Abstract

Measurements of the skylight polarized radiance distribution were performed at different measurement sites, atmospheric conditions, and three wavelengths with our newly developed Polarization Radiance Distribution Camera System (RADS-IIP), an analyzer-type Stokes polarimeter. Three Stokes parameters of skylight (I, Q, U), the degree of polarization, and the plane of polarization are presented in image format. The Arago point and neutral lines have been observed with RADS-IIP. Qualitatively, the dependence of the intensity and polarization data on wavelength, solar zenith angle, and surface albedo is in agreement with the results from computations based on a plane-parallel Rayleigh atmospheric model.

© 1997 Optical Society of America

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References

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  1. K. N. Liou, An Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).
  2. H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  3. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, Hampton, Va., 1988).
  4. H. H. Kimball, “The effect of the atmospheric turbidity of 1912 on solar radiation intensities and skylight polarization,” Bull. Mt. Weather Obs. 5, 295–312 (1913).
  5. T. Takashima, H. S. Chen, C. R. N. Rao, “Polarimetric investigations of the turbidity of the atmosphere over Los Angeles,” in Planets, Stars, and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1974) pp. 500–509.
  6. K. L. Coulson, “Characteristics of skylight at the zenith during twilight as indicators of atmospheric turbidity. I. Degree of polarization,” Appl. Opt. 19, 3469–3480 (1980).
    [CrossRef] [PubMed]
  7. K. L. Coulson, “The polarization of light in the environment,” in Planets, Stars, and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1974) pp. 444–471.
  8. Y Liu, “Measurement of the intensity and polarization of light in the atmosphere,” Ph.D. dissertation (University of Miami, Miami, Fla., 1996).
  9. K. J. Voss, Y. Liu, “Polarized radiance distribution of skylight. I. System description and characterization,” Appl. Opt. 36, 6083–6094 (1997).
    [CrossRef] [PubMed]
  10. S. Chandrasekhar, Radiative Transfer (Clarendon, Oxford, 1950).
  11. K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging From a Planetary Atmosphere With Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960).
  12. J. W. Chamberlain, Theory of Planetary Atmospheres, Vol. 22 of International Geophysics Series (Academic, New York, 1978).
  13. G. N. Plass, G. W. Kattawar, “Polarization of the radiation reflected and transmitted by the earth’s atmosphere,” Appl. Opt. 9, 1122–1130 (1970).
    [CrossRef] [PubMed]
  14. G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
    [CrossRef]
  15. G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
    [CrossRef]
  16. H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978).
    [CrossRef] [PubMed]
  17. H. R. Gordon, J. L. Mueller, R. C. Wrigley, “Atmospheric correction of Nimbus-7 Coastal Zone Color Scanner imagery,” in Remote Sensing of Atmospheres and Oceans, A. Deepak, ed. (Academic, New York, 1980) pp. 457–483.
    [CrossRef]
  18. H. R. Gordon, D. J. Castano, “Coastal Zone Color Scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
    [CrossRef] [PubMed]
  19. H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. I. The Rayleigh scattering component,” Appl. Opt. 31, 4247–4260 (1992).
    [CrossRef] [PubMed]
  20. H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. II. Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
    [CrossRef] [PubMed]
  21. C. N. Adams, G. W. Kattawar, “Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system,” Appl. Opt. 32, 4610–4617 (1993).
    [CrossRef] [PubMed]
  22. M. Wang, H. R. Gordon, “Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations,” Appl. Opt. 32, 4598–4609 (1993).
    [CrossRef] [PubMed]
  23. M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).
  24. H. E. Gerber, E. E. Hindman, eds., Light Absorption by Aerosol Particles (Spectrum, Hampton, Va., 1982).
  25. Z. Sekera, “Recent developments in the study of the polarization of skylight,” in Advances in Geophysics (Academic, New York, 1956), Vol. 3, pp. 43–104.
    [CrossRef]
  26. K. Bullrich, “Scattered radiation in the atmosphere and the natural aerosol,” in Advances in Geophysics (Academic, New York, 1964) Vol. 10, pp. 99–260.
    [CrossRef]
  27. R. S. Fraser, “Atmospheric neutral points over water,” J. Opt. Soc. Am. 58, 1029–1031 (1968).
    [CrossRef]
  28. R. S. Fraser, “Atmospheric neutral points outside of the principal plane,” Contrib. Atmos. Phys. 54, 286–297 (1981).
  29. J. J. Michalsky, R. Perez, R. Stewart, “Design and development of a rotating shadowband radiometer solar radiation/daylight network,” Sol. Energy 41, 577–581 (1988).
    [CrossRef]

1997

1993

1992

1989

M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

1988

J. J. Michalsky, R. Perez, R. Stewart, “Design and development of a rotating shadowband radiometer solar radiation/daylight network,” Sol. Energy 41, 577–581 (1988).
[CrossRef]

1987

1981

R. S. Fraser, “Atmospheric neutral points outside of the principal plane,” Contrib. Atmos. Phys. 54, 286–297 (1981).

1980

1978

1973

G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

1970

1968

1913

H. H. Kimball, “The effect of the atmospheric turbidity of 1912 on solar radiation intensities and skylight polarization,” Bull. Mt. Weather Obs. 5, 295–312 (1913).

Adams, C. N.

C. N. Adams, G. W. Kattawar, “Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system,” Appl. Opt. 32, 4610–4617 (1993).
[CrossRef] [PubMed]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Arao, K.

M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Bullrich, K.

K. Bullrich, “Scattered radiation in the atmosphere and the natural aerosol,” in Advances in Geophysics (Academic, New York, 1964) Vol. 10, pp. 99–260.
[CrossRef]

Castano, D. J.

Chamberlain, J. W.

J. W. Chamberlain, Theory of Planetary Atmospheres, Vol. 22 of International Geophysics Series (Academic, New York, 1978).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Clarendon, Oxford, 1950).

Chen, H. S.

T. Takashima, H. S. Chen, C. R. N. Rao, “Polarimetric investigations of the turbidity of the atmosphere over Los Angeles,” in Planets, Stars, and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1974) pp. 500–509.

Coulson, K. L.

K. L. Coulson, “Characteristics of skylight at the zenith during twilight as indicators of atmospheric turbidity. I. Degree of polarization,” Appl. Opt. 19, 3469–3480 (1980).
[CrossRef] [PubMed]

K. L. Coulson, “The polarization of light in the environment,” in Planets, Stars, and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1974) pp. 444–471.

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, Hampton, Va., 1988).

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging From a Planetary Atmosphere With Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960).

Dave, J. V.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging From a Planetary Atmosphere With Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960).

Fraser, R. S.

R. S. Fraser, “Atmospheric neutral points outside of the principal plane,” Contrib. Atmos. Phys. 54, 286–297 (1981).

R. S. Fraser, “Atmospheric neutral points over water,” J. Opt. Soc. Am. 58, 1029–1031 (1968).
[CrossRef]

Gordon, H. R.

Guinn, J. A.

G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

Kattawar, G. W.

C. N. Adams, G. W. Kattawar, “Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system,” Appl. Opt. 32, 4610–4617 (1993).
[CrossRef] [PubMed]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

G. N. Plass, G. W. Kattawar, “Polarization of the radiation reflected and transmitted by the earth’s atmosphere,” Appl. Opt. 9, 1122–1130 (1970).
[CrossRef] [PubMed]

Kimball, H. H.

H. H. Kimball, “The effect of the atmospheric turbidity of 1912 on solar radiation intensities and skylight polarization,” Bull. Mt. Weather Obs. 5, 295–312 (1913).

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).

Liu, Y

Y Liu, “Measurement of the intensity and polarization of light in the atmosphere,” Ph.D. dissertation (University of Miami, Miami, Fla., 1996).

Liu, Y.

Michalsky, J. J.

J. J. Michalsky, R. Perez, R. Stewart, “Design and development of a rotating shadowband radiometer solar radiation/daylight network,” Sol. Energy 41, 577–581 (1988).
[CrossRef]

Mueller, J. L.

H. R. Gordon, J. L. Mueller, R. C. Wrigley, “Atmospheric correction of Nimbus-7 Coastal Zone Color Scanner imagery,” in Remote Sensing of Atmospheres and Oceans, A. Deepak, ed. (Academic, New York, 1980) pp. 457–483.
[CrossRef]

Nakajima, M.

M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Nakanishi, Y.

M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Perez, R.

J. J. Michalsky, R. Perez, R. Stewart, “Design and development of a rotating shadowband radiometer solar radiation/daylight network,” Sol. Energy 41, 577–581 (1988).
[CrossRef]

Plass, G. N.

G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

G. N. Plass, G. W. Kattawar, “Polarization of the radiation reflected and transmitted by the earth’s atmosphere,” Appl. Opt. 9, 1122–1130 (1970).
[CrossRef] [PubMed]

Rao, C. R. N.

T. Takashima, H. S. Chen, C. R. N. Rao, “Polarimetric investigations of the turbidity of the atmosphere over Los Angeles,” in Planets, Stars, and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1974) pp. 500–509.

Sekera, Z.

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging From a Planetary Atmosphere With Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960).

Z. Sekera, “Recent developments in the study of the polarization of skylight,” in Advances in Geophysics (Academic, New York, 1956), Vol. 3, pp. 43–104.
[CrossRef]

Shiobara, M.

M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Stewart, R.

J. J. Michalsky, R. Perez, R. Stewart, “Design and development of a rotating shadowband radiometer solar radiation/daylight network,” Sol. Energy 41, 577–581 (1988).
[CrossRef]

Takashima, T.

T. Takashima, H. S. Chen, C. R. N. Rao, “Polarimetric investigations of the turbidity of the atmosphere over Los Angeles,” in Planets, Stars, and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1974) pp. 500–509.

Tanaka, M.

M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Voss, K. J.

Wang, M.

Wrigley, R. C.

H. R. Gordon, J. L. Mueller, R. C. Wrigley, “Atmospheric correction of Nimbus-7 Coastal Zone Color Scanner imagery,” in Remote Sensing of Atmospheres and Oceans, A. Deepak, ed. (Academic, New York, 1980) pp. 457–483.
[CrossRef]

Yamano, M.

M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

Appl. Opt.

K. J. Voss, Y. Liu, “Polarized radiance distribution of skylight. I. System description and characterization,” Appl. Opt. 36, 6083–6094 (1997).
[CrossRef] [PubMed]

H. R. Gordon, D. J. Castano, “Coastal Zone Color Scanner atmospheric correction algorithm: multiple scattering effects,” Appl. Opt. 26, 2111–2122 (1987).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. I. The Rayleigh scattering component,” Appl. Opt. 31, 4247–4260 (1992).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Surface-roughness considerations for atmospheric correction of ocean color sensors. II. Error in the retrieved water-leaving radiance,” Appl. Opt. 31, 4261–4267 (1992).
[CrossRef] [PubMed]

C. N. Adams, G. W. Kattawar, “Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system,” Appl. Opt. 32, 4610–4617 (1993).
[CrossRef] [PubMed]

M. Wang, H. R. Gordon, “Retrieval of the columnar aerosol phase function and single-scattering albedo from sky radiance over the ocean: simulations,” Appl. Opt. 32, 4598–4609 (1993).
[CrossRef] [PubMed]

K. L. Coulson, “Characteristics of skylight at the zenith during twilight as indicators of atmospheric turbidity. I. Degree of polarization,” Appl. Opt. 19, 3469–3480 (1980).
[CrossRef] [PubMed]

G. N. Plass, G. W. Kattawar, “Polarization of the radiation reflected and transmitted by the earth’s atmosphere,” Appl. Opt. 9, 1122–1130 (1970).
[CrossRef] [PubMed]

H. R. Gordon, “Removal of atmospheric effects from satellite imagery of the oceans,” Appl. Opt. 17, 1631–1636 (1978).
[CrossRef] [PubMed]

Bull. Mt. Weather Obs.

H. H. Kimball, “The effect of the atmospheric turbidity of 1912 on solar radiation intensities and skylight polarization,” Bull. Mt. Weather Obs. 5, 295–312 (1913).

Contrib. Atmos. Phys.

R. S. Fraser, “Atmospheric neutral points outside of the principal plane,” Contrib. Atmos. Phys. 54, 286–297 (1981).

J. Meteorol. Soc. Jpn.

M. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May 1982 at Nagasaki. II. Models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

J. Opt. Soc. Am.

J. Phys. Oceanogr.

G. W. Kattawar, G. N. Plass, J. A. Guinn, “Monte Carlo calculations of the polarization of radiation in the earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372 (1973).
[CrossRef]

Limnol. Oceanogr.

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Sol. Energy

J. J. Michalsky, R. Perez, R. Stewart, “Design and development of a rotating shadowband radiometer solar radiation/daylight network,” Sol. Energy 41, 577–581 (1988).
[CrossRef]

Other

H. R. Gordon, J. L. Mueller, R. C. Wrigley, “Atmospheric correction of Nimbus-7 Coastal Zone Color Scanner imagery,” in Remote Sensing of Atmospheres and Oceans, A. Deepak, ed. (Academic, New York, 1980) pp. 457–483.
[CrossRef]

K. L. Coulson, “The polarization of light in the environment,” in Planets, Stars, and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1974) pp. 444–471.

Y Liu, “Measurement of the intensity and polarization of light in the atmosphere,” Ph.D. dissertation (University of Miami, Miami, Fla., 1996).

H. E. Gerber, E. E. Hindman, eds., Light Absorption by Aerosol Particles (Spectrum, Hampton, Va., 1982).

Z. Sekera, “Recent developments in the study of the polarization of skylight,” in Advances in Geophysics (Academic, New York, 1956), Vol. 3, pp. 43–104.
[CrossRef]

K. Bullrich, “Scattered radiation in the atmosphere and the natural aerosol,” in Advances in Geophysics (Academic, New York, 1964) Vol. 10, pp. 99–260.
[CrossRef]

T. Takashima, H. S. Chen, C. R. N. Rao, “Polarimetric investigations of the turbidity of the atmosphere over Los Angeles,” in Planets, Stars, and Nebulae Studied with Photopolarimetry, T. Gehrels, ed. (U. Arizona Press, Tucson, Ariz., 1974) pp. 500–509.

K. N. Liou, An Introduction to Atmospheric Radiation (Academic, San Diego, Calif., 1980).

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, Hampton, Va., 1988).

S. Chandrasekhar, Radiative Transfer (Clarendon, Oxford, 1950).

K. L. Coulson, J. V. Dave, Z. Sekera, Tables Related to Radiation Emerging From a Planetary Atmosphere With Rayleigh Scattering (U. California Press, Berkeley, Calif., 1960).

J. W. Chamberlain, Theory of Planetary Atmospheres, Vol. 22 of International Geophysics Series (Academic, New York, 1978).

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Figures (12)

Fig. 1
Fig. 1

Normalized radiance on the principal plane with an azimuth angle of ϕ = 180° and a solar zenith angle of 53.1°. Radiance data are computed for a plane parallel Rayleigh atmospheric model with an underlying surface and then normalized to the solar constant; τ and R represent optical depth and surface albedo, respectively. Data are shown for two optical depths, 0.05 and 0.25. Data for the Lambertian surface are from Coulson et al.11

Fig. 2
Fig. 2

Degree of polarization at various optical depths, from Coulson et al.11 Data are computed in the same atmosphere as in Fig. 1; τ and R represent optical depth and surface albedo, respectively.

Fig. 3
Fig. 3

AOD, measured with a shadowband radiometer, as a function of time, on 5 February and 12 February 1996.

Fig. 4
Fig. 4

Measurement site at the Science and Administration Building, RSMAS, used on 5 February 1996.

Fig. 5
Fig. 5

Contour plots of skylight radiance [units 10−2 μW/(nm cm2 sr)]. The data shown were taken on top of the James L. Knight Physics Building at the University of Miami on 12 February 1996. The origin of the coordinate shown corresponds to the zenith, and the inner and outer circles to 30° and 60° zenith angles, respectively. The rectangular area blocked by Sun occulter on the solar half of the hemisphere is left blank (no data). The black dot is the sun’s position. (a) Measurement wavelength 439 nm, solar zenith angle 45.3°, AOD (410 nm) 0.17; (b) measurement wavelength 667 nm, solar zenith angle is 47.2°, AOD (410 nm) is 0.20; (c) measurement wavelength 439 nm, solar zenith angle 77°, AOD (410 nm) 0.14.

Fig. 6
Fig. 6

Contour plots of skylight radiance [units 10−2 μW/(nm cm2 sr)]. The data shown were taken on top of the Science and Administration building at RSMAS (Fig. 4) on 5 February 1996. The plots are prepared in the same way as in Fig. 5. (a) Measurement wavelength 439 nm, solar zenith angle 46.3°, AOD (410 nm) 0.35. Note that the radiance distribution is not symmetric to the principal plane owing to the inhomogenous underlying surface. The minimum region is shifted toward the direction over water. (b) Measurement wavelength 667 nm, solar zenith angle 44.7°, AOD (410 nm) 0.30.

Fig. 7
Fig. 7

Contour plots of the Stokes parameter Q. Data shown are normalized to radiance and then multiplied by 1000. The plots are prepared in the same way as in Fig. 5, and the measurement descriptions for (a), (b), and (c) correspond to Figs. 5(a), 5(b), and 5(c), respectively. Neutral lines (lines of Q = 0) are designated by the number zero. At lower solar elevation (c) contours are more jagged than those at higher solar elevation, (a) and (b); the same is true for U (Fig. 8) and P (Fig. 9). Note that Q is symmetric to the principal plane.

Fig. 8
Fig. 8

Contour plot of the Stokes parameter U. Data shown are normalized to radiance and then multiplied by 1000. The plots are prepared in the same way as in Fig. 5, and the measurement descriptions for (a), (b), and (c) correspond to Figs. 5(a), 5(b), and 5(c), respectively. Lines of U = 0 appears on the solar half of the atmosphere and on the principal plane. Note that U is antisymmetric to the principal plane.

Fig. 9
Fig. 9

Contour plots of the degree of polarization P. Data shown are amplified by a factor of 1000. The plots are prepared in the same way as in Fig. 5, and the measurement descriptions for (a), (b), and (c) correspond to Figs. 5(a), 5(b), and 5(c), respectively. The maximum degree of polarization appears at 90° scattering angles. Note that P is symmetric to the principal plane.

Fig. 10
Fig. 10

Observed angular distance of the Arago point from the antisolar point versus solar elevation; data obtained on 12 February 1996.

Fig. 11
Fig. 11

Contour plots of angle of the plane of polarization χ (degrees). Data shown are amplified by a factor of 100. The plots are prepared in the same way as in Fig. 5, and the measurement descriptions for (a), (b), and (c) correspond to Figs. 5(a), 5(b), and 5(c), respectively. These figures can be best understood by comparison with corresponding Q and U plots. Note that χ is antisymmetric to the principal plane.

Fig. 12
Fig. 12

Contour plots of the degree of polarization P. The data shown were taken on top of the Science and Administration building at RSMAS (Fig. 4) on 5 February 1996 and are amplified by a factor of 1000. The plots are prepared in the same way as in Fig. 6, and the measurement descriptions for (a) and (b) correspond to Figs. 6(a) and 6(b), respectively. Note that P is antisymmetric to the principal plane and that the maximum regions are shifted toward the direction over water.

Tables (6)

Tables Icon

Table 1 Minimum Q/I (×1000) on the Principal Plane as a Function of Solar Zenith Angle θ0 at 439 nm

Tables Icon

Table 2 Minimum Q/I (×1000) on the Principal Plane

Tables Icon

Table 3 Maximum U/I (×1000)

Tables Icon

Table 4 Maximum P (×1000) on the principal plane as a function of Solar-Zenith Angle θ0 at 560 nm

Tables Icon

Table 5 Maximum P (×1000) on the Principal Plane

Tables Icon

Table 6 Illustration of the Maximum Degree of Polarization (θ0 =45°)a

Equations (1)

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I = I l + I r , Q = I l - I r , U = I 45 - I 135 , V = I rc - I lc ,

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