1 Introduction

Laser-induced breakdown spectroscopy (LIBS) is a potential green analysis method that rapidly detects multiple elements in situ. The method requires little or no sample preparation and causes no surface damage during application [1]. As a qualitative and quantitative analysis technique, LIBS has been applied in diverse fields such as environmental studies [2], industry [3], geological [4], planetary [5], art works [6], biomedicine [7], and hazardous environment exploration [8]. The major drawbacks of LIBS are its relatively low detection sensitivity and accuracy, which have restricted its development [9, 10]. To overcome these drawbacks, researchers have proposed techniques such as spark-assisted LIBS [11], microwave- and flame-assisted heating LIBS [12, 13], dual-pulse excitation LIBS [14], nanoparticle-enhanced LIBS [15] and radical fluorescence-assisted LIBS [16]. These techniques have considerably enhanced the spectral intensity and improved the detection sensitivity and analysis accuracy of LIBS, but have also increased the system complexity and the cost of LIBS. A simpler and more economical technique is spatial confinement, which is easily implemented by installing a pair of plates, a cylindrical wall, or a hemisphere. Confinement enhances the spectral intensity, detection sensitivity, and analysis accuracy of LIBS [17, 18]. Laser ablation of a target generates a shockwave together with the laser plasma. When reflected back, this shock wave compresses the plasma plume and increases the collision rate in the plasma. Encounters between the plasma plume and obstacles such as plates and cylindrical walls, regulate this process, thereby enhancing the number of atoms in high-energy excited states and boosting the spectral intensity. Popov et al. [19, 20] enhanced the spectral intensity and sensitivity of LIBS in a small brass chamber. They achieved a tenfold increase in the spectral intensity of iron in a metallic sample. Meanwhile, the spectral intensity and limit of detection (LOD) of arsenic in soil were increased by three–fivefold and two–fivefold, respectively. Shen et al. [21] reported a spectral enhancement of approximately ninefold in round pipe confinement and approximately 6.5-fold in parallel plates confinement. Su et al. [22] reported that cavity confinement improves the spectral intensity by 2.5–3.5-fold and also reduces the relative standard deviation (RSD). These experiments confirm that spatial confinement enhances the spectral intensity, sensitivity, and accuracy of LIBS.

Heavy metal pollution in soil, mainly caused by industrial pollution, followed by traffic pollution and household garbage pollution has become increasingly problematic. Human activities continue to increase the level of heavy metals circulating in the environment. Heavy metals are easily absorbed by crops and transferred to food, where they propagate through the food chain and eventually accumulate (potentially to damaging levels) in human tissues. Popov et al. [23] measured the Ag, Cu, Mo, and Pb elements in soil by ns-LIBS and concluded that LIBS is a feasible analytical method for detecting heavy metals in soil. However, the soil is an extremely complex mixture of various components such as transition metals, silica, alumina, minor elements, and trace constituents. The matrix of the multicomponents will severely degrade the analysis accuracy of LIBS.

In recent years, femtosecond LIBS (fs-LIBS) has improved the efficiency and precision of ablation, reduced the heat affected zone, and lowered the ablated mass, and fractionation vaporization of LIBS [24]. Lucia et al. [25] detected explosive residues by fs-LIBS and highlighted two main advantages of fs-LIBS over nanosecond LIBS (ns-LIBS): negligible air entrainment and reduced background continuum emission. Fornarini et al. [26] promoted a theoretical model of the ns- and fs-LIBS analyses of quaternary bronze alloys. They found that the predicted improvement in signal-to-background ratio and the concentration accuracy are related to the temperature determination; moreover, the LOD and spectral reproducibility are better in fs-LIBS than in ns-LIBS. Consequently, fs-LIBS can acquire a low continuous spectrum, allowing the accumulation of spectral signals with many laser shots [27]. But, the reduced interaction between the excitation light source and the produced plasma could be decreasing the emission intensity. Wang et al. [28] investigated the effect of spatial confinement on fs laser-induced Cu plasmas to enhance spectra. In cavities with diameters of 2 and 3 mm, the emission intensities of the Cu atomic lines were increased by 1.92 and 3.00-fold, respectively. Therefore, spatially confined fs-LIBS can be improving the accuracy and sensitivity of heavy metal analysis in soil. In this study, we present the time-resolved spectral intensity of Pb in femtosecond laser-induced soil plasma confined in a cylindrical cavity. The spatial confinement enhanced the spectral intensity and improved the quantitative analysis parameters of fs-LIBS namely as, the LOD, coefficient of determination (\( R^{2} \)), relative standard deviation (RSD), and the root mean squared error of cross-validation (RMSECV).

2 Experimental method

Figure 1 is a schematic of the spatial confinement fs-LIBS experimental setup. The femtosecond laser system is a one-box ultrafast Ti: sapphire amplifier (Libra-Usp-He, USA, Coherent) with a wavelength of 800 nm and a width of 50 fs at a repetition rate of 1.0 kHz. The laser energy can be tuned by a combined half-wave plate and Glan polarizer. Here the laser energy was set to 2.5 mJ during the whole experiment and the energy stability was 0.5%. The laser beam was reflected by a dichromatic mirror with an optical transmission waveband of 400–700 nm and was focused onto the soil sample surface by a quartz lens (L1) with a focal length of 50 mm. The soil plasma induced by the femtosecond pulse laser was confined within a cylindrical cavity and the plasma emission spectroscopy was collected by a fused quartz lens L2 (focal length of 75 mm) and coupled into a grating spectrometer (Spectra Pro500i, American PI, slit width of 30 μm) equipped with an ICCD detector (PI MAXII, 1024 × 256 pixels). The spectral resolution was 0.05 nm and the grating parameter was 1200 lines/mm at a 500 nm blaze wavelength. The soil target was mounted on a XYZ-3D translation stage to avoid excessive ablation and to ensure that each laser spot ablated the fresh surface. The ICCD detector was triggered by the femtosecond laser with an adjustable delay time for acquiring the time-resolved spectroscopy. Lead nitrate (Pb(NO3)2, 99% purity) was added to the standard soil materials (serial number GBW07458 (ASA-7)) and the experimental soil pallets were prepared by the processes such as dissolving, drying, grinding, and compression, finally, a soil pallet with a diameter of 30 mm and thickness of 4 mm was obtained. The Pb concentrations in soil samples #1–#10 are shown in Table 1. All measurements were conducted in the atmospheric environment and the cylindrical cavity was 5 mm high.

Fig. 1
figure 1

Schematic of the spatial confinement fs-LIBS experimental setup

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Table 1 Pb concentrations in the soil samples
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3 Results and discussion

Figure 2 shows the soil plasma emission spectrum generated by the femtosecond pulse laser in the 3 mm diameter cylindrical cavity. The spectroscopy was acquired from 385 to 426 nm with an ICCD delay time of 760 ns and a gate width of 300 ns. The inset is an enlargement of the spectrum in the 402–410 nm regions, in which the Pb signal appears at 405.78 nm.

Fig. 2
figure 2

Plasma emission spectrum of soil sample #2 with and without confinement in a cylindrical cavity

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As shown in Fig. 2, the soil plasma emission spectrum is crowded with the signals of many elements. The unconfined spectral intensity is weak and the signals are not easily distinguished. In the cylindrical cavity with a diameter of 3 mm, the soil plasma emission spectroscopy was obviously enhanced overall and the spectral line of Pb(I) 405.78 nm was enhanced by 5.7-fold. After ablation by a femtosecond laser, the soil plasma rapidly expands forward and compresses the ambient air gas, forming a shock wave. When the shock wave encounters an obstacle, it is reflected and compresses the expanding plasma plume into a small volume, increasing the collision probability in the plasma plume. Consequently, the particle concentration in the upper energy level increases and enhances the plasma emission spectroscopy [15, 29, 30]. Concisely, the spectral intensity is enhanced by shock wave compression during reverse transmission [31]. As evidenced in the inset of Fig. 2, the cylindrical cavity improved both the intensities and resolutions of the spectral lines.

Figure 3 shows the time-resolved plasma emission spectral intensities in cylindrical cavities of different diameters (3, 4, 5, and 6 mm), and in the unconfined plasma. The spectra around the maximum Pb 405.78 nm spectral line are magnified in the insets. As shown in the figure, the cavity enhanced the Pb 405.78 nm line in all cases. Increasing the cavity diameter markedly altered the temporal evolution profile of the emission intensity. We know that the plasma emission can be enhanced the emission with a cylindrical cavity than that without confinement, but the maximum enhancement factor, enhancement time duration, and the time delay of peak appearance all depended on the cavity diameter. The effect of spatial confinement would delay and weaken with the cavity diameter increasing. The emission enhancement was delayed by 600, 760, 1070, and 1450 ns in the cavities of diameters 3, 4, 5, and 6 mm, respectively. The maximum enhancement factors were 4.13, 4.55, 5.1, and 3.3 at delays of 760, 1000, 1160, and 1520 ns, respectively. The spatial confinement effect was maximized in the 3 mm diameter cavity. The spatial constraints obviously benefit the plasma spectrum in a diameter-dependent manner. In Sedov–Taylor theory, the expansion distance of the shock wave is given as [32]

$$ D = \lambda_{0} \left( {\frac{{E_{0} }}{{\rho_{0} }}} \right)^{{\frac{1}{2 + d}}} t^{{\frac{2}{2 + d}}} , $$
(1)

where D is the location of the wave front, \( \lambda_{0} \) is a dimensionless parameter that depends on the specific heat of the ambient gas, \( E_{0} \) is the energy released in the plasma, \( \rho_{0} \) is the undisturbed density of the ambient gas, d is the dimensionality of the propagation, and t is the expansion time. As seen in Eq. (1), the propagation distance of the shock wave is related to the expansion time. Increasing the cavity diameter increases the path of the shock wave and prolongs the delay of spectral enhancement. Because the energy of the shock wave dissipates quickly in the larger diameter cavity, the shock wave must travel for a longer time before being reflected, which attenuates the spatial confinement effect. So, for the larger cylindrical cavity confinement femtosecond induced plasma, the delay time of the spectral enhancement was later and the enhancement effect was weaken [33].

Fig. 3
figure 3

Time-resolved plasma emission spectral intensities during confinement in cavities with diameters of 3 mm (a), 4 mm (b), 5 mm (c), and 6 mm (d). The insets show the peaks around 760 ns (a), 1000 ns (b), 1160 ns (c), and 1520 ns (d)

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During the early stage of laser-induced plasma expansion, the neutral atom radiation separation spectrum is overwhelmed by continuous background (bremsstrahlung and recombination emissions). After a certain delay time, the continuous spectrum disappears and the resolution and signal-to-background ratio of the separated spectrum improve as the signal-to-noise ratio decreases continuously [34]. Considering the spectral acquisition delay time, we assessed the figures of merit of LIBS in the 3 mm diameter cavity.

The R2 coefficient, which evaluates the linearity of the relation between the signal intensity yi and concentration of the target element xi, is given by [35]:

$$ R^{2} = \frac{{\left[ {\sum\nolimits_{i - 1}^{n} {(x_{i} - \bar{x})(y_{i} - \bar{y})} } \right]^{2} }}{{\sum\nolimits_{i - 1}^{n} {(x_{i} - \bar{x})^{2} \cdot \sum\nolimits_{i - 1}^{n} {(y_{i} - \bar{y})}^{2} } }}, $$
(2)

where the \( \bar{x} \) and \( \bar{y} \) represent the average concentration and signal intensity in the whole sample, respectively. The R2 coefficients were determined as 0.983 and 0.976 in the presence and absence of the cylindrical cavity, respectively.

The RMSECV evaluates the predicted results by the leave-one-out cross-validation method. It is calculated as:

$$ {\text{RMSECV}} = \sqrt {\frac{{\sum\nolimits_{i - 1}^{n} {(\hat{y}_{i} - y_{i} )} }}{n}} , $$
(3)

where \( \hat{y}_{i} \) and \( y_{i} \) represent the certified and predicted concentrations of sample i, respectively, and n denotes the number of samples. The RMSECV values were 0.459% and 0.543% in the presence and absence of the cylindrical cavity, respectively.

The LOD, which measures the sensitivity of the LIBS, is expressed as:

$$ {\text{LODs}} = 3\frac{{S_{\text{bac}} }}{M}, $$
(4)

where \( S_{\text{bac}} \) is the standard deviation of the background signal and \( M \) is the slope of the calibration curve (Fig. 4). The \( S_{\text{bac}} \) was evaluated as 1.62 and 1.85 in the presence and absence of the cylindrical cavity, respectively. From the slopes of the calibration curve, the corresponding LODs were determined as 8.85 ± 0.16 and 33.16 ± 1.45 mg/kg.

Fig. 4
figure 4

Calibration curves of Pb element with and without a cylindrical cavity (D = 3 mm)

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As evidenced in Table 2, the spatial confinement improved the performance of the LIBS; the LOD (sensitivity measure) was decreased by 3.75-fold, while the RMSECV and RSD (accuracy measures) were decreased by 1.18-fold and 2.54-fold, respectively. Meanwhile, the R2 value was increased by 1.3%. Therefore, the sensitivity and accuracy of quantifying Pb in soil samples were improved by the spatial confinement. When the shock wave encounters the cavity wall and is reflected to compress the plasma plume in the confined space, the plasma plume is homogenized, enhancing the spectral intensity and improving the spectral stability. Consequently, the sensitivity, accuracy, and precision of the LIBS analysis are improved and the analysis becomes easier and clearer [36, 37].

Table 2 Parameters of LIBS analysis in the cavity (D = 3 mm) and in the unconstrained plasma
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4 Conclusions

This work investigated the effect of spatial confinement on fs-LIBS measurements of a heavy metal element (Pb) in soil. After optimizing the spatial diameter (3 mm) and the delay time, the emission spectrum was increased by ~ 4.2-fold and the LOD, \( R^{2} \), RSD, and RMSECV were 8.85 ± 0.16 mg/kg, 0.45%, 4.98%, and 98.34%, respectively (versus 33.16 ± 1.45 mg/kg, 0.54%, 8.21%, and 97.66%, respectively, in the unconfined plasma). Therefore, the spatial confinement improved the sensitivity and accuracy of quantifying heavy metal elements in soil by LIBS. The study results provide a new pathway for improving the analytical ability of ultrafast optical LIBS technology.