ratio between the average connection weights defined above. This result indicates a disadvantaged use of normalized spectra in the machine learning multivariate calibration model training process.
Identical data processing was then applied to the other two test samples, S4 and S6. All the obtained results are summarized in Table 5. We can see that similar results are obtained for S4 and S6, confirming those obtained and discussion with the sample S5. For more generality, RSD values are averaged over the three test samples. The most advantaged configuration is clearly to process with the generalized spectrum resulted from the concatenation of the selected features from raw spectra and the laser pulse energy, leading to an average RSD of 6.3% for the predicted Mg concentration. We remark that in the case where the laser pulse energy is not measured, a measurement on a correlated physical quantity, such the acoustic signal, would be useful for a better reduction of the spectral fluctuation induced by laser pulse energy change.
Table 5. RSD values of the predicted magnesium concentrations by the multivariate correction model for the 3 test samples S4, S5 and S6, using the raw and laser pulse energy normalized spectra, with the selected features or the generalized spectrum.
4. Conclusion
In conclusion, we have in this work investigated the fluctuation behaviors and correction methods of LIBS line intensity with respect to laser fluence changes caused in our experiment by a variation of laser pulse energy. More generally, such change can also be caused by a variation of the laser focus spot, in a remote detection with LIBS for example, when the target distance varies. Two specific magnesium lines, the Mg I 285.2 nm line and the Mg II 280.3 nm line, were studied, we believe that they would have a certain degree of representability for atomic and ionic lines more generally. Different behaviors for atomic and ionic emission lines were observed in the experiment upon varying with laser fluence. On one hand, the atomic line exhibited a smaller fluctuation range with respect to the laser fluence change (over a quite large range in our experiment), but a univariate correction with laser pulse energy or total spectral intensity led to an unsatisfactory result. On the other hand, the ionic line was more sensitive to laser fluence change, however, a univariate correction resulted in a better efficiency. In our experiment for the Mg II 280.3 nm line, a residual fluctuation of about 10% was observed after the correction with the laser pulse energy, which changed over one order of magnitude. A quantity which can be extracted from the spectrum and believed to be closely correlated to the laser pulse energy, such as the total spectra intensity, allowed a correction with a similar efficiency, 14% for the Mg II 280.3 nm line in our experiment. Since the emission line intensity from a plasma in LTE can be expressed in a simple way as a function of the plasma density and temperature, the simultaneous correction with the crater volume and the plasma temperature led to an efficient reduction of intensity fluctuation with a RSD of about 7% for the Mg II 280.3 nm line. The limitation of this correction method would be certainly the difficulty to measure the crater volume as well as the time-resolved plasma temperature in many practical applications. Multivariate correction based on machine learning has been demonstrated being able to effectively correct line intensity fluctuation even in absence of any knowledge about laser fluence change, offering a RSD of the predicted Mg concentration of about 8% for a laser fluence change over one order of magnitude. If the information about the laser fluence change is available in the experiment, the use of the generalized spectrum further improved the RSD to about 6%. We believe that the findings in this work would be helpful for many applications of LIBS for in situ, online as well as remote detection and analysis.
Funding
National Natural Science Foundation of China (11574209, 11805126, 61975190).
Disclosures
The authors declare no conflicts of interest.
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