OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 28 — Oct. 1, 2011
  • pp: F142–F151

Crepuscular rays: laboratory experiments and simulations

Stanley David Gedzelman and Michael Vollmer  »View Author Affiliations

Applied Optics, Vol. 50, Issue 28, pp. F142-F151 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (881 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Model simulations of laboratory-generated and natural crepuscular rays are presented. Rays are created in the laboratory with parallel light beams that pass through artificial fogs and milk–water solutions. Light scattered by 90 ° in a dilute mixture of whole milk first increases in intensity with distance from the source to a maximum as a result of multiple scattering by mainly small angles before decreasing exponentially due to extinction as distance continues to increase. Crepuscular rays are simulated for three cloud configurations. In case 1, the Sun at the zenith is blocked by a cloud with an overhanging anvil. The rays appear white against blue sky and are brightest when atmospheric turbidity, β 11 . Shading by the anvil separates maximum brightness from apparent cloud edge. In case 2, a ray passes through a rectangular gap in a cloud layer. The ray is faint blue in a molecular atmosphere but turns pale yellow as β and solar zenith angle, ϕ sun , increase. At ϕ sun = 60 ° it appears most striking when the cloud is optically thick, β 5 , and the beam width Δ x 1000 m . In these cases, increasing aerosol radius, r aer , to about 1000 nm brightens, narrows, and shortens rays. In case 3, the twilight Sun is shaded by a towering cloud or mountain. The shaded rays are deeper blue than the sunlit sky because the light originates higher in the atmosphere, where short waves have suffered less depletion from scattering. The long optical path taken by sunlight at twilight makes color and lighting contrasts of the rays greatest when the air is quite clean, i.e., for β 1 1 . In all cases, the brightest rays occur when sunlight passes through an optical thickness of atmosphere, τ O ( 1 ) .

© 2011 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(290.1090) Scattering : Aerosol and cloud effects
(010.1615) Atmospheric and oceanic optics : Clouds

Original Manuscript: May 23, 2011
Revised Manuscript: August 17, 2011
Manuscript Accepted: August 17, 2011
Published: September 30, 2011

Stanley David Gedzelman and Michael Vollmer, "Crepuscular rays: laboratory experiments and simulations," Appl. Opt. 50, F142-F151 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Minnaert, The Nature of Light and Color in the Open Air, 1938 ed. (Dover, 1954), pp. 1–3, 257–277, reprint of 1938 edition.
  2. R. Greenler, Rainbows, Halos and Glories (Cambridge University, 1980), pp. 129–131, 181–182.
  3. D. K. Lynch and W. Livingston, Color and Light in Nature, 2nd ed. (Cambridge University, 2001), pp. 1–19.
  4. M. Vollmer, Lichtspiele in der Luft: Atmosphärische Optik für Einsteiger (Elsevier Spektrum, 2006), pp. 297–309.
  5. D. Lynch, “Optics of sunbeams,” J. Opt. Soc. Am. 4, 609–611(1987). [CrossRef]
  6. M. S. Van Den Broeke, W. H. Beasley, and M. B. Richman, “The role of atmospheric conditions in determining intensity of crepuscular and anticrepuscular rays,” Mon. Weather Rev. 138, 2883–2894 (2010). [CrossRef]
  7. S. D. Gedzelman, M. Á. López-Álvarez, J. Hernandez-Andrés, and R. Greenler, “Quantifying the “milky sky” experiment,” Appl. Opt. 47, H128–H132, doi:10.1364/AO.47.00H128 (2008). [CrossRef] [PubMed]
  8. S. D. Gedzelman and M. Vollmer, “Atmospheric optical phenomena and radiative transfer,” Bull. Am. Meteorol. Soc. 89, 471–485 (2008). [CrossRef]
  9. A. A. Lacis and J. E. Hansen, “A parameterization for the absorption of solar radiation in the Earth’s atmosphere,” J. Atmos. Sci. 31, 118–133 (1974). [CrossRef]
  10. G. Pretor-Pinney, “The Cloud Appreciation Society,” http://www.cloudappreciationsociety. org. Click on gallery, and then select the category “Optical Effects: Crepuscular Rays & Cloud Shadows.”
  11. S. D. Gedzelman, “Simulating colors of clear and partly cloudy skies,” Appl. Opt. 44, 5723–5736 (2005). [CrossRef] [PubMed]
  12. R. L. Lee and J. Hernández-Andrés, “Measuring and modeling twilight’s purple light,” Appl. Opt. 42, 445–457 (2003). [CrossRef] [PubMed]
  13. J. L. Monteith, “Crepuscular rays formed by the Western Ghats,” Weather 41, 292–299 (1986).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited