Active Optics—Advances of Cycloid-like Variable Curvature Mirrors for the VLTI Array

Round 1

Reviewer 1 Report

This paper describes one of the great successes of active optics, the variable curvature mirror. While the original invention dates back to the 1970s and its main application, as pupil refocusing mirror in the VLTI interferometer delay lines, dates back to the 1990s, this paper reports on the theoretical developments behind the invention, comparison of these theoretical results with numerical simulations, and the practical implementation of their manufacture.

While interesting and informative, this paper lacks clarity in terms of what material is classical and already published, and what is new material. In particular, Sec. 2 (5 pages) goes into great mathematical detail. If this is new material I would urge the author to state it clearly. If, as I suspect, this development has already been published, then it should at least be clearly stated and referenced, and it should be made clear why it is found useful to repeat it here. And even if a repeat would be deemed appropriate, for example due to unavailability of the original publication, I would suggest to put it into an appendix. In any case, I suggest replacing this section with a short overview of the development, stating the main results, supported by due references.

Indeed, this rather long and heavy section tends to overshadow the more recent, seemingly unpublished, work on comparison with numerical simulations (Sec. 4). The results reported confirm the theoretical approach and paves the way for further developments. It might even be useful to extend this section somewhat indicating the possible implications of these results (if any) for future research. I also note that the last sentence of the conclusion (line 627) states that a significantly increased FOV is available, a statement that I cannot find described in the text.

Similarly, it is not clear if the impressive and interesting details of the manufacturing process (Sec. 5) have already been published. If, as it seems, this is not the case, then they should be and I think the opportunity of this paper is excellent for such a publication. Again, however, the novelty (or not) of the publication should be clearly stated.

The manuscript will need English language revisions; I will not report on such in the following except if I think there can be cause for misunderstandings. I will also not report missing definitions of acronyms, as, for example, VLTI, UT, AT in lines 21 -22.

Mathematical formulae should be numbered allowing provision of clear references within the text, for example between numerical results in Sec. 4 (line 373) and theoretical developments in Sec. 2.

Line 82: Please state that the wanted shape is a parabola, as indicated by the formula.

Line 89 etc: Please provide references for the "classical" results concerning thin plate rigidity, solution to the bilaplacian, etc. Your reviewer was poorly chosen and is unfortunately not mathematically equipped to recognise these results. While he is prepared to believe the statements made, he would be interested to have the possibility to learn about (if not to verify) them.

Line 118, 126, ...: Inconsistent notations: Missing curly brackets in the text: Mrb→Mr{b}, typographic symbols, eg T20, etc

Lines 229-231: Part of text or of the legend?

Line 244: The use of Rayleigh's criterion can be practical, but in the context of a single component which will in general be part of a larger system, reference to this criterion appears simplistic. Instead, the larger system will be subject to a system-level specification (which might be the Rayleigh criterion), while individual components will be subject to sub-specifications produced by an error budget. It might be useful to acknowledge this, and, if possible, give an indication of how the surface error varies with stem truncation.

Line 272: This sentence repeats the statement made in the previous sentence.

Line 276: It is not clear where this has been shown. Please explain or provide a reference.

Line 327: Should this not refer to Fig. 7? Still, the symbols used in this formula do not correspond to those used in the legend of Fig. 7: α → β, β → 1-β. This is confusing.

Line 354: Reference to the inset of Fig. 10 would be helpful.

Line 392 etc: Sec. 5.1 is for a large part a repeat of Sec. 1. I suggest you use this information to complete the introduction, as this will increase the visibility and accessibility of the paper.

Line 456: The setup is not clear: "powered lenses, as collimators, for null tests". I think a more thorough explanation, possibly accompanied by a schematic of the bench, would be useful.

Lines 461 etc: References to Fig. 19 would be useful. Clearly, the way this process is laid out, it is highly manual and artisanal. Is this inherent or is there a possibility of industrialization? A short discussion of this question might be of interest.

Line 498: Please be consistent when referring to co-authors. Here "Lanzoni" while "P. Vola" in line 296.

Line 507: This paragraph would appear better integrated in the text following Line 462.

Line 512: The table might gain in clarity by adding a column indicating the units.

Line 534: Please give subsection number.

Line 568: This phrase is incomplete and the meaning is not clear. Maybe it should read "Phase maps are calculated from He-Ne interferograms obtained (...) after reduction by Quick Fringes (...)" ?

Line 572: Fringe images are nice but not easily quantifiable by the reader. The text refers to analysis using software (previous comment); if available, it would be useful to show the corresponding phase (or surface) maps.

Line 579: A red point appears at WFE=0.25λ on the left side of this plot. Is it an actual specification? It might need explanation. Also, there is a red (or violet?) line which nearly doubles the blue line, not explained in the legend. What does it represent? Maybe it could be removed for clarity? Are these results representative of the ensemble of produced units? Maybe a cloud of curves could be plotted, or error bars added to indicate spread in the performance? At the very minimum, a statement in the text about performance repeatability should be added.

Line 616: The adjunction of the statements "pure coincidence" and "absolutely identical" appears to be a bit over the top; claiming an "identity" to be "coincidental" would seem to be strong enough, using neither quotes nor italics. This is still a great and precious result which in itself merits this publication and which would benefit from being put forwards from the start of the paper.

Line 627: This final sentence of the conclusion reports a result that (unless I missed it) is not discussed in the text. Please make sure it is and that it is given the importance that it would seem to merit.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript is well written and deserves to be published in an archival journal. There few minor typos and misspelling that would benefit from a thorough editing of the manuscript. Some examples:

on line 155 the equation is missing the "-" sign it should be [12(1-υ²)]. 

line 339 NASTRAN is misspelled

Line 388 the sentence is not well written. Probably is missing a main verb. 

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The article is very interesting and provides a detailed description of cycloid-like variable curvature mirrors. It is highly significant in high-angular resolution imaging applications. I suggest authors address the following comments before publication.

Could the authors provide more details on the experimental validation of the developed VCMs? The interferometric results are not very clear in the current form, please provide more description. Lack of qualitative results.  

Have the authors used any air pressure actuation system to understand the performance of the VCM?
For example surface figure deviation under various applied pressure
Also, please provide a comparison of the experimental results with modeling/FEA.

Please add some more background information on VCMs in the introduction.

Would be nice if the authors could provide some more details on the comparison of cycloid-like or tulip-like, with the pros and cons of the two.
And what benefits do they expect in the tulip-like VCMs?

I would suggest removing the title from the figures. It's good to have consistency in the figures.

In the abstract probably remove the "106" after the solution sequence. Could be confusing for readers.

Fig: 10: What's the inset here? please explain.
Fig: 17: Please provide more details in the caption, I couldn't get any info from the top picture here. And explicitly say what are the two pictures here.
Table 2: provide dimensions for t, r etc.
Fig 18: What are the dimensions?
Fig 23: Please explain in the caption explicitly what are two figures? What's the color code?
Fig 25: Obtained results color is "pink" instead of blue?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Thanks for addressing my comments. I think its good to go. Keep up the impressive work!

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.