Analysis of Porosity in Aluminum Alloy (AlSi10Mg) Using Tomographic Image Processing
Pei Wei
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript presents a well-structured study on porosity characterization in AlSi10Mg alloy fabricated via laser powder bed fusion (L-PBF) using X-ray computed tomography (XCT) and digital image processing techniques. However, the manuscript suffers from several major weaknesses that must be addressed before it can be considered for publication.
- The combination of CT and image processing for porosity analysis is well-established in the literature. Please clarify the novel technical contributions of your approach in comparison to existing methods (see references [15–19, 26]).
- If your workflow improves segmentation accuracy, reduces analysis time, or enables detection of smaller pores/productivity in certain geometries (e.g., gyroid structures), please emphasize this in the Abstract and Introduction.
- Please provide details about voltage, current, exposure time for every stack during CT acquisition; explain how you addressed potential reconstruction artifacts due to inconsistent acquisition.
- The most serious issue is the reported calculated density for the GD sample: 3.071 g/cm³. This value is physically impossible, as it is significantly higher than the theoretical density of solid AlSi10Mg (approx. 2.68 g/cm³). A porous sample cannot have a density greater than its solid counterpart. The authors' explanation on lines 242-244 ("This variation in density is attributed to the image cropping...which altered measurable values such as mass") is scientifically unsound and reveals a misunderstanding of the density calculation. Cropping the image stack reduces the calculated volume. If the authors used the original mass of the full sample with this smaller, cropped volume, the density would be artificially and incorrectly inflated. Mass and volume must be calculated for the exact same physical object.
- The GD stack was cropped to 465×530 pixels and the mass used in the density calculation does not correspond to the cropped volume (authors state mass cannot be remeasured). This makes the GD density value plainly unreliable. Either (a) re-scan the GD specimen (preferred) using the same protocol as the others, or (b) remove the GD density comparison and explicitly present GD as a qualitatively analyzed scan only. Do not include GD in quantitative density error comparisons unless consistent data are available.
- The manuscript reports only volumetric porosity and number of pores. Modern porosity analysis usually includes pore size distribution (volume per pore), equivalent diameter, sphericity, aspect ratio, connectivity, and classification into closed vs open porosity. Please provide at least: pore size distribution (histogram and summary statistics), median and mean pore size, and a statement on closed vs open pores (if possible from CT).
- The choice of dome height H = 67 grayscale levels, threshold = 31, two-layer filter, and growth threshold = 5 appears to be based on a limited test region. Provide more detail on how representative these values are across the entire stack, and sensitivity analyses showing porosity and density variation as these parameters vary, and whether adaptive or local thresholding could yield more robust results.
Author Response
Comment 1: The combination of CT and image processing for porosity analysis is well-established in the literature. Please clarify the novel technical contributions of your approach in comparison to existing methods (see references [15–19, 26]).
Response 1: While XCT and image processing have been extensively applied for porosity analysis, existing segmentation strategies often neglect 3D connectivity information, which may lead to inaccurate detection of small or interconnected pores. In contrast, our methodology introduces a reproducible workflow that integrates histogram normalization, morphological reconstruction, and a 3D region-growing algorithm with 18-neighborhood connectivity. This enables a more precise characterization of pore morphology and continuity in AlSi10Mg alloys fabricated via LPBF. The revised text has been added on page 02, lines 80–93.
Comment 2: If your workflow improves segmentation accuracy, reduces analysis time, or enables detection of smaller pores/productivity in certain geometries (e.g., gyroid structures), please emphasize this in the Abstract and Introduction.
Response 2: We have revised both the Abstract and the final part of the Introduction to emphasize the practical contributions of our workflow. Specifically, the revised text highlights that our method improves segmentation accuracy, enables the detection of small and interconnected pores, and facilitates the analysis of complex geometries in AlSi10Mg alloys fabricated via LPBF. The corresponding changes can be found in the Abstract (page 01, lines 11–16) and Introduction (page 02, lines 80-93).
Comment 3: Please provide details about voltage, current, exposure time for every stack during CT acquisition; explain how you addressed potential reconstruction artifacts due to inconsistent acquisition.
Response 3: The manuscript include a more detailed description of the acquisition protocol and the procedures used to minimize reconstruction artifacts. Specifically, we now state that all projection images were corrected for detector dark current and flat-field response. Projections from stacks with different exposure parameters were scaled by the ratio of (current × exposure time) and calibrated using reference phantom scans to ensure a common CT-number scale. Overlapping regions (~15%) between stacks were registered by cross-correlation and blended using histogram matching and linear feathering. Beam-hardening and ring-artifact corrections were applied prior to reconstruction, and final volumes were reconstructed using filtered backprojection with Parker weighting. The reconstructed data were verified against the phantom to confirm uniformity and absence of stitching seams, and iterative reconstruction and denoising were used as needed to suppress residual artifacts. These details have been incorporated into the revised manuscript (page 03, lines 112–132).
Comment 4: The most serious issue is the reported calculated density for the GD sample: 3.071 g/cm³. This value is physically impossible, as it is significantly higher than the theoretical density of solid AlSi10Mg (approx. 2.68 g/cm³). A porous sample cannot have a density greater than its solid counterpart. The authors' explanation on lines 242-244 ("This variation in density is attributed to the image cropping...which altered measurable values such as mass") is scientifically unsound and reveals a misunderstanding of the density calculation. Cropping the image stack reduces the calculated volume. If the authors used the original mass of the full sample with this smaller, cropped volume, the density would be artificially and incorrectly inflated. Mass and volume must be calculated for the exact same physical object.
Response 4: As re-scanning the GD specimen is not possible, we have removed it from the quantitative density analysis, as suggested. All density comparisons and error analyses are now restricted to the remaining samples acquired with consistent protocols. This revision has been implemented in the Result section (page 12, lines 271–306).
Comment 5: The GD stack was cropped to 465×530 pixels and the mass used in the density calculation does not correspond to the cropped volume (authors state mass cannot be remeasured). This makes the GD density value plainly unreliable. Either (a) re-scan the GD specimen (preferred) using the same protocol as the others, or (b) remove the GD density comparison and explicitly present GD as a qualitatively analyzed scan only. Do not include GD in quantitative density error comparisons unless consistent data are available.
Response 5: As re-scanning the GD specimen is not possible, we have removed it from the quantitative density analysis, as suggested. All density comparisons and error analyses are now restricted to the remaining samples acquired with consistent protocols. This revision has been implemented in the Result section (page 12, lines 271–306).
Comment 6: The manuscript reports only volumetric porosity and number of pores. Modern porosity analysis usually includes pore size distribution (volume per pore), equivalent diameter, sphericity, aspect ratio, connectivity, and classification into closed vs open porosity. Please provide at least: pore size distribution (histogram and summary statistics), median and mean pore size, and a statement on closed vs open pores (if possible from CT).
Response 6: In addition to the volumetric porosity and number of pores initially reported, we have now included a quantitative pore size analysis. Specifically: The pore size distribution was obtained using the equivalent spherical diameter (defined as the diameter of a sphere with the same volume as the pore). The corresponding histograms for stacks G1 and G2. Summary statistics of the pore size distributions, including mean, median, standard deviation, minimum, maximum, and P10–P90 ranges. These details have been incorporated into the revised manuscript (page 12-13, lines 265–300).
Comment 7: The choice of dome height H = 67 grayscale levels, threshold = 31, two-layer filter, and growth threshold = 5 appears to be based on a limited test region. Provide more detail on how representative these values are across the entire stack, and sensitivity analyses showing porosity and density variation as these parameters vary, and whether adaptive or local thresholding could yield more robust results.
Response 7: Grayscale morphological reconstruction was employed as a key technique for refining pore boundaries and improving detection. The selection of parameters (dome height H=67, threshold = 31, two-layer filter, growth threshold = 5) was based on an analysis of 200 pore-like dome structures across 40 representative subregions (20 from the GD stack and 20 from the G2 stack), each covering ~10% of the image area and containing at least five pores. This approach ensured that the tested regions included a sufficient number and variety of pores, making the selected parameters representative of the full dataset.
Although a complete sensitivity study across all stacks was not performed, the consistency of the porosity and density results obtained for G1 and G2 (Tables 8 and 9) supports the robustness of the chosen parameters. In addition, the low porosity values and the narrow distribution of pore sizes indicate that the analysis is not strongly affected by small variations in thresholding. Adaptive or local thresholding methods were considered but not implemented, as the global approach already provided stable and reproducible results across stacks.
Author Response File:
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis article aims at investigating methods to detect and analyze porosity in LPBF AlSiMg alloy. It is a recurrent problem to select suitable segmentation algorithms and filtering techniques therefore this topic is important for scientific community. LPBF AlSiMg alloy is known to always have residual porosity after LPBF process, therefore it is a suitable material for this study. However, the presented method seems difficult to be generalize to everyone. If the aim of the paper is the comparison of defect depending on sample geometry, the analysis should be more exhaustive.
Some detailed comments are listed below:
- In literature review, the actual state of art about porosity characterization in LPBF is missing (I’ve found this reference but feel free to add more appropriate ones) : https://www.sciencedirect.com/science/article/pii/S2215016118301481
https://www.sciencedirect.com/science/article/pii/S2215016118301481
https://27028629.fs1.hubspotusercontent-eu1.net/hubfs/27028629/PDFs/Dichtewaage/Analysis%20of%20measurement%20methods%20for%20density%20determination%20in%20additive%20manufacturing.pdf
https://www.emerald.com/rpj/article-abstract/17/5/380/368909/Comparison-of-density-measurement-techniques-for?redirectedFrom=fulltext
- In literature review “The effectiveness of digital image processing and computed tomography in evaluating internal structures has also been demonstrated in other fields” The example on bones is too specific for literature parts, authors should consider tomography effectiveness in metal characterization in general (you can pickup some ideas from this paper) https://journals.sagepub.com/doi/full/10.1179/1743280413Y.0000000023
- Methods: some Xray tomography parameters are missing (energy, rotating on 180 or 360°C, voxel lateral isotropic size…). Could you comment on the voxel size with the expected average pore size?
- Methods: please add citations for image j and used plugins (https://imagej.net/contribute/citing) and add some information on used functions ie does “region growing algorithm” correspond to “image j ““dilate” function?
- “10% of the total size of each original image (see Table 2 and Figure 3a)” have you checked if 10% is higher than your Representative Volume Element (RVE)?
- “the height "H" of each pore was measured” which criterion do you use to define a pore ? or a non-pores (Table 3) ?
- “This underscores the need for an individualized application to achieve optimal segmentation results” is an important result, however any idea to improve the methodology to avoid this individualization?
- “Unit Volume Filter”: to characterize a volume, 10 voxels are often considered as a minimum value, why did you select the value of 1?
- L204 to L233 should be included in method part
- L232 “threshold of 31”: have you measure the result variability between threshold 31 and the optimum threshold?
- How the real density value is measured?
- How can you explain the large error between real and measured density for GD sample
- Could you add a discussion part?
- Please clarify paper aims: is it to provide result on AlSiMg porosity depending on samples shape or to provide new image processing methodology ?
Some minors comments are listed below:
-Fig 1: please add a scale on images (sample a do not seem smaller although it is)
-Fig 6: please specify what is ROC, S and 1-E and their units. Figure should be understood without reading text.
-Figure and table caption are very short (ie Table 8 results) could you provide more detailed captions ?
-ref 20: url link is not working. Moreover this reference is not pertinent for the study. Due to high density difference between metal and polymer, image processing do not show the same bottlenecks
Author Response
Comment 1: In literature review, the actual state of art about porosity characterization in LPBF is missing (I’ve found this reference but feel free to add more appropriate ones):
Response 1: In the revised version of the manuscript, we have expanded the literature review to include the current state of the art on porosity characterization in laser powder bed fusion (L-PBF). We now discuss conventional methods such as the Archimedes principle and metallographic cross-sections, as well as advanced approaches including X-ray computed tomography (XCT). Furthermore, we incorporated recent contributions on the standardization of porosity evaluation using microCT and on the comparative analysis of density and porosity measurement techniques across different additive manufacturing processes and materials. This addition highlights both the advantages and limitations of destructive and non-destructive methods. A new paragraph was added in the Introduction section (page 02, lines 36–51)
Comment 2: In literature review “The effectiveness of digital image processing and computed tomography in evaluating internal structures has also been demonstrated in other fields” The example on bones is too specific for literature parts, authors should consider tomography effectiveness in metal characterization in general (you can pickup some ideas from this paper)
Response 2: Following this recommendation, we have revised the section and replaced the original biomedical example with a broader discussion on the effectiveness of computed tomography in metallic materials characterization. Specifically, we now emphasize how quantitative X-ray tomography has evolved into a robust tool for analyzing porosity, defect morphology, and density variations in metals and alloys. The previous paragraph referring to trabecular bone architecture has been replaced (page 02, lines 52–56)
Comment 3: Methods: some Xray tomography parameters are missing (energy, rotating on 180 or 360°C, voxel lateral isotropic size…). Could you comment on the voxel size with the expected average pore size?
Response 3: We have added the missing X-ray tomography acquisition parameters, including tube voltage, current, exposure time, rotation range, and reconstructed voxel size. Specifically, scans were performed at 200 kV and 180 µA, with an exposure of 250 ms per projection, over a 360° rotation to minimize reconstruction artifacts. The reconstructed voxel size was 47 µm (laterally isotropic). We have also clarified how this voxel size relates to pore detection. The chosen resolution ensures that pores of interest are sampled by multiple voxels, following the guideline that at least 3–5 voxels are required for detection and ≥10 voxels for precise quantification. These details have been incorporated into the revised manuscript (page 03, lines 112–132).
Comment 4: Methods: please add citations for image j and used plugins (https://imagej.net/contribute/citing) and add some information on used functions ie does “region growing algorithm” correspond to “image j ““dilate” function?
Response 4: The ImageJ software has now been properly cited following the official citation guidelines (https://imagej.net/contribute/citing). In addition, the specific algorithms used for image analysis have been detailed and referenced in the Materials and Methods section.
The grayscale morphological reconstruction is now explicitly described as following the method of Vincent (1993), implemented for ImageJ as presented by Forero et al. (2010). Likewise, the region-growing algorithm used for three-dimensional pore segmentation follows the quantitative implementation reported by Forero et al. (2012). Both citations have been included in the revised manuscript to clarify the origin and implementation of the algorithms employed.
Furthermore, we specify that additional filtering operations applied in this study—namely the Unit Volume Filter and the Two Consecutive Layers Filter—were developed by the authors as simple logical filters to reduce noise and ensure volumetric continuity. These algorithms are straightforward and do not require external citation.
Comment 5: “10% of the total size of each original image (see Table 2 and Figure 3a)” have you checked if 10% is higher than your Representative Volume Element (RVE)?
Response 5: Our samples are based on a gyroid structure, which contains a large fraction of empty space. For this reason, a strict RVE analysis as applied to fully dense materials is not directly applicable. Increasing the window size beyond 10% of the image side would mainly add background rather than solid volume, and would not improve the statistical representativity of pore measurements. Instead, to ensure meaningful sampling, we adopted the criterion that each selected 10% window must contain at least five visible pores. This approach guarantees that the analyzed regions correspond to pore-bearing areas of the structure, while avoiding artificial dilution of porosity values due to large volumes of surrounding void. We have clarified this methodological choice in the revised manuscript (Methods section, page 05, lines 156–160).
Comment 6: “the height "H" of each pore was measured” which criterion do you use to define a pore ? or a non-pores (Table 3) ?
Response 6: In our study, pores were identified qualitatively as dome-shaped grayscale depressions in the tomographic images, based on the morphology typically associated with lack-of-fusion or gas porosity in AlSi10Mg alloys. The identification was performed jointly by the co-authors with expertise in aluminum alloy additive manufacturing, ensuring consistency across the dataset. For this reason, 200 structures were selected across the 40 analyzed images, each exhibiting the characteristic dome-like geometry. Although no quantitative threshold (e.g., grayscale intensity or size) was applied, this expert-driven approach ensured that only well-defined pores were included, while excluding ambiguous features or noise.
Comment 7: “This underscores the need for an individualized application to achieve optimal segmentation results” is an important result, however any idea to improve the methodology to avoid this individualization?
Response 7: To reduce this dependency, several strategies could be considered in future work: the use of adaptive thresholding methods (e.g., Otsu, local adaptive, or histogram-based approaches) that adjust automatically to local contrast conditions. The integration of machine learning or deep learning algorithms trained to recognize pores in additive manufacturing datasets, which could provide more robust and generalized segmentation.
Comment 8: “Unit Volume Filter”: to characterize a volume, 10 voxels are often considered as a minimum value, why did you select the value of 1?
Response 8: The “Unit Volume Filter” applied in our workflow is not intended as a criterion to characterize pores, but rather as a noise-reduction step. Specifically, it removes isolated single voxels generated during binarization, which do not correspond to physical pores but to image noise or reconstruction artifacts. For this reason, a threshold of 1 voxel was chosen: this ensures that only these unit elements are discarded, while all connected voxel clusters (including the smallest real pores) are preserved for analysis. Larger thresholds (e.g., 10 voxels) could risk eliminating true pores of small size, which we aimed to retain. We have clarified this methodological choice in the revised manuscript (Methods section, page 08, lines 203–207).
Comment 9: L204 to L233 should be included in method part
Response 9: Following the recommendation, the content previously located between lines 204–233 has been moved to the Methods section.
Comment 10: L232 “threshold of 31”: have you measure the result variability between threshold 31 and the optimum threshold?
Response 10: The threshold value of 31 was selected based on a ROC curve analysis applied to both stacks jointly. As shown in Table 4 of the revised manuscript, the optimum threshold differs for each stack when considered individually (39 for GD and 22 for G2). However, when both stacks were analyzed together, a threshold of 31 provided the best overall compromise between sensitivity and specificity (with a minimal distance from the point (0,1) in the ROC space). For consistency across the study and to allow a common processing pipeline, we therefore adopted 31 as the fixed threshold.
Comment 11: How the real density value is measured?
Response 11: The real density of the samples was calculated as the ratio between mass and actual volume. The mass was measured using an analytical balance, while the volume was determined by the Archimedes method.
Comment 12: How can you explain the large error between real and measured density for GD sample
Response 12: his point was also raised by Reviewer 1, who suggested either re-scanning the GD specimen or excluding it from the quantitative density analysis. As re-scanning was not possible, we followed that recommendation and removed the GD sample from all quantitative density results and comparisons. In the revised manuscript, the GD data are presented only in the qualitative porosity analysis. This correction has been implemented in the Results section (page 12, lines 271–306).
Comment 13: Could you add a discussion part?
Response 13: A dedicated Discussion section has been added to the revised manuscript, where the results are compared with previous studies, the limitations of the methodology are acknowledged, and potential future improvements are outlined.
Comment 14: Please clarify paper aims: is it to provide result on AlSiMg porosity depending on samples shape or to provide new image processing methodology ?
Response 14: The main aim of the paper is to present and validate a new image processing methodology for porosity characterization based on XCT data. The AlSi10Mg samples with different geometries were used as case studies to apply and demonstrate the method, but the novelty and contribution of the work lie in the image processing approach rather than in comparing porosity as a function of sample shape.
Comment 15: -Fig 1: please add a scale on images (sample a do not seem smaller although it is)
Response 15: A scale bar has been added to each image to reflect the real dimensions of the samples
Comment 16: -Fig 6: please specify what is ROC, S and 1-E and their units. Figure should be understood without reading text.
Response 16: The abbreviations are now explicitly defined in the caption: ROC = Receiver Operating Characteristic, S = Sensitivity (true positive rate), 1–E = False positive rate (1–Specificity). These quantities are dimensionless and take values between 0 and 1.
Comment 17: -Figure and table caption are very short (ie Table 8 results) could you provide more detailed captions ?
Response 17: All figure and table captions have been revised and expanded to provide sufficient detail, so that they can be understood independently of the main text.
Comment 18: -ref 20: url link is not working. Moreover this reference is not pertinent for the study. Due to high density difference between metal and polymer, image processing do not show the same bottlenecks
Response 18: Reference 20 has been removed from the manuscript, as suggested, since it was not directly relevant to the present study.
Author Response File:
Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsRevised manuscript has been modified carefully, and I think it can be received in the current state.
Author Response
Comment1: Revised manuscript has been modified carefully, and I think it can be received in the current state.
Response 1: We sincerely thank the reviewer for the positive evaluation and constructive feedback provided throughout the review process.
Note to the Editor
Minor typographical corrections were made in the numerical tables to unify the notation style according to journal standards. Decimal commas were replaced with decimal points, and exponential expressions (e.g., 5.75e–04) were reformatted as 5.75 × 10⁻⁴. These changes do not affect any numerical values or scientific conclusions.
Reviewer 2 Report
Comments and Suggestions for AuthorsThank you very much for the improvements. However I have some questions
- What is the size of the smallest pore that you consider in this study ?
- (ref comment 11 and 12), if you analyze only 10% of the object by image analysis how can you compare with the measure of the full object by Archimede method ?
- L315 “ (0.060% and 0.073%, respectively) are in close agreement with values reported in the literature for AlSi10Mg fabricated by laser powder bed fusion (L-PBF).” It is often said that Al alloys can’t reach very high density >99.5% by LPBF. Your values are very low. Could you add some references to asset your findings ? Could this result be explained by voxel resolution (so only large pores are detected) ?
Author Response
Comment 1: What is the size of the smallest pore that you consider in this study?
Response 1: The smallest pore that can be effectively analyzed in this study is limited by the tomographic resolution and the logical continuity filters applied during segmentation. The reconstructed voxel size was 0.0477 mm (isotropic). Since the Unit Volume Filter removes isolated single-voxel artifacts and the Two Consecutive Layers Filter requires continuity across at least two adjacent slices, the smallest spatially resolvable pore corresponds to approximately two voxels in size, i.e., about 0.09 mm in physical dimension.
Although Table 10 lists a minimum equivalent spherical diameter of 0.075 mm, this value results from the geometric conversion of pore volume to the diameter of an equivalent sphere and does not imply that smaller features were actually resolved. The small difference between the geometric and physical limits arises from voxel discretization and the non-spherical morphology of real pores.
To clarify this point, the following sentence has been added to the Materials and Methods section (page 8, lines 214–216).
Comment 2: (ref comment 11 and 12), if you analyze only 10% of the object by image analysis how can you compare with the measure of the full object by Archimede method?
Response 2: In the initial stage of image analysis, 10% subwindows were extracted from different regions of the tomographic stacks to perform a representative evaluation of the grayscale and morphological characteristics of the pores. These windows were randomly selected within pore-bearing areas, following the criterion that each region should contain at least five identifiable pores. This approach ensured the representativity of the selected regions with respect to the overall pore morphology and contrast conditions within each sample.
The purpose of these 10% subvolumes was to determine an optimal binarization threshold through the ROC analysis, which was subsequently applied to the entire image stack during porosity quantification. Therefore, the final porosity and density values reported in Tables 8 and 9 correspond to the complete reconstructed volume of each sample, not just to the analyzed subwindows.
Thus, the comparison with the Archimedes method is valid, as both approaches refer to the whole specimen. The use of representative subregions served only as part of the threshold calibration process, ensuring that the segmentation parameters were physically consistent with the overall material microstructure.
Comment 3: L315 “ (0.060% and 0.073%, respectively) are in close agreement with values reported in the literature for AlSi10Mg fabricated by laser powder bed fusion (L-PBF).” It is often said that Al alloys can’t reach very high density >99.5% by LPBF. Your values are very low. Could you add some references to asset your findings ? Could this result be explained by voxel resolution (so only large pores are detected)?
Response 3: The obtained porosity values (0.060% and 0.073%) correspond to relative densities of 99.94% and 99.93%, which are consistent with recent XCT and Archimedes measurements reported for AlSi10Mg produced by L-PBF. For instance, Ghasemi et al. (2022) reported relative densities of 99.95% for AlSi10Mg, 99.96% for AlSi12, and 99.87% for pure Al, confirming that porosity levels below 0.1% are achievable under optimized laser processing and substrate preheating conditions (Additive Manufacturing 59, 103148) [29].
Regarding the possible influence of voxel resolution, we acknowledge that the tomographic voxel size (0.0477 mm) may limit the detection of the smallest pores. However, the porosity values obtained in this study are in the same order of magnitude as those reported by Ghasemi et al. (2022) [29] and are therefore considered representative of the actual defect content in the analyzed samples.
No modification to the manuscript text was necessary, as reference [29] (Ghasemi et al., 2022) is already cited in the Introduction (page 3, line 79) to support the reported density and porosity levels.
Author Response File:
Author Response.pdf
Round 3
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors
Thank you for your answer and the improvement
Best regards,
