Abstract

We have developed a Monte Carlo code that utilizes the complete Stokes vector to examine the structure of the degree of linear polarization in the complete observable solid angle at any level in an atmosphere–ocean system. By performing these calculations we are able to compute the positions of neutral points in the upwelling light above and beneath the ocean surface. The locations of these points in a single-scatter calculation and a Monte Carlo treatment are shown for various conditions. The presence of aerosols in the atmosphere and hydrosols in the ocean was found to have an effect on the location of these neutral points.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Chandrasekhar, D. D. Elbert, “The illumination and polarization of the sunlit sky on Rayleigh scattering,” Trans. Am. Philos. Soc. B 44, 643–728.
  2. R. S. Fraser, “Atmospheric neutral points over water,” J. Opt. Soc. Am. 58, 1029–1031 (1968).
    [CrossRef]
  3. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, Hampton, Va., 1988).
  4. C. Cox, W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).
  5. A Preliminary Cloudless Standard Atmosphere for Radiation Computation (International Association for Meteorology and Atmospheric Physics, Boulder, Colo., 1984).
  6. R. C. Smith, K. S. Baker, “Optical properties of the clearest natural waters (100–800 nm),” Appl. Opt. 20, 177–184 (1981).
    [CrossRef] [PubMed]
  7. R. H. Stavn, A. D. Weidemann, “Optical modeling of clear ocean light fields,” Appl. Opt. 27, 4002–4010 (1988).
    [CrossRef] [PubMed]
  8. N. P. Romanov, V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR) 38, 646–648 (1975).
  9. T. Takashima, K. Masuda, “Degree of radiance and polarization of the upwelling radiation from an atmosphere-ocean system,” Appl. Opt. 24, 2423–2429 (1985).
    [CrossRef] [PubMed]
  10. T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, San Diego, Calif., 1972).
  11. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  12. S. Chandrasekhar, Radiative Transfer (Dover, Toronto, Ontario, 1960).
  13. B. R. Marshall, Raman Scattering in Ocean Water (U. California Press, Santa Barbara, Calif., 1989).
  14. 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]
  15. 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. Ocean. 3, 353–372 (1973).
    [CrossRef]
  16. Concise Dictionary of Scientific Biography (Scribner, New York, 1981), p. 643. It is interesting to note that Willebrord Snel van Royen used only one l in his last name. In the English-speaking community, however, a convention of using two l’s has arisen, and it is difficult to find an English physics text that does not use this convention.
  17. T. H. Waterman, “Polarization of marine light fields and animal orientation,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 431–437 (1988).
    [CrossRef]

1989 (1)

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 (1)

1985 (1)

1981 (1)

1975 (1)

N. P. Romanov, V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR) 38, 646–648 (1975).

1973 (1)

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. Ocean. 3, 353–372 (1973).
[CrossRef]

1968 (1)

1954 (1)

C. Cox, W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Adams, C. N.

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]

Baker, K. S.

Chandrasekhar, S.

S. Chandrasekhar, D. D. Elbert, “The illumination and polarization of the sunlit sky on Rayleigh scattering,” Trans. Am. Philos. Soc. B 44, 643–728.

S. Chandrasekhar, Radiative Transfer (Dover, Toronto, Ontario, 1960).

Coulson, K. L.

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

Cox, C.

C. Cox, W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Elbert, D. D.

S. Chandrasekhar, D. D. Elbert, “The illumination and polarization of the sunlit sky on Rayleigh scattering,” Trans. Am. Philos. Soc. B 44, 643–728.

Fraser, R. S.

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. Ocean. 3, 353–372 (1973).
[CrossRef]

Kattawar, G. W.

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. Ocean. 3, 353–372 (1973).
[CrossRef]

Marshall, B. R.

B. R. Marshall, Raman Scattering in Ocean Water (U. California Press, Santa Barbara, Calif., 1989).

Masuda, K.

Munk, W.

C. Cox, W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, San Diego, Calif., 1972).

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. Ocean. 3, 353–372 (1973).
[CrossRef]

Romanov, N. P.

N. P. Romanov, V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR) 38, 646–648 (1975).

Shulkin, V. S.

N. P. Romanov, V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR) 38, 646–648 (1975).

Smith, R. C.

Stavn, R. H.

Takashima, T.

van de Hulst, H. C.

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

Waterman, T. H.

T. H. Waterman, “Polarization of marine light fields and animal orientation,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 431–437 (1988).
[CrossRef]

Weidemann, A. D.

Appl. Opt. (3)

J. Mar. Res. (1)

C. Cox, W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).

J. Opt. Soc. Am. (1)

J. Phys. Ocean. (1)

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. Ocean. 3, 353–372 (1973).
[CrossRef]

Limnol. Oceanogr. (1)

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]

Opt. Spectrosc. (USSR) (1)

N. P. Romanov, V. S. Shulkin, “Raman scattering cross section of liquid water,” Opt. Spectrosc. (USSR) 38, 646–648 (1975).

Trans. Am. Philos. Soc. B (1)

S. Chandrasekhar, D. D. Elbert, “The illumination and polarization of the sunlit sky on Rayleigh scattering,” Trans. Am. Philos. Soc. B 44, 643–728.

Other (8)

Concise Dictionary of Scientific Biography (Scribner, New York, 1981), p. 643. It is interesting to note that Willebrord Snel van Royen used only one l in his last name. In the English-speaking community, however, a convention of using two l’s has arisen, and it is difficult to find an English physics text that does not use this convention.

T. H. Waterman, “Polarization of marine light fields and animal orientation,” in Ocean Optics IX, M. A. Blizard, ed., Proc. SPIE925, 431–437 (1988).
[CrossRef]

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

A Preliminary Cloudless Standard Atmosphere for Radiation Computation (International Association for Meteorology and Atmospheric Physics, Boulder, Colo., 1984).

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, San Diego, Calif., 1972).

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

S. Chandrasekhar, Radiative Transfer (Dover, Toronto, Ontario, 1960).

B. R. Marshall, Raman Scattering in Ocean Water (U. California Press, Santa Barbara, Calif., 1989).

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 (16)

Fig. 1
Fig. 1

Geometry of a scattering event for a photon scattered through an angle Θ; k i is the initial photon direction, k f is the scattered direction of the photon, and Φ and Ψ are rotation angles for the Stokes vector.

Fig. 2
Fig. 2

Contribution to the observed Stokes vector from light scattered between τ and τ + dτ. The top of the atmosphere is denoted by τ′.

Fig. 3
Fig. 3

Data format for the gray-scale images of the polarization. The center of the image is the nadir and represents the polarization seen for an observer looking straight down. The outer edge is the horizon; the principal plane is defined by the incident sunlight direction and the nadir.

Fig. 4
Fig. 4

Degree of linear polarization in the upwelling light for an observer directly above the ocean surface in a single-scatter calculation. Here θsol = 60° and τ for the atmosphere was 0.155. The shading for the gray scaling was log scaled and is given by the scale bar at right.

Fig. 5
Fig. 5

Different possible contributions to the observed light field in the single-scatter calculation for an observer placed above the ocean surface. The surface of the ocean is labeled τ = τ1.

Fig. 6
Fig. 6

Degree of linear polarization in the upwelling light for an observer placed directly above the ocean surface. Results are (a) in the Fresnel model and (b) when light transmitted from beneath the surface is included. Values of the azimuth and nadir angles denoted by the lines and circles are given in Fig. 3.

Fig. 7
Fig. 7

Degree of linear polarization for an observer placed directly beneath the ocean surface in the single-scatter model. Two neutral points are formed in the principal plane at 21° and 60° from the nadir.

Fig. 8
Fig. 8

Nadir angles of the neutral points formed in the upwelling light for an observer placed beneath the ocean surface in the single-scattering case. The solid curve represents the direction opposite that of the refracted sunlight. Note the formation of two neutral points in the principal plane for every solar angle.

Fig. 9
Fig. 9

Incident and refracted solar beam directions, along with the line of sight to each of the two neutral points formed in the upwelling light for an observer placed directly beneath the ocean surface.

Fig. 10
Fig. 10

Positions of neutral points for an observer placed directly above the surface in the single-scatter model for different wavelengths. Circles and diamonds represent the positions in a single-scatter calculation and in a Monte Carlo simulation, respectively. The pairs are labeled according to increasing wavelength: 1, 2, 3, 4, and 5 are 400, 500, 550, 600, and 700 nm, respectively.

Fig. 11
Fig. 11

Positions of the neutral points in the upwelling light field for five solar zenith angles: 1, 10°; 2, 30°; 3, 50°; 4, 70°; 5, 90°. Circles, diamonds, and boxes indicate Rayleigh scattering in all regions, the addition of aerosol layers in the atmosphere, and the addition of a hydrosol layer in the ocean, respectively. Note that the outer edge of the graph represents a nadir angle of 60° because all neutral points displayed have nadir angles <60°.

Fig. 12
Fig. 12

Degree of linear polarization in the upwelling light for θsol = 60° in a Monte Carlo simulation, for an observer placed (a) directly beneath and (b) directly above the ocean surface. The wavelength in both cases was 518 nm.

Fig. 13
Fig. 13

Positions of the neutral points in the upwelling light field for a range of solar zenith angles when Raman scattering is first neglected and then included in the ocean. Only half of the observed solid angle is shown because the formation of the neutral points is symmetric about the principal plane. Circles indicate elastic fluctuation scattering only; diamonds show the addition of Raman scattering in the ocean. Solar zenith angles by group are 1, 20°; 2, 40°; 3, 60°; 4, 80°; 5, 90°.

Fig. 14
Fig. 14

Positions of the neutral points for an observer above the surface for three atmospheric and oceanic models. The solar zenith angles by group are 1, 30°; 2, 50°; 3, 70°; 4, 90°. Symbol definitions are the same as in Fig. 11.

Fig. 15
Fig. 15

Positions of the neutral points in the principal plane in the upwelling light for an observer beneath the surface in a Monte Carlo calculation for a range of solar zenith angles. For solar zenith angles <15° the positions of the neutral points were indeterminate; at solar zenith angles >75° the neutral points formed outside the principal plane.

Fig. 16
Fig. 16

Locations of neutral points in the upwelling light for an observer placed directly above the surface at different wind speeds. Scattering in the atmosphere and ocean is treated as Rayleigh scattering. Points are labeled according to increasing wind speed: 1, 0 kn; 2, 5 kn; 3, 10 kn; 4, 20 kn. As the wind speed increases the trend is to smaller nadir and higher azimuthal angles.

Tables (2)

Tables Icon

Table 1 Aerosol Parameters for the MAR-I Modela

Tables Icon

Table 2 Optical Parameters of the Ocean Used in the Calculationsa

Equations (10)

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

dNirdlog r=Nilog σi*2π exp-log r-log ri22log σi*2,
dNrdr=kr-4,  0.1 μmr22 μm,  dNrdr=0,  r > 22 μm; r<0.1 μm.
I¯=IQUV.
P=Q2+U2I.
If=Rπ-ΨLΘR-ΦIi,
RΨ=10000cos2Ψsin2Ψ00-sin2Ψcos2Ψ00001.
LΘ=121+μ2μ2-100μ2-11+μ200002μ00002μ,
m=11-ρμ2-11+μ2+3-μ2ρ001-ρμ2-11+μ2+3-μ2ρ1-ρμ2+11+μ2+3-μ2ρ00002-2ρμ1+μ2+3-μ2ρ00002-6ρμ1+μ2+3-μ2ρ,
dI=exp-τ-τ/μ-τ/μo×Rπ-ΨLΘR-ΦI0dτμ.
θnp=2θref-θsol,

Metrics