Research on Gas Detection Algorithm Based on Reconstruction of Background Infrared Radiation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper  adopts a reconstructed gas detection method based on infrared radiation background, carries out theoretical analyses and method details, and completes experiments to verify its validity, which is of reference value in the research field of harmful gas leakage detection technology.
Suggestion:

Supplement the descriptions of the technical requirements of the instrumentation used for radiation calibration, temperature calibration and atmospheric correction involving gas detection in chapters 3.2,3.3 to facilitate the restoration and use of the technique.
Improvement of the normality of the diagrams, the meaning of the grey scale in Fig. 4, the expression of the normative vertical coordinate units in Fig. 5, the meaning of the y variable in Fig. 5, Fig. 6, etc.

Author Response

Dear Reviewer:

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions in track changes in the re-submitted files.

Comments 1: Supplement the descriptions of the technical requirements of the instrumentation used for radiation calibration, temperature calibration and atmospheric correction involving gas detection in chapters 3.2,3.3 to facilitate the restoration and use of the technique. Improvement of the normality of the diagrams, the meaning of the grey scale in Fig. 4, the expression of the normative vertical coordinate units in Fig. 5, the meaning of the y variable in Fig. 5, Fig. 6, etc.

Response 1: Thank you for pointing this out. We have carefully revised the manuscript and supplemented detailed descriptions regarding the instrumentation and technical parameters used in radiation calibration, temperature calibration, and atmospheric correction to ensure the reproducibility and technical clarity of our method. The specific modifications are as follows:

1. Atmospheric Correction Method:
   The atmospheric correction in this study is based on the HITRAN (High-resolution Transmission Molecular Absorption Database) 2020 version. At the current stage, only the influence of water vapor (H₂O) has been considered, as it is the dominant absorber in near-surface infrared radiation transmission. This approach allows us to model the atmospheric transmittance affecting gas detection with reasonable accuracy.
2. Source of Meteorological Parameters:
   During field experiments, temperature and humidity data are retrieved in real time from the local meteorological station, ensuring timely and accurate input for the atmospheric correction model. In laboratory experiments, temperature and pressure sensors are connected to the gas cell to monitor its internal physical conditions, while environmental temperature and humidity sensors are used to measure ambient conditions.
3. Calibration Instrumentation:
   Radiation and temperature calibration are performed using a large-area blackbody radiation source system, independently developed by the University of Chinese Academy of Sciences, Hangzhou Institute for Advanced Study. The system consists of a temperature controller, a planar radiating cavity, and a water chiller. It provides a highly stable and uniform radiation reference for infrared systems.

Large-area blackbody radiation source (300×300 mm²)

Technical specifications of the temperature-controllable blackbody source:

• Operating temperature range: 0 ~ 90 °C
• Temperature resolution: 0.001 °C
• Temperature stability: ±0.002 °C @ 35 min
• Aperture size: 300×300 mm²
• Emissivity: ≥ 0.995 ± 0.001
• Power supply: 220V / 115V AC, 50/60Hz
• Power consumption: < 1000 W
• Dimensions: 570 × 315 × 500 mm (L × W × H)
• Weight: < 30 kg

These additions have been incorporated into Sections 3.2 and 3.3 of the revised manuscript to improve technical completeness and ensure the reproducibility of our method.

Comments 2: Supplement the descriptions of the technical requirements of the instrumentation used for radiation calibration, temperature calibration and atmospheric correction involving gas detection in chapters 3.2,3.3 to facilitate the restoration and use of the technique. Improvement of the normality of the diagrams, the meaning of the grey scale in Fig. 4, the expression of the normative vertical coordinate units in Fig. 5, the meaning of the y variable in Fig. 5, Fig. 6, etc.

Response 2: Thank you for pointing this out. we have revised Figure 4 to clarify the meaning of the grayscale, corrected the vertical axis units in Figure 5, and clarified the meaning of the "y" variable in Figures 5 and 6, following the reviewer’s suggestions for diagram normalization and variable annotation.

We sincerely appreciate the reviewer’s constructive feedback, which helped us improve the clarity and rigor of our manuscript. We believe these revisions have significantly enhanced the completeness, reproducibility, and technical accuracy of our work. The above-mentioned modifications have been incorporated into the corresponding sections of the revised manuscript. We hope the revised version meets the expectations and standards of the journal.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a novel and promising approach but requires addressing the following points to fully establish its technical soundness and practical relevance.

1. The current experiments focus solely on SF6 gas in a controlled environment. To strengthen the robustness of the proposed method, additional tests under varying environmental conditions (e.g., humidity gradients, temperature fluctuations, or dynamic backgrounds) should be included. This would validate the algorithm’s adaptability to real-world industrial scenarios.

2. The study focuses exclusively on SF6 Extending the experiments to other industrially relevant gases (e.g., CH4, CO2) with distinct absorption spectra would demonstrate the universality of the dual-band reconstruction approach.

3. A comparative analysis with existing techniques in terms of detection accuracy, false-alarm rates, and computational cost would better contextualize the method’s advantages.

4. For industrial applications, a brief discussion on safety standards compliance would highlight the method’s societal relevance.

5. Some recent literatures about gas detection should be cited in the introduction to support the advancement of this article, such as Chemical Engineering Journal 499 (2024) 156604.

Author Response

Dear Reviewer,

Thank you for your thoughtful and constructive feedback. We have carefully addressed each of your comments as follows. Please find the detailed responses below and the corresponding revisions in track changes in the re-submitted files.

Comments 1: The current experiments focus solely on SF6 gas in a controlled environment. To strengthen the robustness of the proposed method, additional tests under varying environmental conditions (e.g., humidity gradients, temperature fluctuations, or dynamic backgrounds) should be included. This would validate the algorithm’s adaptability to real-world industrial scenarios.

Response 1: Thank you for pointing this out. We fully agree on the importance of validating algorithm robustness in variable conditions. To this end, we have added supplementary experiments conducted in a laboratory setup with a gas cell. The test was performed with a blackbody temperature of 50°C and a background temperature of 20°C, under both gas-filled and gas-free conditions. The results, shown in the figures, demonstrate the algorithm’s effective performance under temperature gradient conditions. Figure (a) presents the detection result with gas present in gas pool, while Figure (b) shows the result without gas.

 

 

(a)Gas present in the gas pool           (b)Non-gas present in the gas pool

Comments 2: The study focuses exclusively on SF6 Extending the experiments to other industrially relevant gases (e.g., CH4, CO2) with distinct absorption spectra would demonstrate the universality of the dual-band reconstruction approach.

Response 2: Agree. We acknowledge the necessity of evaluating the algorithm on different industrial gases such as CH₄ and CO₂. However, due to current equipment limitations, we are unable to conduct such experiments at this stage. We have noted this limitation in the manuscript and suggested that future research could extend the study to a broader range of gases.

Comments 3: A comparative analysis with existing techniques in terms of detection accuracy, false-alarm rates, and computational cost would better contextualize the method’s advantages.

Response 3: Thank you for pointing this out. We understand that a comparative study would provide a clearer context for our method’s advantages. Nevertheless, due to certain practical constraints and lack of access to standardized datasets or comparable algorithms, we are unable to include such comparisons in the current version. This limitation is clearly stated in the revised manuscript, and we have identified it as a key direction for future work.

Comments 4: For industrial applications, a brief discussion on safety standards compliance would highlight the method’s societal relevance.

Response 4: Thank you for pointing this out. We have added a brief discussion in the manuscript referencing relevant industrial standards, such as IEC 60079 and ISO 26142. These standards address the safety and performance requirements for gas detection in hazardous environments. Although formal compliance testing is not part of this study, the proposed method’s characteristics—such as non-contact operation and real-time response—suggest strong potential for industrial deployment.

Comments 5: Some recent literatures about gas detection should be cited in the introduction to support the advancement of this article, such as Chemical Engineering Journal 499 (2024) 156604.

Response 5:Thank you for your helpful recommendation. We have cited the suggested recent work—Chemical Engineering Journal 499 (2024) 156604—in the introduction to strengthen the background and relevance of our research.

We appreciate your valuable comments, which have significantly improved the clarity and scope of our manuscript. The above-mentioned modifications have been incorporated into the corresponding sections of the revised manuscript. We hope the revised version meets the expectations and standards of the journal.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors propose gas detection algorithm based on an infrared radiation physical model. Optical gas imaging is an important research area and while the authors demonstrate promising methodology and results, I have some concerns as listed below.

In the introduction, the state of the art is presented, where current gas leak detection methods are categorized into two technical approaches: image processing-based and deep learning-based techniques. Later, the authors propose a physics-based gas detection and concentration inversion algorithm using dual-band infrared image reconstruction.

It may create an impression that gas detection with dual-band approach is a novel idea proposed by the authors, as it is not mentioned in the state of the art. In practice, however, dual-band approach is well known - let us take an example of the paper [R1] dated 2009. Moreover, there are commercially available cameras with filter wheels, such as described in [R2], where even more spectra bands are used for gas detection.

In my opinion, the reviewed paper shouldn’t be published without clearly presenting the state of the art in the field of gas imaging with filters. While in [R1] CH4 is detected and the authors of the reviewed paper deal with SF6, the idea of using two filters with partially overlapping band is the same. Additionally, in [R1] one can find a model including the influence of atmosphere transmission, spectra characteristic of the objective and optical filters.

Due to the above, for the reviewed paper to be published, the authors have to clearly state what is the novelty they introduced to already known solutions. In the current version of the paper it is very difficult to figure it out and it requires in-depth knowledge about optical gas imaging.

If the novelty is in reconstruction of theoretical background radiation (assuming no gas presence) within the absorption band, it should be clearly demonstrated what is the benefit of this approach versus simply calculating the difference of images captured in two bands, after normalizing both of it. Looking at Figure 7, the results are qualitatively good, but there is a lack of quantitative aspect, such as colorbar scaled in appropriate units. Are the row 1 and row 2 images scaled in digital units or radiance? If the difference between those images is shown in row 3, why the lowest values (darkest areas) correspond to detected gas, while the expected difference value there is higher (brighter area) than for the rest of the differential image? Is the palette inversed?

What is more, there is an important limitation not mentioned by the authors in their approach - the camera needs to be stationary. It is imposed by the sentence: "Temperature drift is a low-frequency signal and Scene changes (e.g., moving objects) are high-frequency signals." This assumption is taken for thermal drift correction and it is true only for stationary camera, hence no camera panning or tilt is possible. This information should be clearly provided.

Moreover, it is unknown if there are two infrared detectors with separate filters or one detector with filter wheel. In case of single detector, how the problem of moving objects (human visible in the image) is addressed? In this case, the image captured with and without filter will differ due to being registered in different time instants and moving objects will change place creating ghosting effect in differential radiance image. If dual detector system is employed, it should also be clearly mentioned as it increases the cost for practical applications.

In addition, the authors state more than once that “Experimental results demonstrate that this method enables gas morphology detection and concentration inversion”. I have not found in the paper any results demonstrating the calculation of gas concentration in units such as ppm or ppm-m or mg/m3. There are only qualitative results provided in Fig. 7 row 3, but still it is impossible to tell if the concentration of the visible gas is low, medium or high.

Finally, there is no information if the presented research is performed in compliance with the standard GB/T 44653-2024.

Taking into account the above, my recommendation is to reject the paper in its current form. Nevertheless, I encourage resubmission after improving the listed issues.

[R1] M. Kastek, T. Sosnowski, T. Orżanowski, K. Kopczyński, M. Kwaśny, Multispectral gas detection method, WIT Transactions on Ecology and the Environment, Vol 123,  www.witpress.com, ISSN 1743-3541 (on-line), doi:10.2495/AIR090211

[R2] Gagnon, Marc-André & Jahjah, Karl-Alexandre & Marcotte, Frédérick & Tremblay, Pierre & Farley, Vincent & Chamberland, Martin. (2014). Time-resolved thermal infrared multispectral imaging of gases and minerals. 9249. 90700J. 10.1117/12.2050569.

Comments on the Quality of English Language

The title of the paper is not clear, especially regarding phrases "reconstruction gas detection algorithm" and "infrared radiation background". In my opinion, the paper shouldn’t be published with this title. After reading the paper, I guess that the meaning should be something like "Research on gas detection algorithm based on reconstruction of background infrared radiation".

Author Response

Dear Reviewer,

Thank you very much for your valuable comments and constructive suggestions. We have carefully addressed each of your concerns as follows, Please find the detailed responses below and the corresponding revisions in track changes in the re-submitted files.

Comments 1: In the introduction, the state of the art is presented, where current gas leak detection methods are categorized into two technical approaches: image processing-based and deep learning-based techniques. Later, the authors propose a physics-based gas detection and concentration inversion algorithm using dual-band infrared image reconstruction.It may create an impression that gas detection with dual-band approach is a novel idea proposed by the authors, as it is not mentioned in the state of the art. In practice, however, dual-band approach is well known - let us take an example of the paper [R1] dated 2009. Moreover, there are commercially available cameras with filter wheels, such as described in [R2], where even more spectra bands are used for gas detection.

In my opinion, the reviewed paper shouldn’t be published without clearly presenting the state of the art in the field of gas imaging with filters. While in [R1] CH4 is detected and the authors of the reviewed paper deal with SF6, the idea of using two filters with partially overlapping band is the same. Additionally, in [R1] one can find a model including the influence of atmosphere transmission, spectra characteristic of the objective and optical filters. Due to the above, for the reviewed paper to be published, the authors have to clearly state what is the novelty they introduced to already known solutions. In the current version of the paper it is very difficult to figure it out and it requires in-depth knowledge about optical gas imaging.

Response 1: Thank you for pointing this out.We fully agree with your observation that the “dual-band infrared gas detection” approach is not novel per se and has been previously reported (e.g., [R1]) and used in some commercial systems. Accordingly, we have revised the introduction to cite and discuss relevant literature [R1, R2], and clearly stated that our work is based on a physics-driven modeling approach, which differs significantly from conventional image-processing or deep-learning-based methods.While the use of dual-band detection is not new, our core innovations lie in the following aspects:

• Reconstruction of a theoretical gas-free infrared background using a radiative transfer model and atmospheric correction, avoiding the need for prior reference images;
• Introduction of the assumption that the background has equal temperature in both bands, enabling quantitative estimation of background brightness;
• Detection of gas presence based on the difference between observed and reconstructed images, enhancing applicability in dynamic scenes;
• A distinct algorithmic structure from previous works, with improved generality and robustness in complex environments.

Comments 2: If the novelty is in reconstruction of theoretical background radiation (assuming no gas presence) within the absorption band, it should be clearly demonstrated what is the benefit of this approach versus simply calculating the difference of images captured in two bands, after normalizing both of it. Looking at Figure 7, the results are qualitatively good, but there is a lack of quantitative aspect, such as colorbar scaled in appropriate units. Are the row 1 and row 2 images scaled in digital units or radiance? If the difference between those images is shown in row 3, why the lowest values (darkest areas) correspond to detected gas, while the expected difference value there is higher (brighter area) than for the rest of the differential image? Is the palette inversed?

Response 2: Thank you for pointing this out. Comparison with Conventional Image Subtraction Methods

Our approach is fundamentally different from simple normalized image subtraction between two bands. It is based on physical modeling and background reconstruction, offering several advantages:

• No need for a reference image with clean background;
• Potential for quantitative gas concentration retrieval;
• Enhanced robustness by integrating atmospheric transmittance and temperature drift correction;
• Better suitability for uncooled infrared sensors in practical deployments.

Next, We will explanation Figure 8 Units, Display, and Color Representation

• The first and second rows in Figure 8 show original infrared images, in units of digital number (DN) output by the sensor.
• The third row presents difference radiance maps calculated by our model, in units of W/m²·sr·µm. These maps represent the reduction in radiance due to gas absorption and are not color-inverted. Darker areas indicate lower radiance, consistent with physical expectations.

The relationship between image contrast and gas/background temperature difference is expressed as:

When ，we have  ，and gas appears darker. This is the typical case in our experiments.

Comments 3: What is more, there is an important limitation not mentioned by the authors in their approach - the camera needs to be stationary. It is imposed by the sentence: "Temperature drift is a low-frequency signal and Scene changes (e.g., moving objects) are high-frequency signals." This assumption is taken for thermal drift correction and it is true only for stationary camera, hence no camera panning or tilt is possible. This information should be clearly provided.

Response 3: Thank you for pointing this out. As now clarified in the revised manuscript, our temperature drift correction assumes that the drift is a low-frequency signal and is only valid when the camera is stationary. The method is not applicable to camera rotation or translation.

Comments 4: Moreover, it is unknown if there are two infrared detectors with separate filters or one detector with filter wheel. In case of single detector, how the problem of moving objects (human visible in the image) is addressed? In this case, the image captured with and without filter will differ due to being registered in different time instants and moving objects will change place creating ghosting effect in differential radiance image. If dual detector system is employed, it should also be clearly mentioned as it increases the cost for practical applications.

Response 4: Thank you for pointing this out. We use a snapshot-type multi-aperture spectral camera, which utilizes regionally-distributed filters for synchronous multi-band imaging. The following figure shows its imaging principle. This avoids misalignment issues typical in traditional rotating filter-wheel systems and is particularly suitable for dynamic gas scenes. Although spatial resolution is somewhat reduced, it ensures temporal consistency. This has been added to the Methods section.

The imaging principle of multi-aperture cameras

Comments 5:In addition, the authors state more than once that “Experimental results demonstrate that this method enables gas morphology detection and concentration inversion”. I have not found in the paper any results demonstrating the calculation of gas concentration in units such as ppm or ppm-m or mg/m3. There are only qualitative results provided in Fig. 7 row 3, but still it is impossible to tell if the concentration of the visible gas is low, medium or high.

Response 5: Thank you for pointing this out. We acknowledge the inappropriate expression in the original manuscript. Our current experiments only perform gas morphology detection without retrieving concentration values. The statement has been corrected to: “The method has potential for concentration inversion, but only morphology detection is conducted in this study.”

 

Response to Comments on the Quality of English Language

Point 1: The title of the paper is not clear, especially regarding phrases "reconstruction gas detection algorithm" and "infrared radiation background". In my opinion, the paper shouldn’t be published with this title. After reading the paper, I guess that the meaning should be something like "Research on gas detection algorithm based on reconstruction of background infrared radiation".

Response 1: Thank you for pointing this out. Following your suggestion, we have revised the paper title to better reflect the actual content.

We sincerely appreciate your careful review and thoughtful comments. The above-mentioned modifications have been incorporated into the corresponding sections of the revised manuscript. We hope the revised version meets the expectations and standards of the journal.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors,
thank you very much for addressing my comments with recommendations and improving your paper.

I fully accept your responses no 1, 3, 4, 5.

In the new fragment you introduced, you use the blackbody radiation source with really good parameters for the purpose of radiometric calibration. You use linear equation to recalculate DN to spectral radiance. While you grant the stability of DN for constant blackbody temperature by applying thermal drift correction, how do you assure the repeatability of baseline mean when the camera may be switched on at different ambient temperatures? Is there a shutter or another technique to eliminate possible offset that can affect the validity of the radiometric calibration? This question needs to be answered, as the radiometric calibration is an important part of the proposed method, and possible detector offset, even well stabilised at the baseline, may affect the results.

You use linear formula to recalculate DN to spectral radiance (Fig. 6)- it is fine, because this dependency is expected to be linear. However, you also apply linear conversion of DN to temperature, which is non-linear according to the Stefan–Boltzmann law. While this simplification may work for relatively narrow temperature range (Fig. 7), I imagine that the proposed approach may be also used for scenes with greater temperature span. Therefore my recommendation is to explain in the paper that in general case the calibration should be based on e.g. RBFO model [R3] and only for special case of narrow span it can be linearized.

Regarding your response no 2, I appreciate the details you provided and explanation that your approach is fundamentally different from simple normalized image subtraction between two bands. Nevertheless, it is not demonstrated in the paper how this fundamental difference corresponds to increase in the gas detection performance. I insist on providing in the paper clear examples showing the result of normalized image subtraction versus radiation difference images. It can be done by adding a new row (after row 3) in Fig. 8 with normalized image subtraction, and adding row 5 with those images thresholded. 

I performed an experiment and took two corresponding images from row 1 and 2 in Fig. 8. Those images, as you explained in your answer, are as obtained from the sensor in units of digital number (DN). I normalized them and calculated difference, then thresholded. Please compare my result (attached) with the one provided by your method. My operations took place on compressed 8-bit images from my pdf file instead of 14-bit (I guess) raw DN data that you have. Therefore when you calculate the difference of normalized DN images, it will be of much better quality, and it will demonstrate the benefits of your approach. I believe that such comparison is really necessary for the paper to be published, because it will clearly demonstrate the benefits behind your approach versus known, simple method.

Moreover, I recommend adding in your paper colorbars to fig. 8 to each row, with numbers and units. One colorbar per row is sufficient assuming the span for all figures in a row is the same.

[R3] N. Horny, FPA camera standardisation, Infrared Physics & Technology, Volume 44, Issue 2, 2003, Pages 109-119, ISSN 1350-4495, https://doi.org/10.1016/S1350-4495(02)00183-4. (https://www.sciencedirect.com/science/article/pii/S1350449502001834)

Comments for author File: Comments.pdf

Author Response

Dear Reviewer:

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions in track changes in the re-submitted files.

Comments 1: In the new fragment you introduced, you use the blackbody radiation source with really good parameters for the purpose of radiometric calibration. You use linear equation to recalculate DN to spectral radiance. While you grant the stability of DN for constant blackbody temperature by applying thermal drift correction, how do you assure the repeatability of baseline mean when the camera may be switched on at different ambient temperatures? Is there a shutter or another technique to eliminate possible offset that can affect the validity of the radiometric calibration? This question needs to be answered, as the radiometric calibration is an important part of the proposed method, and possible detector offset, even well stabilised at the baseline, may affect the results.

Response 1: We thank you for raising this important issue. As correctly noted, turning on the camera under varying ambient temperatures may lead to baseline offset, which can significantly impact the accuracy of radiometric calibration. The infrared camera used in our experiment is equipped with an internal motorized shutter mechanism. This shutter automatically closes once during each power-up cycle to acquire a dark-frame image under no external radiation input. This dark frame is typically used for radiometric correction to eliminate offset caused by ambient temperature variations. However, due to certain objective reasons, we did not acquire shutter-based calibration data in this study. The results presented in the manuscript are therefore based directly on the raw measurement data without applying this correction. For this reason, the shutter mechanism was not explicitly described in the manuscript.

Comments 2: You use linear formula to recalculate DN to spectral radiance (Fig. 6)- it is fine, because this dependency is expected to be linear. However, you also apply linear conversion of DN to temperature, which is non-linear according to the Stefan–Boltzmann law. While this simplification may work for relatively narrow temperature range (Fig. 7), I imagine that the proposed approach may be also used for scenes with greater temperature span. Therefore my recommendation is to explain in the paper that in general case the calibration should be based on e.g. RBFO model [R3] and only for special case of narrow span it can be linearized.

Response 2: We sincerely thank you for the insightful and constructive comment. As correctly pointed out, while the use of a linear formula to convert DN to spectral radiance (as shown in Fig. 6) is justified, the linear conversion from DN to temperature shown in Fig. 7 is indeed a simplification. In our study, this linear approximation was applied due to the relatively narrow temperature range under investigation, where the non-linearity is minimal and the resulting error is negligible. However, we fully agree with the reviewer that for scenes involving a wider temperature span, the linear model becomes insufficient to capture the nonlinear relationship governed by the Stefan–Boltzmann law. In general cases, more accurate calibration models—such as the RBFO model (as suggested in reference [R3])—should be employed to ensure reliable temperature retrieval. We will include a clarification in the paper that linearization is only suitable for limited temperature ranges and that nonlinear models should be used for broader applications.

Comments 3: Regarding your response no 2, I appreciate the details you provided and explanation that your approach is fundamentally different from simple normalized image subtraction between two bands. Nevertheless, it is not demonstrated in the paper how this fundamental difference corresponds to increase in the gas detection performance. I insist on providing in the paper clear examples showing the result of normalized image subtraction versus radiation difference images. It can be done by adding a new row (after row 3) in Fig. 8 with normalized image subtraction, and adding row 5 with those images thresholded. I performed an experiment and took two corresponding images from row 1 and 2 in Fig. 8. Those images, as you explained in your answer, are as obtained from the sensor in units of digital number (DN). I normalized them and calculated difference, then thresholded. Please compare my result (attached) with the one provided by your method. My operations took place on compressed 8-bit images from my pdf file instead of 14-bit (I guess) raw DN data that you have. Therefore when you calculate the difference of normalized DN images, it will be of much better quality, and it will demonstrate the benefits of your approach. I believe that such comparison is really necessary for the paper to be published, because it will clearly demonstrate the benefits behind your approach versus known, simple method.Moreover, I recommend adding in your paper colorbars to fig. 8 to each row, with numbers and units. One colorbar per row is sufficient assuming the span for all figures in a row is the same.

Response 3: Thank you very much for your valuable suggestions. I agree that your comments are meaningful. We have also tried performing normalized image subtraction followed by thresholding on the same set of images. However, in our experiments, we found that the results are highly sensitive to the choice of threshold, which makes it difficult to produce stable and representative outcomes. Therefore, we believe that our method’s advantage should not rely on carefully tuning the threshold in such a way.

 

On the other hand, your suggestion to add colorbars with numerical values and physical units is indeed very constructive. In response, we have already added such a colorbar to the third row in Fig. 8 to improve both interpretability and physical clarity of the presented images.

 

We sincerely appreciate the reviewer’s constructive feedback, which helped us improve the clarity and rigor of our manuscript. We believe these revisions have significantly enhanced the completeness, reproducibility, and technical accuracy of our work. The above-mentioned modifications have been incorporated into the corresponding sections of the revised manuscript. We hope the revised version meets the expectations and standards of the journal.

 

Best regards,
Li Chen

Author Response File: Author Response.pdf