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Celestial polarization patterns sufficient for Viking
navigation with the naked eye: detectability of Haidinger’s
brushes on the sky versus meteorological conditions
Gábor Horváth, Péter Takács, Balázs Kretzer, Szilvia Szilasi, Dénes Száz, Alexandra
Farkas and András Barta
Article citation details
R. Soc. open sci. 4: 160688.
http://dx.doi.org/10.1098/rsos.160688
Review timeline
Original submission:
Revised submission:
Final acceptance:
10 September 2016
9 January 2017
9 January 2017
Note: Reports are unedited and appear as
submitted by the referee. The review history
appears in chronological order.
Review History
RSOS-160688.R0 (Original submission)
Review form: Reviewer 1 (Shelby Temple)
Is the manuscript scientifically sound in its present form?
Yes
Are the interpretations and conclusions justified by the results?
Yes
Is the language acceptable?
Yes
Is it clear how to access all supporting data?
Yes
Do you have any ethical concerns with this paper?
No
© 2017 The Authors. Published by the Royal Society under the terms of the Creative Commons
Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use,
provided the original author and source are credited
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2
Have you any concerns about statistical analyses in this paper?
No
Recommendation?
Accept with minor revision (please list in comments)
Comments to the Author(s)
Comments to Authors
General Comments
This is a great analysis of the proportion of the sky that would be useful for human navigation
using celestial polarisation patterns relative to meteorological conditions.
My only major concern with the manuscript is the comparison of the three different wavelength
bands used. It is not necessary to provide all three colour bands, and in fact it detracts from the
story by making it more complicated than it needs to be. The entoptics phenomenon of
Haidinger's brushes is mediated by the absorption of short-wavelength light by the macular
carotenoids (lutien, zeaxanthin and meso-zeaxanthin) (Müller et al 2016, and Bone 1984) and is
not visible at wavelengths above about 500 nm, therefore the two colour bands in the green and
red are not useful for perception of polarization and therefore do not add to your argument.
Instead the extra data makes the story more confusing. If you remove the colour component you
can focus on the main effect in the blue and make the story more concise and more easily
accessible.
In case you are interested, the original experiments we did (Temple et al. 2015) were done with
humans looking at a modified LCD screen, however, I have since measured the human threshold
using a sheet of rotating polarizer combined with a series of my custom made depolarizing filters
and found that the human threshold is even lower than 23% we originally reported. Out of 20
people studied, four individuals could see HB down to 16% and one could go as low as 12%. In
this study the mean d* was 32.4% and the min was 70%. If you want to add these results to this
paper you could report them as unpublished data or personal communication. This work was
done as part of a preliminary experiment that showed a correlation between threshold for
detecting HB (d*) and macular pigment optical density (MPOD) measured on a dual wavelength
scanning laser ophthalmoscope (Heidelberg Spectralis). These results concur with recent findings
of Müller et al. 2016 (Müller PL, Müller S, Gliem M, et al. Perception of Haidinger brushes in
macular disease depends on macular pigment density and visual acuity. Invest Ophthalmol Vis
Sci. 2016;57:1448–1456. DOI:10.1167/ iovs.15-19004).
It is not helpful for the reader when sentences have too many equations (e.g. P5 L5-11 ) or are
written around a figure (e.g. start with "Figure x shows..."). It is much easier to read and
understand the point being made if the sentences are written in words and just tell the story,
leaving the equations and figures to the end to be put in parentheses e.g. Page 3 Line 56 "Figure 2
shows a totally overcast sky taken with our full-sky imaging polarimeter when the solar elevation
was θ = 0º and the cloud percent was ρ = 100 %." It is much easier to understand if you focus on
the results not the figure, as I have tried to do here "When skies are clear the proportion of the
celestial hemisphere P suitable for human polarimetric navigation based on perception of
Haidinger's brushes is high (insert P-value here; Figure 2). However, when the sky is overcast, P
approaches 0 making it infeasible for navigation by this means (Fig. 3)." NOTE I would reverse
the order in which these two points are presented and start with the positive situation in which
polarimetric navigation IS possible rather than starting with when it IS NOT.
Specific Comments
To preclude, I really like this work and think that it will be a valuable contribution to the field but
that it needs to be written in a way that makes it more accessible to the reader, so I have provided
numerous suggestions below.
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3
Page 1 Title
The title is long and not easily understandable, specifically the expression "sky-polarization
prerequisite" is not clear.
Please consider an alternative, for example a variation of:
Limits of human polarization perception support Viking navigation with the naked eye based on
celestial polarization patterns.
OR
Celestial polarization patterns sufficient for Viking Navigation with Haidinger's brushes.
OR
Viking navigation with Haidinger's brushes: assessment of the meteorological conditions and
proportion of the sky suitable based on human threshold for polarization perception.
Page 1 Line 25 (P1 L25) Here 'brush' is used rather than "brushes" I recommend brushes but pick
one and stick to it for consistency.
P1 L25 you have already said '8-shaped' and I am not sure that 'brush-like' is a good description, I
recall that the word brush was a poor translation of the German that was meant to be bushel, like
a bushel of wheat. A better description is 'bowtie-like' rather than 'brush-like'
P1 L25-28 This Sentence is long and difficult to understand with novel terminology that needs
defining upon first use.
"Since the celestial great circle passing through any sky point with high enough d-values and
parallel to the yellow Haidinger’s brush crosses the sun, if two such sky points are selected, the
sun position can be determined, which is at the intersection of the two great circles."
specifically you need to define or come up with a better description of "the celestial great circle"
And this statement is really unclear "passing through any sky point with high enough d-values
and parallel to the yellow Haidinger’s brush crosses the sun" please see if you can reword this.
The last part refers to "two great circles" but the first part makes it seem like there should only be
one "the celestial great circle".
Personally, I can see HB quite easily both in clear skies and in the forest when only a very small
portion of the clear sky is visible through the canopy, and I don't think it is necessary to talk
about 'great circles' but rather I think you could talk about a band of high degree of polarization
that arcs across the sky at about 90 degrees to the position of the sun and that a person could pick
two points on that band and observe the yellow brushes of HB and from that triangulate the
position of the sun based on the orientation of those two observed brushes. But equally it does
not need to be static observation. by sweeping your eye across the band of high DoP it is possible
to get a dynamic view of HB that point directly at the sun.
P1 L30 in addition to occlusion by cloud and fog, HB can also be used to locate the sun when it is
below the horizon or occluded by objects on the horizon.
P1 L30 the expression 'atmospheric optical prerequisite' is overly complicated, and this sentence
could be simplified to something like "In order to determine the position of the sun using the
celestial polarization pattern the d of the portion of the sky used, must be greater than the
viewers degree of polarization threshold (d*) for perception of Haidinger's brushes."
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4
P1 L34 remove the red and green here and throughout the paper (see general comment above)
P1 L36 recommend changing 'cloud percent' to 'cloud cover (in percentage)'
P1 L37 the statement 'We obtained that P is large enough only for the most sensitive human
observers having perception threshold d*min = 23 % of Haidinger's brushes." does not make
sense. "Large enough" for what?
P1 L38 no space required between the number and the percent symbol, whereas there is a space
required between a number and most of other units (e.g. nm) but not degree.
P1 L39 recommend change to 'with cloud coverage of p = 0%, when the sun's position is already
easily determined." delete "since it is visible with a big chance".
P1 L42 again what does 'P is large enough' mean?
if P is the proportion of the sky where d>d* then surely an observer only needs a couple of small
areas of the sky that are larger the 5 degrees in radius (size of HB perception) to observe HB and
detect the position of the sun, so if the d is high then only a small portion of the sky located near
the band of maximum d is required. So what does 'large enough' mean?
P1 L45 change 'great' to 'large'
P1 L48 because on-line search engines will search your title and abstract it is redundant to use
keywords that are already in your title and abstract in your list of keywords. Instead consider
using other words that a potential reader might use to search for similar articles. e.g. calcite,
orientation, sea-faring, orienteering, migration, vision, macula, macular pigment etc...
P1 L53 see comment above about 'brush-like'
could add that the two 8-shaped figures combine to form a Maltese cross shape
P1 L54 & L55 stick to the '8-shaped figure' or perhaps 'bowtie-like shape' as used elsewhere
P1 L55 delete 'well-known'. Haidinger's brushes are certainly not well known. I have been
interested in this subject for near 20 years and very few vision scientists, optometrist, visual
ecologist have ever heard of them and even few of the general population.
P2 L2 change to 'brushes' here and throughout.
P2 L2 suggest removing the word 'well' most people find it difficult to perceive HB at the best of
times, and even those of us that can see them consistently would not say they are easy to see or
are highly salient, it suffices to say that they can be perceived.
P2 L4 suggest change to "when large portions of the sky are red and orange, or when the sky is..."
P2 L11 correct 'treshold' to 'threshold'
P2 L10 it is much easier to read if words are used rather than equations e.g. 'Recently, Temple et
al [13] measured the degree of polarization threshold, d*, at which humans could just detect
Haidinger's brushes.
P2 L14 consider adding to this sentence as such "determined by the relative position of the
observer, the sun and the celestial point observed (Fig. 1)."
P2 L21 this 'celestial great circle' needs to be well defined earlier in the paper if it is going to be
used. Otherwise consider 'band of highest polarization'
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5
P2 L24 if is not clear why there are now 'two great circles'. I know what you are talking about but
it is not written clearly enough for someone slightly unfamiliar with the specifics to understand it
well enough. Furthermore there are no 'great circles' in your figure 1, nor should there be. I think
it easier to describe it somewhat as I have in my comment above re P1 L25-28.
P2 L34 change to 'they had their own analyser..."
P2 L43 change to past tense 'the aim of this work was to study'
P2 L44-45 remove red and green from here and the paper in general
P2 L47 change to 'percent cloud cover' here and throughout the manuscript
P2 L50 used past conditional past tense ' navigation could have been based on the perception...'
P3 L14 change to 'coverage of the visible sky estimated by visual examination [40].'
P3 L15 suggest 'refer to ever increasing cloud coverage'
P3 L24 spelling 'approximately'
P3 L30-32 this is a bit confusing, it is clear that there were 12 sun azimuth groups and 9 cloud
coverage groups, but what are the '12 different skies"? Are these just 12 examples/samples of
each of the above 108 groups? if so then this needs to me spelled out (described) more clearly.
P3 L32-34 delete reference to colour
P3 L43 consider 'probability that a viewer (Viking) with high, average and low sensitivity,
respectively, ...'
P3 L45 remove reference to colour
P3 L50 the statement says that the areas that were not sky were masked out but they still show up
in the figures (e.g. Fig 2 c,d, & e and 4 c,d & e) with red and blue regions suggesting under and
overexposed regions, but really this just detracts from the message you are trying to get accross,
so I recommend blacking out the non-sky regions in these images to remove the red a blue that is
not in the sky (the only part of interest here).
P3L57 see note in general comments about the order of presentation of results. Start with the
positive situation i.e. clear skies (section 3.2 rather than 3.1) and use full sentences that do not
start with "Figure X shows..."
Actually by the time you remove the parts of 3.1 and 3.2 that belong in discussion and remove the
reference to red and green the sections will be short enough that they can be combined into a
single section that just focuses on percent cloud cover.
P4 L9-12 this statement is interpretation of the results and therefore belongs in discussion section
not results.
P4 L16 change sentence so it does not start with "Figure 4A..."
P4 L22-29 this statement is interpretation of the results and therefore belongs in discussion
section not results.
P4 L31 consider changing to "sun elevation-cloud cover matrix..."
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6
P4 L33 change sentence so it does not start with "Figure 6..."
P4 L44 change sentence so it says something more like "A person having low polarization
sensitivity (e.g. d*max = 87%) can only detect HB under a select few meteorological conditions
(Fig 6; Supplementary table S3, S6, S9) and would therefore be an unlikely choice for a Viking
navigator."
In the discussion, you could suggest that Viking navigators were likely those that had the highest
polarization sensitivity (So move P4 L59 to discussion), you could also add that a diet rich in fish,
which is a good source of macular carotenoids, may have contributed to Viking's general ability
to see HB.
P4 L50 same as above.
P5L5-11 this paragraph is almost incomprehensible, it is written as an equation masquerading as
a sentence. Rewrite as a sentence with words rather than symbols.
P5 L20 This paragraph starts off well with clear words used to describe everything and then the
reader gets to this line that starts with <P>(θ,ρ), and gets totally lost. Please write out in words
what these symbols mean as you did in the first two sentences.
P5 L25 need to change this to blue since polarization sensitivity has nothing to do with the
human spectral sensitivity curve that peaks in green, and everything to do with the polarization
sensitivity, which is maximal at 460 nm (2nd sentence of Chapter 14 of your book Gábor that we
wrote together) due to absorption of macular pigments (Bone 1980 Vision research 20:213-220).
The statement that blue can be ignored is incorrect. In blue light the HB become clearer, and it is
thought that the yellow colour a person sees under full spectrum illumination is a psychophysical
effect of the eye where yellow is perceived when there is an absence of blue.
I agree that the blue brushes of HB are or little utility for navigation but that has nothing to do
with the spectral content of the sky.
P5 L31 & 34 again consider rewording the 'great circle passing the sun', especially the last part
'passing the sun' this does not make sense.
P5 L35-45 suggest changing to something like... "We found that the proportion of the sky suitable
for the humans with a high sensitivity to Haidinger's brushes (d*min = 23%) is high under
numerous meteorological conditions, particularly when the sun is low on the horizon and when
the sky is clear of cloud. When the sun is below the horizon, and therefore not possible to see or
accurately locate, the proportion of the sky suitable for sky polarimetric navigation is between
40% and 77% depending on cloud cover.
P5 L48 Need to define "3rd step" of just use the word-based description first and then put '3rd
step' in brackets and state that this is what they called it.
P5 L51 need to provide a very brief description of a twilight board and how it is used, or else this
statement is meaningless to the reader.
P6 L3 The few seconds before fading are irrelevant if you tilt your head back and forth while
looking at the sky and then use an object in the peripheral foreground (e.g. your arm) to point in
the direction of the yellow brushes.
P6 L11 You need to describe the 3 steps, otherwise the reader has no idea what you are referring
to.
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7
figures
Figures 3 and 5 are confusing. I am well aware of the topic but cannot easily determine what
these plots are showing
Again I have no idea what Figure 7 is attempting to show, and the associated text in the
manuscript P4 L41 does not help. Please write out in words what the statement you are
attempting to make is and then use the figure to support that statement. This is important
because you want your reader to understand your results and be able to use them, if not why
bother publishing.
Review form: Reviewer 2 (Barbara Webb)
Is the manuscript scientifically sound in its present form?
Yes
Are the interpretations and conclusions justified by the results?
Yes
Is the language acceptable?
Yes
Is it clear how to access all supporting data?
Yes
Do you have any ethical concerns with this paper?
No
Have you any concerns about statistical analyses in this paper?
No
Recommendation?
Accept with minor revision (please list in comments)
Comments to the Author(s)
This is an interesting paper that evaluates the hypothesis that Vikings could navigate using
polarisation patterns visible to the naked eye. This is assessed by using a large database of
recorded polarization levels in whole skies for different sun elevations and cloud cover
percentage, and comparing these to previously established thresholds for perception of
Haidinger's brushes.
The title seems overlong, Perhaps’delectability of polarization cues for navigation under varied
celestial conditions' would suffice?
The final sentence of the abstract wcould be clearer it rearranged - ‘is most useful after sunset and
prior to sunrise, when the sun is not visible and great sky' etc.
line 55- l don't think the brushes would be well known to the typical reader. This is also why I
suggest they are not featured in the title
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8
p.2 line 10, it would be helpful to say a bit more about the thresholds. E-g. what percentile of
tested subjects meet the most sensitive threshold? Or do they mean to say the lowest threshold
measured for any subject was 23%, and the highest 87%? Is the distribution symmetric enough for
the average to be meaningful? Briefly, how was the threshold determined?
line 46, could mention the latitude of the measurements here (and somewhere in the discussion
explain whether and how this might affect the polarisaton
the final sentence of the introduction is uninformative, either remove or give an indication of the
results.
p3 liner 5, delete "from which we selected 1296 different skies". The grouping happens before the
selection. It does not seem necessary to spell out all the ranges, or to use a numerical subscript
rather than one that contains the relevant information.
p4 line 3 (fig 3) I do not understand the description of this figure as plotting P(d*). It plots d
against % sky with at least that value of d. The thresholds d* could be included in the figure, as
vertical lines at the relevant valves. The same applies to fig 5.
P4 line 28, if the elevation shown is 0 (as stated on line 16) then the elevation is not >0, so it is not
clear what point is being made here. The sun is not visible in fig 4A.
P5 lines 5 onward, it is not clear what information should be taken from the variance or delta_P.
How might this affect the use of the method?
P6 lines 7 onward, is it beyond the scope of this paper to carry out the error propagation steps to
determine the practicality of the method?
Decision letter (RSOS-160688)
04-Jan-2017
Dear Dr Horvath
On behalf of the Editors, I am pleased to inform you that your Manuscript RSOS-160688 entitled
"Sky-polarization prerequisite of Viking navigation with Haidinger’s brushes" has been accepted
for publication in Royal Society Open Science subject to minor revision in accordance with the
referee suggestions. Please find the referees' comments at the end of this email.
The reviewers and handling editors have recommended publication, but also suggest some minor
revisions to your manuscript. Therefore, I invite you to respond to the comments and revise your
manuscript.
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9
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11
Reviewer comments to Author:
Reviewer: 1
Comments to the Author(s)
Comments to Authors
General Comments
This is a great analysis of the proportion of the sky that would be useful for human navigation
using celestial polarisation patterns relative to meteorological conditions.
My only major concern with the manuscript is the comparison of the three different wavelength
bands used. It is not necessary to provide all three colour bands, and in fact it detracts from the
story by making it more complicated than it needs to be. The entoptics phenomenon of
Haidinger's brushes is mediated by the absorption of short-wavelength light by the macular
carotenoids (lutien, zeaxanthin and meso-zeaxanthin) (Müller et al 2016, and Bone 1984) and is
not visible at wavelengths above about 500 nm, therefore the two colour bands in the green and
red are not useful for perception of polarization and therefore do not add to your argument.
Instead the extra data makes the story more confusing. If you remove the colour component you
can focus on the main effect in the blue and make the story more concise and more easily
accessible.
In case you are interested, the original experiments we did (Temple et al. 2015) were done with
humans looking at a modified LCD screen, however, I have since measured the human threshold
using a sheet of rotating polarizer combined with a series of my custom made depolarizing filters
and found that the human threshold is even lower than 23% we originally reported. Out of 20
people studied, four individuals could see HB down to 16% and one could go as low as 12%. In
this study the mean d* was 32.4% and the min was 70%. If you want to add these results to this
paper you could report them as unpublished data or personal communication. This work was
done as part of a preliminary experiment that showed a correlation between threshold for
detecting HB (d*) and macular pigment optical density (MPOD) measured on a dual wavelength
scanning laser ophthalmoscope (Heidelberg Spectralis). These results concur with recent findings
of Müller et al. 2016 (Müller PL, Müller S, Gliem M, et al. Perception of Haidinger brushes in
macular disease depends on macular pigment density and visual acuity. Invest Ophthalmol Vis
Sci. 2016;57:1448–1456. DOI:10.1167/ iovs.15-19004).
It is not helpful for the reader when sentences have too many equations (e.g. P5 L5-11 ) or are
written around a figure (e.g. start with "Figure x shows..."). It is much easier to read and
understand the point being made if the sentences are written in words and just tell the story,
leaving the equations and figures to the end to be put in parentheses e.g. Page 3 Line 56 "Figure 2
shows a totally overcast sky taken with our full-sky imaging polarimeter when the solar elevation
was θ = 0º and the cloud percent was ρ = 100 %." It is much easier to understand if you focus on
the results not the figure, as I have tried to do here "When skies are clear the proportion of the
celestial hemisphere P suitable for human polarimetric navigation based on perception of
Haidinger's brushes is high (insert P-value here; Figure 2). However, when the sky is overcast, P
approaches 0 making it infeasible for navigation by this means (Fig. 3)." NOTE I would reverse
the order in which these two points are presented and start with the positive situation in which
polarimetric navigation IS possible rather than starting with when it IS NOT.
Specific Comments
To preclude, I really like this work and think that it will be a valuable contribution to the field but
that it needs to be written in a way that makes it more accessible to the reader, so I have provided
numerous suggestions below.
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12
Page 1 Title
The title is long and not easily understandable, specifically the expression "sky-polarization
prerequisite" is not clear.
Please consider an alternative, for example a variation of:
Limits of human polarization perception support Viking navigation with the naked eye based on
celestial polarization patterns.
OR
Celestial polarization patterns sufficient for Viking Navigation with Haidinger's brushes.
OR
Viking navigation with Haidinger's brushes: assessment of the meteorological conditions and
proportion of the sky suitable based on human threshold for polarization perception.
Page 1 Line 25 (P1 L25) Here 'brush' is used rather than "brushes" I recommend brushes but pick
one and stick to it for consistency.
P1 L25 you have already said '8-shaped' and I am not sure that 'brush-like' is a good description, I
recall that the word brush was a poor translation of the German that was meant to be bushel, like
a bushel of wheat. A better description is 'bowtie-like' rather than 'brush-like'
P1 L25-28 This Sentence is long and difficult to understand with novel terminology that needs
defining upon first use.
"Since the celestial great circle passing through any sky point with high enough d-values and
parallel to the yellow Haidinger’s brush crosses the sun, if two such sky points are selected, the
sun position can be determined, which is at the intersection of the two great circles."
specifically you need to define or come up with a better description of "the celestial great circle"
And this statement is really unclear "passing through any sky point with high enough d-values
and parallel to the yellow Haidinger’s brush crosses the sun" please see if you can reword this.
The last part refers to "two great circles" but the first part makes it seem like there should only be
one "the celestial great circle".
Personally, I can see HB quite easily both in clear skies and in the forest when only a very small
portion of the clear sky is visible through the canopy, and I don't think it is necessary to talk
about 'great circles' but rather I think you could talk about a band of high degree of polarization
that arcs across the sky at about 90 degrees to the position of the sun and that a person could pick
two points on that band and observe the yellow brushes of HB and from that triangulate the
position of the sun based on the orientation of those two observed brushes. But equally it does
not need to be static observation. by sweeping your eye across the band of high DoP it is possible
to get a dynamic view of HB that point directly at the sun.
P1 L30 in addition to occlusion by cloud and fog, HB can also be used to locate the sun when it is
below the horizon or occluded by objects on the horizon.
P1 L30 the expression 'atmospheric optical prerequisite' is overly complicated, and this sentence
could be simplified to something like "In order to determine the position of the sun using the
celestial polarization pattern the d of the portion of the sky used, must be greater than the
viewers degree of polarization threshold (d*) for perception of Haidinger's brushes."
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13
P1 L34 remove the red and green here and throughout the paper (see general comment above)
P1 L36 recommend changing 'cloud percent' to 'cloud cover (in percentage)'
P1 L37 the statement 'We obtained that P is large enough only for the most sensitive human
observers having perception threshold d*min = 23 % of Haidinger's brushes." does not make
sense. "Large enough" for what?
P1 L38 no space required between the number and the percent symbol, whereas there is a space
required between a number and most of other units (e.g. nm) but not degree.
P1 L39 recommend change to 'with cloud coverage of p = 0%, when the sun's position is already
easily determined." delete "since it is visible with a big chance".
P1 L42 again what does 'P is large enough' mean?
if P is the proportion of the sky where d>d* then surely an observer only needs a couple of small
areas of the sky that are larger the 5 degrees in radius (size of HB perception) to observe HB and
detect the position of the sun, so if the d is high then only a small portion of the sky located near
the band of maximum d is required. So what does 'large enough' mean?
P1 L45 change 'great' to 'large'
P1 L48 because on-line search engines will search your title and abstract it is redundant to use
keywords that are already in your title and abstract in your list of keywords. Instead consider
using other words that a potential reader might use to search for similar articles. e.g. calcite,
orientation, sea-faring, orienteering, migration, vision, macula, macular pigment etc...
P1 L53 see comment above about 'brush-like'
could add that the two 8-shaped figures combine to form a Maltese cross shape
P1 L54 & L55 stick to the '8-shaped figure' or perhaps 'bowtie-like shape' as used elsewhere
P1 L55 delete 'well-known'. Haidinger's brushes are certainly not well known. I have been
interested in this subject for near 20 years and very few vision scientists, optometrist, visual
ecologist have ever heard of them and even few of the general population.
P2 L2 change to 'brushes' here and throughout.
P2 L2 suggest removing the word 'well' most people find it difficult to perceive HB at the best of
times, and even those of us that can see them consistently would not say they are easy to see or
are highly salient, it suffices to say that they can be perceived.
P2 L4 suggest change to "when large portions of the sky are red and orange, or when the sky is..."
P2 L11 correct 'treshold' to 'threshold'
P2 L10 it is much easier to read if words are used rather than equations e.g. 'Recently, Temple et
al [13] measured the degree of polarization threshold, d*, at which humans could just detect
Haidinger's brushes.
P2 L14 consider adding to this sentence as such "determined by the relative position of the
observer, the sun and the celestial point observed (Fig. 1)."
P2 L21 this 'celestial great circle' needs to be well defined earlier in the paper if it is going to be
used. Otherwise consider 'band of highest polarization'
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14
P2 L24 if is not clear why there are now 'two great circles'. I know what you are talking about but
it is not written clearly enough for someone slightly unfamiliar with the specifics to understand it
well enough. Furthermore there are no 'great circles' in your figure 1, nor should there be. I think
it easier to describe it somewhat as I have in my comment above re P1 L25-28.
P2 L34 change to 'they had their own analyser..."
P2 L43 change to past tense 'the aim of this work was to study'
P2 L44-45 remove red and green from here and the paper in general
P2 L47 change to 'percent cloud cover' here and throughout the manuscript
P2 L50 used past conditional past tense ' navigation could have been based on the perception...'
P3 L14 change to 'coverage of the visible sky estimated by visual examination [40].'
P3 L15 suggest 'refer to ever increasing cloud coverage'
P3 L24 spelling 'approximately'
P3 L30-32 this is a bit confusing, it is clear that there were 12 sun azimuth groups and 9 cloud
coverage groups, but what are the '12 different skies"? Are these just 12 examples/samples of
each of the above 108 groups? if so then this needs to me spelled out (described) more clearly.
P3 L32-34 delete reference to colour
P3 L43 consider 'probability that a viewer (Viking) with high, average and low sensitivity,
respectively, ...'
P3 L45 remove reference to colour
P3 L50 the statement says that the areas that were not sky were masked out but they still show up
in the figures (e.g. Fig 2 c,d, & e and 4 c,d & e) with red and blue regions suggesting under and
overexposed regions, but really this just detracts from the message you are trying to get accross,
so I recommend blacking out the non-sky regions in these images to remove the red a blue that is
not in the sky (the only part of interest here).
P3L57 see note in general comments about the order of presentation of results. Start with the
positive situation i.e. clear skies (section 3.2 rather than 3.1) and use full sentences that do not
start with "Figure X shows..."
Actually by the time you remove the parts of 3.1 and 3.2 that belong in discussion and remove the
reference to red and green the sections will be short enough that they can be combined into a
single section that just focuses on percent cloud cover.
P4 L9-12 this statement is interpretation of the results and therefore belongs in discussion section
not results.
P4 L16 change sentence so it does not start with "Figure 4A..."
P4 L22-29 this statement is interpretation of the results and therefore belongs in discussion
section not results.
P4 L31 consider changing to "sun elevation-cloud cover matrix..."
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15
P4 L33 change sentence so it does not start with "Figure 6..."
P4 L44 change sentence so it says something more like "A person having low polarization
sensitivity (e.g. d*max = 87%) can only detect HB under a select few meteorological conditions
(Fig 6; Supplementary table S3, S6, S9) and would therefore be an unlikely choice for a Viking
navigator."
In the discussion, you could suggest that Viking navigators were likely those that had the highest
polarization sensitivity (So move P4 L59 to discussion), you could also add that a diet rich in fish,
which is a good source of macular carotenoids, may have contributed to Viking's general ability
to see HB.
P4 L50 same as above.
P5L5-11 this paragraph is almost incomprehensible, it is written as an equation masquerading as
a sentence. Rewrite as a sentence with words rather than symbols.
P5 L20 This paragraph starts off well with clear words used to describe everything and then the
reader gets to this line that starts with <P>(θ,ρ), and gets totally lost. Please write out in words
what these symbols mean as you did in the first two sentences.
P5 L25 need to change this to blue since polarization sensitivity has nothing to do with the
human spectral sensitivity curve that peaks in green, and everything to do with the polarization
sensitivity, which is maximal at 460 nm (2nd sentence of Chapter 14 of your book Gábor that we
wrote together) due to absorption of macular pigments (Bone 1980 Vision research 20:213-220).
The statement that blue can be ignored is incorrect. In blue light the HB become clearer, and it is
thought that the yellow colour a person sees under full spectrum illumination is a psychophysical
effect of the eye where yellow is perceived when there is an absence of blue.
I agree that the blue brushes of HB are or little utility for navigation but that has nothing to do
with the spectral content of the sky.
P5 L31 & 34 again consider rewording the 'great circle passing the sun', especially the last part
'passing the sun' this does not make sense.
P5 L35-45 suggest changing to something like... "We found that the proportion of the sky suitable
for the humans with a high sensitivity to Haidinger's brushes (d*min = 23%) is high under
numerous meteorological conditions, particularly when the sun is low on the horizon and when
the sky is clear of cloud. When the sun is below the horizon, and therefore not possible to see or
accurately locate, the proportion of the sky suitable for sky polarimetric navigation is between
40% and 77% depending on cloud cover.
P5 L48 Need to define "3rd step" of just use the word-based description first and then put '3rd
step' in brackets and state that this is what they called it.
P5 L51 need to provide a very brief description of a twilight board and how it is used, or else this
statement is meaningless to the reader.
P6 L3 The few seconds before fading are irrelevant if you tilt your head back and forth while
looking at the sky and then use an object in the peripheral foreground (e.g. your arm) to point in
the direction of the yellow brushes.
P6 L11 You need to describe the 3 steps, otherwise the reader has no idea what you are referring
to.
figures
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16
Figures 3 and 5 are confusing. I am well aware of the topic but cannot easily determine what
these plots are showing
Again I have no idea what Figure 7 is attempting to show, and the associated text in the
manuscript P4 L41 does not help. Please write out in words what the statement you are
attempting to make is and then use the figure to support that statement. This is important
because you want your reader to understand your results and be able to use them, if not why
bother publishing.
Reviewer: 2
Comments to the Author(s)
This is an interesting paper that evaluates the hypothesis that Vikings could navigate using
polarisation patterns visible to the naked eye. This is assessed by using a large database of
recorded polarization levels in whole skies for different sun elevations and cloud cover
percentage, and comparing these to previously established thresholds for perception of
Haidinger's brushes.
The title seems overlong, Perhaps’delectability of polarization cues for navigation under varied
celestial conditions' would suffice?
The final sentence of the abstract wcould be clearer it rearranged - ‘is most useful after sunset and
prior to sunrise, when the sun is not visible and great sky' etc.
line 55- l don't think the brushes would be well known to the typical reader. This is also why I
suggest they are not featured in the title
p.2 line 10, it would be helpful to say a bit more about the thresholds. E-g. what percentile of
tested subjects meet the most sensitive threshold? Or do they mean to say the lowest threshold
measured for any subject was 23%, and the highest 87%? Is the distribution symmetric enough for
the average to be meaningful? Briefly, how was the threshold determined?
line 46, could mention the latitude of the measurements here (and somewhere in the discussion
explain whether and how this might affect the polarisaton
the final sentence of the introduction is uninformative, either remove or give an indication of the
results.
p3 liner 5, delete "from which we selected 1296 different skies". The grouping happens before the
selection. It does not seem necessary to spell out all the ranges, or to use a numerical subscript
rather than one that contains the relevant information.
p4 line 3 (fig 3) I do not understand the description of this figure as plotting P(d*). It plots d
against % sky with at least that value of d. The thresholds d* could be included in the figure, as
vertical lines at the relevant valves. The same applies to fig 5.
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17
P4 line 28, if the elevation shown is 0 (as stated on line 16) then the elevation is not >0, so it is not
clear what point is being made here. The sun is not visible in fig 4A.
P5 lines 5 onward, it is not clear what information should be taken from the variance or delta_P.
How might this affect the use of the method?
P6 lines 7 onward, is it beyond the scope of this paper to carry out the error propagation steps to
determine the practicality of the method?
Author's Response to Decision Letter for (RSOS-160688)
See Appendix A.
Decision letter (RSOS-160688.R1)
09-Jan-2017
Dear Dr Horvath,
I am pleased to inform you that your manuscript entitled "Sky-polarimetric Viking navigation
with Haidinger’s brushes" is now accepted for publication in Royal Society Open Science.
You can expect to receive a proof of your article in the near future. Please contact the editorial
office ([email protected] and [email protected]) to let us know if
you are likely to be away from e-mail contact. Due to rapid publication and an extremely tight
schedule, if comments are not received, your paper may experience a delay in publication.
Royal Society Open Science operates under a continuous publication model
(http://bit.ly/cpFAQ). Your article will be published straight into the next open issue and this
will be the final version of the paper. As such, it can be cited immediately by other researchers.
As the issue version of your paper will be the only version to be published I would advise you to
check your proofs thoroughly as changes cannot be made once the paper is published.
In order to raise the profile of your paper once it is published, we can send through a PDF of your
paper to selected colleagues. If you wish to take advantage of this, please reply to this email with
the name and email addresses of up to 10 people who you feel would wish to read your article.
On behalf of the Editors of Royal Society Open Science, we look forward to your continued
contributions to the Journal.
Best wishes,
Alice Power
Editorial Coordinator
Royal Society Open Science
[email protected]
Appendix A
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Dear Editorial Office of the Royal Soceity Open Science,
I would like to submit our revised manuscript RSOS-160688_R1 entitled
Celestial polarization patterns sufficient for Viking navigation with the naked eye: detectability
of Haidinger's brushes on the sky versus meteorological conditions
by Gabor Horvath, Peter Takacs, Balazs Kretzer, Szilvia Szilasi, Denes Szaz, Alexandra Farkas,
Andras Barta
to the Royal Society Open Science as a research article.
Our manuscript was revised on the basis of the reports of two Reviewers. All relevant changes
performed on the basis of the comments of Referee 1 and Referee 2 are marked by violet and green,
respectively. Here we give our response to the points of Reviewer 1.
Our Point-by-Point Response to the Comments of Reviewers 1 and 2 can be found below.
Sincerely yours: Gabor Horvath (corresponding author)
Dr. Gabor Horvath (D.Sc.)
Environmental Optics Laboratory,
Department of Biological Physics,
Physical Institute,
Eötvös University,
H-1117 Budapest, Pazmany setany 1, Hungary
e-mail: [email protected]
http://arago.elte.hu
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Point-by-Point Response to the Comments of Reviewer 1
We thank for the positive and constructive comments of Referee 1. Our manuscript was revised on the
basis of the reports of two Reviewers. All relevant changes performed on the basis of the comments of
Referee 1 and Referee 2 are marked by violet and green, respectively. Here we give our response to the
points of Reviewer 1.
Referee 1 wrote: My only major concern with the manuscript is the comparison of the three different
wavelength bands used. It is not necessary to provide all three colour bands, and in fact it detracts
from the story by making it more complicated than it needs to be. The entoptics phenomenon of
Haidinger's brushes is mediated by the absorption of short-wavelength light by the macular
carotenoids (lutien, zeaxanthin and meso-zeaxanthin) (Müller et al 2016, and Bone 1984) and is not
visible at wavelengths above about 500 nm, therefore the two colour bands in the green and red are not
useful for perception of polarization and therefore do not add to your argument. Instead the extra data
makes the story more confusing. If you remove the colour component you can focus on the main effect
in the blue and make the story more concise and more easily accessible.
Answer: As suggested, in our revised paper we limited our study onto the blue (450 nm) spectral
range. The text, tables and figures were changed accordingly.
Referee 1 wrote: In case you are interested, the original experiments we did (Temple et al. 2015) were
done with humans looking at a modified LCD screen, however, I have since measured the human
threshold using a sheet of rotating polarizer combined with a series of my custom made depolarizing
filters and found that the human threshold is even lower than 23% we originally reported. Out of 20
people studied, four individuals could see HB down to 16% and one could go as low as 12%. In this
study the mean d* was 32.4% and the min was 70%. If you want to add these results to this paper you
could report them as unpublished data or personal communication. This work was done as part of a
preliminary experiment that showed a correlation between threshold for detecting HB (d*) and
macular pigment optical density (MPOD) measured on a dual wavelength scanning laser
ophthalmoscope (Heidelberg Spectralis). These results concur with recent findings of Müller et al.
2016 (Müller PL, Müller S, Gliem M, et al. Perception of Haidinger brushes in macular disease
depends on macular pigment density and visual acuity. Invest Ophthalmol Vis Sci. 2016;57:1448–
1456. DOI:10.1167/ iovs.15-19004).
Answer: Your preliminary results mentioned above were not included into our revised manuscript. We
wait for their publication.
Referee 1 wrote: It is not helpful for the reader when sentences have too many equations (e.g. P5 L511 ) or are written around a figure (e.g. start with "Figure x shows..."). It is much easier to read and
understand the point being made if the sentences are written in words and just tell the story, leaving the
equations and figures to the end to be put in parentheses e.g. Page 3 Line 56 "Figure 2 shows a totally
overcast sky taken with our full-sky imaging polarimeter when the solar elevation was θ = 0º and the
cloud percent was ρ = 100 %." It is much easier to understand if you focus on the results not the figure,
as I have tried to do here "When skies are clear the proportion of the celestial hemisphere P suitable
for human polarimetric navigation based on perception of Haidinger's brushes is high (insert P-value
here; Figure 2). However, when the sky is overcast, P approaches 0 making it infeasible for navigation
by this means (Fig. 3)." NOTE I would reverse the order in which these two points are presented and
start with the positive situation in which polarimetric navigation IS possible rather than starting with
when it IS NOT.
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Answer: The order of overcast and clear skies was reversed, and the text was changed as suggested.
Referee 1 wrote: Page 1 Title: The title is long and not easily understandable, specifically the
expression "sky-polarization prerequisite" is not clear. Please consider an alternative, for example a
variation of:
Limits of human polarization perception support Viking navigation with the naked eye based on
celestial polarization patterns
OR
Celestial polarization patterns sufficient for Viking Navigation with Haidinger's brushes
OR
Viking navigation with Haidinger's brushes: assessment of the meteorological conditions and
proportion of the sky suitable based on human threshold for polarization perception
Answer: Taking into consideration the suggestions of both Referees, the new title is:
Celestial polarization patterns sufficient for Viking navigation with the naked eye:
detectability of Haidinger's brushes on the sky versus meteorological conditions
Referee 1 wrote: Page 1 Line 25 (P1 L25) Here 'brush' is used rather than "brushes". I recommend
brushes but pick one and stick to it for consistency.
P1 L25 you have already said '8-shaped' and I am not sure that 'brush-like' is a good description, I
recall that the word brush was a poor translation of the German that was meant to be bushel, like a
bushel of wheat. A better description is 'bowtie-like' rather than 'brush-like'
Answer: These changes were done in the revised manuscript.
Referee 1 wrote: P1 L25-28 This Sentence is long and difficult to understand with novel terminology
that needs defining upon first use. "Since the celestial great circle passing through any sky point with
high enough d-values and parallel to the yellow Haidinger’s brush crosses the sun, if two such sky
points are selected, the sun position can be determined, which is at the intersection of the two great
circles." Specifically you need to define or come up with a better description of "the celestial great
circle". And this statement is really unclear "passing through any sky point with high enough d-values
and parallel to the yellow Haidinger’s brush crosses the sun" please see if you can reword this. The
last part refers to "two great circles" but the first part makes it seem like there should only be one "the
celestial great circle". Personally, I can see HB quite easily both in clear skies and in the forest when
only a very small portion of the clear sky is visible through the canopy, and I don't think it is necessary
to talk about 'great circles' but rather I think you could talk about a band of high degree of polarization
that arcs across the sky at about 90 degrees to the position of the sun and that a person could pick two
points on that band and observe the yellow brushes of HB and from that triangulate the position of the
sun based on the orientation of those two observed brushes. But equally it does not need to be static
observation. by sweeping your eye across the band of high DoP it is possible to get a dynamic view of
HB that point directly at the sun.
Answer: This sentence was rewritten as follows:
’A band of high d arcs across the sky at 90o from the sun. A person can pick two points on that band,
observe the yellow brushes, and triangulate the position of the sun based on the orientation of the two
observed brushes.’
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Referee 1 wrote: P1 L30 in addition to occlusion by cloud and fog, HB can also be used to locate the
sun when it is below the horizon or occluded by objects on the horizon.
Answer: The following sentence was here added:
’Furthermore, Haidinger’s brushes can also be used to locate the sun when it is below the horizon or
occluded by objects on the horizon.’
Referee 1 wrote: P1 L30 the expression 'atmospheric optical prerequisite' is overly complicated, and
this sentence could be simplified to something like "In order to determine the position of the sun using
the celestial polarization pattern the d of the portion of the sky used, must be greater than the viewers
degree of polarization threshold (d*) for perception of Haidinger's brushes."
Answer: This change was performed.
Referee 1 wrote: P1 L34 remove the red and green here and throughout the paper (see general
comment above)
P1 L36 recommend changing 'cloud percent' to 'cloud cover (in percentage)'
Answer: As suggested, red and green data were deleted throughout the paper.
Referee 1 wrote: P1 L37 the statement 'We obtained that P is large enough only for the most sensitive
human observers having perception threshold d*min = 23 % of Haidinger's brushes." does not make
sense. "Large enough" for what?
Answer: This sentence was deleted.
Referee 1 wrote: P1 L38 no space required between the number and the percent symbol, whereas
there is a space required between a number and most of other units (e.g. nm) but not degree.
Answer: These changes were done throughout the revised manuscript..
Referee 1 wrote: P1 L39 recommend change to 'with cloud coverage of p = 0%, when the sun's
position is already easily determined." delete "since it is visible with a big chance".
Answer: These changes were done.
Referee 1 wrote: P1 L42 again what does 'P is large enough' mean? If P is the proportion of the sky
where d>d* then surely an observer only needs a couple of small areas of the sky that are larger the 5
degrees in radius (size of HB perception) to observe HB and detect the position of the sun, so if the d is
high then only a small portion of the sky located near the band of maximum d is required. So what does
'large enough' mean?
Answer: This sentence was rewritten as follows:
’If the sun is below the horizon (–5o ≤ θ < 0°) during twilight, P = 76.17 ± 4.18% for d*min = 23%
under clear sky conditions.’
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Referee 1 wrote: P1 L45 change 'great' to 'large'
Answer: This change was done.
Referee 1 wrote: P1 L48 because on-line search engines will search your title and abstract it is
redundant to use keywords that are already in your title and abstract in your list of keywords. Instead
consider using other words that a potential reader might use to search for similar articles. e.g. calcite,
orientation, sea-faring, orienteering, migration, vision, macula, macular pigment etc...
Answer: We kept the original keywords, because the suggested ones are not typical for the content of
our paper. However, we added the keyword human polarization vision.
Referee 1 wrote: P1 L53 see comment above about 'brush-like'. Could add that the two 8-shaped
figures combine to form a Maltese cross shape
P1 L54 & L55 stick to the '8-shaped figure' or perhaps 'bowtie-like shape' as used elsewhere
Answer: These changes were done.
Referee 1 wrote: P1 L55 delete 'well-known'. Haidinger's brushes are certainly not well known. I have
been interested in this subject for near 20 years and very few vision scientists, optometrist, visual
ecologist have ever heard of them and even few of the general population.
Answer: In this sentence ’well-known’ was replaced by ’so-called’.
Referee 1 wrote: P2 L2 change to 'brushes' here and throughout.
P2 L2 suggest removing the word 'well' most people find it difficult to perceive HB at the best of times,
and even those of us that can see them consistently would not say they are easy to see or are highly
salient, it suffices to say that they can be perceived.
P2 L4 suggest change to "when large portions of the sky are red and orange, or when the sky is..."
P2 L11 correct 'treshold' to 'threshold'
P2 L10 it is much easier to read if words are used rather than equations e.g. 'Recently, Temple et al
[13] measured the degree of polarization threshold, d*, at which humans could just detect Haidinger's
brushes.
P2 L14 consider adding to this sentence as such "determined by the relative position of the observer,
the sun and the celestial point observed (Fig. 1)."
Answer: All these changes were done.
Referee 1 wrote: P2 L21 this 'celestial great circle' needs to be well defined earlier in the paper if it is
going to be used. Otherwise consider 'band of highest polarization'
P2 L24 if is not clear why there are now 'two great circles'. I know what you are talking about but it is
not written clearly enough for someone slightly unfamiliar with the specifics to understand it well
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enough. Furthermore there are no 'great circles' in your figure 1, nor should there be. I think it easier
to describe it somewhat as I have in my comment above re P1 L25-28.
Answer: Referee 1 mistakes here two quite different concepts: The band of highest degrees of
polarization is at 90o from the sun, and has nothing to do with a spherical geometric celestial great
circle passing through a given sky point. The concept ’great circle’ is used only in this paragraph, and
its meaning should be clear in Figure 1.
Referee 1 wrote: P2 L34 change to 'they had their own analyser..."
P2 L43 change to past tense 'the aim of this work was to study'
P2 L44-45 remove red and green from here and the paper in general
P2 L47 change to 'percent cloud cover' here and throughout the manuscript
P3 L14 change to 'coverage of the visible sky estimated by visual examination [40].'
P3 L15 suggest 'refer to ever increasing cloud coverage'
P3 L24 spelling 'approximately'
Answer: All these changes were done.
Referee 1 wrote: P3 L30-32 this is a bit confusing, it is clear that there were 12 sun azimuth groups
and 9 cloud coverage groups, but what are the '12 different skies"? Are these just 12 examples/samples
of each of the above 108 groups? If so then this needs to me spelled out (described) more clearly.
Answer: This sentence was changed as follows:
’Thus, we created 12 × 9 = 108 (θ, ρ) groups. In each group we selected 12 different sky samples (with
θ- and ρ-values falling into the θ- and ρ-interval of the given group) from our polarimetric sky
archives.’
Referee 1 wrote: P3 L32-34 delete reference to colour
P3 L43 consider 'probability that a viewer (Viking) with high, average and low sensitivity, respectively,
...'
P3 L45 remove reference to colour
Answer: Done.
Referee 1 wrote: P3 L50 the statement says that the areas that were not sky were masked out but they
still show up in the figures (e.g. Fig 2 c,d, & e and 4 c,d & e) with red and blue regions suggesting
under and overexposed regions, but really this just detracts from the message you are trying to get
accross, so I recommend blacking out the non-sky regions in these images to remove the red a blue that
is not in the sky (the only part of interest here).
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Answer: In the patterns of the degree of polarization d, black means d = 100%, thus the non-sky
regions as well as the under- and overexposed celestial areas cannot be blacked out, otherwise the
reader could think that these regions and areas are also maximally polarized. Thus, we kept the original
d-patterns with blue (underexposed) and red (overexposed) colours. This is our traditional colour code
used in our numerous publications presenting polarization patterns.
Referee 1 wrote: P3 L57 see note in general comments about the order of presentation of results. Start
with the positive situation i.e. clear skies (section 3.2 rather than 3.1) and use full sentences that do not
start with "Figure X shows..."
Actually by the time you remove the parts of 3.1 and 3.2 that belong in discussion and remove the
reference to red and green the sections will be short enough that they can be combined into a single
section that just focuses on percent cloud cover.
P4 L9-12 this statement is interpretation of the results and therefore belongs in discussion section not
results.
P4 L16 change sentence so it does not start with "Figure 4A..."
P4 L22-29 this statement is interpretation of the results and therefore belongs in discussion section not
results.
P4 L31 consider changing to "sun elevation-cloud cover matrix..."
P4 L33 change sentence so it does not start with "Figure 6..."
P4 L44 change sentence so it says something more like "A person having low polarization sensitivity
(e.g. d*max = 87%) can only detect HB under a select few meteorological conditions (Fig 6;
Supplementary table S3, S6, S9) and would therefore be an unlikely choice for a Viking navigator."
In the discussion, you could suggest that Viking navigators were likely those that had the highest
polarization sensitivity (So move P4 L59 to discussion), you could also add that a diet rich in fish,
which is a good source of macular carotenoids, may have contributed to Viking's general ability to see
HB.
P4 L50 same as above.
P5 L5-11 this paragraph is almost incomprehensible, it is written as an equation masquerading as a
sentence. Rewrite as a sentence with words rather than symbols.
P5 L20 This paragraph starts off well with clear words used to describe everything and then the reader
gets to this line that starts with <P>(θ,ρ), and gets totally lost. Please write out in words what these
symbols mean as you did in the first two sentences.
Answer: These changes were done.
Referee 1 wrote: P5 L25 need to change this to blue since polarization sensitivity has nothing to do
with the human spectral sensitivity curve that peaks in green, and everything to do with the
polarization sensitivity, which is maximal at 460 nm (2nd sentence of Chapter 14 of your book Gábor
that we wrote together) due to absorption of macular pigments (Bone 1980 Vision research 20:213-
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220). The statement that blue can be ignored is incorrect. In blue light the HB become clearer, and it is
thought that the yellow colour a person sees under full spectrum illumination is a psychophysical effect
of the eye where yellow is perceived when there is an absence of blue.
I agree that the blue brushes of HB are or little utility for navigation but that has nothing to do with the
spectral content of the sky.
P5 L31 & 34 again consider rewording the 'great circle passing the sun', especially the last part
'passing the sun' this does not make sense.
Answer: This paragraph was revised in the following way:
’In the analysis of the proportion P of the sky for which the degree d of sky polarization is larger than
the perception threshold d* (= 23, 56, 87%), the most important spectral range is the blue, in which the
human eye perceives Haidinger’s brushes with a maximal sensitivity at 460 nm due to absorption of
macular pigments [39]. In blue light the Haidinger’s brushes become clearer, and it is thought that the
yellow colour a person sees under full spectrum illumination is a psychophysical effect of the eye
where yellow is perceived when there is an absence of blue [1,2]. Thus, our study was restricted to this
part of the spectrum. We obtained that the mean <P> of P is large only for the most sensitive-eyed
human observers (Viking navigators) having a perception threshold d*min = 23% of Haidinger’s
brushes. Viking navigators were likely those that had the highest polarization sensitivity (i.e. having the
lowest threshold d*). A diet rich in fish, which is a good source of macular carotenoids, may have
contributed to Viking's general ability to see Haidinger’s brushes (Shelby Temple, personal
communication).’
Referee 1 wrote: P5 L35-45 suggest changing to something like... "We found that the proportion of the
sky suitable for the humans with a high sensitivity to Haidinger's brushes (d*min = 23%) is high under
numerous meteorological conditions, particularly when the sun is low on the horizon and when the sky
is clear of cloud. When the sun is below the horizon, and therefore not possible to see or accurately
locate, the proportion of the sky suitable for sky polarimetric navigation is between 40% and 77%
depending on cloud cover.
Answer: This change was done.
Referee 1 wrote: P5 L48 Need to define "3rd step" of just use the word-based description first and
then put '3rd step' in brackets and state that this is what they called it.
Answer: This sentence was revised as follows:
’This finding corresponds to the results of Száz et al. [38], who also found that regarding the estimation
of solar elevation angle with numbers of fist and finger of outstretched arms in the the third step of skypolarimetric Viking navigation, the most appropriate time for navigation is around sunset and sunrise.’
Referee 1 wrote: P5 L51 need to provide a very brief description of a twilight board and how it is
used, or else this statement is meaningless to the reader.
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Answer: All details of the rather complicated use of a twilight board, a shadow-stick and sunstone
crystals are described in the cited paper of Bernáth et al. [31]. The only important issue here is that this
method functions well at twilight. Thus, we omitted a very brief description of a twilight board and
how it is used.
[31] Bernáth B, Farkas A, Száz D, Blahó M, Egri Á, Barta A, Åkesson S, Horváth G (2014) How could
the Viking sun compass be used with sunstones before and after sunset? Twilight board as a new
interpretation of the Uunartoq artefact fragment. Proceedings of the Royal Society A 470: article
number 20130787
This paragraph was slightly rewritten as follows:
’The navigation method deduced by Bernáth et al. [31] based on the Uunartoq artefact fragment
functioning as a twilight board is useful also during twilight and under clear skies, when the sun is
close to the horizon (when −8° ≤ θ ≤ +10°). Using a twilight board, a shadow-stick and sunstone
crystals could have allowed Vikings to navigate during long twilight periods on the basis of
polarization patterns of clear skies. Based on our results in this paper, we can conclude, that
birefringent (e.g. calcite) or dichroic (e.g. tourmaline or cordierite) sunstone crystals could be replaced
with Haidinger’s brushes in the sky-polarimetric Viking navigation.’
Referee 1 wrote: P6 L3 The few seconds before fading are irrelevant if you tilt your head back and
forth while looking at the sky and then use an object in the peripheral foreground (e.g. your arm) to
point in the direction of the yellow brushes.
Answer: The criticized sentences were revised in the following way:
’For example, it is questionable whether the few seconds prior to fading of the Haidinger’s brushes
when looking at the polarized sky with a fixed head are enough to determine the position of the
occluded sun in the sky. However, this few seconds before fading are irrelevant, if our head is tilted
periodically back and forth while looking at the sky and then we use an object in the peripheral
foreground (e.g. our arm) to point in the direction of the yellow Haidinger’s brushes. Nevertheless, it
would be worth studying the accuracy and reliability of Viking navigation based on Haidinger’s
brushes under real open air conditions.’
Referee 1 wrote: P6 L11 You need to describe the 3 steps, otherwise the reader has no idea what you
are referring to.
Answer: This sentence was rewritten as follows:
’Such computations have been presented by Farkas et al. [34] and Száz et al. [37,38] for this navigation
method using dichroic and birefringent sunstone crystals.’
Referee 1 wrote: Figures 3 and 5 are confusing. I am well aware of the topic but cannot easily
determine what these plots are showing
Answer: The original Figs. 3 and 5 were merged to the present Fig. 3 with a more understandable
legend.
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Referee 1 wrote: Again I have no idea what Figure 7 is attempting to show, and the associated text in
the manuscript P4 L41 does not help. Please write out in words what the statement you are attempting
to make is and then use the figure to support that statement. This is important because you want your
reader to understand your results and be able to use them, if not why bother publishing.
Answer: About Fig. 4B (originally Fig. 7) in our revised manuscript we wrote:
’The most sensitive persons (d*min = 23%) possess the widest range of the standard deviation (1.97% ≤
ΔP ≤ 29.66%) for medium percents of cloud cover ρ ≤ 75% and solar elevations not larger than 35º
(Fig. 4B, Table 4). Persons with an average sensitivity (d*ave = 56%) have small standard deviations
(3.14% ≤ ΔP ≤ 10.26%) for smaller percents of cloud cover ρ ≤ 25% and lower solar elevations θ ≤ 15º
(Fig. 4B, Table 5). For the least polarization-sensitive persons (with d*max = 87%) the standard
deviations of <P> are practically zero (ΔP ≤ 0.2681%; Fig. 4B, Table 6). The larger the standard
deviation ΔP at a given meteorological situation (θ-ρ cell), the smaller the reliability of the navigation
method based on Haidinger’s brushes under that sky conditions.’
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Point-by-Point Response to the Comments of Reviewer 2
We thank for the positive and constructive comments of Referee 2. Our manuscript was revised on the
basis of the reports of two Reviewers. All relevant changes performed on the basis of the comments of
Referee 1 and Referee 2 are marked by violet and green, respectively. Here we give our response to the
points of Reviewer 2.
Referee 2 wrote: The title seems overlong, Perhaps ’detectability of polarization cues for navigation
under varied celestial conditions' would suffice?
Answer: Taking into consideration the suggestions of both Referees, the new title is:
Celestial polarization patterns sufficient for Viking navigation with the naked eye:
detectability of Haidinger's brushes on the sky versus meteorological conditions
Referee 2 wrote: The final sentence of the abstract could be clearer it rearranged - ‘is most useful
after sunset and prior to sunrise, when the sun is not visible and great sky' etc.
Answer: This sentence was rewritten as follows:
’Consequently, the sky-polarimetric Viking navigation based on Haidinger’s brushes is most useful
after sunset and prior to sunrise, when the sun is not visible and large sky regions are bright, clear and
polarized enough for perception of Haidinger’s brushes.’
Referee 2 wrote: line 55, I don't think the brushes would be well known to the typical reader. This is
also why I suggest they are not featured in the title.
Answer: The criticized word ’well-known’ was replaced by so-called:
’These are the so-called Haidinger’s brushes, the angular extension of which is about 5o centered at the
fovea of the human retina, and are mediated by dichroic carotenoids in the macula lutea [1-7].’
However, we kept ’Haidinger’s brushes’ in the title, because they are the main subject of this paper.
Referee 2 wrote: p.2 line 10, it would be helpful to say a bit more about the thresholds. E-g. what
percentile of tested subjects meet the most sensitive threshold? Or do they mean to say the lowest
threshold measured for any subject was 23%, and the highest 87%? Is the distribution symmetric
enough for the average to be meaningful? Briefly, how was the threshold determined?
Answer: As requested, in the revised Introduction we added the following:
’Recently, Temple et al. [13] measured the degree of polarization threshold d*, at which humans could
just detect Haidinger's brushes. They presented gratings in polarization-only contrast at varying degrees
of polarization d in order to measure the lower limits of human polarized light detection. Participants
were, on average, able to perform the task down to a threshold of d*ave = 56 ± 3%, and there was a
normal continuous distribution of threshold values extending down to as low as d*min = 23% and up to
as high as d*max = 87% [13].’
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Referee 2 wrote: line 46, could mention the latitude of the measurements here and somewhere in the
discussion explain whether and how this might affect the polarisaton.
Answer: As requested, in the revised Introduction we wrote:
’Using full-sky imaging polarimetry, we measured the d-pattern of skylight in the blue (450 nm)
spectral range for 1296 different meteorological conditions with different solar elevation angles θ and
percent cloud cover ρ in Hungary (at latitude 47° 15' 29.83” N).’
In the revised Discussion we wrote:
’Although we measured the sky polarization for 1296 meteorological situations with different solar
elevations θ and cloudinesses ρ in Hungary at latitude 47° 15' 29.83” N, this might not affect
considerably sky polarizaton, because for a given ρ, celestial polarization depends predominantly on θ,
and we restricted our measurements to solar elevations –5o ≤ θ ≤ +55o occurring at 61o latitude where
the main Viking sailing route ran. The range 0 okta ≤ ρ ≤ 8 oktas used by us covered the whole range
of cloudiness that can also occur at 61o latitude.’
Referee 2 wrote: The final sentence of the introduction is uninformative, either remove or give an
indication of the results.
Answer: As suggested, this sentence was deleted.
Referee 2 wrote: p3 line 5, delete "from which we selected 1296 different skies". The grouping
happens before the selection. It does not seem necessary to spell out all the ranges, or to use a
numerical subscript rather than one that contains the relevant information.
Answer: The criticized sentence part was deleted.
Referee 2 wrote: p4 line 3 (fig 3) I do not understand the description of this figure as plotting P(d*). It
plots d against % sky with at least that value of d. The thresholds d* could be included in the figure, as
vertical lines at the relevant values. The same applies to fig 5.
Answer: The legend of Figure 3 (being merged with Fig. 5) was revised as suggested:
’Figure 3: Proportion P (%) of the clear and overcast skies in Fig. 2 with degrees of skylight
polarization not lower than d in the blue (450 nm) spectral range. The vertical lines show the values d*
= 23, 56, 87% being the three characteristic perception thresholds of Haidinger’s brushes.’
Referee 2 wrote: P4 line 28, if the elevation shown is 0 (as stated on line 16) then the elevation is not
> 0, so it is not clear what point is being made here. The sun is not visible in fig 4A.
Answer: Referee 2 is right, therefore the criticized following sentence was deleted:
’However, in this case this would have been unnecessary, because the sun is visible under clear sky
conditions, if the solar elevation θ > 0º.’
Referee 2 wrote: P5 lines 5 onward, it is not clear what information should be taken from the variance
or delta_P. How might this affect the use of the method?
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Answer: At the end the Results section we added:
’The larger the standard deviation ΔP at a given meteorological situation (θ-ρ cell), the smaller the
reliability of the navigation method based on Haidinger’s brushes under that sky conditions.’
Referee 2 wrote: P6 lines 7 onward, is it beyond the scope of this paper to carry out the error
propagation steps to determine the practicality of the method?
Answer: At the end of the revised Discussion we wrote:
’It is beyond the scope of this paper to carry out such error propagation to determine the practicality of
the navigation method based on Haidinger’s brushes. This can be an interesting task of future research.’