A CNN-GS Hybrid Algorithm for Generating Pump Light Fields in Atomic Magnetometers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper the authors refine the Gerchberg–Saxton algorithm using a convolution neural network. The main authors’ claim is that the final goal is to transform guassian beams into flat-top pump light field so that the performance of atomic magnetometers is improved.

The topic is potentially good for publication but in its present form is not adequate for publication. In the following I list the main issues of the paper to be addressed in a following draft.

From a substantial point of view:

1) The main problem of the paper is that it is incomplete. I don’t see any magnetometer there, I don’t see any Rb cell (I suppose it is a Rb cell used by the authors but they don’t say). They say that the magnetometer sensitivity is improved but there is evidence of this claim. So I invite the authors to add the part associated to the characterization of the magnetometer with the old and improve performances:

From a more technical point of view, the manuscript presents a Machine Learning/Deep Learning (ML/DL) framework employing Convolutional Neural Networks (CNNs), potentially augmented with U-Net architecture and GS optimization. While the proposed approach may offer promising insights, the current state of the manuscript suffers from a lack of clarity, consistency, and completeness in describing the ML methodology. Again, these issues limit its current readiness for publication. More in detail:

2) The manuscript does not sufficiently emphasize that the CNN-based model is trained using supervised learning. This should be explicitly stated in the abstract and consistently reinforced throughout the introduction and methodology sections. 

3) Data Origin: The abstract does not specify the data source, and in the text (line 222) it is only mentioned that the data is "custom generated". Please clarify whether the dataset consists of synthetic, real, or a hybrid of both. If it is a hybrid, specify the proportion of synthetic versus real data.

4) Literature Review: The introduction includes only a limited set of references, with the sole cited source being from 2019 ([33]). Please expand the literature review to provide a more comprehensive overview that contextualizes the problem and clearly defines the novelty of your approach within the current state-of-the-art. Including a recent, strong survey or review paper summarizing relevant advances in the field would greatly strengthen this section.  

5) In Section 2.1.2: Improved Algorithm Based on GS and CNN Line 153–155: The claim lacks supporting references. Provide at least one strong literature review that surveys GS-CNN integration or similar hybrid optimization techniques.

 

6) Figure 6: The network diagram lacks references to the symbols E2, Phi1 (output), Phi1 (label), and E1. Please incorporate these symbols into the figure, explicitly define them in the caption and in the main text, and clarify their respective roles and relationships within the model’s output. 

7) Line 179: It is unclear if Phi1 is the predicted output or the ground-truth label. This distinction must be clarified.

8) Lines 183–189: There is a discrepancy between the parameters described here and those mentioned later in Section 3. Cross-verify all hyperparameters (e.g., pooling, activation functions, epoch count, loss function etc.) and ensure consistency throughout the manuscript. Additionally, while it can be inferred that padding was used to preserve spatial dimensions, this should be explicitly stated in the text.

9) Regularization: No mention is made of common regularization techniques such as batch normalization or dropout. Specify what, if any, methods were used and where in the architecture they were applied.

10) Section 3.1: Dataset Preparation Custom Dataset: Specify whether the dataset was synthetically generated (e.g., using simulations) or collected from real-world measurements.

11) Dataset Size: Report the number of samples in the training, validation, and test sets. Note that the validation set is intended for hyperparameter tuning and should not be used to assess final model performance. Therefore, a separate test set is necessary to provide an unbiased evaluation of the model’s performance. Please include such a test set and report performance metrics accordingly.

12) Generalization Concerns: If the dataset is synthetic, provide justification that it adequately captures the full range of physical scenarios under study.

13) Section 3.2: Network Architecture, U-Net Architecture: The U-Net architecture inherently uses skip connections. Clarify whether these are included in the implemented model. If yes, explain why they are not visible in Figure 9. If the network follows a standard encoder-decoder design without skip connections, avoid referring to it as U-Net and provide appropriate references for the actual architecture.

14) Figure 9: There is a mismatch between the labels in the figure and the textual description. Ensure that layer names, shapes, and transitions match the narrative.

15) Optimizer Choice: Adam optimizer is mentioned, but no rationale is provided. Include a brief justification and mention if alternative optimizers (e.g., SGD with momentum) were tested and discarded.

 

16) Activation Functions: The ReLU activation is used throughout, including the output layer. This is questionable if the output is expected to lie within [0,1]. Consider whether a sigmoid function is more appropriate for the final activation.

17) Table 2: The table is currently incomplete and inconsistent with the earlier described network configuration. Please update it to comprehensively include all relevant parameters, such as layer types and sizes, activation functions, max pooling operations, and any regularization techniques applied. 

18) Figure 10: Loss curves for training and validation are displayed on separate subplots, preventing effective visual comparison. Combine these into a single plot with a shared y-axis for better interpretability.

19) Overfitting Discussion: There is no discussion of overfitting. Explain why overfitting is not a concern and describe the steps taken to prevent it. Please provide a brief explanation supported by evidence that the dataset includes sufficient variety to capture the full range of physical phenomena. Alternatively, if overfitting is prevented due to the use of regularization techniques, please specify and discuss these methods.

20) Conclusion. The manuscript introduces a potentially valuable contribution through a CNN-based method supported by optimization, but suffers from a lack of methodological clarity, incomplete architecture description, inconsistent parameter reporting, and limited connection to existing literature.

A particularly critical issue is the absence of a separate test set, which is essential for an unbiased assessment of model performance. This omission undermines the validity of the reported results and must be addressed.

Key Revisions Needed:

 

Clarify supervision type (supervised/unsupervised).

Describe dataset (real/synthetic/hybrid) and provide data splits.

Describe dataset origin (real/synthetic/hybrid) and provide clear data splits, including training, validation, and an independent test set. 

Expand literature review to include relevant ML/DL works.

Complete and unify the CNN architecture description across figures, tables, and text.

Address regularization and overfitting.

Consolidate loss plots and standardize parameter reporting.

Once these corrections are addressed and technical clarity is improved, the article may be reconsidered.

Minor issue, in the text please insert a space before references throughout the paper.

In the introduction it is not clear what the authors mean for alphaT. GS in the title and in the abstract is not clearly understandable, please define.

Author Response

Please see the attachment.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The authors discuss and realise a method for changing the intensity profile of an originally Gaussian beam (here specifically a 0-0 mode) in the direction of an intensity distribution that is constant over the beam cross-section. The beam generated in this way is used to excite an optical magnetometer. This results in a lower inherent noise of the magentometer compared to a conventional Gaussian beam cross-section. This behaviour is understandable because the power broadening of the atomic resonances with a constant intensity profile at the same total laser power is not as pronounced as with the Gaussian 0-0 mode beam with high intensity in the beam centre. This means a smaller detected linewidth and thus a better signal-to-noise ratio.

The scientific approach of the authors follows the rules of good scientific practice.

The topic discussed is of interest to researchers in the field of optical magnetometry as well as to other research areas where laser beam shaping can be used profitably.

In my opinion, only minor corrections are necessary in the preceding text. For example, the polarisation planes (the polarisation state) should be shown in the figures. Furthermore, I only noticed a few minor typos. In my opinion, the text is suitable for publication after correction.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

A CNN-GS Hybrid Algorithm for Generating Pump Light Fields in Atomic Magnetometers has been thoroughly reviewed. Following is a detailed review of the manuscript, the following are the major technical comments that should be addressed by the authors:

1. It is described in the paper that an improved CNN-GS hybrid algorithm has been developed, but there are not enough details about the CNN architecture and the training process for full reproducibility to be achieved. There is a mention of a U-Net-like structure, but no discussion is given regarding layer configurations, activation functions, and loss metrics within that structure. In your presentation, you should include a detailed diagram or table with the number of filter layers, kernel sizes, and type of activation. In order to understand how the CNN works, you need to clarify its input and output formats.
2. This study utilized only 500 samples for the training of the CNN, and the dataset was generated synthetically using a random phase map in order to generate the dataset. It is too small and can cause overfitting or poor generalization in real-world experiments if the sample is too small. The size of the dataset should be justified and data augmentation, or independent test sets should be used to determine generalizability. Analyze how the quality of the training data impacts the performance of CNNs.
3. Even though simulations were carried out as well as a single beam shaping experiment, only a circular flat-top beam was tested experimentally, despite simulations being carried out for both square as well as circular beams. You should include experimental results for square flat-top beams, or you should explain why they were omitted.
4. In this evaluation, mean squared error (MSE) and peak non-uniformity are used, but there is a lack of statistical robustness (e.g. standard deviation, confidence intervals across trials). Calculate beam shaping metrics over multiple trials, taking variability and noise into account. Analyze the data statistically or provide error bars.
5. CNN is not superior to other machine learning models (e.g., transformers, GANs, or physics-informed networks). There is no comparison with alternative methods of learning. The purpose of selecting a CNN should be explained. It would be helpful if baseline comparisons were included if possible.
6. According to the authors, the simulations assume an ideal Gaussian beam and perfect optical alignment, which deviates from the actual experiments. It is necessary to conduct a sensitivity analysis in order to determine whether beam imperfections or alignment errors will affect the output and CNN performance.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This new draft of the paper has been improved concerning the part related to the machine learning. In this case, the authors have properly addressed the points I raised in my previous report. However, the physics part related to the magnetometer is still incomplete in my opinion. Again, I don't see any picture showing the Rb vapor cell there is no descritpion about how the system works like a magnetometer. I don't undestad this reticence to show the picture of the magnetometer setup. So definitely I let the Editor the decision wether to publish or not this paper. My job is in any case done. 

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Authors address all the comments properly.

Author Response

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Author Response File: Author Response.docx