Abstract

The knowledge on the optics of fogbows is scarce, and their polarization characteristics have never been measured to our knowledge. To fill this gap we measured the polarization features of 16 fogbows during the Beringia 2005 Arctic polar research expedition by imaging polarimetry in the red, green and blue spectral ranges. We present here the first polarization patterns of the fogbow. In the patterns of the degree of linear polarization p, fogbows and their supernumerary bows are best visible in the red spectral range due to the least dilution of fogbow light by light scattered in air. In the patterns of the angle of polarization α fogbows are practically not discernible because their α-pattern is the same as that of the sky: the direction of polarization is perpendicular to the plane of scattering and is parallel to the arc of the bow, independently of the wavelength. Fogbows and their supernumeraries were best seen in the patterns of the polarized radiance. In these patterns the angular distance δ between the peaks of the primary and the first supernumerary and the angular width σ of the primary bow were determined along different radii from the center of the bow. δ ranged between 6.08° and 13.41°, while σ changed from 5.25° to 19.47°. Certain fogbows were relatively homogeneous, meaning small variations of δ and σ along their bows. Other fogbows were heterogeneous, possessing quite variable δ- and σ-values along their bows. This variability could be a consequence of the characteristics of the high Arctic with open waters within the ice shield resulting in the spatiotemporal change of the droplet size within the fog.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]

2011 (1)

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

2007 (4)

2003 (1)

2002 (1)

2001 (3)

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. 106(D19), 22647–22653 (2001).
[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, 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).
[PubMed]

1998 (1)

1991 (4)

1983 (1)

K. Lenggenhager, “Erklärung der im Vergleich zum Regen- und Nebelbogen umgekehrten Teilpolarisation der Nebelglorien,” Arch. Met. Geoph. Biocl. A 32, 165–172(1983).
[CrossRef]

1982 (2)

S. D. Gedzelman, “Rainbow brightness,” Appl. Opt. 21, 3032–3037 (1982).
[CrossRef] [PubMed]

K. Lenggenhager, “Ergänzungen zur Entstehung der Regenbogen, inneren Nebenbogen und Nebelbogen,” Arch. Met. Geoph. Biocl. A 31, 147–156 (1982).
[CrossRef]

1979 (4)

1974 (1)

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

1969 (1)

1963 (1)

K. von Bullrich, “Der Beginn der Nebelbildung und seine optische Auswirkung,” Zeitschrift für angewandte Mathematik und Physik 14, 434–441 (1963).
[CrossRef]

1940 (1)

T. E. W. Schumann, “Theoretical aspects of the size distribution of fog particles,” Q. J. R. Meteorol. Soc. 66, 195–208(1940).
[CrossRef]

1921 (1)

A. F. Hunter, “Rainbows, fogbows and their associated phenomena,” J. R. Astron. Soc. Can. 15, 345–358 (1921).

1890 (1)

J. C. McConnel, “The theory of fog-bows,” Philos. Mag. 29, 453–461 (1890).

1884 (1)

J. Tyndall, “Note on the white rainbow,” Philos. Mag. 17, 148–150 (1884).

Åkesson, S.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

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 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, 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] [PubMed]

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]

Barta, A.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

A. Barta, G. Horváth, B. Bernáth, and V. B. Meyer-Rochow, “Imaging polarimetry of the rainbow,” Appl. Opt. 42, 399–405(2003).
[CrossRef] [PubMed]

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] [PubMed]

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. 106(D19), 22647–22653 (2001).
[CrossRef]

Bernáth, B.

Coulson, K. L.

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

Dave, J. V.

de Boer, J. H.

Fraser, A. B.

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

Futterman, S. N.

Gál, J.

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] [PubMed]

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]

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. 106(D19), 22647–22653 (2001).
[CrossRef]

Gedzelman, S. D.

Greenler, R.

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

Haiman, O.

Hegedüs, R.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

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 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, 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] [PubMed]

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]

Horváth, G.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

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 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, 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] [PubMed]

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]

A. Barta, G. Horváth, B. Bernáth, and V. B. Meyer-Rochow, “Imaging polarimetry of the rainbow,” Appl. Opt. 42, 399–405(2003).
[CrossRef] [PubMed]

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] [PubMed]

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).
[PubMed]

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. 106(D19), 22647–22653 (2001).
[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]

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

Hunter, A. F.

A. F. Hunter, “Rainbows, fogbows and their associated phenomena,” J. R. Astron. Soc. Can. 15, 345–358 (1921).

Khare, V.

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

Können, G. P.

Lee, R. L.

Lenggenhager, K.

K. Lenggenhager, “Erklärung der im Vergleich zum Regen- und Nebelbogen umgekehrten Teilpolarisation der Nebelglorien,” Arch. Met. Geoph. Biocl. A 32, 165–172(1983).
[CrossRef]

K. Lenggenhager, “Ergänzungen zur Entstehung der Regenbogen, inneren Nebenbogen und Nebelbogen,” Arch. Met. Geoph. Biocl. A 31, 147–156 (1982).
[CrossRef]

Lynch, D. K.

McConnel, J. C.

J. C. McConnel, “The theory of fog-bows,” Philos. Mag. 29, 453–461 (1890).

Meyer-Rochow, V. B.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

A. Barta, G. Horváth, B. Bernáth, and V. B. Meyer-Rochow, “Imaging polarimetry of the rainbow,” Appl. Opt. 42, 399–405(2003).
[CrossRef] [PubMed]

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]

Minnaert, M.

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

Mobbs, S. D.

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

Pomozi, I.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

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).
[PubMed]

Sassen, K.

Schumann, T. E. W.

T. E. W. Schumann, “Theoretical aspects of the size distribution of fog particles,” Q. J. R. Meteorol. Soc. 66, 195–208(1940).
[CrossRef]

Schwartz, P.

Suhai, B.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

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] [PubMed]

Tricker, R. A. R.

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

Tyndall, J.

J. Tyndall, “Note on the white rainbow,” Philos. Mag. 17, 148–150 (1884).

van de Hulst, H. C.

Varjú, D.

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

von Bullrich, K.

K. von Bullrich, “Der Beginn der Nebelbildung und seine optische Auswirkung,” Zeitschrift für angewandte Mathematik und Physik 14, 434–441 (1963).
[CrossRef]

Wang, R. T.

Wehner, R.

G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, V. 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] [PubMed]

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]

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).
[PubMed]

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]

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. 106(D19), 22647–22653 (2001).
[CrossRef]

Appl. Opt. (11)

J. V. Dave, “Scattering of visible light by large water spheres,” Appl. Opt. 8, 155–164 (1969).
[CrossRef] [PubMed]

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

S. D. Gedzelman, “Rainbow brightness,” Appl. Opt. 21, 3032–3037 (1982).
[CrossRef] [PubMed]

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

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

D. K. Lynch and S. N. Futterman, “Ulloa’s observation of the glory, fogbow, and an unidentified phenomenon,” Appl. Opt. 30, 3538–3541 (1991).
[CrossRef] [PubMed]

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

R. L. Lee, “Mie theory, Airy theory, and the natural rainbow,” Appl. Opt. 37, 1506–1519 (1998).
[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] [PubMed]

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[PubMed]

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[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Simulated appearance of the fogbow as a function of the droplet diameter D ranging from 5 to 100 μm . The fogbow patterns were computed by the software IRIS (© Les Cowley [23], http://atoptics.co.uk). φ: angle (clockwise from the vertical) of the direction of a given radius. δ: angular distance between the peaks of the primary bow and the first supernumerary bow. σ: angular width of the primary bow. θ: angular distance from the bow center along a radius.

Fig. 2
Fig. 2

Color picture (A), polarized radiance P I = p · I (B), and patterns of the radiance I (C)–(E), degree of linear polarization p (F)–(H) and angle of polarization α (I)–(K) of an Arctic fogbow measured by imaging polarimetry in the red, green, and blue parts of the spectrum. Angle α is measured clockwise from the vertical. Figure b is a composite image of the polarized radiance P I : in the red, green, and blue channels the P I values measured in the red, green, and blue spectral ranges, respectively, are displayed.

Fig. 3
Fig. 3

(A) Directions φ = 60 ° , 30 ° , 0 ° , + 30 ° , + 60 ° of the radii from the bow center, along which the data in Figs. 3, 4, 5 are measured. (B)–(D) Change of the degree of linear polarization p as a function of the angular distance θ from the center of the bow measured along five different radii (from the center of the bow) of the fogbow in Fig. 2 in the red (B), green (C), and blue (D) parts of the spectrum. The directions φ (clockwise from the vertical) of the radii are given in the inset.

Fig. 4
Fig. 4

Change of the polarized radiance P I (in relative units) as a function of the angular distance θ from the center of the bow measured along five different radii (from the center of the bow) of the Arctic fogbows 6 (A) and 10 (B) in Table 1. The lower insets show the pattern of the polarized radiance P I of the fogbows. Along the bow the polarized radiance P I , the angular distance δ between the peaks of the primary bow and the first supernumerary bow, and the angular width σ of the primary bow change only moderately due to the small change of the droplet size. The directions φ (clockwise from the vertical) of the radii are given in the upper inset.

Fig. 5
Fig. 5

As Fig. 4 for the Arctic fogbows 7 (A) and 11 (B) in Table 1, along the bow of which the polarized radiance P I , the angular distance δ between the peaks of the primary bow and the first supernumerary bow, and the angular width σ of the primary bow change strongly due to the large change of the droplet size.

Fig. 6
Fig. 6

Comparison of six fogbows (a)–(f) in the pattern of polarized radiance P I measured in the high Arctic by imaging polarimetry.

Tables (1)

Tables Icon

Table 1 Angular Distance δ between Peaks of Primary Bow and First Supernumerary Bow, and Angular Width σ of Primary Bow of Arctic Fogbows Measured by Imaging Polarimetry Along Different Radii (from Center of Bow), the Direction φ of Which Is Measured Clockwise from the Vertical

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