Dynamic Micro-Vibration Monitoring Based on Fractional Optical Vortex

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The submitted article addresses the field of micro-vibration monitoring using fractional optical vortices (FOVs). The authors propose a method for micro-vibration measurement based on the interference between a Gaussian beam (used as the measurement arm) and a fractional vortex beam (used as the reference arm). The core innovation of the paper lies in the use of optical vortices with a fractional topological charge (TC). According to the authors, this approach significantly simplifies the measurement of rotation angle required to determine the amplitude of micro-vibrations, in comparison with traditional methods based on integer-order vortices.

Before recommending the article for publication, the authors should address the following comments:

1. The theoretical part of the paper is notably weak. For example, Equation (1) is presented as a general form of the wave field, but it does not reproduce the spatial (radial and axial) structure of a Gaussian beam.
2. The authors employ a highly simplified model of a fractional vortex, without citing previous foundational works on fractional optical vortices. In particular, I was surprised to see no reference to the seminal paper [DOI: 10.1088/1464-4258/6/2/018].
3. The interferometric model does not account for the Gouy phase term \zeta(z), which arises during Gaussian beam propagation. This phase shift can affect the interference pattern and, consequently, the measurement accuracy.
4. In the expression for intensity, the notation E2′ is used, while previously E2 denoted the reference beam. The notations should be made consistent, and it should be clearly stated which fields are complex-conjugated.
5. The amplitude of the fractional vortex beam is given as A2=\ell^2|\ell|\exp{-2r^2}, but a proper fractional vortex amplitude should include the dependence r^{|\ell|}.
6. The article claims that the radius for tracking the intensity minimum is determined by maximizing A2(\ell,r), but for the expression \exp(-r^2), the maximum formally occurs at the center. For the correct form r^{|\ell|}\exp(-r^2), the amplitude reaches its maximum at  w_0\sqrt{|\ell|/2}.
7. The article does not clearly explain the physical mechanism responsible for the simplification of the interference pattern (i.e., appearance of a single petal instead of several) when using fractional vortices with TC≤1.
8. The effects of CCD pixel pitch and ADC bit depth on the angular resolution of the petal tracking should be considered, as they impose fundamental limits on measurement precision.
9. In the discussion section, the authors touch upon the impact of CCD frame rate on measurement accuracy. However, a more detailed analysis of possible limitations and guidance on selecting the optimal frame rate depending on the vibration spectrum would be helpful for the readers.

Comments on the Quality of English Language

The manuscript would benefit from thorough language editing. There are issues with article use, prepositions, and verb tense consistency. Several sentences are overly long or awkwardly structured, affecting clarity. Some terminology is repetitive or imprecise, and the abstract and conclusion could be more concise and focused. A careful proofreading or professional editing is recommended to improve readability and overall presentation.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors This article presents a novel method for dynamic micro-vibration measurement using fractional optical vortex (FOV) beams and Gaussian beams in an interferometric system. The study is well-structured and provides a detailed explanation of the principles, experimental setup, and results. The findings demonstrate high accuracy and robustness, making it a valuable contribution to the field of photonics. Overall, the article is suitable for publication in Photonics with minor revisions. However, a few minor improvements could be considered:

1. Some figures could benefit from clearer annotations and labels to enhance their readability and comprehension. For instance, the colorbars were missing for figure 1b, figures 6&7 can be combined
2. I don't understand why the authors need two setup figures, figures 1 & 3, the caption discription for figure 3 is missing, that make the readers even confusing
3. The authors didn't make enough comparison with existing methods: A more detailed comparison with other state-of-the-art vibration measurement techniques would strengthen the paper's impact.
4. The backgroud introduction is poor. The statement of the problems is very unclear. Since the work is focusing on optical vortices. For instance I am surprised the authors didn‘t cite the important Optical Vortices 30 year on LSA review and high-dimensional structured light perspectives articles. Some original works on fractional vortices were also missing
5. The authors may need to briefly discuss potential future applications or improvements could provide additional context and direction for readers interested in this area.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript “Dynamic Micro-vibration Monitoring Based on Fractional Optical Vortex” demonstrated an interferometric system for vibration measurement by analyzing the interference pattern of a fractional optical vortex beam as and a Gaussian beam. The experiments are well implemented and shown. This manuscript is interesting and can be accepted after addressing the following comments:

1. The proposed system uses the Gaussian beam as the measurement path and the fractional optical vortex beam as the reference. The compared system uses vortex beam with integral TC as the reference instead. Why not use the conjugate vortex beam as the measurement and reference light? In my opinion, higher TC which indicates more petals in the interference pattern can lead to a higher resolution of displacement measurement, as the multi-petals interference pattern will have more significant and distinguished variation with displacement. I think the author should objectively explain this.
2. Considering the results shown in Fig. 5, the interference pattern when the measurement beam is FOV beam should be shown.
3. As the authors said “it is more vulnerable to environmental perturbations that tend to distort its spatial structure.” The use of fractional optical vortex beam as the reference also faces this problem. It should be objectively explained.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors took into account my comments. Paper can be accepted for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed all the comments well and the manuscript can be accepted.