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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 9 — Sep. 1, 1980
  • pp: 1145–1148

Analytic sun pillar model

Alistair B. Fraser and Gary J. Thompson  »View Author Affiliations


JOSA, Vol. 70, Issue 9, pp. 1145-1148 (1980)
http://dx.doi.org/10.1364/JOSA.70.001145


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Abstract

An analytic sun pillar model is developed which indicates that large hexagonal ice columns can cause sun pillars. The model shows that the Stuchtey method for explaining sun pillars is not incorrect, only incomplete. The model uses an expression for the intensity of the sun pillar that considers both the optical mapping of light for a single crystal orientation and for the probability of having that particular orientation. The model, which is extended to a sun of finite size, clearly shows that the portion of the pillar that is seen above the horizon is brightest when the sun is below the horizon.

Citation
Alistair B. Fraser and Gary J. Thompson, "Analytic sun pillar model," J. Opt. Soc. Am. 70, 1145-1148 (1980)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-70-9-1145


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References

  1. M. Minnaert, Light and Colour in the Open Air (Dover, New York, 1954), pp. 201–202.
  2. Karl Stuchtey, "Subsuns and Light Pillars on Sun and Moon," Ann. Phys. IV, (59), 33–55 (1919).
  3. Robert G. Greenler et al., "The Origin of Sun Pillars," Am. Sci. 60, (3), 292–302 (1972).
  4. For nomenclature buffs, it should be noted that this use of the word intensity is correct in that what will be calculated is a (relative) power per unit solid angle that leaves an infinitesimal volume containing ice crystals. Because it is the relative intensity, it can also be interpreted as the relative radiance from the sky, or if the reader wants to multiply by the response function of the eye, the relative luminance.
  5. This is the only crystal type that is considered so that nothing is deduced here either for or against the ability of plates to cause sun pillars.
  6. It was noticed while the paper was in press that only one polarization component is represented by Eq. (6). A quick calculation showed, however, that no qualitative difference is produced by the proper inclusion of both components. The quantitative difference is very small.

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