Abstract

Distant objects like clouds, mountains, and the Sun can appear to have colors that are significantly different from their intrinsic colors: the low Sun is often red, white clouds and snow-capped peaks appear yellow or pink, and dark green or gray mountains can appear blue or purple. The color alteration increases with distance, or alternatively, optical depth. We investigate the perceived colors of distant objects by computing the CIE chromaticity coordinates from their spectra. For sources viewed through significant amounts of atmosphere (e.g., the low Sun), MODTRAN4 radiative-transfer calculations are used to retrieve the spectra. In addition to clouds and mountains, the colors of stars, the Sun, and the sky are presented as a function of solar elevation under a variety of atmospheric conditions.

© 2005 Optical Society of America

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References

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  1. Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107, 274 (1871).
  2. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, 1952).
  3. E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976).
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    [CrossRef]
  5. http://www.cie.co.at/cie/ .
  6. M. Fairchild, Color Appearance Models (Addison-Wesley, Reading, Mass., 1998).
  7. L. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: a moderate resolution model for LOWTRAN7,” (Hanscom Air Force Base, Mass., 1989).
  8. W. Kalkofen, ed., Methods in Radiative Transfer (Cambridge University, Cambridge, 1984).
  9. W. Kalkofen, ed., Numerical Radiative Transfer (Cambridge University, Cambridge, 1987).
  10. There are a few galaxies that are visible to the naked eye, and they are more distant than the stars. But they are too faint to elicit a color response in the eye.
  11. A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
    [CrossRef]
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    [CrossRef]
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  15. G. Wysecki, W. S. Stiles, Color Science (Wiley, New York, 1967).
  16. There is another reason that very hot and very cool sources appear to be the same color regardless of temperature: At the extreme wavelength limits of human vision, most of the light is exciting only the red or blue rhodopsin. Color discrimination depends on the relative ratios of the R, G, and B rhodopsins, and when only one is excited, only one color is seen.
  17. R. L. Kurucz, in Atomic Spectra and Oscillator strengths for Astrophysics and Fusion Research, J. R. Hansen, ed. (North-Holland, Amsterdam), p. 20.
  18. R. L. Kurucz, in Stellar Atmospheres: Beyond Classical Models, L. Crivellari, I. Hubeny, D. G. Hummer, eds., NATO ASI Ser. C341, (1991), p. 441.
    [CrossRef]
  19. R. L. Kurucz, in The Stellar Populations of Galaxies, B. Barbuy, A. Renzini, eds., Int. Astron. Union Symp.149, 225 (1992).
    [CrossRef]
  20. B. H. Soffer, D. K. Lynch, “Some paradoxes, errors and resolutions concerning the spectral optimization of human vision,” Am. J. Phys. 67, 946 (1999).
    [CrossRef]
  21. These results are substantially the same for giant and supergiant stars, which tend to be the ones that are brightest in the night sky. Most stars in the galaxy are faint red dwarfs, but the brightest stars, i.e., the ones visible from the greatest distance, are giants and supergiants.
  22. W. Romanishin, An Introduction to Astronomical Photometry Using CCDs www.nhn.ou.edu/~wjr/research/wrccded2.pdf (1999).
  23. R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–46384959 (1994).
    [CrossRef] [PubMed]
  24. J. Hernández-Andrés, R. L. Lee, J. Romero, “Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities,” Appl. Opt. 38, 5703–5709 (1999).
    [CrossRef]
  25. J. Hernández-Andrés, R. L. Lee, “Color and luminance asymmetries in the clear sky,” Appl. Opt. 42, 458–464 (2003).
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  26. M. A. Box, A. Deepak, “Retrieval of aerosol size distribution by inversion of solar aureole data in the presence of multiple scattering,” Appl. Opt. 18, 1376–1382 (1979).
    [CrossRef] [PubMed]
  27. J. T. Twitty, “The inversion of aureole measurements to derive aerosol size distribution,” J. Atmos. Sci. 32, 584–591 (1975).
    [CrossRef]
  28. D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, 2001).
  29. L. Bell, “Star colors: a study in physiological optics,” Astrophys. J. 31, 234–257 (1910).
    [CrossRef]
  30. M. Minnaert, “Colour and colour perception,” Proc. Acad. Amsterdam B 56, 148 (1953).
  31. R. C. Henry, S. Mahadev, S. Urquijo, D. Chitwood, “Color perception through atmospheric haze,” J. Opt. Soc. Am. A 17, 831–835 (2000).
    [CrossRef]

2003 (1)

2000 (1)

1999 (4)

J. Hernández-Andrés, R. L. Lee, J. Romero, “Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities,” Appl. Opt. 38, 5703–5709 (1999).
[CrossRef]

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

B. H. Soffer, D. K. Lynch, “Some paradoxes, errors and resolutions concerning the spectral optimization of human vision,” Am. J. Phys. 67, 946 (1999).
[CrossRef]

1994 (1)

R. L. Lee, “Twilight and daytime colors of the clear sky,” Appl. Opt. 33, 4629–46384959 (1994).
[CrossRef] [PubMed]

1993 (1)

W. R. Hamann, L. Koesterke, U. Wessolowski, “Spectra analysis of the galactic Wolf–Rayet stars—a comprehensive study of the WN class,” Astron. Astrophys. 274, 397 (1993).

1987 (1)

C. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).
[CrossRef]

1979 (1)

1975 (1)

J. T. Twitty, “The inversion of aureole measurements to derive aerosol size distribution,” J. Atmos. Sci. 32, 584–591 (1975).
[CrossRef]

1953 (1)

M. Minnaert, “Colour and colour perception,” Proc. Acad. Amsterdam B 56, 148 (1953).

1910 (1)

L. Bell, “Star colors: a study in physiological optics,” Astrophys. J. 31, 234–257 (1910).
[CrossRef]

1871 (1)

Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107, 274 (1871).

1867 (1)

C. J. Wolf, G. Rayet, Comptes Rendus Acad. Sci. 65, 292 (1867).

Beichman, C. A.

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

Bell, L.

L. Bell, “Star colors: a study in physiological optics,” Astrophys. J. 31, 234–257 (1910).
[CrossRef]

Berk, L.

L. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: a moderate resolution model for LOWTRAN7,” (Hanscom Air Force Base, Mass., 1989).

Bernstein, L. S.

L. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: a moderate resolution model for LOWTRAN7,” (Hanscom Air Force Base, Mass., 1989).

Bohren, C.

C. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).
[CrossRef]

Box, M. A.

Brown, M. E.

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

Burgasser, A. J.

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

Chitwood, D.

Cutri, R. M.

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

Dahn, C. C.

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

Deepak, A.

Fairchild, M.

M. Fairchild, Color Appearance Models (Addison-Wesley, Reading, Mass., 1998).

Gizis, J. E.

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

Hamann, W. R.

W. R. Hamann, L. Koesterke, U. Wessolowski, “Spectra analysis of the galactic Wolf–Rayet stars—a comprehensive study of the WN class,” Astron. Astrophys. 274, 397 (1993).

Henry, R. C.

Hernández-Andrés, J.

Kirkpatrick, J. D.

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

Koesterke, L.

W. R. Hamann, L. Koesterke, U. Wessolowski, “Spectra analysis of the galactic Wolf–Rayet stars—a comprehensive study of the WN class,” Astron. Astrophys. 274, 397 (1993).

Kurucz, R. L.

R. L. Kurucz, in Atomic Spectra and Oscillator strengths for Astrophysics and Fusion Research, J. R. Hansen, ed. (North-Holland, Amsterdam), p. 20.

R. L. Kurucz, in Stellar Atmospheres: Beyond Classical Models, L. Crivellari, I. Hubeny, D. G. Hummer, eds., NATO ASI Ser. C341, (1991), p. 441.
[CrossRef]

R. L. Kurucz, in The Stellar Populations of Galaxies, B. Barbuy, A. Renzini, eds., Int. Astron. Union Symp.149, 225 (1992).
[CrossRef]

Lee, R. L.

Liebert, J.

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, 2001).

Lynch, D. K.

B. H. Soffer, D. K. Lynch, “Some paradoxes, errors and resolutions concerning the spectral optimization of human vision,” Am. J. Phys. 67, 946 (1999).
[CrossRef]

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, 2001).

Mahadev, S.

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976).

Middleton, K.

K. Middleton, Vision Through the Atmosphere (University of Toronto Press, 1952).

Minnaert, M.

M. Minnaert, “Colour and colour perception,” Proc. Acad. Amsterdam B 56, 148 (1953).

Monet, D. G.

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

Nelson, B.

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

Rayet, G.

C. J. Wolf, G. Rayet, Comptes Rendus Acad. Sci. 65, 292 (1867).

Rayleigh,

Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107, 274 (1871).

Reid, I. N.

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

Robertson, D. C.

L. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: a moderate resolution model for LOWTRAN7,” (Hanscom Air Force Base, Mass., 1989).

Romero, J.

Skrutskie, M. F.

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

Soffer, B. H.

B. H. Soffer, D. K. Lynch, “Some paradoxes, errors and resolutions concerning the spectral optimization of human vision,” Am. J. Phys. 67, 946 (1999).
[CrossRef]

Stiles, W. S.

G. Wysecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

Strutt, J. W.

Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107, 274 (1871).

Twitty, J. T.

J. T. Twitty, “The inversion of aureole measurements to derive aerosol size distribution,” J. Atmos. Sci. 32, 584–591 (1975).
[CrossRef]

Urquijo, S.

Wessolowski, U.

W. R. Hamann, L. Koesterke, U. Wessolowski, “Spectra analysis of the galactic Wolf–Rayet stars—a comprehensive study of the WN class,” Astron. Astrophys. 274, 397 (1993).

Wolf, C. J.

C. J. Wolf, G. Rayet, Comptes Rendus Acad. Sci. 65, 292 (1867).

Wysecki, G.

G. Wysecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

Am. J. Phys. (2)

C. Bohren, “Multiple scattering of light and some of its observable consequences,” Am. J. Phys. 55, 524–533 (1987).
[CrossRef]

B. H. Soffer, D. K. Lynch, “Some paradoxes, errors and resolutions concerning the spectral optimization of human vision,” Am. J. Phys. 67, 946 (1999).
[CrossRef]

Appl. Opt. (4)

Astron. Astrophys. (1)

W. R. Hamann, L. Koesterke, U. Wessolowski, “Spectra analysis of the galactic Wolf–Rayet stars—a comprehensive study of the WN class,” Astron. Astrophys. 274, 397 (1993).

Astrophys. J. (3)

A. J. Burgasser, J. D. Kirkpatrick, M. E. Brown, I. N. Reid, J. E. Gizis, C. C. Dahn, D. G. Monet, C. A. Beichman, J. Liebert, R. M. Cutri, M. F. Skrutskie, “Discovery of four field methane (T-type) dwarfs with the two micron all-sky survey,” Astrophys. J. 522, L65–L68 (1999).
[CrossRef]

J. D. Kirkpatrick, I. N. Reid, J. Liebert, R. M. Cutri, B. Nelson, C. A. Beichman, C. C. Dahn, D. G. Monet, J. E. Gizis, M. F. Skrutskie, “Dwarfs cooler than “M”: the definition of spectral type “L” using discoveries from the 2 micron all-sky survey (2MASS),” Astrophys. J. 519, 802–833 (1999).
[CrossRef]

L. Bell, “Star colors: a study in physiological optics,” Astrophys. J. 31, 234–257 (1910).
[CrossRef]

Comptes Rendus Acad. Sci. (1)

C. J. Wolf, G. Rayet, Comptes Rendus Acad. Sci. 65, 292 (1867).

J. Atmos. Sci. (1)

J. T. Twitty, “The inversion of aureole measurements to derive aerosol size distribution,” J. Atmos. Sci. 32, 584–591 (1975).
[CrossRef]

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

Philos. Mag. (1)

Rayleigh, J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107, 274 (1871).

Proc. Acad. Amsterdam B (1)

M. Minnaert, “Colour and colour perception,” Proc. Acad. Amsterdam B 56, 148 (1953).

Other (16)

K. Middleton, Vision Through the Atmosphere (University of Toronto Press, 1952).

E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976).

http://www.cie.co.at/cie/ .

M. Fairchild, Color Appearance Models (Addison-Wesley, Reading, Mass., 1998).

L. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: a moderate resolution model for LOWTRAN7,” (Hanscom Air Force Base, Mass., 1989).

W. Kalkofen, ed., Methods in Radiative Transfer (Cambridge University, Cambridge, 1984).

W. Kalkofen, ed., Numerical Radiative Transfer (Cambridge University, Cambridge, 1987).

There are a few galaxies that are visible to the naked eye, and they are more distant than the stars. But they are too faint to elicit a color response in the eye.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, 2001).

These results are substantially the same for giant and supergiant stars, which tend to be the ones that are brightest in the night sky. Most stars in the galaxy are faint red dwarfs, but the brightest stars, i.e., the ones visible from the greatest distance, are giants and supergiants.

W. Romanishin, An Introduction to Astronomical Photometry Using CCDs www.nhn.ou.edu/~wjr/research/wrccded2.pdf (1999).

G. Wysecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

There is another reason that very hot and very cool sources appear to be the same color regardless of temperature: At the extreme wavelength limits of human vision, most of the light is exciting only the red or blue rhodopsin. Color discrimination depends on the relative ratios of the R, G, and B rhodopsins, and when only one is excited, only one color is seen.

R. L. Kurucz, in Atomic Spectra and Oscillator strengths for Astrophysics and Fusion Research, J. R. Hansen, ed. (North-Holland, Amsterdam), p. 20.

R. L. Kurucz, in Stellar Atmospheres: Beyond Classical Models, L. Crivellari, I. Hubeny, D. G. Hummer, eds., NATO ASI Ser. C341, (1991), p. 441.
[CrossRef]

R. L. Kurucz, in The Stellar Populations of Galaxies, B. Barbuy, A. Renzini, eds., Int. Astron. Union Symp.149, 225 (1992).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Brightness I versus optical depth t of an object seen through an ideal, purely scattering atmosphere at an arbitrary wavelength. Io is the object’s intrinsic spectrum, and S is the source function. These are solutions of Eq. (1). When τ = 0 (completely clear), then I = Io and the object’s color appears without alteration. When τ = ∞, then I = S, indicating that the original object is completely obscured and light from its direction has been replaced by integrated light from the source function. Extinction or airlight may dominate depending on the ratio S/Io.

Fig. 2
Fig. 2

Spectra of main sequence stars from Kurucz.1618

Fig. 3
Fig. 3

CIE xy trajectory of a series of blackbodies ranging from 1000 K to over a million degrees. Above about 20, 000 K, the colors do not change perceptibly. Also shown are the actual colors of main sequence stars from Fig. 3. Despite the strong departures from a blackbody that cool stars show, they have little effect on the perceived color.

Fig. 4
Fig. 4

Spectra of the Sun as a function of elevation angle for pure Rayleigh scattering. From top to bottom the spectra are for elevations 90, 60, 30, 20, 10, 5, 3, 2, 1, and 0.5 degrees. Near the zenith the solar spectrum (W cm−2 nm−1) peaks near 500 nm, but at lower elevations the shorter wavelengths are attenuated more than the longer ones and the spectrum grows redder. Very near the horizon there is virtually no blue and very little green light.

Fig. 5
Fig. 5

Colors of the setting Sun in a pure Rayleigh-scattering atmosphere (from Fig. 5). From left to right the elevations of the Sun are 90, 60, 30, 20, 10, 5, 3, 2, 1, and 0.5 degrees. Also plotted is the trajectory of a cooling blackbody. Note that the Sun is always slightly more yellowish than a blackbody. Note that the high Sun is white and broadband, while the low Sun is red and much narrower across the spectrum. The colors are always slightly more yellow than those of blackbodies.

Fig. 6
Fig. 6

Colors of the setting Sun in a relatively clear atmosphere (MODTRAN4, midlatitude summer, visibility of 23 km).

Fig. 7
Fig. 7

Spectra of the sky computed by MODTRAN4 for a pure Rayleigh atmosphere. The sky is darkest and most colorful overhead (lowest curve) and whitest and brightest near the horizon (top curve).

Fig. 8
Fig. 8

CIE colors of the spectra in Fig. 8. Near the horizon H, the sky is very close to being ideal white, i.e., near the achromatic point. Overhead at the zenith (Z) the sky is bluer than the hottest blackbody, though still far from saturated.

Fig. 9
Fig. 9

CIE spectra of a black object viewed at various distances (optical depths from bottom to top are 0.01, 0.03, 0.1, 0.3, 1, 3, 10) with a horizontal LOS. The object begins faint and faintly blue (bottom curve). With increasing distance, the object appears to grow brighter and whiter until at very large distances it is spectral identical to the source function, in this case the 5700 K blackbody approximating the color spectrum.

Fig. 10
Fig. 10

Colors of the spectra from Fig. 10.

Fig. 11
Fig. 11

Spectra of a white object at various distances through the atmosphere for a value of A = 0.5.

Fig. 12
Fig. 12

CIE colors corresponding to the spectra from Fig. 12.

Fig. 13
Fig. 13

CIE of six colors for A = 1.0 (bright-colored reflective paper).

Fig. 14
Fig. 14

CIE of six colors for A = 10.0 (dark-colored rocks).

Fig. 15
Fig. 15

CIE of six colors for A = 0.1 (bright self-luminous sources like city lights).

Equations (7)

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I = I o e - τ + S ( 1 - e - τ ) , or I / I o = e - τ + ( 1 - e - τ ) S / I o ,
S = j / k ,
S ( 1 - e - τ ) = S ( 1 - 1 + τ - τ 2 / 2 ! + τ 3 / 3 ! .. ) S τ .
τ ( λ ) = N ( R ) σ T ( λ ) d R ,
τ ( λ ) = R N σ T ( λ ) ,
σ P = ( 4.16 e - 20 ) / λ 4 m 2 molecule - 1 ,
AM = sec z - 0.0018167 * ( sec z - 1 ) - 0.002875 * ( sec z - 1 ) 2 - 0.0008083 * ( sec z - 1 ) 3 ,

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