# Mobile Laser-Induced Breakdown Spectroscopy for Future Application in Precision Agriculture—A Case Study

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}> 0.85 can be obtained via univariate analysis for the determination of Ca, Mg, P, Fe, and Na. Nicolodelli et al. [15] demonstrated that LIBS performance can be improved via the application of double laser pulses instead of single-pulse LIBS. The importance of different machine learning methods, such as artificial neural networks (ANN) [16], partial least squares (PLS), and support vector machine (SVM) regression [17] for the determination of the total contents of various elements was intensively investigated.

## 2. Experimental Part and Data Analysis

#### 2.1. Materials

#### 2.2. Reference Analysis

_{2}, and SOM was determined using elemental analysis via the total C content, where total C equaled organic C in the carbonate-free samples.

#### 2.3. LIBS Measurements

**Sample preparation.**The soil samples were air dried, pestled, and sieved (2 mm mesh). Soil pellets were produced by taking 3 g of dried soil sample and mixing it with 90 µL of water to establish a standardized moisture. Then, the soil samples were homogenized using a ball mill (MM 400, Retsch, Hahn, Germany) and pressed into pellets at 80 kN without applying binding agents (TP 40, Herzog Maschinenfabrik, Osnabrück, Germany).

**LIBS measurement procedure.**The pellets were measured using an echelle spectrometer (Aryelle Butterfly, LTB, Berlin, Germany). This lab benchtop (Lab) spectrometer has two separate measurement ranges: the UV and VIS spectral regimes. The VIS range was used in this work and covers the range from 278 to 769 nm with a resolution between 25 and 60 pm. An iCCD camera (iStar, Andor Technology, Belfast, UK) was used as detector. Five laser shots were accumulated. Apart from the lab benchtop instrument a spectrometer to be potentially used on a sensor platform and a handheld (HH) spectrometer were applied. The HH instrument has a detection range of 190–950 nm and is equipped with a laser of 1064 nm at ca. 6 mJ. Here, the samples are measured in an 8 × 8 grid (64 shots over 1 mm

^{2}surface area) at a frequency of 10 Hz. For the sensor platform, a multichannel CMOS spectrometer (AvaSpec Mini 2048CL, Avantes B.V., Apeldoorn, The Netherlands), that is further referred to as platform (PF) spectrometer as well as a handheld Spectrometer (HH; Z-300, SciAps, Woburn, MA, USA) for single-point measurements, were used. The PF spectrometer consists of four modules with wavelength ranges of 210–328 nm, 325–476 nm, 473–700 nm, and 695–890 nm, respectively. The laser (Bernoulli LIBS 150-25, Litron Lasers, Warwickshire, UK) used for the measurements in the Lab and the PF spectrometer emits radiation at a wavelength of 1064 nm, with a repetition rate of 25 Hz, a pulse duration of 10 ns and pulse energy attenuated to 40 mJ. The pellets were rotated and linearly translated during measurements on a sample holder forming a spiral-like trace of ablation events. Thus, each spectrum is measured on a new point of the pellet. A total of 200 spectra were recorded per sample in the VIS range. Emissions were collected via a CC52 Collector/Collimator (Andor Technology, Belfast, UK), coupled into an optical fiber, and guided to the Lab or PF spectrometer. Optimization of LIBS spectra acquired using the Lab spectrometer led to the following measurement parameters: a detection delay of 2 µs, a measurement window of 10 µs, as well as a constant amplification factor of the iCCD camera of 2000.

#### 2.4. Data Analysis

**Data preparation.**The following procedure of spectra preparation was applied. First, the remaining background, which is still formed by the continuous radiation after a delay of 2 µs, was removed. This procedure is based on the top-hat filter and was implemented in Matlab (imtophat function, square as structure element). Then, all spectra were normalized via standard normal variate (SNV) normalization. Finally, all spectra within one sample (pellet) were averaged. In order to identify any existing outliers in the data set, the robust principal components analysis (ROBPCA) method of Hubert et al. [26] was applied.

**Feature selection.**As mentioned in the introduction, high-resolution Lab, PF, and HH spectra consist of 37,633; 7744; and 7810 data points and contain redundant information (e.g., noise). The methods tested for feature selection are CARS and PCA. Additionally, a very simple method, referred to as threshold method in this work, cuts parts of the full spectrum below a selected threshold. The remaining part of the spectrum above the threshold is then used for regression.

**Competitive adaptive reweighted sampling (CARS).**The CARS algorithm is computationally intensive and consists of 4 steps that are iteratively carried out [25]. In the first step, the samples for a PLS model are randomly selected. PLS is carried out and a normalized weight for evaluating the importance of each wavelength is calculated. In the second step, the number of wavelengths is reduced sequentially using an exponentially decreasing function. In the third step, adaptive reweighted sampling is employed to eliminate the wavelengths in a competitive way. This step considers the calculated weights in step 1. In the fourth step, the RMSECV is calculated. After N sampling runs, N subsets of wavelengths and the corresponding RMSECV are obtained. In the final step, the subset with the lowest RMSECV is selected. The RMSECV-Monte Carlo sampling number curve often has several local minima, in addition to the global minimum, which are representing different-sized subsets of wavelengths. CARS often generates very compact feature sets compared to other feature selection methods.

**Principal component analysis**. The PCA algorithm will find a linear combination of the given wavelengths (features) with the highest variance and set it as the first PCA component. The subsequent components are found by looking for the highest variance linear combination in the subspace orthogonal to their previous components. As a result, uncorrelated linear projections of the original data are obtained. In PCA, to overcome the under- and over-fitting of the regression model with the resulting components, the largest variance criteria together with the heuristic approach called elbow method are applied. That way, a point in the explained variance plot is found, after which only diminishing returns are obtained. Those were neglected for further analysis since the corresponding components do not carry additional, meaningful information.

**Multivariate methods.**Four multivariate methods, namely PLS, Lasso, GP, and SVM regression, were used for obtaining calibration models.

**PLS**regression, which has often been described in detail, is widely applied in the LIBS community and can be regarded as a reference method.

**Lasso**is a linear regression method that constrains the coefficient estimates and shrinks those that do not significantly contribute to the correlation to zero. This enables a robust linear regression and a simplified interpretation of the coefficients. In this work, the number of coefficients was always reduced to the number necessary for an error one standard deviation above the minimum (one standard error, 1SE). In addition to these two linear approaches, two non-linear regression methods were also used. Popular non-linear regression methods are SVM and GP regression. In contrast to PLS and Lasso regression,

**GP**regression is a nonparametric and kernel-based Bayesian approach. It is a local regression approach, which uses a kernel for weighting neighboring observations in the estimation. Compared to other kernel methods, such as splines and support vector machines, GP regression is slower but yields properly tuned probabilistic outputs and is sometimes more robust and flexible. An additional benefit of GP regression is its good suitability for small datasets.

**SVM**regression is also considered a nonparametric technique because it relies on kernel functions similar to GP regression. SVM regression tries to find an appropriate line (or hyperplane in higher dimensions) to fit the data. The algorithm uses margins that are controlled by a hyperparameter ε. The aim is to fit as many instances as possible inside the margins while limiting margin violations. For any value that falls outside of the margins, its deviation from the margin can be described by slack variables. These are part of the objective function that will be minimized. Nonlinear regression tasks will be solved using a kernelized SVM model. One of the main advantages of SVM regression is that its computational complexity does not depend on the dimensionality of the input space. Additionally, it has an excellent generalization capability with high prediction accuracy. All methods were implemented in Matlab (Version 2020a, MathWorks, Natick, MA, USA). PLS regression was based on plsregress, Lasso regression on lasso, GP regression on fitrgp, and SVM regression on fitrsvm. All functions are included in Matlab’s Statistics and Machine Learning Toolbox.

**Validation.**Different validation procedures were tested. All multivariate methods were 10-fold cross-validated. The determination of the RMSECV and the coefficients of determination is based on this 10-fold cross-validation. Additionally, the data were randomly split into a 70% training (N

_{train}= 48) and a 30% test (unseen data, N

_{test}= 20) data set using the cvpartition function in Matlab. The test data were not used for the feature selection methods and training of the multivariate model. Furthermore, stratified sampling was used for validation that reduces the variance by constraining a proportion of the samples to specific subsets of the sample space (percentiles of the specific soil parameter).

**Interpretability.**Especially for the determination of soil pH, soil texture, and SOM content, the influence of the individual lines (elements) and the identification of the most important lines is interesting. Two metrics were used to identify these lines: the PLS weights and the variable importance for the projection (VIP) score. The PLS weights are part of the PLS result, and the weights of the first principal components were considered. The VIP score attributes each wavelength (feature) a measure of its contribution to the PLS regression. The VIP value [27] is defined in Equation (1) as follows:

_{jf}as the weight value for the wavelength j and the component f, SSY

_{f}as the sum of squares of explained variance for the fth component, J as the number of wavelengths, SSY

_{total}as the total sum of squares of explained variance, and F as the total number of components. The VIP values reflect how important the information of each wavelength is for the PLS regression. There is an arbitrary threshold, which is often selected as 1.

## 3. Results

#### 3.1. Determination of Soil Parameters

**Total contents of metal macronutrients.**The metal macronutrients K, Ca, and Mg belong to the alkali and alkaline earth metals, which can be sensitively detected in the laser-induced plasma. The three elements have their strongest lines in the wavelength range of the Lab spectrometer between 278.4 and 768.9 nm (Ca: 393.36 nm, K: 766.5 nm, Mg: 279.56 nm). The concentration range of the three nutrients is between 0.44 and 1.96 w%. The median of the total nutrient contents increases from 0.59 w% for Ca over 0.65 w% for Mg to 1.71 w% for K. Ca has the greatest variation in the total contents at 86% compared to Mg at 63% and K at 60% (all range 90%). Multivariate regression of the total high-resolution spectra yields good results. The coefficients of determination for cross-validation are 0.80 (for Mg), 0.86 (for Ca), and 0.92 (for K), and for the validation between 0.79 (for Mg) and 0.92 (for K). The order of the coefficients of determination correlates well with, on the one hand, the median and, on the other hand, the variation of the concentration range of the nutrients. K has the largest median, and Ca has the largest concentration range with a comparable median to Mg. LIBS, in combination with multivariate regression, should allow for a good to excellent quantitative determination of the metal macronutrients (Figure 1).

**Total contents of non-metal macronutrients.**Nitrogen and phosphorous are essential, non-metal plant macronutrients, and their content and dynamics in soil depend largely on biological processes. The two elements are difficult to detect within the wavelength range of the echelle spectrometer. Although they have a few lines in this range, their line strengths are weak. The most intense lines are outside of the wavelength range of the spectrometer. Both elements can be detected preferentially in the vacuum ultraviolet (VUV) range. Alternatively, phosphorus can be detected at 213.62 nm. The significantly lower concentration compared to Mg, Ca and K makes their detection even more difficult. The median of N content, 0.13 w%, is slightly larger than the median of P content, 0.09 w%. In contrast, the variation of the P contents with 106% is larger than that of N with 48%. Accordingly, the coefficients of determination for PLS regression of the entire spectra are lower in comparison to the metal nutrients. These vary from R

^{2}= 0.71 for N (smaller variation) to R

^{2}= 0.82 for P (for validation).

**Total contents of metal micronutrients.**From an agricultural perspective, Zn, Mn, Cu, and Fe are micronutrients, but their total contents in soil differ strongly. While the median of the Fe content is high (3.51 w%), the other three elements are considered trace elements and have, thus, much lower medians. But their medians also vary strongly. Mn has the highest median (0.1 w%). The medians of Zn (0.01 w%) and Cu (0.003 w%) are much lower. For the three trace elements, the variation of the total contents increases with decreasing median: Mn (102%), Zn (167%), and Cu (200%). Compared to the metal macronutrients, these four elements have their most intense lines outside of the wavelength range of the spectrometer: 200–215 nm for Zn, 257–261 nm for Mn, 198–225 nm for Cu, and 233–275 nm for Fe. The lines inside the wavelength range of the spectrometer are much weaker for Zn and Fe. In contrast, Cu and Mn have sufficiently strong lines. Despite the significantly lower concentrations compared to the macronutrients and the fact that the most intense lines are outside of the wavelength range of the spectrometer, the coefficients of determination are similar. They vary between R

^{2}= 0.85 for Mn, R

^{2}= 0.76 for Zn, R

^{2}= 0.87 for Cu, and R

^{2}= 0.92 for Fe (validation).

**Additional soil parameters.**For agricultural purposes, further soil properties are relevant, such as soil pH, SOM content, and soil texture (silt and clay content). Though, their determination via LIBS is challenging because they cannot be measured directly. They are based on correlations to certain elements, which are often unknown and difficult to determine. For example, in the case of pH that may be the Ca content, as demonstrated earlier [9,20]. The challenge in measuring SOM content is generally due to the presence of both organic and inorganic carbon in the soil, and the fact that the carbon lines are outside the measurement range of the echelle spectrometer. In Bölingen, the determination of organic carbon is somewhat easier since no inorganic carbon is present here. Soil texture is characterized in this work by determining the clay and silt fractions (Figure 2). The characterization of the clay fraction, for example, is based on the correlation to the elements Al, Fe, and K via LIBS.

^{2}= 0.57). This rather weak result allows only to distinguish between high and low values. In a preliminary study, much better results (R

^{2}> 0.9) were obtained for the soil pH; yet, the pH variation at the Wilmersdorf field [9] is much larger than at Bölingen, where the pH variation is 1.15 pH units (range 90%). This can explain the poorer regression result. In the case of the determination of the SOM content (R

^{2}= 0.71), approximate quantitative predictions are possible. The regression results are slightly better than for the Wilmersdorf measurements (R

^{2}= 0.58). This can be explained by the higher SOM content in Bölingen (median: 2.4 vs. 1.8 w%) and the larger variation in clay content because, in general, SOM tends to show a correlation to clay content. In contrast, LIBS is much better suited for the characterization of soil texture. PLS of the total spectra yields good coefficients of determination for the clay (R

^{2}= 0.91) and the silt content (R

^{2}= 0.88). This result corresponds to the inorganic character of clay and silt, which are, to a large extent, built up by elements within the LIBS spectra (i.e., Ca, Mg, K, Fe, Mn).

#### 3.2. Matrix Influence

**Principal component analysis (PCA).**To obtain an impression of the spectroscopic homogeneity of the soil of the field in Bölingen, the samples from there were compared with samples from two other fields via PCA, which originate from geographically distant areas with different geopedological settings. The red dots in the score plot (Figure 3) of the first two principal components belong to the field in Bölingen. Their area is very small. In contrast, the areas of the fields near Wilmersdorf (green dots) and Booßen (blue dots) are much larger. This illustrates that the field in Bölingen consists of a spectroscopically relatively homogeneous matrix.

**Wavelength influence on regression.**It is interesting to know which wavelengths, in particular, contribute to the regression model. In PLS regression, this can be achieved by calculating the PLS weights or using the variable importance in projection (VIP) scores. In the case of determining the total element contents, the question is which lines, in particular, contribute to the regression. This can help to estimate to what extent the regression is sensitive, e.g., line superpositions by other elements. In the case of the determination of soil parameters such as soil pH, SOM content, or clay content, which can only be determined indirectly, the identification of elements that are important for the determination of these soil parameters is of outstanding interest. In addition, indications of soil chemical or soil physical relationships can potentially be obtained. A further aspect is a deeper characterization of the matrix effect. This includes the identification of matrix elements that directly affect the regression model.

^{2+}(Figure 4d).

#### 3.3. Different Aspects of Measurement and Data Analysis

**Comparison of different spectrometers.**Precision agriculture requires on-field measurements. These can include single-point measurements using a robust and less expensive handheld spectrometer, but also much faster measurements on a sensor platform allowing the spatially resolved mapping of soil parameters on whole fields. To obtain an impression of the performance of potential LIB spectrometers for these application profiles, two instruments (HH and PF spectrometer) were characterized in comparison to a high-resolution Lab instrument. The main differences between the spectrometers with respect to LIBS measurements are the resolution and sensitivity of the spectrometers and the pulse energy of the excitation laser. For example, the resolution of the lab benchtop spectrometer is 20–30 pm, while the other two instruments have resolutions of 100–250 pm. Pulse energies vary from 6 mJ for the HH spectrometer to 40 mJ in the case of the Lab and PF spectrometers. The instruments also differ in other parameters, such as costs, size, weight, robustness, and measurement speed. We take as a metric of comparison the figures of merit of the regression models (in this case the coefficients of determination) for the different soil parameters. The results are summarized in Table 2.

^{2}on the level of the handheld spectrometer. The strongest degradation of R

^{2}is observed for the soil parameter pH. The strength of the Lab spectrometer lies in the better detection of the non-metallic nutrients (N, P) and the soil parameters SOM, pH, silt, and clay. Since the main difference between the HH and PF spectrometers is the resolution, the separation of the different lines seems to be of great importance.

**Comparison of regression methods.**In order to identify and eliminate any existing outliers in the data set, the robust principal components analysis (ROBPCA) method of Hubert et al. [26] was applied. As a result, an outlier map (Figure 6) was obtained, which allows for the detection of any existing outliers. Here, the orthogonal distance is plotted against the score distance. The two upper quadrants contain the potential outliers, the so-called bad leverage points, and the orthogonal outliers. In particular, the orthogonal outliers should be removed.

^{2}(CV) = 0.79), PCR (R

^{2}(CV) = 0.76), SVM (R

^{2}(CV) = 0.74), and GP (R

^{2}(CV) = 0.79). The correlation between full spectra and concentrations seems to be linear, with some exceptions. This assumption is based on the observation that PLS, as a linear regression method, as well as GP, as a non-linear regression method, yield similar results. Exceptions were Mg, P, and N, where GP regression achieves better results than the linear regression methods PLS and PCR. This is also reflected in the better coefficients of determination of all macronutrients. Here, GP regression yields slightly better results on average than PLS, PCR, and SVM regression. This suggests that GP regression is slightly better at dealing with complex data, which contains noise and non-informative data points.

**Feature selection.**The combination of only 68 labeled soil samples and 37,633 features (Lab spectrometer) is a challenging regression task. Feature selection methods can overcome this problem by removing non-informative wavelengths, which only contribute to noise. This also improves the interpretability of the regression models. In this work, different feature selection methods based on different algorithms are applied, such as PCA, CARS, and Lasso. In addition to the methods mentioned above, a very simple method, referred to as the threshold method in this work, cuts parts of the full spectrum below a selected threshold. The remaining part of the spectrum above the threshold is then used for PLS regression. A systematic increase in the threshold reduces the size of the spectra and, of course, reduces the information available. The results of the PLS regression of the determination of Ca contents after feature reduction using the threshold method are shown in Figure 7 for different sizes of spectra. As the size of the spectra decreases, a maximum of the coefficients of determination is first reached, which transitions to a plateau and only declines sharply when the number of features is very small.

^{2}= 0.76 of full spectra to an average of R

^{2}= 0.77 of both PCA-reduced spectra and R

^{2}= 0.80 of CARS-reduced spectra. A closer look shows that CARS, in particular, improves the determination of Mg, P, and the soil pH. In most cases, similar results are obtained via PCA and CARS with greatly reduced data size. Furthermore, it is noteworthy that both PCA-reduced spectra, regardless of the different sizes, yield almost equal results.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Villas-Boas, P.R.; Franco, M.A.; Martin-Neto, L.; Gollany, H.T.; Milori, D.M.B.P. Applications of laser-induced breakdown spectroscopy for soil analysis, part I: Review of fundamentals and chemical and physical properties. Eur. J. Soil. Sci.
**2019**, 71, 789–804. [Google Scholar] [CrossRef] - Heggemann, T.; Welp, G.; Amelung, W.; Angst, G.; Franz, S.O.; Koszinski, S.; Schmidt, K.; Pätzold, S. Proximal gamma-ray spectrometry for site-independent in situ prediction of soil texture on ten heterogeneous fields in Germany using support vector machines. Soil Tillage Res.
**2017**, 168, 99–109. [Google Scholar] [CrossRef] - Gebbers, R.; Lück, E.; Dabas, M.; Domsch, H. Comparison of instruments for geoelectrical soil mapping at the field scale. Near Surf. Geophys.
**2009**, 7, 179–190. [Google Scholar] [CrossRef] - Adamchuk, V.I.; Morgan, M.T.; Ess, D.R. An Automated Sampling System for Measuring Soil pH. Trans. ASAE
**1999**, 42, 885–892. [Google Scholar] [CrossRef] - Botto, A.; Campanella, B.; Legnaioli, S.; Lezzerini, M.; Lorenzetti, G.; Pagnotta, S.; Poggialini, F.; Palleschi, V. Applications of laser-induced breakdown spectroscopy in cultural heritage and archaeology: A critical review. J. Anal. At. Spectrom.
**2019**, 34, 81–103. [Google Scholar] [CrossRef] - Cremers, D.A.; Chinni, R.C. Laser-Induced Breakdown Spectroscopy—Capabilities and Limitations. Appl. Spectrosc. Rev.
**2009**, 44, 457–506. [Google Scholar] [CrossRef] - Hahn, D.W.; Omenetto, N. Laser-induced breakdown spectroscopy (LIBS), part II: Review of instrumental and methodological approaches to material analysis and applications to different fields. Appl. Spectrosc.
**2012**, 66, 347–419. [Google Scholar] [CrossRef] - Zorov, N.B.; Popov, A.M.; Zaytsev, S.M.; Labutin, T.A. Qualitative and quantitative analysis of environmental samples by laser-induced breakdown spectrometry. Russ. Chem. Rev.
**2015**, 84, 1021–1050. [Google Scholar] [CrossRef] - Erler, A.; Riebe, D.; Beitz, T.; Löhmannsröben, H.-G.; Gebbers, R. Soil Nutrient Detection for Precision Agriculture Using Handheld Laser-Induced Breakdown Spectroscopy (LIBS) and Multivariate Regression Methods (PLSR, Lasso and GPR). Sensors
**2020**, 20, 418. [Google Scholar] [CrossRef] [Green Version] - Riebe, D.; Erler, A.; Brinkmann, P.; Beitz, T.; Löhmannsröben, H.-G.; Gebbers, R. Comparison of Calibration Approaches in Laser-Induced Breakdown Spectroscopy for Proximal Soil Sensing in Precision Agriculture. Sensors
**2019**, 19, 5244. [Google Scholar] [CrossRef] [Green Version] - Rühlmann, M.; Büchele, D.; Ostermann, M.; Bald, I.; Schmid, T. Challenges in the quantification of nutrients in soils using laser-induced breakdown spectroscopy—A case study with calcium. Spectrochim. Acta Part B At. Spectrosc.
**2018**, 146, 115–121. [Google Scholar] [CrossRef] - Villas-Boas, P.R.; Franco, M.A.; Martin-Neto, L.; Gollany, H.T.; Milori, D.M.B.P. Applications of laser-induced breakdown spectroscopy for soil characterization, part II: Review of elemental analysis and soil classification. Eur. J. Soil Sci.
**2020**, 71, 805–818. [Google Scholar] [CrossRef] - Nicolodelli, G.; Cabral, J.; Menegatti, C.R.; Marangoni, B.; Senesi, G.S. Recent advances and future trends in LIBS applications to agricultural materials and their food derivatives: An overview of developments in the last decade (2010–2019). Part I. Soils and fertilizers. TrAC Trends Anal. Chem.
**2019**, 115, 70–82. [Google Scholar] [CrossRef] - Díaz, D.; Hahn, D.W.; Molina, A. Evaluation of Laser-Induced Breakdown Spectroscopy (LIBS) as a Measurement Technique for Evaluation of Total Elemental Concentration in Soils. Appl. Spectrosc.
**2012**, 66, 99–106. [Google Scholar] [CrossRef] - Nicolodelli, G.; Senesi, G.S.; de Oliveira Perazzoli, I.L.; Marangoni, B.S.; de Melo Benites, V.; Milori, D.M.B.P. Double pulse laser induced breakdown spectroscopy: A potential tool for the analysis of contaminants and macro/micronutrients in organic mineral fertilizers. Sci. Total Environ.
**2016**, 565, 1116–1123. [Google Scholar] [CrossRef] - El Haddad, J.; Villot-Kadri, M.; Ismaël, A.; Gallou, G.; Michel, K.; Bruyère, D.; Laperche, V.; Canioni, L.; Bousquet, B. Artificial neural network for on-site quantitative analysis of soils using laser induced breakdown spectroscopy. Spectrochim. Acta Part B At. Spectrosc.
**2013**, 79–80, 51–57. [Google Scholar] [CrossRef] [Green Version] - Guo, G.; Niu, G.; Shi, Q.; Lin, Q.; Di, T.; Duan, Y. Multi-element quantitative analysis of soils by laser induced breakdown spectroscopy (LIBS) coupled with univariate and multivariate regression methods. Anal. Methods
**2019**, 11, 3006–3013. [Google Scholar] [CrossRef] - Ebinger, M.H.; Norfleet, M.L.; Breshears, D.D.; Cremers, D.A.; Ferris, M.J.; Unkefer, P.J.; Lamb, M.S.; Goddard, K.L.; Meyer, C.W. Extending the Applicability of Laser-Induced Breakdown Spectroscopy for Total Soil Carbon Measurement. Soil Sci. Soc. Am. J.
**2003**, 67, 1616–1619. [Google Scholar] [CrossRef] - Martin, M.Z.; Mayes, M.A.; Heal, K.R.; Brice, D.J.; Wullschleger, S.D. Investigation of laser-induced breakdown spectroscopy and multivariate analysis for differentiating inorganic and organic C in a variety of soils. Spectrochim. Acta Part B At. Spectrosc.
**2013**, 87, 100–107. [Google Scholar] [CrossRef] - Ferreira, E.C.; Gomes Neto, J.A.; Milori, D.M.; Ferreira, E.J.; Anzano, J.M. Laser-induced breakdown spectroscopy: Extending its application to soil pH measurements. Spectrochim. Acta Part B At. Spectrosc.
**2015**, 110, 96–99. [Google Scholar] [CrossRef] [Green Version] - Villas-Boas, P.R.; Romano, R.A.; de Menezes Franco, M.A.; Ferreira, E.C.; Ferreira, E.J.; Crestana, S.; Milori, D.M.B.P. Laser-induced breakdown spectroscopy to determine soil texture: A fast analytical technique. Geoderma
**2016**, 263, 195–202. [Google Scholar] [CrossRef] [Green Version] - Knadel, M.; Gislum, R.; Hermansen, C.; Peng, Y.; Moldrup, P.; de Jonge, L.W.; Greve, M.H. Comparing predictive ability of laser-induced breakdown spectroscopy to visible near-infrared spectroscopy for soil property determination. Biosyst. Eng.
**2017**, 156, 157–172. [Google Scholar] [CrossRef] - Xu, X.; Du, C.; Ma, F.; Shen, Y.; Zhou, J. Fast and Simultaneous Determination of Soil Properties Using Laser-Induced Breakdown Spectroscopy (LIBS): A Case Study of Typical Farmland Soils in China. Soil Syst.
**2019**, 3, 66. [Google Scholar] [CrossRef] [Green Version] - Dyar, M.D.; Carmosino, M.L.; Breves, E.A.; Ozanne, M.V.; Clegg, S.M.; Wiens, R.C. Comparison of partial least squares and lasso regression techniques as applied to laser-induced breakdown spectroscopy of geological samples. Spectrochim. Acta Part B At. Spectrosc.
**2012**, 70, 51–67. [Google Scholar] [CrossRef] - Li, H.; Liang, Y.; Xu, Q.; Cao, D. Key wavelengths screening using competitive adaptive reweighted sampling method for multivariate calibration. Anal. Chim. Acta
**2009**, 648, 77–84. [Google Scholar] [CrossRef] - Hubert, M.; Rousseeuw, P.J.; Vanden Branden, K. ROBPCA: A New Approach to Robust Principal Component Analysis. Technometrics
**2005**, 47, 64–79. [Google Scholar] [CrossRef] - Andersen, C.M.; Bro, R. Variable selection in regression-a tutorial. J. Chemom.
**2010**, 24, 728–737. [Google Scholar] [CrossRef]

**Figure 1.**Correlation of predicted contents (LIBS) and total contents obtained via reference analysis (WDXRF) of (

**left**) K and (

**right**) Ca; GP regression of full echelle spectra, values in w%.

**Figure 2.**Correlation of measured (reference analysis) and predicted (LIBS) silt (

**left**) and clay (

**right**) contents, GPR of full echelle spectra, values in %.

**Figure 3.**(

**left**) PCA of three different agricultural fields which are situated in different geological landscapes of Germany and represent different soil parent materials; (

**right**) averaged point-to-point distance for the corresponding fields calculated in N-dimensional PC space. All distances were normalized to the maximum value of the set.

**Figure 4.**Weights of PLS regression of (

**a**) Ca content, (

**b**) soil pH, (

**c**) clay content, and (

**d**) humus content.

**Figure 6.**Outlier map obtained via the robust principal components analysis (ROBPCA) method [26].

**Figure 7.**Effect of feature reduction using the threshold method on the coefficient of determination for the Ca prediction via GP regression.

**Table 1.**Soil parameters and descriptive statistics (median, interquartile range (IQR), range between 95th and 5th percentile, which includes 90% of all sample points, all in w%, except pH) as well as an overview of coefficients of determination (R

^{2}) and RMSECV for various soil parameters, which are the result of the regression of predicted contents (LIBS, lab spectrometer, 40 mJ) and contents obtained via reference analysis (WDXRF and lab soil analysis). Results of the best regression method. (SP: soil parameters, CV: cross-validation, Val: validation (70/30)).

SP | Method | Median | IQR | Range (90%) | R^{2} (CV) | R^{2} (Val) | RMSECV | RMSEV |
---|---|---|---|---|---|---|---|---|

Ca | GP | 0.59 | 0.21 | 0.50 | 0.86 | 0.86 | 0.0645 | 0.0775 |

Mg | GP | 0.65 | 0.16 | 0.41 | 0.80 | 0.79 | 0.0561 | 0.0602 |

K | GP | 1.71 | 0.43 | 1.02 | 0.92 | 0.92 | 0.0901 | 0.0655 |

P | GP | 0.09 | 0.04 | 0.10 | 0.77 | 0.82 | 0.0174 | 0.0184 |

N | GP | 0.13 | 0.02 | 0.06 | 0.62 | 0.71 | 0.0118 | 0.011 |

Fe | GP | 3.51 | 1.71 | 4.52 | 0.93 | 0.92 | 0.3489 | 0.431 |

Mn | PLS | 0.10 | 0.04 | 0.10 | 0.79 | 0.77 | 0.0189 | 0.0203 |

Zn | PLS | 0.01 | 0.01 | 0.02 | 0.87 | 0.84 | 0.0018 | 0.002 |

Cu | PLS | 0.003 | 0.002 | 0.006 | 0.87 | 0.85 | 6.62 × 10^{−4} | 7.11 × 10^{−4} |

SOM | GP | 2.39 | 0.57 | 1.43 | 0.67 | 0.71 | 0.2583 | 0.227 |

pH | GP | 6.07 | 0.27 | 1.15 | 0.54 | 0.57 | 0.2203 | 0.2343 |

Silt | GP | 58.57 | 12.34 | 28.43 | 0.83 | 0.89 | 3.4688 | 3.1757 |

Clay | GP | 26.51 | 11.86 | 28.84 | 0.91 | 0.91 | 2.6018 | 3.0933 |

**Table 2.**Comparison of different spectrometers and plasma excitation conditions by coefficients of determination (R

^{2}(CV)), which are the result of the regression between predicted contents (LIBS) and contents obtained via reference analysis (WDXRF and lab soil analysis). HH: handheld spectrometer, Lab: lab benchtop spectrometer, PF: platform spectrometer, laser excitation energies in mJ, ML method: GP regression.

Soil Parameter | HH | Lab/10 mJ | Lab/40 mJ | PF/25 mJ | PF/40 mJ |
---|---|---|---|---|---|

R^{2} (CV) | |||||

Ca | 0.85 | 0.74 | 0.86 | 0.91 | 0.95 |

K | 0.96 | 0.92 | 0.92 | 0.86 | 0.95 |

Mg | 0.88 | 0.60 | 0.79 | 0.89 | 0.84 |

P | 0.69 | 0.63 | 0.82 | 0.75 | 0.62 |

N | 0.59 | 0.64 | 0.71 | 0.30 | 0.59 |

Mn | 0.69 | 0.68 | 0.77 | 0.40 | 0.94 |

Fe | 0.94 | 0.87 | 0.92 | 0.87 | 0.88 |

SOM | 0.55 | 0.63 | 0.71 | 0.65 | 0.35 |

soil pH | −0.06 | 0.10 | 0.57 | 0.31 | 0.55 |

silt | 0.86 | 0.84 | 0.89 | 0.85 | 0.83 |

clay | 0.83 | 0.86 | 0.91 | 0.93 | 0.94 |

**Table 3.**Comparison of the regression methods PLS, PCR, SVM, and GP for different soil parameters (Lab spectrometer).

PLS | PCR | SVM | GP | |||||
---|---|---|---|---|---|---|---|---|

Soil Parameter | R^{2} (CV) | R^{2} (Val) | R^{2} (CV) | R^{2} (Val) | R^{2} (CV) | R^{2} (Val) | R^{2} (CV) | R^{2} (Val) |

Ca | 0.86 | 0.84 | 0.82 | 0.82 | 0.82 | 0.82 | 0.86 | 0.86 |

K | 0.92 | 0.91 | 0.92 | 0.93 | 0.91 | 0.93 | 0.92 | 0.92 |

Mg | 0.77 | 0.74 | 0.74 | 0.76 | 0.74 | 0.76 | 0.8 | 0.79 |

P | 0.72 | 0.69 | 0.71 | 0.71 | 0.73 | 0.73 | 0.77 | 0.82 |

N | 0.49 | 0.48 | 0.55 | 0.68 | 0.64 | 0.7 | 0.67 | 0.75 |

Cu | 0.87 | 0.87 | 0.87 | 0.86 | 0.65 | 0.56 | 0.81 | 0.76 |

Mn | 0.81 | 0.85 | 0.72 | 0.78 | 0.72 | 0.85 | 0.72 | 0.76 |

Zn | 0.85 | 0.76 | 0.82 | 0.69 | 0.58 | 0.59 | 0.82 | 0.66 |

Fe | 0.93 | 0.98 | 0.93 | 0.92 | 0.93 | 0.92 | 0.93 | 0.92 |

Humus | 0.64 | 0.62 | 0.63 | 0.69 | 0.62 | 0.74 | 0.67 | 0.71 |

pH | 0.54 | 0.39 | 0.48 | 0.52 | 0.52 | 0.49 | 0.54 | 0.57 |

Silt | 0.88 | 0.86 | 0.83 | 0.88 | 0.84 | 0.89 | 0.83 | 0.89 |

Clay | 0.93 | 0.9 | 0.92 | 0.89 | 0.92 | 0.9 | 0.91 | 0.91 |

Mean (K, Ca, Mg) | 0.85 | 0.83 | 0.83 | 0.84 | 0.82 | 0.84 | 0.86 | 0.86 |

Mean (MN) | 0.75 | 0.73 | 0.75 | 0.78 | 0.77 | 0.79 | 0.80 | 0.83 |

Mean (TN) | 0.87 | 0.87 | 0.84 | 0.81 | 0.72 | 0.73 | 0.82 | 0.78 |

Mean (SP) | 0.75 | 0.69 | 0.72 | 0.75 | 0.73 | 0.76 | 0.74 | 0.77 |

Mean | 0.79 | 0.76 | 0.76 | 0.78 | 0.74 | 0.76 | 0.79 | 0.79 |

**Table 4.**Comparison of different feature reduction methods for determination of soil parameters (SP), PLS as regression method and reference, Lab spectrometer.

SP | Method | Features | R^{2} (CV) | R^{2} (Val) | SP | Method | Features | R^{2} (CV) | R^{2} (Val) |
---|---|---|---|---|---|---|---|---|---|

Ca | PLS | 37,633 | 0.86 | 0.84 | N | PLS | 37,633 | 0.49 | 0.48 |

PCA | 242 | 0.87 | 0.85 | PCA | 242 | 0.58 | 0.56 | ||

PCA | 17 | 0.86 | 0.84 | PCA | 17 | 0.57 | 0.56 | ||

CARS | 1012/61 | 0.80 | 0.84 | CARS | 5/8 | 0.56 | 0.64 | ||

Lasso | 14 | 0.65 | Lasso | 36 | 0.44 | ||||

Mg | PLS | 37,633 | 0.77 | 0.74 | SOM | PLS | 37,633 | 0.64 | 0.62 |

PCA | 242 | 0.80 | 0.78 | PCA | 242 | 0.65 | 0.65 | ||

PCA | 17 | 0.79 | 0.76 | PCA | 17 | 0.65 | 0.65 | ||

CARS | 22/61 | 0.90 | 0.80 | CARS | 12/7 | 0.64 | 0.69 | ||

Lasso | 9 | 0.53 | Lasso | 12 | 0.46 | ||||

K | PLS | 37,633 | 0.92 | 0.91 | Silt | PLS | 37,633 | 0.88 | 0.86 |

PCA | 242 | 0.93 | 0.92 | PCA | 242 | 0.87 | 0.87 | ||

PCA | 17 | 0.92 | 0.91 | PCA | 17 | 0.87 | 0.85 | ||

CARS | 7/61 | 0.93 | 0.96 | CARS | 7/453 | 0.89 | 0.90 | ||

Lasso | 21 | 0.83 | Lasso | 13 | 0.73 | ||||

P | PLS | 37,633 | 0.72 | 0.69 | Clay | PLS | 37,633 | 0.93 | 0.90 |

PCA | 242 | 0.72 | 0.68 | PCA | 242 | 0.93 | 0.91 | ||

PCA | 17 | 0.72 | 0.61 | PCA | 17 | 0.92 | 0.90 | ||

CARS | 6172/4130 | 0.75 | 0.75 | CARS | 7545/22 | 0.92 | 0.91 | ||

Lasso | 11 | 0.40 | Lasso | 8 | 0.81 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Erler, A.; Riebe, D.; Beitz, T.; Löhmannsröben, H.-G.; Leenen, M.; Pätzold, S.; Ostermann, M.; Wójcik, M.
Mobile Laser-Induced Breakdown Spectroscopy for Future Application in Precision Agriculture—A Case Study. *Sensors* **2023**, *23*, 7178.
https://doi.org/10.3390/s23167178

**AMA Style**

Erler A, Riebe D, Beitz T, Löhmannsröben H-G, Leenen M, Pätzold S, Ostermann M, Wójcik M.
Mobile Laser-Induced Breakdown Spectroscopy for Future Application in Precision Agriculture—A Case Study. *Sensors*. 2023; 23(16):7178.
https://doi.org/10.3390/s23167178

**Chicago/Turabian Style**

Erler, Alexander, Daniel Riebe, Toralf Beitz, Hans-Gerd Löhmannsröben, Mathias Leenen, Stefan Pätzold, Markus Ostermann, and Michal Wójcik.
2023. "Mobile Laser-Induced Breakdown Spectroscopy for Future Application in Precision Agriculture—A Case Study" *Sensors* 23, no. 16: 7178.
https://doi.org/10.3390/s23167178