Topological Charge Detection Using Generalized Contour-Sum Method from Distorted Donut-Shaped Optical Vortex Beams: Experimental Comparison of Closed Path Determination Methods
Round 1
Reviewer 1 Report
The manuscript describes and compares several approaches to determining the topological charge of a vortex beam. The results are interesting and the comparisons are done well.
The vertical axis of figure is not well described. It appears to be the WTCMR metric, but it is not clearly explained.
How the 15 lateral translations of the Shack Hartmann sensor was used in the method would be useful. More information on the algorithms coded could be included in supplemental or appendix to better enable replication of the study. How the intensity profile of the vortex beam were collected could be better explained.
Some minor grammatical changes could help with readability.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The content of the article is important and useful, and definitely should be published. The authors very clearly show that the two perfect-round-circle methods considered are quite inferior to the three watershed-transformation and maximum-average-intensity-loop extraction based methods that are also considered. The performances of those three latter methods (WTMWTM, MAICMMAICM, and WT-MAICM in the authors' nomenclature) are fairly similar to one another, and it is only in figures 9 and 10 that we can see significant differences between the performance of those three methods. Figure 9 needs a "WTCMR" label next to the y-axis on the left-hand sides of (a) and (c), and an "r0/D" label next to each of the x-axes.
Figure 10 leaves the reader with a question: the MAICMMAICM-determined closed path appears to me to be only one possible *local*-maximum-average-intensity loop; there would be another such *local*-maximum-average-intensity loop (and, in this case, a far better closed path for TC determination) further out, which would be much closer (if not identical) to the (much better) WT-MAICM determined closed path. Thus, it seems to me that the problem with MAICM is that it can get stuck in local minima -- and thus there might be another method -- a "global maximum average intensity circle method" -- that could look for *multiple* local maximum average intensity loops, and if more than one such loop exists, then choose the loop with the largest overall average intensity from those choices. I am guessing that such an algorithm would have a similar performance to the WT-MAICM (although it might be slower, depending on how it was implemented).
My one other scientific comment is that code, or pseudo-code, for the WT-MAICM algorithm that is used should probably be provided somewhere, either in supplementary article info, or in a link, or at very least just "code available from authors" should be stated: the article text explains it well, however even with that explanation, there are a few different choices that could be made in exactly how one would implement it in code; and, thus, the code that was used should be available.
My main comment is not a scientific one: it is just that the article very sorely needs English editing by a native English speaker. The content is clear to native English speakers like me; but even so, nearly every sentence has some form of misuse of English in it, such as incorrect prepositions, very poor word choice, etc. Hamamatsu Photonics has several U.S. offices; perhaps finding a native English speaker from one of those offices to edit the article for better English might be possible?
Anyway, it is a good article, and I hope the fairly minor comments above could be incorporated.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
I would recommend a minor editing regarding the use of english (see, for example, lines 31 (... its ...), 55 (... the to be measured ...), 69 (In aim ...), 160-161, 218 (To verification ...), 252-254, etc.). In the abstract, the statement "... while the perfect-round circle method is the worst ..." could become more moderate (e.g. the authors could list the methods according to their efficiency).
Author Response
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Author Response File: Author Response.pdf
