Abstract

The blue sky was observed near 90° from the sun, in the vertical plane through the direction of the sun, with the sun above and just below the horizon. The observations were made with six filters ranging from 3250 to 9400 Å. For a normal clear sky at the McDonald Observatory with the sun 11.°5 above the horizon, 75% polarization was found at 5500 Å. The agreement of the Rayleigh–Chandrasekhar theory with the observations is good. The difference of the above 75% with 100% polarization appears to be due to multiple scattering (6%), molecular anisotropy (6%), and reflection by the ground (5%), while a residual 8% is presumably due to aerosols. At the McDonald Observatory, the polarization of the daytime sky has a maximum near 5500 Å, with a decrease toward longer as well as toward shorter wavelengths. The decline in the ultraviolet is caused by multiple scattering, while in the infrared it is mostly due to ground reflection, which is especially strong when green plants are present.

© 1962 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Z. Sekera, Advances in Geophysics, edited by H. E. Landsberg, (Academic Press Inc., New York, 1956) Vol. 3.
    [CrossRef]
  2. Z. Sekera, Handbuch der Physik, edited by S. Flügge, (Springer-Verlag, Berlin, 1957), Vol. 48, Pt. II.
  3. G. V. Rosenberg, Usp. Fiz. Nauk. 71, 173 (1960); transl. Sov. Phys. Usp. 3, 346 (1960).
  4. N. N. Kalitin, Meteor. Z. 43, 132 (1926).
  5. H. C. van de Hulst, The Atmospheres of the Earth and Planets, edited by G. P. Kuiper (The University of Chicago Press, Chicago, 1952), Chap. III.
  6. T. Gehrels and T. M. Teska, Publs. Astron. Soc. Pacific 72, 115 (1960).
    [CrossRef]
  7. T. Gehrels, Astron. J. 65, 466 (1960).
    [CrossRef]
  8. T. Gehrels, Astron. J. 65, 470 (1960).
    [CrossRef]
  9. T. Gehrels and R. E. Samuelson, Astrophys. J. 134, 1022 (1961).
    [CrossRef]
  10. T. Gehrels, Astron. J. (to be published).
  11. V. G. Fesenkov, Astron. Zhur. 37, 785 (1960); transl. Sov. AJ 4, 741 (1961).
  12. J. Stebbins and G. E. Kron, Astrophys. J. 126, 266 (1957).
    [CrossRef]
  13. See reference 2, p. 324.
  14. R. Robley, Ann. Géophys. 8, 1 (1952).
  15. See reference 1, Fig. 22.
  16. See reference 1, Fig. 3.
  17. J. Strong, Concepts of Classical Optics (W. H. Freeman and Company, Inc., San Francisco and London, 1958), p. 108.
  18. J. V. Dave, Proc. Indian Acad. Sci. 43A, 336 (1956).
    [CrossRef]
  19. E. V. Ashburn and R. G. Weldon, J. Opt. Soc. Am. 46, 583 (1956).
  20. S. Chandrasekhar and D. D. Elbert, Trans. Am. Phil. Soc. 44, 643 (1954).
  21. K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).
  22. Rayleigh (J. W. Strutt), Phil. Mag. 35, 373 (1918); also Scientific Papers (Cambridge University Press, Cambridge, England, 1920), Vol. 6, p. 540.
  23. G. de Vaucouleurs, Ann. Phys. 6, 213 (1951).
  24. A. A. Pulido, dissertation, Chemistry Department, Indiana University (1961).
  25. See reference 1, Fig. 1.
    [CrossRef]
  26. See reference 19, Table 1.
  27. D. Deirmendjian, Quart. J. Roy. Meteorol. Soc. 86, 371 (1960) and references given.
  28. Handbook of Geophysics, rev. ed. (The Macmillan Co., New York, 1960), Chap. 14; the original Krinov reference is at Laboratoriia Aerometodov, Akad. Nauk SSSR, (1947).
  29. J. B. Irwin (personal communication).
    [CrossRef]
  30. The Atmospheres of the Earth and Planets, rev. ed. edited by G. P. Kuiper (The University of Chicago Press, Chicago, 1952), Fig. 88.
    [CrossRef]
  31. D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 478 (1951).
  32. J. Lenoble and Z. Sekera, Proc. Natl. Acad. Sci. 47, 372 (1961).
    [CrossRef]

1961 (2)

T. Gehrels and R. E. Samuelson, Astrophys. J. 134, 1022 (1961).
[CrossRef]

J. Lenoble and Z. Sekera, Proc. Natl. Acad. Sci. 47, 372 (1961).
[CrossRef]

1960 (6)

D. Deirmendjian, Quart. J. Roy. Meteorol. Soc. 86, 371 (1960) and references given.

V. G. Fesenkov, Astron. Zhur. 37, 785 (1960); transl. Sov. AJ 4, 741 (1961).

G. V. Rosenberg, Usp. Fiz. Nauk. 71, 173 (1960); transl. Sov. Phys. Usp. 3, 346 (1960).

T. Gehrels and T. M. Teska, Publs. Astron. Soc. Pacific 72, 115 (1960).
[CrossRef]

T. Gehrels, Astron. J. 65, 466 (1960).
[CrossRef]

T. Gehrels, Astron. J. 65, 470 (1960).
[CrossRef]

1957 (1)

J. Stebbins and G. E. Kron, Astrophys. J. 126, 266 (1957).
[CrossRef]

1956 (2)

J. V. Dave, Proc. Indian Acad. Sci. 43A, 336 (1956).
[CrossRef]

E. V. Ashburn and R. G. Weldon, J. Opt. Soc. Am. 46, 583 (1956).

1954 (1)

S. Chandrasekhar and D. D. Elbert, Trans. Am. Phil. Soc. 44, 643 (1954).

1952 (1)

R. Robley, Ann. Géophys. 8, 1 (1952).

1951 (2)

D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 478 (1951).

G. de Vaucouleurs, Ann. Phys. 6, 213 (1951).

1926 (1)

N. N. Kalitin, Meteor. Z. 43, 132 (1926).

1918 (1)

Rayleigh (J. W. Strutt), Phil. Mag. 35, 373 (1918); also Scientific Papers (Cambridge University Press, Cambridge, England, 1920), Vol. 6, p. 540.

Rayleigh (J. W. Strutt), Phil. Mag. 35, 373 (1918); also Scientific Papers (Cambridge University Press, Cambridge, England, 1920), Vol. 6, p. 540.

Ashburn, E. V.

Chandrasekhar, S.

S. Chandrasekhar and D. D. Elbert, Trans. Am. Phil. Soc. 44, 643 (1954).

Coulson, K. L.

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).

Dave, J. V.

J. V. Dave, Proc. Indian Acad. Sci. 43A, 336 (1956).
[CrossRef]

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).

de Vaucouleurs, G.

G. de Vaucouleurs, Ann. Phys. 6, 213 (1951).

Deirmendjian, D.

D. Deirmendjian, Quart. J. Roy. Meteorol. Soc. 86, 371 (1960) and references given.

Elbert, D. D.

S. Chandrasekhar and D. D. Elbert, Trans. Am. Phil. Soc. 44, 643 (1954).

Fesenkov, V. G.

V. G. Fesenkov, Astron. Zhur. 37, 785 (1960); transl. Sov. AJ 4, 741 (1961).

Gehrels, T.

T. Gehrels and R. E. Samuelson, Astrophys. J. 134, 1022 (1961).
[CrossRef]

T. Gehrels and T. M. Teska, Publs. Astron. Soc. Pacific 72, 115 (1960).
[CrossRef]

T. Gehrels, Astron. J. 65, 466 (1960).
[CrossRef]

T. Gehrels, Astron. J. 65, 470 (1960).
[CrossRef]

T. Gehrels, Astron. J. (to be published).

Irwin, J. B.

J. B. Irwin (personal communication).
[CrossRef]

Kalitin, N. N.

N. N. Kalitin, Meteor. Z. 43, 132 (1926).

Kron, G. E.

J. Stebbins and G. E. Kron, Astrophys. J. 126, 266 (1957).
[CrossRef]

Lenoble, J.

J. Lenoble and Z. Sekera, Proc. Natl. Acad. Sci. 47, 372 (1961).
[CrossRef]

Lock, C.

Packer, D. M.

Pulido, A. A.

A. A. Pulido, dissertation, Chemistry Department, Indiana University (1961).

Rayleigh,

Rayleigh (J. W. Strutt), Phil. Mag. 35, 373 (1918); also Scientific Papers (Cambridge University Press, Cambridge, England, 1920), Vol. 6, p. 540.

Robley, R.

R. Robley, Ann. Géophys. 8, 1 (1952).

Rosenberg, G. V.

G. V. Rosenberg, Usp. Fiz. Nauk. 71, 173 (1960); transl. Sov. Phys. Usp. 3, 346 (1960).

Samuelson, R. E.

T. Gehrels and R. E. Samuelson, Astrophys. J. 134, 1022 (1961).
[CrossRef]

Sekera, Z.

J. Lenoble and Z. Sekera, Proc. Natl. Acad. Sci. 47, 372 (1961).
[CrossRef]

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).

Z. Sekera, Advances in Geophysics, edited by H. E. Landsberg, (Academic Press Inc., New York, 1956) Vol. 3.
[CrossRef]

Z. Sekera, Handbuch der Physik, edited by S. Flügge, (Springer-Verlag, Berlin, 1957), Vol. 48, Pt. II.

Stebbins, J.

J. Stebbins and G. E. Kron, Astrophys. J. 126, 266 (1957).
[CrossRef]

Strong, J.

J. Strong, Concepts of Classical Optics (W. H. Freeman and Company, Inc., San Francisco and London, 1958), p. 108.

Strutt, J. W.

Rayleigh (J. W. Strutt), Phil. Mag. 35, 373 (1918); also Scientific Papers (Cambridge University Press, Cambridge, England, 1920), Vol. 6, p. 540.

Teska, T. M.

T. Gehrels and T. M. Teska, Publs. Astron. Soc. Pacific 72, 115 (1960).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, The Atmospheres of the Earth and Planets, edited by G. P. Kuiper (The University of Chicago Press, Chicago, 1952), Chap. III.

Weldon, R. G.

Ann. Géophys. (1)

R. Robley, Ann. Géophys. 8, 1 (1952).

Ann. Phys. (1)

G. de Vaucouleurs, Ann. Phys. 6, 213 (1951).

Astron. J. (2)

T. Gehrels, Astron. J. 65, 466 (1960).
[CrossRef]

T. Gehrels, Astron. J. 65, 470 (1960).
[CrossRef]

Astron. Zhur. (1)

V. G. Fesenkov, Astron. Zhur. 37, 785 (1960); transl. Sov. AJ 4, 741 (1961).

Astrophys. J. (2)

J. Stebbins and G. E. Kron, Astrophys. J. 126, 266 (1957).
[CrossRef]

T. Gehrels and R. E. Samuelson, Astrophys. J. 134, 1022 (1961).
[CrossRef]

J. Opt. Soc. Am. (2)

Meteor. Z. (1)

N. N. Kalitin, Meteor. Z. 43, 132 (1926).

Phil. Mag. (1)

Rayleigh (J. W. Strutt), Phil. Mag. 35, 373 (1918); also Scientific Papers (Cambridge University Press, Cambridge, England, 1920), Vol. 6, p. 540.

Proc. Indian Acad. Sci. (1)

J. V. Dave, Proc. Indian Acad. Sci. 43A, 336 (1956).
[CrossRef]

Proc. Natl. Acad. Sci. (1)

J. Lenoble and Z. Sekera, Proc. Natl. Acad. Sci. 47, 372 (1961).
[CrossRef]

Publs. Astron. Soc. Pacific (1)

T. Gehrels and T. M. Teska, Publs. Astron. Soc. Pacific 72, 115 (1960).
[CrossRef]

Quart. J. Roy. Meteorol. Soc. (1)

D. Deirmendjian, Quart. J. Roy. Meteorol. Soc. 86, 371 (1960) and references given.

Trans. Am. Phil. Soc. (1)

S. Chandrasekhar and D. D. Elbert, Trans. Am. Phil. Soc. 44, 643 (1954).

Usp. Fiz. Nauk. (1)

G. V. Rosenberg, Usp. Fiz. Nauk. 71, 173 (1960); transl. Sov. Phys. Usp. 3, 346 (1960).

Other (15)

See reference 2, p. 324.

See reference 1, Fig. 22.

See reference 1, Fig. 3.

J. Strong, Concepts of Classical Optics (W. H. Freeman and Company, Inc., San Francisco and London, 1958), p. 108.

H. C. van de Hulst, The Atmospheres of the Earth and Planets, edited by G. P. Kuiper (The University of Chicago Press, Chicago, 1952), Chap. III.

Z. Sekera, Advances in Geophysics, edited by H. E. Landsberg, (Academic Press Inc., New York, 1956) Vol. 3.
[CrossRef]

Z. Sekera, Handbuch der Physik, edited by S. Flügge, (Springer-Verlag, Berlin, 1957), Vol. 48, Pt. II.

T. Gehrels, Astron. J. (to be published).

K. L. Coulson, J. V. Dave, and Z. Sekera, Tables Related to Radiation Emerging from a Planetary Atmosphere with Rayleigh Scattering (University of California Press, Berkeley and Los Angeles, 1960).

A. A. Pulido, dissertation, Chemistry Department, Indiana University (1961).

See reference 1, Fig. 1.
[CrossRef]

See reference 19, Table 1.

Handbook of Geophysics, rev. ed. (The Macmillan Co., New York, 1960), Chap. 14; the original Krinov reference is at Laboratoriia Aerometodov, Akad. Nauk SSSR, (1947).

J. B. Irwin (personal communication).
[CrossRef]

The Atmospheres of the Earth and Planets, rev. ed. edited by G. P. Kuiper (The University of Chicago Press, Chicago, 1952), Fig. 88.
[CrossRef]

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

The polarization of the blue sky, near quarter-phase, about the time of sunrise. Percentage polarization obtained with Infrared, Green, and Ultraviolet filters, as a function of geometrical sun’s elevation. The start of sunrise is actually observed earlier due to refraction, etc.

Fig. 2
Fig. 2

Observed percentage polarization, of the clear blue sky near 90° phase, as a function of the inverse of the wavelength in microns. Solid line, for the sun 4° above the horizon. Broken line, for the sun 3° below the horizon. A typical case, as observed on the morning of August 31, 1960, at the McDonald Observatory.

Fig. 3
Fig. 3

Typical patterns for different days and seasons of blue-sky polarization, normalized to 61.1% in the green, as a function of the inverse of the wavelength in microns. Arbitrarily divided into two groups, namely with weak and strong infrared polarizations.

Fig. 4
Fig. 4

Percentage polarization, observed by Sekera (1956) at Cactus Peak, as a function of the inverse of the wavelength in microns.

Fig. 5
Fig. 5

The percentage of incident light reflected, as a function of the inverse of the wavelength in microns, determined by E. L. Krinov (see Handbook of Geophysics, 1960). Curve (1) is for fresh snow, (2) for bare desert and rocks, (3) for green grass and deciduous trees, (4) for dry grass and coniferous trees, and (5) is for black soil.

Tables (7)

Tables Icon

Table I Data on aspect and sky conditions.

Tables Icon

Table II Polarization measures of the daytime sky.

Tables Icon

Table III Polarization measures for the crepuscular sky.

Tables Icon

Table IV Observations of colors for the daytime sky and standard stars.

Tables Icon

Table V Percentage polarization, interpolated in elevation, and normalized to 61.1% at λ = 1.89.

Tables Icon

Table VI Averages of percentage polarization, normalized to 61.1% at 1/λ = 1.89.

Tables Icon

Table VII Comparison of theory with observations of polarization.

Equations (3)

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

cos i = - sin δ sin δ - cos δ cos δ cos Δ α ,
sin E = sin δ sin γ + cos δ cos γ cos H A ,
P = 100 ( I 1 - I 2 ) / ( I 1 + I 2 ) ,