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I was impressed with the technique developed for the analysis of CT scans of compound eyes and the calculation of their visual properties that are reported in this preprint. Having developed a similar analysis procedure myself (Taylor et al. 2018; DOI: 10.7554/eLife.40613), I can appreciate that a substantial amount of work has gone into developing this technique. Moreover, I congratulate the authors for developing a procedure that appears to be largely automated, as the time required for manual processing of CT scans has been a major limiting factor in such analysis previously. The accuracy of the analysis technique is impressive, and the fact that the same basic technique can broadly be applied to analyse images of eye replicas, whole eyes and microCT should enable a wide range of studies. I thought the analysis of the vertical and horizontal visual angles of horizontal and diagonal ommatidia pairs based on cluster analysis was an innovative approach that demonstrated the methodological robustness of the analysis technique.

Only two major omissions stood out to me in this work. The first was the lack of a manual count for the ommatidia of the moth and bumblebee CT datasets against which the analysis results could be compared. The presence of such a count for the 2D analysis lead to me expect it for the 3D analysis as well (although I recognize that I myself did not provide such a count in Taylor et al. 2018). I do not think that this should be treated as a revision required for journal publication, although it would be nice to include it for completeness. 

Secondly, the authors approximated lens diameter from CT data based on the distance between centroids of adjacent crystalline cones. However, the diameter relevant for optics is that of the corneal surface. As the cones centroids are to the corneal lens, I would expect the cone diameters to be slightly smaller than the lens diameters. I think that the difference between the corneal and crystalline cone diameters is likely to be negligible for the large compound eyes used in this study (indeed the mean crystalline cone diameter from this study is actually slightly larger than the mean lens diameter for the same bumblebee eye, although that may be because the smaller lenses in the dorsal eye were missed), but I expect the relative magnitude of the difference would increase for smaller eyes, where the corneal and crystalline cone thickness are non-negligible relative to the eyes radius. This measurement difference should be clearly noted in the text and its limitations discussed. Additionally, I would also encourage the authors to provide some qualitative estimates of the difference for different different sized eyes that could be used for guidance. Such estimates could be made using published data from histological sections from which these thicknesses and diameters can be measured and Taylor et al. 2018 also include data on the thicknesses of the crystalline cones and cornea, as well as the corneal lens diameter, for bumblebee eyes of different sizes which may also be useful. I think that this point should be addressed before this work is published. 

Otherwise, I have included a number of minor comments below. The number and my detail is mostly a reflection of my familiarity with analysing CT data from compound eyes and my enthusiasm for the topic rather than an indication of many points requiring attention. I hope the authors will find these comments useful and will consider incorporating some of the suggestions into their manuscript, although besides the comments relating to data availability, I do not think any are critical to address before journal publication. I wish the authors luck with the remainder of the publication process and look forward to seeing the results of using this technique for studies on other insects. 

Gavin Taylor

--- Minor comments:

Smaller compound eyes are often spherical and homogenous because photon noise and diffraction constrain IO angle and ommatidial size (Snyder, Stavenga, et al. 1977).

This reference to a theoretical paper and while I agree that the paper indicates photon noise and diffraction do constrain the vision of small eyes, I don’t recall a statement referring to empirical data being provided that small eyes are often spherical or homogenous. Indeed, from my own experience working with compound eyes, I have observed many small compound eyes that are not particularly spherical (e.g. the eyes of small stingless bees are oval) and I would suggest rephrasing this sentence to remove that claim or provided a reference to empirical evidence supporting it.

many compound eyes are non-spherical, with ommatidial axes askew to the eye surface.

I don’t think non-sphericity and skewness are always linked together as is implied by this sentence (although I agree they are probably often found together). I don’t know of any anatomical data showing this, but Rotowski et al. 2009 (DOI: 10.1016/j.asd.2008.08.003) found the butterflies with hemispherical eys and hemispherical fields of view still had IO angles that varied by up to a factor of x2 across the frontal visual field, while diameter varied at most by a factor of x1.3 (see Table 3; C. eurilochus). Although I don’t think that paper commented about the possibility of skewed ommatidial axes, if the eye curvature is consonant (hemispherical eye) and the interommatidial angle is varied by a substantially greater factor than the diameter, then I think this implies local variation skewness would then be necessary to get the IO angle variation (given IO=D/R; although I’m not 100% sure about this reasoning, it would be worth thinking through it more). Likewise, it also seems possible that a non-spherical eye could have non-skewed ommatidia, although I can’t think of any examples of this. I would rephrase the sentence to indicate the non-spherical eyes usually have skewed ommatidia.

The 2D histograms and the superimposed ommatidial centres suggested that the first count was more accurate for M. sexta while the second count was more accurate for D. elpenor.

I am confused about what process ‘counts’ is referring to here. I think it is step 4 of the microCT pipeline, but it’s not clear what the difference between the first and second counts is. I think this should be clarified.

To better characterize their visual field, we projected the ommatidial axes onto a sphere outside of the eye, much like the world-referenced projection of Taylor et al. (2018; Figure 7C). However, instead of using the centre of the head as our centre, we used the centre found in step B of ODA-3D, which is near but not exactly the centre of the head. We chose a radius of 10 cm based on visual fixation behaviour (Wehner and Flatt 1977).

At what radius is the sphere effectively at infinity for the projection? (i.e. beyond what distance does the spatial dimensions of the eye no longer influence the angular projection). Seidl and Kaiser 1981 (DOI: 10.1007/BF00606065) calculated this distance to be 193 mm for a honeybee (although I am not sure their calculation is entirely equivalent, see Fig. 4).

The moth specimens are from the Florida Natural History Museum. Were they from the collection and were they stored in ethanol for a substantial period of time (i.e. years?). If so then the authors could consider commenting on the applicability of their technique to studying preserved specimens in a more detailed manner than that demonstrated by Taylor et al. 2020 (DOI: 10.1098/rsif.2019.0750), which would support the case for facilitating studies on a wide range of non-model organisms, which is harder to do if fresh specimens are required for analysis. 

(2) the horizontal and vertical angles for diagonal IO pairs (± 60° orientations) are Δφh2 and Δφv; 

Should the horizontal angle be squared here? This seems wrong.

This differs from the previous measurements taken on the same scan, which found that the anatomical IO angle increases from about 1.26° to 1.90° from the lateral to central eye with a strong positive correlation (r = 0.50, df = 3,471, p  0.001; Taylor et al., 2018). This is likely because the previous measurements did not account for skewness, which we find increases laterally, and partially explains why our anatomical IO angle measurement exceeds theirs by about 0.16o.

I agree with the skewness would contribute to the observed difference, but would also note that the horizontal azimuthal profile in Taylor et al. 2018 incorporated the full dorsal region of the bumblebee eye, where facets had larger IO angles that were projected frontally, which would contribute to an increase in average IO angle between the lateral and central eye. Additionally, Taylor et al. 2018 calculated projections centred on the head and out to infinity, which may also introduce a discrepancy in where points lie on the profiles. If the authors agree these factors could have contributed to the difference then I think they should be noted in the text. 

Skewness angles were insignificant in moth eyes, which generally require approximate sphericity for proper optical superposition.

I agree, although as always there are exceptions to the rule. See for instance the description of the aspherical superposition eye of ​​Macroglossum stellatarum in Warrant et al. 1999 (doi:10.1242/jeb.202.5.497)

This was mostly due to differential exposure across the eye

and B. terrestris had uneven exposure

I recommend changing exposure to contrast agent penetration or similar. Exposure is also an imaging parameter (e.g. 0.5s exposures) and could lead to confusion in this context.

Light passing through an eye refracts depending on the incident angle and index of refraction (Stavenga 1979). But our approximations used only incident angle, so our measurements of the aperture-diminishing effect of skewness represent lower bounds, and our measurements of IO angles are anatomical, not functional IO angles.

Has the corneal refractive index been published for any of the species in this study (or their relatives, or for any insect species)? If so, that value could be used to provide an indication of roughly how much refraction would influence the adjusted lens diameters.

the ODA-3D should be tested on non-spherical non-oval eyes

I would suggest noting an example insect with such an eye for this test case as examples were provided for the other cases. 

Additionally, I would suggest noting explicitly that technique should be tested on Dipteran eyes. The reason for this is that I have observed that the crystalline cones in fly eyes usually appear as hollow outlines (as do the photoreceptors), in contrast to the filled cones shown from the bumblebee eye. I suspect this is related to the fact flys have open rhabdoms although I am not sure why this influences the structure/composition of the crystalline cones, and it may also vary depending on the contrast agent used (I observed it when using OsO4). Unfortunately, I have never published material clearly showing this and do not currently have access to this data. However, this phenomenon is somewhat apparent in the volume rendering of a Drosophila hydei stained with iodine from Sombke et al. 2015 (DOI: 10.1002/cne.23741; see Figure 2A left) based on the absence of crystalline cones between the corneal lenses and photoreceptors. Additionally, hollow cone outlines are visible in an unstained fungus gnat eye published in Taylor et al. 2020 (Figure S2). Additional examples may be available in the literature. May the authors can speculate about whether the current FFT 2D FFT approach is likely to work on the cone outlines and/or what modifications could allow it to do so.

The ODA calculated ommatidial count and lens diameter from different media (eye molds, microscope images, and µCT scans), taxa (ants, flies, moths, and a bee), sizes (hundreds to tens of thousands of ommatidia), and eye type (apposition, neural superposition, and optical superposition).

I wonder if it would also be possible to perform the 2D analysis on an isosurface from a CT scan of an eye. This could be useful in cases where contrast agent cannot be applied to crystalline cones of an eye (e.g. dried or amber embedded specimens, see Taylor et al. 2020; DOI: 10.1098/rsif.2019.0750) or if reusing a dataset from a CT scan that was conducted for another reason. The authors could speculate about this, and if they wish to test it, the datasets from Taylor et al. 2020 are publically available on Morphosource. 

The preprint from Tichit et al. 2020 (DOI: 10.1101/2020.12.15.422850) is another recent example of applying automated analysis techniques to segment the crystalline cones of compound eyes. I have not read that paper in detail but given the obvious similarities, I think a comparison should be made between that study and the technique and results presented in this preprint.

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Figure 1. 

It could be helpful to include a pictogram indicating that C and D represent perpendicular cross-sections on an oval eye. 

I think it would also be useful to include a diagram of skew ommatidia as characterising this aspect of compound eyes is an important contribution made by this work, but as they are so rarely considered by other anatomical studies, readers are likely to be less familiar with skew ommatidia and so a diagram would ensure they are correctly conceptualized. 

Figure 3.

The diagram of the crystalline cones appears to include the corneal lens (the cone is drawn with a concave front in Figure 1).

Additionally, the difference between the crystalline cone centroid and the corneal lens diameter should be clearly shown in D, whereas diameter (D) is currently drawn to indicate the lens diameter.

Figure 4

The authors find that the ommatidial axes of the bumblebee are substantially skewed from the ideal axes. I think it would be useful to depict this skewness in D by drawing the ideal axes for comparison (perhaps just in a few of the insets), so the reader can clearly see how the skewness is present in the anatomy of the eye.

Additionally, it would also be helpful to indicate where the horizontal and vertical cross-sections are taken from on a diagram of the compound eye; this should at least be indicated in the caption (it does not appear to be currently), but a diagram would be clearer.

Figure 6

The spherical projection of the bumblebee eye seems to be an anatomical projection. Is that intentional? If so, it is mislabelled in the caption.

A dash is used to separate numbers in the count row of the table. To me, this reads as indicating a range whereas my understanding is that it is actually indicating two separate values (count one and count two). I think it would be better to separate the values with a coma to make this clearer.

Figure 7. 

I was initially confused by what the maps in A indicated as the X-axis is in degrees, as are those in the adjacent maps in B, which also have a similar range. I think it would be useful to have small diagrams reminding the reader that A is referring to angles in the eye lattice while B is referring to angles in world coordinates.

99% CIs of medians are plotted on the maps in A and B. This may be a somewhat philosophical point, but confidence intervals are used to indicate a range in which the true value of a given parameter for distribution is expected to be found, based on having sampled some values from that distribution. But in this case, my understanding is that the entire distribution has been sampled (all ommatidia on the eye, excluding those missed in the dorsal region), so isn’t the median of the distribution known exactly? I think it would be more appropriate just to just plot the ranges (in addition to the existing median and IQR).

In both Figures 6 and 7 I think the authors make a very sensible choice to limit the plots of world coordinates to plus/minus 50 degrees. The removes the worst distortion in the equirectangular projection but is more intuitive than using a sinusoidal projection as Taylor et al. 2018 did.

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It is not clear which bumblebee eye scan from Taylor et al. 2018 is used in the analysis for this preprint, as a hyperlink is provided to a Morphosource project containing multiple datasets of scans and labels. Each dataset in the project has its own DOI, and I recommend that this is included as a data reference. Additionally, Taylor et al. 2018 used bee and eye size as the independent variable, and so to facilitate comparison between these two studies it would be helpful to mention the inter-tegula width corresponding to the bumblebee eye that is analysed here. (based on the number of facets it seems to be the largest one?)

Related to the above point, I would also encourage the authors to upload the CT image data from the two moths they analysed in this project to Morphosource (and include the DOIs as data references) to facilitate reuse by other investigators.

If the images of any eye replicas and fruit fly eyes are not publicly available, then I would similarly encourage them to upload these to a suitable data depository.

Finally, I would also recommend the authors make the data from analysis (final and appropriate intermediary stages) available in a data depository.