Investigation of the self-absorption effect using time-resolved laser-induced breakdown spectroscopy

Yun Tang; Shixiang Ma; Yanwu Chu; Tao Wu; Yuyang Ma; Zhenlin Hu; Lianbo Guo; Xiaoyan Zeng; Jun Duan; Yongfeng Lu

doi:10.1364/OE.27.004261

1. Introduction

Laser-induced breakdown spectroscopy (LIBS) is an appealing analytical technique for elemental determination [1]. LIBS has many attractive advantages, such as no or simple sample preparation, rapid, in situ, remote, and simultaneous multi-elemental analysis [2]. It has been widely applied in environmental monitoring [3], the metallurgy industry [4], agriculture [5], biomedicine [6], geological applications [7], and space exploration [8], etc. However, compared with traditional element analysis technology, the accuracy of LIBS quantitative analysis is still unsatisfactory, which limits further development and application of this technology. An important reason for the poor accuracy of LIBS quantitative analysis is the existence of the self-absorption effect. The self-absorption effect seriously interferes with the emission spectra of laser plasma and destroys the mapping relationship between spectral intensity and element concentration [9]. Therefore, to achieve high precision, quantitative analysis of LIBS, it is necessary to effectively suppress and eliminate the negative effect caused by self-absorption.

Up to now, several approaches have been developed to reduce the self-absorption effect. For instance, some researchers established a theoretical model of optical thickness to estimate and correct the self-absorption effect [10,11]; and some researchers utilized special equipment (e.g., a duplicating mirror) to evaluate and reduce self-absorption [12,13]. We also used an additional microwave generator [14] or an optical parametric oscillator (OPO) wavelength-tunable laser [9,15] to reduce self-absorption in our previous work. These methods reduced self-absorption effectively, but there are also some shortcomings. Due to the complexity of the interaction mechanism between laser and matter, establishing self-absorption mathematical models is not easy. Also, adding extra devices makes LIBS equipment more complex. It has been found that self-absorption is related to the acquisition delay time of spectra [16]. Accordingly, it would be much simpler to acquire the spectrum in a proper time window. Self-absorption with temporal evolution has been studied in some of the literature [17–20]. However, few works have focused on investigating the reduction of self-absorption by acquiring spectra at the early stage of plasma expansion to improve the quantitative analyses performance of LIBS.

In this work, copper (Cu) and manganese (Mn) elements in steel were used as examples, to investigate the temporal evolution of the self-absorption effect from plasma generation to extinction by establishing exponential calibration curves. The temporal evolution mechanism of the self-absorption effect was investigated. The quantitative analyses under different spectral acquisition time windows were compared. The self-absorption factor ( $α$ ) and the concentration of upper bound of linearity (C_int) were used to evaluate self-absorption. The root mean square error of cross-validation (RMSECV), and average relative error (ARE) were used to evaluate the analytical accuracy. The average relative standard deviation (ARSD) was used to evaluate analytical stability.

2. Experimental setup and samples

2.1 Experimental setup

As shown in Fig. 1, the LIBS experimental setup included five instruments: a Q-switch Nd:YAG laser (Quantel Ultra 100, wavelength of 532 nm, pulse duration of 7 ns), a Czerny-Turner spectrometer (Andor Technology, Shamrock 500), an intensified charge-coupled device (ICCD) (Andor Technology, iStar 320T), a digital delay generator (Wuhan N&D Laser Engineering, LDG 3.0), and a computer. The Q-switched Nd:YAG laser operating at 4 mJ and 10 Hz was used for ablating samples. The laser beam was reflected by a mirror and then focused on the sample surface by a UV-grade quartz lens (f = 25 mm) for plasma generation. The focal spot diameter on the sample was about 20 μm. The sample was mounted on a motorized XYZ translation stage to provide a fresh surface for each laser pulse. The plasma emission light was collected by using a light collector, and then transmitted to the spectrometor through a multicore fiber. The angle between the direction of spectral acquisition and laser beam was about 40°. The spectrometer equipped with an ICCD was used to record the spectra. The grating groove density of the spectrometer was set to 1800 lines per mm. The ablation laser and ICCD were controlled by a digital delay generator (Wuhan N&D Laser Engineering, LDG 3.0). The input side slit width was set to 300 μm. To improve the intensity stability, each spectral intensity was accumulated for 100 pulses and repeated 10 times.

Fig. 1 Schematic diagram of the experimental setup.

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2.2 Samples

Seven standard microalloyed steel samples (Central Iron & Steel Research Institute of China) were used in this work. The certified concentrations of Cu and Mn in these samples are provided in Table 1.

Table 1. The certified concentration of Cu and Mn elements in the steel samples (wt. %).

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3. Results and discussion

3.1 Spectral background removal based on wavelet transform

In the early stage of laser-induced plasma generation, the influence of the spectral continuum background is very serious. The continuum background is mainly caused by the electron bremsstrahlung radiation, the recombination radiation of ions and electrons, and stray lights [21]. To investigate the evolution of the self-absorption effect from plasma generation to extinction, we should eliminate the continuum background in LIBS. Some methods have been proposed to remove the continuum background in LIBS [22–25]. In this work, we adopted an algorithm based on wavelet transform to eliminate the background. Figure 2 shows the LIBS spectra of samples No. 1-7 under a gate delay of 0.2 μs. Obviously, the original LIBS spectra existed intense continuum background. After background correction, the spectra were lower than the original spectra, as shown in Fig. 2(b); and the distinction of Cu I 327.40 nm of 7 samples was more obvious.

Fig. 2 The original (a) and background corrected and (b) LIBS spectra of samples No.1-7 under a gate delay of 0.2 μs.

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3.2 Evaluation of self-absorption under different acquisition gate delays

In most cases, the self-absorption cannot be well observed from the spectral profiles. Some studies used curves of growth (COGs) methodology to estimate self-absorption [26–29]. Some studies adopted self-absorption coefficient (SA) to evaluate self-absorption [10,30,31]. In our previous works, we used exponential calibration curves for evaluation of self-absorption [9,15,32]. As deduced in our previous works, the spectral intensity can be expressed as:

I (C) = A (1 - e^{- α C}) + I_{b},

where

C

is the elemental concentration,

A

is the relative spectral intensity coefficient,

I_{b}

is the background intensity, and

α

is the self-absorption factor. The greater the

α

value, the more serious the self-absorption;

α

can be obtained from the exponential fitting of Eq. (1).

The relationship between $α$ and SA is as follow [9]:

S A = \frac{1 - e^{- α C}}{α C},

SA values range from 0 to 1, and the greater the value of SA is, the minimum self-absorption is. Which is inversely proportional to $α$ and $C$ .

As shown in Fig. 3, a series of exponential calibration curves for Cu I 327.40 nm and Mn I 403.31 nm under different gate delay times were established according to Eq. (1). The gate delay time of the ICCD ranged from 0.2 μs to 9 μs. The gate width was fixed to 1 μs. The spectral intensity was very weak at 9 μs. Therefore, we investigated the temporal evolution of the self-absorption effect from plasma generation to extinction. The value of $α$ of each calibration curve was obtained from the fitting of Eq. (1). As shown in Fig. 3, the value of R² of the calibration curves was very high, all above 0.99, which indicated that the calibration model was very appropriate; and the values of $α$ obtained from the exponential fitting were more credible.

Fig. 3 The calibration curves of Cu I 327.40 nm (a) and Mn I 403.31 nm (b) with different gate delay times.

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As is known to all, self-absorption causes the calibration curve to bend downward [33]. As depicted in Fig. 3, the linearity of the calibration curves was different. To clarify, the values of $α$ and SA of Cu I 327.40 nm and Mn I 403.31 nm with different gate delay times are shown in Fig. 4. For both Cu and Mn elements, the value of $α$ increased at first and then decreased. The results indicated that the self-absorption increased at first and then decreased along with the gate delay time, and the minimum self-absorption occurred at the gate delay time of 0.2 μs.

Fig. 4 $α$ and SA of Cu I 327.40 nm (a) and Mn I 403.31 nm (b) with different gate delay times.

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3.3 Evaluation of self-absorption under different acquisition gate widths

As described in Section 3.2, self-absorption increased at first and then decreased along with the gate delay time. The spectral intensity was too weak at a later gate delay, and the minimum self-absorption occurred at a gate delay time of 0.2 μs. So the gate delay was fixed at 0.2 μs. Then, the effect of different gate widths on self-absorption was investigated. The calibration curves for Cu I 327.40 nm and Mn I 403.31 nm under different gate widths are shown in Fig. 5. The gate widths were set from 0.2 to 10 μs. As shown in Fig. 5, the values of exponential fitting R² were all above 0.99, meaning that the values of $α$ obtained were highly reliable.

Fig. 5 The calibration curves of Cu I 327.40 nm (a) and Mn I 403.31 nm (b) with different gate widths.

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The values of $α$ and SA of Cu I 327.40 nm and Mn I 403.31 nm with different gate widths are shown in Fig. 6. For both Cu and Mn elements, the value of $α$ increased at first and then little changed. The results indicated that self-absorption increased at first and then stabilized along with the gate delay time; and the minimum self-absorption occurred at gate widths of 0.2 μs.

Fig. 6 $α$ and SA of Cu I 327.40 nm (a) and Mn I 403.31 nm (b) with different gate widths.

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3.4 Mechanism of the self-absorption effect temporal evolution

As deduced in our previous work [14], assuming thermodynamic equilibrium (LTE) and homogeneous plasma, the self-absorption can also be evaluated by the following equation:

K = \frac{1}{4 π^{2} c} \frac{N g_{k}}{U (T)} e^{- \frac{E_{i}}{k T}} λ_{0}^{4} A_{k i} l,

where

c

is the speed of light,

N

is the total atomic density in the plasma,

g_{k}

is the statistical weight of the upper level,

U (T)

is a partition function,

E_{i}

is the lower level energy,

k

is the Boltzmann constant,

T

is the plasma temperature,

λ_{0}

is the central wavelength,

A_{k i}

is the transition probability, and

l

is the absorption path length.

For a particular spectral line, the spectroscopic parameters under different delay times were the same, except for $N$ , $U (T)$ , $T$ , and $l$ . The lower level energy values of Cu I 327.40 nm and Mn I 403.31 nm were zero. Therefore, Eq. (3) can be modified as:

K = B \frac{N l}{U (T)},

where

B

is a constant in this case, and

N l

is the columnar density (total atomic number density times the length of the plasma along the line-of-sight). The higher value of

K

corresponds to the more serious self-absorption effect; and

K

is proportional to

N l

, while it is inversely proportional to

U (T)

. There is a positive correlation between

U (T)

and plasma temperature

T

. According to Eq. (4), plasma with high temperature and low columnar density can reduce the self-absorption effect in LIBS; and this phenomenon has been reported in the literature [34].

Moreover, according to the Boltzmann distribution:

N = \frac{N_{0}}{g_{0}} U (T),

where

N_{0}

is the ground state atomic density, and

g_{0}

is the statistical weight of the ground state.

Using Eq. (5), $K$ can be expressed as:

K = B_{0} N_{0} l,

where

B_{0} = \frac{B}{g_{0}}

is a constant. The parameter of

N_{0} l

represents the ground state atomic columnar density. The higher

N_{0} l

corresponds to more serious self-absorption. This provides a basis for judging the severity of self-absorption.

Here, we focus on the temporal evolution of the self-absorption effect. Due to the plasma temperature decreased along with increases in the gate delay [18,35]. At the time window of 0.2-0.4 μs, the number of ground state atom were small because of the high plasma temperature and plasma’s high ionization degree. Therefore, the ground state atomic columnar density was low; and the self-absorption was weak at this time window. Not only does the temperature of plasma decrease with the gate delay, but also the plasma morphology evolves with the gate delay. Fast images of the plasma plumes in LIBS under gate delay of 0.2 to 9 μs as shown in Fig. 7. These plasma images of the sample No. 1 were obtained by an Andor ICCD (iStar DH334T) equipped with a Nikon lens (105 mm, f/2.8 G). Each image was accumulated for 100 shots. To show the plasma morphology more clearly, intensities were normalized in each image. As shown in Fig. 7, the plasma morphology became flatter after gate delay of 6 μs. Thus leading to decreased optical depth along the fiber’s line-of-sight. Therefore, the self-absorption became weaker after the gate delay of 6 μs.

Fig. 7 Fast images of the plasma plumes in LIBS under different gate delay times.

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3.5 Quantitative analyses

Usually, the spectral acquisition time window is optimized by the signal-to-noise ratio (SNR) when analyzing spectral line intensity. The optimal spectral acquisition time window for both Cu and Mn elements based on minimum SNR was 2-3 μs. In fact, the self-absorption effect should also be considered. As discussed in Sections 3.2 and 3.3, the minimum self-absorption (SA) was obtained at a gate delay of 0.2 μs and a gate width of 0.2 μs. This means that the optimal spectral acquisition time window based on the minimum self-absorption criterion was 0.2-0.4 μs. Here, quantitative analyses of Cu and Mn elements at two different time windows were compared. The calibration curves of Cu I 327.40 nm and Mn I 403.31 nm are shown in Fig. 8. The solid lines are exponential fitting calibration curves, and the short dashed lines is linear curves of low concentration.

Fig. 8 The calibration curves of Cu I 327.40 nm (a) and Mn I 403.31 nm (b) at time windows of 2-3 and 0.2-0.4 μs.

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The detailed quantitative analysis results are provided in Table 2 for comparison. The self-absorption factor ( $α$ ) and the concentration of upper bound of linearity (C_int) were used to evaluate self-absorption. The value of C_int is corresponding to the concentration of 10% departure from linearity. The RMSECV and ARE were employed to evaluate the analytical accuracy. The ARSD was used to evaluate the analytical stability and reproducibility. As listed in Table 2, the values of $α$ at the time window of 0.2-0.4 μs lower than 2-3 μs. In addition, the value of C_int was 2.000 wt. % for the Mn element at a time window of 0.2-0.4 μs, much higher than 0.363 wt. % at a time window of 2-3 μs. The most commonly used linear fitting curves were established for the determination of element contents. The RMSECV and ARE were 0.0096 wt. % and 2.089% at a time window of 0.2-0.4 μs, respectively, both much lower than the values at a time window of 2-3 μs. The ARSD was 1.1778% at a time window of 0.2-0.4 μs, lower than 2.1241% at a time window of 2-3 μs. The same results were compared for the Cu element. These indicated that self-absorption was weaker and that the analytical accuracy and stability also improved at a time window of 0.2-0.4 μs.

Table 2. Comparison of quantitative analyses at a time window of 0.2-0.4 and 2-3 μs.

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Furthermore, Table 3 shows a comparison between the self-absorption reduction for Cu and Mn elements presented in this work and that presented in the literature. The samples used in the literature were the same as used in this work. As shown in Table 3, the values of self-absorption factor ( $α$ ) in this work were close to the literature, among them the $α$ value of Mn I 403.31 nm was less than the literature. Moreover, additional equipment was used in the literature. Therefore, self-absorption can be reduced effectively by optimizing the spectral acquisition time window without the need for additional equipment.

Table 3. Comparison between self-absorption reduction in this work and other works.

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4. Conclusions

In summary, the temporal evolution of the self-absorption effect from plasma generation to extinction by calibration curve was investigated. The results showed that self-absorption increased at first and then decreased along with the gate delay time. The minimum self-absorption occurred at the early stage of plasma expansion, and the temporal evolution mechanism of the self-absorption effect was discussed. Assuming an LTE condition and homogeneous plasma, the high plasma temperature can reduce self-absorption. Finally, a quantitative analysis of time windows and traditional optimization (0.2-0.4 μs) and self-absorption optimization (2-3 μs) was compared. The linearity of the calibration curves at a time window of 0.2-0.4 μs was much better than 2-3 μs. The results demonstrated that self-absorption was weaker, and the analytical accuracy and stability also improved at the early stage of plasma expansion. Furthermore, this work provides a simple and effective method for reducing the self-absorption effect in LIBS.

Funding

National Natural Science Foundation of China (61575073, 51429501).

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No.	CISRI	Cu	Mn
1	GSB 03-3453-2008-1	0.154	0.151
2	GSB 03-3453-2008-2	0.201	1.100
3	GSB 03-3453-2008-3	0.105	0.571
4	GSB 03-3453-2008-4	0.054	1.500
5	GSB 03-3453-2008-5	0.021	2.000
6	GSB 03-3453-2008-6	0.288	0.110
7	GSB 03-3453-2008-7	0.346	0.043

Spectral line	Time window (μs)	α	C_int (wt. %)	RMSECV (wt. %)	ARE (%)	ARSD (%)
Cu I 327.40 nm	0.2-0.4	1.5908	0.161	0.0115	5.810	2.4807
Cu I 327.40 nm	2-3	5.5539	0.109	0.0307	23.419	2.5854
Mn I 403.31 nm	0.2-0.4	0.0001	2.000	0.0096	2.089	1.1778
Mn I 403.31 nm	2-3	0.9658	0.363	0.1612	24.362	2.1241

Spectral line	Method	Additional equipment	α	Ref
Cu I 327.40 nm	reduced air pressure	a vacuum chamber	1.2048	[32]
Cu I 327.40 nm	this method	none	1.5908	this work
Mn I 403.31 nm	reduced air pressure	a vacuum chamber	0.1315	[32]
Mn I 403.31 nm	this method	none	0.0001	this work

No.	CISRI	Cu	Mn
1	GSB 03-3453-2008-1	0.154	0.151
2	GSB 03-3453-2008-2	0.201	1.100
3	GSB 03-3453-2008-3	0.105	0.571
4	GSB 03-3453-2008-4	0.054	1.500
5	GSB 03-3453-2008-5	0.021	2.000
6	GSB 03-3453-2008-6	0.288	0.110
7	GSB 03-3453-2008-7	0.346	0.043

Spectral line	Time window (μs)	α	C_int (wt. %)	RMSECV (wt. %)	ARE (%)	ARSD (%)
Cu I 327.40 nm	0.2-0.4	1.5908	0.161	0.0115	5.810	2.4807
Cu I 327.40 nm	2-3	5.5539	0.109	0.0307	23.419	2.5854
Mn I 403.31 nm	0.2-0.4	0.0001	2.000	0.0096	2.089	1.1778
Mn I 403.31 nm	2-3	0.9658	0.363	0.1612	24.362	2.1241

Investigation of the self-absorption effect using time-resolved laser-induced breakdown spectroscopy

Abstract

1. Introduction

2. Experimental setup and samples

2.1 Experimental setup

2.2 Samples

3. Results and discussion

3.1 Spectral background removal based on wavelet transform

3.2 Evaluation of self-absorption under different acquisition gate delays

3.3 Evaluation of self-absorption under different acquisition gate widths

3.4 Mechanism of the self-absorption effect temporal evolution

3.5 Quantitative analyses

4. Conclusions

Funding

References

Cited By

Figures (8)

Tables (3)

Equations (6)

Optics Express