Reviewers' comments: Reviewer #1 (Remarks to the Author): The authors describe a novel photonic structure on spider abdomens, and do an admirably comprehensive job accounting for the observed visually striking and complex scattering using a combination of numerical modeling, analytical modeling, hyperspectral imaging, and then nanoscale 3D printing to validate their mechanistic explanation for the scattering they observe. They show that by wrapping a "standard" 2D diffraction grating around a scale with an air-foil-like shape and radius of curvature of ~100's of microns, the resulting scattering is that of a broadband illuminant angularly separated into a full spectrum of saturated colors that are all observable at very small distances/angular displacements from the spider's body. This is distinct and novel relative to flat gratings or other curvatures, where large distances and/or angular separations are needed to observe the saturated colors resulting from the wavelength-dependent scattering of the whole broadband spectrum. When viewed from the perspective of the methods section and figures alone, the results are pretty convincing. However, the rest of the manuscript as a whole suffers from some imprecise framing and imprecise writing that, as written, obscure the actual analytical work the authors have done. It is true that subwavelength optics are interesting, complex, and important. It is also true that nature and the scientific literature are rife with an ever-increasing array of examples of well- described, sophisticated, subwavelength optics in organisms. So it seems to me that at this point in the evolution of this field, statements like "Light dispersion is crucial to fields ranging from life sciences and biotechnology to material sciences and engineering" are too general to be interesting or useful. What specific problem, or class of problems, might this "little rainbow" effect found in spiders be useful for? Really tiny spectrometers? If so, why are those useful? If there isn't (yet) an especially compelling, granular answer to these questions, then the paper's framing would be more convincing kept to the realm of basic science investigation, in the context of what is and isn't known about grating geometry and function (which is not a bad thing!). I'm also unsure about the authors' use of the term "dispersion" here. I think I know what they mean, but most usually, this term describes how the refractive index of a material changes as a function of wavelength. Unless I'm missing something that should then be better explained in the paper, this isn't the effect they claim for the spider structures, but instead, the wavelength-dependent effects the authors document have to do with the near-wavelength geometry of the structure, and not with the relation between incident wavelength and refractive index or a material property per se. The spider effect seems to me something more like "wavelength-dependent scattering" or "complex bidirectional reflectance distribution function" or just "diffraction", rather than "dispersion". If "dispersion" can be used in some contexts to describe any systematic wavelength effect regardless of the underlying cause, then this should be clear. The feature that distinguishes the spider structures described here from simple flat gratings or other biological gratings is specifically the curvature of the scales on which grating-like ridges are found. For this reason, it was a little unsatisfying that this curvature is never quantified or further investigated, but only described as "not concentric arcs". What is special about the spider's curvature, and how can it be described, beyond just "not a concentric arc"? This seems to me to be the nub of their results, and is fairly readily quantifiable, but it isn't reported. If these "tiny rainbows"/high resolution diffraction effect is as important as they say, then it seems as important to then quantify the curvature that gives rise to them. Also, it gets a little confusing which aspect is "horizontal" and which is "vertical" - an additional schematic would be helpful in that respect. The authors also write that this shape enhances the "degree of iridescence" compared to other gratings they considered, and later in the discussion say that the work they've done "explains the striking iridescence". "Iridescence" isn't a term with much particular physical meaning, so I wasn't sure what specifically they were trying to claim in context. My advice would be to avoid this term altogether, in favor of specific physical statements about the effect of interest in each case. I'm also not sure it is fair to claim that they have found "the first rainbow-iridescent signal" in nature, given that they conclude that spiders are unlikely to be perceiving the full reflected, spatially separated spectrum at any given time. In order to be a signal, a stimulus needs to be received, but the authors argue that the tiny rainbow per se probably isn't received in this case since the spiders' angular acuity is likely too low. The more interesting question to me is, given the comparatively low angular resolution of spiders' eyes compared to this rainbow, and the very complex scattering effects from the scales at relevant lengthscales, what then is the salient part of this signal to the spider? Would that give any more clues as to what the most physically interesting features are likely to be? What would these diffraction patterns look like to something with many eyes, low spatial acuity, but high spectral resolution (as I think I understand the spiders to be)? Without considering this issue in more experimental detail, it would be my advice to avoid making any "the first" claims, and just focus on what is especially interesting and demonstrably true about the structure. Minor comments: extended figure 5: "scar bar"; some editing mistakes around line 585; Reviewer #2 (Remarks to the Author): I have reviewed this submission to Nature communications with interest, but frankly I have to confess that the more I read the more disappointed I got on the document. Perhaps I was moved initially by the title and abstract to expect something extraordinary, but this is truly not the case. I find their claims of extraordinary optical properties, really lacking support. The diffraction presented by this spiders did not strike to me as anything remarkable, it is just a nanostructured mounted on a microstructure. Very much a like the one presented by butterflies, but clearly with its on particularities. The diffraction is not selective, quite broadband actually. their central claim "scales achieve resolving power beyond the performance of conventional 2D diffraction gratings" seems unfair to diffraction gratings. I am quite positive one can give the required performance to an optical engineer and most likely a solution will be found with standard technology. After all, what we see here is a diffractive structure just riding a non-flat microstructure. I give actually a bit more credit to the group that simulated and fabricated the artificial replica via 2 photon lithography. That seems nice but it is not a technological feat. So, there is nothing particularly wrong here, in fact they present a substantial amount of well done work, but in my opinion this paper's impact is modest. It is already a cliché to look in nature for inspiration, but in this particular instance the structure is not even hard to identify or reproduce. So, to suggest it might change how optical designers think or imagine building dispersive structure is quite an exaggerated view. My suggestion is pick a more specialized journal. Reviewer #3 (Remarks to the Author): This paper reports a very thorough study of an original and unusual case of iridescence in nature, and employs the best possible methods to determine the structures involved and the precise optical reflections (I particularly like the scatterometer), and to characterize the optical effect. The level of effort and care to gather data from such small scales pays off when the authors can reveal the important effect of a 3D (rather than flat) surface which houses the diffraction gratings. The engineered devices are useful to confirm the principles hypothesised (as always with such studies, the thoughts on commercial applications require specialized and extensive study). I believe that such a comprehensive study has led to results that be trusted and therefore this is a valuable contribution that will interest researchers in many fields. I recommend that this paper is published after minor editing. Andrew Parker Point-by-point responses to the reviewers’ comments on the manuscript "Rainbow peacock spiders inspire miniature super iridescent optics" We thank the reviewers for their careful reading of our manuscript and for their comments and suggestions to improve the quality of the text. The following responses address all of the reviewers’ comments in a point–by-point fashion. Reviewer #1 Specific Comments Comment #1 “The authors describe a novel photonic structure on spider abdomens, and do an admirably comprehensive job accounting for the observed visually striking and complex scattering using a combination of numerical modeling, analytical modeling, hyperspectral imaging, and then nanoscale 3D printing to validate their mechanistic explanation for the scattering they observe. They show that by wrapping a "standard" 2D diffraction grating around a scale with an air-foil-like shape and radius of curvature of ~100's of microns, the resulting scattering is that of a broadband illuminant angularly separated into a full spectrum of saturated colors that are all observable at very small distances/angular displacements from the spider's body. This is distinct and novel relative to flat gratings or other curvatures, where large distances and/or angular separations are needed to observe the saturated colors resulting from the wavelength-dependent scattering of the whole broadband spectrum. When viewed from the perspective of the methods section and figures alone, the results are pretty convincing. However, the rest of the manuscript as a whole suffers from some imprecise framing and imprecise writing that, as written, obscure the actual analytical work the authors have done. It is true that subwavelength optics are interesting, complex, and important. It is also true that nature and the scientific literature are rife with an ever-increasing array of examples of well-described, sophisticated, subwavelength optics in organisms. So it seems to me that at this point in the evolution of this field, statements like "Light dispersion is crucial to fields ranging from life sciences and biotechnology to material sciences and engineering" are too general to be interesting or useful. What specific problem, or class of problems, might this "little rainbow" effect found in spiders be useful for? Really tiny spectrometers? If so, why are those useful? If there isn't (yet) an especially compelling, granular answer to these questions, then the paper's framing would be more convincing kept to the realm of basic science investigation, in the context of what is and isn't known about grating geometry and function (which is not a bad thing!).” Response: We thank the reviewer for the great summary of our research and opinion about the framing of this manuscript. We modified the manuscript and reframed it as potential biological inspiration for future designs for miniature light-dispersive components. We have also explained why and how these miniature designs could have a large impact in fields from life science and biotechnology to material sciences and engineering in the Discussion, for example, small and powerful spectrometers that could be contained within wearable devices could help soldiers and explorers avoid hazardous environments in war zones or during expeditions. But this is only one example, and more extensive information is provided in Line 298~305. Comment #2 “I'm also unsure about the authors' use of the term "dispersion" here. I think I know what they mean, but most usually, this term describes how the refractive index of a material changes as a function of wavelength. Unless I'm missing something that should then be better explained in the paper, this isn't the effect they claim for the spider structures, but instead, the wavelength-dependent effects the authors document have to do with the near-wavelength geometry of the structure, and not with the relation between incident wavelength and refractive index or a material property per se. The spider effect seems to me something more like "wavelength-dependent scattering" or "complex bidirectional reflectance distribution function" or just "diffraction", rather than "dispersion". If "dispersion" can be used in some contexts to describe any systematic wavelength effect regardless of the underlying cause, then this should be clear.” Response: We thank the reviewer for pointing this out. Indeed, the term “Dispersion” can be used to describe any systematic wavelength effect regardless of the underlying cause. Therefore, “Dispersion” under the context of a diffraction grating will have a different definition than that of a prism. We made this clear to the readers by adding a new paragraph in Supplementary Note 2. Comment #3 “The feature that distinguishes the spider structures described here from simple flat gratings or other biological gratings is specifically the curvature of the scales on which grating-like ridges are found. For this reason, it was a little unsatisfying that this curvature is never quantified or further investigated, but only described as "not concentric arcs". What is special about the spider's curvature, and how can it be described, beyond just "not a concentric arc"? This seems to me to be the nub of their results, and is fairly readily quantifiable, but it isn't reported. If these "tiny rainbows"/high resolution diffraction effect is as important as they say, then it seems as important to then quantify the curvature that gives rise to them. Also, it gets a little confusing which aspect is "horizontal" and which is "vertical" - an additional schematic would be helpful in that respect.” Response: We agree with the reviewer’s suggestion. In fact, we indeed attempted to quantify it. However, as the curvature of the natural spider scales does not follow any spherical /circular shape (i.e. freeform curvatures), it was not straightforward to define the radius of curvature in a quantitative manner. We have already analytically shown that the microscopic triangular shape has significant impact on the grating performance. Nevertheless, following the reviewer’s suggestion, we derived Equation 4 considering ellipsoidal curvature. Several previous literatures (for example, H. Noda, T. Namioka, and M. Seya, "Geometric theory of the grating," J. Opt. Soc. Am. 64, 1031-1036 (1974)) implied that curvature effect modifies the effective grating periodicity. According to the newly derived Eq. 4, we found that the effective grating period changes with a factor of π/√8 and indeed, the curvature effect improves grating performance roughly 10% in addition to the macroscopic shape. This is now added in the manuscript in Line 207~213. We also modified Fig. 4 to make it clear what do we mean by “horizontal” and “vertical”. Comment #4 “The authors also write that this shape enhances the "degree of iridescence" compared to other gratings they considered, and later in the discussion say that the work they've done "explains the striking iridescence". "Iridescence" isn't a term with much particular physical meaning, so I wasn't sure what specifically they were trying to claim in context. My advice would be to avoid this term altogether, in favor of specific physical statements about the effect of interest in each case.” Response: Iridescence is usually defined as a “change in hue of a surface with varying observation angles” (doi:10.1126/science.1173324). Hence, in this manuscript we define the “degree of iridescence” as “the change in hue with the same amount of scattering angle variation”, and use this definition as the basis for our quantification. The definition has been clarified in our manuscript (Line 204~206). Comment #5 “I'm also not sure it is fair to claim that they have found "the first rainbow-iridescent signal" in nature, given that they conclude that spiders are unlikely to be perceiving the full reflected, spatially separated spectrum at any given time. In order to be a signal, a stimulus needs to be received, but the authors argue that the tiny rainbow per se probably isn't received in this case since the spiders' angular acuity is likely too low. The more interesting question to me is, given the comparatively low angular resolution of spiders' eyes compared to this rainbow, and the very complex scattering effects from the scales at relevant length scales, what then is the salient part of this signal to the spider? Would that give any more clues as to what the most physically interesting features are likely to be? What would these diffraction patterns look like to something with many eyes, low spatial acuity, but high spectral resolution (as I think I understand the spiders to be)? Without considering this issue in more experimental detail, it would be my advice to avoid making any "the first" claims, and just focus on what is especially interesting and demonstrably true about the structure.” Response: We agree with the reviewer that for anything to be a “signal”, it has to be perceivable by the intended receivers. With that said, we argue that this is indeed “the first rainbow-iridescent signal” in nature. As iridescence is defined as “change in hue over varying observation angles”, the essence of an “iridescent signal” is that it is “dynamic” (doi:10.1126/science.1173324, doi: 10.1016/j.cobeha.2015.08.007). Therefore, while female spiders can probably not perceive the “static” rainbow, their exceptional spectral resolution (tetrachromacy) makes it likely that they can perceive the change in hue from individual scales. Females have the acuity and spectral resolution to perceive colour variation across the male’s abdomen. This emphasizes our point that the iridescence itself is likely the salient portion of the visual signal, and we have added some text to the discussion on this point. See our explanation in the text at Line 269~281. Comment #6 “extended figure 5: "scar bar"; some editing mistakes around line 585” Response: We fixed the typo and grammar. Thank you. Reviewer #2 General Comments Comment #1: “I have reviewed this submission to Nature communications with interest, but frankly I have to confess that the more I read the more disappointed I got on the document. Perhaps I was moved initially by the title and abstract to expect something extraordinary, but this is truly not the case.” Response: We are glad to hear that the title and abstract of this manuscript gathered the reviewer’s attention and interests. The changes made to the manuscript substantially increase its novelty and impact as detailed below. Critical changes can be found in Line 30~41, Line 83~89, Line 187~220, Line 269~281, and Line 295~305. These changes address the broad sense of the document and provide a stronger story to the observations. Comment #2: “I find their claims of extraordinary optical properties, really lacking support. The diffraction presented by this spiders did not strike to me as anything remarkable, it is just a nanostructured mounted on a microstructure. Very much a like the one presented by butterflies, but clearly with its on particularities. The diffraction is not selective, quite broadband actually. their central claim "scales achieve resolving power beyond the performance of conventional 2D diffraction gratings" seems unfair to diffraction gratings. I am quite positive one can give the required performance to an optical engineer and most likely a solution will be found with standard technology. After all, what we see here is a diffractive structure just riding a non-flat microstructure. I give actually a bit more credit to the group that simulated and fabricated the artificial replica via 2 photon lithography. That seems nice but it is not a technological feat. So, there is nothing particularly wrong here, in fact they present a substantial amount of well done work, but in my opinion this paper's