Chemometrics and Numerical Methods in LIBS

A practical guide to the application of chemometric methods to solve qualitative and quantitative problems in LIBS analyses

Chemometrics and Numerical Methods in LIBS, delivers an authoritative and practical exploration of the use of advanced chemometric methods to laser-induced breakdown spectroscopy (LIBS) cases. The book discusses the fundamentals of chemometrics before moving on to solutions that can be applied to data analysis methods. It is a concise guide designed to help readers at all levels of knowledge solve commonly encountered problems in the field.

The book includes three sections: LIBS information simplification, LIBS classification, and quantitative analysis by LIBS. Each section of the book is divided into a description of relevant techniques and practical examples of its applications. Contributors to this edited volume are the most recognized international experts on the chemometric techniques relevant to LIBS analysis.

Chemometrics and Numerical Methods in LIBS also includes:

• A thorough introduction to the simplification of LIBS information, including principal component analysis, independent component analysis, and parallel factor analysis
• Comprehensive explorations of classification by LIBS, including spectral angle mapping, linear discriminant analysis, graph clustering, self-organizing maps, and artifical neural networks
• Practical discussions of linear methods for quantitative analysis by LIBS, including calibration curves, partial least squares regression, and limit of detection
• In-depth examinations of multivariate analysis and non-linear methods, including calibration-free LIBS, the non-linear Kalman filter, artificial and convolutional neural networks for quantification

Relevant for researchers and PhD students seeking practical information on the application of advanced statistical methods to the analysis of LIBS spectra, Chemometrics and Numerical Methods in LIBS will also earn a place in the libraries of students taking courses involving LIBS spectro-analytical techniques

Vincenzo Palleschi is a Senior Researcher with the Institute of Chemistry of Organometallic Compounds, Italian Research Council and Professor of Advanced Analytical Chemistry at the University of Pisa. He is Associate Editor of the Journal of Advanced Research and a member of the Editorial Advisory Boards of Spectrochimica Acta B and Reviews in Analytical Chemistry. He has published more than 140 scientific papers on LIBS, making him the most productive author in LIBS ever. His paper on Calibration-Free LIBS, published in 1999, is the most quoted research paper in LIBS. In 2000 he was the organizer and chairperson of the First International Conference on LIBS in Pisa (Italy).

List of Contributors xiii

Preface xvii

Introduction and Brief Summary of the LIBS Development 1

Part I Introduction to LIBS 5

1 LIBS Fundamentals 7
Mohamad Sabsabi

1.1 Interaction of Laser Beam with Matter 8

1.2 Basics of Laser–Matter Interaction 9

1.3 Processes in Laser-Produced Plasma 10

1.4 Factors Affecting Laser Ablation and Laser-Induced Plasma Formation 11

1.4.1 Influence of Laser Parameters on the Laser-Induced Plasmas 11

1.4.2 Laser Wavelength (λ) 12

1.4.3 Laser Pulse Duration (τ) 12

1.4.4 Laser Energy (E) 13

1.4.5 Influence of Ambient Gas 13

1.5 Plasma Properties and Plasma Emission Spectra 14

References 15

2 LIBS Instrumentations 19
Mohamad Sabsabi and Vincenzo Palleschi

2.1 Basics of LIBS instrumentations 19

2.2 Lasers in LIBS Systems 20

2.3 Desirable Requirements for Atomic Emission Spectrometers/Detectors 22

2.4 Spectrometers 23

2.4.1 Czerny–Turner Optical Configuration 23

2.4.2 Paschen–Runge Design 24

2.4.3 Echelle Spectrometer Configuration 25

2.5 Detectors 26

2.5.1 Photomultiplier Detectors 26

2.5.2 Solid-State Detectors 27

2.5.3 The Interline CCD Detectors 27

2.5.3.1 The Image Intensifier 28

References 29

3 Applications of LIBS 31
Vincenzo Palleschi and Mohamad Sabsabi

3.1 Industrial Applications 31

3.1.1 Metal Industry 31

3.1.2 Energy Production 34

3.2 Biomedical Applications 34

3.3 Geological and Environmental Applications 36

3.4 Cultural Heritage and Archaeology Applications 37

3.5 Other Applications 37

References 38

Part II Simplications of LIBS Information 45

4 LIBS Spectral Treatment 47
Sabrina Messaoud Aberkane, Noureddine Melikechi and Kenza Yahiaoui

4.1 Introduction 47

4.2 Baseline Correction 47

4.2.1 Polynomial Algorithm 48

4.2.2 Model-free Algorithm 49

4.2.3 Wavelet Transform Model 52

4.3 Noise Filtering 55

4.3.1 Wavelet Threshold De-noising (WTD) 55

4.3.2 Baseline Correction and Noise Filtering 59

4.4 Overlapping Peak Resolution 60

4.4.1 Curve Fitting Method 61

4.4.2 The Wavelet Transform 64

4.5 Features Selection 66

4.5.1 Principal Component Analysis 68

4.5.2 Genetic Algorithm (GA) 68

4.5.3 Wavelet Transformation (WT) 68

References 71

5 Principal Component Analysis 81
Mohamed Abdel-Harith and Zienab Abdel-Salam

5.1 Introduction 81

5.1.1 Laser-Induced Breakdown Spectroscopy (LIBS) 81

5.2 The Principal Component Analysis (PCA) 82

5.3 PCA in Some LIBS Applications 83

5.3.1 Geochemical Applications 83

5.3.2 Food and Feed Applications 85

5.3.3 Microbiological Applications 88

5.3.4 Forensic Applications 91

5.4 Conclusion 94

References 94

6 Time-Dependent Spectral Analysis 97
Fausto Bredice, Ivan Urbina, and Vincenzo Palleschi

6.1 Introduction 97

6.2 Time-Dependent LIBS Spectral Analysis 98

6.2.1 Independent Component Analysis 98

6.2.2 3D Boltzmann Plot 102

6.2.2.1 Principles of the Method 103

6.3 Applications 109

6.3.1 3D Boltzmann Plot Coupled with Independent Component Analysis 109

6.3.2 Analysis of a Carbon Plasma by 3D Boltzmann Plot Method 109

6.3.3 Assessment of the LTE Condition Through the 3D Boltzmann Plot Method 114

6.3.4 Evaluation of Self-Absorption 114

6.3.5 Determination of Transition Probabilities 118

6.3.6 3D Boltzmann Plot and Calibration-free Laser-induced Breakdown Spectroscopy 121

6.4 Conclusion 123

References 123

Part III Classification by LIBS 127

7 Distance-based Method 129
Hua Li and Tianlong Zhang

7.1 Cluster Analysis 132

7.1.1 Introduction 132

7.1.2 Theory 133

7.1.2.1 K-means Clustering 133

7.1.2.2 Hierarchical Clustering 134

7.1.3 Application 135

7.2 Independent Components Analysis 138

7.2.1 Introduction 138

7.2.2 Theory 138

7.2.3 Application 140

7.3 K-Nearest Neighbor 143

7.3.1 Introduction 143

7.3.2 Theory 143

7.3.3 Application 145

7.4 Linear Discriminant Analysis 145

7.4.1 Introduction 145

7.4.2 Theory 148

7.4.2.1 The Calculation Process of LDA (Two Categories) 148

7.4.3 Application 151

7.5 Partial Least Squares Discriminant Analysis 153

7.5.1 Introduction 153

7.5.2 Theory 155

7.5.3 Application 157

7.6 Principal Component Analysis 161

7.6.1 Introduction 161

7.6.2 Theory 164

7.6.3 Application 166

7.7 Soft Independent Modeling of Class Analogy 174

7.7.1 Introduction 174

7.7.2 Theory 175

7.7.3 Application 177

7.8 Conclusion and Expectation 180

References 181

8 Blind Source Separation in LIBS 189
Anna Tonazzini, Emanuele Salerno, and Stefano Pagnotta

8.1 Introduction 189

8.2 Data Model 193

8.3 Analyzing LIBS Data via Blind Source Separation 193

8.3.1 Second-order BSS 193

8.3.2 Maximum Noise Fraction 194

8.3.3 Independent Component Analysis 196

8.3.4 ICA for Noisy Data 197

8.4 Numerical Examples 197

8.5 Final Remarks 206

References 207

9 Artificial Neural Networks for Classification 213
Jakub Vrábel, Erik Képeš, Pavel Pořízka, and Jozef Kaiser

9.1 Introduction and Scope 213

9.2 Artificial Neural Networks (ANNs) 214

9.3 Cost Functions and Training 216

9.4 Backpropagation 219

9.5 Convolutional Neural Networks 221

9.6 Evaluation and Tuning of ANNs 224

9.7 Regularization 227

9.8 State-of-the-art LIBS Classification Using ANNs 229

9.9 Summary 233

Acknowledgments 234

References 234

10 Data Fusion: LIBS + Raman 241
Beatrice Campanella and Stefano Legnaioli

10.1 Introduction 241

10.2 Data Fusion Background 242

10.3 Data Treatment 244

10.4 Working with Images 245

10.4.1 Vectors Concatenation 246

10.4.2 Vectors Co-addition 246

10.4.3 Vectors Outer Sum 246

10.4.4 Vectors Outer Product 247

10.4.5 Data Analysis 247

10.5 Applications 248

10.6 Conclusion 253

References 253

Part IV Quantitative Analysis 257

11 Univariate Linear Methods 259
Stefano Legnaioli, Asia Botto, Beatrice Campanella, Francesco Poggialini, Simona Raneri, and Vincenzo Palleschi

11.1 Standards 259

11.2 Matrix Effect 260

11.3 Normalization 261

11.4 Linear vs. Nonlinear Calibration Curves 264

11.5 Figures of Merit of a Calibration Curve 267

11.5.1 Coefficient of Determination 270

11.5.2 Root Mean Squared Error of Calibration 270

11.5.3 Limit of Detection 270

11.6 Inverse Calibration 273

11.7 Conclusion 274

References 274

12 Partial Least Squares 277
Zongyu Hou, Weiran Song, and Zhe Wang

12.1 Overview 277

12.2 Partial Least Squares Regression Algorithms 278

12.2.1 Nonlinear Iterative PLS 278

12.2.2 SIMPLS Algorithm 279

12.2.3 Kernel Partial Least Squares 279

12.2.4 Locally Weighted Partial Least Squares 280

12.2.5 Dominant Factor-based Partial Least Squares 281

12.3 Partial Least Squares Discriminant Analysis 282

12.4 Results of Partial Least Squares in LIBS 283

12.4.1 Coal Analysis 283

12.4.2 Metal Analysis 285

12.4.3 Rocks, Soils, and Minerals Analysis 285

12.4.4 Organics Analysis 291

12.5 Conclusion 291

References 295

13 Nonlinear Methods 303
Francesco Poggialini, Asia Botto, Beatrice Campanella, Stefano Legnaioli, Simona Raneri, and Vincenzo Palleschi

13.1 Introduction 303

13.2 Multivariate Nonlinear Algorithms 304

13.2.1 Artificial Neural Networks 304

13.2.1.1 Conventional Artificial Neural Networks 304

13.2.1.2 Convolutional Neural Networks 310

13.2.2 Other Nonlinear Multivariate Approaches 312

13.2.2.1 The Franzini–Leoni Method 312

13.2.2.2 The Kalman Filter Approach 313

13.2.2.3 Calibration-Free Methods 314

13.3 Conclusion 315

References 316

14 Laser Ablation-based Techniques – Data Fusion 321
Jhanis Gonzalez

14.1 Introduction 321

14.2 Data Fusion of Multiple Analytical Techniques 322

14.2.1 Low-level Fusion 322

14.2.2 Mid-level Fusion 323

14.2.3 High-level Fusion 324

14.3 Data Fusion of Laser Ablation-Based Techniques 324

14.3.1 Introduction 324

14.3.2 Classification of Edible Salts 326

14.3.2.1 LIBS and LA-ICP-MS Measurements of the Salt Samples 327

14.3.2.2 Mid-Level Data Fusion of LIBS and LA-ICP-MS of Salt Samples 327

14.3.2.3 PLS-DA Classification Model for Salt Samples 333

14.3.3 Coal Discrimination Analysis 334

14.3.3.1 LIBS and LA-ICP-TOF-MS Measurements of the Coal Samples 335

14.3.3.2 Mid-Level Data Fusion of LIBS and LA-ICP-TOF-MS of Coal Samples 335

14.3.3.3 PCA Combined with K-means Cluster Analysis for Coal Samples 338

14.3.3.4 PLS-DA and SVM for Coal Samples Analysis 340

14.4 Comments and Future Developments 341

Acknowledgments 343

References 343

Part V Conclusions 347

15 Conclusion 349
Vincenzo Palleschi

Index 351

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