With the technological advances in analytical chemistry over the past decades, the study of spectroscopy has become popular, providing rich and comprehensive information about chemical and mechanical properties, such as Raman spectroscopy,1^–3 infrared spectroscopy,4^–6 Brillouin spectroscopy,7^–9 etc.10^,11 Plasma spectroscopy, a main branch of spectroscopy, utilizes plasma as the source of emission spectra, offering a readily available and reliable technique commonly employed to observe elemental content and distribution. Nowadays, many plasma-based spectroscopic techniques have been developed, such as direct reading spark emission spectroscopy, laser-induced breakdown spectroscopy (LIBS), glow discharge optical emission spectroscopy (GD-OES), inductively coupled plasma emission spectroscopy (ICP-OES), and so on.12^–15 However, in many cases, plasmas typically have high temperatures, small sizes, and short lifetimes, making their behavior highly unstable and unpredictable. They are susceptible to various interferences, such as spectral fluctuation, matrix effect, etc., which can significantly deteriorate the final analytical results.

Finding an effective and universal method to realize accurate analysis is one of the predominant challenges for complex analyte analysis, high throughput detection, and industrial applications. To this end, researchers have proposed various improved methods.16^–19 Although they have made significant progress, a high degree of specificity confines them to aspecific spectroscopic techniques and prevents developments in the whole field of plasma spectroscopy. In addition, some algorithms have also been developed.20^–22 However, they are constrained by weak physical interpretation and the insufficiency of the spectral information and have a limited processing effect in improving accuracy. In summary, existing methods are only suitable for certain conditions, and a solution for practical applications in real-world scenarios has not yet been reported.

As previously mentioned, in most cases, the source of issues is the plasma, so the key lies in getting more information from the plasma, thus assessing the severity of interference and correcting the results. Many studies have shown the influence of plasma parameters on spectral results, including plasma temperature, total number density, electron density, etc.23^–25 Unfortunately, it is difficult to obtain them directly due to the small size and short lifetime of the plasma. A promising concept is the plasma image, which can potentially be designed to provide more information than the conventional spectrum, another kind of presentation of plasma.26^–28 Although the combination of plasma image and spectrum showed higher performance than conventional methods, they were not widely adopted. Limited by the unsatisfactory data-processing algorithms, only simple features can be extracted manually, while further information is still beyond reach. More recently, artificial intelligence (AI)-enabled spectral processing schemes have been noted, which offer an appealing approach for optimized measurement and intelligent rapid analysis. However, the lack of data sets is a barrier to their universal adoption. The performance of conventional supervised learning depends on the quality and quantity of manual labels, but ideal spectra and labels cannot be experimentally obtained in real-world scenarios.

To address the aforementioned issues, in this work, we have proposed a self-learning scheme avoiding the need for data and have explored the extension of conventional single-spectrum spectroscopy techniques to plasma image-spectrum fusion detection. A novel quantitative method termed by self-supervised image-spectrum twin information fusion detection (SISTIFD) is proposed for auto-extract deep features, faithful reconstruction of the plasma state, and optimization of quantitative accuracy in a physics-driven manner. In essence, the image and spectrum are a pair of twin signals originating from the plasma, providing us with a different kind of information about the plasma. With this approach, image-spectrum twin information fusion acquisition was achieved, which can provide the multidimensional information about plasma and lay a solid foundation for plasma modeling. After that, a self-supervised framework called a plasma image-spectrum attention network (PISA-Net) was established. It combines physical modeling with deep learning and can provide reliable results for accurate quantification. As a result, we successfully reconstruct the plasma state and get excellent quantitative results. PISA-Net has two pipelines to process plasma images and spectra, respectively, and a submodule specially designed based on the characteristics of the task, takes into consideration the challenges posed by the sparsity and less texture of the data. This scheme is completely self-supervised and enables parameters self-optimization without human intervention or preprocessing, thus achieving automatic analysis. To the best of our knowledge, this is the first method that is applicable to all fields of plasma spectroscopy based on AI-driven plasma modeling.

We used numerous experiments to evaluate SISTIFD. The first data set is constructed to overcome the lack of available data in this field. With this aim, we performed the experiment based on the LIBS platform, which is an ideal and representative testbed for plasma spectroscopy because of its poor quantitative performance. In addition, GD-OES is another common technique that is suitable for evaluation. Using LIBS and GD-OES as the application examples, the results show that SISTIFD outperforms other existing methods and achieves state-of-the-art performance in terms of accuracy, precision, complexity, and efficiency. Except for the experimental data trial, we validated its capability on each specific interference using different conditions. All the evidence points to the fact that SISTIFD significantly eliminates the interferences and achieves fantastic quantitative accuracy, which shows that it has the potential to become the universal issue of all plasma spectroscopy and bring revolutionary guidance to this field.

According to classical plasma emission theory, for a plasma under local thermal equilibrium (LTE) condition, the emission intensity of a spectral line Iij is expressed as29Iij=Fnsrgiexp[−Ei/(kT)]U(T),(1)where most of the variables are constant, with only the plasma temperature T, the total number density ns, and the electron density ne yet to be determined. In other words, as long as these three parameters can be accurately measured, the performance can be improved. However, the common methods cannot meet the requirements.30 Because the generation of plasma is complex and nonlinear, there are still more implicit interference factors that cannot be directly quantified but significantly affect the results. Consequently, we propose the SISTIFD to overcome existing shortcomings and achieve accurate quantitation (Fig. 1) (see the Supplementary Material for more derivations and details).

SISTIFD has two key parts. First, for the detection, the strategy based on the image-spectrum fusion acquisition is considered. In essence, plasma’s images and spectra are a pair of twin signals from plasma, providing a different kind of information. With this method, spectra can provide information about the types and quantities of particles within the plasma, while plasma images can offer insight into the spatial distributions of these particles. Unlike conventional single-spectrum acquisition, we regard spectra and images as distinct but equal representations of the same information source. In other words, their weights for the results are balanced. By asynchronously acquiring plasma images and emission spectra at the same frequency and performing pixel-level fusion, a solid foundation for plasma reconstruction and parameter retrieval is established. Generally speaking, the process of plasma evolution is highly complex and nonlinear, making it difficult to understand directly. Fortunately, AI provides a novel routine. In a recent study, deep learning was used to discover potential patterns and relationships between physical objects.31^–33 Inspired by these, we propose a universal and efficient framework named PISA-Net. PISA-Net employs an attention mechanism to extract both explicit features and implicit information from fusion data, infer plasma parameters, and correct spectral biases. Based on such a process, the parameters of the plasma are accurately calculated, and accurate and precise quantitative results can be obtained. It is completely self-supervised and end-to-end, thus needing no manual intervention and achieving automatic detection.

The workflow of PISA-Net is shown in Fig. 2. The core purpose of training is to make the network learn the fitting relationship of plasma parameters and integrate it into the signal correction process, thus outputting the final result directly. The advantage is obvious: we do not need to know the exact plasma parameters, and we can complete the extraction of plasma parameters while achieving the correction of the final result. The preprocessing is performed automatically by the system, as illustrated in Fig. 2(a). The images will be cropped first, and then be normalized and subsampled to decrease the feature space for the model. Similarly, PISA-Net will find the spectral peak of the spectra, normalize the total spectral line, and subsample it to a lightweight structure. Figure 2(b) is the main body of PISA-Net, which is trained on pairs of plasma images and plasma emission spectra. There are two pipelines to process. The image pipeline’s target is to extract features from plasma images based on the novel layers termed by residual attention cells (RACell) we specially designed. For the spectrum pipeline, the one-dimensional data are processed through some preprocess layers, convolution layers, and a leaky ReLU layer,34 resulting in spectrum features. After that, all the features, including plasma parameters and encoded vectors, will be merged into the plasma feature stack and fused to calculate the correct results. The RACell illustrated in Fig. 2(c) is an innovative structure for extracting features from the plasma image. Inspired by Transformer,35 we have a small net that can learn a set of weight coefficients for each channel to represent its importance. The channel-dependent self-gate attention mechanism learns the activation of specific samples for each channel, thus using global information to selectively emphasize specific features and suppress less useful features. In addition, we added soft thresholding as a simple but effective trick for denoising. (See the Supplementary Material for more details.)

Benefiting from these advanced structures, our method has achieved excellent performance in monitoring and predicting plasma parameters. As shown in Fig. 3, we obtained plasma images and spectra with different temperatures by changing the laser energy [Figs. 3(a) and 3(b)], and we compared the results obtained by our method with the plasma temperature calculated using the Boltzmann plot method [Fig. 3(c)]. For the intercept m of the Boltzmann plot, the plasma temperature T can be calculated as T=−1/mkb, where kb is the Boltzmann constant.

To better illustrate the capability for plasma temperature calculation, we measured 50 times under each laser energy condition and calculated their plasma temperature using both the Boltzmann plot method and PISA-Net. Figure 3(d) provides a comparison of the results for energies ranging from 20 to 80 mJ. Statistical testing is performed with a standard two-tailed t-test, and the results indicate that there is no significant difference between them (p>0.05), showing the accuracy of temperature calculations under various conditions. To be more specific, we selected all the 50 measurement results at the laser energy of 50 mJ and calculated the relative deviations between the two methods. As shown in Fig. 3(e), the relative deviation between the two methods is <1%, and in the majority of cases, it is <0.4%. This result primarily indicates the stability and robustness of the plasma temperature calculation of SISTIFD.

Similarly, for electron density ne, we obtained the full width at half-maximum (FWHM) through Lorentzian fitting of the spectral line of Fe at 404.581 nm and calculated the plasma electron density at different energies based on the Stark broadening method, as shown in Fig. 3(f). For typical plasma, the contribution from ion broadening is generally negligible. Thus, the electron density ne of a plasma can be expressed as ne=FWHM×1016/2ω, where the electron impact parameter ω can be found in the literature.

We also calculated the electron density ne of 50 plasmas under each energy condition. Figures 3(g) and 3(h) show the final results; the results of two-tailed t-test indicated the deviation is not statistically significant. It is worth noting that although the Stark broadening method is the currently better-performing method, the calculated results are not perfectly accurate. Therefore, larger standard deviations and relative deviations between the results of the two methods are understandable. All the results are relatively advanced compared to existing methods, demonstrating that our method can calculate the plasma parameters very well.

A comparison of final quantitative results can better evaluate the reliability of the plasma parameter calculation. We used seven soil samples with varying Mg concentrations and induced plasma by laser with random fluctuations in the energy range of 47.2 to 53.9 mJ. Figure 3(i) shows the spectra we collected. We conducted linear fitting on the original spectral intensity [Fig. 3(j)], the intensity corrected by plasma temperature T and electron density ne that we calculated before [Fig. 3(k)], and the intensity corrected by all of the parameters (T, ne, ns, and δ) of PIAS-Net [Fig. 3(l)], to obtain calibration curves for Mg II 279.553 nm spectral line. It can be observed that the unprocessed spectra performed the worst, with the determination coefficient R2 of the calibration curve being only 0.8717. The curve’s linearity significantly improved after the correction by T and ne, reaching an R2 of 0.9314, which further validates the previous conclusions. Finally, comparing it with the calibration curve corrected finally, the R2 of the curve further increased to 0.9989, indicating the accuracy of our calculation for all parameters.

Previously, we analyzed the theoretical feasibility of calculating the plasma parameters. Next, using LIBS [Fig. 4(a)] as the example, we will further verify the quantitative effectiveness of the method. Under real-world conditions, the spectral intensity is influenced by various interferences, including spectral fluctuation, matrix effect, etc. (Detailed explanations are in Sec. 2.5.) It is challenging to establish reliable regression curves for quantitative analysis. We set a series of factors to simulate this complex process. To verify the performance of our method, we set the laser energy fluctuating between 45.4 and 54.7 mJ, and two different kinds of samples, including K2CO3-soil and potash feldspar samples, were used. In addition, because of the high concentration of K element, the occurrence of self-absorption is foreseeable. Figure 4(b) shows examples of plasma spectra and images under different conditions.

Part of the collected images and spectra in the quantitative experiments are shown in Figs. 4(c) and 4(d), and we can see the difference clearly because of the interferences. The visual calibration curves are as shown in Figs. 4(e) and 4(f). Figure 4(e) shows the original results, and the data points cannot be fit with a straight line, demonstrating the significant influence on the quantitative results by interferences. The results corrected by SISTIFD are shown in Fig. 4(f). We selected three samples as the test set that was completely excluded from the training process. The evaluation parameters are in Table 1. The R2 increases from 0.0359 to 0.9996, and the root mean square error (RMSE) and mean relative error (MRE), the indicators of accuracy, decline from 0.6032 and 0.3471 to 0.0109 and 0.0062, respectively. In addition, the relative standard deviation (RSD) improves from 0.1428 to 0.0037, which means the precision of results has also been improved. The results show that, compared with the poor accuracy and precision of the original spectra, the samples in the test set could be calibrated with almost no errors in our method, especially under extremely harsh conditions, which fully demonstrates the capability of our method.

To illustrate the universality of SISTIFD for plasma spectroscopy, we also verified its effectiveness using GD-OES [Fig. 5(a)]. We used samples with different concentrations of Cs and Li elements. By applying the voltage at both ends to excite the plasma, we collected their emission spectra using the spectrometer. To obtain reliable results, an 852.1 nm spectral line of Cs element and a 670.8 nm spectral line of Li element were selected for analysis. Figures 5(b) and 5(c) present the plasma images of the Li and Cs elements, respectively.

The results are shown in Figs. 5(d)–5(i) and Table 2. Figure 5(d) shows the corresponding spectra of Li; the calibration curves are shown in Figs. 5(e) and 5(f), where Fig. 5(e) is the result using conventional GD-OES; the result of SISTIFD is given in Fig. 5(f). The R2 of the calibration curve was increased from 0.9355 to 0.9997, and the MRE of the test set declined from 0.1033 to 0.0033, which supports our idea that SISTIFD is also effective for other plasma spectroscopy techniques and can help to improve their performance. To provide more evidence, Fig. 5(g) shows the spectra of the Cs 852.1 nm element; the calibration curves are in Figs. 5(h) and 5(i). The R2 of the calibration curve increased from 0.9784 to 0.9993, and the MRE of the test set improved from 0.0293 to 0.0110, demonstrating a very significant improvement in quantitative results. Based on the results of the GD-OES, SISTIFD has also demonstrated significant effectiveness and universality. We have reason to believe that it has the potential to be applied to all detection techniques based on plasma emission spectroscopy as a “universal method.”

To better illustrate the mechanism of SISTIFD to provide accurate results, it is necessary to analyze the individual effect of the different interferences specifically. It is proper to use LIBS as the example because the influence is more significant. In this research, both atomic and ionic spectral lines of different elements are selected for quantitative analysis to support our scheme. We studied the contents of Si, Fe, Mg, Mg, and K elements in powder-pressed samples (potash feldspar and soil) and metal samples (aluminum alloy, micro-alloyed steel). The method was compared with the original LIBS, an advanced method called IA-LIBS.36 All of these worked well and were representative. We used both metal and pressed samples to conduct the experimental study and followed the same setting to execute algorithms.

As shown in Fig. 6, we researched four different interferences, including spectral fluctuation, unstable excitation, matrix effect, and self-absorption. They are the dominant interferences that may be faced in real-world applications. Among them, experimental case 1 is spectral fluctuation, which shows the influence of slight changes in environmental factors. It results in different intensities for the same experimental parameters. Experimental case 2 is unstable excitation, which represents the consequences of the instability of the excitation source. Both of them are precision-influencing conditions. After that, the interferences of the matrix effect and self-absorption are set as the experimental conditions 3 and 4 to illustrate their accuracy. The reason for the matrix effect is the difference in the samples; self-absorption refers to the fact that particles in the outer layer of the plasma absorb some photons, resulting in an abnormally low spectral intensity.

Due to the sensitivity of the plasma, the slight change of experimental conditions, such as temperature, sample state, and instrument noise, can lead to significant fluctuation in spectral intensities, greatly compromising the precision of detection. Therefore, we explored the effectiveness of our method for spectral fluctuation. We used a Si I 250.690 nm line in potash feldspar samples and Fe II 239.563 nm in aluminum alloy and collected the spectral intensities of each sample under 50 laser pulses.

The calibration curves are shown in Figs. 6(a) and 6(b); evaluation parameters are given in Table 3. The RSD of the calibration curves declined from 0.0743 and 0.0983 to 0.0014 and 0.0032, which suggested that the precision and stability improved significantly. Besides, the R2, RMSE, and MRE of Si I 250.690 nm were enhanced from 0.9801, 0.9813, and 0.0589 to 0.9998, 0.0091, and 0.0014. The R2, RMSE, and MRE of Fe II 293.931 nm were optimized from 0.9210, 0.0538, and 0.3490 to 0.9984, 0.0017, and 0.0049. The results indicate that our method can effectively eliminate the spectral fluctuation according to the information in plasma. Compared to existing methods, our approach can distribute appropriate weights to the twin information and extract adequate information to achieve better performance.

As the excitation source for the plasma, the laser is the most important external factor affecting the spectrum. In practical detection, many laser parameters will fluctuate, and the change in energy can have the most significant impact on the results. In this study, we evaluate the performance of our proposal and other methods under different energy conditions (40, 45, 50, 55, and 60 mJ). We used Si in potash feldspar samples with a 250.690 nm spectral line and Mg in soil with a 279.553 nm spectral line for experiments.

The calibration curves of Si are shown in Figs. 6(c) and 6(d); the evaluation parameters are shown in Table 3, which suggests the R2, RMSE, MRE, and RSD of the curves improved greatly. The indicators of precision, RSD for Si I 250.690 nm and Mg II 279.553 nm, diminished from 2.2465 and 1.7154 to 0.0501 and 0.0448. The values of R2 improved from 0.2210 and 0.1320 to 0.9959 and 0.9992, respectively. Likewise, for Si, the RMSE and MRE decreased from 0.5123 and 0.8081 to 0.0260 and 0.0647. As for Mg, the RMSE and MRE lessened from 0.3931 and 1.6359 to 0.0155 and 0.0505. Figures S2 and S3 in the Supplementary Material provide more results about the Si and Mg elements.

In general, the matrix effect refers to the inconsistent spectral response of the same concentration of elements in different kinds of samples. The matrix effect is primarily manifested in the inconsistency of the calibration curves, which greatly limits the accuracy and precision of quantification, which hinders its further popularization in the industry. Our SISTIFD has the potential to be applied to the correction of the matrix effect, and the experimental results support our claim. The spectral line at 293.931 nm of Mn element in metal samples was selected for visual analysis in Figs. 6(e) and 6(f); Mg I 285.213 nm, Si I 250.690 nm, and Mn II 257.610 nm were also used for the test.

The intensities of Mn II 293.931 nm and Mg I 285.213 nm in different kinds of samples were studied to indicate the validity of our network; the results are shown in Table 3. There are also some other quantitative results in Fig. S4 and Table S2 in the Supplementary Material. We can see that the spectral intensities could be fitted very well by the calibration curves, although they come from totally different kinds of samples, which illustrates the effectiveness of our proposal. The R2 of calibration curves of Mn and Mg increased from 0.4151 and 0.0244 to 0.9952 and 0.9998. The RMSE and MRE of Mn II 293.931 nm in aluminum alloy and micro-alloyed steel were improved from 0.4326 and 0.4457 to 0.0042 and 0.0098 with our model. In the same way, the RMSE and MRE of Mg I 285.213 nm in pressed samples declined from 0.1382 and 0.6330 to 0.0013 and 0.0064, respectively, proving that SISTIFD achieves the SOTA performance.

Self-absorption is due to the absorption of photons emitted from the inner layer by the outer plasma, and it is another reason for inaccuracy in LIBS quantitation because of its nonlinear performance. To overcome the potential self-absorption, SISTIFD is designed to ameliorate this effect to improve the accuracy and precision of LIBS quantification. Considering that potassium element (K) is prone to induce self-absorption and is easy to obtain, we use K I 766.490 nm in K2CO3-soil mixed samples and K I 769.896 nm in potash feldspar samples for the experiment.

The calibration curves of K I 766.490 nm are shown in Figs. 6(g) and 6(h) as an example; the results are given in Table 3. For the original data, with the increasing of K content, the spectral intensity value grows more and more slowly, and the calibration curve is obviously concave and can no longer be fitted by a straight line. Using exponential fitting, the RMSE and MRE were 0.4266, 0.3669 and 0.2138, 0.3852, respectively. Corrected by our model, the value of R2 was improved to 0.9995 and 0.9989 even using the linear fitting, and RMSE and MRE decreased to 0.0041, 0.0053 and 0.0019, 0.0046, which proves that our proposal can effectively eliminate the self-absorption effect and improve the quantitative accuracy.

In this experiment, we analyzed the necessity and efficiency of PISA-Net, as shown in Table 4. First, we examined the model size by changing the number of channels. In this case, the model degraded regardless of whether the parameter count increased or decreased. Next, we removed several key structures, including attention net, soft thresholding, and skip connection. However, the absence of them brought a larger loss. This is because certain features were not accurately extracted. Finally, we compared the performance of different loss functions. The conclusion is that the weighted loss we used is most beneficial for the model.

As for the runtime, our approach takes an average of 7 ms (143 Hz) for calculation on a computer with Intel Xeon 6230R CPU and Nvidia GeForce RTX 2080Ti GPU, which can meet the requirement of real-time detection. In general, the total time cost for the mainstream detection is about only 1 s (1 Hz), which means our scheme does not lead to a significant increase in detection time compared to conventional techniques.

Here, we report what we believe is a novel, accurate, effective, and universal scheme SISTIFD for improving the performance of plasma spectroscopy, especially in cross-interference scenarios. The proposed SISTIFD relies on the innovative construction of a self-supervised learning approach based on the relationship between spectral twin signals and physical parameters. The first stage of the workflow is the experimental strategy based on image-spectrum twin information fusion acquisition, which contributes to much more information than conventional techniques about plasma. The second stage is an AI-driven framework called PISA-Net, which injects plasma images and spectra into different pipelines and applies residual attention cells to conduct self-supervised training, enabling one to obtain the plasma parameters and compute appropriate correction coefficients for accurate analysis. Using LIBS and GD-OES as the testbed, we achieved state-of-the-art performance and all the evaluation indices, including RMSE, MRE, and RSD, declined 2 orders of magnitude, demonstrating the effectiveness and universality of SISTIFD.

The improvements based on conventional single-spectrum techniques have shown remarkable capability in the face of single interference or simple applications, but insufficient information in the spectrum under cross-interference conditions is the barrier to widespread application. Detecting multidimensional twin signals of plasma is a novel idea that can provide a wealth of information to better understand the behavior of plasma. Although deep learning-based methods showed higher efficiency than rule-based methods, they were not widely adopted. The performance of supervision-based neural networks relies on the quality and quantity of training data. However, ideal spectra without interferences and noises cannot be experimentally obtained. To solve this problem, we propose a self-supervised network to learn the pattern from unordered data to physical parameters as part of our quantitative scheme. SISTIFD provides an efficient, accurate, precise, and robust workflow for quantitative analysis in high throughput, cross-interference, complex, and diverse applications, by retaining the rapid, easy to operate, and in situ advantages of conventional spectroscopic techniques. In addition, the scheme introduces excessive time overhead; of course, some cost increase is necessary (an extra ICCD camera is needed).

With the development of advanced analytical techniques over the past years, the universality of a new proposal interdisciplinary field is becoming increasingly important. To the best of our knowledge, existing spectroscopic techniques only focused on the problems in their own field, and there is no one universal method that works for the entire field of plasma spectroscopy. SISTIFD is a new method that establishes a unified framework for materials analysis based on plasma spectroscopy. The achievement has been verified in LIBS and GD-OES, and we believe that our concept can also be applied to other techniques, such as ICP-OES, spark-emission spectroscopy, and others. This may boost multispectral technology because all the above-mentioned concepts still rely on the need for more spectral information acquisition and more accurate algorithms. One can expect other novel universal methods in the future, and we believe our proposal is the first facilitator for a universal analysis paradigm, making spectroscopy more accessible to academia as well as industry.

Lianbo Guo is a full professor at the Wuhan National Laboratory for Optoelectronics (WNLO), Huazhong University of Science and Technology (HUST). He is a spectroscopy scientist and his research interests include laser-induced breakdown spectroscopy (LIBS), Raman spectroscopy, photoacoustic spectroscopy, etc., and their applications in fields such as biology, geology, and metallurgy. He has authored over 100 papers and served as a reviewer for over 40 international journals.

Biographies of the other authors are not available.