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Abstract
Gas composition in randomly distributed and fast-moving bubbles was optically measured aided by laser-induced breakdown spectroscopy (LIBS). Laser pulses were focused at a point in a stream of bubbles to induce plasmas for the LIBS measurements. The distance between the laser focal point and liquid-gas interface, or ‘depth,’ plays a major role in determining the plasma emission spectrum in two-phase fluids. However, the ‘depth’ effect has not been investigated in previous studies. Therefore, we evaluated the ‘depth’ effect in a calibration experiment near a still and flat liquid-gas interface using proper orthogonal decomposition, and a support vector regression model was trained to exclude the influence of the interfacing liquid and extract gas composition information from the spectra. The gaseous molecular oxygen mole fraction in the bubbles was accurately measured under realistic two-phase fluid conditions.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Laser-induced breakdown spectroscopy (LIBS) is a widely used quantitative optical measurement method for analyzing the characteristics of remote materials. LIBS utilizes focused laser pulses to generate plasmas in or on the measured target materials in the solid, liquid, or gaseous phases. Optical breakdown occurs when the laser intensity at the focus exceeds the breakdown threshold, and the laser beam generates a small volume of plasma that spontaneously emits photons. The photon energy spectrum contains information on the various material properties; therefore, the plasma emission spectra have been analyzed and calibrated to estimate the material properties of interest.
In-situ LIBS measurements are possible in various test environments because of their non-intrusive and simple optical setup. For example, LIBS measurements have been conducted in high-pressure or supersonic combustion environments [1–3] and liquids [4–8]. However, LIBS in two-phase fluids is challenging because the liquid-gas interface near the plasma in the gas plays a critical role in the breakdown process by reflecting and refracting the focusing laser beam and producing gaseous species from the evaporation of the interfacing liquid. Therefore, liquid-gas interfaces on jets [4], flats [7], or droplets [5,9] must be carefully controlled for quantitative LIBS measurements, which severely limits the application of LIBS in practical two-phase fluid conditions.
Two-phase flows accompanying complex liquid-gas interfaces are common in practices such as liquid fuel boiling and cavitation in supply lines, fuel cavitation in turbopumps, boiling in heat exchangers, and underwater gas leaks. Most LIBS measurements previously reported in two-phase fluids analyzed liquid-phase components because liquids are incompressible and induce easily distinguishable emission signals that are less affected by the plasma location relative to the liquid-gas interface. However, only a few attempts have been made to analyze the gas phase composition near irregular liquid-gas interfaces [10,11].
Measurements of the gas composition and properties in bubbles are essential for revealing the mechanism of abrupt phase changes, such as cavitation, that can severely damage solid surfaces and remarkably lower system efficiency.
Liquid-gas interfaces in the beam path or near the plasma affect the emission spectrum in two primary ways. First, the liquid is evaporated and mixed into the plasma later to be dissociated, excited and emit photons that interfere with the spectral signal of the gaseous species initially in the bubbles. Second, beam reflection and refraction caused by refractive index discontinuities affect the plasma temperature and shape by changing the amount and spatial distribution of the photon energy that participates in the plasma generation process.
Presumably, the distance between the laser focal point and liquid-gas interface, hereinafter referred to as the ‘depth,’ plays a major role in determining the plasma emission spectrum in two-phase fluids. A very recent work addressed the ‘depth’ effect [12] while keeping the laser incident direction parallel to the liquid surface. However, in typical two-phase fluid measurement environments, the focusing laser beam crosses the liquid-gas interface at random incident angles. Hence, the impact of beam reflection or refraction on the surface could not be investigated independently of the liquid-vapor effect. Therefore, because the ‘depth’ effect has not been taken into account in practice nor quantitatively evaluated in previous studies, it is necessary to consider the ‘depth’ effect in the calibration process for two-phase LIBS.
In this study, a multi-dimensional calibration experiment is designed to consider the effects of the ‘depth’ simultaneously with the gas concentration variation in two-phase fluids. Accordingly, a novel calibration model that uses the plasma emission spectra collected in a stream of fast-moving bubbles as the input to accurately predict the gas composition in randomly distributed and fast-moving bubbles is proposed.
2. Methods
2.1 Experimental setup
The three experimental set-ups used in this study are shown in Fig. 1. Figures 1(a) and 1(b) illustrate the side view of the experimental setup used for calibration that requires the collection of the plasma emission spectra near a liquid-gas interface with varied gas composition and ‘depth.’ For comparison, two separate calibration experiments were conducted as the laser pulse converged from the liquid side (Fig. 1(a), A-set) or the gas side (Fig. 1(b), B-set). Figure 1(c) (C-set) shows a top view of a typical two-phase measurement setup with a stream of fast upward moving and randomly distributed bubbles.
Fig. 1. Schematic diagrams of the experimental setups for (a) liquid-to-gas (A-set) and (b) gas-to-liquid (B-set) calibration experiments, and (c) practical gas bubble composition measurements (C-set); FL: plano-convex focusing lens (f = 75 mm), DM: 550 nm short-pass dichroic mirror, and LM: 532 nm reflection mirror for the laser pulse.
For the calibration experiments (A- and B-sets), approximately 60% of the quartz cuvette with a volume of 50 × 50 × 50 mm3 was filled with deionized water, and the rest on top of the water was left for the purge gas, which simulated the gas inside the bubbles under typical two-phase measurement conditions, as in the C-set. The mole fraction of oxygen balanced by nitrogen in the purge gas was varied from 0% to 21% using two mass flow controllers (FC-280, Tylan) and a static mixer. To maintain the prescribed gas composition in the cuvette, which was less affected by water vapor and plasma products, the purge gas was continuously refreshed at a rate of 4 L/min. The horizontal liquid-gas interface in the cuvette was moved by 500 µm vertically using a micrometer-controlled translational stage from 3 mm below to 2 mm above the reference horizontal plane, where the laser pulses were focused from below (A-set) and above (B-set), respectively.
The water level in the cuvette was monitored and maintained constant. The bubbles illustrated in Fig. 1(c) were generated by infusing gas mixtures through a sintered metal filter (diameter of 23.5 mm) into an acrylic tank (130 × 130 × 210 mm3) filled with deionized water. The tank had a rectangular quartz window on each side for optical access, the mixture gas flow rate was fixed at 4 L/min while the gas composition varied, and the horizontal path of the converging laser pulse below the water surface was 30 mm above the metal filter.
The second harmonic 532 nm laser pulses from an Nd:YAG laser (Powerlite 8000, Continuum) equipped with an injection seeder were focused with a 75-mm focal length plano-convex lens (FL). The laser pulse repetition rate was set to 1 Hz for the calibration experiments to flatten the water surface before the arrival of consecutive laser pulses at the focal point. The pulse energy was fixed at 50 mJ for the B-set and 52 mJ for the A- and C-sets to compensate for the Fresnel reflection (4%) at the air-quartz interface. Compressed air was continuously blown onto the lower face of the focusing lens (FL) via a 12-gauge needle at 10 L/min to keep the lens surface dry in the B-set, where the plasma intermittently splashed water.
The plasma photon emission was collected backward, that is in the direction opposite to the laser pulse propagation (Fig. 1), to prevent a decrease in the photon collection efficiency, particularly in C-set, due to the random dislocation of the plasma along the laser path. The plasma moved back and forth along the laser path depending on the fluid property distribution near the focal point, which was determined by the randomly distributed and fast-moving bubbles near the focus. For consistency, the same backward collection configuration was used in the calibration experiments: A- and B-sets.
A dichroic mirror (DM) reflected the photons from the plasma above a wavelength of 550 nm toward a broadband mirror, and an off-axis parabolic mirror guided the photons to the entrance slit of the spectrometer (SpectraPro-300i, Acton Research Corporation). An off-axis mirror was selected to minimize the relative aberration error in the three optical setups.
Neutral density filters and a 532-nm notch filter were used to adjust the light intensity level and block stray laser light. The spectrometer had a ruled grating of 300 grooves per millimeter, and the grating was rotated to cover a spectral range from 630 to 800 nm, which included the H-alpha (656 nm), N I (743–747 nm), and O I (777 nm) lines.
An intensified sCMOS camera (pco.dicam C1, PCO) recorded the spectra on the output plane of the spectrometer 500 ns after the laser pulse arrival with a 4-ns exposure. For calibration with a stationary liquid-gas interface (A- and B-sets), 30 emission spectra were recorded for a given oxygen concentration and ‘depth’, and 2,000 shots were collected in the stream of bubbles (C-set) for each oxygen concentration condition.
2.2 Spectrum analysis
Proper orthogonal decomposition (POD) has been used to reduce the dimensions of spectral data prior to analysis by machine learning or deep learning techniques. POD approximates a spectrum as the linear sum of N orthonormal spectrum bases that capture the characteristic changes in the spectrum. Subsequently, a set of N scores—coefficients associated with the bases—indicates how much each basis participates in the spectrum approximation and serves as a coordinate in the N-dimensional score space. The score space of a significantly reduced data dimension can be conveniently adopted in spectrum clustering for sample discrimination [13–15] and spectrum regression model fitting for combustion monitoring [16].
In this study, it was found that the liquid (water) gas interface near a laser-induced plasma affects the plasma emission spectra by enhancing the H-alpha (656 nm) line, selective line broadening from the electron number density change, and overall line narrowing from accelerated plasma quenching. Thus, it is challenging to achieve accurate gas concentration measurements using LIBS in two-phase fluids. To account for and exclude the effects of the nearby water-gas interface on LIBS measurements, every variation in the spectrum with decreasing ‘depth’ was clearly quantified. POD identified the characteristic spectral features, that is, the bases, especially sensitive to the ‘depth’ and gas composition utilizing the spectrum database provided by the aforementioned calibration experiments. Subsequently, the dimensions of the spectral data were reduced to the number of primary bases. The four major bases sufficiently described the plasma emission spectra collected in this study.
After mapping the spectra from the calibration database into a 4-dimensional score space, support vector regression (SVR) was applied to fit the regression model. SVR is a machine learning technique that allows multivariate regression and fits a nonlinear model without degrading computational efficiency when combined with the ‘kernel’ trick. This is one of the most effective methods tested in previous studies analyzing spectrum databases [17–19]. In this study, SVR was employed to fit the regression model that maps the sets of the four scores to the corresponding oxygen mole fractions (ℝ4 → ℝ1) with a second-order polynomial kernel.
3. Results and discussion
3.1 Depth effect on LIBS spectrum
Figure 2 shows the change in the plasma emission spectrum owing to the ‘depth’ effect in the B-set with air fed as the purge gas. For each ‘depth’, 30 shots were averaged and normalized to the area under the spectrum. As expected, in general, the H-alpha line at 656 nm strengthened (Fig. 2(b)) relative to the other emission lines including O I (Fig. 2(c)) and N I (743–747 nm) as the plasma approached the liquid-gas interface because of the plasma-liquid interaction. However, when the plasma moved into the liquid region (depth > 0), the trend became unclear with noticeable spectral line narrowing owing to the water dissociation and fast plasma quenching in liquid. Nevertheless, POD effectively captured this abrupt change of the spectrum characteristics across the interface to distinguish the gas signals from the liquid signals.
Fig. 2. (a) The emission spectra depending on the depth in the B-set with air as the purge gas. (b) The H-alpha (656 nm), and (c) O I (777 nm) lines are magnified for comparison.
The four major POD bases, B1, B2, B3, and B4, extracted from the calibration database, are presented in Fig. 3. These four bases describe 74.4% (B1), 22.4% (B2), 2.4% (B3), and 0.4% (B4) of the characteristic spectrum variations (99.6% in total), that were induced by the change of the ‘depth’ and the oxygen mole fraction in gas. Compared with the actual spectrum, the relative root mean squared error of the spectrum reconstructed by the linear summation of the four bases was below 0.012%. This confirmed that the four bases were sufficient to fully describe the spectra in the spectrum database. The four bases separately indicated the strengthening of the H-alpha (B1, Fig. 3(b)) and O I (B2, Fig. 3(c)) emission lines, thinning of every prominent emission line in the spectral range (B3), and selective broadening of the H-alpha line (B4, Fig. 3(b)).
Fig. 3. POD bases (a) in the entire spectral range, near (b) the H-alpha (656 nm) line, and (c) the O I (777 nm) line.
Figure 4 visualizes the 3D score space of the first three major bases, B1–B3. The 2D projections of the 3D space captured from two different angles clarified the impacts of the ‘depth’ (Fig. 4(a)) and the oxygen mole fraction (Fig. 4(b)). For the gas-to-liquid incident (B-set) case (the inverted triangles in Fig. 4), as the plasma generated in the gas region approached the liquid surface (from -3 to 0 mm), score 1 increased indicating the strengthening of the H-alpha line owing to the intensified liquid water-plasma interaction. When the laser focus moved further below the water surface (from 0 to 2 mm), score 3 increased rapidly, implying the thinning of plasma emission lines due to fast plasma quenching in the liquid. For the liquid-to-gas incident (A-set) case (the upright triangles in Fig. 4), score 1 was quite insensitive to the ‘depth’ (Fig. 4(a)) while score 3 rapidly increased as the plasma approached the surface (from -3 to 0 mm), again implying faster plasma quenching in the liquid. We conjecture that quenching in the A-set (higher score 3) is faster than that of the B-set because of the asymmetric expansion of the plasma in the gas which is much stronger upstream of the laser pulse [20]. The liquid water quickly quenched the plasma that was generated in the gas region, but expanded toward the water surface, as in the A-set; recall that the plasma expanded toward the gas side in the B-set to survive longer and stay stronger, activating the H-alpha line (higher score 1). The score 2 represents the strengthening of the oxygen atomic emission line; therefore, it directly indicates the oxygen concentration in gas, as confirmed in Fig. 4(b). Nevertheless, both scores 1 and 2 increased simultaneously as the gaseous plasma approached the water surface because water molecules contain oxygen atoms as well as hydrogen. Accordingly, score 1 in the B-set and score 3 in the A-set served as the primary indicators of the ‘depth’, and were used to exclude its influence from the gas concentration measurements.
Fig. 4. 2D projections of the 3D score space seen from two different angles. The color represents (a) the ‘depth’ and (b) the oxygen mole fraction in gas.
3.2 Gas composition prediction in bubbles
The photos of bubbles in the C-set (Fig. 5) were taken with an exposure of 30 µs around the probing location, 30 mm above the metal filter, to capture their shapes and length scale. In Fig. 5, the backlit bubbles that are overlapping each other, distorted, and randomly distributed appear dark owing to the severe deflections of light on the liquid-gas interfaces. The deflections made the bubbles opaque and limited optical access to the gas in the bubbles. The bubble size ranged from 2 to 5 mm, which is comparable to the length of cylindrical plasma under atmospheric conditions; therefore, severe plasma-liquid interaction occurred for the measurement conditions of the C-set. The data-driven approach employed in this study effectively separated the impact of plasma-liquid interactions from that of the change in gas composition. Nevertheless, it would still be better to reduce the plasma size to avoid or minimize the stochastic plasma-liquid interaction. In future studies, shorter laser pulses with a focusing lens of a shorter focal length will be used to reduce the plasma size.
Figure 6 illustrates the score space of the spectra collected in the C-set using the same bases extracted from the calibration database shown in Fig. 3. The oxygen mole fraction of the gas injected through the metal filter for generating fast-moving bubbles varied from 0% to 21%, as in the calibration experiments. At first glance, the score distribution of the C-set spectra in 3D space is surprisingly similar to that seen in Fig. 4 for the calibration spectra collected under steady and flat surface conditions (A- and B-sets). This indicates that the two sets (A- and B-sets) of calibration experiments covered the most possible measurement conditions that should be considered in practical two-phase experiments. Figure 6 shows selected data (score 1 < 0) from the C-set, color-coded by oxygen concentration. The remaining data, that is, score 1 > 0 or spectrum signal intensity below a threshold (< 1% of the sensor signal span, which are probably liquid plasma signals), were omitted from the figure and prediction. A low score 1 implied weak H-alpha emission and less plasma-liquid water interactions. Figure 6(b) confirms that grouping the score points based on the oxygen concentration is convenient in the score space as shown in Fig. 4.
The prediction accuracy of the SVR model using the POD scores as the input is illustrated in Fig. 7; the maximum bias was 1.93% and the largest standard deviation was 1.3%. This is a high accuracy considering that the C-set configuration demonstrated severe unsteadiness, volumetric plasma confinement in small bubbles, curved and poorly distorted liquid-gas interfaces, overlapping of the bubbles in the path of the laser beam and the plasma emission light, different water tank sizes, etc., conditions not considered in the calibration experiments. The slight bias in prediction may be due to the different fluid conditions. Presumably, spectrum variations caused by these uncontrollable factors would be characterized by scores 3 and 4, which are nearly independent of the most gas-concentration-sensitive score 2. Therefore, the influence of beam refraction and reflection, which are the primary and unwanted factors affecting the emission spectrum, was also determined by POD analysis, and the prediction accuracy remarkably improved.
Fig. 7. Prediction accuracy of the SVR model (a) compared with conventional LIBS calibration methods and (b) bias and standard deviation of the proposed method.
For comparison with conventional LIBS techniques, the oxygen concentrations in the bubbles were estimated by calibrating the O/N and O/H line intensity ratios. The O I (777 nm), N I (743–747 nm), and H-alpha (656 nm) lines were chosen for calibration. Since the calibration in conventional techniques does not consider the influence of the ‘depth’ or the nearby liquid-gas interface, a single spectrum per gas composition was collected to get corresponding O/N or O/H line intensity ratios for calibration. Accordingly, the estimation with the spectra obtained from the C-set shows high scattering, as shown in Fig. 7(a), which is unacceptable for quantitative measurements.
4. Conclusions
Measuring the gas concentration in fast-moving and randomly distributed gas bubbles in liquid is challenging because sampling of the gas and optical access into the bubble are difficult under typical two-phase fluid conditions. High-peak-power laser pulses enable plasma generation in bubbles for laser-induced breakdown spectroscopy (LIBS). However, the plasma location relative to the liquid-gas interface, defined as the ‘depth’ here, affects the plasma emission spectra, which significantly increases the measurement uncertainty.
In this study, we systematically quantified the impact of the ‘depth’ on the plasma emission spectrum using proper orthogonal decomposition (POD), and trained a support vector regression (SVR) model to accurately predict the gas composition in randomly distributed bubbles. Novel calibration experimental setups were designed to consider all possible plasma-liquid surface interactions occurring under practical measurement conditions. Accordingly, four major POD bases highly sensitive to the ‘depth’ and the gas concentration were extracted from the calibration spectrum database to build a 4D score space for SVR model training. The SVR model can accurately predict the gas concentration in bubbles, which are fast-moving, distorted, and randomly distributed. Using a set of plasma emission spectra collected in the bubble stream and decomposed by the POD bases as the input, a maximum bias of 1.93% and standard deviation of 1.3% were obtained in the worst-case prediction scenario. This is surprising because the realistic two-phase fluid conditions tested here, such as bubble surface distortion and plasma confinement in small bubbles, were not considered in the calibration experiments. It is clear that POD worked effectively to extract the most concentration-and ‘depth’-sensitive features from the spectrum database collected in well-designed calibration experiments. Therefore, the impacts of conditional factors other than the oxygen concentration variation can be separated, and the most concentration-sensitive features in the spectra can be selectively extracted and considered for estimating the oxygen concentration in bubbles.
Funding
Agency for Defense Development (UD210034SD); National Research Foundation of Korea (2021R1A2C2012697, 2021R1A4A1032023).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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