# Arxive - Comparison of Baseline Correction Methods for LIBS Technique for
Total Carbon Quantification in Brazilian Soils

Comparison of Algorithms for Baseline Correction of LIBS Spectra for
Quantifying Total Carbon in Brazilian Soils

Marco Aurélio de Menezes Franco1,*, Débora Marcondes Bastos Pereira Milori2,
Paulino Ribeiro Villas Boas2,

1 Institute of Physics, University of São Paulo, São Paulo, SP, Brazil
2 Embrapa Instrumentation, São Carlos, SP, Brazil

*<EMAIL_ADDRESS>
## Abstract

LIBS is a promising and versatile technique for multi-element analysis that
usually takes less than a minute and requires minimal sample preparation and
no reagents. Despite the recent advances in elemental quantification, the LIBS
still faces issues regarding the baseline produced by background radiation,
which adds non-linear interference to the emission lines. In order to create a
calibration model to quantify elements using LIBS spectra, the baseline has to
be properly corrected. In this paper, we compared the performance of three
filters to remove random noise and five methods to correct the baseline of
LIBS spectra for the quantification of total carbon in soil samples. All
combinations of filters and methods were tested, and their parameters were
optimized to result in the best correlation between the corrected spectra and
the carbon content in a training sample set. Then all combinations with the
optimized parameters were compared with a separate test sample set. A
combination of Savitzky-Golay filter and 4S Peak Filling method resulted in
the best correction: Pearson’s correlation coefficient of 0.93 with root mean
square error of 0.21. The result was better than using a linear regression
model with the carbon emission line 193.04 nm (correlation of 0.91 with error
of 0.26). The procedure proposed here opens a new possibility to correct the
baseline of LIBS spectra and to create multivariate methods based on the a
given spectral range.

## Introduction

Laser-induced breakdown spectroscopy (LIBS) is a multi-element analytical
technique widely employed in the last years [3, 31, 8, 28, 13, 35] and has
great potential to be applied in field [14, 4, 9]. A LIBS measurement usually
takes less than a minute and can be remotely applied in hazardous areas or of
difficult access, for example, Mars, deep sea water, and radioactive or toxic
places [15, 30, 37, 2]. The LIBS also satisfies the precept of “green
chemistry”, in which no toxic residue is generated during the analytical
process, since the technique does not require chemical reagents [3, 34]. The
LIBS is also considered a promising technique for many applications, specially
for soil analysis ranging from the quantification of carbon [25], nutrients
[17] to contaminants [27]. Nonetheless, the technique suffers from a low
reproducibility and repeatability compared to other analytical techniques
(e.g. inductively coupled plasma - ICP), mainly due to matrix effects [23, 7,
33]. Such effects comprise the radiation-matter interaction, composition and
aggregation state of samples, homogeneity, laser pulse energy density, and
optical alignment. Each LIBS measurement, therefore, results in an unique
plasma formation, whose line emissions and background radiation depends on. To
overcome such difficulties, hundreds of LIBS measurements are generally
performed and averaged for each sample, and the delay time between the laser
shot and spectral acquisition is adjusted for the best signal to noise ratio
and for attenuating the background radiation. Even with the adjustment of
delay time, the background radiation is still present in the spectra, which
corresponds to the spectral baseline as in Figure 1, and imposes difficulties
for quantitative elemental analysis.

Figure 1: A example of LIBS spectrum without correction depicking a pronounced
irregular baseline. Seven distinct regions can be identified in this spectrum,
each one corresponding to a spectrometer.

A common solution for the background radiation issues in LIBS is to correct
the baseline by subtracting a straight line that connects the neighbourhood of
the emission line of interest [6]. Such solution is, however, limited to non-
interfered emission lines with a neighbourhood clearly belonging to the
baseline (without other emission lines). Furthermore, a proper automated
method for a broad spectral range has not been developed exclusively for LIBS.

Thus, the purpose of this work was to find a combination of random noise
filters and baseline correction methods that minimized the influence of the
background radiation over calibration models for quantifying soil carbon. We
compared the performance three filters: Low Pass [1], Median [16], and
Savitzky-Golay [32] to remove random noise; and five methods to correct the
baseline: Statistics-Sensitive Non-Linear Iterative Peak-Cliping (SNIP) [29,
24], Top Hat (TH) [36, 12], Median [12], Rolling Balls (RB) [18], and 4S Peak
Filling (PF) [20], which were developed for other photonic techniques such as
X ray, Raman, infrared and atomic mass spectroscopy. All combinations of
filters and baseline correction methods were optimized with a training soil
sample set to get the best correlation with the reference technique. Then all
optimized combinations were tested with a separated validation set. After the
filtering and the baseline correction, the corrected spectra were used as
input variables in the partial least square regression method, and the models
built were tested with 10-fold cross-validation. The results were given in the
Pearson’s correlation coefficient $\rho$ and the root mean square error (RMSE)
for each combination. The combinations were then ranked according to $\rho$.

##  1 Materials and methods

###  1.1 Samples and reference measures

All the soil samples used in this experiment were extracted from Canchim Farm,
São Carlos, Brazil. These soil samples were prepared to be used by drying the
samples, homogenizing them and transforming them in pellets by applying a
pressure of $8~{}\times~{}10^{8}~{}Nm^{-2}$ for approximately 30 seconds.
These samples were utilized by LIBS measures. For reference measures of carbon
in the soil samples, that were made in a Perkin-Elmer 2400 CHNS/O analyser,
the samples were milled into smaller particles which 0.15 mm, them they were
weighed inside a tin capsule and after placed at the analyzer.

###  1.2 LIBS spectroscopy

The LIBS measures were made with a LIBS2500+ spectrometer of the Ocean Optics,
Dunedin, USA, equipped with a pulsed Nd:YAG Q-switched $1064~{}nm$ produced by
Quantel (Big Sky Laser Ultra 50) and that works with $50mW$ of maximum energy
and $10Hz$ what is sufficient for plasma formation. The laser beam was focused
at the surface of the samples that were located inside an ablation chamber and
the plasma emission was collected by a collection of optical fibers connected
at seven spectrometers.

All the measures were taken in a presence of atmospheric air and the spectra
acquisition was made between $189-966~{}nm$ with optical resolution of
$0.1~{}nm$. O The spectrum generated by the emission of excited species was
analyzed in the regions UV-VIS-IP, but it’s important to notice that the X-ray
are also possible, depending of the incident laser energy on the sample. To
improve the precision of the results 60 spectra were captured for each soil
sample, where each spectra corresponds to a different place on the sample. The
experimental setup of the LIBS used to make the measures is shown at the
Figure 2.

Figure 2: Aparato experimental do sistema LIBS composto por laser, conjunto
óptico, câmera de ablação, conjunto de espectrômetros com sete fibras ópticas
e computador.

###  1.3 Spectral processing

####  1.3.1 Tradicional baseline correction

The method of traditional correction by three points [6], also known as a
heuristic method, consists of correct the baseline by subtracting the spectral
region around the peak of interest by the straight line which connects the
side of the peak . Thus, it is possible to obtain values for the height or the
peak area, from which are generated models of single or multivariable linear
regression. The height is the maximum intensity of the peak corrected, while
the area is the integral of the peak or the area of a fitted distribution
(e.g., Gaussian, Lorentzian or Voigt).

####  1.3.2 Noise suppression

Three signal smoothing filters were previously applied to the spectra, later
to be made automatic baseline correction. They are: Savitzky-Golay Filter
(SGF), Low Pass Filter (LPF) and Median Filter. The SGF smoothes the data,
increasing the signal to noise ratio without significantly distort the
signal.This is possible from a convolution of successive subsets of adjacent
data points with a polynomial using the method of linear least squares [32].
The LPF has been improved by the group through a Voight profile [26], which
attenuates noises greater than those related to a cutoff frequency. In this
way some parameters are adjusted, which are constituents of the convolution
function. Finally, there is the Median, that replaces each input element
(noise) by the median of the inputs of the neighbors, where the standard of
neighbors is called _window_ and moves by the full spectrum [16].

####  1.3.3 Automatic methods for baseline correction

The methods for baseline correction selected by visual inspection were SNIP,
TH, Median, RB and FP [10, 21, 24, 29, 36, 11, 20].The method SNIP
(Statistics-Sensitive Non-Linear Iterative Peak-Clipping) is an algorithm
developed to be applied in atomic mass spectroscopy, that was constructed in
three stages for obtaining the baseline, independently of the data acquisition
system. This is possible due to application of digital filter called _Low
Statistics_ , smoothes the spectrum in accordance with a small amount of
pixels per window. TP is a structured method from a Fourier transform of the
spectrum intensity, which extracts small elements and details of the spectrum
data that are more relevant than those of their proximity (noise) through a
sliding window, whose size is indicated by user.

The Median method is based on local averages calculations, where each spectral
point is replaced by the average of the neighbors. These averages are made,
for example, between the surrounding places of peaks or between noise regions,
all built in local windows, that is, given a series of numbers and a fixed
size subset, the first element of the moving average is obtained by taking the
average subset initially set by the user. Then, the subset is modified through
a window offset, creating new subset of numbers whose average is calculated
again.This process is repeated iterate times throughout the data set. RB is a
method developed originally for processing data of X-ray spectroscopy that was
built thinking in a sphere with fixed radius that is rolling under the
spectrum. Its trajectory creates a smoothed line that is used to extract the
baseline of the spectrum. And the last used method is called 4S Peak Filling,
PF, that is an iterative method based on suppression of baseline by averaging
local windows. For this purpose, the method requires as input the second
derivative for primary smoothing, which indicates that the baseline should be
monotonically decreasing, the average size of the data window, the number of
used windows and the number of iterations made in loop suppression of
baseline. In an established local window, the minimum of averages and
iterations is selected as the new baseline.

####  1.3.4 Calibration model

The method of multivariate regression by Partial Least Squares (PLS) was used
to construct a calibration model of the LIBS spectra for prediction of total
carbon in the samples. This method was used because it reduces the dimension
of the input variables and maximizing the correlation with the response
variable [22, 5]. With the established prediction model, was made the
validation of the results obtained with those of the reference method, which
gives the Pearson coefficients that measure the degree of correlation between
two variables. They are represented by $\rho$ and assumes values between $-1$
and $1$, where $\rho\geq 0.7$ indicates strong correlation, $0.3<\rho<0.7$
indicates moderate correlation and $\rho\leq 0.3$ corresponds to a weak
correlation between the results [19]. The most used value to quantify
differences between estimated values by the model and the reference measures
is the root mean square uncertainty (RMSE) of the correlation, which can be
estimated by the equation::

$RMSE=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}{(y_{i}-\hat{y}_{i})^{2}}},$ (1)

where $\hat{y}_{i}$ is the value estimated by the model for the $i$-th sample
and $n$ is the number of samples.

####  1.3.5 Analysis proceedings

The approach to the problem of determining the best baseline correction method
was as follows: the set of corrected spectra were obtained and divided into
two parts, $\frac{2}{3}$ of the total spectrum to build the PLS model and
optimization signal filter parameters and line correction method, and the rest
for test of the model.For the optimization was constructed a regression model
with the corrected spectra and the carbon content measured by the reference
method _CHNS_. The model validation occurred through cross-validation,
obtaining a value of $\rho$ and $\epsilon$, where $\rho$ corresponds to the
Pearson coefficient, and $\epsilon$ represents the uncertainty of the model
given in mass percentage of total carbon. This process was repeated iterated
times, and the values of $\rho$ were saved, so that the end of the iterative
process, $\bar{\rho}$ was calculated the the associated uncertainty. The
greatest value of $\bar{\rho}$ with the lowest $\epsilon$ was used as a
condition for determining the set of parameters. Thus, this set was applied to
the second set of spectra for building a regression model that was validated
by cross validation.

##  2 Results and discussions

The study was focused in the spectral range of $190-289nm$, corresponding to
the first equipment spectrometer. In this range there are two peaks of
interest for the study of total carbon in soil, which are located in
$193,04~{}nm$ and $247,86~{}nm$, respectively. However, that range has a high
degree of complexity as the determination of their corresponding baseline
because of the large amount of chemical species emitting radiation
simultaneously and strong presence of radiation at all wavelengths (white
radiation) caused mainly by thermal effect of the plasma. The Figure 3
represents the average of a LIBS spectrum of a sample without any treatment
and a hypothetical baseline that could correct the spectral range. In Figure
it is remarkable how much the continuum background radiation interferes on the
spectrum shape, making the baseline quite pronounced, particularly in regions
between 230 and 265$~{}nm$. It is important to notice that this spectral range
has many emissions due to different degrees of ionization of many chemical
species such as Fe, C, Al and Si.

Figure 3: Average spectrum from a soil sample without baseline correction and
its supposed baseline.

The traditional method for baseline corrections allows to correct only the
spectral range that contains the peak of interest of C in $193.04~{}nm$ and
fails when it is applied to other peak located at $247~{}nm$, since this peak
is surrounded by several other emission lines and it is not possible to find a
lateral region to the peak that is sufficient to correct their baseline. Thus,
it was built a linear model with the peak area $193.04~{}nm$ and carbon
concentrations, which returned $\bar{\rho}_{training}=0.92$ with
$\epsilon_{training}=0.24$ for the training set, and $\bar{\rho}_{test}=0.91$
with $\epsilon_{test}=0.26$ for the test set, where $\epsilon$ is the
uncertainty for the content total carbon.

The baseline correction methods PF, RB, TH, Median and SNIP were combined with
the smoothing filters Median, LPF and SGF and they were applied independently
for the treining and test sets . The optimized parameters of these
combinations are shown in Table 1 and Pearson coefficients for the cross-
validation of reference measurements and prediction model with its respective
uncertainty for percentage of total carbon are shown in Table 2.

Table 1: Set of optimized parameters through training set, applied to the test
set, with respect to baseline correction methods and noise smoothing filters.

Method | Filter | Filter Par. | $\lambda$ | $\beta$ | I | $\alpha$
---|---|---|---|---|---|---
SNIP | SGF | [O.P.,P.J.] = [8, 13] | - | - | 100 | -
| $LPF$ |  $\sigma=0.44$, $\gamma=10.25$ | - | - | 103 | -
| Median | N= 1 | - | - | 14 | -
TH | SGF | [O.P.,P.J.] = [8, 15] | - | 274 | - | -
| $LPF$ |  $\sigma=0.20$, $\gamma=4.6$ | - | 276 | - | -
| Median | N= 2 | - | 14 | - | -
Median | SGF | [O.P.,P.J.]= [1, 13] | - | 260 | - | -
| $LPF$ |  $\sigma=1.22$, $\gamma=16.22$ | - | 277 | - | -
| Median | N= 1 | - | 14 | - | -
RB | SGF | [O.P.,P.J.] = [6, 13] | - | [wn,ws] = [340, 30] | - | -
| $LPF$ |  $\sigma=0.43$, $\gamma=11$ | - | [wn,ws] = [374,47] | - | -
| Median | N= 3 | - | [wn,ws] = [340,30] | - | -
PF | SGF | [O.P.,P.J.] = [8, 13] | 3 | 10 | 9 | 70
| $LPF$ |  $\sigma=0.20$, $\gamma=4.6$ | 3 | 10 | 9 | 70
| Median | N= 2 | 3 | 10 | 9 | 70

O.P. = polynomial order
P.J. = Window points for smoothing
I = Number of iterations
N = Number of points for moving window Median filter
$\sigma$, $\gamma$ = Setting parameters of Voigh profile curve of the LPF
$\lambda$ = penalty parameter to the second derivative to primary smoothing,
according to [20]
$\alpha$ = Number of areas where spectrum is divided
$\beta$ = window number of points
wn = local window points to minimize / maximize
ws = local window points for smoothing

Table 2: Pearson Coeficient ($\bar{\rho}$) and RMSE($\epsilon$) to validate the model _PLS_ with relation to the various noise filter combinations and baseline correction method for training and test sets. Method | Filter | $\bar{\rho}_{treining}$ | $\epsilon_{treining}$ | $\bar{\rho}_{test}$ | $\epsilon_{test}$
---|---|---|---|---|---
SNIP | SGF | 0,96 | 0.17 | 0.92 | 0.21
| $LPF$ | 0.95 | 0.17 | 0.91 | 0.23
| Median | 0.95 | 0.19 | 0.93 | 0.21
TH | SGF | 0.96 | 0.17 | 0.93 | 0.20
| $LPF$ | 0.96 | 0.18 | 0.92 | 0.21
| Median | 0.96 | 0.19 | 0.88 | 0.26
Median | SGF | 0.97 | 0.16 | 0.92 | 0.21
| $LPF$ | 0.96 | 0.18 | 0.92 | 0.22
| Median | 0.94 | 0.22 | 0.90 | 0.24
RB | SGF | 0.95 | 0.19 | 0,93 | 0,20
| $LPF$ | 0.95 | 0.19 | 0.92 | 0.21
| Median | 0.95 | 0.19 | 0.92 | 0.21
PF | SGF | 0.96 | 0.17 | 0.93 | 0.21
| $LPF$ | 0.95 | 0.19 | 0.91 | 0.22
| Median | 0.95 | 0.20 | 0.91 | 0.23
Traditional |  | 0.92 | 0.24 | 0.91 | 0.26

The SNIP method was able to correct the spectra, without significantly deform
peaks of interest and returned apreciable results for $\bar{\rho}$ when it was
applied together to SGF. Complicated ranges such as those between $230$ to
$265~{}nm$ showed a smooth baseline, as it were expected. However, this did
not happen when SNIP was applied with Median and LPF. In those cases, the
baseline was overestimated and many peaks were deformed, as well as the whole
spectrum shape. So, it is impossible to analyse carbon or other chemical
species with these data treatments. The best result obtained for the
combination method-filter SNIP-SGF. resulted in $\bar{\rho}_{training}=0.96$
with $\epsilon_{training}=0.17$ for the training set, and
$\bar{\rho}_{test}=0.92$ with $\epsilon_{test}=0.21$ for the test set.

The spectra corrected by combinations of those three smoothing filters with
the TH method had issues with determining an useful baseline, because it used
some spectrum points that were not expected belonging to the baseline. With
this, all calculated baselines were overestimated, even if there is high
correlation between calibration and reference model. The same issue was
observed when the procedure previously discussed was applied to the Median
method. All method-filter combinations result in spectra with many peaks whose
baseline was overestimated, what returned spectra with peaks with negative
values for relative intensity. This therefore shows that combinations of the
method Median with those three types of smoothing filter is also inadequate
for the treatment of LIBS spectra.

When RB was combined with those smoothing filters good results was obtained
for the baseline when the peaks are not belonging to spectral ranges in which
there are a lot of emissions ($230$ to $265~{}nm$). However, the method fails
to estimate a baseline for transition regions between points with few
emissions and those with many emissions. Even so, the method returned
appreciable results for correlation, with $\bar{\rho}_{training}=0.95$ and
$\epsilon_{training}=0.19$ for training set and $\bar{\rho}_{test}=0,93$ com
$\epsilon_{test}=0,20$ for test set for the combination RB - SGF.

The PF method presented the best results for correction of LIBS spectra,
especially with high Pearson coefficients for all smoothing filter
combinations. The combination that stood out the most was the one that used
SGF. In this case, the peaks were fairly defined and all spectral regions were
corrected satisfactorily. This can means that the corrections did not
compromise spectral information that could lead to errors in predicting
carbon. The model constructed with the training set obtained the following
results: $\bar{\rho}_{training}=0.96$ with $\epsilon_{training}=0.17$, and for
the test set: $\bar{\rho}_{test}=0.93$ with $\epsilon_{test}=0.21$. The
combination of _4S Peak Filling_ with Median filter also returned relevant
results and its PLS model obtained a good prediction for the total carbon
concentration, which was not achieved through LPF, since the spectra were
distorted by degree of smoothing. Figure 4 shows the corrected spectra of a
sample for each PF/smoothing filter combination.

Figure 4: Spectra corrected by the 4S Peak Filling method for three different
smoothing filters.

The baseline correction through the traditional method achieves a good result
when the peak in question is relatively isolated from other peaks, with free
lateral regions, so that a straight line connecting them can be constructed.
In the case of the peak of carbon 193.04 nm, this one is interfered with by
aluminum, even so, the method was able to satisfactorily solve these peaks by
bilorentzian deconvolution, calculate the area of the peak of the carbon and
construct multivariate model with this value . However, such a method is only
useful in relatively unpopulated regions of emission lines, which is not so
common to be found in LIBS spectra. And this completely restricts application
of the traditional method.

The use of the smoothing filters was of fundamental importance in the
definition of the peak shapes of the different chemical species and in the
noise removal, which generates greater precision in the quantification of
total carbon of the samples. In particular, the SGF was able to satisfactorily
model the spectra for all methods. The principle of this filter is to find a
polynomial function of degree $n$ that fits the spectrum and its different
spectral regions, be they the most complex as found between 230 and 265 nm.
The black spectrum of Figure 4 represents the combination of PF-SGF, in which
the power of correction of this technique can be verified. In the problematic
region cited, the baseline found was fairly smooth, as can be seen in Figure
5.

Figure 5: Baseline estimated by the 4S Peak Filling method for the spectral
region between 193.04 nm and 247.86 nm.

##  3 Conclusions

This study aimed to compare different baseline correction methods with the
purpose of application to correct LIBS spectra, since the literature is very
poor in alternatives to those who seek an effective correction for this type
of spectroscopy. The SNIP, Top Hat, Median, 4S Peak Filling and Rolling Balls
methods were evaluated in combination with the LPF, SGF and Median noise
filters, and compared to the traditional baseline correction method to find
the best path for data processing for the LIBS spectra that maximized carbon
quantification.

For each method combined with the filters and also for the traditional method
PLS models were constructed with cross validation and their results for the
training and test sets were compared. Each method was optimized to improve the
correlation between LIBS spectra and carbon concentration in the samples. Some
filters combined with baseline correction methods distorted the spectrum, thus
compromising the definition of peaks and, consequently, making it impossible
to quantify chemical elements. Others of them have significantly improved the
spectrum format, emphasizing spectral regions that were not well understood
before. Smoothing filters have been able to define important peaks for
quantification of different chemical species, especially carbon.

It should be noted that the Peak Filling 4S method, which combined with the
Savitzky-Golay polynomial noise filter, returned the Pearson coefficient
$\bar{\rho_{test}}=0.93$ and RMSE $\epsilon_{test}=0.21$ for the test set.
This result was significantly better than that of the traditional baseline
correction method, whose result obtained with the 193.04 nm peak was
$\bar{\rho_{test}}=0.91$ with RMSE $\epsilon_{test}=0.26$. This shows that the
baselines of the LIBS spectra can be corrected satisfactorily by the 4S Peak
Filling baseline correction method added to the Savitzky-Golay noise filter.
Thus, the processing of the LIBS spectral data is significantly more robust
when using the method proposed in thi swork, compared to the traditional
method. In addition, the LIBS technique proved promising for the determination
of total carbon in soils and possibly for quantification of other elements in
matrices as complex as the soil. This work can also be extended to predict
nutrients in plants,whose objective is the detection of plant diseases in the
asymptomatic phase.

##  4 Acknowledgements

This work has been supported by the Embrapa Instrumentation and Brazilian
Research Council CAPES.

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