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An Image Auxiliary Method for the Quantitative Analysis of Laser-Induced Breakdown Spectroscopy Peng Zhang, Lanxiang Sun, Haibin Yu, Peng Zeng, Lifeng Qi, and Yong Xin Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b05284 • Publication Date (Web): 02 Mar 2018 Downloaded from http://pubs.acs.org on March 4, 2018

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Analytical Chemistry

An Image Auxiliary Method for Quantitative Analysis of LaserInduced Breakdown Spectroscopy Peng Zhang,a,b,c Lanxiang Sun,*,a,c Haibin Yu,a,c Peng Zeng,a,c Lifeng Qi,a,c and Yong Xina,b,c a

Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China.

b

University of Chinese Academy of Sciences, Beijing 100049, China.

c

Key Laboratory of Networked Control System, CAS, Shenyang 110016, China.

ABSTRACT: Improving both the stability and accuracy of laser-induced breakdown spectroscopy (LIBS) is an issue in quantitative analysis. For certain environments outside of the laboratory, consistently and exactly maintaining the distance from the optical system to the sample surface is difficult, and fluctuations of this distance severely affect the stability of the spectrum. In this work, the principal components of the plasma images are extracted and used to correct the spectral line intensities as an auxiliary method to reduce spectral fluctuation. The presented image auxiliary method is combined with univariate analysis and multivariate analysis, and the element concentrations of Cu, Mn, V and Cr in steel samples are analyzed. For univariate analysis, all the determination coefficients (R2) of the 4 elements exceed 0.99, whereas the average relative standard deviations (RSDs) of the intensities decrease from 30.45%, 23.14%, 27.03% and 22.04% to 2.13%, 3.38%, 2.49% and 3.58%, respectively. For the multivariate analysis, the R2 values for Cu, Mn, V and Cr also all exceed 0.99, and the average RSDs of the predicted concentrations of the validation samples decrease to 2.87%, 3.82%, 2.86% and 6.51%, respectively.

Laser-induced breakdown spectroscopy (LIBS) is a type of

uncertainty in LIBS measurements12,13. An increasing number

atomic emission spectroscopy that focuses additional

of studies currently focus on spectral correction instead of

attention on the potential for rapid in situ and on-line analyses

sample preparation to retain the advantages of LIBS in rapid,

in industrial applications and on the capabilities of multi-

in situ and on-line analysis10,14. The internal standard method

element synchronous analysis and light element analysis. As

has been proven to be a useful method for LIBS spectra15,16;

a “future superstar” in the analytical atomic spectrometry

however, selecting the reference line of the internal standard

1

field , LIBS has demonstrated great potential in numerous 2-7

element is difficult, and in certain cases, no appropriate

applications . Although the advantages of LIBS are highly

element can be found. Normalization with the intensity of the

attractive (e.g., no or little sample preparation, quasi-

spectral area or the background emission is also commonly

nondestructive measurement, short measurement times, and

used in LIBS to reduce the influence of the matrix effect and

versatility in sample styles and states), poor measurement

the pulse-to-pulse fluctuation16-18. Selected associated signals

repeatability and

from

have also been introduced in LIBS as reference signals, such

becoming as popular as other established quantitative analysis

as electrical current19,20 and acoustic waves21,22, which are

techniques8-10. In industrial fields, the inline chemical analysis

generated synchronously with the plasma. Many multivariate

of processes and products is the most important application

analysis methods such as principal component analysis (PCA),

for LIBS; however, the poor stability of LIBS measurements

neural network (NN), support vector machine (SVM), and

is an obstacle to this method’s practical application .

partial least square (PLS) have been applied in LIBS23,24, and

reproducibility prevent

LIBS

11

Extensive research has been conducted to reduce the

combinations of these methods have been used for both

ACS Paragon Plus Environment

Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

qualitative analysis and quantitative analysis25,26.

Page 2 of 11

steel samples were used to construct the calculation model and

The plasma temperature, electron density and number

validate the availability of the method. The comparison results

density of species are the most important parameters that

prove that the presented method can improve the stability and

reflect the plasma conditions. Normalizing the spectrum with

accuracy simultaneously.

the calculated plasma parameters has been proven to be an effective approach14. Wang et al.27 and Li et al.28,29 used a standardization method, in which a standard state with specific plasma parameters was described, and the spectrum was compensated to this standard state with the residual of the

EXPERIMENTAL SECTION Experimental setup. A schematic of the experimental setup used in this work is shown in Figure 1. A 1064 nm Nd:YAG laser beam with a pulse energy, repetition rate and pulse width of 80 mJ, 1 Hz and 8 ns, respectively, was reflected by a laser

plasma parameters.

reflector and focused via a convergent lens with a focal length The plasma image is a direct presentation of the plasma condition, which is the foundation underlying research on temporal and spatial resolution of the plasma30-33. However, in most of this work, the plasma image is used as a supplementary method to demonstrate the reason for the spectrum fluctuation instead of as a reference signal to correct the spectrum. Ma et al.34 and Bai et al.35 established correlations between the spatial distribution of the plasma and the spectral intensities of several characteristic lines corresponding to different elements. In further work, MottoRos et al.36 presented a servo system to correct the fluctuation due to the different heights of the sample surfaces, with automatic positioning of the collection optical fiber using real-time imaging. Ni et al.37 presented a spectral

of 75 mm (Lens 1 in Figure 1). The sample was placed on a 3D electric displacement platform. The collection system was positioned coaxially with the laser beam, and the emission was divided into 2 parts by a beam splitter. Approximately 10% of the emission was reflected into an ICCD camera (Andor iStar 334T) for imaging. Simultaneously, nearly 90% of the emission was transmitted, converged by a 35 mm collector and collected by an optical fiber connected with a spectrometer (AvaSpec ULS2048, wavelength range 245-355 nm). The entire system was controlled using a synchronized trigger board designed in our lab. For synchronization of the spectral signal and image signal, the delay time and gate width of both the ICCD camera and the spectrometer were fixed at 1.5 µs and 1100 µs, respectively.

normalization method in which the sum of pixels in a certain plasma image area was calculated and used as the reference

Samples and data. A total of 21 certified reference materials were used in the experiment: 5 high-alloy steel samples, 6

signal. In a previous study38, we proposed an intensity correction

carbon steel samples and 10 low-alloy steel samples. The concentrations of the major elements are listed in Table 1,

method using plasma position information. However, in practical applications, the plasma image in the horizontal direction could not be obtained and the plasma position could not be extracted directly. In the present work, we further studied the spectral fluctuation caused primarily by the

laser plasma emission fiber control line data line

different heights of the sample surfaces. The plasma image

Computer

Spectrometer Collector

was collected coaxially with the laser beam, perpendicular to the sample surface. Instead of extracting the position were preprocessed and used to directly correct the spectral

Beam splitter

Camera

information from the plasma image, the plasma image data

Laser reflector

Laser

line intensity, and an image auxiliary method was proposed. PCA was used to reduce the dimensionality of the image data,

Lens 1 Trigger board sample

3D platform

and the principal components of the images were used to construct the correction model. Subsequently, the correction method was combined with univariate analysis and

Figure 1. Schematic of the LIBS system.

multivariate analysis. Good results were obtained when 21


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where samples 1-5 are high-alloy steels, samples 6-11 are

sample 1/height 1 is shown in Figure 2(a), and the pseudo-

carbon steels and samples 12-21 are low-alloy steels.

color images of the plasma emission intensity of sample 1,

However, because of the limits of the transmittance of the

sample 7, sample 12 and sample 17 at 20 heights (where

beam splitter, the spectral detection range, the resolution of

heights 1-20 correspond to LTSDs from 69.1 to 71 mm, with

the spectrometer and other reasons, only Cu, Mn, V and Cr

0.1 mm as the step size) are shown in Figure 2(b), (c), (d) and

were considered in this paper. For each sample, 10 sampling

(e), respectively. For all pseudo-color images in Figure 2, the

points were chosen. By moving the displacement platform

uniform scale bar is shown on the right side of Figure 2(a),

along the z-axis (with 0.1 mm as the step size), we varied the

and the range of the pixel intensity is 0-255. As the figure

distance from Lens 1 to the sample surface (LTSD) from 67.5

shows, at different heights of the same sample, the plasma

mm to 72.5 mm, approximately. Therefore, 50 heights were

images differ substantially. The main cause of these variations

chosen for each point. In addition, for each height, an average

might be that different LTSDs lead to different defocus values

of 10 spectra and the corresponding average of 10 plasma

and to different collection efficiencies. However, at the same

images were recorded. At heights close to 67.5 mm, the focus

height of different samples, the plasma images are quite

of the laser beam was too deep to induce suitable plasma. At

similar because, for different samples with the same matrix

heights close to 72.5 mm, the collection fiber could not collect

(in this work, all samples are steels, and Fe is considered the

the entire emission from the plasma. Therefore, only the

matrix) and the same experimental conditions (pulse energy,

middle 20 heights, whose average spectral intensities were

LTSD, delay time and gate width of the spectrometer, etc.),

relatively large, were considered. In total, 4200 (21×10×20)

the morphology features of the plasma are similar, and the

spectra and 4200 images were collected for training and

entire emission intensity fluctuation is not as strong.

validation.

Therefore, we consider that the plasma image could be used to describe the spectral differences due to the plasma

MODEL DESCRIPTION

fluctuation.

The pseudo-color image of the plasma emission intensity of Table 1. Element concentrations of the alloy steel samples (%) No.

C

Mn

Si

Ni

Cr

V

Mo

Ti

Cu

Fe

1

0.0400

0.1300

0.2230

0.5000

14.2600

0.0590

0.0640

0.0410

0.0560

84.5500

2*

0.2450

0.3370

0.4200

0.3930

11.0300

0.1510

0.3530

0.0790

0.2840

86.3457

3

0.1590

0.4950

0.5680

0.2070

12.5200

0.0890

0.1570

0.0910

0.1710

85.2895

4

0.3400

0.7400

0.7720

0.4610

9.3700

0.2010

0.2440

0.3710

0.3740

86.6454

5

0.4720

0.9830

0.4870

0.7710

7.8400

0.2870

0.4870

0.1870

0.5220

87.2700

6

0.6920

0.7120

0.2820

0.5070

0.2800

0.1080

0.1600

0.1320

0.1610

96.7510

7

0.9820

0.3420

0.3680

0.3940

0.1620

0.0630

0.0830

0.1450

0.0910

97.0550

*

0.3690

1.0200

0.1890

0.0840

0.2230

0.1720

0.2290

0.0510

0.2260

97.1504

9

0.0560

0.0580

0.0310

0.0250

0.4930

0.2420

0.3030

0.0120

0.2800

98.0190

10

1.2700

1.2700

0.5170

0.2150

0.0940

0.0490

0.0140

0.1680

0.0630

96.1120

11

0.1890

0.2260

0.1380

0.2860

0.3770

0.2860

0.3990

0.1900

0.3300

96.9290

12

0.0009

0.0100

0.0000

0.0100

0.0100

0.0010

0.0010

0.0010

0.0100

99.9479

13

0.1000

0.1500

0.6000

0.0500

4.0200

0.4000

0.5000

0.0220

0.0700

93.7498

14

0.1490

0.7500

0.4000

0.1000

3.2200

0.0270

0.4000

0.1000

0.6900

93.7790

15

0.2100

2.0000

0.0600

0.5000

2.5100

0.0000

0.3000

0.3000

0.1100

93.7190

16

0.2600

1.6000

0.2500

1.0500

2.0200

0.3000

0.0920

0.0140

0.4000

93.6845

17

0.3400

1.2900

0.3400

1.5500

1.4900

0.0580

0.2000

0.0540

0.4900

93.7267

18*

0.5000

1.0200

0.3000

2.0200

1.0200

0.1100

0.6000

0.2000

0.2000

93.6126

19

0.6400

0.5100

0.1500

2.5300

0.5300

0.1600

1.0200

0.1600

0.3000

93.7264

20

0.8000

0.3100

0.2000

3.2600

0.1200

0.2000

0.8200

0.0000

0.1700

93.7627

21

0.9900

0.1000

0.1100

4.0600

0.0500

0.4900

0.0590

0.0000

0.0500

93.6620

8

*

Validation sample for univariate analysis



200

Page 4 of 11

The spectral intensity 𝐈̅ is defined as the average intensity of a specific line and is described as

150 100

S1H1

50 1mm

I̅ =

0

(1)

𝑞

where q is the number of spectra in one sample, and Ii is the intensity of the ith measurement. In a common quantitative analysis

(a)

𝑞

∑𝑖=1 I𝑖

model

produced

by

linear

regression,

the

concentration is described as a linear combination of a series of I̅ values at different wavelengths (multivariate analysis)

H1~H5

or an expression of an individual I̅ (univariate analysis).

H6~H10

Therefore, the stability of the measurement is determined by the deviation of I from I̅ to a certain extent. For a specific I,

H11~H15

the relative deviation is described as follows 𝑒=

H16~H20

(b)

I−I̅ I̅

(2)

If e can be estimated by other functions, then I̅ can be

H1~H5

described as

H6~H10

I̅ =

H11~H15

I 1+𝑒

(3)

That is, if we can estimate the relative deviation using the image data, the intensity calculated via Eq. (3) instead of

H16~H20

multiple measurements can be used to estimate the average

(c)

value. Therefore, for applications in which multiple H1~H5

measurements cannot be performed, the measurement stability could be improved.

H6~H10

PCA and partial least squares regression (PLSR) are used H11~H15

to build the model for estimation of the relative deviation. The algorithm diagram is shown in Figure 3, where Prep, PCA

H16~H20

and PLSR are image data preprocessing, image principal

(d)

component analysis and partial least squares regression, H1~H5

respectively. For a data set with m samples and q spectra and images for each sample, there are 𝑛 = 𝑞 × 𝑚observations

H6~H10

(spectra and images) for the data set. H11~H15

The modeling procedure is described in Figure 3(b). (1) Image data preprocessing: The h-by-v original image

H16~H20

matrix is mapped to a 1-by-p array (𝑝 = ℎ × 𝑣, as shown in

(e)

Figure 3 (a)) and the n-by-p image training matrix (Matim) Figure 2. Plasma emission intensity image(s) of (a) sample

with n arrays converted by n original images is composed.

1/height 1; (b) sample 1/heights 1-20; (c) sample 7/heights

(2) Image principal component analysis: The principal

1-20; (d) sample 12/heights 1-20; (e) sample 17/heights 1-

component coefficients matrix (Matcoeff, p-by-p) of Matim is

20. Heights 1-20 correspond to LTSD 69.1-71 mm (with

computed using PCA, the appropriate top k (𝑘 ≤ 𝑝) columns

0.1 mm as the step size).

of Matcoeff are selected as the image feature extraction matrix


Page 5 of 11

h-by-v matrix 1

2

RESULTS AND DISCUSSION

1-by-p array

… v

1

2

… v

1

2

… v

1

2

Principal component analysis of the images. A total of

… v

…

1

90000 (300-by-300) pixels are present in a plasma image. The

2

number of pixels was too large for the relative deviation to be

…

…

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


h

fit directly; therefore, PCA was first conducted to reduce the

(a)

Image

I

Image

Prep

Eq.(1)

Prep

Matim

I

PCA

Eq.(2)

dimensions of the image data. The total variances explained

I

by the top k principal components are shown in Figure 4,

PCs

PLSR

A1

A2

A1

where the x-axis indicates the number of principal

Vecim

components and the y-axis indicates the ratio of the cumulative sum of the variances explained by the top k

PCs

e

A2

Eq.(4)

principal components and the total variance explained by all

Eq.(5)

the principal components. The red dotted line and the blue I

(b)

(c)

solid line indicate the average value of the validation samples (samples 2, 8 and 18 in Table 1) and the average value of the

Figure 3. Schematic of (a) 2D-to-1D mapping of image

training samples (the other 18 samples in Table 1),

data; (b) the modeling procedure; (c) the use procedure.

respectively. Figure 4(a) shows the values from 1 to 50 principal components, and Figure 4(b) shows an enlarged

A1 (p-by-k) and the top k principal components of Matim are extracted (recorded as PCs, n-by-k).

view of the portion in the green box in Figure 4(a). The two lines are strongly similar, which means that the principal

(3) Relative deviation fitting: The average intensity is

component coefficients calculated by the training data were

computed in a sample-by-sample manner using Eq. (1), and all the average intensities are recorded as 𝐈̅ . The relative

also suitable for principal component extraction of the test

deviation e is computed using Eq. (2), the PLS regression of

principal components exceeded 0.95, whereas these values for

e on the PCs is computed, and the PLS regression coefficients

30 and 100 principal components were approximated as 0.99

vector A2 ((k+1)-by-1) is returned.

and 0.999, respectively.

(4) A1 and A2 compose the final computing model.

data. For both lines in Figure 4, the variance ratios of 10

The original and rebuilt images are shown in Figure 5. To

The use procedure is described in Figure 3(c).

prove that the image feature extraction matrix A1 was

(1) Image data preprocessing (Prep): The h-by-v original

applicable to both the training samples and the validation

image matrix is mapped to a 1-by-p array Vecim. (2) Principal component extraction: The first k principal components’ PCs (1-by-k) are extracted using the product of Vecim multiplied by A1. (3) Relative deviation estimation: The eout is computed using Eq. (4): eout = 𝐀𝟐 (1) + ∑𝑘𝑗=1 PCs(𝑗) × 𝐀𝟐 (𝑗 + 1)

(4)

where 𝐀𝟐 (𝑗) and PCs(𝑗)indicate the jth value of A2 and the PCs, respectively. (4) Spectral line intensity correction: The correction intensity ̃I is computed using Eq. (5): ̃I =

I 1+eout

(5)

Figure 4. Variances ratios explained by (a) the top 1-50 image data principal components and (b) enlarged view of the top 1-10 image data principal components.



Original image

Image rebuilt with k principal components k = 200

k = 100

k = 50

k = 30

k = 10

Page 6 of 11

with original spectral intensities, the calibration with intensities normalized by the entire spectral area (wavelengths from 245 nm to 355 nm), the internal standard method and the

S1H5

internal standard method with image auxiliary correction S1H15

(proposed image auxiliary method), respectively. The black solid line indicates the fitting curve; Stl1t, Stl2t and Stl3t

S8H5

represent the training samples of high-alloy steel, carbon steel S8H15

and low-alloy steel, respectively, and Stl1v, Stl2v and Stl3v

Figure 5. Original images and rebuilt images with different principal components. Cu 327.4 nm

samples, the 4 rows (S1H5, S1H15, S8H5 and S8H15)

Legend

represent the images of sample 1/height 5, sample 1/height 15,

fitting Stl1t

sample 8/height 5, and sample 8/height 15, respectively

(a)

(b) Stl2t

(sample 1 and sample 8 were obtained from the training set

Stl3t

and the validation set, respectively). The first column shows

Stl1v

the original image, and columns 2-6 show the images rebuilt

Stl2v

by different A1 (k equal to 200, 100, 50, 30, and 10,

Stl3v

respectively). The rebuilding procedure was performed by (1) multiplying the PCs (1-by-k) by the transpose of A1 (k-by-p),

(c)

(d)

and (2) mapping the product (1-by-p) to an h-by-v image matrix (as shown in Figure 3(a)). When the number of principal components was greater than 30, the similarity

Figure 6. Calibrations of Cu with the spectral line at 327.4

between the original image and the rebuilt image showed no

nm using (a) the original spectral intensity, (b) the entire

significant improvement with increasing number of principal

spectral area normalization, (c) the internal standard

components; when 10 principal components were extracted,

method and (d) the image auxiliary method.

the rebuilt images could not adequately describe the original images. Therefore, 30 was chosen as the number of principal components used in modeling.

Mn 293.9 nm

Combination with univariate analysis. The bold italic

Legend

samples in Table 1 (samples 2, 8 and 18) were selected as the

fitting Stl1t

validation samples, and the other samples were used to build

(a)

(b)

Stl2t

the calculation model for the univariate analysis. After

Stl3t

optimization, the spectral lines at 327.4 nm, 293.9 nm, 311.1

Stl1v

nm and 313.2 nm were selected as the analytical lines of Cu,

Stl2v

Stl3v

Mn, V and Cr, respectively, and the characteristic spectral lines of Fe at 298.1 nm, 325.9 nm, 298.1 nm and 346.9 nm (c)

were selected as the reference lines for the internal standard

(d)

calibrations of Cu, Mn, V and Cr, respectively. The analytical lines and reference lines were all corrected using the proposed image auxiliary method. The concentration calibrations of Cu, Mn, V and Cr using quadratic function fitting are shown in Figure 6, Figure 7, Figure 8 and Figure 9, respectively. The subfigures (a), (b), (c) and (d) correspond to the calibration

Figure 7. Calibrations of Mn with the spectral line at 293.9 nm using (a) the original spectral intensity, (b) the entire spectral area normalization, (c) the internal standard method and (d) the image auxiliary method.


Page 7 of 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


tendencies of the concentration changes with the intensities V 311.1 nm

were different); therefore, poor determination coefficients were obtained; and (3) the combination of the image auxiliary

Legend

(a)

fitting

method and the internal standard method could obtain smaller

Stl1t

standard deviations than the internal standard method without

Stl2t

correction.

(b) Stl3t Stl1v

Further comparison results are shown in Table 2, where

Stl2v

RSD_C is the average value of the relative standard deviations

Stl3v

of the intensities of all calibration samples, RSD_P is the average value of the relative standard deviations of the

(c)

(d)

intensities of all validation samples, R2 is the determination coefficients of all the samples, RMSE_C and RMSE_P are the root-mean-square errors of the calibration samples and the

Figure 8. Calibrations of V with the spectral line at 311.1

validation samples, respectively, and MDL is the method

nm using (a) the original spectral intensity, (b) the entire

detection limit (calculated by Eq. (7)39, with 𝑡 = 2.539 for

spectral area normalization, (c) the internal standard

𝑛 = 20 and 𝛼 = 99%, where s is the standard deviation of

method and (d) the image auxiliary method.

the 20 measurements from different heights).

Cr 313.2 nm

Table 2. Comparison results for different univariate analysis methods

Legend

Stl1t (a)

(b) Stl2t Stl3t

Cu

Stl1v Stl2v Stl3v

Mn (c)

(d)

Figure 9. Calibrations of Cr with the spectral line at 313.2

V

nm using (a) the original spectral intensity, (b) the entire spectral area normalization, (c) the internal standard method and (d) the image auxiliary method. Cr

represent the validation samples of high-alloy steel, carbon steel and low-alloy steel, respectively. As the figures show, (1)

4.66 2.36

Cm2e Cal

2.20 1.68 0.995 0.013 0.013 0.0057 23.13 23.20 0.994 0.033 0.070 0.1307

4.76 0.995 0.013 0.011 0.0159 1.96 0.978 0.026 0.029 0.0058

Nor

8.90

9.08 0.877 0.216 0.152 0.0375

Int Cm1

7.28 3.53

5.90 0.993 0.037 0.073 0.0631 2.49 0.996 0.033 0.028 0.0168

Cm2 Cal

3.11 1.85 0.993 0.037 0.073 0.0191 26.97 27.37 0.985 0.016 0.013 0.0377

Nor

3.44

2.87 0.895 3.272 3.219 0.0058

Int Cm1

5.04 2.48

4.53 0.995 0.010 0.003 0.0043 2.58 0.985 0.016 0.012 0.0052

Cm2 Cal Nor Int

2.09 21.97 10.08 8.40

1.56 22.46 9.67 8.21

Cm1 Cm2

4.00 3.42

4.82 0.975 1.039 0.929 0.0231 4.53 0.998 0.178 0.430 0.0158

0.995 0.970 0.947 0.998

0.010 1.149 1.538 0.203

0.003 0.092 1.415 0.312

0.0041 0.1369 0.0587 0.0284

Calibration with original spectral intensities;

b

Calibration with intensities normalized by the entire spectral area;

c

Internal standard method;

d

Calibration with intensities corrected by the image auxiliary method;

e

Internal standard method with intensities corrected by the image

deviations; (2) for the calibration with the intensities normalized by the entire spectral area, matrix effects obviously occurred (i.e., for different types of steel samples, prevented the sum of the spectral area from adequately

Intc Cm1d

a

the direct calibrations exhibited the largest standard

different concentrations of major elements Fe and Cr

Cala Norb

RSD (%) RMSE MDL R2 C P C P (%) 30.43 30.60 0.981 0.025 0.017 0.0819 6.82 7.23 0.825 0.093 0.074 0.0177

Element Method

fitting

auxiliary method.

representing the entire plasma emission such that the variation



MDL = 𝑠 × 𝑡(𝑛−1,1−𝛼)

Page 8 of 11

(7) IA

IR

IS

The results in Table 2 show that (1) with the internal Image Auxiliary Method

standard method, the RSDs of Cu, Mn, V and Cr decreased from more than 30%, 20%, 25% and 20% to approximately C

4.5%, 6.5%, 5% and 8.5%, respectively. After combination with image auxiliary method, the values further decreased to

IA

IR

fitting

Cout

IS

less than 2.5%, 3.5%, 2.5% and 5%, respectively. (2) For Cu, V and Cr, the values of R2 improved from 0.981, 0.985 and 0.970 (direct calibration) to 0.995, 0.995 and 0.998 (internal standard method); the values of RMSE_C and RMSE_P were

PLSR Internal Standard Method

B1

PLS regression

B2

improved; and the MDLs decreased from 0.0819%, 0.0377% and

0.1369%

to

0.0159%,

0.0043%

and

0.0284%,

respectively. The combination of the image auxiliary method and

the internal standard method

guaranteed

Figure 10. Modeling procedure consisting of a combination of the image auxiliary method, the internal standard method and PLSR.

these

improvements in R2 and RMSE and resulted in lower MDLs

procedure is described as follows: (1) IA, IR and IS are

(0.0057%, 0.0041% and 0.0158% for Cu, V and Cr,

corrected using the proposed image auxiliary method; (2) the

respectively). (3) For Mn, the values of R2, RMSE_C and

fitting coefficients of the internal standard method B1 and the

RMSE_P with the internal standard method were worse than those values with direct calibration, which means that an

predicted concentration Cout are fitted; (3) the concentration residual ε (𝜺 = 𝐂𝐨𝐮𝐭 − 𝐂 and the PLS regression of ε on 𝐈̃𝐒

appropriate reference line might not exist for the analytical

are computed and the regression coefficients B2 are obtained.

line of Mn at 293.9 nm in the recorded spectrum. Therefore,

For the validation data, the predicted concentration C was the

the combination of the image auxiliary method and the

sum of Cout (the concentration predicted by the internal

internal standard method was meaningless, and the

standard method) and ε (the concentration residual predicted

combination of the image auxiliary method and direct

by the PLSR).

calibration resulted in better values of R2, RMSE and MDL.

A leave-one-out (LOO) validation was performed. The

In conclusion, when both stability and accuracy are

validation results for Cu, Mn, V and Cr of the 11 samples

considered, the combination of the proposed image auxiliary

(samples 2, 3, 5-8, 11, and 16-19, whose concentrations of Cu,

method and univariate analysis was more appropriate than the

Mn, V and Cr were neither the highest nor the lowest) are

entire spectral area normalization and the internal standard

shown in Figure 11, Figure 12, Figure 13 and Figure 14,

method.

respectively, where Stl1, Stl2 and Stl3 correspond to high-

Combination with multivariate analysis. As shown in

alloy steels (samples 2, 3, 5), carbon steels (samples 6, 7, 8,

Figure 4, Figure 5 and the corresponding descriptions, 30

11) and low-alloy steels (samples 16, 17, 18, 19), respectively,

principal components could contain most of the image

and R. C. and P. C. are the abbreviations for reference

information. Therefore, 30 was the number of image principal

concentration and predicted concentration, respectively.

components used in modeling. PLSR was introduced as the

First, the PLSR of the concentrations was performed on the

multivariate analysis method to further improve the

entire spectra. The prediction results are shown in subfigure

calibration performance. The combination procedure is

(a) of Figure 11-Figure 14. For comparison, the prediction

shown in Figure 10, where IA, IR, IS and C are the analytical

results of the internal standard method with the image

line intensity of the internal standard method, the reference

auxiliary method are shown in subfigure (b) of Figure 11-

line intensity of the internal standard method, the spectral line

Figure 14. The analytical lines, reference lines and image

intensities selected for PLSR and the reference concentrations, respectively; 𝐈̃𝐀 , 𝐈̃𝐑 and 𝐈̃𝐒 are the corresponding

auxiliary method were all the same as described in the

intensities corrected by the image auxiliary method; and

the internal standard method and the PLSR without image

fitting is the internal standard method. The specific modeling

auxiliary correction are shown in subfigures (c) of Figure 11-

previous section. The prediction results of the combination of


Page 9 of 11 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cu

V

Legend

Legend

y=x

y=x

Stl1

Stl1

Stl2

Stl2

Stl3

Stl3

Figure 11. Prediction results of Cu using (a) PLSR on the

Figure 13. Prediction results of V using (a) PLSR on the

entire spectra, (b) the internal standard method combined


with image auxiliary method, (c) the internal standard


method combined with PLSR and (d) a combination of the


image auxiliary method, the internal standard method and


PLSR.

PLSR.

Mn

Cr

Legend

Legend

y=x

y=x

Stl1

Stl1

Stl2

Stl2

Stl3

Stl3

Figure 12. Prediction results of Mn using (a) PLSR on the

Figure 14. Prediction results of Cr using (a) PLSR on the


entire spectra, (b) an internal standard method combined


with image auxiliary method, (c) an internal standard





PLSR.

PLSR.

Figure 14. The modeling procedure is similar to that of

results of the combination of the image auxiliary method, the

Figure 10 (without the upper dashed box) and the work of

internal standard method and PLSR are shown in subfigures

Feng et al.40. For prediction of each element concentration, 8

(d) of Figure 11-Figure 14.

spectral line intensities that exhibited the largest correlations

Figure 11-Figure 14 show that (1) for the PLSRs of the

with ε were selected as the input of the PLSR. The prediction

concentrations on the entire spectra, no better determination



coefficients and mean relative standard deviations exist than those of the internal standard method; (2) the combination of

Page 10 of 11

AUTHOR INFORMATION Corresponding Author

the image auxiliary method, internal standard method and PLSR could obtain smaller RSDs than the combination of the internal standard method and PLSR without the image

* Phone: 86-024-83601700. Fax: 86-024-23970013. E-mail: [email protected].

auxiliary method and the internal standard method combined

Notes

with the image auxiliary method; (3) the combination of the

The authors declare no competing financial interests.

image auxiliary method, the internal standard method and PLSR could obtain better determination coefficients for Cu,

ACKNOWLEDGMENTS

Mn and V than the internal standard method combined with

The authors acknowledge financial support from the National

the image auxiliary method; and (4) the combination of the

Natural Science Foundation of China (No. 61473279), the

internal standard method and PLSR could not further improve

National Key Research and Development Program of China (No.

the prediction results for Cr because the range of the

2016YFF0102502), the Key Research Program of Frontier

concentrations was too large to describe the residual with a

Sciences CAS (No. QYZDJ-SSW-JSC037) and the Youth

universal PLSR model. In conclusion, for multivariate

Innovation Promotion Association CAS.

analysis combining PLSR with the internal standard method, use of the image auxiliary method can further improve the accuracy and stability of the predictions of Cu, Mn and V.

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For LIBS measurements with sample surface fluctuation, the stability of the spectra is difficult to ensure. In this work, an image auxiliary method was proposed to reduce the fluctuation induced by nonconformity of the sample surface. The principal components of the plasma images were extracted and used to correct the spectral line intensities. A total of 21 steel samples were used to build the calculation model and validate the availability. The concentrations of Cu, Mn, V and Cr were considered, and the comparison results prove that the proposed image auxiliary method improves the stability and

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