Abstract

Neutral points are specific directions in the light field where the three Stokes parameters Q, U, V, and thus the degree of polarization simultaneously go to zero. We have made the first measurement of non-principal-plane neutral points in the upwelling light field in natural waters. These neutral points are located at approximately 40°- 80° nadir angle and between 120° - 160° azimuth to the sun which is well off of the principal plane. Calculations show that the neutral point positions are very sensitive to the balance in the incident light between the partially polarized skylight and the direct solar beam.

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  9. Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. On Geoscience Remote Sens. 3611), 51–60 (1998).
    [CrossRef]
  10. C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, New York, NY, 1983).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. S. Pegau, J. R. V. Zaneveld, B. G. Mitchell, J. L. Mueller, M. Kahru, J. Wieland, and M. Stramska, “Ocean Optics Protocols For Satellite Ocean Color Sensor Validation, Revision 4, Volume IV: Inherent Optical Properties: Instruments, Characterizations, Field Measurements, and Data Analysis Protocols,” NASA/TM-2003–21621/Rev4-Vol IV (Goddard Space Flight Center, Greenbelt, MD, 2002).
  18. A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30(30), 4427–4438 (1991).
    [CrossRef] [PubMed]
  19. K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl. Opt. 23(23), 4427–4439 (1984).
    [CrossRef] [PubMed]
  20. T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (University of California, San Diego, Scripps Institution of Oceanography Visibility Laboratory, 1972).
  21. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]
  22. J. T. Adams, E. Aas, N. K. Hjøerslev, and B. Lundgren, “Comparison of radiance and polarization values observed in the Mediterranean Sea and simulated in a Monte Carlo model,” Appl. Opt. 41(15), 2724–2733 (2002).
    [CrossRef] [PubMed]
  23. J. Lenoble and C. Broquez, “A comparitive review of radiation aerosol models,” Contrib. Atmos. Phys. 57, 1–20 (1984).
  24. C. Cox and W. Munk, “Statistics of the sea surface derived from sun glitter,” J. Mar. Res. 13, 198–227 (1954).
  25. J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
    [CrossRef] [PubMed]
  26. J. T. Adams and D. J. Gray, “Neutral points in an atmosphere-ocean system. 2: Downwelling light field,” Appl. Opt. 50(3), 335–346 (2011).
    [CrossRef] [PubMed]

2011 (1)

2010 (1)

2008 (1)

2006 (1)

2005 (1)

2002 (2)

1998 (1)

Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. On Geoscience Remote Sens. 3611), 51–60 (1998).
[CrossRef]

1997 (1)

1992 (1)

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37(3), 491–500 (1992).
[CrossRef]

1991 (1)

1990 (1)

1984 (2)

K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl. Opt. 23(23), 4427–4439 (1984).
[CrossRef] [PubMed]

J. Lenoble and C. Broquez, “A comparitive review of radiation aerosol models,” Contrib. Atmos. Phys. 57, 1–20 (1984).

1968 (1)

1958 (1)

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

1954 (1)

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

1941 (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

1888 (1)

M. J. L. Soret, “Influence des surfaces d’eau sur la polarisation atmospherique et observation de deux points neutres a droite et a gauche de Soleil,” Compt. Rend. 107, 867–870 (1888).

1884 (1)

M. A. Cornu, “Observations relatives a la couronne visible actuellement autour du Soleil,” Compt. Rend. 99, 488–493 (1884).

1847 (1)

D. Brewster, “On the polarisation of the atmosphere,” Phil. Mag. J. Sci. 31, 444–454 (1847).

1840 (1)

J. Babinet, “Sur un nouveau point neutre dans l’atmosphere,” CR (East Lansing, Mich.) 11, 618–620 (1840).

Aas, E.

Adams, J. T.

Babinet, J.

J. Babinet, “Sur un nouveau point neutre dans l’atmosphere,” CR (East Lansing, Mich.) 11, 618–620 (1840).

Barta, A.

Bernath, B.

Brewster, D.

D. Brewster, “On the polarisation of the atmosphere,” Phil. Mag. J. Sci. 31, 444–454 (1847).

Broquez, C.

J. Lenoble and C. Broquez, “A comparitive review of radiation aerosol models,” Contrib. Atmos. Phys. 57, 1–20 (1984).

Cairns, B.

Chapin, A. L.

Chowdhary, J.

Cornu, M. A.

M. A. Cornu, “Observations relatives a la couronne visible actuellement autour du Soleil,” Compt. Rend. 99, 488–493 (1884).

Cox, C.

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

Ding, K.

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37(3), 491–500 (1992).
[CrossRef]

Fraser, R. S.

Fry, E. S.

Gentili, B.

Gordon, H. R.

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37(3), 491–500 (1992).
[CrossRef]

Gray, D. J.

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hjøerslev, N. K.

Horvath, G.

Ivanoff, A.

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

Kattawar, G. W.

Kawata, Y.

Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. On Geoscience Remote Sens. 3611), 51–60 (1998).
[CrossRef]

Lenoble, J.

J. Lenoble and C. Broquez, “A comparitive review of radiation aerosol models,” Contrib. Atmos. Phys. 57, 1–20 (1984).

Lundgren, B.

Morel, A.

Munk, W.

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

Soret, M. J. L.

M. J. L. Soret, “Influence des surfaces d’eau sur la polarisation atmospherique et observation de deux points neutres a droite et a gauche de Soleil,” Compt. Rend. 107, 867–870 (1888).

Souaidia, N.

Suhai, B.

Teillet, P. M.

Travis, L. D.

Voss, K. J.

Waterman, T. H.

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

Wehner, R.

Yamazaki, A.

Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. On Geoscience Remote Sens. 3611), 51–60 (1998).
[CrossRef]

Yang, P.

Zhai, P.-W.

Appl. Opt. (8)

K. J. Voss and E. S. Fry, “Measurement of the Mueller matrix for ocean water,” Appl. Opt. 23(23), 4427–4439 (1984).
[CrossRef] [PubMed]

P. M. Teillet, “Rayleigh optical depth comparisons from various sources,” Appl. Opt. 29(13), 1897–1900 (1990).
[CrossRef] [PubMed]

J. T. Adams and G. W. Kattawar, “Neutral points in an atmosphere-ocean system. 1: upwelling light field,” Appl. Opt. 36(9), 1976–1986 (1997).
[CrossRef] [PubMed]

A. Morel and B. Gentili, “Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution,” Appl. Opt. 30(30), 4427–4438 (1991).
[CrossRef] [PubMed]

J. T. Adams, E. Aas, N. K. Hjøerslev, and B. Lundgren, “Comparison of radiance and polarization values observed in the Mediterranean Sea and simulated in a Monte Carlo model,” Appl. Opt. 41(15), 2724–2733 (2002).
[CrossRef] [PubMed]

J. Chowdhary, B. Cairns, and L. D. Travis, “Contribution of water-leaving radiances to multiangle, multispectral polarimetric observations over the open ocean: bio-optical model results for case 1 waters,” Appl. Opt. 45(22), 5542–5567 (2006).
[CrossRef] [PubMed]

P.-W. Zhai, G. W. Kattawar, and P. Yang, “Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. I. Monte Carlo method,” Appl. Opt. 47(8), 1037–1047 (2008).
[CrossRef] [PubMed]

J. T. Adams and D. J. Gray, “Neutral points in an atmosphere-ocean system. 2: Downwelling light field,” Appl. Opt. 50(3), 335–346 (2011).
[CrossRef] [PubMed]

Astrophys. J. (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Compt. Rend. (2)

M. A. Cornu, “Observations relatives a la couronne visible actuellement autour du Soleil,” Compt. Rend. 99, 488–493 (1884).

M. J. L. Soret, “Influence des surfaces d’eau sur la polarisation atmospherique et observation de deux points neutres a droite et a gauche de Soleil,” Compt. Rend. 107, 867–870 (1888).

Contrib. Atmos. Phys. (1)

J. Lenoble and C. Broquez, “A comparitive review of radiation aerosol models,” Contrib. Atmos. Phys. 57, 1–20 (1984).

CR (East Lansing, Mich.) (1)

J. Babinet, “Sur un nouveau point neutre dans l’atmosphere,” CR (East Lansing, Mich.) 11, 618–620 (1840).

IEEE Trans. On Geoscience Remote Sens. (1)

Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. On Geoscience Remote Sens. 3611), 51–60 (1998).
[CrossRef]

J. Mar. Res. (2)

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

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

J. Opt. Soc. Am. (1)

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

Limnol. Oceanogr. (1)

H. R. Gordon and K. Ding, “Self-shading of in-water optical instruments,” Limnol. Oceanogr. 37(3), 491–500 (1992).
[CrossRef]

Opt. Express (2)

Phil. Mag. J. Sci. (1)

D. Brewster, “On the polarisation of the atmosphere,” Phil. Mag. J. Sci. 31, 444–454 (1847).

Other (4)

K. L. Coulson, Polarization and intensity of light in the Atmosphere (A. Deepak Publishing, 1988).

S. Pegau, J. R. V. Zaneveld, B. G. Mitchell, J. L. Mueller, M. Kahru, J. Wieland, and M. Stramska, “Ocean Optics Protocols For Satellite Ocean Color Sensor Validation, Revision 4, Volume IV: Inherent Optical Properties: Instruments, Characterizations, Field Measurements, and Data Analysis Protocols,” NASA/TM-2003–21621/Rev4-Vol IV (Goddard Space Flight Center, Greenbelt, MD, 2002).

T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (University of California, San Diego, Scripps Institution of Oceanography Visibility Laboratory, 1972).

C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley and Sons, New York, NY, 1983).

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Figures (8)

Fig. 1
Fig. 1

Upwelling radiance (left) and Q/I and U/I for this image. The radiance units are μW cm−2 nm−1 sr−1, Q/I and U/I are dimensionless. This was collected off of Hawaii (December 12, 2005, 20.83° N, 157.18° W, 10:25 local time). The wavelength was 436 nm and the solar zenith angle was 51°.

Fig. 2
Fig. 2

Averaged data corresponding to data shown in Fig. 1. On the left, normalized stokes parameters Q/I and U/I. On the right is the standard deviation (SD) of the data points that constructed the mean images on the left. The SD is predominately less than 0.05 for most of the images. Also shown on these images, and the following images, are white lines depicting 30° and 60° nadir angles, and radial lines at azimuthal angles of 45°, 90°, 135°. The white circle on each is located at the refracted anti-solar position for reference. In the Q/I and U/I images, black lines are at Q/I=0 and U/I=0.

Fig. 3
Fig. 3

Degree of polarization (DOP) and plane of polarization (χ) for image shown in Fig. 1. Color scales are shown for each image, DOP runs from 0 to 100%, while χ runs from −90° to 90°.

Fig. 4
Fig. 4

Percent DOP illustrating large area of low polarization at 526 nm.

Fig. 5
Fig. 5

Measured positions of neutral points. A, B correspond to 412 nm; C, D correspond to 442 nm; E, F correspond to 482 nm: G, H correspond to 526 nm. A, C, E, and G plot the nadir angle (0 is straight down). B, D, F, and H plot the azimuth angle (0 is in the anti-solar direction, so 45° corresponds to an azimuth of 135° with respect to the solar position. Lines in figures A, C, E, and G show the refracted solar position.

Fig. 6
Fig. 6

Maximum DOP in images as a function of solar zenith angle A: 412 nm, B: 442 nm, C: 486 nm, and D: 526 nm. The maximum DOP can be seen to increase with increasing wavelength and decrease with increasing solar zenith angle.

Fig. 7
Fig. 7

Q/I and U/I shown for the case of single scattering, Rayleigh ocean, illuminated by a direct, unpolarized, solar beam. Also shown are black lines representing the Q=0 and U=0 contour lines for these images. This case is for a solar zenith angle of 50°.

Fig. 8
Fig. 8

Patterns of the Q/I (a-c), and U/I (d-f) parameters in the in-water upwelling radiance field. The system parameters are as described in Section 3.2. To take into account the aerosol, an aerosol layer of optical thickness 0.1 based on a maritime aerosol model [23] was included. Panel (a): contribution to the total Q/I field due to the direct sunlight (attenuated in the atmosphere); panel (b): contribution to the total Q/I field due to the diffuse skylight scattered in the atmosphere; and panel (c): the total Q/I field. The black lines are the contour lines of zero, i.e., the Q neutral lines. Panels d-f are similar to a-c, but for U.

Equations (8)

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E = E 0 exp [ i ( ω t + δ ) ]
E r = E r 0 exp [ i ( ω t + δ r ) ]
I E E * + E r E r * = E 0 2 + E r 0 2
Q E E * E r E r * = E 0 2 E r 0 2
U E E r * + E r E * = 2 E 0 E r 0 cos δ
V i ( E E r * E r E * ) = 2 E 0 E r 0 sin δ
D O P = Q 2 + U 2 I 2
tan 2 χ = U Q

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