Abstract

The polarization distribution in the sky during a total solar eclipse is calculated with a simple secondary light-scattering model. This model uses the light-intensity measurements near the horizon during the eclipse and the pretotality and posttotality skylight polarization observations as input. It is found that the model can explain various observations during totality, including the quantitative measurements of Shaw [ Appl. Opt. 14, 388 ( 1975)] of the polarization distribution of the sky in the solar vertical during the 1973 total eclipse.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. E. Shaw, “Sky brightness and polarization during the 1973 African eclipse,” Appl. Opt. 14, 388–394 (1975).
    [CrossRef] [PubMed]
  2. W. E. Sharp, S. M. Silverman, J. W. F. Lloyd, “Summary of sky brightness measurements during eclipses of the sun,” Appl. Opt. 10, 1207–1210 (1971).
    [CrossRef] [PubMed]
  3. S. M. Silverman, E. G. Mullen, “Sky brightness during eclipses: a review,” Appl. Opt. 14, 2838–2843 (1975).
    [CrossRef] [PubMed]
  4. G. E. Shaw, “Sky radiance during a total solar eclipse: a theoretical model,” Appl. Opt. 17, 272–276 (1978).
    [CrossRef] [PubMed]
  5. S. D. Gedzelman, “Sky color near the horizon during a total solar eclipse,” Appl. Opt. 14, 2831–2837 (1975).
    [CrossRef] [PubMed]
  6. N. Piltschikoff, “Sur la polarisation du ciel pendant les éclipses du soleil,”C. R. Acad. Sci. Paris 142, 1449 (1906).
  7. E. de Bary, K. Bullrich, D. Lorenz, “Messungen der Himmelsstrahlung und deren Polarisationgrad während der Sonnenfinsternis am 15.2.1961 in Viareggio (Italien),” Geofis. Pura Appl. 48, 193–198 (1961).
    [CrossRef]
  8. J. G. Moore, C. R. N. Rao, “Polarization of the daytime sky during the total solar eclipse of 30 May 1965,” Ann. Geophys. 22, 147–150 (1966).
  9. R. E. Miller, W. G. Fastie, “Skylight intensity, polarization and airglow measurements during the total solar eclipse of 30 May 1965,” J. Atmos. Terr. Phys. 34, 1541–1546 (1972).
    [CrossRef]
  10. C. R. N. Rao, T. Takashima, J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,”J. Atmos. Terr. Phys. 34, 573–576 (1972).
    [CrossRef]
  11. B. S. Dandekar, J. P. Turtle, “Day sky brightness and polarization during the total eclipse of 7 March 1970,” Appl. Opt. 10, 1220–1224 (1971).
    [CrossRef] [PubMed]
  12. H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas and Applications, Vol. 2 (Academic, New York, 1980).
  13. J. L. Soret, “Sur la polarisation atmosphérique,” Ann. Chim. Phys. 14, 503–541 (1888).
  14. F. Ahlgrimm, “Zur Theorie der atmosphärischen Polarisation,” Jahrb. Hamburger Wiss. Anst. 32, 1–66 (1914).
  15. K. Serkowski, “Polarimeters for optical astronomy,” in T. Gehrels, Planets, Stars and Nebula, Studied with Photopolarimetry (University of Arizona, Tucson, Ariz., 1974), pp. 135–174.
  16. E. Collet, “The description of polarization in classical physics,” Am. J. Phys. 36, 713–725 (1968).
    [CrossRef]
  17. D. W. Jannink, Royal Netherlands Meteorological Institute, De Bilt, The Netherlands (personal communication, 1981).
  18. G. P. Können, Polarized Light in Nature (Cambridge U. Press, Cambridge, 1985).

1978

1975

1972

R. E. Miller, W. G. Fastie, “Skylight intensity, polarization and airglow measurements during the total solar eclipse of 30 May 1965,” J. Atmos. Terr. Phys. 34, 1541–1546 (1972).
[CrossRef]

C. R. N. Rao, T. Takashima, J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,”J. Atmos. Terr. Phys. 34, 573–576 (1972).
[CrossRef]

1971

1968

E. Collet, “The description of polarization in classical physics,” Am. J. Phys. 36, 713–725 (1968).
[CrossRef]

1966

J. G. Moore, C. R. N. Rao, “Polarization of the daytime sky during the total solar eclipse of 30 May 1965,” Ann. Geophys. 22, 147–150 (1966).

1961

E. de Bary, K. Bullrich, D. Lorenz, “Messungen der Himmelsstrahlung und deren Polarisationgrad während der Sonnenfinsternis am 15.2.1961 in Viareggio (Italien),” Geofis. Pura Appl. 48, 193–198 (1961).
[CrossRef]

1914

F. Ahlgrimm, “Zur Theorie der atmosphärischen Polarisation,” Jahrb. Hamburger Wiss. Anst. 32, 1–66 (1914).

1906

N. Piltschikoff, “Sur la polarisation du ciel pendant les éclipses du soleil,”C. R. Acad. Sci. Paris 142, 1449 (1906).

1888

J. L. Soret, “Sur la polarisation atmosphérique,” Ann. Chim. Phys. 14, 503–541 (1888).

Ahlgrimm, F.

F. Ahlgrimm, “Zur Theorie der atmosphärischen Polarisation,” Jahrb. Hamburger Wiss. Anst. 32, 1–66 (1914).

Bullrich, K.

E. de Bary, K. Bullrich, D. Lorenz, “Messungen der Himmelsstrahlung und deren Polarisationgrad während der Sonnenfinsternis am 15.2.1961 in Viareggio (Italien),” Geofis. Pura Appl. 48, 193–198 (1961).
[CrossRef]

Collet, E.

E. Collet, “The description of polarization in classical physics,” Am. J. Phys. 36, 713–725 (1968).
[CrossRef]

Dandekar, B. S.

de Bary, E.

E. de Bary, K. Bullrich, D. Lorenz, “Messungen der Himmelsstrahlung und deren Polarisationgrad während der Sonnenfinsternis am 15.2.1961 in Viareggio (Italien),” Geofis. Pura Appl. 48, 193–198 (1961).
[CrossRef]

Fastie, W. G.

R. E. Miller, W. G. Fastie, “Skylight intensity, polarization and airglow measurements during the total solar eclipse of 30 May 1965,” J. Atmos. Terr. Phys. 34, 1541–1546 (1972).
[CrossRef]

Gedzelman, S. D.

Jannink, D. W.

D. W. Jannink, Royal Netherlands Meteorological Institute, De Bilt, The Netherlands (personal communication, 1981).

Können, G. P.

G. P. Können, Polarized Light in Nature (Cambridge U. Press, Cambridge, 1985).

Lloyd, J. W. F.

Lorenz, D.

E. de Bary, K. Bullrich, D. Lorenz, “Messungen der Himmelsstrahlung und deren Polarisationgrad während der Sonnenfinsternis am 15.2.1961 in Viareggio (Italien),” Geofis. Pura Appl. 48, 193–198 (1961).
[CrossRef]

Miller, R. E.

R. E. Miller, W. G. Fastie, “Skylight intensity, polarization and airglow measurements during the total solar eclipse of 30 May 1965,” J. Atmos. Terr. Phys. 34, 1541–1546 (1972).
[CrossRef]

Moore, J. G.

C. R. N. Rao, T. Takashima, J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,”J. Atmos. Terr. Phys. 34, 573–576 (1972).
[CrossRef]

J. G. Moore, C. R. N. Rao, “Polarization of the daytime sky during the total solar eclipse of 30 May 1965,” Ann. Geophys. 22, 147–150 (1966).

Mullen, E. G.

Piltschikoff, N.

N. Piltschikoff, “Sur la polarisation du ciel pendant les éclipses du soleil,”C. R. Acad. Sci. Paris 142, 1449 (1906).

Rao, C. R. N.

C. R. N. Rao, T. Takashima, J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,”J. Atmos. Terr. Phys. 34, 573–576 (1972).
[CrossRef]

J. G. Moore, C. R. N. Rao, “Polarization of the daytime sky during the total solar eclipse of 30 May 1965,” Ann. Geophys. 22, 147–150 (1966).

Serkowski, K.

K. Serkowski, “Polarimeters for optical astronomy,” in T. Gehrels, Planets, Stars and Nebula, Studied with Photopolarimetry (University of Arizona, Tucson, Ariz., 1974), pp. 135–174.

Sharp, W. E.

Shaw, G. E.

Silverman, S. M.

Soret, J. L.

J. L. Soret, “Sur la polarisation atmosphérique,” Ann. Chim. Phys. 14, 503–541 (1888).

Takashima, T.

C. R. N. Rao, T. Takashima, J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,”J. Atmos. Terr. Phys. 34, 573–576 (1972).
[CrossRef]

Turtle, J. P.

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas and Applications, Vol. 2 (Academic, New York, 1980).

Am. J. Phys.

E. Collet, “The description of polarization in classical physics,” Am. J. Phys. 36, 713–725 (1968).
[CrossRef]

Ann. Chim. Phys.

J. L. Soret, “Sur la polarisation atmosphérique,” Ann. Chim. Phys. 14, 503–541 (1888).

Ann. Geophys.

J. G. Moore, C. R. N. Rao, “Polarization of the daytime sky during the total solar eclipse of 30 May 1965,” Ann. Geophys. 22, 147–150 (1966).

Appl. Opt.

C. R. Acad. Sci. Paris

N. Piltschikoff, “Sur la polarisation du ciel pendant les éclipses du soleil,”C. R. Acad. Sci. Paris 142, 1449 (1906).

Geofis. Pura Appl.

E. de Bary, K. Bullrich, D. Lorenz, “Messungen der Himmelsstrahlung und deren Polarisationgrad während der Sonnenfinsternis am 15.2.1961 in Viareggio (Italien),” Geofis. Pura Appl. 48, 193–198 (1961).
[CrossRef]

J. Atmos. Terr. Phys.

R. E. Miller, W. G. Fastie, “Skylight intensity, polarization and airglow measurements during the total solar eclipse of 30 May 1965,” J. Atmos. Terr. Phys. 34, 1541–1546 (1972).
[CrossRef]

C. R. N. Rao, T. Takashima, J. G. Moore, “Polarimetry of the daytime sky during solar eclipses,”J. Atmos. Terr. Phys. 34, 573–576 (1972).
[CrossRef]

Jahrb. Hamburger Wiss. Anst.

F. Ahlgrimm, “Zur Theorie der atmosphärischen Polarisation,” Jahrb. Hamburger Wiss. Anst. 32, 1–66 (1914).

Other

K. Serkowski, “Polarimeters for optical astronomy,” in T. Gehrels, Planets, Stars and Nebula, Studied with Photopolarimetry (University of Arizona, Tucson, Ariz., 1974), pp. 135–174.

H. C. van de Hulst, Multiple Light Scattering, Tables, Formulas and Applications, Vol. 2 (Academic, New York, 1980).

D. W. Jannink, Royal Netherlands Meteorological Institute, De Bilt, The Netherlands (personal communication, 1981).

G. P. Können, Polarized Light in Nature (Cambridge U. Press, Cambridge, 1985).

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 (3)

Fig. 1
Fig. 1

Geometry of the two-step scattering model. The definitions of the angles are given in the text.

Fig. 2
Fig. 2

Polarization distribution in the solar vertical during totality. The dashed line is the observed polarization reported by Shaw.1 The solid line is the calculated polarization of the present two-step scattering model with parameters ID = 1.22 and a2 = 0.1, taken from Shaw’s pretotality, posttotality, and intensity observations. Note that the model is essentially unable to describe the behavior for low h, where singly scattered light becomes dominant.

Fig. 3
Fig. 3

Comparison of the observed degree of polarization during several eclipses with the theory. The observations are transformed into a degree of polarization Pred for standard circumstances. The theoretical curve is Eq. (19) with ID = 1. The numbers at the points correspond to those in Table 1.

Tables (1)

Tables Icon

Table 1 Summary of Instrumental Observations of Skylight Polarization at Mideclipsea

Equations (31)

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

S = [ I Q U ] [ I I P cos 2 ϕ I P sin 2 ϕ ] .
T ( ϕ ) = [ 1 0 0 0 cos 2 ϕ sin 2 ϕ 0 - sin 2 ϕ cos 2 ϕ ] .
S 2 = T ( - ϕ 3 ) M T ( ϕ 2 ) S 1 .
M = [ 1 + cos 2 θ + I D - sin 2 θ 0 - sin 2 θ 1 + cos 2 θ 0 0 0 2 cos θ ] ,
P Q 2 + U 2 I = sin 2 θ 1 + cos 2 θ + I D ,
P = 1 1 + I D .
ψ 1 = ψ + α
S 1 = T ( - ϕ 1 ) M S 0 f ( ψ 1 ) ,
cos θ 1 = cos z cos ψ 1
tan ϕ 1 = - sin ψ 1 / tan z ,
f ( ψ 1 ) r - 1 ( ψ 1 ) ,
f ( ψ 1 ) = ( 1 - cos 2 z cos 2 ψ 1 ) 1 / 2 1 - ½ cos 2 z cos 2 ψ 1 .
f ( ψ 1 ) = 1 + cos z cos ψ 1 .
f ( ψ 1 ) = 1 - a 2 cos 2 ψ 1 ,
S 1 = [ f ( ψ + α ) 0 0 ] .
cos θ 2 = cos α cos h , tan ϕ 2 = - sin α / tan h , tan ϕ 3 = - tan α / sin h .
I 2 ( h , ψ , α ) = ( 1 + I D + cos 2 h cos 2 α ) f ( ψ + α ) , Q 2 ( h , ψ , α ) = ( 1 - [ 1 + sin 2 h ] cos 2 α ) f ( ψ , α ) , U 2 ( h , ψ , α ) = sin 2 α sin h f ( ψ + α ) .
S ¯ 2 ( h , ψ ) = S ¯ 2 ( h , ψ + 180° )
I ¯ 2 ( h , ψ ) = π [ 2 ( 1 + I D ) + cos 2 h ] , Q ¯ 2 ( h , ψ ) = π cos 2 h , U ¯ 2 ( h , ψ ) = 0 ,
P ( h , ψ ) = Q ¯ 2 I ¯ 2 = cos 2 h 2 ( 1 + I D ) + cos 2 h ,
I ¯ 2 ( h , ψ ) = π [ ( 2 - a 2 ) ( 1 + I D ) + ( 1 - ¼ a 2 cos 2 ψ - ½ a 2 ) cos 2 h ] Q ¯ 2 ( h , ψ ) = π [ ½ a 2 cos 2 ψ + ( 1 - ¼ a 2 cos 2 ψ - ½ a 2 ) cos 2 h ] U ¯ 2 ( h , ψ ) = ½ π a 2 sin 2 ψ sin h ,
P ( h , 0 ) = P ( h , 180° ) = Q ¯ 2 ( h , 0 ) I ¯ 2 ( h , 0 ) = ½ a 2 + ( 1 - ¾ a 2 ) cos 2 h ( 2 - a 2 ) ( 1 + I D ) + ( 1 + ¾ a 2 ) cos 2 h .
cos 2 h n = 2 a 2 4 - a 2 ,
P red = 2 ( 1 + I D ) + cos 2 h 4 + cos 2 h P tot = 2 P pret - 1 + cos 2 h 4 + cos 2 h P tot .
S 2 ( h = 90° ) = [ 2 I 1 - Q 1 ( - I 1 + Q 1 ) cos 2 α ( I 1 - Q 1 ) sin 2 α ] ,
S 2 ( h = ) = [ I 1 ( 2 + cos 2 α ) + Q 1 sin 2 α Q 1 ( 1 + cos 2 α ) + I 1 sin 2 α 2 U 1 cos α ] ,
S 1 = [ I 1 Q 1 U 1 ] = [ 1 + I D cos 2 z - cos 2 α cos 2 z sin α sin 2 z ] .
P ( h = 90° ) = - ½ cos 2 z 4 ( 1 + I D ) - 3 cos 2 z + 2 ,
P ( h = ) = ( 1 + I D ) + ¹⁷ / cos 2 z - 3 5 ( 1 + I D ) + / cos 2 z - 1 .
0 < P ( 90° ) - P ( 90° ) < 0.07 cos 2 z ,
P ( ) - P ( ) = ¹⁴ / - ³⁹ / ₁₀ cos 2 z 5 ( 1 + I D ) + / cos 2 z - 1 ,

Metrics