Polarization of the Sky

Chapter
Part of the Springer Series in Vision Research book series (SSVR, volume 2)

Abstract

Based on full-sky imaging polarimetric measurements, in this chapter we demonstrate that the celestial distribution of the angle of polarization (or E-vector direction) of skylight is a very robust pattern being qualitatively always the same under all possible sky conditions. Practically the only qualitative difference among clear, partly cloudy, overcast, foggy, smoky and tree-canopied skies occurs in the degree of linear polarization d: The higher the optical thickness of the non-clear atmosphere, the lower the d of skylight. We review here how well the Rayleigh model describes the E-vector pattern of clear and cloudy skies. We deal with the polarization patterns of foggy, partly cloudy, overcast, twilight, smoky and total-solar-eclipsed skies. We describe the possible influences of the changed polarization pattern of smoky and eclipsed skies on insect orientation. We consider the polarization of ‘water-skies’ above Arctic open waters and the polarization characteristics of fogbows. Finally, we deal with the change of skylight polarization due to the transmission through Snell’s window of the flat water surface.

Supplementary material

71484_2_En_18_MOESM1_ESM.zip (906 kb)
Supplementary Fig. 18.1(a) Distribution of the radiance of clear skies versus the solar elevation angle θS from the horizon. The centre 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 = |αmeasuredαRayleigh| ≤ 5° are shaded grey, ‘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 compass directions. Note that East and West are transposed in the compass rose, because we are looking upward at the sky-dome rather than downward at a map [after Fig. 1 on page 1671 of Suhai and Horváth (2004)] (CDR 912 kb)
71484_2_En_18_MOESM2_ESM.zip (939 kb)
Supplementary Fig. 18.2As Supplementary Fig. 18.1 for partly cloudy skies with approximately the same solar elevation angles θS and the same solar azimuth angles as in Supplementary Fig. 18.1 [after Fig. 2 on page 1673 of Suhai and Horváth (2004)] (CDR 945 kb)
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Supplementary Fig. 18.3Photograph and patterns of the radiance I, degree of linear polarization d and angle of polarization α of a foggy Arctic sky measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm) and blue (450 nm) parts of the spectrum. The optical axis of the fisheye lens was vertical; thus the horizon is the perimeter and the centre of the circular patterns is the zenith. (b) Theoretical α-pattern of the clear sky calculated on the basis of the model of Berry et al. (2004) for the same sun position as in the foggy sky in picture (a). The positions of the sun as well as the Arago and Babinet neutral points are marked by dots in the α-patterns (CDR 2779 kb)
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Supplementary Fig. 18.4As Supplementary Fig. 18.3 for a clear Arctic sky (CDR 2691 kb)
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Supplementary Fig. 18.5As Supplementary Fig. 18.3 for a partly cloudy Arctic sky (CDR 2792 kb)
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Supplementary Fig. 18.6Photographs and patterns of the angle of polarization α (measured clockwise from the local meridian) of Arctic and Hungarian total overcast skies S1–S15 measured by full-sky imaging polarimetry in the blue (450 nm) part of the spectrum. Quite similar α-patterns were obtained in both the green (550 nm) and red (650) spectral ranges [after Fig. 3 on page 2352 of Hegedüs et al. (2007c)] (CDR 11140 kb)
71484_2_En_18_MOESM7_ESM.zip (1.7 mb)
Supplementary Fig. 18.7Photograph (a) and patterns of the degree of linear polarization d (ce) and angle of polarization α (fh) of the reddish smoky sky above Fairbanks (64° 49′ N, 147° 45′ W) measured by full-sky imaging polarimetry in the red (c, f), green (d, g) and blue (e, h) parts of the spectrum on 17 August 2005 at 15:01 h (local summer time = UTC − 8). (b) Theoretical α-pattern of the clear sky calculated on the basis of the multiple-scattering model of Berry et al. (2004) for the same sun position as in photograph (a). In patterns ch the estimated positions of the Arago and Babinet neutral points are shown by ‘ar’ and ‘ba’, respectively. The optical axis of the fisheye lens was vertical; thus the horizon and zenith is the perimeter and the centre of the circular patterns, respectively. The position of the sun is represented by a dot. The underexposed trees near the horizon are marked by a checkered pattern [after Fig. 3 on page 2720 of Hegedüs et al. (2007d)] (CDR 1769 kb)
71484_2_En_18_MOESM8_ESM.zip (1.9 mb)
Supplementary Fig. 18.8Photograph (a) and patterns of the degree of linear polarization d (ce) and angle of polarization α (fh) of the reddish smoky sky above Fairbanks (64° 49′ N, 147° 45′ W) measured by full-sky imaging polarimetry in the red (c, f), green (d, g) and blue (e, h) parts of the spectrum on 17 August 2005 at 20:20 h (local summer time = UTC − 8). (b) Theoretical α-pattern of the clear sky calculated on the basis of the multiple-scattering model of Berry et al. (2004) for the same sun position as in photograph (a). In patterns ch the estimated positions of the Arago and Babinet neutral points are shown by ‘ar’ and ‘ba’, respectively. The optical axis of the fisheye lens was vertical; thus the horizon and zenith is the perimeter and the centre of the circular patterns, respectively. The position of the invisible sun occluded by the thick smoke layer near the horizon is represented by a dot. The solar position was obtained from the online solar position calculator of U.S. Naval Observatory, Astromonical Applications Department (http://aa.usno.navy.mil) on the basis of the exact time and geographical coordinates of the site of measurements. The underexposed trees near the horizon are marked by a checkered pattern [after Fig. 4 on page 2721 of Hegedüs et al. (2007d)] (CDR 1919 kb)
71484_2_En_18_MOESM9_ESM.zip (2.3 mb)
Supplementary Fig. 18.9Photograph (a) and patterns of the degree of linear polarization d (ce) and angle of polarization α (fh) of a clear blue sky above the Arctic ice cover measured by full-sky imaging polarimetry in the red (c, f), green (d, g) and blue (e, h) parts of the spectrum on 25 August 2005 at 21:20 h (local summer time = UTC − 8) at the site 78° 28′ N and 149° 9′W. (b) Theoretical α-pattern of the clear sky calculated on the basis of the multiple-scattering model of Berry et al. (2004) for the same sun position as in photograph (a). In patterns ch the estimated positions of the Arago and Babinet neutral points are shown by ‘ar’ and ‘ba’, respectively. The optical axis of the fisheye lens was vertical; thus the horizon and zenith are the perimeter and the centre of the circular patterns, respectively. The position of the sun is represented by a dot. The overexposed sky region around the sun and the underexposed contour of the icebreaker Oden are marked by a checkered pattern [after Fig. 5 on page 2723 of Hegedüs et al. (2007d)] (CDR 2314 kb)
71484_2_En_18_MOESM10_ESM.zip (521 kb)
Supplementary Fig. 18.10Map of Turkey showing the path of the moon’s shadow (umbra) during the total solar eclipse on 29 March 2006. The full-sky imaging polarimetric measurements of Sipőcz et al. (2008) were performed in the immediate vicinity of Side, the ancient maritime city, on the coast of the Mediterranean sea [after Fig. 1 on page H2 of Sipőcz et al. (2008)] (CDR 526 kb)
71484_2_En_18_MOESM11_ESM.zip (16.8 mb)
Supplementary Fig. 18.11Patterns of d of skylight measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm) and blue (450 nm) parts of the spectrum during the total solar eclipse on 29 March 2006 in Turkey [after Fig. 3 on page H5 of Sipőcz et al. (2008)] (CDR 17191 kb)
71484_2_En_18_MOESM12_ESM.zip (12.5 mb)
Supplementary Fig. 18.12As Supplementary Fig. 18.11 for the angle of polarization α of skylight [after Fig. 4 on page H5 of Sipőcz et al. (2008)] (CDR 12815 kb)
71484_2_En_18_MOESM13_ESM.zip (682 kb)
Supplementary Fig. 18.13(a) 180° field-of-view photograph of the sky above the Arctic ice with a polynya stretching at the right half of the picture on 11 September 2005 at 07:30 (local summer time = UTC − 8) at the geographical coordinates 89° 15.5′ N and 172° 22.6′ W. (b, c) Patterns of the degree of linear polarization d and the angle of polarization α of the sky measured by 180° field-of-view imaging polarimetry in the blue (450 nm) part of the spectrum. These patterns were very similar to those measured in the green (550 nm) and red (650 nm) parts of the spectrum. The optical axis of the fisheye lens was horizontal; thus the horizon is the horizontal diameter of the circular picture, the upper and lower parts of which show the sky and the ice cover with a polynya, respectively. Only a fraction of the ice surface is shown at the bottom left part of the picture. The horizontal celestial bright band below the grey water-sky is due to the bright ice-sky light reaching the observer through the more or less transparent rising vapour below the fog cloud. Thus, the light from this bright band has approximately the same radiance and polarization as the original ice-sky light [after Fig. 4 on page 137 of Hegedüs et al. (2007a)] (CDR 689 kb)
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Supplementary Fig. 18.14Photograph of the sky and celestial intensity and polarization patterns measured by imaging polarimetry and calculated on the basis of the single-scattering Rayleigh model when the sun is on the horizon (CDR 3787 kb)
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Supplementary Fig. 18.15As Supplementary Fig. 18.14 for a higher solar elevation angle (CDR 3509 kb)
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Supplementary Fig. 18.16As Supplementary Fig. 18.14 for a higher solar elevation angle (CDR 3753 kb)
71484_2_En_18_MOESM17_ESM.zip (7.5 mb)
Video Clip 18.1Colour picture of skylight and earthlight photographed from a hot air balloon at a height of 3,500 m on 25 June 2001 by a 180° field-of-view imaging polarimeter at sunrise. The 180° field-of-view circular sky and earth pictures are displayed on the celestial and terrestrial hemispheres, respectively. The two hemispheres compose a rotating sphere that demonstrates how an observer sees the scenery when looking around (copyright holders: Dr. Balázs Bernáth, Bence Suhai and Dr. Gábor Horváth) (GIF 7709 kb)
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Video Clip 18.2Degree of linear polarization p of skylight and earthlight measured by 180° field-of-view imaging polarimetry in the green (550 nm) spectral range from a hot air balloon at a height of 3,500 m on 25 June 2001 at sunrise. The 180° field-of-view circular p-patterns of skylight and earthlight are displayed on the celestial and terrestrial hemispheres, respectively. The two hemispheres compose a rotating sphere that demonstrates how a polarization-sensitive observer sees the scenery when looking around. The Arago/fourth and the Babinet/Brewster neutral points of atmospheric polarization are above/below the anti-sun and sun, respectively (copyright holders: Dr. Balázs Bernáth, Bence Suhai and Dr. Gábor Horváth) (GIF 9709 kb)
71484_2_En_18_MOESM19_ESM.zip (10.3 mb)
Video Clip 18.3Angle of polarization α of skylight and earthlight measured by 180° field-of-view imaging polarimetry in the green (550 nm) spectral range from a hot air balloon at a height of 3,500 m on 25 June 2001 at sunrise. The 180° field-of-view circular α-patterns of skylight and earthlight are displayed on the celestial and terrestrial hemispheres, respectively. The two hemispheres compose a rotating sphere that demonstrates how a polarization-sensitive observer sees the scenery when looking around. The Arago/fourth and the Babinet/Brewster neutral points of atmospheric polarization are above/below the anti-sun and sun, respectively (copyright holders: Dr. Balázs Bernáth, Bence Suhai and Dr. Gábor Horváth) (GIF 10553 kb)
71484_2_En_18_MOESM20_ESM.zip (2.3 mb)
Video Clip 18.4Pattern of the degree δ (left) and angle α (clockwise from the local meridian; right) of linear polarization of skylight calculated on the basis of the single-scattered Rayleigh model as a function of time (sun position) on 21 June 2000 at Maharés (Tunisia). The sun position is marked by a black dot. In the α-pattern the local direction of polarization of skylight is shown by a black bar. East and West are transposed in the compass rose, because we are looking upward at the sky-dome rather than downward at a map (copyright holders: Dr. József Gál and Dr. Gábor Horváth) (GIF 8981 kb)
71484_2_En_18_MOESM21_ESM.zip (9.8 mb)
Video Clip 18.5Patterns of the intensity I (upper row), degree d (middle row) and angle α (clockwise from the local meridian, lower row) of linear polarization of light from a clear sky during 24 h as a function of time at Sodankylä (Finland) in June 1999 when the sun did not set below the horizon. The patterns were measured by 180° field-of-view imaging polarimetry in the red (650 nm, left column), green (550 nm, middle column) and blue (450 nm, right column) parts of the spectrum. The higher the d-value, the darker the grey shade (white: p = 0 %, black: p = 100 %). The centre and perimeter of the circular patterns are the zenith and the horizon, respectively. The sun was occluded by a small disc. One of the radial bars is the wire of the sun occulter rotating together with the solar meridian. The other, constant, bar is the metal rod of a meteorological tower. In the α-patterns the overexposed sky regions are shaded black (copyright holders: Dr. József Gál and Dr. Gábor Horváth) (GIF 21545 kb)
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Video Clip 18.6Colour picture and the patterns of the degree d and angle α of linear polarization of the sky measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm) and blue (450 nm) parts of the spectrum at Kecel (Hungary) on 11 August 1999 at 12:51 (=local summer time = UTC + 2 h) prior to the totality of a solar eclipse. The 180° field-of-view circular patterns are displayed on a rotating hemisphere. The sun is occluded by a small disc held by a wire. The overexposed sky regions are red and black in the d- and α-patterns, respectively (copyright holders: Bence Suhai, Dr. József Gál, Dr. István Pomozi and Dr. Gábor Horváth) (GIF 14278 kb)
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Video Clip 18.7Colour picture and the patterns of the degree d and angle α of linear polarization of the sky measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm) and blue (450 nm) parts of the spectrum at Kecel (Hungary) on 11 August 1999 at 12:52 (=local summer time = UTC + 2 h) during the totality of a solar eclipse. The 180° field-of-view circular patterns are displayed on a rotating hemisphere. In the d-patterns the weakly polarized or unpolarized (neutral) points of the sky and their surroundings are displayed by blue–green–yellow colours (copyright holders: Bence Suhai, Dr. József Gál, Dr. István Pomozi and Dr. Gábor Horváth) (GIF 14278 kb)
71484_2_En_18_MOESM24_ESM.zip (4.1 mb)
Video Clip 18.8Colour picture and the patterns of the degree d and angle α of linear polarization of the sky measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm) and blue (450 nm) parts of the spectrum at Kecel (Hungary) on 11 August 1999 at 12:52 (=local summer time = UTC + 2 h) during the totality of a solar eclipse. The 180° field-of-view circular patterns are displayed on a rotating hemisphere. The overexposed sky regions are red and black in the d- and α-patterns, respectively (copyright holders: Bence Suhai, Dr. József Gál, Dr. István Pomozi and Dr. Gábor Horváth) (GIF 14278 kb)
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Video Clip 18.9Colour picture and the patterns of the degree d and angle α of linear polarization of the normal, partly cloudy sky measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm) and blue (450 nm) parts of the spectrum at Kecel (Hungary) on 12 August 1999 (subsequent day of the total solar eclipse of 11 August 1999) at 12:52 (=local summer time = UTC + 2 h). The 180° field-of-view circular patterns are displayed on a rotating hemisphere. The clouds are red and black in the d- and α-patterns, respectively. The sun is occluded by a small disc held by a wire (copyright holders: Bence Suhai, Dr. József Gál, Dr. István Pomozi and Dr. Gábor Horváth) (GIF 14278 kb)
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Video Clip 18.10Colour picture and the patterns of the degree d and angle α of linear polarization of the normal, clear sky measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm) and blue (450 nm) parts of the spectrum in Tunisia on 26 August 1999 at 12:00 (=local summer time = UTC + 1 h) for the same zenith angle of 32° of the sun as that during the totality of the solar eclipse on 11 August 1999. The 180° field-of-view circular patterns are displayed on a rotating hemisphere. The overexposed sky regions are red and black in the d- and α-patterns, respectively. The sun is occluded by a small disc held by a wire (copyright holders: Bence Suhai, Dr. József Gál, Dr. István Pomozi and Dr. Gábor Horváth) (GIF 14278 kb)
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Video Clip 18.11Colour picture and the patterns of the degree d and angle α of linear polarization of the sky measured by full-sky imaging polarimetry in the red (650 nm), green (550 nm) and blue (450 nm) parts of the spectrum at Kecel (Hungary) on 11 August 1999 from the pre-eclipse (11:29−12:51 = local summer time = UTC + 2 h) through the totality (12:52−12:53) to the post-eclipse (13:01−14:13) during the total solar eclipse. In the d-patterns the over- and underexposed sky regions are red and blue, respectively. In the α-patterns the over- or underexposed sky regions are black. During the pre- and post-eclipse the sun is occluded by a small disc held by a wire (copyright holders: Dr. István Pomozi, Dr. József Gál and Dr. Gábor Horváth) (GIF 9358 kb)
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Video Clip 18.12180° field-of-view (full-sky) colour photographs of the sky taken at Kunfehértó (Hungary) on 11 August 1999 from the pre-eclipse through the totality to the post-eclipse during the total solar eclipse (local summer time = UTC + 2 h). East and West are transposed in the compass rose, because we are looking upward at the sky-dome rather than downward at a map (copyright holders: Dr. Balázs Bernáth, Bence Suhai, Dr. József Gál and Dr. Gábor Horváth) (GIF 18085 kb)
71484_2_En_18_MOESM29_ESM.zip (710 kb)
Video Clip 18.13Patterns of the intensity I (upper row), degree d (middle row) and angle α (clockwise from the vertical, lower row) of linear polarization of light from the solar corona measured by imaging polarimetry in the red (650 nm, left column), green (550 nm, middle column) and blue (450 nm, right column) parts of the spectrum at Kecel (Hungary) on 11 August 1999 during the totality of the solar eclipse. The higher the d-value, the darker the grey shade (white: p = 0 %, black: p = 100 %). In the d-patterns the over- and underexposed sky regions are red and blue, respectively. In the α-patterns the over- or underexposed sky regions are black (copyright holders: Dr. István Pomozi and Dr. Gábor Horváth) (GIF 5174 kb)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Gábor Horváth
    • 1
  • András Barta
    • 2
  • Ramón Hegedüs
    • 3
    • 4
    • 5
  1. 1.Environmental Optics Laboratory, Department of Biological Physics, Physical InstituteEötvös UniversityBudapestHungary
  2. 2.Estrato Research and Development LtdBudapestHungary
  3. 3.Max Planck Institute for InformaticsSaarbrueckenGermany
  4. 4.INRIA Sud-Ouest BordeauxTalenceFrance
  5. 5.Laboratoire Photonique, Numérique et Nanosciences (L2PN), UMR 5298CNRS IOGS University Bordeaux, Institut d’Optique d’AquitaineTalenceFrance

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