Dark-Field Lau Interferometer: Barker-Babinet Gratings
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsInteresting results, which are to be published. However, current version of the manuscript lacks normal introduction. Our standard position is that the paper should be readable to the specialists without prior reading of some other papers or textbooks. Current version of the manuscript is definitely not the case.
Of course, the Talbot effect is well known to all opticians, but still requires a brief explanation. Meanwhile, the authors are to be more specific. It requires not the coherent light, but the spatially coherent light, or, in original terms, the plane wave of monochrome radiation.
The Lau effect is not widely known. For instance, the reviewer has spent nearly half a century working in the field of interferometry and holography, but till this case never heard of it. So the authors are to devote several paragraphs to this rare and interesting technique.
Then the authors are to introduce briefly the Barker and the Babinet masks (better with drawings) and their properties. Then the scheme of the proposed dark field Lau interferometer has to be outlined clearly and concisely. The sketch and the optical scheme with the description of all elements and explanation of the ray tracing is obligatory.
The list of references has to be checked. First, there are some mistakes – for instance in Ref.2. Second, non-English titles are to be translated also to English. It is desirable that the non-English original papers by Lau and by Babinet are to be accompanied by some corresponding English references, if available. And seemingly there are too many self-references. Please check is all of them are really necessary.
Author Response
Please see the attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript might be interesting for the community, but it needs substantial revision, both in terms of presentation and formatting.
The structure of the manuscript is also have to be redesigned. It is unclear, where the theoretical description ends and where the results obtained by the authors begin.
Unfortunately, in my opinion, the manuscript is not ready for the publication in its current form. I would recommend the authors to carefully reorganize the manuscript, make the clear structure (Intro, Theory, Methods, Results, Conclusions), apply proper formatting to the text, equations and figures, and reorganize figures (remove unnecessary graphics, compact the existing graphics). Since the research is within the scope of the journal, I would recommend the authors to make necessary corrections and resubmit the manuscript to this journal.
Below are a few recommendations that might help the authors to improve the quality of their research.
There is no explanation in the introduction what is the pros and cons of a new technology compared to existing ones. Please, provide a few paragraphs explaining why and in which cases the proposed technique is better than the others.
Provide limitations of the proposed technique.
What is t(x,y) mentioned prior to eq. 1 and where is it in equation?
Provide explanations of each component of the equation right after it, for each equation (what is b(x,y) in eq. 1? What is the meaning of all components of eq. 4?)
Why the equation 2 is a necessary condition and equation 3 is a sufficient one?
I would recommend to reorganize figures in order to decrease a size occupied by them.
Subfigures of fig. 1 could be placed in row.
Same is for Fig. 2.
Fig. 2 has no caption. The text under the possible Fig. 2 is formatted as a caption of figure, not as a main text.
There is some extra symbol in eq. 7.
Denote the direction of light propagation in Fig. 3. Where is the source and the target.
Equations in Section 3 have to be explicitly explained.
To show a plot in Fig. 7 the authors used Eq. 29, but the last equation is 26.
Comments on the Quality of English LanguageThe language is in general good. Just a small formatting might be useful
Author Response
Please see the attachement
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe manuscript presents the design and theoretical foundation of a dark-field Lau interferometer employing Barker-Babinet complementary masks. By coding gratings with Barker sequences and their Babinet complements, the authors derive a matrix-based framework to describe cross-correlations and beam deviations induced by phase gradients. They extend this analysis to include the effect of randomly distributed phase gradients, modeled via an average point spread function. Finally, they demonstrate how these Barker-Babinet grating pairs can be incorporated into a Lau interferometer operating under noncoherent illumination, suggesting potential optical configurations and applications in dark-field imaging. The work is mathematically rigorous, well-grounded in classical interferometry, and contributes an elegant coding approach to enhance sensitivity to phase gradients.
-
While the theoretical framework is comprehensive, the manuscript lacks experimental verification or even numerical simulations that closely mimic real-world optical conditions. This leaves open the question of whether the proposed dark-field interferometer can robustly handle noise, alignment errors, or fabrication tolerances. Incorporating at least a feasibility analysis or simulated results would strengthen confidence in its applicability.
-
The article does not provide a sufficiently detailed comparison between the proposed Barker-Babinet interferometer and other established dark-field or Lau interferometric techniques. Highlighting differences in sensitivity, resolution, or robustness would clarify the unique advantages of the approach and help readers understand the practical contexts where this method outperforms alternatives.
-
Much of the presentation emphasizes mathematical derivations, but the physical intuition behind key results is sometimes underexplored. For instance, the significance of the modulation by the characteristic function in the presence of random prisms could be connected more explicitly to physical imaging performance. Adding schematic interpretations or analogies could broaden accessibility and impact.
-
The manuscript mentions potential applications (e.g., fluid dynamics visualization) but does not develop them in detail. A more explicit discussion of the potential fields where Barker-Babinet masks could offer measurable advantages—along with limitations such as sequence length constraints or difficulties in extending beyond Barker sequences—would provide balance and realism. This would also position the work more convincingly within applied optics.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsI am satisfied by corrections and addenda. The only note is regarding the Ref.[2]. There is a mistake in the list of its authors. It should look like following:
Hall L.A., Yessenov M., Ponomarenko S.A., Abouraddy A.F. The space–time Talbot effect. Appl. Phys. Lett. 330 Photon.6, 056105 (2021).
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsAuthors addressed most of issues.
Please, pay attention to the Section naming. They should start from capital letter, and they should not be too long, as it is for Section 3 currently.
The results section does not provide any results, actually. No graphics, no tables, no numbers. Just equations. Perhaps, it is a matter of reorganization of the manuscript (i.e., you might move the results from the previous sections).
The discussions section is missing.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe revisions addressed the previous concerns well, and the work is now solid. I’m recommend it for acceptance.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
