Abstract

We deal with some halos generated by the divergent light from a nearby source. After discussing how the divergent light transforms some halo features, we give an outline of a method of handling the simulation of a divergent-light halo. The simulation method is then successfully tested on some well-documented halo observations. We also present a “simulation atlas” that shows halos produced by crystals of different shapes and for different light-source elevations and distances between the observer and the light source. The simulation method also admits a three-dimensional visualization of the phenomena.

© 2003 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 en Dampkring 26, 51–54 (1928).
  2. J. O. Mattsson, “Sub-sun and light pillars of street lamps,” Weather 28, 66–68 (1973).
    [CrossRef]
  3. J. O. Mattsson, “Experiments on horizontal haloes in divergent light,” Weather 29, 148–150 (1974).
    [CrossRef]
  4. C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
    [CrossRef]
  5. J. O. Mattsson, “Concerning haloes, rainbows and dewbows in divergent light,” Weather 53, 176–181 (1998).
    [CrossRef]
  6. J. O. Mattsson, L. Bärring, E. Almqvist, “Experimenting with Minnaert’s Cigar,” Appl. Opt. 39, 3604–3611 (2000).
    [CrossRef]
  7. Brief reports on the parhelic circle in divergent light are given in the Finnish journal Ursa Minor, published in Finnish, with some figure captions in English, by Tähtitieteellinen yhdistys Ursa in Helsinki. The pages and issues in question are 11, 1/2000 (a simulation by Walter Tape of a surface similar to the one in Fig. 1) and 13–14, 3/2001 (some observations).
  8. A. J. Mallmann, J. L. Hock, R. G. Greenler, “Comparison of sun pillars with light pillars from nearby light sources,” Appl. Opt. 37, 1441–1449 (1998).
    [CrossRef]
  9. L. Gislén, “Procedure for simulating divergent-light halos,” Appl. Opt., submitted for publication.
  10. W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
    [CrossRef]
  11. R. Greenler, Rainbows, Halos, and Glories (Printstar Books, Milwaukee, Wisc., 1999).

2000 (1)

1998 (2)

1980 (1)

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

1974 (1)

J. O. Mattsson, “Experiments on horizontal haloes in divergent light,” Weather 29, 148–150 (1974).
[CrossRef]

1973 (1)

J. O. Mattsson, “Sub-sun and light pillars of street lamps,” Weather 28, 66–68 (1973).
[CrossRef]

1928 (1)

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

Almqvist, E.

Bärring, L.

Floor, C.

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

Gislén, L.

L. Gislén, “Procedure for simulating divergent-light halos,” Appl. Opt., submitted for publication.

Greenler, R.

R. Greenler, Rainbows, Halos, and Glories (Printstar Books, Milwaukee, Wisc., 1999).

Greenler, R. G.

Hock, J. L.

Mallmann, A. J.

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, “Experiments on horizontal haloes in divergent light,” Weather 29, 148–150 (1974).
[CrossRef]

J. O. Mattsson, “Sub-sun and light pillars of street lamps,” Weather 28, 66–68 (1973).
[CrossRef]

Minnaert, M.

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

Tape, W.

W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
[CrossRef]

Appl. Opt. (2)

Hemel en Dampkring (1)

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

Weather (4)

J. O. Mattsson, “Sub-sun and light pillars of street lamps,” Weather 28, 66–68 (1973).
[CrossRef]

J. O. Mattsson, “Experiments on horizontal haloes in divergent light,” Weather 29, 148–150 (1974).
[CrossRef]

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]

Other (4)

Brief reports on the parhelic circle in divergent light are given in the Finnish journal Ursa Minor, published in Finnish, with some figure captions in English, by Tähtitieteellinen yhdistys Ursa in Helsinki. The pages and issues in question are 11, 1/2000 (a simulation by Walter Tape of a surface similar to the one in Fig. 1) and 13–14, 3/2001 (some observations).

L. Gislén, “Procedure for simulating divergent-light halos,” Appl. Opt., submitted for publication.

W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
[CrossRef]

R. Greenler, Rainbows, Halos, and Glories (Printstar Books, Milwaukee, Wisc., 1999).

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Figures (9)

Fig. 1
Fig. 1

Locations of ice crystals forming the parhelic circle in light from a nearby pointlike source situated obliquely above the observer. The crystals are located on a distorted “double cone” with one vertex in the light source and the other one in the eye. Source elevation 45°.

Fig. 2
Fig. 2

Rotations on the sphere that move the hitpoint of the scattered ray into the eye of the observer.

Fig. 3
Fig. 3

(a) Parhelic circle in the light of a nearby street-lamp. The lamp elevation is 53°. Observation and photograph by Marko Riikonen. The position of the light source is marked by a small cross on the photo. (b) Simulation of the halo observation. (c) Parallel light simulation for comparison.

Fig. 4
Fig. 4

Divergent-light display, including parhelia, superparhelia, and a light pillar. Observation by Marko Riikonen and Leena Virta. Photograph by Marko Riikonen. (b) Simulation of the display; (c) parallel light simulation for comparison.

Fig. 5
Fig. 5

(a) complex halo observed by Teemu Öhman, who also made the sketch. (b) Fisheye simulation of the display. (c) Details of the simulated halo around the sun. (d) and (e) Parallel light simulations for comparison.

Fig. 6
Fig. 6

Simulation of halos by plate crystals (c/a ratio 0.3, tilt 0.5°) for different source elevations and distance parameters. The top row represents a light source very nearby (distance parameter p = 0.01), the middle row represents a somewhat more distant source (p = 0.05), and the bottom row represents a distant source (p = 0.1).

Fig. 7
Fig. 7

Simulation of halos by columnar crystals (c/a ratio 2.0, tilt from the horizontal 0.5°) for different source elevations and distance parameters. The distance parameters are the same as in Fig. 6.

Fig. 8
Fig. 8

Simulations of halos by randomly oriented crystals with c/a = 1.0 and for different distance parameters (0.01; 0.05; 0.1). Source elevation is 30°.

Fig. 9
Fig. 9

Simulation of a halo by plate crystals (c/a = 0.3) with very small tilts to show the 120° parhelia. The source elevation is 45°.

Equations (2)

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z=hx2+y21/2x2+y21/2+x-a2+y21/2,
I  a2a2+t2, where a=dpdCλD,

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