Abstract

Both folklore and theory imply that naturally occurring rainbows display a wide range of nearly pure colors. However, digital image analysis of color slides shows that the natural rainbow’s colors are not especially pure and that the bow’s background causes much of this desaturation.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. We define a “natural rainbow” here as any rainbow seen in sunlit raindrops.
  2. P. D. Schweizer, “John Constable, Rainbow Science, and English Color Theory,” Art Bulletin 64, 424–445 (1982).
    [CrossRef]
  3. Aristotle, Meteorologica, translated by H. D. P. Lee (Harvard U. Press., Cambridge, Mass, 1952), Sec. III, paragraphs 372–375.
  4. Seneca the Younger, Physical Science in the Time of Nero: Being a Translation of the Quaestiones Naturales of Seneca, translated by John Clark (Macmillan, London, 1910), p. 21.
  5. J. M. Pernter, F. M. Exner, Meteorologische Optik (Wilhelm Braumüller, Vienna, 1922), pp. 565–588.
  6. J. A. Prins, J. J. M. Reesinck, “Buigingstheorie en Trichromatische Specificatie van de Regenboogkleuren,” Physica 11, 49–60 (1944).
    [CrossRef]
  7. F. E. Volz, “Der Regenbogen” in Handbuch der Geophysik, F. Linke, F. Möller, eds. (Gebruder Borntraeger, Berlin, 1961), Vol. 8, pp. 943–1026.
  8. S. Rösch, “Der Regenbogen in Wissenschaft und Kunst,” Appl. Opt. 7, 233–239 (1968).
    [CrossRef] [PubMed]
  9. R. A. R. Tricker, Introduction to Meteorological Optics (Elsevier, New York, 1970), pp. 169–190.
  10. A. J. Patitsas, “Rainbows, Glories, and the Scalar Field Approach,” Can. J. Phys. 50, 3172–3183 (1972).
    [CrossRef]
  11. R. L. Lee, “Colorimetric Calibration of a Video Digitizing System: Algorithm and Applications,” Color Res. Appl. 13, 180–186 (1988).
    [CrossRef]
  12. W. J. Humphreys, Physics of the Air (Dover, New York, 1964; reprinting of 1940 edition), p. 476.
  13. J. A. Lock, “Observability of Atmospheric Glories and Supernumerary Rainbows,” J. Opt. Soc. Am. A 6, 1924–1930 (1989).
    [CrossRef]
  14. S. D. Gedzelman, “Rainbow Brightness,” Appl. Opt. 21, 3032–3037 (1982).
    [CrossRef] [PubMed]
  15. S. D. Gedzelman, “Visibility of Halos and Rainbows,” Appl. Opt. 19, 3068–3074 (1980).
    [CrossRef] [PubMed]
  16. A. B. Fraser, “Why Can the Supernumerary Bows Be Seen in a Rain Shower?,” J. Opt. Soc. Am. 73, 1626–1628 (1983).
    [CrossRef]
  17. A. B. Fraser, “Chasing Rainbows: Numerous Supernumeraries Are Super,” Weatherwise 36, 280–289 (1983).
    [CrossRef]
  18. A. B. Fraser, “Inhomogeneities in the Color and Intensity of the Rainbow,” J. Atmos. Sci. 29, 211–212 (1972).
    [CrossRef]
  19. We distinguish between the rainbow’s observed colors (background included) and its intrinsic colors (background excluded). Also, we use luminance and brightness as synonyms in this paper, while recognizing that the two quantities are not linearly related (see, for example, Ref. 20, p. 495).
  20. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), p. 503.
  21. We use the term clock angle to describe the angle that changes as we look around the bow at a fixed angular radius from the antisolar point.
  22. G. P. Können, Polarized Light in Nature (Cambridge, U. Press., London, 1985), pp. 46–56.
  23. G. P. Können, J. H. de Boer, “Polarized Rainbow,” Appl. Opt. 18, 1961–1965 (1979).
    [CrossRef]
  24. C. D. Hendley, S. Hecht, “The Colors of Natural Objects and Terrains, and Their Relation to Visual Color Deficiency,” J. Opt. Soc. Am. 39, 870–873 (1949).
    [CrossRef] [PubMed]
  25. G. J. Burton, I. R. Moorhead, “Color and Spatial Structure in Natural Scenes,” Appl. Opt. 26, 157–170 (1987).
    [CrossRef] [PubMed]
  26. C. F. Bohren, A. B. Fraser, “Colors of the Sky,” Phys. Teach. 23, 267–272 (1985).
    [CrossRef]

1989

1988

R. L. Lee, “Colorimetric Calibration of a Video Digitizing System: Algorithm and Applications,” Color Res. Appl. 13, 180–186 (1988).
[CrossRef]

1987

1985

C. F. Bohren, A. B. Fraser, “Colors of the Sky,” Phys. Teach. 23, 267–272 (1985).
[CrossRef]

1983

A. B. Fraser, “Chasing Rainbows: Numerous Supernumeraries Are Super,” Weatherwise 36, 280–289 (1983).
[CrossRef]

A. B. Fraser, “Why Can the Supernumerary Bows Be Seen in a Rain Shower?,” J. Opt. Soc. Am. 73, 1626–1628 (1983).
[CrossRef]

1982

S. D. Gedzelman, “Rainbow Brightness,” Appl. Opt. 21, 3032–3037 (1982).
[CrossRef] [PubMed]

P. D. Schweizer, “John Constable, Rainbow Science, and English Color Theory,” Art Bulletin 64, 424–445 (1982).
[CrossRef]

1980

1979

1972

A. B. Fraser, “Inhomogeneities in the Color and Intensity of the Rainbow,” J. Atmos. Sci. 29, 211–212 (1972).
[CrossRef]

A. J. Patitsas, “Rainbows, Glories, and the Scalar Field Approach,” Can. J. Phys. 50, 3172–3183 (1972).
[CrossRef]

1968

1949

1944

J. A. Prins, J. J. M. Reesinck, “Buigingstheorie en Trichromatische Specificatie van de Regenboogkleuren,” Physica 11, 49–60 (1944).
[CrossRef]

Aristotle,

Aristotle, Meteorologica, translated by H. D. P. Lee (Harvard U. Press., Cambridge, Mass, 1952), Sec. III, paragraphs 372–375.

Bohren, C. F.

C. F. Bohren, A. B. Fraser, “Colors of the Sky,” Phys. Teach. 23, 267–272 (1985).
[CrossRef]

Burton, G. J.

de Boer, J. H.

Exner, F. M.

J. M. Pernter, F. M. Exner, Meteorologische Optik (Wilhelm Braumüller, Vienna, 1922), pp. 565–588.

Fraser, A. B.

C. F. Bohren, A. B. Fraser, “Colors of the Sky,” Phys. Teach. 23, 267–272 (1985).
[CrossRef]

A. B. Fraser, “Why Can the Supernumerary Bows Be Seen in a Rain Shower?,” J. Opt. Soc. Am. 73, 1626–1628 (1983).
[CrossRef]

A. B. Fraser, “Chasing Rainbows: Numerous Supernumeraries Are Super,” Weatherwise 36, 280–289 (1983).
[CrossRef]

A. B. Fraser, “Inhomogeneities in the Color and Intensity of the Rainbow,” J. Atmos. Sci. 29, 211–212 (1972).
[CrossRef]

Gedzelman, S. D.

Hecht, S.

Hendley, C. D.

Humphreys, W. J.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964; reprinting of 1940 edition), p. 476.

Können, G. P.

G. P. Können, J. H. de Boer, “Polarized Rainbow,” Appl. Opt. 18, 1961–1965 (1979).
[CrossRef]

G. P. Können, Polarized Light in Nature (Cambridge, U. Press., London, 1985), pp. 46–56.

Lee, R. L.

R. L. Lee, “Colorimetric Calibration of a Video Digitizing System: Algorithm and Applications,” Color Res. Appl. 13, 180–186 (1988).
[CrossRef]

Lock, J. A.

Moorhead, I. R.

Patitsas, A. J.

A. J. Patitsas, “Rainbows, Glories, and the Scalar Field Approach,” Can. J. Phys. 50, 3172–3183 (1972).
[CrossRef]

Pernter, J. M.

J. M. Pernter, F. M. Exner, Meteorologische Optik (Wilhelm Braumüller, Vienna, 1922), pp. 565–588.

Prins, J. A.

J. A. Prins, J. J. M. Reesinck, “Buigingstheorie en Trichromatische Specificatie van de Regenboogkleuren,” Physica 11, 49–60 (1944).
[CrossRef]

Reesinck, J. J. M.

J. A. Prins, J. J. M. Reesinck, “Buigingstheorie en Trichromatische Specificatie van de Regenboogkleuren,” Physica 11, 49–60 (1944).
[CrossRef]

Rösch, S.

Schweizer, P. D.

P. D. Schweizer, “John Constable, Rainbow Science, and English Color Theory,” Art Bulletin 64, 424–445 (1982).
[CrossRef]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), p. 503.

Tricker, R. A. R.

R. A. R. Tricker, Introduction to Meteorological Optics (Elsevier, New York, 1970), pp. 169–190.

Volz, F. E.

F. E. Volz, “Der Regenbogen” in Handbuch der Geophysik, F. Linke, F. Möller, eds. (Gebruder Borntraeger, Berlin, 1961), Vol. 8, pp. 943–1026.

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), p. 503.

Appl. Opt.

Art Bulletin

P. D. Schweizer, “John Constable, Rainbow Science, and English Color Theory,” Art Bulletin 64, 424–445 (1982).
[CrossRef]

Can. J. Phys.

A. J. Patitsas, “Rainbows, Glories, and the Scalar Field Approach,” Can. J. Phys. 50, 3172–3183 (1972).
[CrossRef]

Color Res. Appl.

R. L. Lee, “Colorimetric Calibration of a Video Digitizing System: Algorithm and Applications,” Color Res. Appl. 13, 180–186 (1988).
[CrossRef]

J. Atmos. Sci.

A. B. Fraser, “Inhomogeneities in the Color and Intensity of the Rainbow,” J. Atmos. Sci. 29, 211–212 (1972).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Phys. Teach.

C. F. Bohren, A. B. Fraser, “Colors of the Sky,” Phys. Teach. 23, 267–272 (1985).
[CrossRef]

Physica

J. A. Prins, J. J. M. Reesinck, “Buigingstheorie en Trichromatische Specificatie van de Regenboogkleuren,” Physica 11, 49–60 (1944).
[CrossRef]

Weatherwise

A. B. Fraser, “Chasing Rainbows: Numerous Supernumeraries Are Super,” Weatherwise 36, 280–289 (1983).
[CrossRef]

Other

We define a “natural rainbow” here as any rainbow seen in sunlit raindrops.

F. E. Volz, “Der Regenbogen” in Handbuch der Geophysik, F. Linke, F. Möller, eds. (Gebruder Borntraeger, Berlin, 1961), Vol. 8, pp. 943–1026.

Aristotle, Meteorologica, translated by H. D. P. Lee (Harvard U. Press., Cambridge, Mass, 1952), Sec. III, paragraphs 372–375.

Seneca the Younger, Physical Science in the Time of Nero: Being a Translation of the Quaestiones Naturales of Seneca, translated by John Clark (Macmillan, London, 1910), p. 21.

J. M. Pernter, F. M. Exner, Meteorologische Optik (Wilhelm Braumüller, Vienna, 1922), pp. 565–588.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964; reprinting of 1940 edition), p. 476.

We distinguish between the rainbow’s observed colors (background included) and its intrinsic colors (background excluded). Also, we use luminance and brightness as synonyms in this paper, while recognizing that the two quantities are not linearly related (see, for example, Ref. 20, p. 495).

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982), p. 503.

We use the term clock angle to describe the angle that changes as we look around the bow at a fixed angular radius from the antisolar point.

G. P. Können, Polarized Light in Nature (Cambridge, U. Press., London, 1985), pp. 46–56.

R. A. R. Tricker, Introduction to Meteorological Optics (Elsevier, New York, 1970), pp. 169–190.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(a) Portion of the CIE 1976 UCS diagram (spectrum locus drawn with dot–dash line) showing the colorimetric gamut ĝ of the Fig. 1 rainbow, both with background luminances included (ĝ = 0.00701, thick line) and subtracted (ĝ = 0.134, thin line). (b) Radial variation of relative luminances in the Plate 1 rainbow, both with background luminances included (thick line) and subtracted (thin line). Each point on the curves is an average over many rainbow clock angles.

Fig. 2
Fig. 2

(a) Colorimetric gamut of the Plate 2 rainbow, both with background luminances included (ĝ = 0.0195, thick line) and for the ‖-polarized component colorimetrically subtracted from the ⊥ component (ĝ = 0.0746, thin line). (b) Radial variation of relative luminances in the Plate 2 rainbow, both with background luminances included (thick line) and for the difference of the ⊥ and ‖ polarization components (thin line).

Fig. 3
Fig. 3

(a) Colorimetric gamut of the Plate 3 rainbow, both with background luminances included (ĝ = 0.0507, thick line) and subtracted ĝ = 0.181, thin line). (b) Radial variation of relative luminances in the Plate 3 rainbow, both with background luminances included (thick line) and subtracted (thin line).

Fig. 4
Fig. 4

(a) Colorimetric gamut of the Plate 4 rainbow, both with background luminances included (ĝ = 0.0424, thick line) and subtracted (ĝ = 0.156, thin line). (b) Radial variation of relative luminances in the Plate 4 rainbow, both with background luminances included (thick line) and subtracted (thin line). The dashed curve is the luminance difference of the ⊥ and ‖ polarization components.

Fig. 5
Fig. 5

(a) Colorimetric gamut of the Plate 5 rainbow, both with background luminances included (ĝ = 0.0342, thick line) and subtracted (ĝ = 0.203, thin line). The dashed chromaticity curve is the colorimetric difference of the ⊥ and ‖ polarization components; its ĝ = 0.0883. (b) Radial variation of relative luminances in the Fig. 5 rainbow, both with background luminances included (thick line) and subtracted (thin line). The dashed curve is the luminance difference of the ⊥ and ‖ polarization components.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

g = ( { i = 1 N [ ( u i - u ) 2 + ( v i - v ) 2 ] } / N ) 1 / 2 .
g ^ = g / g s .
n i = ( { j = 1 M [ ( u j - u i ) 2 + ( v j - v i ) 2 ] } / M ) 1 / 2 .

Metrics