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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 28 — Oct. 1, 2011
  • pp: F152–F161

Visibility of natural tertiary rainbows

Raymond L. Lee, Jr. and Philip Laven  »View Author Affiliations


Applied Optics, Vol. 50, Issue 28, pp. F152-F161 (2011)
http://dx.doi.org/10.1364/AO.50.00F152


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Abstract

Naturally occurring tertiary rainbows are extraordinarily rare and only a handful of reliable sightings and photographs have been published. Indeed, tertiaries are sometimes assumed to be inherently in visible because of sun glare and strong forward scattering by raindrops. To analyze the natural tertiary’s visibility, we use Lorenz–Mie theory, the Debye series, and a modified geometrical optics model (including both interference and nonspherical drops) to calculate the tertiary’s (1) chromaticity gamuts, (2) luminance contrasts, and (3) color contrasts as seen against dark cloud backgrounds. Results from each model show that natural tertiaries are just visible for some unusual combinations of lighting conditions and raindrop size distributions.

© 2011 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(010.3920) Atmospheric and oceanic optics : Meteorology
(290.4020) Scattering : Mie theory
(330.1730) Vision, color, and visual optics : Colorimetry
(010.7295) Atmospheric and oceanic optics : Visibility and imaging

History
Original Manuscript: May 23, 2011
Manuscript Accepted: July 1, 2011
Published: September 30, 2011

Virtual Issues
Vol. 6, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Raymond L. Lee, Jr. and Philip Laven, "Visibility of natural tertiary rainbows," Appl. Opt. 50, F152-F161 (2011)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-28-F152


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References

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  48. While light that forms the primary and secondary rainbows (p=2 and 3, respectively) is negligible for θ=37°–43°, we include it here for completeness. Note that Eq.  calculates the C(θ) that results from adding p=4 and 5 rays at a givenθ rather than comparing luminances at adjacent θ. As a result, Fig.  shows the contrast consequences of higher-order scattering.
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  50. In order to demonstrate how the tertiary’s visibility separately depends on color and luminance contrast, here we do not use a combined metric for color and luminance differences such as the CIELUV color difference ΔEuv*.
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  54. For example, excluding p=0 rays from Fig.  would increase its peak Cb_0 contrast C by <0.2%. Similarly, excluding p=0 rays from Fig.  would increase its peak Cb_0 color difference Δu′v′ by <14% of the JND given there. Both of these changes are negligible visually.
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  59. J. R. Prescott, “Tertiary rainbows,” Phys. World 17, 18(2004).
  60. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 1982, 2nd ed.), pp. 138–139. Figure 11 was developed for a Sony Trinitron display with the following CIE 1976 primaries: u′(red)=0.4289, v′(red)=0.5268, u′(green)=0.1169, v′(green)=0.5594, u′(blue)=0.1721, v′(blue)=0.1744; each color channel has a gray-level gamma of 1.8.
  61. Similar techniques are used in R. J. Kubesh, “Computer display of chromaticity coordinates with the rainbow as an example,” Am. J. Phys. 60, 919–923 (1992). [CrossRef]
  62. K. Sassen, “Angular scattering and rainbow formation in pendant drops,” J. Opt. Soc. Am. 69, 1083–1089 (1979). [CrossRef]
  63. D. S. Langley and P. L. Marston, “Generalized tertiary rainbow of slightly oblate drops: observations with laser illumination,” Appl. Opt. 37, 1520–1526 (1998). [CrossRef]
  64. C. Hartwell, “Description of a tertiary rainbow,” American Journal of Science and Arts 17 (2nd series), 56–57 (1854).
  65. J. R. Prescott, “Tertiary rainbows,” Phys. World 17, 18(2004).

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