Abstract

We present the first high-resolution maps of Rayleigh behavior in clear and cloudy sky conditions measured by full-sky imaging polarimetry at the wavelengths of 650 nm (red), 550 nm (green), and 450 nm (blue) versus the solar elevation angle θs. Our maps display those celestial areas at which the deviation Δα= |αmeas-αRayleigh| is below the threshold αthres=5°, where αmeas is the angle of polarization of skylight measured by full-sky imaging polarimetry, and αRayleigh is the celestial angle of polarization calculated on the basis of the single-scattering Rayleigh model. From these maps we derived the proportion r of the full sky for which the single-scattering Rayleigh model describes well (with an accuracy of Δα=5°) the E-vector alignment of skylight. Depending on θs, r is high for clear skies, especially for low solar elevations (40%<r<70% for θs13°). Depending on the cloud cover and the solar illumination, r decreases more or less under cloudy conditions, but sometimes its value remains remarkably high, especially at low solar elevations (rmax=69% for θs=0°). The proportion r of the sky that follows the Rayleigh model is usually higher for shorter wavelengths under clear as well as cloudy sky conditions. This partly explains why the shorter wavelengths are generally preferred by animals navigating by means of the celestial polarization. We found that the celestial E-vector pattern generally follows the Rayleigh pattern well, which is a fundamental hypothesis in the studies of animal orientation and human navigation (e.g., in aircraft flying near the geomagnetic poles and using a polarization sky compass) with the use of the celestial α pattern.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Horváth, D. Varjú, Polarized Light in Animal Vision—Polarization Patterns in Nature (Springer, Berlin, 2003).
  2. A. Barta, G. Horváth, “Why is it advantageous to perceive the polarization of downwelling light under clouds and canopies in the UV?” J. Theor. Biol. 226, 429–437 (2004).
    [CrossRef] [PubMed]
  3. K. Kirschfeld, M. Lindauer, H. Martin, “Problems of menotactic orientation according to polarized light of the sky,” Z. Naturforsch. 30c, 88–90 (1975).
  4. R. Wehner, “Polarized-light navigation by insects,” Sci. Am. 235(7), 106–115 (1976).
    [CrossRef] [PubMed]
  5. H. W. van der Glas, “Models for unambiguous E-vector navigation in the bee,” J. Comp. Physiol. A 113, 129–159 (1977).
    [CrossRef]
  6. S. Rossel, R. Wehner, M. Lindauer, “E-vector orientation in bees,” J. Comp. Physiol., A 125, 1–12 (1978).
    [CrossRef]
  7. M. L. Brines, “Dynamic patterns of skylight polarization as clock and compass,” J. Theor. Biol. 86, 507–512 (1980).
    [CrossRef] [PubMed]
  8. K. P. Able, “Skylight polarization patterns at dusk influence migratory orientation in birds,” Nature 299, 550–551 (1982).
    [CrossRef]
  9. J. B. Phillips, J. A. Waldvogel, “Reflected light cues generate the short-term deflector-loft effect,” in Avian Navigation, F. Papi, H. G. Wallraff, eds. (Springer, Heidelberg, Germany, 1982), pp. 190–202.
  10. S. Rossel, R. Wehner, “The bee’s map of the E-vector pattern in the sky,” Proc. Natl. Acad. Sci. USA 79, 4451–4455 (1982).
    [CrossRef]
  11. R. Wehner, “Celestial and terrestrial navigation: human strategies—insect strategies,” in Neuroethology and Behavioral Physiology, F. Huber, H. Markl, eds. (Springer, Heidelberg, Germany, 1983), pp. 366–381.
  12. R. Wehner, “Astronavigation in insects,” Annu. Rev. Entomol. 29, 277–298 (1984).
    [CrossRef]
  13. R. Wehner, S. Rossel, “The bee’s celestial compass—a case study in behavioral neurobiology,” Fortschr. Zool. 31, 11–53 (1985).
  14. R. Wehner, “The hymenopteran skylight compass: matched filtering and parallel coding,” J. Exp. Biol. 146, 63–85 (1989).
  15. K. P. Able, M. A. Able, “Ontogeny of migratory orientation in the savannah sparrow, Passerculus sandwichensis: mechanisms at sunset,” Anim. Behav. 39, 1189–1198 (1990).
    [CrossRef]
  16. K. Schmidt-Koenig, J. U. Ganzhorn, R. Ranvaud, “The sun compass,” in Orientation in Birds, P. Berthold, ed. (Birkhäuser, Basel, 1991), pp. 1–15.
  17. C. W. Hawryshyn, “Polarization vision in fish,” Am. Sci. 80, 164–175 (1992).
  18. R. Wehner, “The polarization-vision project: championing organismic biology,” Fortschr. Zool. 39, 103–143 (1994).
  19. R. Wehner, “The ant’s celestial compass system: spectral and polarization channels,” in Orientation and Communication in Arthropods, M. Lehrer, ed. (Birkhäuser, Basel, 1997), pp. 145–185.
  20. N. Shashar, T. W. Cronin, L. B. Wolff, M. A. Condon, “The polarization of light in a tropical rain forest,” Biotropica 30, 275–285 (1998).
    [CrossRef]
  21. T. Labhart, 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] [PubMed]
  22. M. J. Freake, “Evidence for orientation using the E-vector direction of polarized light in the sleepy lizard Tiliqua rugosa,” J. Exp. Biol. 202, 1159–1166 (1999).
  23. K. von Frisch, The Dance Language and Orientation of Bees (Harvard U. Press, Cambridge, Mass., 1967).
  24. T. Ramskou, “Solstenen,” Skalk 2, 16–17 (1967).
  25. T. Ramskou, Solstenen—Primitiv Navigation I Norden for Kompasset (Rhodos, Copenhagen, 1969).
  26. W. Britton, “The Britton Viking sun-stone expedition,” Nutr. Today, May/June1972, pp. 14–23.
  27. B. E. Schaefer, “Vikings and polarization sundials,” Sky Telesc. 1997(5), 91–94.
  28. M. L. Brines, J. L. Gould, “Skylight polarization patterns and animal orientation,” J. Exp. Biol. 96, 69–91 (1982).
  29. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, Hampton, Va., 1988).
  30. J. A. North, M. J. Duggin, “Stokes vector imaging of the polarized sky-dome,” Appl. Opt. 36, 723–730 (1997).
    [CrossRef] [PubMed]
  31. K. J. Voss, Y. Liu, “Polarized radiance distribution measurements of skylight. I. System description and characterization,” Appl. Opt. 36, 6083–6094 (1997).
    [CrossRef] [PubMed]
  32. J. Gál, G. Horváth, V. B. Meyer-Rochow, 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. London Ser. A 457, 1385–1399 (2001).
    [CrossRef]
  33. G. Horváth, A. Barta, J. Gál, B. Suhai, 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] [PubMed]
  34. I. Pomozi, G. Horváth, 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).
    [PubMed]
  35. G. P. Können, Polarized Light in Nature (Cambridge U. Press, Cambridge, UK, 1985).

2004

A. Barta, G. Horváth, “Why is it advantageous to perceive the polarization of downwelling light under clouds and canopies in the UV?” J. Theor. Biol. 226, 429–437 (2004).
[CrossRef] [PubMed]

2002

2001

J. Gál, G. Horváth, V. B. Meyer-Rochow, 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. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

I. Pomozi, G. Horváth, 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).
[PubMed]

1999

T. Labhart, 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] [PubMed]

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

1998

N. Shashar, T. W. Cronin, L. B. Wolff, M. A. Condon, “The polarization of light in a tropical rain forest,” Biotropica 30, 275–285 (1998).
[CrossRef]

1997

1994

R. Wehner, “The polarization-vision project: championing organismic biology,” Fortschr. Zool. 39, 103–143 (1994).

1992

C. W. Hawryshyn, “Polarization vision in fish,” Am. Sci. 80, 164–175 (1992).

1990

K. P. Able, M. A. Able, “Ontogeny of migratory orientation in the savannah sparrow, Passerculus sandwichensis: mechanisms at sunset,” Anim. Behav. 39, 1189–1198 (1990).
[CrossRef]

1989

R. Wehner, “The hymenopteran skylight compass: matched filtering and parallel coding,” J. Exp. Biol. 146, 63–85 (1989).

1985

R. Wehner, S. Rossel, “The bee’s celestial compass—a case study in behavioral neurobiology,” Fortschr. Zool. 31, 11–53 (1985).

1984

R. Wehner, “Astronavigation in insects,” Annu. Rev. Entomol. 29, 277–298 (1984).
[CrossRef]

1982

K. P. Able, “Skylight polarization patterns at dusk influence migratory orientation in birds,” Nature 299, 550–551 (1982).
[CrossRef]

S. Rossel, R. Wehner, “The bee’s map of the E-vector pattern in the sky,” Proc. Natl. Acad. Sci. USA 79, 4451–4455 (1982).
[CrossRef]

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

1980

M. L. Brines, “Dynamic patterns of skylight polarization as clock and compass,” J. Theor. Biol. 86, 507–512 (1980).
[CrossRef] [PubMed]

1978

S. Rossel, R. Wehner, M. Lindauer, “E-vector orientation in bees,” J. Comp. Physiol., A 125, 1–12 (1978).
[CrossRef]

1977

H. W. van der Glas, “Models for unambiguous E-vector navigation in the bee,” J. Comp. Physiol. A 113, 129–159 (1977).
[CrossRef]

1976

R. Wehner, “Polarized-light navigation by insects,” Sci. Am. 235(7), 106–115 (1976).
[CrossRef] [PubMed]

1975

K. Kirschfeld, M. Lindauer, H. Martin, “Problems of menotactic orientation according to polarized light of the sky,” Z. Naturforsch. 30c, 88–90 (1975).

1972

W. Britton, “The Britton Viking sun-stone expedition,” Nutr. Today, May/June1972, pp. 14–23.

1967

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

Able, K. P.

K. P. Able, M. A. Able, “Ontogeny of migratory orientation in the savannah sparrow, Passerculus sandwichensis: mechanisms at sunset,” Anim. Behav. 39, 1189–1198 (1990).
[CrossRef]

K. P. Able, “Skylight polarization patterns at dusk influence migratory orientation in birds,” Nature 299, 550–551 (1982).
[CrossRef]

Able, M. A.

K. P. Able, M. A. Able, “Ontogeny of migratory orientation in the savannah sparrow, Passerculus sandwichensis: mechanisms at sunset,” Anim. Behav. 39, 1189–1198 (1990).
[CrossRef]

Barta, A.

A. Barta, G. Horváth, “Why is it advantageous to perceive the polarization of downwelling light under clouds and canopies in the UV?” J. Theor. Biol. 226, 429–437 (2004).
[CrossRef] [PubMed]

G. Horváth, A. Barta, J. Gál, B. Suhai, 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] [PubMed]

Brines, M. L.

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

M. L. Brines, “Dynamic patterns of skylight polarization as clock and compass,” J. Theor. Biol. 86, 507–512 (1980).
[CrossRef] [PubMed]

Britton, W.

W. Britton, “The Britton Viking sun-stone expedition,” Nutr. Today, May/June1972, pp. 14–23.

Condon, M. A.

N. Shashar, T. W. Cronin, L. B. Wolff, M. A. Condon, “The polarization of light in a tropical rain forest,” Biotropica 30, 275–285 (1998).
[CrossRef]

Coulson, K. L.

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

Cronin, T. W.

N. Shashar, T. W. Cronin, L. B. Wolff, M. A. Condon, “The polarization of light in a tropical rain forest,” Biotropica 30, 275–285 (1998).
[CrossRef]

Duggin, M. J.

Freake, M. J.

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

Gál, J.

G. Horváth, A. Barta, J. Gál, B. Suhai, 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] [PubMed]

J. Gál, G. Horváth, V. B. Meyer-Rochow, 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. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

Ganzhorn, J. U.

K. Schmidt-Koenig, J. U. Ganzhorn, R. Ranvaud, “The sun compass,” in Orientation in Birds, P. Berthold, ed. (Birkhäuser, Basel, 1991), pp. 1–15.

Gould, J. L.

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

Haiman, O.

Hawryshyn, C. W.

C. W. Hawryshyn, “Polarization vision in fish,” Am. Sci. 80, 164–175 (1992).

Horváth, G.

A. Barta, G. Horváth, “Why is it advantageous to perceive the polarization of downwelling light under clouds and canopies in the UV?” J. Theor. Biol. 226, 429–437 (2004).
[CrossRef] [PubMed]

G. Horváth, A. Barta, J. Gál, B. Suhai, 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] [PubMed]

I. Pomozi, G. Horváth, 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).
[PubMed]

J. Gál, G. Horváth, V. B. Meyer-Rochow, 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. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

G. Horváth, D. Varjú, Polarized Light in Animal Vision—Polarization Patterns in Nature (Springer, Berlin, 2003).

Kirschfeld, K.

K. Kirschfeld, M. Lindauer, H. Martin, “Problems of menotactic orientation according to polarized light of the sky,” Z. Naturforsch. 30c, 88–90 (1975).

Können, G. P.

G. P. Können, Polarized Light in Nature (Cambridge U. Press, Cambridge, UK, 1985).

Labhart, T.

T. Labhart, 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] [PubMed]

Lindauer, M.

S. Rossel, R. Wehner, M. Lindauer, “E-vector orientation in bees,” J. Comp. Physiol., A 125, 1–12 (1978).
[CrossRef]

K. Kirschfeld, M. Lindauer, H. Martin, “Problems of menotactic orientation according to polarized light of the sky,” Z. Naturforsch. 30c, 88–90 (1975).

Liu, Y.

Martin, H.

K. Kirschfeld, M. Lindauer, H. Martin, “Problems of menotactic orientation according to polarized light of the sky,” Z. Naturforsch. 30c, 88–90 (1975).

Meyer, E. P.

T. Labhart, 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] [PubMed]

Meyer-Rochow, V. B.

J. Gál, G. Horváth, V. B. Meyer-Rochow, 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. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

North, J. A.

Phillips, J. B.

J. B. Phillips, J. A. Waldvogel, “Reflected light cues generate the short-term deflector-loft effect,” in Avian Navigation, F. Papi, H. G. Wallraff, eds. (Springer, Heidelberg, Germany, 1982), pp. 190–202.

Pomozi, I.

I. Pomozi, G. Horváth, 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).
[PubMed]

Ramskou, T.

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

T. Ramskou, Solstenen—Primitiv Navigation I Norden for Kompasset (Rhodos, Copenhagen, 1969).

Ranvaud, R.

K. Schmidt-Koenig, J. U. Ganzhorn, R. Ranvaud, “The sun compass,” in Orientation in Birds, P. Berthold, ed. (Birkhäuser, Basel, 1991), pp. 1–15.

Rossel, S.

R. Wehner, S. Rossel, “The bee’s celestial compass—a case study in behavioral neurobiology,” Fortschr. Zool. 31, 11–53 (1985).

S. Rossel, R. Wehner, “The bee’s map of the E-vector pattern in the sky,” Proc. Natl. Acad. Sci. USA 79, 4451–4455 (1982).
[CrossRef]

S. Rossel, R. Wehner, M. Lindauer, “E-vector orientation in bees,” J. Comp. Physiol., A 125, 1–12 (1978).
[CrossRef]

Schaefer, B. E.

B. E. Schaefer, “Vikings and polarization sundials,” Sky Telesc. 1997(5), 91–94.

Schmidt-Koenig, K.

K. Schmidt-Koenig, J. U. Ganzhorn, R. Ranvaud, “The sun compass,” in Orientation in Birds, P. Berthold, ed. (Birkhäuser, Basel, 1991), pp. 1–15.

Shashar, N.

N. Shashar, T. W. Cronin, L. B. Wolff, M. A. Condon, “The polarization of light in a tropical rain forest,” Biotropica 30, 275–285 (1998).
[CrossRef]

Suhai, B.

van der Glas, H. W.

H. W. van der Glas, “Models for unambiguous E-vector navigation in the bee,” J. Comp. Physiol. A 113, 129–159 (1977).
[CrossRef]

Varjú, D.

G. Horváth, D. Varjú, Polarized Light in Animal Vision—Polarization Patterns in Nature (Springer, Berlin, 2003).

von Frisch, K.

K. von Frisch, The Dance Language and Orientation of Bees (Harvard U. Press, Cambridge, Mass., 1967).

Voss, K. J.

Waldvogel, J. A.

J. B. Phillips, J. A. Waldvogel, “Reflected light cues generate the short-term deflector-loft effect,” in Avian Navigation, F. Papi, H. G. Wallraff, eds. (Springer, Heidelberg, Germany, 1982), pp. 190–202.

Wehner, R.

I. Pomozi, G. Horváth, 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).
[PubMed]

J. Gál, G. Horváth, V. B. Meyer-Rochow, 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. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

R. Wehner, “The polarization-vision project: championing organismic biology,” Fortschr. Zool. 39, 103–143 (1994).

R. Wehner, “The hymenopteran skylight compass: matched filtering and parallel coding,” J. Exp. Biol. 146, 63–85 (1989).

R. Wehner, S. Rossel, “The bee’s celestial compass—a case study in behavioral neurobiology,” Fortschr. Zool. 31, 11–53 (1985).

R. Wehner, “Astronavigation in insects,” Annu. Rev. Entomol. 29, 277–298 (1984).
[CrossRef]

S. Rossel, R. Wehner, “The bee’s map of the E-vector pattern in the sky,” Proc. Natl. Acad. Sci. USA 79, 4451–4455 (1982).
[CrossRef]

S. Rossel, R. Wehner, M. Lindauer, “E-vector orientation in bees,” J. Comp. Physiol., A 125, 1–12 (1978).
[CrossRef]

R. Wehner, “Polarized-light navigation by insects,” Sci. Am. 235(7), 106–115 (1976).
[CrossRef] [PubMed]

R. Wehner, “Celestial and terrestrial navigation: human strategies—insect strategies,” in Neuroethology and Behavioral Physiology, F. Huber, H. Markl, eds. (Springer, Heidelberg, Germany, 1983), pp. 366–381.

R. Wehner, “The ant’s celestial compass system: spectral and polarization channels,” in Orientation and Communication in Arthropods, M. Lehrer, ed. (Birkhäuser, Basel, 1997), pp. 145–185.

Wolff, L. B.

N. Shashar, T. W. Cronin, L. B. Wolff, M. A. Condon, “The polarization of light in a tropical rain forest,” Biotropica 30, 275–285 (1998).
[CrossRef]

Am. Sci.

C. W. Hawryshyn, “Polarization vision in fish,” Am. Sci. 80, 164–175 (1992).

Anim. Behav.

K. P. Able, M. A. Able, “Ontogeny of migratory orientation in the savannah sparrow, Passerculus sandwichensis: mechanisms at sunset,” Anim. Behav. 39, 1189–1198 (1990).
[CrossRef]

Annu. Rev. Entomol.

R. Wehner, “Astronavigation in insects,” Annu. Rev. Entomol. 29, 277–298 (1984).
[CrossRef]

Appl. Opt.

Biotropica

N. Shashar, T. W. Cronin, L. B. Wolff, M. A. Condon, “The polarization of light in a tropical rain forest,” Biotropica 30, 275–285 (1998).
[CrossRef]

Fortschr. Zool.

R. Wehner, S. Rossel, “The bee’s celestial compass—a case study in behavioral neurobiology,” Fortschr. Zool. 31, 11–53 (1985).

R. Wehner, “The polarization-vision project: championing organismic biology,” Fortschr. Zool. 39, 103–143 (1994).

J. Comp. Physiol. A

H. W. van der Glas, “Models for unambiguous E-vector navigation in the bee,” J. Comp. Physiol. A 113, 129–159 (1977).
[CrossRef]

J. Comp. Physiol., A

S. Rossel, R. Wehner, M. Lindauer, “E-vector orientation in bees,” J. Comp. Physiol., A 125, 1–12 (1978).
[CrossRef]

J. Exp. Biol.

R. Wehner, “The hymenopteran skylight compass: matched filtering and parallel coding,” J. Exp. Biol. 146, 63–85 (1989).

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

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

I. Pomozi, G. Horváth, 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).
[PubMed]

J. Theor. Biol.

M. L. Brines, “Dynamic patterns of skylight polarization as clock and compass,” J. Theor. Biol. 86, 507–512 (1980).
[CrossRef] [PubMed]

A. Barta, G. Horváth, “Why is it advantageous to perceive the polarization of downwelling light under clouds and canopies in the UV?” J. Theor. Biol. 226, 429–437 (2004).
[CrossRef] [PubMed]

Microsc. Res. Tech.

T. Labhart, 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] [PubMed]

Nature

K. P. Able, “Skylight polarization patterns at dusk influence migratory orientation in birds,” Nature 299, 550–551 (1982).
[CrossRef]

Nutr. Today

W. Britton, “The Britton Viking sun-stone expedition,” Nutr. Today, May/June1972, pp. 14–23.

Proc. Natl. Acad. Sci. USA

S. Rossel, R. Wehner, “The bee’s map of the E-vector pattern in the sky,” Proc. Natl. Acad. Sci. USA 79, 4451–4455 (1982).
[CrossRef]

Proc. R. Soc. London Ser. A

J. Gál, G. Horváth, V. B. Meyer-Rochow, 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. London Ser. A 457, 1385–1399 (2001).
[CrossRef]

Sci. Am.

R. Wehner, “Polarized-light navigation by insects,” Sci. Am. 235(7), 106–115 (1976).
[CrossRef] [PubMed]

Skalk

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

Sky Telesc.

B. E. Schaefer, “Vikings and polarization sundials,” Sky Telesc. 1997(5), 91–94.

Z. Naturforsch.

K. Kirschfeld, M. Lindauer, H. Martin, “Problems of menotactic orientation according to polarized light of the sky,” Z. Naturforsch. 30c, 88–90 (1975).

Other

G. Horváth, D. Varjú, Polarized Light in Animal Vision—Polarization Patterns in Nature (Springer, Berlin, 2003).

J. B. Phillips, J. A. Waldvogel, “Reflected light cues generate the short-term deflector-loft effect,” in Avian Navigation, F. Papi, H. G. Wallraff, eds. (Springer, Heidelberg, Germany, 1982), pp. 190–202.

R. Wehner, “Celestial and terrestrial navigation: human strategies—insect strategies,” in Neuroethology and Behavioral Physiology, F. Huber, H. Markl, eds. (Springer, Heidelberg, Germany, 1983), pp. 366–381.

R. Wehner, “The ant’s celestial compass system: spectral and polarization channels,” in Orientation and Communication in Arthropods, M. Lehrer, ed. (Birkhäuser, Basel, 1997), pp. 145–185.

K. Schmidt-Koenig, J. U. Ganzhorn, R. Ranvaud, “The sun compass,” in Orientation in Birds, P. Berthold, ed. (Birkhäuser, Basel, 1991), pp. 1–15.

T. Ramskou, Solstenen—Primitiv Navigation I Norden for Kompasset (Rhodos, Copenhagen, 1969).

K. von Frisch, The Dance Language and Orientation of Bees (Harvard U. Press, Cambridge, Mass., 1967).

G. P. Können, Polarized Light in Nature (Cambridge U. Press, Cambridge, UK, 1985).

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

A, Distribution of the total radiance of clear skies versus the solar elevation angle θs from the horizon. The center of the circular pictures is the zenith, the perimeter is the horizon, and the zenith angle ϕ is proportional to the radius (ϕzenith=0°, ϕhorizon=90°). B, C, D, Maps of the proportion r of the sky that follows the Rayleigh model for clear skies at the wavelengths 650 nm (red), 550 nm (green), and 450 nm (blue) versus θs. “Rayleigh” points with Δα= |αmeas-αRayleigh|5° are shaded gray, “non-Rayleigh” points with Δα>5° are white, and overexposed points are black. The approximately hourly positions of the sun are represented by dots or the disk of the sun occulter. The radial bar in the circular pictures is the wire of the sun occulter. The compass rose shows the geographic (true) compass directions. Note that east and west are transposed in the compass rose, because we are looking upward at the skydome rather than downward at a map. The numerical values of r, n, and o determined for these skies are shown in Table 1.

Fig. 2
Fig. 2

As Fig. 1 but for partly cloudy skies, with approximately the same solar elevation angles θs and the same solar azimuth angles (due to appropriate rotations of the sky patterns around the zenith) as in Fig. 1. The numerical values of r, n, and o determined for these skies are shown in Tables 2 and 3.

Tables (3)

Tables Icon

Table 1 Values of r , n , and o for the Clear Skies in Fig. 1 a

Tables Icon

Table 2 Values (%) of rclouds, rclear, nclouds, nclear and o at 650 nm (Red), 550 nm (Green), and 450 nm (Blue) for the Cloudy and Clear Regions of the Partly Cloudy Skies in Fig. 2 . a

Tables Icon

Table 3 Values (%) of r=rclouds+rclear, n=nclouds+nclear, and o at 650 nm (Red), 550 nm (Green), and 450 nm (Blue) for the Partly Cloudy Skies in Fig. 2 a

Metrics