Image-Based Laser-Beam Diagnostics Using Statistical Analysis and Machine Learning Regression
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsTayyab Imran proposed a method of laser beam diagnosis, which provides a robust frame for real-time beam quality evaluation and improves the sensitivity to subtle distortion. I think this manuscript is acceptable, but the following problems need to be solved:
- The placement angle of BS in Figure 1 is wrong and needs to be corrected.
- It is necessary to increase the comparison of sensitivity and robustness of different methods to illustrate the advantages of the methods proposed in the manuscript.
- It is necessary to explain the specific details of machine learning in detail, including but not limited to data volume, network type and training environment.
- The proportion of references in the manuscript in the past five years is too low. It is suggested that the author add some new high-quality academic achievements, such as:
(1) Application of femtosecond laser in micro nano device manufacturing:
https://opg.optica.org/optica/abstract.cfm?URI=optica-3-4-448.
(2) Application of dual frequency laser in precision optical measurement:
https://doi.org/10.1002/lpor.202401659 and https://doi.org/10.1038/s41377-025-01785-2.
(3) High energy laser pulse compression field:
https://doi.org/10.1038/s41467-023-39164-3.
Author Response
Comments 1: The placement angle of BS in Figure 1 is wrong and needs to be corrected.
Response 1: We appreciate that the reviewer pointed this out. The figure is updated.
Comments 2: It is necessary to increase the comparison of sensitivity and robustness of different methods to illustrate the advantages of the methods proposed in the manuscript.
Response 2: We thank the reviewer for this valuable suggestion. In the revised manuscript, we have briefly added a comparison-based statement in the conclusion section to highlight the sensitivity and robustness advantages of our integrated statistical and regression-based approach over traditional methods. While a detailed numerical comparison is beyond the current scope, we emphasize that our method's ability to track subtle beam fluctuations and predict trends demonstrates improved diagnostic sensitivity and long-term robustness. (highlighted in the revised manuscript)
Comments 3: It is necessary to explain the specific details of machine learning in detail, including but not limited to data volume, network type and training environment.
Response 3: We thank the reviewer for this insightful comment. Our study utilized linear regression as a supervised machine learning technique due to its interpretability and suitability for small datasets. The dataset comprised 50 sequential beam profile images, each represented by horizontal and vertical intensity metrics. Since linear regression is a non-iterative, low-complexity model, no neural network architecture or GPU-based training environment was required. We have clarified this in the revised manuscript by briefly adding the data volume and justification for the chosen model in the Predictive Modelling section. (highlighted in the revised manuscript)
Comments 4: The proportion of references in the manuscript in the past five years is too low. It is suggested that the author add some new high-quality academic achievements,
Response 4: References are updated. Some new references have also been added (highlighted in the revised manuscript).
Additional clarifications
Thank you very much for your detailed review. In addition to addressing your comments, we have also made revisions based on the other reviewer's feedback. All changes have been highlighted in the revised manuscript for your reference.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper reports some progress on laser beam diagnostics with an 870 nm fiber laser, including centroid displacement, FWHM, ellipticity ratio, and asymmetry index. Also, based on a dataset of 50 sequential beam profile images, linear regression technique is used for predicting trends in intensity.
The paper is well written. I have the following suggestions:
- ‘Figure 5(a) shows the variation of X- and Y-direction FWHM values across the entire image sequence. ……This behavior indicates horizontal beam divergence or degradation of collimation quality over time, potentially due to thermal lensing effects.’ Why there is no thermal lensing effects in the vertical direction? Is there a practical reason? Please add some discussion about this.
- It is better to improve the block diagrams in Figure 3 and Figure 9, please adjust the layouts and add arrows to the flows.
- For Figure 10, May be to replace “True vs. predicted normalized intensity” with “Tested value and predicted value of the normalized intensity”?
Author Response
Comments 1: Figure 5(a) shows the variation of X- and Y-direction FWHM values across the entire image sequence. ……This behavior indicates horizontal beam divergence or degradation of collimation quality over time, potentially due to thermal lensing effects.’ Why there is no thermal lensing effects in the vertical direction? Is there a practical reason? Please add some discussion about this.
Response 1: We appreciate the reviewer’s thoughtful observation. In the revised manuscript, we have briefly explained the absence of significant thermal lensing effects in the vertical direction. While thermal lensing can occur in both axes, the relative stability of the Y-direction FWHM in our results suggests that the optical path and component alignment in the vertical plane are less susceptible to heat-induced distortions, possibly due to symmetric heat dissipation or a lower thermal gradient in that axis. A sentence has been added to Section 2.2.2 to clarify this (highlighted in the revised manuscript).
Comments 2: It is better to improve the block diagrams in Figure 3 and Figure 9, please adjust the layouts and add arrows to the flows.
Response 2: We sincerely thank the reviewer for this constructive suggestion. In response, we have revised the layouts of both Figure 3 and Figure 9 to improve clarity. The diagrams have been reoriented from vertical to horizontal flow, and arrows have been added to illustrate the logical sequence of operations better. We hope these changes enhance the readability and understanding of the methodological steps presented. We appreciate the feedback and will certainly consider more detailed design enhancements in our future work.
Comments 3: For Figure 10, May be to replace “True vs. predicted normalized intensity” with “Tested value and predicted value of the normalized intensity”?
Response 3: We thank the reviewer for the thoughtful suggestion regarding the caption of Figure 10. We agree that the proposed phrasing improves clarity, and we have updated the caption to read: “Tested value and predicted value of the normalized intensity” as recommended (highlighted in the revised manuscript).
Additional clarifications
Thank you very much for your thorough and detailed review. In addition to addressing your comments, we have also incorporated changes based on the feedback from the other reviewer. All modifications have been highlighted within the manuscript for your reference.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThis paper reports a comprehensive experimental and computational study on high-resolution laser beam diagnostics, integrating classical statistical techniques, digital image processing, and machine learning-based predictive modeling. It provides an effective method for monitoring beam stability and alignment accuracy in femtosecond laser applications. The design of this work is innovative and has potential application. However, there are several questions that should be addressed and parts that need to be discussed in much more detail before accepting this paper for publication.
- Only 50 images were collected in the experiment. Can these 50 images fully represent the characteristics of the laser beam under various conditions? Have you considered increasing the number of image collections to enhance the reliability and universality of the experimental results?
- To enhance the practical relevance and academic robustness of this work, provide clear examples of application scenarios where the proposed diagnostic framework can address existing challenges. Additionally, systematically discuss methodological limitations, such as dataset constraints or others.
This paper is well written.
Author Response
Comment 1: Only 50 images were collected in the experiment. Can these 50 images fully represent the characteristics of the laser beam under various conditions? Have you considered increasing the number of image collections to enhance the reliability and universality of the experimental results?
Response 1: We thank the reviewer for the thoughtful comment. As noted in Section 2.1 (line 14), the number of images was limited to 50 due to thermal stability constraints of the laser system. These images were acquired during the most stable operational period and were sufficient to reveal meaningful trends in beam behavior. While a larger dataset could improve generalization, we aimed to demonstrate the method’s effectiveness under practical experimental conditions.
Comment 2: To enhance the practical relevance and academic robustness of this work, provide clear examples of application scenarios where the proposed diagnostic framework can address existing challenges. Additionally, systematically discuss methodological limitations, such as dataset constraints or others.
Response 2: We sincerely thank the reviewer for this valuable comment. To enhance practical relevance and academic robustness, we have added brief examples of potential application scenarios in the Conclusion section, such as beam alignment monitoring and laser machining diagnostics. Additionally, we have included a short statement on dataset
size and experimental duration as methodological limitations. These additions aim to strengthen the broader context and acknowledge the study’s current constraints (highlighted in the revised manuscript).
Additional clarifications
Thank you for your valuable suggestion. In addition to addressing your comments, we have also incorporated changes based on feedback from the other reviewers. All modifications have been highlighted within the manuscript for your reference.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors present a method for analyzing the laser-beam images and predicting trends. As the topic is of interest to the community, I’d suggest the paper to be published. Before publication, however, there are some small issues that need consideration:
- In this paper, the vertical and horizontal beam characteristics are analyzed separately. However, if the laser beam is elliptical and inclined relative to the coordinate axis, it should be rotated to accurately calculate the beam width and beam ellipticity.
- In Line 190 of the manuscript, equation (3) is incomplete for converting a given full width at the half maximum (FWHM) value to the standard deviation (sigma).
- In Fig. 5(a) and 5(b), the relationship between beam width and FWHM is not clear. What is the main difference?
- In Fig.8, the calculated FWHM width (approximately 700 pixels) from the laser-beam intensity profiles is inconsistent with that shown in Fig. 5.
- In Fig. 10, the fitted curves and measured results appear discrete. How the accuracy of the model is verified?
Author Response
Comment 1: In this paper, the vertical and horizontal beam characteristics are analyzed separately. However, if the laser beam is elliptical and inclined relative to the coordinate axis, it should be rotated to accurately calculate the beam width and beam ellipticity.
Response 1: We sincerely thank the reviewer for this insightful observation. We agree that a coordinate transformation would provide more precise measurements in the case of a rotated elliptical beam. In our current work, the beam remained largely aligned with the coordinate axes throughout the acquisition period, as confirmed through visual inspection and intensity profiles. Therefore, the horizontal and vertical analyses accurately represented this study's observed beam behavior (highlighted in the revised manuscript).
Comment 2: In Line 190 of the manuscript, equation (3) is incomplete for converting a given full width at the half maximum (FWHM) value to the standard deviation (sigma).
Response 2: We sincerely thank the reviewer for identifying the issue with Equation (3). The original expression for converting the full width at half maximum (FWHM) to the standard deviation (σ) was indeed presented in an abbreviated form. We have corrected this in the revised manuscript to show the complete and accurate formula.
Comment 3: In Fig. 5(a) and 5(b), the relationship between beam width and FWHM is not clear. What is the main difference?
Response 3: We thank the reviewer for this helpful comment. In Figure 5(a), we present the variation of beam width using the raw FWHM values directly extracted from the image matrix in pixel units. In contrast, Figure 5(b) shows the same FWHM values after normalization and smoothing to highlight relative trends along the X and Y axes. We have revised the figure caption to explain that Figure 5(a) presents raw FWHM values in pixels, while Figure 5(b) displays the corresponding normalized and smoothed data to highlight relative trends. We hope this modification improves the clarity and interpretation of the results (highlighted in the revised manuscript).
Comment 4: In Fig.8, the calculated FWHM width (approximately 700 pixels) from the laser-beam intensity profiles is inconsistent with that shown in Fig. 5.
Response 4: We sincerely thank the reviewer for this careful observation. The apparent inconsistency arises because the profiles shown in Figure 8 represent summed intensity distributions across each axis, not direct single-frame measurements. These integrated profiles span a broader pixel range, which can visually appear wider than the actual FWHM values calculated frame-by-frame and shown in Figure 5. We have added a brief clarification in the caption for Figure 8 to avoid confusion (highlighted in the revised manuscript).
Comments 5: In Fig. 10, the fitted curves and measured results appear discrete. How the accuracy of the model is verified?
Response 5: We thank the reviewer for the valuable comment. The apparent discreteness between the fitted curves and measured values in Figure 10 is due to natural fluctuations in beam intensity across the 50-image dataset. A simple linear regression model was used, and the goal was to identify overall trends rather than achieve perfect point-wise matching. Despite the scatter, the fitted lines closely follow the general direction of intensity variation, which confirms the model's suitability for capturing gradual beam behavior. We have noted this clarification in the revised text to improve understanding of the model's purpose and limitations (highlighted in the revised manuscript).
Additional clarifications
We sincerely appreciate your detailed and thoughtful review. Your valuable feedback has been instrumental in improving the clarity and accuracy of our manuscript. In addition to addressing your comments, we have also incorporated revisions based on the other reviewer's feedback. All changes have been carefully implemented and highlighted in the manuscript. Thank you once again for your time and effort in reviewing our work.
Author Response File: Author Response.pdf
