Abstract

Using full-sky imaging polarimetry, we measured the celestial distribution of polarization during sunset and sunrise at partial (78% and 72%) and full (100%) moon in the red (650 nm), green (550 nm), and blue (450 nm) parts of the spectrum. We investigated the temporal change of the patterns of degree p and angle α of linear polarization of sunlit and moonlit skies at dusk and dawn. We describe here the position change of the neutral points of sky polarization, and present video clips about the celestial polarization transition at moonlit twilight. We found that at partial moon and at a medium latitude (47° 15.481′ N) during this transition there is a relatively short (10–20 min) period when (i) the maximum of p of skylight decreases, and (ii) from the celestial α pattern neither the solar–antisolar nor the lunar–antilunar meridian can be unambiguously determined. These meridians can serve as reference directions of animal orientation and Viking navigation based on sky polarization. The possible influence of these atmospheric optical phenomena during the polarization transition between sunlit and moonlit skies on the orientation of polarization-sensitive crepuscular/nocturnal animals and the hypothesized navigation of sunstone-aided Viking seafarers is discussed.

© 2014 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2013 (2)

B. Bernáth, M. Blahó, Á. Egri, A. Barta, and G. Horváth, “An alternative interpretation of the Viking sundial artefact: an instrument to determine latitude and local noon,” Proc. R. Soc. A 469, 20130021 (2013).
[Crossref]

B. Bernáth, M. Blahó, Á. Egri, A. Barta, G. Kriska, and G. Horváth, “Orientation with a Viking sun-compass, a shadow-stick, and two calcite sunstones under various weather conditions,” Appl. Opt. 52, 6185–6194 (2013).
[Crossref]

2011 (4)

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011).
[Crossref]

S. F. Reid, A. Narendra, J. M. Hemmi, and J. Zeil, “Polarized skylight and the landmark panorama provide night-active bull ants with compass information during route following,” J. Exp. Biol. 214, 363–370 (2011).
[Crossref]

G. Horváth, R. Hegedüs, A. Barta, A. Farkas, and S. Åkesson, “Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic,” Appl. Opt. 50, F64–F71 (2011).
[Crossref]

R. Muheim, “Behavioral and physiological mechanisms of polarized light sensitivity in birds,” Phil. Trans. R. Soc. B 366, 763–771 (2011).
[Crossref]

2008 (1)

2007 (6)

2006 (3)

2004 (4)

E. J. Warrant, A. Kelber, A. Gislen, B. Greiner, W. Ribi, and W. Wcislo, “Nocturnal vision and landmark orientation in a tropical halictid bee,” Curr. Biol. 14, 1309–1318 (2004).
[Crossref]

B. Greiner, W. A. Ribi, and E. J. Warrant, “Retinal and optical adaptations for nocturnal vision in the halictid bee Megalopta genalis,” Cell Tissue Res. 316, 377–390 (2004).

M. V. Berry, M. R. Dennis, and R. L. Lee, “Polarization singularities in the clear sky,” New J. Phys. 6, 162 (2004).
[Crossref]

B. Suhai and G. Horváth, “How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study,” J. Opt. Soc. Am. A 21, 1669–1676 (2004).
[Crossref]

2003 (2)

G. Horváth, I. Pomozi, and J. Gál, “Neutral points of skylight polarization observed during the total eclipse on 11 August 1999,” Appl. Opt. 42, 465–475 (2003).
[Crossref]

M. Dacke, P. Nordström, and C. H. Scholtz, “Twilight orientation to polarized light in the crepuscular dung beetle Scarabaeus zambesianus,” J. Exp. Biol. 206, 1535–1543 (2003).
[Crossref]

2002 (2)

2001 (8)

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. A 457, 1385–1399 (2001).
[Crossref]

I. Pomozi, G. Horváth, and R. Wehner, “How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation,” J. Exp. Biol. 204, 2933–2942 (2001).

I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Fine structure of the celestial polarization pattern and its temporal change during the total solar eclipse of 11 August 1999,” Remote Sens. Environ. 76, 181–201 (2001).
[Crossref]

J. Gál, G. Horváth, A. Barta, and R. Wehner, “Polarization of the moonlit clear night sky measured by full-sky imaging polarimetry at full moon: comparison of the polarization of moonlit and sunlit skies,” J. Geophys. Res. D 106, 22647–22653 (2001).

L. Baldavári, “Change of honeybee behavior in an apiary during the total solar eclipse on 11 August 1999,” Állattani Közlemények 86, 137–143 (2001) (in Hungarian).

B. Bernáth, I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Skylight polarization during the total solar eclipse of 11 August 1999 and its possible biological implications,” Állattani Közlemények 86, 81–92 (2001) (in Hungarian).

F. Szentkirályi and L. Szalay, “Influence of the total solar eclipse of 11 August 1999 on the behavior and collecting activity of honeybees,” Állattani Közlemények 86, 115–136 (2001) (in Hungarian).

I. Novales-Flamarique and H. I. Browman, “Foraging and prey-search behavior of small juvenile rainbow trout (Oncorhynchus mykiss) under polarized light,” J. Exp. Biol. 204, 2415–2422 (2001).

1999 (4)

T. Labhart and E. P. Meyer, “Detectors for polarized skylight in insects: a survey of ommatidial specializations in the dorsal rim area of the compound eye,” Microsc. Res. Tech. 47, 368–379 (1999).
[Crossref]

M. J. Freake, “Evidence for orientation using the e-vector direction of polarised light in the sleepy lizard Tiliqua rugosa,” J. Exp. Biol. 202, 1159–1166 (1999).

G. Horváth and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” J. Comp. Physiol. A 184, 1–7 (1999).
[Crossref]

G. Horváth and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” Erratum: J. Comp. Physiol. A 184, 347–349 (1999).

1998 (1)

G. Horváth, J. Gál, I. Pomozi, and R. Wehner, “Polarization portrait of the Arago point: video-polarimetric imaging of the neutral points of skylight polarization,” Naturwissenschaften 85, 333–339 (1998).
[Crossref]

1997 (4)

1995 (1)

G. Horváth and D. Varjú, “Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell’s window of the flat water surface,” Vis. Res. 35, 1651–1666 (1995).
[Crossref]

1994 (1)

1991 (1)

S. M. Goddard and F. B. Forward, “The role of the underwater polarized light pattern, in sun compass navigation of the grass shrimp, Palaemonetes vulgaris,” J. Comp. Physiol. A 169, 479–491 (1991).
[Crossref]

1987 (1)

1982 (1)

M. L. Brines and J. L. Gould, “Skylight polarization patterns and animal orientation,” J. Exp. Biol. 96, 69–91 (1982).

1980 (1)

1979 (1)

J. S. Auburn and D. H. Taylor, “Polarized light perception and orientation in larval bullfrogs Rana catesbeiana,” Anim. Behav. 27, 658–668 (1979).
[Crossref]

1975 (1)

1972 (1)

C. R. N. Rao, T. Takashima, and J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,” J. Atmos. Terr. Phys. 34, 573–576 (1972).
[Crossref]

1971 (1)

1967 (1)

T. Ramskou, “Solstenen,” Skalk 2, 16–17 (1967).

1955 (1)

J. V. Dave and K. R. Ramanathan, “On the intensity and polarisation of the light from the sky during twilight,” Proc. Indian Acad. Sci. A 43, 67–68 (1955).

Åkesson, S.

G. Horváth, R. Hegedüs, A. Barta, A. Farkas, and S. Åkesson, “Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic,” Appl. Opt. 50, F64–F71 (2011).
[Crossref]

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?” Appl. Opt. 46, 2717–2726 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Polarization of “water-skies” above arctic open waters: how polynyas in the ice-cover can be visually detected from a distance,” J. Opt. Soc. Am. A 24, 132–138 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Polarization patterns of thick clouds: overcast skies have distribution of the angle of polarization similar to that of clear skies,” J. Opt. Soc. Am. A 24, 2347–2356 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[Crossref]

S. Åkesson and A. Hedenström, “How migrants get there: migratory performance and orientation,” BioScience 57, 123–133 (2007).
[Crossref]

R. Muheim, J. B. Phillips, and S. Åkesson, “Polarized light cues underlie compass calibration in migratory songbirds,” Science 313, 837–839 (2006).
[Crossref]

Auburn, J. S.

J. S. Auburn and D. H. Taylor, “Polarized light perception and orientation in larval bullfrogs Rana catesbeiana,” Anim. Behav. 27, 658–668 (1979).
[Crossref]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1989).

Baldavári, L.

L. Baldavári, “Change of honeybee behavior in an apiary during the total solar eclipse on 11 August 1999,” Állattani Közlemények 86, 137–143 (2001) (in Hungarian).

Barta, A.

B. Bernáth, M. Blahó, Á. Egri, A. Barta, and G. Horváth, “An alternative interpretation of the Viking sundial artefact: an instrument to determine latitude and local noon,” Proc. R. Soc. A 469, 20130021 (2013).
[Crossref]

B. Bernáth, M. Blahó, Á. Egri, A. Barta, G. Kriska, and G. Horváth, “Orientation with a Viking sun-compass, a shadow-stick, and two calcite sunstones under various weather conditions,” Appl. Opt. 52, 6185–6194 (2013).
[Crossref]

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011).
[Crossref]

G. Horváth, R. Hegedüs, A. Barta, A. Farkas, and S. Åkesson, “Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic,” Appl. Opt. 50, F64–F71 (2011).
[Crossref]

R. Hegedüs, A. Barta, B. Bernáth, V. B. Meyer-Rochow, and G. Horváth, “Imaging polarimetry of forest canopies: how the azimuth direction of the sun, occluded by vegetation, can be assessed from the polarization pattern of the sunlit foliage,” Appl. Opt. 46, 6019–6032 (2007).
[Crossref]

S. Sabbah, A. Barta, J. Gál, G. Horváth, and N. Shashar, “Experimental and theoretical study of skylight polarization transmitted through Snell’s window of a flat water surface,” J. Opt. Soc. Am. A 23, 1978–1988 (2006).
[Crossref]

G. Horváth, A. Barta, J. Gál, B. Suhai, and O. Haiman, “Ground-based full-sky imaging polarimetry of rapidly changing skies and its use for polarimetric cloud detection,” Appl. Opt. 41, 543–559 (2002).
[Crossref]

G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A 19, 2085–2099 (2002).
[Crossref]

J. Gál, G. Horváth, A. Barta, and R. Wehner, “Polarization of the moonlit clear night sky measured by full-sky imaging polarimetry at full moon: comparison of the polarization of moonlit and sunlit skies,” J. Geophys. Res. D 106, 22647–22653 (2001).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1989).

Beckman, C.

Bernáth, B.

Berry, M. V.

M. V. Berry, M. R. Dennis, and R. L. Lee, “Polarization singularities in the clear sky,” New J. Phys. 6, 162 (2004).
[Crossref]

Blahó, M.

B. Bernáth, M. Blahó, Á. Egri, A. Barta, G. Kriska, and G. Horváth, “Orientation with a Viking sun-compass, a shadow-stick, and two calcite sunstones under various weather conditions,” Appl. Opt. 52, 6185–6194 (2013).
[Crossref]

B. Bernáth, M. Blahó, Á. Egri, A. Barta, and G. Horváth, “An alternative interpretation of the Viking sundial artefact: an instrument to determine latitude and local noon,” Proc. R. Soc. A 469, 20130021 (2013).
[Crossref]

Brines, M. L.

M. L. Brines and J. L. Gould, “Skylight polarization patterns and animal orientation,” J. Exp. Biol. 96, 69–91 (1982).

Browman, H. I.

I. Novales-Flamarique and H. I. Browman, “Foraging and prey-search behavior of small juvenile rainbow trout (Oncorhynchus mykiss) under polarized light,” J. Exp. Biol. 204, 2415–2422 (2001).

Coulson, K. L.

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, 1988).

Cronin, T. W.

Dacke, M.

M. Dacke, P. Nordström, and C. H. Scholtz, “Twilight orientation to polarized light in the crepuscular dung beetle Scarabaeus zambesianus,” J. Exp. Biol. 206, 1535–1543 (2003).
[Crossref]

Dandekar, B. S.

Dave, J. V.

J. V. Dave and K. R. Ramanathan, “On the intensity and polarisation of the light from the sky during twilight,” Proc. Indian Acad. Sci. A 43, 67–68 (1955).

Dennis, M. R.

M. V. Berry, M. R. Dennis, and R. L. Lee, “Polarization singularities in the clear sky,” New J. Phys. 6, 162 (2004).
[Crossref]

Duggin, M. J.

Egri, Á.

B. Bernáth, M. Blahó, Á. Egri, A. Barta, and G. Horváth, “An alternative interpretation of the Viking sundial artefact: an instrument to determine latitude and local noon,” Proc. R. Soc. A 469, 20130021 (2013).
[Crossref]

B. Bernáth, M. Blahó, Á. Egri, A. Barta, G. Kriska, and G. Horváth, “Orientation with a Viking sun-compass, a shadow-stick, and two calcite sunstones under various weather conditions,” Appl. Opt. 52, 6185–6194 (2013).
[Crossref]

Farkas, A.

Forward, F. B.

S. M. Goddard and F. B. Forward, “The role of the underwater polarized light pattern, in sun compass navigation of the grass shrimp, Palaemonetes vulgaris,” J. Comp. Physiol. A 169, 479–491 (1991).
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M. J. Freake, “Evidence for orientation using the e-vector direction of polarised light in the sleepy lizard Tiliqua rugosa,” J. Exp. Biol. 202, 1159–1166 (1999).

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S. Sabbah, A. Barta, J. Gál, G. Horváth, and N. Shashar, “Experimental and theoretical study of skylight polarization transmitted through Snell’s window of a flat water surface,” J. Opt. Soc. Am. A 23, 1978–1988 (2006).
[Crossref]

G. Horváth, I. Pomozi, and J. Gál, “Neutral points of skylight polarization observed during the total eclipse on 11 August 1999,” Appl. Opt. 42, 465–475 (2003).
[Crossref]

G. Horváth, A. Barta, J. Gál, B. Suhai, and O. Haiman, “Ground-based full-sky imaging polarimetry of rapidly changing skies and its use for polarimetric cloud detection,” Appl. Opt. 41, 543–559 (2002).
[Crossref]

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. A 457, 1385–1399 (2001).
[Crossref]

I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Fine structure of the celestial polarization pattern and its temporal change during the total solar eclipse of 11 August 1999,” Remote Sens. Environ. 76, 181–201 (2001).
[Crossref]

J. Gál, G. Horváth, A. Barta, and R. Wehner, “Polarization of the moonlit clear night sky measured by full-sky imaging polarimetry at full moon: comparison of the polarization of moonlit and sunlit skies,” J. Geophys. Res. D 106, 22647–22653 (2001).

B. Bernáth, I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Skylight polarization during the total solar eclipse of 11 August 1999 and its possible biological implications,” Állattani Közlemények 86, 81–92 (2001) (in Hungarian).

G. Horváth, J. Gál, I. Pomozi, and R. Wehner, “Polarization portrait of the Arago point: video-polarimetric imaging of the neutral points of skylight polarization,” Naturwissenschaften 85, 333–339 (1998).
[Crossref]

Gislen, A.

E. J. Warrant, A. Kelber, A. Gislen, B. Greiner, W. Ribi, and W. Wcislo, “Nocturnal vision and landmark orientation in a tropical halictid bee,” Curr. Biol. 14, 1309–1318 (2004).
[Crossref]

Goddard, S. M.

S. M. Goddard and F. B. Forward, “The role of the underwater polarized light pattern, in sun compass navigation of the grass shrimp, Palaemonetes vulgaris,” J. Comp. Physiol. A 169, 479–491 (1991).
[Crossref]

Gould, J. L.

M. L. Brines and J. L. Gould, “Skylight polarization patterns and animal orientation,” J. Exp. Biol. 96, 69–91 (1982).

Greiner, B.

T. W. Cronin, E. J. Warrant, and B. Greiner, “Celestial polarization patterns during twilight,” Appl. Opt. 45, 5582–5589 (2006).
[Crossref]

E. J. Warrant, A. Kelber, A. Gislen, B. Greiner, W. Ribi, and W. Wcislo, “Nocturnal vision and landmark orientation in a tropical halictid bee,” Curr. Biol. 14, 1309–1318 (2004).
[Crossref]

B. Greiner, W. A. Ribi, and E. J. Warrant, “Retinal and optical adaptations for nocturnal vision in the halictid bee Megalopta genalis,” Cell Tissue Res. 316, 377–390 (2004).

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G. Horváth, R. Hegedüs, A. Barta, A. Farkas, and S. Åkesson, “Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic,” Appl. Opt. 50, F64–F71 (2011).
[Crossref]

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011).
[Crossref]

B. Sipőcz, R. Hegedüs, G. Kriska, and G. Horváth, “Spatiotemporal change of sky polarization during the total solar eclipse on 29 March 2006 in Turkey: polarization patterns of the eclipsed sky observed by full-sky imaging polarimetry,” Appl. Opt. 47, H1–H10 (2008).
[Crossref]

R. Hegedüs, A. Barta, B. Bernáth, V. B. Meyer-Rochow, and G. Horváth, “Imaging polarimetry of forest canopies: how the azimuth direction of the sun, occluded by vegetation, can be assessed from the polarization pattern of the sunlit foliage,” Appl. Opt. 46, 6019–6032 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?” Appl. Opt. 46, 2717–2726 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Polarization patterns of thick clouds: overcast skies have distribution of the angle of polarization similar to that of clear skies,” J. Opt. Soc. Am. A 24, 2347–2356 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Polarization of “water-skies” above arctic open waters: how polynyas in the ice-cover can be visually detected from a distance,” J. Opt. Soc. Am. A 24, 132–138 (2007).
[Crossref]

Hemmi, J. M.

S. F. Reid, A. Narendra, J. M. Hemmi, and J. Zeil, “Polarized skylight and the landmark panorama provide night-active bull ants with compass information during route following,” J. Exp. Biol. 214, 363–370 (2011).
[Crossref]

Horváth, G.

B. Bernáth, M. Blahó, Á. Egri, A. Barta, and G. Horváth, “An alternative interpretation of the Viking sundial artefact: an instrument to determine latitude and local noon,” Proc. R. Soc. A 469, 20130021 (2013).
[Crossref]

B. Bernáth, M. Blahó, Á. Egri, A. Barta, G. Kriska, and G. Horváth, “Orientation with a Viking sun-compass, a shadow-stick, and two calcite sunstones under various weather conditions,” Appl. Opt. 52, 6185–6194 (2013).
[Crossref]

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011).
[Crossref]

G. Horváth, R. Hegedüs, A. Barta, A. Farkas, and S. Åkesson, “Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic,” Appl. Opt. 50, F64–F71 (2011).
[Crossref]

B. Sipőcz, R. Hegedüs, G. Kriska, and G. Horváth, “Spatiotemporal change of sky polarization during the total solar eclipse on 29 March 2006 in Turkey: polarization patterns of the eclipsed sky observed by full-sky imaging polarimetry,” Appl. Opt. 47, H1–H10 (2008).
[Crossref]

R. Hegedüs, A. Barta, B. Bernáth, V. B. Meyer-Rochow, and G. Horváth, “Imaging polarimetry of forest canopies: how the azimuth direction of the sun, occluded by vegetation, can be assessed from the polarization pattern of the sunlit foliage,” Appl. Opt. 46, 6019–6032 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Polarization of “water-skies” above arctic open waters: how polynyas in the ice-cover can be visually detected from a distance,” J. Opt. Soc. Am. A 24, 132–138 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?” Appl. Opt. 46, 2717–2726 (2007).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Polarization patterns of thick clouds: overcast skies have distribution of the angle of polarization similar to that of clear skies,” J. Opt. Soc. Am. A 24, 2347–2356 (2007).
[Crossref]

S. Sabbah, A. Barta, J. Gál, G. Horváth, and N. Shashar, “Experimental and theoretical study of skylight polarization transmitted through Snell’s window of a flat water surface,” J. Opt. Soc. Am. A 23, 1978–1988 (2006).
[Crossref]

B. Suhai and G. Horváth, “How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study,” J. Opt. Soc. Am. A 21, 1669–1676 (2004).
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G. Horváth, I. Pomozi, and J. Gál, “Neutral points of skylight polarization observed during the total eclipse on 11 August 1999,” Appl. Opt. 42, 465–475 (2003).
[Crossref]

G. Horváth, A. Barta, J. Gál, B. Suhai, and O. Haiman, “Ground-based full-sky imaging polarimetry of rapidly changing skies and its use for polarimetric cloud detection,” Appl. Opt. 41, 543–559 (2002).
[Crossref]

G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A 19, 2085–2099 (2002).
[Crossref]

J. Gál, G. Horváth, A. Barta, and R. Wehner, “Polarization of the moonlit clear night sky measured by full-sky imaging polarimetry at full moon: comparison of the polarization of moonlit and sunlit skies,” J. Geophys. Res. D 106, 22647–22653 (2001).

B. Bernáth, I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Skylight polarization during the total solar eclipse of 11 August 1999 and its possible biological implications,” Állattani Közlemények 86, 81–92 (2001) (in Hungarian).

I. Pomozi, G. Horváth, and R. Wehner, “How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation,” J. Exp. Biol. 204, 2933–2942 (2001).

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. A 457, 1385–1399 (2001).
[Crossref]

I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Fine structure of the celestial polarization pattern and its temporal change during the total solar eclipse of 11 August 1999,” Remote Sens. Environ. 76, 181–201 (2001).
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G. Horváth and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” J. Comp. Physiol. A 184, 1–7 (1999).
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G. Horváth and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” Erratum: J. Comp. Physiol. A 184, 347–349 (1999).

G. Horváth, J. Gál, I. Pomozi, and R. Wehner, “Polarization portrait of the Arago point: video-polarimetric imaging of the neutral points of skylight polarization,” Naturwissenschaften 85, 333–339 (1998).
[Crossref]

G. Horváth and D. Varjú, “Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell’s window of the flat water surface,” Vis. Res. 35, 1651–1666 (1995).
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G. Horváth and D. Varjú, Polarized Light in Animal Vision Polarization Patterns in Nature (Springer-Verlag, 2004).

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D. L. Johnson, D. Naylor, and G. Scudder, “Red sky in day, bugs go astray,” in annual Meeting of the Canadian Association of Geographers, Western Division, Lethbridge, Alberta, Canada, 12 March2005, Conference Abstracts, p. 145.

Kelber, A.

E. J. Warrant, A. Kelber, A. Gislen, B. Greiner, W. Ribi, and W. Wcislo, “Nocturnal vision and landmark orientation in a tropical halictid bee,” Curr. Biol. 14, 1309–1318 (2004).
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Kriska, G.

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M. V. Berry, M. R. Dennis, and R. L. Lee, “Polarization singularities in the clear sky,” New J. Phys. 6, 162 (2004).
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J. Meeus, Astronomical Algorithms, 2nd ed. (Willmann-Bell, 1998).

Meyer, E. P.

T. Labhart and E. P. Meyer, “Detectors for polarized skylight in insects: a survey of ommatidial specializations in the dorsal rim area of the compound eye,” Microsc. Res. Tech. 47, 368–379 (1999).
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Meyer-Rochow, B.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011).
[Crossref]

Meyer-Rochow, V. B.

R. Hegedüs, A. Barta, B. Bernáth, V. B. Meyer-Rochow, and G. Horváth, “Imaging polarimetry of forest canopies: how the azimuth direction of the sun, occluded by vegetation, can be assessed from the polarization pattern of the sunlit foliage,” Appl. Opt. 46, 6019–6032 (2007).
[Crossref]

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. A 457, 1385–1399 (2001).
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Moore, J. G.

C. R. N. Rao, T. Takashima, and J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,” J. Atmos. Terr. Phys. 34, 573–576 (1972).
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R. Muheim, “Behavioral and physiological mechanisms of polarized light sensitivity in birds,” Phil. Trans. R. Soc. B 366, 763–771 (2011).
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R. Muheim, J. B. Phillips, and S. Åkesson, “Polarized light cues underlie compass calibration in migratory songbirds,” Science 313, 837–839 (2006).
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Narendra, A.

S. F. Reid, A. Narendra, J. M. Hemmi, and J. Zeil, “Polarized skylight and the landmark panorama provide night-active bull ants with compass information during route following,” J. Exp. Biol. 214, 363–370 (2011).
[Crossref]

Naylor, D.

D. L. Johnson, D. Naylor, and G. Scudder, “Red sky in day, bugs go astray,” in annual Meeting of the Canadian Association of Geographers, Western Division, Lethbridge, Alberta, Canada, 12 March2005, Conference Abstracts, p. 145.

Nordström, P.

M. Dacke, P. Nordström, and C. H. Scholtz, “Twilight orientation to polarized light in the crepuscular dung beetle Scarabaeus zambesianus,” J. Exp. Biol. 206, 1535–1543 (2003).
[Crossref]

North, J. A.

Novales-Flamarique, I.

I. Novales-Flamarique and H. I. Browman, “Foraging and prey-search behavior of small juvenile rainbow trout (Oncorhynchus mykiss) under polarized light,” J. Exp. Biol. 204, 2415–2422 (2001).

Phillips, J. B.

R. Muheim, J. B. Phillips, and S. Åkesson, “Polarized light cues underlie compass calibration in migratory songbirds,” Science 313, 837–839 (2006).
[Crossref]

Pomozi, I.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011).
[Crossref]

G. Horváth, I. Pomozi, and J. Gál, “Neutral points of skylight polarization observed during the total eclipse on 11 August 1999,” Appl. Opt. 42, 465–475 (2003).
[Crossref]

I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Fine structure of the celestial polarization pattern and its temporal change during the total solar eclipse of 11 August 1999,” Remote Sens. Environ. 76, 181–201 (2001).
[Crossref]

I. Pomozi, G. Horváth, and R. Wehner, “How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation,” J. Exp. Biol. 204, 2933–2942 (2001).

B. Bernáth, I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Skylight polarization during the total solar eclipse of 11 August 1999 and its possible biological implications,” Állattani Közlemények 86, 81–92 (2001) (in Hungarian).

G. Horváth, J. Gál, I. Pomozi, and R. Wehner, “Polarization portrait of the Arago point: video-polarimetric imaging of the neutral points of skylight polarization,” Naturwissenschaften 85, 333–339 (1998).
[Crossref]

Ramanathan, K. R.

J. V. Dave and K. R. Ramanathan, “On the intensity and polarisation of the light from the sky during twilight,” Proc. Indian Acad. Sci. A 43, 67–68 (1955).

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T. Ramskou, “Solstenen,” Skalk 2, 16–17 (1967).

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C. R. N. Rao, T. Takashima, and J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,” J. Atmos. Terr. Phys. 34, 573–576 (1972).
[Crossref]

Reid, S. F.

S. F. Reid, A. Narendra, J. M. Hemmi, and J. Zeil, “Polarized skylight and the landmark panorama provide night-active bull ants with compass information during route following,” J. Exp. Biol. 214, 363–370 (2011).
[Crossref]

Ribi, W.

E. J. Warrant, A. Kelber, A. Gislen, B. Greiner, W. Ribi, and W. Wcislo, “Nocturnal vision and landmark orientation in a tropical halictid bee,” Curr. Biol. 14, 1309–1318 (2004).
[Crossref]

Ribi, W. A.

B. Greiner, W. A. Ribi, and E. J. Warrant, “Retinal and optical adaptations for nocturnal vision in the halictid bee Megalopta genalis,” Cell Tissue Res. 316, 377–390 (2004).

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M. Dacke, P. Nordström, and C. H. Scholtz, “Twilight orientation to polarized light in the crepuscular dung beetle Scarabaeus zambesianus,” J. Exp. Biol. 206, 1535–1543 (2003).
[Crossref]

Scudder, G.

D. L. Johnson, D. Naylor, and G. Scudder, “Red sky in day, bugs go astray,” in annual Meeting of the Canadian Association of Geographers, Western Division, Lethbridge, Alberta, Canada, 12 March2005, Conference Abstracts, p. 145.

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F. Szentkirályi and L. Szalay, “Influence of the total solar eclipse of 11 August 1999 on the behavior and collecting activity of honeybees,” Állattani Közlemények 86, 115–136 (2001) (in Hungarian).

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G. Horváth and D. Varjú, “Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell’s window of the flat water surface,” Vis. Res. 35, 1651–1666 (1995).
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T. W. Cronin, E. J. Warrant, and B. Greiner, “Celestial polarization patterns during twilight,” Appl. Opt. 45, 5582–5589 (2006).
[Crossref]

B. Greiner, W. A. Ribi, and E. J. Warrant, “Retinal and optical adaptations for nocturnal vision in the halictid bee Megalopta genalis,” Cell Tissue Res. 316, 377–390 (2004).

E. J. Warrant, A. Kelber, A. Gislen, B. Greiner, W. Ribi, and W. Wcislo, “Nocturnal vision and landmark orientation in a tropical halictid bee,” Curr. Biol. 14, 1309–1318 (2004).
[Crossref]

Wcislo, W.

E. J. Warrant, A. Kelber, A. Gislen, B. Greiner, W. Ribi, and W. Wcislo, “Nocturnal vision and landmark orientation in a tropical halictid bee,” Curr. Biol. 14, 1309–1318 (2004).
[Crossref]

Wehner, R.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011).
[Crossref]

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[Crossref]

G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A 19, 2085–2099 (2002).
[Crossref]

J. Gál, G. Horváth, A. Barta, and R. Wehner, “Polarization of the moonlit clear night sky measured by full-sky imaging polarimetry at full moon: comparison of the polarization of moonlit and sunlit skies,” J. Geophys. Res. D 106, 22647–22653 (2001).

B. Bernáth, I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Skylight polarization during the total solar eclipse of 11 August 1999 and its possible biological implications,” Állattani Közlemények 86, 81–92 (2001) (in Hungarian).

I. Pomozi, G. Horváth, and R. Wehner, “How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation,” J. Exp. Biol. 204, 2933–2942 (2001).

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. A 457, 1385–1399 (2001).
[Crossref]

I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Fine structure of the celestial polarization pattern and its temporal change during the total solar eclipse of 11 August 1999,” Remote Sens. Environ. 76, 181–201 (2001).
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G. Horváth and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” Erratum: J. Comp. Physiol. A 184, 347–349 (1999).

G. Horváth and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” J. Comp. Physiol. A 184, 1–7 (1999).
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G. Horváth, J. Gál, I. Pomozi, and R. Wehner, “Polarization portrait of the Arago point: video-polarimetric imaging of the neutral points of skylight polarization,” Naturwissenschaften 85, 333–339 (1998).
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Zeil, J.

S. F. Reid, A. Narendra, J. M. Hemmi, and J. Zeil, “Polarized skylight and the landmark panorama provide night-active bull ants with compass information during route following,” J. Exp. Biol. 214, 363–370 (2011).
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Állattani Közlemények (3)

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B. Bernáth, I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Skylight polarization during the total solar eclipse of 11 August 1999 and its possible biological implications,” Állattani Közlemények 86, 81–92 (2001) (in Hungarian).

F. Szentkirályi and L. Szalay, “Influence of the total solar eclipse of 11 August 1999 on the behavior and collecting activity of honeybees,” Állattani Közlemények 86, 115–136 (2001) (in Hungarian).

Anim. Behav. (1)

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Appl. Opt. (14)

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B. Sipőcz, R. Hegedüs, G. Kriska, and G. Horváth, “Spatiotemporal change of sky polarization during the total solar eclipse on 29 March 2006 in Turkey: polarization patterns of the eclipsed sky observed by full-sky imaging polarimetry,” Appl. Opt. 47, H1–H10 (2008).
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T. W. Cronin, E. J. Warrant, and B. Greiner, “Celestial polarization patterns during twilight,” Appl. Opt. 45, 5582–5589 (2006).
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K. J. Voss and Y. Liu, “Polarized radiance distribution measurements of skylight. I. System description and characterization,” Appl. Opt. 36, 6083–6094 (1997).
[Crossref]

G. Horváth, A. Barta, J. Gál, B. Suhai, and O. Haiman, “Ground-based full-sky imaging polarimetry of rapidly changing skies and its use for polarimetric cloud detection,” Appl. Opt. 41, 543–559 (2002).
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G. Horváth, R. Hegedüs, A. Barta, A. Farkas, and S. Åkesson, “Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic,” Appl. Opt. 50, F64–F71 (2011).
[Crossref]

R. Hegedüs, S. Åkesson, and G. Horváth, “Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies?” Appl. Opt. 46, 2717–2726 (2007).
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R. Hegedüs, A. Barta, B. Bernáth, V. B. Meyer-Rochow, and G. Horváth, “Imaging polarimetry of forest canopies: how the azimuth direction of the sun, occluded by vegetation, can be assessed from the polarization pattern of the sunlit foliage,” Appl. Opt. 46, 6019–6032 (2007).
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B. Bernáth, M. Blahó, Á. Egri, A. Barta, G. Kriska, and G. Horváth, “Orientation with a Viking sun-compass, a shadow-stick, and two calcite sunstones under various weather conditions,” Appl. Opt. 52, 6185–6194 (2013).
[Crossref]

BioScience (1)

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[Crossref]

Cell Tissue Res. (1)

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Curr. Biol. (1)

E. J. Warrant, A. Kelber, A. Gislen, B. Greiner, W. Ribi, and W. Wcislo, “Nocturnal vision and landmark orientation in a tropical halictid bee,” Curr. Biol. 14, 1309–1318 (2004).
[Crossref]

Erratum: J. Comp. Physiol. A (1)

G. Horváth and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” Erratum: J. Comp. Physiol. A 184, 347–349 (1999).

J. Atmos. Terr. Phys. (1)

C. R. N. Rao, T. Takashima, and J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,” J. Atmos. Terr. Phys. 34, 573–576 (1972).
[Crossref]

J. Comp. Physiol. A (2)

G. Horváth and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” J. Comp. Physiol. A 184, 1–7 (1999).
[Crossref]

S. M. Goddard and F. B. Forward, “The role of the underwater polarized light pattern, in sun compass navigation of the grass shrimp, Palaemonetes vulgaris,” J. Comp. Physiol. A 169, 479–491 (1991).
[Crossref]

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[Crossref]

S. F. Reid, A. Narendra, J. M. Hemmi, and J. Zeil, “Polarized skylight and the landmark panorama provide night-active bull ants with compass information during route following,” J. Exp. Biol. 214, 363–370 (2011).
[Crossref]

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I. Novales-Flamarique and H. I. Browman, “Foraging and prey-search behavior of small juvenile rainbow trout (Oncorhynchus mykiss) under polarized light,” J. Exp. Biol. 204, 2415–2422 (2001).

I. Pomozi, G. Horváth, and R. Wehner, “How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation,” J. Exp. Biol. 204, 2933–2942 (2001).

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J. Geophys. Res. D (1)

J. Gál, G. Horváth, A. Barta, and R. Wehner, “Polarization of the moonlit clear night sky measured by full-sky imaging polarimetry at full moon: comparison of the polarization of moonlit and sunlit skies,” J. Geophys. Res. D 106, 22647–22653 (2001).

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Naturwissenschaften (1)

G. Horváth, J. Gál, I. Pomozi, and R. Wehner, “Polarization portrait of the Arago point: video-polarimetric imaging of the neutral points of skylight polarization,” Naturwissenschaften 85, 333–339 (1998).
[Crossref]

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R. Muheim, “Behavioral and physiological mechanisms of polarized light sensitivity in birds,” Phil. Trans. R. Soc. B 366, 763–771 (2011).
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B. Bernáth, M. Blahó, Á. Egri, A. Barta, and G. Horváth, “An alternative interpretation of the Viking sundial artefact: an instrument to determine latitude and local noon,” Proc. R. Soc. A 469, 20130021 (2013).
[Crossref]

R. Hegedüs, S. Åkesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[Crossref]

J. Gál, G. Horváth, V. B. Meyer-Rochow, and R. Wehner, “Polarization patterns of the summer sky and its neutral points measured by full-sky imaging polarimetry in Finnish Lapland north of the Arctic Circle,” Proc. R. Soc. A 457, 1385–1399 (2001).
[Crossref]

Remote Sens. Environ. (1)

I. Pomozi, J. Gál, G. Horváth, and R. Wehner, “Fine structure of the celestial polarization pattern and its temporal change during the total solar eclipse of 11 August 1999,” Remote Sens. Environ. 76, 181–201 (2001).
[Crossref]

Science (1)

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G. P. Können, Polarized Light in Nature (Cambridge University, 1985).

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, 1988).

G. Horváth and D. Varjú, Polarized Light in Animal Vision Polarization Patterns in Nature (Springer-Verlag, 2004).

Supplementary Material (9)

» Media 1: MOV (18987 KB)     
» Media 2: MOV (3068 KB)     
» Media 3: MOV (9019 KB)     
» Media 4: MOV (8981 KB)     
» Media 5: MOV (13174 KB)     
» Media 6: MOV (6042 KB)     
» Media 7: MOV (5906 KB)     
» Media 8: MOV (1766 KB)     
» Media 9: MOV (692 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Photographs and patterns of the degree of linear polarization p and angle of polarization α (clockwise from the local meridian) of the clear sky measured by full-sky imaging polarimetry in the blue (450 nm) part of the spectrum after sunset in Szombathely, Hungary (47° 15.481′ N, 16° 36.213′ E) on 22 March 2013 when 78% of the moon disc was sunlit. (A)–(C) 18:33 h (= local winter time = GMT+1 h, where GMT is Greenwich Mean Time). (D)–(F) 19:03 h. (G)–(I) 19:43 h. The small patches in the pictures and p patterns are due to raindrops on the plexi-dome of the polarimeter. The positions of sun (below the horizon), moon (above the horizon), and neutral points of skylight polarization are shown by dots. sAr, solar Arago neutral point; sN, solar neutral point; N, lunar neutral point; sBa, solar Babinet neutral point; Ba, lunar Babinet neutral point; Br, lunar Brewster neutral point.

Fig. 2.
Fig. 2.

Same as Fig. 1 after sunset/moonrise on 25 April 2013 when 100% of the moon disc was sunlit (full moon). (A)–(C) 20:23 h (= GMT + 2 h). (D)–(F) 21:13 h. (G)–(I) 23:03 h. sAr: solar Arago neutral point, sBa, solar Babinet neutral point; Ba, lunar Babinet neutral point; Ar, lunar Arago neutral point.Pattern of α, where black bars show the average local direction of polarization (Media 1) Simulated α pattern with weight w=1, meaning that the contributions of scattered sunlight and moonlight to sky polarization are equal (Media 2). Pattern of |α90°|, where black and white pixels correspond to directions of polarization perpendicular and parallel to the local meridian, respectively, yellow and blue lines show the solar and lunar meridians, respectively, and the green line shows the axis of mirror symmetry of sky polarization (Media 3). Pattern of |α90°|, where the red overlay shows sky areas where the degree of linear polarization p is less than 10% (Media 4). All four video clips show the patterns from 19:23 h on 25 April 2013 to 06:03 h on 26 April 2013 during dusk, night, and dawn in the blue spectral range when 100% of the moon disc was sunlit. (Yellow and blue dots show the solar and lunar positions, respectively.)

Fig. 3.
Fig. 3.

Same as Fig. 1 prior to sunrise on 26 April 2013 when 100% of the moon disc was sunlit (full moon). (A)–(C) 03:33 h (= GMT + 2 h). (D)–(F) 04:23 h. (G)–(I) 05:13 h. Ba, lunar Babinet neutral point; Ar, lunar Arago neutral point; sAr, solar Arago neutral point; sBa, solar Babinet neutral point.

Fig. 4.
Fig. 4.

Same as Fig. 1 prior to sunrise on 28 June 2013 when 72% of the moon disc was sunlit. (A)–(C) 03:04 h (= local summer time = GMT + 2 h). (D)–(F) 03:28 h. (G)–(I) 03:56 h. Ba, lunar Babinet neutral point; Ar, lunar Arago neutral point; sN, solar neutral point; N, lunar neutral point; sAr, solar Arago neutral point; sBa, solar Babinet neutral point. Pattern of α, where black bars show the average local direction of polarization (Media 5). Pattern of |α90°|, where black and white pixels correspond to directions of polarization perpendicular and parallel to the local meridian, respectively, yellow and blue lines show the solar and lunar meridians, respectively, and the green line shows the axis of mirror symmetry of sky polarization (Media 6). Pattern of |α90°|, where the red overlay shows sky areas where the degree of linear polarization p is less than 10% (Media 7). All three video clips show the patterns in the blue spectral range from 02:07 to 06:00 h on 28 June 2013 during dawn when 72% of the moon disc was sunlit. (Yellow and blue dots show the solar and lunar positions, respectively.)

Fig. 5.
Fig. 5.

Maximum pmax of the degree of linear polarization p of skylight measured in the green (550 nm) spectral range averaging the p values in small circular celestial regions at 90° from the sun (empty circles) and the moon (solid black circles) as a function of time for the four different situations shown in Figs. 14. The vertical bars represent the standard deviation of pmax. Insets: typical p patterns belonging to the points of time shown by the arrows. The solar and lunar positions are represented by white and black dots, respectively. The occulted or CCD-void sky regions are marked by a checkered pattern.

Fig. 6.
Fig. 6.

(A) Azimuth angle of the sun, the moon, and the symmetry axis of the celestial |α90°| pattern, where α is the angle of polarization of skylight as a function of time (GMT + 2 h = local summer time) measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm), and blue (450 nm) parts of the spectrum in Szombathely, Hungary (47° 15.481′ N, 16° 36.213′ E) on 28 June 2013 when 72% of the moon disc was sunlit (situation as in Figs. 4 and 5D). (B) Zenith angle of the lunar Babinet neutral point Ba (or solar Arago neutral point sAr) versus time for the same case as (A), (C), (D). Same as (A) and (B) on 25–26 April 2013 at full moon when 100% of the moon disc was sunlit (situations as in Figs. 2, 3, 5B, and 5C).

Fig. 7.
Fig. 7.

Photograph and patterns of the degree of linear polarization p and angle of polarization α (clockwise from the local meridian) of the clear sky measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm), and blue (450 nm) parts of the spectrum prior to sunrise in Szombathely, Hungary (47° 15.481′ N, 16° 36.213′ E) at 03:25 (GMT + 2 h) on 28 June 2013 when 72% of the moon disc was sunlit. The positions of the sun (below the horizon) and moon (above the horizon) are shown by yellow and white dots, respectively. In the α patterns black and white continuous lines show the solar–antisolar and lunar–antilunar meridians, respectively, while black dashed lines show the symmetry axis of the |α90°| patterns.

Fig. 8.
Fig. 8.

Measurements performed prior to sunrise on 28 June 2013 in Szombathely, Hungary (47° 15.481′ N, 16° 36.213′ E) when 72% of the moon disc was sunlit (situation as in Figs. 4 and 5D). (A)–(C) Photographs taken at 03:00, 03:32, and 03:52 h (GMT + 2 h), respectively. (D)–(F) Celestial patterns of |α90°| in the blue (450 nm) part of the spectrum. Red overlays show the areas of sky where the degree of linear polarization p in the blue (450 nm) is less than 10%. Yellow and white lines show the solar–antisolar and lunar–antilunar meridians, respectively. The positions of the sun (below the horizon) and moon (above the horizon) are shown by yellow and white dots, respectively. Ba, lunar Babinet neutral point; Ar, lunar Arago neutral point; sN, solar neutral point; N, lunar neutral point; sBa, solar Babinet point; sAr, solar Arago point; green line, symmetry axis of the |α90°| pattern.

Fig. 9.
Fig. 9.

(A) Photograph of the sky taken on 28 June 2013 at 03:25 (GMT+2 h) in Szombathely, Hungary (47° 15.481′ N, 16° 36.213′ E) when 72% of the moon disc was sunlit (situation as in Figs. 4 and 5D). (B) Pattern of the angle of polarization α of skylight measured in the blue (450 nm) spectral range. Black bars show the average local direction of polarization. (C) Simulated α pattern for the same solar and lunar intensities (with weight w=1, meaning that the contributions of scattered moonlight and skylight to the net polarization of skylight are equal). (D) Celestial pattern of |α90°| in the blue (450 nm) part of the spectrum. Yellow and white lines show the solar–antisolar and lunar–antilunar meridians, respectively, while green line represents the symmetry axis of the |α90°| pattern. (E) Same as (D) with red overlay showing the areas of sky where the degree of linear polarization p in the blue (450 nm) is less than 10%. sN, solar neutral point; N, lunar neutral point. The positions of the sun (below the horizon) and moon (above the horizon) are shown by yellow and white dots, respectively. Simulated α pattern, where black bars show the average local direction of polarization (Media 8). Simulated α pattern, where white dots show the positions of neutral points. Black line shows the axis of mirror symmetry of sky polarization (Media 9). Both video clips show the patterns from 02:07 to 06:00 h on 28 June 2013 during dawn with weight w=1, meaning that the contributions of scattered sunlight and moonlight to sky polarization are equal. (Yellow and blue dots show the solar and lunar positions, respectively.)

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

α=|α90°|.
Mjk=f(x,y)·xjyk·dx·dy,
μjk=f(x,y)·(xxc)j·(yyc)k·dx·dy.
θ=12arctan(2μ11μ20μ02).

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