Neural Network-Assisted Interferogram Analysis Using Cylindrical and Flat Reference Beams

Round 1

Reviewer 1 Report

Summary:

The authors present a study on the sensitivity of interferograms formed using structured reference beams with a flat and cylindrical wavefront. They propose the use of cylindrical reference beams to improve the recognition of aberrations from interferograms using convolutional neural networks. The authors demonstrate that the sensitivity of interferograms increases by at least 10% when using a cylindrical reference beam compared to a flat reference beam for radially asymmetric types of aberrations. The authors also show that the average absolute error is reduced by more than 30% when using a cylindrical reference beam for the recognition of wave aberrations from interferograms using neural networks.

Strengths:

The study provides a detailed analysis of the sensitivity of interferograms formed using structured reference beams with a flat and cylindrical wavefront. The proposed use of cylindrical reference beams to improve the recognition of aberrations from interferograms using convolutional neural networks is innovative and has the potential to improve the accuracy of wavefront sensing in a variety of applications. The authors present convincing evidence that the sensitivity of interferograms increases when using a cylindrical reference beam compared to a flat reference beam for radially asymmetric types of aberrations.

Weaknesses:

The study would benefit from a more detailed description of the experimental setup used to generate the interferograms. The authors should provide more information on the accuracy and precision of the measurements taken during the study. In addition, the authors should consider including a more detailed discussion of the limitations of the proposed approach, including the potential impact of noise and other sources of error on the accuracy of the results.

Conclusion:

 

Overall, this is a well-written and informative study that provides valuable insights into the sensitivity of interferograms formed using structured reference beams. The proposed use of cylindrical reference beams to improve the recognition of aberrations from interferograms using convolutional neural networks is innovative and has the potential to improve the accuracy of wavefront sensing in a variety of applications. The authors have presented convincing evidence to support their claims, but the study would benefit from a more detailed description of the experimental setup and a more thorough discussion of the limitations of the proposed approach.

Author Response

We are thankful for the reviewer’s positive comments. We extended the section with the discussion of the experimental setup and the generated interference fields. By the example of the formation of quadrathole aberration interferograms, we show the reduction of errors in the wavefront for the single-arm scheme compared to the two-arm one. Additional information about the accuracy of measurements made during the study is also included.

Reviewer 2 Report

good work

Comments for author File: Comments.pdf

Author Response

Thanks a lot for the reviewer’s recognition of our work.

Reviewer 3 Report

In this manuscript, the authors proposed a neural network-based method to analysis interferogram. By using a cylindrical beam as the reference beam, the sensitivity of aberration analysis is improved compared with flat reference beams, especially in the case of medium or strong aberration. Before this manuscript is accepted, I hope the following suggestions can be addressed:

1.      I’ll suggest to add a schematic diagram of the neural network used in this work in Section 2.3.

2.      In fact, I feel confused about the specific content and purpose of the so-called ‘aberration recognition’. Is it just a difference in intensity, like saying “look, they are different”? What is the feedback signal? Could you give some examples, instead of showing the error (Table 6) directly? What role does the network play here?

3.      Figures 5-7: The labels for the x-axis and y-axis are missing.

4.      Some typing errors should be corrected.

5.      More details about the Eq. (1-12) should be given. Otherwise, readers will feel confused. Some parameters are not defined or described. Such as uppercase Cnm and lowercase Cnm.

6.      Table 1 captions: what do you mean “Cnm=0,1” or “Cnm=0,5”. Should the comma here be changed to a point?

7.      Line 246-247: What do you mean “However, the image of a cylindrical interferogram retains its structure with the accuracy of the periphery”?

8.      Could you put more discussions for Table-5. Otherwise, I don’t know why a holographic reconstruction is needed here.

9.      Line 329-331: What do you mean “the authors should discuss the relationship between the increase in the sensitivity of interferograms and the decrease in the MAE of recognition due to the expansion of the range of parameters of the reference beam.”

Author Response

Point 1: I’ll suggest to add a schematic diagram of the neural network used in this work in Section 2.3.

Response 1: Thanks for your remark. Added Fig. 6 illustrating the neural network’s architecture.

Point 1: In fact, I feel confused about the specific content and purpose of the so-called ‘aberration recognition’. Is it just a difference in intensity, like saying “look, they are different”? What is the feedback signal? Could you give some examples, instead of showing the error (Table 6) directly? What role does the network play here?

Response 2: Added Fig. 6 with accompanying description in Section 3.3 with an example of a neural network prediction.

Point 3: Figures 5-7: The labels for the x-axis and y-axis are missing.

Response 3: Labels added to Figures 5-7.

Point 4: Some typing errors should be corrected.

Response 4: Corrections have been made to the text and are highlighted in yellow. We also attach the Red-Green Line version of the manuscript.

Point 5: More details about the Eq. (1-12) should be given. Otherwise, readers will feel confused. Some parameters are not defined or described. Such as uppercase Cnm and lowercase Cnm.

Response 5: Explanations of the parameters have been added to equations (1), (2), (5)-(7). Cnm in uppercase and Cnm in lowercase are uniform.

Point 6: Table 1 captions: what do you mean “Cnm=0,1” or “Cnm=0,5”. Should the comma here be changed to a point?

Response 6: The typo has been corrected. There should be a point here, how to divide the decimal number.

Point 7: Line 246-247: What do you mean “However, the image of a cylindrical interferogram retains its structure with the accuracy of the periphery”?

Response 7: We corrected this phrase as follows: “However, the image of a cylindrical interferogram retains its structure with noticeable changes only in the peripheral part.”

Point 8: Could you put more discussions for Table-5. Otherwise, I don’t know why a holographic reconstruction is needed here.

Response 8: Table 5 shows experimental results confirming that the single-arm circuit we used works correctly, which is confirmed by measurements on two-arm interferometer. To address the reviewer's comment, in particularly, we have added the following explanation in the text of the manuscript:
"Table 5 shows the model and reconstructed phase distributions, the cylindrical interferograms for the angle α = 6π with different types of the aberration superposition. The reconstructed phase distributions in Table 5 obtained from experimental interferograms with two-arm scheme match with the simulated phase distributions with the error of the object wavefront reconstruction method and distortions induced with imperfections of experimental scheme such as beam quality and interference fringes period instability. The results confirm that complex interference fields were obtained with amplitude-phase modulation technique [50]."

Point 9: Line 329-331: What do you mean “the authors should discuss the relationship between the increase in the sensitivity of interferograms and the decrease in the MAE of recognition due to the expansion of the range of parameters of the reference beam.”

Response 9: We corrected this phrase as follows: “In this section, we discuss the relationship between an increase in the sensitivity of interferograms due to the structure complexity of the reference beam and a decrease in MAE recognition by the neural network.”