Investigating the impact and mechanisms of integration time on LIBS repeatability and plasma parameter inversion results

Abstract

Although a longer integration time can enhance the spectral intensity, it also obscures more information regarding plasma evolution. In this study, laser-induced plasma (LIP) is detected simultaneously by using both long-integration-time and short-integration-time spectrometers via a Y-shaped fiber, and the effect of integration time on the repeatability and the inversion of plasma parameters for laser-induced breakdown spectroscopy (LIBS) spectra is investigated. The results reveal that (1) the radiation decay rate at the same wavelength varies among different LIPs, leading to increased differences in line intensities with longer integration times. However shorter integration times theoretically improve repeatability, in fact, shorter integration times tend to improve the repeatability of strong emission lines, but reduce the repeatability of weak emission lines by reducing their signal-to-background ratios (SBRs) and signal-to-noise ratios (SNRs). (2) The radiation decay rates at different wavelengths also vary within the same plasma, causing further increases in spectral line intensity differences with longer integration times. This results in greater vertical dispersion of data points in Boltzmann or Saha–Boltzmann plots, leading to underestimated plasma temperatures. (3) Longer integration times may also lead to underestimation of electron densities derived from the Stark broadening method. This study provides significant guidance for optimizing LIBS integration parameters, improving repeatability and advancing plasma spectral diagnostics.

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1. Introduction

The recording of images relies on the integration of light by photosensitive elements, a process referred to as exposure in photography.^1,2 For stationary objects, the duration of exposure typically does not influence the information captured in the image, provided that underexposure or overexposure is avoided.³ However, for moving objects, information about a specific moment can only be captured when the exposure time is significantly shorter than the duration of the object's motion.^4,5 Continuous image acquisition under such conditions enables a comprehensive analysis of the object's state changes.

Laser-induced plasma (LIP), the primary subject of observation and analysis in laser-induced breakdown spectroscopy (LIBS), typically exhibits a lifetime of only a few microseconds.^6–8 Spectral information of LIBS, as a key approach to studying LIPs, is widely used to infer plasma temperature and electron density, thereby elucidating the relationship between plasma evolution and LIBS spectral repeatability.^9–12 To accurately assess the state changes and underlying mechanisms of plasmas through these inferred parameters, the spectrometer's integration time must be significantly shorter than the plasma lifetime, ideally on the nanosecond scale or below.^13–17 During this integration phase, the LIP can be regarded as stationary and unchanging. However, in practical research applications, spectrometer integration times are often set at the microsecond or millisecond scale. During this integration phase, the LIP undergoes rapid changes, resulting in spectra that represent an accumulation of the plasma's spatiotemporal evolution. Although longer integration times can enhance spectral line intensity and improve LIBS detection limits to some extent,^18,19 they inevitably lead to the loss of critical plasma evolution information, such as changes in background, noise, and atomic emissions. This loss hinders the evaluation of characteristic spectral line quality, including metrics such as signal-to-noise ratio (SNR), signal-to-background ratio (SBR), and repeatability. Furthermore, plasma parameters derived from spectral diagnostics lack temporal resolution, providing only apparent values that obscure the analysis and understanding of LIP mechanisms.

Based on the well-documented temporal evolution characteristics of LIPs and current research findings, the influence of integration effects on the SNR and SBR is well-established.^20–26 Specifically, during the later stages of background radiation decay and the early stages of atomic emission, longer integration times generally result in higher SBR and SNR values. However, the impact of integration time on repeatability has received limited attention and has only been studied as part of the optimization of experimental parameters. Consequently, no consensus has been reached and the results have not been interpreted.²⁷ This is because plasma fluctuations can lead to varying repeatability across different sampling sets, even when multiple samplings are performed with identical integration parameters in LIBS. As a result, the impact of plasma fluctuations on repeatability obscures the effect of integration time on repeatability. It remains challenging to determine whether observed variations in repeatability are attributable to changes in integration time or to plasma fluctuations.

Furthermore, research on the impact of integration time on plasma temperature and electron density diagnostics remains insufficient. When discussing the significance, precision, trueness, and accuracy of plasma temperature calculations using the Boltzmann plot method, Bruno Bousquet et al. mentioned that, since all emission lines decay at different rates, the data points used to construct the Boltzmann plot in long-integration LIBS measurements are expected to scatter significantly; this would greatly reduce the accuracy of plasma temperature calculations.²⁸ However, this study focused on the accuracy of temperature calculations and did not report specific differences in plasma temperature with varying integration times, nor did it discuss electron density. In a separate study, Luís Carlos Leva Borduchi et al. compared plasma temperatures and electron densities at different integration times after single-point calibration of spectra obtained at different integration times. They concluded that plasma temperature and electron density are unaffected by integration time.²⁹ However, they did not exclude the influence of plasma fluctuations on the results, nor did they explore the effect of integration time on plasma parameters in the absence of spectral calibration.

In this study, two spectrometers with identical delay times but different integration times are employed to probe the same plasma, thereby enabling a direct comparison while excluding the influence of plasma fluctuations on the results. The impact of integration time on LIBS repeatability and plasma spectroscopic diagnostics is systematically investigated, and the underlying mechanisms are elucidated.

2. Equipment, sample and experiments

2.1 Equipment

The experimental setup is illustrated in Fig. 1. The laser source is a Q-switched Nd:YAG laser (DAWA200, Beamtech Optronics, China), operating at 1064 nm with a pulse duration of less than 8 ns, an energy of up to 150 mJ per pulse, and a repetition rate of 1 Hz. After reflection, the laser beam passes through a dichroic mirror and is then focused by a 20 mm focal length, 10× magnification microscope objective coupled with a microscope camera (preceded by a 0.5× sleeve lens). The sample is mounted on a three-dimensional translation stage, enabling precise focusing of the laser onto the sample surface. The plasma radiation is collected by two plano-convex lenses, each with a focal length of 50 mm, and subsequently directed into a Y-shaped fiber optic. This fiber optic directs the radiation to two distinct devices: a spectrometer (Mechelle 5000, Andor Technology Ltd, UK), equipped with an ICCD detector (iStar DH334T, Andor Technology Ltd, UK), and a spectrometer, equipped with a CCD detector (AvaSpec-ULS2048, Avantes BV, Netherlands). The ICCD spectrometer offers a resolution (λ/Δλ) of 5000, a wavelength range of 200–975 nm, and a gain setting of 2000, while the CCD spectrometer provides a resolution of 0.7 nm and a wavelength range of 188–756 nm.

Fig. 1 Schematic diagram of experimental equipment.

2.2 Sample

The experimental sample is a brass alloy QBYS199515 from the China Steel Research Institute. Table 1 lists the primary constituent elements (Cu, Zn, Pb, and Fe) and their corresponding concentrations. Notably, copper (Cu) and zinc (Zn) collectively account for over 99% of the total composition, rendering them the dominant contributors to the observed characteristic spectral lines.

Table 1 Major elemental concentrations of the brass alloy sample

Sample serial no.	Cu (%)	Zn (%)	Fe (%)	Pb (%)
QBYS199515	60.81	38.59	0.236	0.294

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2.3 Experiments

2.3.1 Timing setting. The timing setup in the experiment is shown in Fig. 2. The ICCD's integrated three-channel (corresponding to ICCD output1, ICCD output2 and ICCD output3 in Fig. 2) triggering mechanism synchronizes both the laser system and CCD spectrometer.

Fig. 2 Timeline diagram of the device.

The CCD spectrometer operates with an inherent 170 µs integration delay, necessitating temporal alignment of the ICCD's triggering sequence. Upon activation of the ‘Start’ command in the ICCD software, the trigger signal is instantaneously transmitted to the CCD spectrometer. After a 20 µs interval, a CLK IN signal is delivered to the laser, followed by the Q IN signal after the full 170 µs delay, thereby activating the laser system. The ICCD's delay time (this delay time is relative to the activation of the “Start” command in the ICCD software) is set to 170 µs. This synchronization ensures simultaneous integration initiation in both the CCD and ICCD spectrometers, with 0 delay relative to laser emission, as illustrated in Fig. 2. The delay times for the two spectrometers mentioned below are all relative to the laser emission.

2.3.2 Sampling and evaluation methods. Given that the radiation lifetime of the LIP in this experiment is approximately 10 µs, the temporal parameters of the detection system are configured as follows: the delay times of both the CCD and ICCD spectrometers are synchronously varied from 0 µs to 5 µs in 1 µs increments; for each delay setting, the integration time of the ICCD spectrometer is set to 1, 2, 4, 6, 8, or 1050 µs, while that of the CCD spectrometer is kept constant at 1050 µs to serve as a reference spectrum.

At the same position, 20 consecutive pulses are shot to simultaneously acquire 20 CCD spectra and 20 ICCD spectra, thus forming one data set. Each time the delay parameter or the integration time of the ICCD spectrometer is changed, a new sampling position is chosen to acquire a data set. Three critical diagnostic ratios are derived from each data set: the ratio of the relative standard deviation (RSD^ICCD/RSD^CCD), the ratio of the average plasma temperature (T^ICCD/T^CCD), and the ratio of the average electron density (n^ICCD_e/n^CCD_e). By comparing the variations of RSD^ICCD/RSD^CCD, T^ICCD/T^CCD, and n^ICCD_e/n^CCD_e with ICCD integration time at a specific delay, the influence of integration time on repeatability, plasma temperature, and electron density can be evaluated.

Two points require clarification:

(1) In traditional studies investigating the effect of integration time on repeatability, plasma temperature, and electron density, a common approach involves collecting one dataset each time the integration time is adjusted. Subsequently, the impact of integration time on these three parameters is evaluated based on the repeatability, average plasma temperature, and average electron density derived from each respective dataset. However, this approach overlooks the discrepancies between different datasets, which arise from the inherent instability of LIP. As a result, the evaluation of how integration time affects the three parameters is subject to randomness. In contrast, the aforementioned evaluation method can effectively avoid the interference caused by the instability of LIP, thereby revealing the intrinsic correlation between integration time and the three parameters with higher accuracy.

(2) Although the use of two spectrometers with different integration times to probe the same plasma ensures that the repeatability, average plasma temperature, and average electron density obtained by both experience identical influences from plasma fluctuations, this approach introduces additional impacts on these three parameters caused by inherent differences in fixed instrumental parameters. The 1050 µs value in the ICCD's integration parameters is specifically set to correspond with the CCD's integration time. When the integration times of both are the same, it becomes possible to visually demonstrate the impact of discrepancies in the fixed instrumental parameters of the two spectrometers on the analysis results. On this basis, by further shortening the integration time of the ICCD and analyzing the changing trends of RSD^ICCD/RSD^CCD, T^ICCD/T^CCD, and n^ICCD_e/n^CCD_e, the influence of integration time on these three parameters while eliminating the effects caused by the fixed instrumental parameters of the two spectrometers can be demonstrated.

2.3.3 Plasma temperature and electron density calculations. The plasma temperature in this experiment is calculated using the Saha–Boltzmann plot method. The Boltzmann formula and the Saha ionization equation are combined to obtain the Saha–Boltzmann equation:where the superscripts sI and sII represent the atomic and the first ionized parameters of species s, respectively. I^sI_mn is the atomic emission line from level m to level n for species s, g^sI_m is the degeneracy of level m, A^sI_mn is the transition probability, h is Planck's constant, n_e is the electron density, k is the Boltzmann constant, m_e is the electron mass, T is the plasma temperature, E_ion is the ionization potential, ΔE_ion is the lowering correction parameter, and E^sI_m is the energy of the excited state m.

Applying ln to both sides of eqn (1) results in the following equation:

and (E_ion − ΔE_ion + E^sII_i − E^sI_m) are linearly related according to eqn (2), and the plasma temperature can be calculated by solving for the slope .

Although the method for calculating plasma temperature described above can also be used to determine the electron density by solving for the intercept , this approach introduces errors from plasma temperature, transition probabilities, ionization energy, and other factors, leading to a relatively large error in the calculated electron density.^30–33 Therefore, the Stark broadening method is chosen in this study for the electron density calculations. The Stark broadening of a line, expressed as the full width at half maximum (FWHM) in nanometers, is given by

Here, the electron impact parameter w, which is temperature-dependent, can be found in the literature. Although w is also affected by the plasma temperature, its variation with temperature is relatively small.

2.3.4 Selection of spectral lines. Fig. 3 shows the spectra of the same LIP obtained by both the CCD and ICCD, with a delay of 1 µs and an integration time of 1050 µs. From the overall view, it can be observed that there are differences in the wavelength coverage and detection efficiency between the two. In the zoomed-in section, the difference due to resolution is also evident: spectral lines that can be resolved in high-resolution spectra are interfered with or even covered by nearby stronger lines in the low-resolution spectra. Additionally, from the marked spectral lines in the figure, it can be seen that the intensity of atomic lines is significantly higher than that of ionic lines.

Fig. 3 CCD and ICCD spectra for the same plasma.

Considering the difference in resolution between the two spectrometers, the Zn I, Cu I, and Cu II spectral lines in the Table 2 are selected as the research subjects. These spectral lines are not affected by neighboring lines in either the high-resolution or low-resolution spectra. Among them, Zn I 472.22 nm and Cu I 324.75 nm lines are relatively strong and have long lifetimes, making them the main focus in the repeatability study. The other Cu lines will be used for plasma temperature calculation. It is important to note that, although Cu I 324.75 nm is a resonance line, no self-absorption phenomenon is observed in this study (in fact, during spectral acquisition, focus is placed on the line shape characteristics of the Cu I 324.75 nm spectral line. If self-absorption occurs in this spectral line, the corresponding spectrum is discarded and re-sampled). Additionally, due to the high intensity of Cu I 324.75 nm, even in the low-resolution spectra, the number of data points for this line is relatively abundant, which is beneficial for fitting and broadening calculations. Therefore, it is used for plasma density calculations.

Table 2 Spectral lines involved in the study

Species	Wavelength (nm)
Zn I	472.22
Cu I	324.75
Cu I	406.26
Cu I	427.51
Cu I	515.32
Cu I	521.82
Cu I	578.21
Cu II	213.59
Cu II	218.14
Cu II	224.31
Cu II	237.07
Cu II	368.65

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For Fe and Pb elements, two key challenges are encountered during the experimental analysis: first, both elements are present at relatively low concentrations in the sample matrix, which results in weak signal intensities of their excited spectral lines; second, Fe has a large number of characteristic spectral lines, while Pb has relatively few characteristic spectral lines. The combination of these two factors makes it particularly difficult to select “clean spectral lines” (i.e., characteristic spectral lines free from interference from other elements' spectral lines or background interference) for these two elements that not only have high signal intensities but also can be effectively resolved by the CCD spectrometer. Therefore, the spectral lines of these two elements are not within the analytical scope of this study.

3. Results

3.1 Effect of integration time on repeatability

Fig. 4 illustrates the variations in line intensities of Zn I 472.22 nm and Cu I 324.75 nm with shot number, as simultaneously recorded by both the CCD and ICCD spectrometers at a delay time of 1 µs and an integration time of 1050 µs. Overall, the intensity variations in the ICCD and CCD spectra are generally consistent, indicating that when the two instruments share identical temporal parameters, differences in other parameters exert minimal influence on data repeatability.

Fig. 4 Variation in the intensity of CCD spectra and ICCD spectra with the number of samples at the same time parameter. (a) Zn I 472.22 nm and (b) Cu I 324.75 nm.

In Fig. 5a and b, the red lines depict variations in the RSD of spectral line intensities at Zn I 472.22 nm and Cu I 324.75 nm obtained by the ICCD at different integration times. Notably, observation of the red line alone might lead to the conclusion that the RSD decreases initially and then increases with integration time.

Fig. 5 Variation in the RSD obtained by the ICCD with integration time (the black dots in the figure are the RSDs obtained by the CCD at a fixed integration time, which are independent of the horizontal coordinate axis and are only a reference for the red line). (a) Zn I 472.22 nm and (b) Cu I 324.75 nm.

However, the variation trends of the black and red lines are generally consistent. The black dots on the black line represent RSD values acquired by the CCD spectrometer at a fixed integration time (1050 µs, independent of the horizontal axis coordinates in the figure), indicating that RSD variations from the CCD are not driven by integration time but by LIP fluctuations within each group. Since black and red dots at the same abscissa correspond to RSD values obtained by simultaneous detection of the same group of LIPs using the CCD and ICCD, respectively, it is suggested that RSD variations observed in the ICCD at different integration times—though seemingly attributed to integration time—are actually dominated by LIP fluctuations. In other words, repeatability variations induced by LIP fluctuations far exceed those caused by integration time, such that the latter are overshadowed by the former.

As the ICCD integration time decreases from 1050 µs, the discrepancy in RSD values between the two spectrometers gradually increases. This variation in RSD discrepancy is solely attributed to changes in the ICCD's integration time. To isolate the influence of plasma fluctuations and quantitatively assess the impact of integration time on repeatability, the ratio RSD^ICCD/RSD^CCD is employed to evaluate the discrepancy between the RSD values obtained by the ICCD and CCD, with analysis focused on its relationship with ICCD integration time.

Fig. 6 illustrates the variation of RSD^ICCD/RSD^CCD with ICCD integration time for Zn I 472.22 nm and Cu I 324.75 nm lines at different delay settings. When the ICCD integration time is 1050 µs, RSD^ICCD/RSD^CCD approaches 1, indicating that for the same group of LIPs, the RSD values from the two spectrometers are nearly identical at identical integration times. As the ICCD integration time decreases, RSD^ICCD/RSD^CCD diminishes progressively, suggesting that for the same group of LIPs, shorter integration times correspond to lower RSD values.

Fig. 6 Variation of RSD^ICCD/RSD^CCD with integration time at different delay times. (a) Zn I 472.22 nm (b) Cu I 324.75 nm.

The RSD^ICCD/RSD^CCD ratios of the other 10 spectral lines at different integration times are further investigated. Table 3 presents these ratios at varying integration times with a 1 µs delay. For all Cu I lines, the ratios increase with integration time, indicating better repeatability at shorter integration times. Among Cu II lines, some (e.g., 213.59 nm and 218.14 nm) exhibit increased ratios at shorter integration times, while others (224.31 nm, 237.07 nm, and 368.65 nm) show no significant correlation.

Table 3 RSD^ICCD/RSD^CCD of Cu I and Cu II series spectral lines at different integration times with a delay of 1 µs

Species	Wavelength (nm)	Integration time (µs)
		RSD^ICCD/RSD^CCD
		1	2	4	6	8	1050
Cu II	213.59	3.430	4.162	2.672	2.615	1.975	3.061
	218.14	4.898	4.311	5.404	2.643	2.327	1.700
	224.31	1.922	2.363	1.047	2.123	1.504	2.411
	237.07	1.255	1.283	1.386	0.995	1.084	1.188
	368.65	0.466	0.741	1.034	0.800	0.854	1.144
Cu I	406.26	0.452	0.552	0.598	0.555	0.789	0.911
	427.51	0.868	0.895	0.902	1.027	1.012	1.017
	515.32	0.594	0.625	0.669	0.816	0.911	1.048
	521.82	0.628	0.633	0.671	0.937	0.916	0.972
	578.21	0.390	0.450	0.534	0.543	0.612	0.993

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3.2 Effect of integration time on the diagnosis of plasma parameters

3.2.1 Effect of integration time on plasma temperature diagnostics. Due to the relatively weak Cu II series lines and their short lifetimes of 3–4 µs, coupled with the presence of strong background at 0 µs, this study only compares the relationship between the diagnostic result of the plasma temperature and integration time for delay times ranging from 1 to 3 µs. After calculation, it is found that the ICCD and CCD spectra satisfy the McWhirter criterion under the 1–3 µs delay conditions (CCD spectra only nominally satisfy the McWhirter criterion).

Fig. 7a and b present typical Saha–Boltzmann plots for ICCD and CCD spectra at a delay time of 1 µs and an integration time of 1050 µs. The data points from the ICCD spectrum exhibit greater vertical dispersion compared to those from the CCD spectrum. Consequently, the plasma temperature derived from the ICCD spectrum is lower than that from the CCD spectrum. This indicates that when the two instruments share identical temporal parameters, discrepancies in other parameters significantly affect the calculation of plasma temperature, which is primarily attributed to differences in their spectral response functions.

Fig. 7 Saha–Boltzmann plot at a delay time of 1 µs and an integration time of 1050 µs. (a) CCD and (b) ICCD.

The black lines in Fig. 8 illustrate the variation of average plasma temperature with integration time across 20 pulses, derived from ICCD and CCD spectra within the 1–3 µs delay range. Despite significant numerical discrepancies in the plasma temperature diagnostic results from the two detectors, their variation trends remain generally consistent. However, the numerical discrepancy gradually diminishes as the ICCD integration time decreases. Since the spectral response function is independent of integration time, it can be deduced that variations in this discrepancy are attributable to differences in integration time.

Fig. 8 Variation of T^ICCD and T^ICCD/T^CCD with integration time at different delay times. (a) 1 µs, (b) 2 µs and (c) 3 µs.

The T^ICCD/T^CCD ratio is employed to evaluate the discrepancy between the plasma temperatures obtained by the ICCD and CCD. Within the 1–3 µs delay range, the relationship between T^ICCD/T^CCD and integration time reveals an inverse correlation, as depicted by the red line in Fig. 8. The T^ICCD/T^CCD increases with decreasing integration time, demonstrating that plasma temperatures derived from spectra with shorter integration times are comparatively higher. Therefore, at a certain delay moment, the plasma temperature derived from the long integration spectrum is lower than the instantaneous plasma temperature at that delay moment.

3.2.2 Effect of integration time on electron density diagnostics. The correlation between electron density and integration time within the 1–3 µs delay range is also investigated. Fig. 9 presents the Lorentzian fitting results for Cu I 324.75 nm in both ICCD and CCD spectra at a delay time of 1 µs and an integration time of 1050 µs. Due to the lower resolution of the CCD compared to the ICCD, fewer data points are included in the Lorentzian fitting of the CCD spectrum, resulting in a broader linewidth in the CCD spectrum than in the ICCD spectrum.

Fig. 9 Lorentzian fitting results for Cu I 324.75 nm at a delay time of 1 µs and an integration time of 1050 µs. (a) CCD and (b) ICCD.

Owing to the differing instrumental broadening of the two spectrometers, the electron density derived from CCD spectra is ultimately significantly higher than that obtained from ICCD spectroscopy. However, as shown by the black lines in Fig. 10, the variation trends of plasma densities obtained from both spectra are largely consistent. Similarly, to investigate the effect of integration time on electron density diagnostics, the relationship between the n^ICCD_e/n^CCD_e ratio and integration time is further illustrated by the red line in Fig. 10. However, the correlation between the n^ICCD_e/n^CCD_e ratio and integration time is not significant, despite a tendency for this ratio to increase as the integration time decreases.

Fig. 10 Variation of n^ICCD_e and n^ICCD_e/n^CCD_e with integration time at different delay times. (a) 1 µs, (b) 2 µs and (c) 3 µs.

4. Discussion

4.1 Reasons for different spectral lines showing different repeatability trends with integration time

The following section will explore the reasons why the RSD of different spectral lines exhibits discrepancies as the integration time varies.

Fig. 3 demonstrates that the Zn I 472.22 nm, Cu I 324.75 nm and other Cu I series lines exhibit significantly greater intensities compared to Cu II series lines. While the SNR exerts limited influence on repeatability for strong emission lines, this parameter substantially governs repeatability in weak-line scenarios. Taking Cu I 324.75 nm and Cu II 237.05 nm as examples, the relationship between the SNR (the data within the 363 nm to 368 nm wavelength band without spectral lines are selected as the noise data for calculating the SNR) and integration time is shown in Fig. 11a and b. As can be seen from the figure, for the two spectrometers with identical temporal parameters, for the Cu I 324.75 nm line, the CCD exhibits a higher SNR than the ICCD, whereas for the Cu II 237.05 nm line, the ICCD demonstrates a superior SNR compared to the CCD. This is attributed to the differential detection efficiencies of the two spectrometers across wavelength regions, as demonstrated in Fig. 3. Here, the intensity of Cu I 324.75 nm is higher in the CCD spectrum compared to the ICCD spectrum, while the reverse holds for Cu II 237.05 nm.

Fig. 11 Variation of the SNR^ICCD and SNR^ICCD/SNR^CCD with integration time. (a) Cu I 324.75 nm and (b) Cu II 237.07 nm.

Fig. 11a and b also clearly illustrate that the SNR of the ICCD increases as the integration time increases, whereas the SNR of the CCD fluctuates randomly within a certain range due to its fixed integration time. Furthermore, as shown by the red line in Fig. 11, the SNR^ICCD/SNR^CCD ratio is negatively correlated with the integration time, indicating a decrease in the SNR as integration time shortens.

At earlier delay times, for high-intensity lines such as Zn I 472.22 nm, Cu I 324.75 nm, and other Cu I series lines, even with short integration times, the SNR remains high. In these cases, noise fluctuations represent a minor component of the spectral signal, with negligible impact on signal repeatability. Thus, it can be inferred that the atomic emission decay rates at the same wavelength differ among various LIPs (exponential decay). LIBS spectra are generated by integrating atomic emission; consequently, longer integration times amplify the cumulative effect of intensity disparities caused by varying atomic emission decay rates. As a result, the repeatability of high-SNR lines improves with decreasing integration time.

For Cu II 213.59 and Cu II 218.14, however, emissions are inherently weak. Even with long integration times, their SNR remains low, and repeatability is dominated by noise. As the integration time shortens, the impact of noise on repeatability becomes more pronounced, far outweighing the beneficial effects of shorter integration times on repeatability. Thus, the repeatability of low-SNR lines decreases as the integration time decreases.

Other Cu II series lines (Cu II 224.31, Cu II 237.07, and Cu II 368.65) exhibit intermediate intensity between strong and weak extremes. As the integration time decreases, noise fluctuations and decay rates collectively affect repeatability. Therefore, for lines with a moderate SNR, no clear correlation exists between repeatability and integration time, as both factors influence the result.

As delay time increases, both the spectral line intensity and SNR diminish. Therefore, for high-SNR spectral lines, the relationship between repeatability and integration time exhibits the three aforementioned scenarios as the delay time increases.

Notably, at earlier delay times, LIP background radiation may still be rapidly declining. As the integration time decreases, the SBR diminishes.²² At this point, repeatability may still be challenged by the background intensity.

In summary, short integration times enhance repeatability for spectral lines with high SNRs and SBRs.

4.2 The reason for the impact of integration time on plasma parameter diagnostics

4.2.1 Plasma temperature. Intuitively, at the same delay time, the plasma temperature calculated for spectra with longer integration times is lower than that for spectra with shorter integration times. This is because, with shorter integration times, the calculated plasma temperature is closer to the instantaneous plasma temperature at that delay time. In contrast, with longer integration times, the plasma temperature decreases over time, thus the plasma temperature calculated with longer integration times represents an averaged plasma temperature in both time and space (a more accurate term would be ‘apparent temperature’).^28,34,35

From the perspective of atomic emission decay rates in the plasma and plasma temperature calculation, using the Saha–Boltzmann plot method employed in this study as an example, different spectral lines decay exponentially at varying rates within the same plasma. Therefore, the intensity differences between different spectral lines increase with longer integration times, leading to an increase in the difference in values. In the Saha–Boltzmann plot, the data points are stretched vertically, while the (E_ion − ΔE_ion + E^sII_i − E^sI_m) remains unchanged, meaning that the horizontal axis stays constant. As a result, the slope decreases, leading to an underestimated final plasma temperature.

Taking the Boltzmann plot method as an example, it is easier to understand that increasing intensity differences between spectral lines with longer integration times correspond to greater differences in ln(I^sII_mnA^sI_mng^sI_m) values. In the Boltzmann plot, data points are stretched vertically, while the E^sI_m remains unchanged, resulting in a smaller slope and an underestimated final plasma temperature.

4.2.2 Electron density. In Fig. 10, no obvious correlation is observed between the calculated electron density results and integration time. Further discussion of the relationship between electron density and integration time is based on eqn (3). As indicated by eqn (3), the FWHM and the electron impact parameter w are critical parameters for determining electron density via the Stark broadening method. Thus, variations in FWHM and w with integration time dictate how electron density evolves with integration time.

w is dependent on the plasma temperature, and the calculation of plasma temperature is influenced by the integration time. Consequently, w should also vary with changes in integration time. Subsequently, the variation of FWHM^ICCD and FWHM^ICCD/FWHM^CCD with integration time is investigated, as shown in Fig. 12. As demonstrated, the trends of FWHM^ICCD/FWHM^CCD and n^ICCD_e/n_eCCD with integration time are essentially identical. Based on the analysis, the influence of w on the electron density calculation is predominantly obscured by the FWHM.

Fig. 12 Variation of FWHM^ICCD and FWHM^ICCD/FWHM^CCD with integration time at different delay times. (a) 1 µs (b) 2 µs (c) 3 µs.

The experimentally measured line broadening results from the convolution of instrumental broadening and physical broadening (In LIBS, physical broadening is dominated by Stark broadening). The difference in instrumental broadening is mainly due to the difference in optical resolution of the two spectrometers, detector pixel size and optical system aberration, and is therefore not affected by the integration time. Therefore, the variation in the discrepancy of spectral line broadening between the two spectrometers with respect to integration time is mainly attributed to the variation of Stark broadening with integration time. In other words, the variation of FWHM^ICCD/FWHM^CCD with integration time is actually the variation of Stark broadening with integration time. However, in practical measurements, the instrumental broadening discrepancies between the two spectrometers are excessively large. The instrumental broadening can interfere with the observation of the relationship between integration time and Stark broadening, resulting in an inconspicuous negative correlation between FWHM^ICCD/FWHM^CCD and integration time. Ideally, FWHM^ICCD/FWHM^CCD and integration time may exhibit a negative correlation. In other words, as the integration time decreases, the plasma density calculated via the Stark broadening method may be higher.

For the short-integration spectra and long-integration spectra acquired at the same delay time, there are significant differences in the plasma parameters derived from their inversion calculations.

In terms of plasma temperature, the inversion results from the short-integration spectra can more accurately reflect the instantaneous plasma temperature at this delay time; in contrast, the plasma temperature inverted from the long-integration spectra is often lower than the instantaneous plasma temperature at this delay time.

In terms of electron density, the pattern is consistent with that of temperature: the inversion results of the short-integration spectra are more consistent with the instantaneous electron density at this delay time; in contrast, the electron density inverted from the long-integration spectra is also lower than the instantaneous electron density at this delay time.

5. Conclusions

In this study, both short-integration and long-integration spectra of the same plasma were acquired by jointly monitoring the plasma with an ICCD spectrometer (short integration times) and a CCD spectrometer (long integration times). The effects of integration time on the repeatability, plasma temperature, and electron density diagnostics of LIBS measurements were analyzed. For different LIPs, the radiation decay rates at the same wavelength differ, and these intensity discrepancies increase as the integration time lengthens. Although shorter integration times improve LIBS repeatability, the influence of integration time on the SNR and SBR must also be considered when analyzing spectra at different wavelengths and delay times. For the same plasma, different spectral lines exhibit varying decay rates, with smaller discrepancies between spectral lines at short integration times than at long integration times. Long integration times cause the data points in the Boltzmann plot to stretch along the vertical axis, resulting in a relatively lower plasma temperature. Additionally, the electron density calculated via the Stark broadening method may be higher at short integration times than at long integration times.

Although the plasma temperature and electron density determined in this research meet the McWhirter criterion, it's crucial to recognize that this criterion serves as a necessary but not sufficient condition for confirming LTE. In addition to satisfying the McWhirter criterion, it is equally vital to verify whether the plasma temperatures of different species are consistent. However, achieving uniform plasma temperatures across various species is highly challenging due to uncertainties in spectral parameters. Moreover, it's important to note that the integration time of the CCD spectrum in our experiments exceeds the lifetime of the LIP. Consequently, the obtained spectrum inevitably includes light intensity contributions from periods when the LIP is not in LTE. Under such circumstances, discussing whether the CCD spectrum fully satisfies LTE conditions becomes somewhat meaningless, as the spectrum is a composite of emissions from both LTE and non-LTE states. This limitation underscores the necessity for future studies to explicitly investigate the dependence of LTE validity on integration time, to ensure more accurate plasma parameter inversion and a deeper understanding of plasma behaviour.

Due to equipment limitations, this study employed two spectrometers with different models, which introduced the influence stemming from the disparities in spectrometer parameters into the evaluation results. It is anticipated that better results would be achieved by using two ICCD spectrometers with identical parameters.

Author contributions

Chao Li (first author): conceptualization, data curation, formal analysis, investigation, methodology, software, validation, visualization, writing – original draft. Yunfeng Bi (corresponding author): conceptualization, funding acquisition, investigation, project administration, resources, supervision, writing – review & editing. Zhongyi Bao: resources, supervision. Tao Zhang: resources, supervision. Caijie Liu: resources, supervision. Meili Guo: resources, supervision. Man Wang: resources, supervision.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data used in the manuscript are available with the authors and will be provided upon request.

Acknowledgements

This research was supported by Natural Science Foundation of Shandong Province (Grant No. ZR2020MD040) and Shandong Province Deep Gold Exploration Big Data Application Development Engineering Laboratory Open Subjects (Grant No. SDK202204)

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