Abstract

Using a Monte Carlo method, we simulate the appearance of light pillars produced by nearby light sources and compare their appearance with simulations of Sun pillars. Photographs of light pillars are also compared with the simulations. We expand the idea of light and Sun pillars by examining the reflected-light patterns from several different known distributions of airborne ice crystals. Polarization properties of light pillars from nearly horizontally oriented plate crystals are also simulated.

© 1998 Optical Society of America

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References

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  1. R. G. Greenler, M. Drinkwine, A. J. Mallmann, G. Blumenthal, “The origin of sun pillars,” Am. Sci. 60, 292–302 (1972).
  2. K. Sassen, “Light pillar climatology,” Weatherwise 33, 259–262 (1980).
    [Crossref]
  3. K. Sassen, “Polarization and Brewster angle properties of light pillars,” J. Opt. Soc. Am. A 4, 570–580 (1987).
    [Crossref]
  4. W. Tape, Atmospheric Halos (American Geophysical Union, Washington, D.C., 1994).
    [Crossref]
  5. R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, New York, 1980).
  6. J. R. Mueller, R. G. Greenler, A. J. Mallmann, “Arcs of Lowitz,” J. Opt. Soc. Am. 69, 1103–1106 (1979).
    [Crossref]
  7. The treatment of Ref. 3 assumes that all the light reflected from the crystal will pass through the eye pupil–lens aperture, an assumption good in only the limit of a point source of light.
  8. This paradox is discussed in many astronomy texts; see, for example, M. Seeds , Foundations of Astronomy , 3rd ed. (Wadsworth, Belmont, Calif., 1992), pp. 398–399.

1987 (1)

1980 (1)

K. Sassen, “Light pillar climatology,” Weatherwise 33, 259–262 (1980).
[Crossref]

1979 (1)

1972 (1)

R. G. Greenler, M. Drinkwine, A. J. Mallmann, G. Blumenthal, “The origin of sun pillars,” Am. Sci. 60, 292–302 (1972).

Blumenthal, G.

R. G. Greenler, M. Drinkwine, A. J. Mallmann, G. Blumenthal, “The origin of sun pillars,” Am. Sci. 60, 292–302 (1972).

Drinkwine, M.

R. G. Greenler, M. Drinkwine, A. J. Mallmann, G. Blumenthal, “The origin of sun pillars,” Am. Sci. 60, 292–302 (1972).

Greenler, R.

R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, New York, 1980).

Greenler, R. G.

J. R. Mueller, R. G. Greenler, A. J. Mallmann, “Arcs of Lowitz,” J. Opt. Soc. Am. 69, 1103–1106 (1979).
[Crossref]

R. G. Greenler, M. Drinkwine, A. J. Mallmann, G. Blumenthal, “The origin of sun pillars,” Am. Sci. 60, 292–302 (1972).

Mallmann, A. J.

J. R. Mueller, R. G. Greenler, A. J. Mallmann, “Arcs of Lowitz,” J. Opt. Soc. Am. 69, 1103–1106 (1979).
[Crossref]

R. G. Greenler, M. Drinkwine, A. J. Mallmann, G. Blumenthal, “The origin of sun pillars,” Am. Sci. 60, 292–302 (1972).

Mueller, J. R.

Sassen, K.

Seeds, M.

This paradox is discussed in many astronomy texts; see, for example, M. Seeds , Foundations of Astronomy , 3rd ed. (Wadsworth, Belmont, Calif., 1992), pp. 398–399.

Tape, W.

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

Am. Sci. (1)

R. G. Greenler, M. Drinkwine, A. J. Mallmann, G. Blumenthal, “The origin of sun pillars,” Am. Sci. 60, 292–302 (1972).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Weatherwise (1)

K. Sassen, “Light pillar climatology,” Weatherwise 33, 259–262 (1980).
[Crossref]

Other (4)

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

R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, New York, 1980).

The treatment of Ref. 3 assumes that all the light reflected from the crystal will pass through the eye pupil–lens aperture, an assumption good in only the limit of a point source of light.

This paradox is discussed in many astronomy texts; see, for example, M. Seeds , Foundations of Astronomy , 3rd ed. (Wadsworth, Belmont, Calif., 1992), pp. 398–399.

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Figures (16)

Fig. 1
Fig. 1

Sun pillar and Sun dog produced by plate crystals with their hexagonal faces roughly horizontally oriented. Photo by R. Greenler.

Fig. 2
Fig. 2

Sun pillar and upper tangent arc produced by columnar crystals with their axes nearly horizontal. Photo by A. J. Mallmann.

Fig. 3
Fig. 3

(a) Angular height of a Sun pillar, with the Sun on the horizon, is restricted to twice the maximum tilt angle for the crystal faces that reflect sunlight to the observer; (b) the angular height of a local light pillar can approach 90°, even for a collection of horizontally oriented crystal faces.

Fig. 4
Fig. 4

Predicted appearances of a light pillar and a Sun pillar produced by plate crystals with a uniform distribution of tilts from the horizontal of 0° to 2°. For the light pillar, the light source is in a field of crystals that extends in all directions from the observer to a distance that is twice the source–observer distance. The same spatial collection of crystals is used to produce the Sun-pillar simulation and to produce the simulations shown in Figs. 5, 6, 9, 11, 12, and 15. The angular height of these simulations is 40°, the same as the angular height of the field of view that would be obtained with a 35-mm camera with a 50-mm focal-length lens. This same angular height is also used for the simulations shown in Figs. 5, 6, 9, 11, and 12.

Fig. 5
Fig. 5

Same as Fig. 4 except for crystals with a maximum tilt angle of 5°.

Fig. 6
Fig. 6

Same as Fig. 4 except for crystals with a maximum tilt angle of 10°.

Fig. 7
Fig. 7

Light pillars probably resulting from plate crystals with their hexagonal faces nearly horizontal. Photo by M. Riikonen.

Fig. 8
Fig. 8

Multiple light-pillar display probably produced by plate crystals with their hexagonal faces nearly horizontal. Photo by W. Tape.4

Fig. 9
Fig. 9

Light-pillar and Sun-pillar appearances for pillars produced by columnar crystals with their symmetry axes horizontally oriented and with all rotational orientations about those horizontal axes.

Fig. 10
Fig. 10

Light pillar with a form expected when light is reflected off the faces of columnar crystals with their axes nearly horizontal. Photo by R. F. Newell Jr.

Fig. 11
Fig. 11

Light-pillar and Sun-pillar appearances for pillars produced by columnar crystals with horizontally oriented symmetry axes and with a pair of long side faces that make an angle with the horizontal of 2° or less. This is the distribution of crystal orientations that produces Parry arcs.

Fig. 12
Fig. 12

Light-pillar and Sun-pillar appearances that result when light is reflected from hexagonal plate crystals that spin around horizontal axes passing through opposite points of hexagonal faces.

Fig. 13
Fig. 13

Light pillars produced by a layer of ice crystals with a limited vertical extent and with the lower boundary above ground level. Photo by P. Parviainen.

Fig. 14
Fig. 14

Angular extent dθ of a pillar is given by dθ = sin θ cos θ(dH/ H), where H is the height of the layer, dH is the thickness of the layer, and θ is the elevation of the pillar above the horizon.

Fig. 15
Fig. 15

Predicted appearance of light pillars as viewed with (left) no polarizing filter, (center) filter oriented to pass horizontally polarized light, and (right) filter oriented to pass vertically polarized light. Each simulation is for pillars produced by plate crystals with a maximum tilt angle of 2° from the horizontal. The angular height of these simulations is 54°, the same as the angular height of the field of view that would be obtained with a 35-mm camera with a 35-mm focal-length, wide-angle lens.

Fig. 16
Fig. 16

Effect of source, crystal, and eye-pupil sizes on intensity: (a) light rays reflected off ice crystal, (b) equivalent ray diagram with crystal replaced by pinhole.

Equations (1)

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d θ = sin   θ   cos   θ d H / H ,

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