Improving the Signal-to-Noise Ratio of Atomic Transition Peaks in LIBS Using Two-dimensional Correlation Analysis

In this stu dy, two dimensional ( 2D correlation analysis wa s utilized for achieving a significant improvement in the signal to noise (S/N) ratio of laser induced breakdown spectroscopy (LIBS) data . Time resolved LIBS spectra of metallic, bimetal lic targets and the normal LIBS spectra of bimetallic targets with varying compositions were used for the detailed analysis . The diagonal of the matrix in the synchronous spectra was used to demonstrate the improvement in the S/N ratio. An improvemen t in the peak intensities by few order s of magnitude accompanied by suppression in the noise was observed. The correlations between LIBS peaks were also visualized using 2 D plots. Correlation strengths of atomic transitions were visualized in Aluminum (Al), Copper (Cu), and Brass whereas correlation strengths of atomic, atomic, and ionic transitions were visualized in Au Ag bimetallic targets with different compositions (Au30Ag70, Au50Ag50, Au80 Ag20). The improved spectra were subsequently used in the principal component analysis for classification studies of four compositions of bimetallic targets Au20Ag80, Au30Ag70, Au50 Ag50, and Au80Ag20 The variance of the first three principal components were found to be improved from the analysis. The accumulated percentage of explained variance of 95 was achieved with the first three components from improved spectra whereas only ~ 80 was achieved with the regular LIBS spectra from PCA studies


Introduction:
Laser induced breakdown spectroscopy (LIBS) analysis employs the spectral emissions from the plasma formed when intense laser pulses are focused on to the sample. 1 Typical LIBS spectra consist of ionic, atomic, and molecular transitions. 2 LIBS technique has the ability to identify individual elements in any material. Furthermore, the information in the varying intensities with different composition of elements coupled with machine learning techniques can be used for classification and identification of samples. Because of its versatile nature, being quick and minimal sample preparation requirements, LIBS found fantastic applications in diverse fields such as bacteria classification [3][4][5] , to geological materials 6 in planetary exploration, minerals, 7 archelogy, 8,9 explosive detection, 10,11 , trace element detection, 12,13 in the study of historic paintings, 14 and in the study of fundamental plasma properties. 15 This technique also found diverse applications because of its suitability to combine with Raman spectroscopy 16,17 to be able to operate easily in double-pulse and/or stand-off mode 18 . The advantage of signal enhancement using nanoparticles 19 and adopting the new trends in machine learning for the LIBS data analysis makes it a powerful tool for different application scenarios. The LIBS spectra of organic materials and few metals contain molecular emissions along with atomic and ionic emissions. [20][21][22] These molecular emissions can be used to understand the material's properties. 23,24 Two-dimensional correlation spectroscopy (2DCOS) was initially developed by Noda et al.. 25 This technique was primarily used to analyze the data from nuclear magnetic resonance (NMR), near-infrared (NIR), and Raman spectroscopy. [25][26][27][28] The resolution of the spectrum was shown to be improved with the 2D spectroscopy. 29 The simultaneous variations or coupling between the two spectral emissions with a small perturbation in the system can be studied. Better interpretation capabilities can be achieved when compared to regular spectra from the shapes and strengths in the 2D correlation plot. 30 Here we have used it to visualize and interpret the correlations in the atomic transitions of Aluminium, Copper, Brass, and a bimetallic target of Au-Ag.
2D correlation technique has been applied to the nanosecond (ns) LIBS data of Aluminium, Copper, Brass, and Au-Ag bimetallic targets. We have demonstrated the 2D correlation spectroscopy application on time-resolved and composition varying LIBS spectra. The analysis can be visualized using two-dimensional contour plots. The strength of the points on diagonal points of the two-dimensional plot represents the self-correlation (or the auto correlation) of the peaks. It provides the information on the time correlation of a particular peak intensity with itself. The strength of the off-diagonal points represents the time correlation of the peak intensity with other peaks. Similarly, the 2D analysis on the spectra with varying concentrations offer information on the auto correlation and cross correlation with composition. Apart from visualization this analysis could also be used in improving the resolution and signal-to-noise ratio (SNR) of the spectrum.
Our detailed analysis confirmed that at least 3-4 orders of magnitude improvement in the signal-to-noise (SNR) of the LIBS data can be achieved using this technique. It is pertinent to note from the collected data/analysis performed that the observed improvements were (a) not limited to few peaks or (b) was not random and it was observed on the complete LIBS spectrum. We have also demonstrated that improved spectra can further be used for improving the classification capabilities (here we used the PCA analysis). This can find impending applications in stand-off LIBS case where the SNR is generally very poor. The perturbation has been achieved by changing the acquisition time and composition of the material. Though this technique has been well established in the improvement/analysis of NMR and IR data we have demonstrated this for the first time using nanosecond LIBS data, to the best of our knowledge.
We have also discussed few prospective applications in the conclusions section. Where ̃( , ) is the averaged spectra used as reference in the calculation of the dynamic spectra. The reference spectra can be either first spectrum or last spectrum of the time resolved spectra and it can also be set to zero as well. 30 The reference spectrum is set to zero in our studies.
The synchronous ( 1 , 2 )and asynchronous ( 1 , 2 )correlation spectra are written as Where ̃is the spectral intensity at a point of variable Spectra were measured with the perturbation in the system of interest like varying magnetic field, electrical field, thermal, chemical, optical, mechanical, or the system varying with time.
The analysis divulges the similarities and dissimilarities in the spectra. Correlation analysis was applied on the time varying metal, bimetallic targets, and composition varying bimetallic targets LIBS spectra. The correlations with systematic variations would be easy to interpret after the two-dimensional (2D) spectroscopy. The resulting similarity spectra is called synchronous and dissimilarity spectra as asynchronous 2D spectra, which are complementary to each other. The asynchronous spectra in this case of study were discarded since they did not contain considerable variations. Figure

Results and Discussion
Four different reference spectra were tried for the analysis as shown in figure 3(a) with the first spectrum (from the time series spectra). Hence, 2D synchronous plots can be used to recover weak signal from a noisy background. As shown in figure 4, the linear spectra along the diagonal of matrix in the 2D analysis were considered to demonstrate the improvement in the signal.

Correlation Studies
The 2D correlation spectra of the LIBS have wavelength as both X-axis and Y-axis. The peaks on the diagonal represent the autocorrelation of the peak called auto-peaks and the off-diagonal peaks correspond to the correlation with the other peaks at the particular wavelength and are called cross-peaks. Python was used for the analysis and in the calculation of the synchronous and asynchronous spectra from the dynamic spectra with the average spectra taken as zero. The shape of the contour refers to the homogeneity of the peak broadening while circular contours indicate homogeneous broadening and elliptical contours indicate inhomogeneous broadening.
The noise in the 2D spectra was suppressed as the randomly varying noise does not have correlations with varying time but the signal with correlation is enhanced thus improving the signal to noise ratio in the 2D plots. Figure  variance only with the first 3 components whereas in the case of regular spectra with noise it took more than 5 components to get 80%, which is much lower compared to earlier number.
The SNR of the spectra improved enormously in the case of the intense peaks in regular spectra and the highly correlated peaks with them. The correlation between the atomic peaks in to report that our initial correlation analysis on the standoff LIBS data of polymers 18 has also provided enhancements in the SNR. Further detailed analysis is pending and will be reported elsewhere.
We summarize the important results from this work and suggestions for future works: • These studies will provide a better understanding of the molecular peaks and their coupling, especially in the femtosecond LIBS spectra. For example, the molecular emissions such as CN, C2, AlO, TiO in the LIBS spectra could add more insights to the LIBS analysis.
• We believe that 2DCOS studies combined with time-resolved LIBS spectra or other perturbation methods would result in better resolution with the same spectrometer, due to the spreading of data over a second dimension, improved resolution and SNR from which overlapped peaks can be distinguished, which are not possible otherwise.
• The same studies can be performed/repeated with other perturbations such as changing ICCD gain, gate delays, input laser energy, the distance at which the emissions are collected, compositions, etc. to get an improved understanding of the transitions and enhancements.
• In the case of the stand-off LIBS the SNR deteriorates as compared to nearfield case and this method can be used for improving it, especially in the case of explosives detection. 18,36,37 Conflicts of interest: The authors declare no conflicts of interest.      Fig. 1(a) Schematic of the nanosecond LIBS experimental setup used for metals, alloys, and bimetallic targets.
(b) Fig. 1(b) The steps followed in data acquisition and data preparation for the analysis.   The regular LIBS spectra of (a) Aluminium target in the spectral range of 303-312 nm and the corresponding (b) 2D correlation spectra and (c) diagonal of the 2D correlation analysis of the LIBS spectra is plotted.  Time-resolved LIBS spectra of (a) Au30Ag70, (b) Au50Ag50, (c) Au80Ag20 bimetallic targets at five different gate delays with regular interval of 1microsecond is used for the 2D correlation studies on the time-resolved spectra of (d) Au30Ag70, (e) Au50Ag50, (f) Au80Ag20 targets, respectively.