The most common types of analysis performed using LIBS spectra are qualitative classification and quantification. A typical LIBS spectrum is made up of multiple emission lines primarily due to atomic species. The specific wavelength of the atomic emission line corresponds to a particular element. Most elements have multiple emission lines: iron for example has hundreds. Fig. 2 shows the LIBS spectrum of a stainless steel standard reference material (SRM 1155). Multiple atomic emission lines of iron are present, as well as chromium and nickel. The nitrogen and oxygen atomic emission lines are due to the surrounding atmosphere. These can be eliminated by blowing a bath gas across the surface if desired. In the inset, we focus on a small section of the spectrum from 335 – 375 nm that contains multiple atomic emission lines due to iron, nickel, and chromium. LIBS used in conjunction with broadband detectors (ultraviolet [UV] – visible [VIS] – near-infrared [NIR] spectral range) can determine the elemental composition of any target material since every element on the periodic table has characteristic atomic emission lines in the UV-VIS-NIR spectral range. Therefore, an elemental inventory can be obtained of any sample of interest using a LIBS spectrum. Beyond tabulating the elements present in a sample, the intensity of an atomic emission line can be correlated to the amount of the material present in the sample. LIBS has been used in numerous quantification studies for steel^{[55], [56] and [57]}, aluminum alloys^{58[60], [61] and [62]}, bronze^{[6] and [63]}, ceramics¹⁰, surface mapping^{[13] and [64]}, and many more applications. In general, limits of detection (LOD) for LIBS are in the parts per million (ppm) range. However, the LOD value of a given element will depend on experimental parameters such as laser energy, surrounding matrix, and the experimental setup. Reported LODs in the literature are intrinsically related to the particular application and experimental apparatus described in the article.

There are several difficulties associated with the collection and analysis of LIBS spectra. Even though the experimental setup of a LIBS system is relatively simple, the non-linear processes underlying the formation of the microplasma are highly complex. Therefore, the shot-to-shot variation is an inherent issue with all LIBS experiments due to the laser material interaction. The properties of the material being interrogated by the laser will influence the LIBS signal due to matrix effects. In addition, if the material is heterogeneous, the microplasma will sample regions in the material with different compositions. Identifying molecular compounds with similar elemental composition is also difficult since LIBS is fundamentally an elemental technique. Some molecular information, such as relative stoichiometries, can be determined from relative atomic peak emission intensities, but it is not a straightforward analysis⁶⁵. In addition, each LIBS experimental setup is intrinsically tied to the application for which it is designed. The data analysis method must be revisited if the experimental setup or application is altered. LIBS is a versatile tool for materials analysis, capable of providing large amounts of data quickly using a relatively simple experimental setup. However, obtaining useful information and analyzing that information requires careful experimentation and an understanding of the underlying system being investigated.

Analysis of LIBS spectra using multivariate analysis

High-resolution, broadband LIBS spectra can contain as many as 100 000 variables as seen in the LIBS spectrum of stainless steel shown in Fig. 2. These variables include atomic emission lines, ionic emission lines, molecular bands, and background emission. Depending on the application, multiple spectral regions may need to be analyzed simultaneously. The ability to quickly process all of the data in a useful manner is a challenge. Multivariate analysis is a technique used to reduce or compress the spectral data into fewer combinations of variables that still retain the essential information describing the data set^{[66], [67] and [68]}. Furthermore, the essential information must then be extracted in a manner that can be easily displayed. The coupling of LIBS spectral data with multivariate analysis techniques has been a major advance for LIBS analysis of materials over the past decade. The increase in LIBS publications using multivariate techniques over the last few years is shown in Fig. 3. The use of multivariate analysis with LIBS for data analysis includes quantitative analysis and classification.

One of the earliest combinations of LIBS with a multivariate technique utilized a principal components regression (PCR) calibration model to determine detection limits of trace heavy metals in soils, sands, and sewage sludge⁶⁹. Another early study used neural networks to classify polymers based on nine spectral regions of interest in the LIBS spectra⁷. Multivariate techniques for classification and quantification have been used for a variety of LIBS material analysis applications. Amador-Hernandez et al. used principal components analysis (PCA)⁷⁰ to obtain sample composition plots of screen-printed electrodes⁷¹. Another classification technique, soft independent modeling of class analogy (SIMCA)⁷², was used to differentiate between bacterial spores, molds, pollens, and nerve agent simulants⁷³. Partial least squares discriminant analysis (PLS-DA)⁷⁴ was used to test the feasibility of classifying rocks based on LIBS spectra for eventual use on the Mars Science Laboratory rover⁷⁵. LIBS spectral data was used for the multivariate calibration technique partial least squares (PLS) regression in order to quantify the amount of gold and silver in gold-silver-copper alloys⁷⁶. In addition to trace heavy metal analysis, PCR has been used to measure the composition of iron ore samples⁷⁷.

At the US Army Research Laboratory (ARL), we have primarily used the multivariate techniques PCA,⁷⁰ SIMCA,⁷² and PLS-DA⁷⁴ to classify hazardous materials such as explosives, biological and chemical weapon simulants^{[73], [78], [79], [80], [81], [82] and [83]}. PCA is an unsupervised multivariate technique that compresses large data sets in order to extract useful information by finding combinations of variables that describe major trends in the data. The large data set is reduced to weighted sums of the original variables. These weighted sums, or scores, are used to describe variations in the data. Since PCA is unsupervised, it seeks to describe the overall variation in the data. This may not be useful for differentiating between different classes of samples. Therefore classification techniques such as SIMCA and PLS-DA are more useful for describing data sets that consist of many measurements of several samples or classes. A SIMCA model consists of a collection of PCA models. Each PCA model within the SIMCA model describes a particular sample type or class from the data set. SIMCA incorporates the properties of PCA models with information about the types of classes incorporated in the sample data set. The SIMCA model is then used to determine the nearest class for unknown test samples. For material analysis performed at ARL, we have found that PLS-DA offers the best classification results⁸³. PLS-DA is a supervised, inverse least-squares discrimination method used to classify samples. In PLS-DA, the predictor variables or latent variables (LV) are generated from the input variables to determine the maximum variance between each sample class, unlike other techniques such as PCA and SIMCA. PLS-DA maximizes the inter-class variance while minimizing the intra-class variance. For LIBS this is important due to the inherent shot-to-shot variability. If the variance in shot-to-shot variability approaches the inter-class variance, then unsupervised techniques like PCA will not be able to separate the different samples. The PLS-DA model calculates the probability that a test sample belongs to a particular class in the model. Parameters that will influence model performance include the chosen spectral regions of interest, the types of samples in a class, the number of classes, and the number of latent variables. It is important to determine the variables that most contribute to the separation between classes in the model. This will assure that the separation is due to the physical or chemical properties of the underlying system. Further iterative testing with independent test sets are needed to optimize the model.

At ARL, we have used LIBS to qualitatively analyze a wide variety of materials. We have analyzed metals to determine the trace impurities in aluminum alloys, the composition of steel parts, and solder compositions. We have used LIBS to analyze thermoplastic polymers⁸⁴, painted surfaces⁸⁴, and plastic land mine casings^{[85] and [86]}. In this paper, we will focus in detail on implementation of multivariate analysis to characterize and classify geomaterials and explosive materials at ARL. Even though we are focusing on two types of material of interest to ARL, the methods we describe can be applied to all types of material classification applications with LIBS.

Materials analysis at ARL

Geomaterials

Using LIBS to analyze geomaterials at ARL began with the desire to detect lead contamination in soil from military installations³³. The potential of LIBS as a field portable instrument for in situ geochemical analysis has been explored^{[19] and [87]}. More recently, LIBS spectra were collected from a wide variety of geomaterials, including garnet samples collected worldwide⁸⁸, obsidian samples from the southwestern United States⁸⁹, and a survey of carbonates, fluorites, silicate rocks, and soils⁴⁰. In general, all of the geomaterials analyzed with PLS-DA and LIBS were classified correctly by the most optimized multivariate model.

The garnet samples consisted of six different types that could be discriminated based on their composition. Interestingly LIBS demonstrated promise for identifying the geographic origin of garnets of the same type. Broadband spectra of each garnet type were used as variable inputs for the PLS-DA models⁸⁸. It was assumed that the PLS-DA model would use the emission wavelengths that were most capable of separating the six garnet types. Subsequent analysis of the model using variable importance in projection (VIP) scores confirmed this assumption. The VIP scores are used to determine how much each variable in a model contributes to the separation between the classes. Generally, a variable with a VIP score greater than 1.0 is important to a model^{[66] and [90]}. In addition, to determine what variables are influencing the classification in a particular model, the variables that do contribute to classification should have physical meaning for the system being investigated. The VIP scores from the composition model and the origin models are displayed in Fig. 4. In this case, the major variables that contribute to classification correspond to the expected chemical properties. For the classification of the six garnet types based on composition, atomic spectral intensities due to the major elements in each garnet composition (Ca, Mg, Al, Fe, Mn, Cr) were responsible for the separation between the classes. For origin determination, atomic spectral intensities from contaminants and impurities (Na, K, Li, H), likely associated with surrounding environment, were largely responsible for the separation. The variables that most influence classification are dependent on how the samples are classified in a particular multivariate model. In this case, we observe the most influential variables for the model based on composition classification differs from the most influential variables for the models based on geographical origin classification.

The obsidian samples were collected from multiple sites at the Coso Volcanic Field (CVF) in California and single sites at four other locations

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