Singularities in Computational Optics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I really like this manuscript and it could be a good popularization of science for those just getting started in computational optics or optical vortices. Therefore, I strongly recommend the acceptance of this manuscript as its current form.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

This is a review manuscript. After review, I think it is a sound manuscript. It has reviewed the research on the singularities in computational optics. Many interesting topics relating to the singular optics are included. It can be quite useful for the beginners who want to know singular optics. 

I have two comments to help the author to improve the manuscript.

1. There is a redundant "?" in page 9. 

2. The pictures are not clear in the whole manuscript, especially the text in the pictures.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

In this manuscript, the authors provide an overview of the applications of optical vortex beams, despite the more general title regarding phase singularity. It covers a wide range of fields—i.e., 20 subsections—and includes many informative references, which I believe are quite useful for audiences with diverse backgrounds to quickly learn about the latest developments in this field. From this perspective, I believe this manuscript should be published.  

Since the manuscript covers such a wide range of topics, I will focus my comments on those related to my expertise, specifically the imaging and phase retrieval sections. Below are my concerns and questions:  

1.     Regarding Sections 2.3, 2.5, 2.6, and 2.7, I am curious about the unique advantage of vortex beams or phase singularity in these contexts.  

For Section 2.3, the conjugate-vortex method is a specifically targeted approach that comes with additional computational costs—specifically, the algorithm must search the entire field of view to locate and eliminate singularities. In contrast, for IFTA, a more natural and efficient approach involves modifying the real-space support, as singularities correspond to zero magnitude. Additionally, based on my experience, the challenging part during IFTA is typically the opposite: ensuring that the algorithm correctly reconstructs a singularity.

Regarding Sections 2.5 and 2.6, as the titles suggest, vortex beams provide additional diversity, which enhances the constraints during the iterative phase retrieval process. However, this advantage can be equally or more effectively achieved using other techniques, such as coded aperture illumination, which offers far greater flexibility in programming the illumination.

For Section 2.7, the method proposed in Fienup’s paper (Ref 40)—the reduced-area support constraint—usually suffices to address twin stagnation. While extra diversity is beneficial, I do not clearly see the unique advantage of vortex beams in this context.

2.     A similar concern arises regarding the imaging section, specifically Sections 2.12, 2.17, and 2.18. Based on the references cited in these sections, most of the related applications derive their benefits from a common characteristic of the vortex beam: its donut-shaped intensity distribution. This distribution enhances higher spatial frequencies compared to traditional Gaussian beams, provides a relatively larger numerical aperture, and introduces additional diversity and redundancy. While these advantages are important for imaging performance, there are many other approaches that can achieve similar or even better outcomes.

Overall, while it is beneficial to mention all of these works to give the audience a broad view of the field, I believe the authors should provide a high-level comparison between vortex beams and other approaches. At the very least, if such a comparison has already been made, appropriate references should be included.  

Author Response

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Reviewer 4 Report

Comments and Suggestions for Authors

The authors have written a good review on the problem of singularities arising in digital information processing methods. I think it can be published, but I have a question related to lines 26, 27, 28. It says that rot grad (phi) is not equal to 0. But this statement is wrong. The phase is a scalar, so the rotor from its gradient is always 0. Why is the opposite statement there?

 

Author Response

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Round 2

Reviewer 4 Report

Comments and Suggestions for Authors

The paper can be published in the present form.