Optimization of Film Thickness Uniformity in Hemispherical Resonator Coating Process Based on Simulation and Reinforcement Learning Algorithms

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper explores how to improve the uniformity of metal film coatings on the inner surface of a hemispherical resonator, used in high-precision gyroscopes. The authors use COMSOL simulations to model particle deposition during coating and apply a reinforcement learning method, specifically PPO, to optimize coating strategies. They also design a physical mask to address low coating coverage in difficult areas and run an experiment to test the method, reporting the achieved uniformity. Here are the weaknesses and issues within this paper:

1. The paper doesn’t explain enough why past coating strategies fail in non-planar geometries like hemispherical resonators. You should provide a more detailed explanation of why previous coating methods fail in such geometries, referencing specific examples of their shortcomings.

2. The rationale for choosing electron beam evaporation over other PVD methods isn't well developed. Offer a clearer and more thorough justification for selecting electron beam evaporation, including a comparison with other PVD methods and explaining why it is the best option for this case.

3. The connection between film non-uniformity and resonator performance degradation is not fully expanded. You need to expand on how non-uniformity in the film directly impacts the performance of the resonator, with more evidence from prior studies to back up your claim.

4. The references used are relevant, but more context is needed around the limitations of existing simulation approaches and the rationale for applying reinforcement learning. Provide more background on the limitations of existing simulation techniques and explain why reinforcement learning, specifically PPO, is appropriate for this problem.

5. More justification is needed to explain why reinforcement learning (PPO) is a valid tool for this problem. You should elaborate on the specific benefits of using reinforcement learning in this scenario, especially in relation to the optimization of deposition angles.

6. In the PPO section, the paper does not describe the network architecture, training parameters, or reward shaping in detail. You need to include more details about the PPO network architecture, the training parameters, and how reward shaping was handled to allow for reproducibility.

7. The COMSOL simulation lacks specifics on mesh resolution, boundary conditions, and assumptions made in simplifying the geometry. Clearly specify the mesh resolution, boundary conditions, and any assumptions made while simplifying the geometry in the COMSOL simulations.

8. Criteria for selecting measurement points in the film thickness measurement process could be clearer. Provide more detail on how you selected the measurement points for film thickness, including the rationale behind the selection process.

9. Figures like 8 and 13 lack clear axis labeling or unit explanations, which makes interpreting the plots difficult. Label the axes and provide units in Figures 8 and 13 to ensure clarity and help the reader interpret the data correctly.

10. The connection between time steps and actual film growth in the PPO output isn’t explained well. You should provide a clearer explanation of how the PPO time steps correlate to actual film growth, and clarify the deposition rate used in the process.

11. The source of the deviation between the simulation and experimental results (5.24% vs 11%) is not quantified or discussed in relation to the figure data. Analyze and discuss the sources of the deviation between the simulation and experimental results, including possible reasons such as deposition rate, chamber conditions, or measurement error.

12. The film thickness measurement data is not adequately explained, and the methods for computing uniformity need more clarity. Clarify the film thickness measurement process and provide more details on how you computed the uniformity to ensure transparency.

13. The gap between simulation and experimental results (5.24% vs 11%) is significant, and the paper doesn’t analyze the sources of the difference, such as deposition rate control, chamber conditions, or measurement error. Address this significant gap by thoroughly analyzing potential sources of error, such as deposition rate variation or environmental factors during experiments.

14. The effect of the correction mask on total electrical resistance or functionality isn’t measured, which weakens the claim of its effectiveness. You need to measure and discuss the effect of the correction mask on the electrical resistance or functionality of the resonator to strengthen your claims about its effectiveness.

15. There is no validation of how improved uniformity affects overall device performance (Q-factor, sensor accuracy). Conduct experiments that validate the impact of improved film uniformity on device performance, such as Q-factor or sensor accuracy, and report these findings in your paper.

16. While the integration of methods like PPO and COMSOL is original, applying PPO for process control in this context isn’t new. Acknowledge that PPO is not new in this context and compare it with other optimization methods like genetic algorithms or grid search to clarify the novelty of your approach.

17. No comparison is made with other optimization methods, such as genetic algorithms or grid search, limiting the novelty claim. Include a comparison of your PPO-based method with other common optimization techniques, such as genetic algorithms or grid search, to better establish the novelty of your approach.

18. The correction mask design is not conceptually new, as masking is well-studied in coating processes. You should clarify how your specific mask design is distinct from prior studies and what unique benefits it offers in this application.

19. The study is useful for HRG fabrication but doesn’t have a significant impact on broader fields like coating science or learning-based process control. To increase the broader impact of your work, you should discuss how the methods applied could be adapted or scaled to other coating applications or fields outside of HRG fabrication.

20. There’s no demonstration of the improved uniformity leading to measurable gains in device performance, limiting the significance of the work. Include data or analysis that demonstrates how the improved coating uniformity results in tangible improvements in device performance, such as increased Q-factor or sensor accuracy.

21. The presentation lacks precision and polish in key areas, including the explanation of the PPO algorithm, figures lacking labels or numerical scales, and a more detailed breakdown of the correction mask design. Refine the presentation by improving the explanation of the PPO algorithm, adding labels or scales to all figures, and providing a more detailed step-by-step breakdown of the correction mask design.

22. The explanations vary in depth, with some parts (like the PPO algorithm and figure details) being unclear and hard to follow. Ensure that the explanations of key concepts, particularly the PPO algorithm and figures, are thorough and clear, making them easier for readers to follow.

23. The mismatch between simulated and experimental film thickness isn’t explored in depth. Provide a more detailed exploration of the mismatch between simulation and experimental results, discussing potential causes and their impact on the overall findings.

24. The reward function used in PPO is deemed mathematically questionable for the goal it aims to optimize. Reevaluate and provide a more detailed justification of the reward function used in PPO, ensuring that it is mathematically sound for the goal of optimizing film uniformity.

25. No functional validation showing how improved uniformity affects device performance. You should perform functional validation to demonstrate how the improved uniformity directly enhances device performance, such as through increased Q-factor or sensor accuracy.

26. The study is limited to a narrow use case (one resonator shape), and the claim that the method can apply to other curved surfaces or optical components requires more justification. Provide more evidence or justification showing that the method can be applied to other geometries, such as different resonator shapes or optical components, to broaden its applicability.

27. While the paper will interest a specific technical audience, its broad appeal is limited due to the dry delivery and lack of explanation of how the PPO algorithm interacts with the coating physics. Enhance the delivery of the paper by improving the explanation of how the PPO algorithm interacts with coating physics, making it more accessible to a broader audience.

28. The absence of performance-based outcomes (like Q-factor improvement) reduces the study's broader appeal. Include performance-based outcomes, such as improvements in Q-factor, to make the study more compelling and relevant to a wider audience.

29. The paper does not introduce new theory or a breakthrough in technique, and the methods used, although integrated effectively, are standard in their fields. Clarify how your work advances existing theory or introduces novel techniques, and emphasize any unique contributions your study makes to the field.

 

I did not detect plagiarism. Sources are cited consistently throughout the paper, including when discussing prior methods like Monte Carlo simulation, thin film modeling, and PVD/ALD techniques. For example, background discussions reference [6–10] for coating techniques, and [11–13] for deposition modeling, which align with standard literature. Descriptions of methods like COMSOL simulations, PPO algorithms, and Knudsen number analysis appear original or are based on standard formulations that are public knowledge in physics and engineering. When specific technical content or data is referenced, the relevant sources [14], [19] are listed. Text structure and phrasing do not resemble known copied segments. The language is sometimes awkward or mechanical, but it does not follow the polished tone or paragraph flow typical of copied material. Reference formatting and attribution are clear. Citations are placed directly after specific claims and not just dumped at the end of sections, which is a common sign of masking plagiarism. There are self-citations in the paper. I checked the author list and their affiliations: Jingyu Pan, Dongsheng Zhang, Shijie Liu, Jianguo Wang, and Jianda Shao, affiliated with Shanghai University and Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. Now here are the self-citations I found:

[6] Ting, Z.; Si-Yu, X.; Ji-Ming, M.; Wen-yao, T.; Chun-qiao, J. Study on metallic coating technique of the hemispherical resonator. Piezoelectrics Acoustooptics 2006.
Reason for self-citation: This is likely authored by colleagues or previous members of the Shanghai Institute of Optics and Fine Mechanics, based on the topic (metallic coating on resonators) and naming structure. While no exact name match is in the author list, this may be cited from a related research group.

[14] Molecular flow module: Simulate rarefied gas flows in vacuum systems. COMSOL blog. Reason for self-citation: Not a self-citation, but rather software documentation. Mentioned here for completeness.

[23] Liu, C.; Kong, M.; Guo, C.; Gao, W.; Li, B. Theoretical design of shadowing masks for uniform coatings on spherical substrates in planetary rotation systems. Opt. Express 2012.
Check: This might be a partial match "Liu" is a common name, but Shijie Liu is listed as a co-author in this paper. However, there is no direct evidence it is the same person based solely on name. The affiliation of this reference is not listed, so this is inconclusive.

Here are the formula issues found in the paper:
Page 4, Finite Element Model – Knudsen Number Formula. The units check out and the form is correct, but the denominator expression is not bracketed, which can lead to misreading. Write it clearly.

Page 10, Film Thickness Uniformity Formula - The formula is conceptually fine, but the variable naming is inconsistent. Elsewhere, the paper uses just “d” for thickness, but here introduces “Δd̅” without defining the bar over delta.

Page 11, PPO Reward Function - This reward function is mathematically unstable if Vmax≈Vmin, leading to division by zero or large fluctuations. Also, the form contradicts the intended behavior: maximizing this expression does not minimize the variation. You likely meant something else.

Page 13, Correction Mask Design Equations (Equations 5 and 6) - Equation structure is unnecessarily complex and not well explained. The use of “cos 40°” inside terms with different multipliers lacks clarity. It’s not clear if the cosine applies only to Dr or to the whole term. Needs parentheses and better grouping to avoid ambiguity.

Few concerns worth noting:

1- The simulation targets 100 nm film thickness, but the experiment achieves only ~50 nm. This is acknowledged but not analyzed. The paper should address the source of this discrepancy whether it's due to deposition rate, QCM miscalibration, or chamber condition deviations. Without this, the validation of the PPO optimization remains only partial.

2- The paper doesn’t report key hyperparameters (learning rate, batch size, episode length), network architecture, or training stability diagnostics. For reproducibility, this information is critical. It also doesn’t benchmark PPO performance against a baseline (uniform rotation), which would strengthen the technical claim.

3- The reported 11.0% film thickness uniformity in the experiment is a single value. There is no mention of measurement error, variability across samples, or repeatability, which is important in coating process validation.

4- The correction mask’s influence on the final device function is not studied. There is no electrical resistance measurement, conductivity test, or functional gyro performance assessment. So while the mask improves thickness at the stem shell junction, we don’t know if it helps or hurts the device as a whole.

References that are not clearly relevant or necessary:
[1] Mellit, A. (1984) – Inertial technology for the future. IEEE Trans. Aerosp. Electron. Syst.
This reference is outdated and general. It discusses inertial technology broadly but does not contribute specifically to the HRG coating or optimization context. It could be removed or replaced with something more recent and targeted.
[8] Fu, Y. et al. – Preparation of crystalline TiNi shape-memory alloy thin film...
This paper is about shape-memory alloys in MEMS, not about film uniformity or resonator coating. The relevance is weak, and it doesn't strengthen the discussion on PVD or ALD applicability for curved geometries.

Recommendations for more relevant articles to be added:
- Jilani, A., Abdel-wahab, M. S., & Hammad, A. H. (2017). Advance Deposition Techniques for Thin Film and Coating. InTech. doi: 10.5772/65702
- Qinghe Gao, Artur M Schweidtmann (2024). Deep reinforcement learning for process design: Review and perspective. Current Opinion in Chemical Engineering, Volume 44, 101012. ISSN 2211-3398. https://doi.org/10.1016/j.coche.2024.101012.

Comments on the Quality of English Language

Moderate editing of English language required.
Below is a list of specific language issues found throughout the manuscript:

Abstract - Replace "valuable insights" with a more neutral term like "useful information" to avoid vague language.

Abstract - Consider specifying what kind of framework. "Provides a framework" is vague and should be clarified.

Introduction - Incomplete phrase. Replace with "navigation applications in GPS-restricted environments [2]".

Introduction - “Perturb” could be replaced with “affect” or “disturb,” which are more straightforward.

Introduction - "Demonstrations exploited" is awkward. Suggest "Several metallization coating methods used in resonators..."

Simulation and Analysis – Finite Element Model - Missing verb. Should be "can be calculated".

Simulation and Analysis – Finite Element Model - Consider rephrasing for clarity: "with vacuum levels as low as 5×10⁻5 Pa".

Simulation and Analysis – Finite Element Model - Ambiguous. Suggest rephrasing to: "approximate real experimental conditions".

Simulation Results - The sentence is too long and unclear. Break it into two sentences for clarity.

Simulation Results - Too formal and redundant. Simplify to: "This suggests that..."

Optimization Algorithm - Overuse of reinforcement learning jargon. Consider simplifying to improve accessibility for non-specialists.

Optimization Algorithm - Could be more clear. Suggest "the model selects the iteration with the lowest PV value".

Correction Mask - Consider rewording as: "This region cannot be coated effectively from all angles due to geometric limitations".

Correction Mask - This is informal. Consider "areas inaccessible to vapor deposition".

Experimental Result - The phrase is dense. Consider explaining briefly how this affects the measurement.

Experimental Result - The word "exclusively" is redundant when "localized" is already used. Drop one.

Conclusion - Vague. Consider stating what kind of efficiency computational? experimental?

Conclusion - Use more neutral wording such as "effectively optimized".

Author Response

Comments 1: The paper doesn’t explain enough why past coating strategies fail in non-planar geometries like hemispherical resonators. You should provide a more detailed explanation of why previous coating methods fail in such geometries, referencing specific examples of their shortcomings.

Response 1: Thank you for pointing this out. We agree with this comment. I added some articles on past coating strategies, which highlight that the methods described in these papers do not effectively address the coating issues of hemispherical resonators. This demonstrates the shortcomings of past coating strategies. -in page 2, paragraph 3, and line 60-65.

 

Comments 2: The rationale for choosing electron beam evaporation over other PVD methods isn't well developed. Offer a clearer and more thorough justification for selecting electron beam evaporation, including a comparison with other PVD methods and explaining why it is the best option for this case.

Response 2: I added the advantages of electron beam evaporation compared to magnetron sputtering, to demonstrate that it is the best option for this case in page 2, paragraph 4, and line 82-86.

 

Comments 3: The connection between film non-uniformity and resonator performance degradation is not fully expanded. You need to expand on how non-uniformity in the film directly impacts the performance of the resonator, with more evidence from prior studies to back up your claim.

Response 3: I have referenced three articles to explain how film non-uniformity affects the Q value, vibration modes, and the control errors of the gyroscope. -in page 2, paragraph 1, and line 43-47.

 

Comments 4: The references used are relevant, but more context is needed around the limitations of existing simulation approaches and the rationale for applying reinforcement learning. Provide more background on the limitations of existing simulation techniques and explain why reinforcement learning, specifically PPO, is appropriate for this problem.

Response 4: I commented on the limitations of some simulation approaches, highlighting the issues with methods such as Monte Carlo, optical simulation, and mathematical modeling. -in page 2, paragraph 3, and line 73-78.

 

Comments 5: More justification is needed to explain why reinforcement learning (PPO) is a valid tool for this problem. You should elaborate on the specific benefits of using reinforcement learning in this scenario, especially in relation to the optimization of deposition angles.

Response 5: The benefits of using the PPO algorithm, were also mentioned in Comments 4, especially compared to genetic algorithms. I referenced two articles to explain this. -in page 10, paragraph 1, and line 267-278.

 

Comments 6: In the PPO section, the paper does not describe the network architecture, training parameters, or reward shaping in detail. You need to include more details about the PPO network architecture, the training parameters, and how reward shaping was handled to allow for reproducibility.

Response 6: I added more details about the PPO network architecture, including Figure 11 and Table 3, which makes this section more complete. -in page 10-12, and line 313-336

 

Comments 7: The COMSOL simulation lacks specifics on mesh resolution, boundary conditions, and assumptions made in simplifying the geometry. Clearly specify the mesh resolution, boundary conditions, and any assumptions made while simplifying the geometry in the COMSOL simulations.

Response 7: I added more details about the COMSOL simulation，including mesh resolution, boundary conditions, and assumptions made in simplifying the geometry in page 4, paragraph 1, and line 135-141.

 

Comments 8: Criteria for selecting measurement points in the film thickness measurement process could be clearer. Provide more detail on how you selected the measurement points for film thickness, including the rationale behind the selection process.

Response 8: I have inserted an image in Figure 20, which shows the location of the selected measurement points and provides a description of them in page 16, paragraph 3, line 448-449, and Figure 20.

 

Comments 9: Figures like 8 and 13 lack clear axis labeling or unit explanations, which makes interpreting the plots difficult. Label the axes and provide units in Figures 8 and 13 to ensure clarity and help the reader interpret the data correctly.

Response 9: I have modified the X-axis of figures 8 and 13, and added explanations to the coordinate axes, making the images clearer and easier to understand. -in page 7, paragraph 1, line 210-214,218-221, and Figure 8,13.

 

Comments 10: The connection between time steps and actual film growth in the PPO output isn’t explained well. You should provide a clearer explanation of how the PPO time steps correlate to actual film growth, and clarify the deposition rate used in the process.

Response 10: I provided an explanation for this issue and briefly described how the operations are carried out based on the output of the PPO algorithm in the experiment. -in page 13, paragraph 2, and line 363-369

 

Comments 11: The source of the deviation between the simulation and experimental results (5.24% vs 11%) is not quantified or discussed in relation to the figure data. Analyze and discuss the sources of the deviation between the simulation and experimental results, including possible reasons such as deposition rate, chamber conditions, or measurement error.

Response 11: I analyzed and discussed the sources of the deviation between the simulation and experimental results from the aspects of experimental environment, equipment issues, and mechanical errors. -in page 17, paragraph 2, and line 470-480

 

Comments 12: The film thickness measurement data is not adequately explained, and the methods for computing uniformity need more clarity. Clarify the film thickness measurement process and provide more details on how you computed the uniformity to ensure transparency.

Response 12: I added some descriptions and Table 5 to make the film thickness measurement data clearer. -in page 17, paragraph 2, line 467-469 and Table 5.

 

Comments 13: The gap between simulation and experimental results (5.24% vs 11%) is significant, and the paper doesn’t analyze the sources of the difference, such as deposition rate control, chamber conditions, or measurement error. Address this significant gap by thoroughly analyzing potential sources of error, such as deposition rate variation or environmental factors during experiments.

Response 13: This response is similar to Response 11, and the comments can refer to Comments 11.

 

Comments 14: The effect of the correction mask on total electrical resistance or functionality isn’t measured, which weakens the claim of its effectiveness. You need to measure and discuss the effect of the correction mask on the electrical resistance or functionality of the resonator to strengthen your claims about its effectiveness.

Response 14: I inserted an image of the resonator without using the correction mask coating in Figure 21, and explained the impact of the modified mask from the perspective of resistance. -in page 18, paragraph 2, line 487-495, and figure 21.

 

Comments 15: There is no validation of how improved uniformity affects overall device performance (Q-factor, sensor accuracy). Conduct experiments that validate the impact of improved film uniformity on device performance, such as Q-factor or sensor accuracy, and report these findings in your paper.

Response 15: Conducting experiments to validate the impact of improved film uniformity on device performance is currently challenging. This is because both Q-factor and sensor accuracy require specialized equipment and personnel for measurement. Moreover, to verify improvements in Q-factor, a mature annealing process is necessary; otherwise, it is difficult to demonstrate the advantages of enhanced film uniformity. These are resources we currently lack. I have used the research results and articles from other sources to illustrate the importance of coating uniformity. For example, uneven film layers can cause resistance discrepancies, leading to control errors; and non-uniform film thickness can lead to uneven stress in the film, which can reduce the Q-factor. I hope these materials can support my argument. This section can refer to Response 3.

 

Comments 16: While the integration of methods like PPO and COMSOL is original, applying PPO for process control in this context isn’t new. Acknowledge that PPO is not new in this context and compare it with other optimization methods like genetic algorithms or grid search to clarify the novelty of your approach.

Response 16: This response is similar to Response 5, and the comments can refer to Comments 5.

 

Comments 17: No comparison is made with other optimization methods, such as genetic algorithms or grid search, limiting the novelty claim. Include a comparison of your PPO-based method with other common optimization techniques, such as genetic algorithms or grid search, to better establish the novelty of your approach.

Response 17: This response is similar to Response 5, and the comments can refer to Comments 5.

 

Comments 18: The correction mask design is not conceptually new, as masking is well-studied in coating processes. You should clarify how your specific mask design is distinct from prior studies and what unique benefits it offers in this application.

Response 18: I use a simulation method to verify the corrected mask, which offers certain advantages compared to not using a simulation. -in page 22, paragraph 1, and line 429-432

 

Comments 19: The study is useful for HRG fabrication but doesn’t have a significant impact on broader fields like coating science or learning-based process control. To increase the broader impact of your work, you should discuss how the methods applied could be adapted or scaled to other coating applications or fields outside of HRG fabrication.

Response 19: I explained that this method can also be applied to other coating fields, such as coating on complex curved surfaces and batch component coating. -in page 22, paragraph 1, and line 523-537

 

Comments 20: There’s no demonstration of the improved uniformity leading to measurable gains in device performance, limiting the significance of the work. Include data or analysis that demonstrates how the improved coating uniformity results in tangible improvements in device performance, such as increased Q-factor or sensor accuracy.

Response 20: This response is similar to Response 3, and the comments can refer to Comments 3.

 

Comments 21: The presentation lacks precision and polish in key areas, including the explanation of the PPO algorithm, figures lacking labels or numerical scales, and a more detailed breakdown of the correction mask design. Refine the presentation by improving the explanation of the PPO algorithm, adding labels or scales to all figures, and providing a more detailed step-by-step breakdown of the correction mask design.

Response 21: I added more details about the PPO algorithm in Comments 6. Additionally, I added and corrected the captions for the figure to make this section clearer in Comments 9. The issue regarding the correction mask is also mentioned in Comments 14 and 18.

 

Comments 22: The explanations vary in depth, with some parts (like the PPO algorithm and figure details) being unclear and hard to follow. Ensure that the explanations of key concepts, particularly the PPO algorithm and figures, are thorough and clear, making them easier for readers to follow.

Response 22: This response is similar to Response 21, and the comments can refer to Comments 21.

 

Comments 23: The mismatch between simulated and experimental film thickness isn’t explored in depth. Provide a more detailed exploration of the mismatch between simulation and experimental results, discussing potential causes and their impact on the overall findings.

Response 23: This response is similar to Response 11, and the comments can refer to Comments 11.

 

Comments 24: The reward function used in PPO is deemed mathematically questionable for the goal it aims to optimize. Reevaluate and provide a more detailed justification of the reward function used in PPO, ensuring that it is mathematically sound for the goal of optimizing film uniformity.

Response 24: The reward function was designed to balance two key objectives: (1) minimizing the peak-to-valley (PV) thickness variation. (2) maintaining a reasonable average thickness. The ratio form ensures that the optimization does not solely focus on uniformity at the expense of overall deposition efficiency. This is critical for practical coating processes where both uniformity and deposition rate matter. The reward function practical efficacy is demonstrated by the results: The PPO algorithm consistently converged to a PV below 15 nm after 250 iterations and finally achieved a uniformity of 5.24%.We acknowledge the reviewer’s concern and agree that a deeper theoretical analysis of the reward function’s properties could strengthen the work. We will include such analysis in a future extended version of this study.

 

Comments 25: No functional validation showing how improved uniformity affects device performance. You should perform functional validation to demonstrate how the improved uniformity directly enhances device performance, such as through increased Q-factor or sensor accuracy.

Response 25: This response is similar to Response 15, and the comments can refer to Comments 15.

 

Comments 26: The study is limited to a narrow use case (one resonator shape), and the claim that the method can apply to other curved surfaces or optical components requires more justification. Provide more evidence or justification showing that the method can be applied to other geometries, such as different resonator shapes or optical components, to broaden its applicability.

Response 26: This response is similar to Response 19, and the comments can refer to Comments 19.

 

Comments 27: While the paper will interest a specific technical audience, its broad appeal is limited due to the dry delivery and lack of explanation of how the PPO algorithm interacts with the coating physics. Enhance the delivery of the paper by improving the explanation of how the PPO algorithm interacts with coating physics, making it more accessible to a broader audience.

Response 27: This response is similar to Response 10, and the comments can refer to Comments 10.

 

Comments 28: The absence of performance-based outcomes (like Q-factor improvement) reduces the study's broader appeal. Include performance-based outcomes, such as improvements in Q-factor, to make the study more compelling and relevant to a wider audience.

Response 28: This response is similar to Response 15, and the comments can refer to Comments 15.

 

Comments 29: The paper does not introduce new theory or a breakthrough in technique, and the methods used, although integrated effectively, are standard in their fields. Clarify how your work advances existing theory or introduces novel techniques, and emphasize any unique contributions your study makes to the field.

Response 29: We acknowledge that individual methods employed in this study are well-established in their respective fields. However, the novelty of our work lies in the systematic integration of these methods to solve a highly specific and challenging problem—uniform coating on hemispherical resonators—which has not been previously addressed through such a combined approach. This integration itself represents a methodological advancement. In fact, this method has also practically and effectively solved the current issues. Moreover, Our method provides a perspective for the process optimization of complex surface coating. The workflow of simulation-algorithm-experiment can be adapted to other geometries。

 

Comments 30: The simulation targets 100 nm film thickness, but the experiment achieves only ~50 nm. This is acknowledged but not analyzed. The paper should address the source of this discrepancy whether it's due to deposition rate, QCM miscalibration, or chamber condition deviations. Without this, the validation of the PPO optimization remains only partial.

Response 30: This response is similar to Response 11, and the comments can refer to Comments 11.

 

Comments 31: The paper doesn’t report key hyperparameters (learning rate, batch size, episode length), network architecture, or training stability diagnostics. For reproducibility, this information is critical. It also doesn’t benchmark PPO performance against a baseline (uniform rotation), which would strengthen the technical claim.

Response 31: This response is similar to Response 6, and the comments can refer to Comments 6.

 

Comments 32: The reported 11.0% film thickness uniformity in the experiment is a single value. There is no mention of measurement error, variability across samples, or repeatability, which is important in coating process validation.

Response 32: We thank the reviewer for raising this critical point. Due to current experimental constraints, we are unable to perform additional repeatability tests. However, the current uniformity results already demonstrate that our optimization method is effective. As for the measurement error, the repeatability precision of our white light interferometer typically reaches 1nm, which is sufficiently accurate for our experiment.

 

Comments 33: The correction mask’s influence on the final device function is not studied. There is no electrical resistance measurement, conductivity test, or functional gyro performance assessment. So while the mask improves thickness at the stem shell junction, we don’t know if it helps or hurts the device as a whole.

Response 33: This response is similar to Response 14, and the comments can refer to Comments 14.

 

Comments 34: References that are not clearly relevant or necessary:
[1] Mellit, A. (1984) – Inertial technology for the future. IEEE Trans. Aerosp. Electron. Syst.
This reference is outdated and general. It discusses inertial technology broadly but does not contribute specifically to the HRG coating or optimization context. It could be removed or replaced with something more recent and targeted.
[8] Fu, Y. et al. – Preparation of crystalline TiNi shape-memory alloy thin film...
This paper is about shape-memory alloys in MEMS, not about film uniformity or resonator coating. The relevance is weak, and it doesn't strengthen the discussion on PVD or ALD applicability for curved geometries.Recommendations for more relevant articles to be added:
- Jilani, A., Abdel-wahab, M. S., & Hammad, A. H. (2017). Advance Deposition Techniques for Thin Film and Coating. InTech. doi: 10.5772/65702
- Qinghe Gao, Artur M Schweidtmann (2024). Deep reinforcement learning for process design: Review and perspective. Current Opinion in Chemical Engineering, Volume 44, 101012. ISSN 2211-3398. https://doi.org/10.1016/j.coche.2024.101012.

 

Response 34: I have removed references [1] and [8], and added the references recommended by the reviewer.

 

Comments 35: Comments on the Quality of English Language

Response 35: I have used MDPI Author Services to improve the language.

Reviewer 2 Report

Comments and Suggestions for Authors

PVD coatings are widely applied in different areas of application. The equal thickness deposition on complex substrates is problem requiring deeper research and investigation. The publication under review is presenting the optimisation of the e-beam evaporation process for deposition of Cr coating oriented to application in hemispherical resonator measurement unit. The investigation includes COMSOL simulations for the film thickness uniformity, reinforcement learning PPO optimisation with correction mask implementation and validation of the obtained results.

The text is corresponding to the requirements for publication and structuring.

The research is doing only film thickness uniformity optimization and the title could be also more specific defined like for example “Optimization of film thickness uniformity in Hemispherical Resonator Coating Process Based on Simulation and Reinforcement Learning Algorithms”.  Because really other parameters of the PVD process and coating are not investigated. 

There are some marks over the text that need to be outworked.

• Lines 80- 81 – the text “while enhances the conductive properties of the film” . This second part either has to be removed or a citation has to be added showing that the conductive properties are improved with the thickness optimization because in the publication validation for conductivity is not provided.
• Line 91 – “gas density”. Please, define the type and class of cleanness of the gas use in the plasma.
• In table 1 the definition for Lt “Distance between rim and stem” is not correctly defined. Maybe distance between rim and the end of the stem or other more precise has to be made.
• Line 158 – Figure 1 – the number is wrong. Please, correct all figures numbering.
• Line 167-169. The sentence needs reviewing and rewriting.
• Line 170 “as the resonator rotates” – Please, give the revolution value.
• Line 171 “Peak and Valley (PV) values of the film thickness remain nearly constant” – either concrete PV range values need to be written or just thickness has to be comment.
• The pictures in figure 4 have to be enlarged.
• Line 189 “specific meridian line was chosen” - How is chosen the specific meridian line?
• Line 190 “The results shown in Figure 6 the PV values …”. In your comments for figure 6 you analyze PV values but in the figure are given values for thickness. Please, unify the comments and figure data. Also introduce the “angular position on the Circle” used as graph axis in the comments.
• Line 204 In Figure 8 for x axis is used Arc thickness (mm). Is it correct?  Following the text Time (sec) is expected. Please, check and correct if necessary, including the necessary definitions in the text.
• Line 221. Please, define how the superposition is made. Fast summation of the film thicknesses in the shell for the different angles makes maximum value of 20-30 nm but in figure 9 the graph starts from around 140 nm. Define in the text and in caption in Figure 9 if the data are for the shell or stem. Again, the x axis caption Arc length is not explained in the text and is not clear if it is correct labeled.
• Please, add information for the software that you use for developing the PPO model in the text.
• Line 258 ” the agent selects one of ten possible thickness distributions”. Please. define in the text how is made the selection of thickness distribution. If it is used any cost function οr it is used consequent or random choice. 
• One sentence is good to be added explaining how the PPO model guarantees not reaching local minimum of the calculated PV value.
• Line 279 “”table 1” – wrong table number reference
• Line 290 - table 3 - Measuring units for the time have to be added.
• Line 296 “demonstrated in the shell with 5.24%” - The calculated value 5.24% can not be identified from the graph. Please, put the value in new sentence as comment and also give the calculated value for junction with stem.  
• Situate fig. 15 and the caption in one page.

As conclusion the authors were made serious investigation on the thickness distribution during coating process of hemispherical resonator measurement unit. They use firstly an innovative combination of FEM modelling and PPO method for optimisation the process. The research is well planed and full. The results are acceptable and novice. I recommend strongly the publication of the text. But some improvement of the presentation of the results has to be done. Mainly, the figures numbering and the explanations of the figures have to be corrected and improved. 

Comments for author File: Comments.pdf

Author Response

Comments 1: The research is doing only film thickness uniformity optimization and the title could be also more specific defined like for example “Optimization of film thickness uniformity in Hemispherical Resonator Coating Process Based on Simulation and Reinforcement Learning Algorithms”.  Because really other parameters of the PVD process and coating are not investigated. 

Response 1: Thank you for pointing this out. We agree with this comment. We have made changes to the title.

 

Comments 2: Lines 80- 81 – the text “while enhances the conductive properties of the film” . This second part either has to be removed or a citation has to be added showing that the conductive properties are improved with the thickness optimization because in the publication validation for conductivity is not provided.

Response 2: We believe you are right, and I have deleted this sentence. The deleted content is in page 3, paragraph 1 and line 99.

 

Comments 3: Line 91 – “gas density”. Please, define the type and class of cleanness of the gas use in the plasma.

Response 3: The gas density mentioned here refers to the air density, so it has been changed to air density in page 3, paragraph 2 and line 108.

 

Comments 4: In table 1 the definition for Lt “Distance between rim and stem” is not correctly defined. Maybe distance between rim and the end of the stem or other more precise has to be made.

Response 4: “Distance between rim and stem” has been changed to “Distance between rim and the end of the stem” in page 4, Table 1 and line 147.

 

Comments 5: Line 158 – Figure 1 – the number is wrong. Please, correct all figures numbering.

Response 5: The figure number in Figure 1 has been modified in page 4 and line 144.

 

Comments 6: Line 167-169. The sentence needs reviewing and rewriting.

Response 6: This sentence has been rewritten in page 6, paragraph 1 and line 188-189.

 

Comments 7: Line 170 “as the resonator rotates” – Please, give the revolution value.

Response 7: The rotational speed is added in page 4, paragraph 1 and line 135.

 

Comments 8: Line 171 “Peak and Valley (PV) values of the film thickness remain nearly constant” – either concrete PV range values need to be written or just thickness has to be comment.

Response 8: The PV range values are added in page 6, paragraph 1 and line 192.

 

Comments 9: The pictures in figure 4 have to be enlarged.

Response 9: Figure 4 has been enlarged in page 6 and figure 4.

 

Comments 10: Line 189 “specific meridian line was chosen” - How is chosen the specific meridian line?

Response 10: The specific meridian line has been changed to an arbitrary meridian line. According to the previous simulation, it was not a specific meridian line that was chosen, but rather an arbitrary selection of a meridian line. -in page 7, paragraph 1 and line 209.

 

Comments 11: Line 190 “The results shown in Figure 6 the PV values …”. In your comments for figure 6 you analyze PV values but in the figure are given values for thickness. Please, unify the comments and figure data. Also introduce the “angular position on the Circle” used as graph axis in the comments.

Response 11: Regarding comments for Figure 6, I have revised the analysis to focus on the thickness, which then leads to the introduction of the PV value. Additionally, I have re-explained the X-axis and added comments to make the figure clearer and easier to understand. -in page 7, paragraph 1 and line 210-214.

 

Comments 12: Line 204 In Figure 8 for x axis is used Arc thickness (mm). Is it correct?  Following the text Time (sec) is expected. Please, check and correct if necessary, including the necessary definitions in the text.

Response 12: I have re-explained the X-axis for Figure 8. This issue is similar to the one in Figure 6. In fact, this figure illustrates the distribution of film thickness on the inner wall, which is not related to time. The new explanation is displayed in in page 7, paragraph 1 and line 218-221.

 

Comments 13: Line 221. Please, define how the superposition is made. Fast summation of the film thicknesses in the shell for the different angles makes maximum value of 20-30 nm but in figure 9 the graph starts from around 140 nm. Define in the text and in caption in Figure 9 if the data are for the shell or stem. Again, the x axis caption Arc length is not explained in the text and is not clear if it is correct labeled.

Response 13: I added a detailed explanation of the superposition process and corrected the description of the X-axis in page 9, paragraph 3 and line 246-252.

 

Comments 14: Please, add information for the software that you use for developing the PPO model in the text.

Response 14: I added the language and software used for developing the PPO algorithm in page 10, paragraph 2 and line 279-280.

 

Comments 15: Line 258 ” the agent selects one of ten possible thickness distributions”. Please. define in the text how is made the selection of thickness distribution. If it is used any cost function οr it is used consequent or random choice. One sentence is good to be added explaining how the PPO model guarantees not reaching local minimum of the calculated PV value.

Response 15: I explained how the PPO algorithm makes selections and also added a sentence describing how to avoid reaching a local minimum in page 10, paragraph 3 and line 299-308.

 

Comments 16: Line 279 “table 1” – wrong table number reference

Response 16: I corrected this problem in page 4, paragraph 1 and line 142.

 

Comments 17: Line 290 - table 3 - Measuring units for the time have to be added.

Response 17: Since I added a new table, Table 3 has now become Table 4. The time units I defined in Table 4 are not standard time units but rather a reference for time. I think it's difficult to add them to the table, so I added some comments to describe this unit of time in page 13, paragraph 1 and line 353-354.

 

Comments 18: Line 296 “demonstrated in the shell with 5.24%” - The calculated value 5.24% can not be identified from the graph. Please, put the value in new sentence as comment and also give the calculated value for junction with stem.  

Response 18: I added the data for Figure 14 to make the uniformity results clearer. – in page 22, paragraph 1 and line 378-381.

I added the data for the junction and stem positions, but I did not calculate the uniformity for this part, as the uniformity of this section is not the focus of our research. I am concerned that including the uniformity calculation might lead to misunderstandings. – in page 22, paragraph 1 and line 385-387.

 

Comments 19: Situate fig. 15 and the caption in one page.

Response 19: I have made adjustments to this figure.