Calculating the Limits of Detection in Laser-Induced Breakdown Spectroscopy: Not as Easy as It Might Seem

Round 1

Reviewer 1 Report

This paper discussed  the calculation of detection limits in the laser-induced breakdown spectroscopy (LIBS) technique. The paper is noteworthy for the LIBS community and I recommend its publication. However, there are a few comments to further enhance the paper's quality.

The authors could provide additional information on the experimental setup, such as the irradiance applied to the samples.

It would be beneficial if they could present a figure with the intensity of the copper lines in samples with lower concentrations, in addition to displaying the full spectrum.

The authors should provide more information about the equations shown in the paper and reference them appropriately. It is also important to specify if the intensity is defined as the area under the curve or the peak-to-background ratio of the signal.

 Since this paper analyzes the detection limits according to the new IUPAC standards, a more comprehensive analysis of the calculation would be helpful. For instance, the authors could plot the signal-to-noise ratio versus concentration, in addition to the intensity of the lines shown in figure 5 . This would give readers a better understanding of the noise in the LIBS signal and how the new calculation process differs from the previous one.

 The authors should also provide more detail about the offset on the vertical axis in the calibration curve shown in Fig. 5. It would be expected that for a sample without copper, there would be no signal and thus a zero area.

 Finally, the limit of detection is mentioned as being between 0.2 to 0.35% in the univariate approach on lines 216 and 260, among other places in the manuscript. However, the intensities corresponding to samples S3 and S5 with concentrations of 0.02 and 0.03% are clearly shown, which seem to contradict the stated LOD of 0.35%. The authors should provide further explanation to clarify this issue.

Author Response

The authors could provide additional information on the experimental setup, such as the irradiance applied to the samples.

We have added the relevant information to the revised manuscript.

It would be beneficial if they could present a figure with the intensity of the copper lines in samples with lower concentrations, in addition to displaying the full spectrum.

Following the suggestion of the two reviewers we removed the figure showing the full LIBS spectrum of cast iron and added a figure displaying the Cu lines at the different concentrations (average spectra).

The authors should provide more information about the equations shown in the paper and reference them appropriately. It is also important to specify if the intensity is defined as the area under the curve or the peak-to-background ratio of the signal.

The equations shown in the paper have been referenced to ref. [13] (old IUPAC definition of LOD), ref. [22] and [24] (new IUPAC definition of LOD and the Long & Winefordner considerations which led to the new definition) and ref. [23] for the Oleneva et al. method. The intensity corresponds to the area under the curve, as shown in Figure (3) (red area).

Since this paper analyzes the detection limits according to the new IUPAC standards, a more comprehensive analysis of the calculation would be helpful. For instance, the authors could plot the signal-to-noise ratio versus concentration, in addition to the intensity of the lines shown in figure 5. This would give readers a better understanding of the noise in the LIBS signal and how the new calculation process differs from the previous one.

We thank the reviewer for the constructive comment. We were indeed considering to add a figure of the signal/noise ratio at different Cu concentration, as suggested by the reviewer. However, for what concerns the LOD, the signal/noise ratio alone does not allow its calculation, without knowing the statistical distribution of the LIBS signal. It is true that this information can be derived from the calibration curve in figure (5), but the LIBS signal is supposed to have a Gaussian statistical distribution, and this hypothesis is, in general, not fulfilled (we have added a new reference about that). At the end, we considered the histograms in figure 6 and 7 (univariate case) and 9 (multivariate case) as more significant since the average LIBS signal and its statistical distribution can be immediately compared with the distribution of the background fluctuations. The non-Gaussian nature of the LIBS signal distribution also comes out clearly from the histograms, in our opinion.  

The authors should also provide more detail about the offset on the vertical axis in the calibration curve shown in Fig. 5. It would be expected that for a sample without copper, there would be no signal and thus a zero area. Finally, the limit of detection is mentioned as being between 0.2 to 0.35% in the univariate approach on lines 216 and 260, among other places in the manuscript. However, the intensities corresponding to samples S3 and S5 with concentrations of 0.02 and 0.03% are clearly shown, which seem to contradict the stated LOD of 0.35%. The authors should provide further explanation to clarify this issue.

We have added a paragraph to clarify the origin of the offset in the calibration curve.

Reviewer 2 Report

The manuscript by Poggialini et al. brings a comparison of methodology in the estimation of LODs in univariate and multivariate analysis. The work extends the body of work from the Palleschi group and provides a good tutorial to LIBS community. The introduction of new IUPAC standard is well described and discussed. The manuscript shows limited results (only LODs for Cu) and there are several points that could be improved. Thus, I suggest publication of this manuscript after major revision.

1) the biggest concern is that LODs are estimated only for Cu and its resonant lines. Surely, other lines for Cu could be found in such a rich spectrum (Figure 1).

2) I recommend to show LODs also for other elements. Table 2 should be extended accordingly.

3) Error propagation should be estimated and LODs should be extended with standard deviation.

4) Gaussian distribution is not met for selected spectral lines. That is no surprise when consulting existing literature; DOI: 10.1016/j.sab.2016.10.002. Relevant literature with extensive discussion should be addded.

 

5) there is no conclusion as such. Discussion is vague and should be more decisive; whether to abandon former IUPAC LOD estimation and why or not.

6) Figure 1 has no analytical meaning unless Cu lines region is highlighted; that is done in Figure 2. Those two figures could be merged.

Author Response

The biggest concern is that LODs are estimated only for Cu and its resonant lines. Surely, other lines for Cu could be found in such a rich spectrum (Figure 1).

Unfortunately, the two resonant lines copper line are the only ones visible/measurable in the low concentration (< 1%) samples, which allow the building of a calibration curve and, consequently, the calculation of the LOD.

I recommend to show LODs also for other elements. Table 2 should be extended accordingly.

This would have been surely interesting in the framework of the proficiency test organized by BAM for the 2008 LIBS Conference in Berlin, from where the cast iron sample came. It is a pity that the results of the test were never published; however, in our case the calculation of the LOD for Cu was intended to be just an example of the application of the old and new IUPAC definition, as well as the extension of the LOD calculation to multivariate calibration. In that sense, we chose Cu because of its well detectable and almost unperturbed emission lines, and also because the analytical problem was already discussed by our group in several papers, using both univariate and multivariate calibration approaches.

Error propagation should be estimated and LODs should be extended with standard deviation.

The reviewer is right. However, the LOD is already a statistical concept, whose precise value depends on the level of ‘reasonable confidence’ with which we suppose to be able to distinguish the sample concentration from the zero hypothesis. The non-Gaussian distribution of the LIBS signal also contributes to make the LOD not exactly determinable.

Gaussian distribution is not met for selected spectral lines. That is no surprise when consulting existing literature; DOI: 10.1016/j.sab.2016.10.002. Relevant literature with extensive discussion should be addded.

We thank the reviewer for pointing out the paper about the non-gaussian distribution of LIBS signals. We have added it to the references and discussed it in the text of the manuscript.

There is no conclusion as such. Discussion is vague and should be more decisive; whether to abandon former IUPAC LOD estimation and why or not.

We thank the reviewer for the suggestion. We added in the final discussion a more decisive statement about the use of the IUPAC formulas.

Figure 1 has no analytical meaning unless Cu lines region is highlighted; that is done in Figure 2. Those two figures could be merged.

Thank you very much for your suggestion. Following also the suggestion of Reviewer 1, we removed Figure 1 and added instead a new figure (Figure 2) showing the average spectra of the samples in the region where the Cu lines are visible. We maintained Figure 3 because it was used for showing the spectral regions used for evaluating the background and the Cu line signal.

Round 2

Reviewer 2 Report

I recommend this manuscript for publication.