Abstract

When seen in divergent light, atmospheric optical phenomena could appear to be modified. We describe some geometric and retroreflectional effects of light divergence on heiligenschein and related phenomena that, to our knowledge, have not been previously reported. These geometric effects are compared with and set in relation to the geometric effects on other atmospheric optical phenomena.

© 2001 Optical Society of America

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References

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  1. M. Minnaert, “Een halo in de onmiddellijke nabijheid van het oog,” Hemel Dampkring 26, 51–54 (1928).
  2. J. O. Mattsson, L. Bärring, E. Almqvist, “Experimenting with Minnaert’s Cigar,” Appl. Opt. 39, 3604–3611 (2000).
    [CrossRef]
  3. C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
    [CrossRef]
  4. C. Floor, “Optic phenomena and optical illusions near lighthouses,” Z. Meteorol. 32, 229–233 (1982).
  5. J. O. Mattsson, “Concerning haloes, rainbows and dewbows in divergent light,” Weather 53, 176–181 (1998).
    [CrossRef]
  6. J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).
  7. D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, England, 1995).
  8. K. Muinonen, “Coherent backscattering by solar system dust particles,” in Asteroids, Comets, Meteors 1993, A. Milani, M. Di Martino, A. Cellino, eds.International Astronomical Union Symposium No. 160 (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 271–293.
    [CrossRef]
  9. J. O. Mattsson, “Heiligenschein and retro-reflection from drop-covered surfaces,” (Department of Physical Geography, Lund University, Lund, Sweden, 1971), in Swedish.
  10. A. B. Fraser, “The sylvanshine: retroreflection from dew-covered trees,” Appl. Opt. 33, 4539–4547 (1994).
    [CrossRef] [PubMed]
  11. J. O. Mattsson, C. Cavallin, “Retroreflection of light from drop-covered surfaces and an image-producing device for registration of this light,” Oikos 23, 285–294 (1972).
    [CrossRef]
  12. R. Greenler, Rainbows, Halos, and Glories (Cambridge University, Cambridge, England, 1980).
  13. J. O. Mattsson, “Dew as a climatic indicator,” Svensk Geografisk Årsbok 47, 29–52 (1971), in Swedish.
  14. J. O. Mattsson, “Climatic information in night-recorded aerial photographs with special regard to registrations made in retroreflected light,” (Department of Physical Geography, Lund University, Lund, Sweden, 1974).
  15. J. O. Mattsson, “Images made by laser-scanner,” Svensk Lantmäteritidskrift 64, 435–441 (1972), in Swedish.

2000 (1)

1998 (1)

J. O. Mattsson, “Concerning haloes, rainbows and dewbows in divergent light,” Weather 53, 176–181 (1998).
[CrossRef]

1994 (1)

1982 (1)

C. Floor, “Optic phenomena and optical illusions near lighthouses,” Z. Meteorol. 32, 229–233 (1982).

1980 (1)

C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
[CrossRef]

1972 (2)

J. O. Mattsson, C. Cavallin, “Retroreflection of light from drop-covered surfaces and an image-producing device for registration of this light,” Oikos 23, 285–294 (1972).
[CrossRef]

J. O. Mattsson, “Images made by laser-scanner,” Svensk Lantmäteritidskrift 64, 435–441 (1972), in Swedish.

1971 (1)

J. O. Mattsson, “Dew as a climatic indicator,” Svensk Geografisk Årsbok 47, 29–52 (1971), in Swedish.

1928 (1)

M. Minnaert, “Een halo in de onmiddellijke nabijheid van het oog,” Hemel Dampkring 26, 51–54 (1928).

Almqvist, E.

Bärring, L.

Cavallin, C.

J. O. Mattsson, C. Cavallin, “Retroreflection of light from drop-covered surfaces and an image-producing device for registration of this light,” Oikos 23, 285–294 (1972).
[CrossRef]

Floor, C.

C. Floor, “Optic phenomena and optical illusions near lighthouses,” Z. Meteorol. 32, 229–233 (1982).

C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
[CrossRef]

Fraser, A. B.

Greenler, R.

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

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, England, 1995).

Lynch, D. K.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, England, 1995).

Mattsson, J. O.

J. O. Mattsson, L. Bärring, E. Almqvist, “Experimenting with Minnaert’s Cigar,” Appl. Opt. 39, 3604–3611 (2000).
[CrossRef]

J. O. Mattsson, “Concerning haloes, rainbows and dewbows in divergent light,” Weather 53, 176–181 (1998).
[CrossRef]

J. O. Mattsson, C. Cavallin, “Retroreflection of light from drop-covered surfaces and an image-producing device for registration of this light,” Oikos 23, 285–294 (1972).
[CrossRef]

J. O. Mattsson, “Images made by laser-scanner,” Svensk Lantmäteritidskrift 64, 435–441 (1972), in Swedish.

J. O. Mattsson, “Dew as a climatic indicator,” Svensk Geografisk Årsbok 47, 29–52 (1971), in Swedish.

J. O. Mattsson, “Climatic information in night-recorded aerial photographs with special regard to registrations made in retroreflected light,” (Department of Physical Geography, Lund University, Lund, Sweden, 1974).

J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).

J. O. Mattsson, “Heiligenschein and retro-reflection from drop-covered surfaces,” (Department of Physical Geography, Lund University, Lund, Sweden, 1971), in Swedish.

Minnaert, M.

M. Minnaert, “Een halo in de onmiddellijke nabijheid van het oog,” Hemel Dampkring 26, 51–54 (1928).

Muinonen, K.

K. Muinonen, “Coherent backscattering by solar system dust particles,” in Asteroids, Comets, Meteors 1993, A. Milani, M. Di Martino, A. Cellino, eds.International Astronomical Union Symposium No. 160 (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 271–293.
[CrossRef]

Nordbeck, S.

J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).

Rystedt, B.

J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).

Appl. Opt. (2)

Hemel Dampkring (1)

M. Minnaert, “Een halo in de onmiddellijke nabijheid van het oog,” Hemel Dampkring 26, 51–54 (1928).

Oikos (1)

J. O. Mattsson, C. Cavallin, “Retroreflection of light from drop-covered surfaces and an image-producing device for registration of this light,” Oikos 23, 285–294 (1972).
[CrossRef]

Svensk Geografisk Årsbok (1)

J. O. Mattsson, “Dew as a climatic indicator,” Svensk Geografisk Årsbok 47, 29–52 (1971), in Swedish.

Svensk Lantmäteritidskrift (1)

J. O. Mattsson, “Images made by laser-scanner,” Svensk Lantmäteritidskrift 64, 435–441 (1972), in Swedish.

Weather (2)

C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
[CrossRef]

J. O. Mattsson, “Concerning haloes, rainbows and dewbows in divergent light,” Weather 53, 176–181 (1998).
[CrossRef]

Z. Meteorol. (1)

C. Floor, “Optic phenomena and optical illusions near lighthouses,” Z. Meteorol. 32, 229–233 (1982).

Other (6)

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

J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, England, 1995).

K. Muinonen, “Coherent backscattering by solar system dust particles,” in Asteroids, Comets, Meteors 1993, A. Milani, M. Di Martino, A. Cellino, eds.International Astronomical Union Symposium No. 160 (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 271–293.
[CrossRef]

J. O. Mattsson, “Heiligenschein and retro-reflection from drop-covered surfaces,” (Department of Physical Geography, Lund University, Lund, Sweden, 1971), in Swedish.

J. O. Mattsson, “Climatic information in night-recorded aerial photographs with special regard to registrations made in retroreflected light,” (Department of Physical Geography, Lund University, Lund, Sweden, 1974).

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Figures (12)

Fig. 1
Fig. 1

Water drops or ice crystals that cause some of the atmospheric optical phenomena in divergent light are situated on the surface of an imaginary body formed by rotation of a circle segment around its chord: (a) the 22° halo, (b) the 46° halo, (c) the secondary rainbow, (d) the primary rainbow. L denotes the light source and O represents the observer’s eye. All the angle values in the figure are phase angles, i.e., angles from the antisolar point. The phase angle equals 180° minus the scattering angle, which is the angle from the light source. All the points that correspond to the indicated angles are localized at the circle segments.

Fig. 2
Fig. 2

Spatial heiligenschein on bare soil. Photograph taken by J. O. Mattsson, near Malmö, Sweden, in 1972.

Fig. 3
Fig. 3

Sylvanshine from a silver spruce (Abies alba) with myriads of dewdrops and fog drops. Flash-lamp photograph taken by J. O. Mattsson at Ljunghusen, South Sweden, 26 November 1999, at 0.30 a.m MET.

Fig. 4
Fig. 4

Composite of flashlight images recorded from an airplane flying over Prästtomta, South Sweden, in the late evening of 16 April 1968. Strong retroreflection from dew characterized open terrain. The figure illustrates an effect related to the sylvanshine. As with the sylvanshine the light source was close to the observer and camera, and the retroreflecting area therefore extended over a large solid angle. In contrast with the sylvanshine, the retroreflection from the trees was minimal or nonexistent. The short sides of the image correspond to approximately 200 m. The photographs were taken by the staff of an experimental station belonging to the Swedish Defence Material Administration in Malmslätt, South Sweden.

Fig. 5
Fig. 5

Circle segments that, by rotation around their chords, form the imaginary rotatory bodies of some atmospheric optical phenomena. For comparison of the size of the patterns and unlike the chords in Fig. 1 all the chords here are the same length. The limit beyond which the phase angle for heiligenschein is less than 5° as well as the intersection lines that correspond to the horizontal surface in some of the subsequent figures are included. For an explanation of the symbols see Fig. 1.

Fig. 6
Fig. 6

Retroreflecting areas (white) calculated for a plane horizontal surface (e.g., the ground) illuminated by divergent light. An asterisk denotes the lamp (a mathematical point); a dot denotes the observer. The lamp is situated 2.5 m above the plane surface; the observer’s eye level is at 2 m. The distance between the footpoints of the lamp and the observer is (a) 0 m, (b) 0.12 m, (c) 0.15 m. The dark patterns in this and the following figures were formed by analogy with transverse sections through an apple. All the measurements are in meters.

Fig. 7
Fig. 7

Same as Fig. 6 but with the lamp 5 m above ground and 2 m between the footpoints of the lamp and the observer.

Fig. 8
Fig. 8

Same as Fig. 7 but with 5 m between the footpoints of the lamp and the observer.

Fig. 9
Fig. 9

Same as Fig. 7 but with the lamp as a 0.23-m cube. The distance between the footpoints of the lamp and the observer is 7 m. The fact that the light source is not regarded as a point results in a diffuse delimitation of the pattern.

Fig. 10
Fig. 10

(a) Same as Fig. 7 but with 7.5 m between the footpoints of the lamp and the observer. (b) The merging of the heiligenschein and the outer retroreflecting area.

Fig. 11
Fig. 11

How a retroreflection circle can be represented.

Fig. 12
Fig. 12

Strong retroreflection from large drops that cover a board in an outdoor experiment. Backscatter was strongest where light incidence was approximately 70°, which could be estimated by comparison with a drop-free track.

Equations (2)

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cos v=|LR·OR||LR|0.5·|OR|0.5=cos 5°.
m=0.5/tanv/2,

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