Abstract

Using imaging polarimetry, we measured the polarization patterns of a rainbow on the shore of the Finnish town of Oulu in July 2001. We present here high-resolution color-coded maps of the spatial distributions of the degree and angle of linear polarization of the rainbow in the red (650 ± 30 nm), green (550 ± 30 nm), and blue (450 ± 30 nm) ranges of the spectrum. The measured polarization characteristics of the investigated rainbow support earlier theoretical and computational results and are in accordance with previous qualitative observations. To our knowledge, this is the first imaging polarimetric study of rainbow polarization.

© 2003 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  21. 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).
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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]

1998

1991

Light and color in the open air, feature issue, J. A. Lock, ed., Appl. Opt. 30, 3381–3552 (1991).

R. L. Lee, “What are ‘all the colors of the rainbow’?” Appl. Opt. 30, 3401–3407 (1991).
[CrossRef] [PubMed]

D. K. Lynch, P. Schwartz, “Rainbows and fogbows,” Appl. Opt. 30, 3415–3420 (1991).
[CrossRef] [PubMed]

R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
[CrossRef] [PubMed]

1986

G. P. Können, “Viewing our world with polarizing glasses,” Endeavour (new series) 10(3), 121–124 (1986).
[CrossRef]

1982

1979

K. Sassen, “Angular scattering and rainbow formation in pendant drops,” J. Opt. Soc. Am. 69, 1083–1089 (1979).
[CrossRef]

G. P. Können, J. H. de Boer, “Polarized rainbow,” Appl. Opt. 18, 1961–1965 (1979).
[CrossRef] [PubMed]

H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
[CrossRef]

S. D. Mobbs, “Theory of the rainbow,” J. Opt. Soc. Am. 69, 1089–1092 (1979).
[CrossRef]

1974

V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
[CrossRef]

1969

Coulson, K. L.

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

Dave, J. V.

de Boer, J. H.

Fraser, A. B.

R. L. Lee, A. B. Fraser, The Rainbow Bridge: Rainbows in Art, Myth, and Science (Pennsylvania State University, Philadelphia, 2001).

Gál, J.

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]

Gedzelman, S. D.

Greenler, R.

R. Greenler, Rainbows, Halos, and Glories (Cambridge University, Cambridge, UK, 1980).

Horváth, G.

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]

Khare, V.

V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
[CrossRef]

Können, G. P.

G. P. Können, “Viewing our world with polarizing glasses,” Endeavour (new series) 10(3), 121–124 (1986).
[CrossRef]

G. P. Können, J. H. de Boer, “Polarized rainbow,” Appl. Opt. 18, 1961–1965 (1979).
[CrossRef] [PubMed]

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

G. P. Können, “Polarization in nature,” in Direct and Inverse Methods in Radar Polarimetry. Part I. W.-M. Boerner, ed. (Kluwer, Amsterdam, 1992), pp. 33–44.

Lee, R. L.

Lynch, D. K.

D. K. Lynch, P. Schwartz, “Rainbows and fogbows,” Appl. Opt. 30, 3415–3420 (1991).
[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]

Minnaert, M.

M. Minnaert, Light and Color in the Open Air (Bell, London, 1940).

Mobbs, S. D.

S. D. Mobbs, “Theory of the rainbow,” J. Opt. Soc. Am. 69, 1089–1092 (1979).
[CrossRef]

Nussenzveig, H. M.

H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
[CrossRef]

V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
[CrossRef]

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]

Sassen, K.

Schwartz, P.

D. K. Lynch, P. Schwartz, “Rainbows and fogbows,” Appl. Opt. 30, 3415–3420 (1991).
[CrossRef] [PubMed]

Tricker, R. A. R.

R. A. R. Tricker, Introduction to Meteorological Optics (Elsevier, New York, 1970).

van de Hulst, H. C.

R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
[CrossRef] [PubMed]

Wang, R. T.

R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
[CrossRef] [PubMed]

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]

Appl. Opt.

D. K. Lynch, P. Schwartz, “Rainbows and fogbows,” Appl. Opt. 30, 3415–3420 (1991).
[CrossRef] [PubMed]

R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
[CrossRef] [PubMed]

Appl. Opt.

Endeavour (new series)

G. P. Können, “Viewing our world with polarizing glasses,” Endeavour (new series) 10(3), 121–124 (1986).
[CrossRef]

J. Exp. Biol.

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. Opt. Soc. Am.

H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
[CrossRef]

S. D. Mobbs, “Theory of the rainbow,” J. Opt. Soc. Am. 69, 1089–1092 (1979).
[CrossRef]

J. Opt. Soc. Am.

Phys. Rev. Lett.

V. Khare, H. M. Nussenzveig, “Theory of the rainbow,” Phys. Rev. Lett. 33, 976–980 (1974).
[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]

Other

G. P. Können, “Polarization in nature,” in Direct and Inverse Methods in Radar Polarimetry. Part I. W.-M. Boerner, ed. (Kluwer, Amsterdam, 1992), pp. 33–44.

R. L. Lee, A. B. Fraser, The Rainbow Bridge: Rainbows in Art, Myth, and Science (Pennsylvania State University, Philadelphia, 2001).

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

M. Minnaert, Light and Color in the Open Air (Bell, London, 1940).

R. A. R. Tricker, Introduction to Meteorological Optics (Elsevier, New York, 1970).

R. Greenler, Rainbows, Halos, and Glories (Cambridge University, Cambridge, UK, 1980).

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

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Figures (4)

Fig. 1
Fig. 1

180° field-of-view color photograph of the shore of Oulu (65° 0′N, 25° 26′E, Finland) with a rainbow above the sea surface (A) and the patterns of radiance I (B, E, H), degree of linear polarization p (C, F, I) and angle of polarization α (D, G, J) measured by 180° imaging polarimetry on 18 July 2001, at 17:42 (local summer time, UTC + 3), in the blue (450 ± 30 nm), green (550 ± 30 nm), and red (650 ± 30 nm) spectral ranges, when the solar elevation was 29° 41′ above the horizon. Time of exposure, 1/250 s; aperture, 5.6; detector, Fujichrome Sensia II; 100 ASA color reversal film. At a given point of the circular patterns, α is measured clockwise from the radius. The black bars in the α patterns show the local direction of polarization at points of a quadratic grid.

Fig. 2
Fig. 2

(A–C) Enlarged rectangular parts of the three polarization color pictures of the rainbow in Fig. 1 taken through a linear polarizer with three different orientations χ (measured from the vertical) of the transmission axis (E-vector). (D) The averaged color picture (as could be seen by the human eye or could be photographed without a polarizer) computed from the three polarization pictures.

Fig. 3
Fig. 3

Patterns of radiance I (A, D, G), degree of linear polarization p (B, E, H) and angle of polarization α (C, F, I) of the rainbow in Fig. 2 measured in the blue (450 nm), green (550 nm), and red (650 nm) spectral ranges. α measured clockwise from the radius and p are shown in the color wheel and gray-scale bar in Fig. 1, respectively. The black bars in the α patterns show the local direction of polarization. The plots in Fig. 4 are based on data measured along the vertical arrows B, C, E, F, H, I.

Fig. 4
Fig. 4

Degree of linear polarization p (A, C, E) and angle of polarization α (B, D, F) in the blue (450 nm), green (550 nm), and red (650 nm) spectral ranges as a function of the angle of elevation θ (horizontal axis) measured along the vertical arrows shown in Fig. 3 (pointing from bottom θ = 0° to top θ = 28°) after subtraction of the contribution of light from the sky background. α is measured clockwise from the radius of the original circular picture in Fig. 1.

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