Abstract

The radiative transfer of sunlight through the deep oceans of the world is a complex and only partially solved environmental optical problem. Empirically, in situ systematic measurements of key parameters such as polarization of deep open seawater have been very sparse in recent decades. Although we have the necessary equation of transfer to solve this complex problem, until it can be solved explicitly, only approximations and partial analytic solutions are possible in addition to some successful computer modeling. Further complexity is added by the diversity of researchers’ interests from academic to international policy making, as well as the ineffective communication between the different disciplines concerned, ranging from mathematics to endangered species. As a result, isolated focused pockets of good data and theory have been developed in recent decades without the needed breadth of understanding. This present review intends to bring together some visual biology and optical physics in order to understand the role of polarization in navigation, communication, and identification of marine animals as well as a possible tool for remotely sensing underwater objects.

© 2013 Optical Society of America

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    [CrossRef]

2012

S. Milius, “Mantis shrimp flub color vision test,” Sci. News 182(6), 11 (2012).

R. D. M. Garcia, “Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium,” J. Quant. Spectrosc. Radiat. Transfer 113, 306–317 (2012).
[CrossRef]

P.-W. Zhai, G. W. Kattawar, and Y. Hu, “Comment on the transmission matrix for a dielectric interface,” J. Quant. Spectrosc. Radiat. Transfer 113, 1981–1984 (2012).
[CrossRef]

J. T. Adams, D. J. Gray, and S. Rayner, “Observation of non-principal plane neutral points in the upwelling polarized light field above a water surface,” Appl. Opt. 51, 5387–5391 (2012).
[CrossRef]

2011

2009

2008

2007

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
[CrossRef]

2006

L. M. Mäthger and R. T. Hanlon, “Anatomical basis for camouflaged polarized light communication in squid,” Biol. Lett 2, 494–496 (2006).
[CrossRef]

2002

I. Flamarique and F. Hárosi, “Visual pigments and dichroism of anchovy cones: a model system for polarization detection,” Vis. Neurosci. 19, 467–473 (2002).
[CrossRef]

N. Shashar, C. Milbury, and R. Hanlon, “Polarization vision in cephalopods: neuroanatomical and behavioral features that illustrate aspects of form and function,” Mar. Freshwater Behav. Physiol. 35, 57–68 (2002).
[CrossRef]

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, 2724–2733 (2002).
[CrossRef]

G. Horvath, B. Bernath, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A 19, 2085–2099(2002).
[CrossRef]

2000

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity on silvery fish,” Vis. Res. 40, 71–75 (2000).
[CrossRef]

1998

J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer, “Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean,” Limnol. Oceanogr. 43, 564–576 (1998).
[CrossRef]

Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. Geosci. Remote Sens. 36, 51–60 (1998).
[CrossRef]

J. S. Bartlett, K. J. Voss, S. Sathyendranath, and A. Vodacek, “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324–3332 (1998).
[CrossRef]

1997

1996

H. R. Gordon and X. Xu, “Marine asymptotic daylight field: effects of inelastic processes,” Appl. Opt. 35, 4194–4205 (1996).
[CrossRef]

N. Shashar, P. Rutledge, and T. Cronin, “Polarization vision in cuttlefish—a concealed communciation channel?” J. Exp. Biol. 199, 2077–2084 (1996).

E. P. Zege and L. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transfer 55, 19–31 (1996).
[CrossRef]

1993

1992

1990

1989

G. W. Kattawar and 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

D. A. Leonard and H. E. Sweeney, “Remote sensing of ocean physical properties: a comparison of Raman and Brillouin techniques,” Proc. SPIE 925, 407–414 (1988).
[CrossRef]

R. H. Stavn and A. D. Weidemann, “Optical modeling of clear ocean light fields: Raman scattering effects,” Appl. Opt. 27, 4002–4011 (1988).
[CrossRef]

1984

D. Collins, J. A. Bell, R. Zanoni, I. S. McDermid, B. Breckinridge, and C. A. Sepulveda, “Recent progress in the measurement of temperature and salinity by optical scattering,” Proc. SPIE 489, 247–269 (1984).
[CrossRef]

S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
[CrossRef]

1983

1981

1977

P. A. K. I. I. Kondilenko, V. A. Klimenko, and O. P. Demyanenko, “Transverse cross section of the Raman scattering of the ν1 vibration of the water molecule in the liquid and gaseous states,” Opt. Spectrosc. 43, 384–386 (1977).

G. D. Bernard and R. Wehner, “Functional similarities between polarization vision and color vision,” Vis. Res. 17, 1019–1028 (1977).
[CrossRef]

1976

1975

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

R. B. Slusher and V. E. Derr, “Temperature dependence and cross sections of some Stokes and anti-Stokes Raman lines in ice lh,” Appl. Opt. 14, 2116–2120 (1975).
[CrossRef]

1971

L. Prieur and A. Morel, “Etude theorique du regime asymptotique: relations entre characteristiques optiques et coefficient d’extinction relatif a la penetration de la lumiere du jour,” Cah. Oceanogr. 23, 35–48 (1971).

1968

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

1967

G. E. Walrafen, “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114–126 (1967).
[CrossRef]

1961

A. Ivanoff, N. Jerlov, and T. H. Waterman, “A comparative study of irradiance, beam transmittance and scattering in the sea near Bermuda,” Limnol. Oceanogr. 6, 129–148 (1961).
[CrossRef]

1959

R. W. Preisendorfer, “On the existence of characteristic diffuse light in natural waters sea,” J. Mar. Res. 18, 1–9 (1959).

1958

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 283–307 (1958).

1956

T. H. Waterman and W. E. Westell, “Quantitative effects of the sun’s position on submarine light polarization,” J. Mar. Res. 15, 149–169 (1956).

1954

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
[CrossRef]

1945

H. H. Poole, “The angular distribution of submarine daylight in deep water,” Sci. Proc. R. Dublin Soc. 24, 29–42 (1945).

1928

C. V. Raman, “A new radiation,” Indian J. Phys. 2, 387–398 (1928).

1888

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

1884

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

1847

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

1840

J. Babinet, “Sur un nouveau point neutre dans l’atmosphere,” C. R. Acad. Sci. Paris 11, 618–620 (1840).

Aas, E.

Adams, C. N.

G. W. Kattawar and 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]

Adams, J. T.

Ahmed, S. A.

Babinet, J.

J. Babinet, “Sur un nouveau point neutre dans l’atmosphere,” C. R. Acad. Sci. Paris 11, 618–620 (1840).

Barral, J. A.

J. A. Barral, Oeuvres de Francois Arago I–V (Gide/Weigel, 1858).

Barta, A.

Bartlett, J. S.

Bell, J. A.

D. Collins, J. A. Bell, R. Zanoni, I. S. McDermid, B. Breckinridge, and C. A. Sepulveda, “Recent progress in the measurement of temperature and salinity by optical scattering,” Proc. SPIE 489, 247–269 (1984).
[CrossRef]

Bernard, G. D.

G. D. Bernard and R. Wehner, “Functional similarities between polarization vision and color vision,” Vis. Res. 17, 1019–1028 (1977).
[CrossRef]

Bernath, B.

Berwald, J.

J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer, “Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean,” Limnol. Oceanogr. 43, 564–576 (1998).
[CrossRef]

Boal, J. G.

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity on silvery fish,” Vis. Res. 40, 71–75 (2000).
[CrossRef]

Brady, P.

Breckinridge, B.

D. Collins, J. A. Bell, R. Zanoni, I. S. McDermid, B. Breckinridge, and C. A. Sepulveda, “Recent progress in the measurement of temperature and salinity by optical scattering,” Proc. SPIE 489, 247–269 (1984).
[CrossRef]

Brewster, D.

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

Bristow, M.

Bundy, D.

Calwell, R.

T. Chiou, S. Kleinlogel, T. Cronin, R. Calwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[CrossRef]

Chaikovskaya, L.

E. P. Zege and L. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transfer 55, 19–31 (1996).
[CrossRef]

Chami, M.

M. Chami, “Importance of the polarization in the retrieval of oceanic constituents from the remote sensing reflectance,” J. Geophys. Res. 112, C05026 (2007).
[CrossRef]

Chang, C. H.

C. H. Chang and L. A. Young, “Seawater temperature measurements from Raman spectra,” Res. Note 920, N62269-72-C-0204, ARPA Order No. 1911 (1972).

Chiao, C. C.

N. Shashar, S. Johnsen, A. Lerner, S. Sabbah, C. C. Chiao, L. M. Mäthger, and R. T. Hanlon, “Underwater linear polarization: physical limitations to biological functions,” Phil. Trans. R. Soc. B 366, 649–654 (2011).
[CrossRef]

Chiou, T.

T. Chiou, S. Kleinlogel, T. Cronin, R. Calwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[CrossRef]

Collins, D.

D. Collins, J. A. Bell, R. Zanoni, I. S. McDermid, B. Breckinridge, and C. A. Sepulveda, “Recent progress in the measurement of temperature and salinity by optical scattering,” Proc. SPIE 489, 247–269 (1984).
[CrossRef]

Copeland, R. A.

Cornu, M. A.

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

Cronin, T.

T. Chiou, S. Kleinlogel, T. Cronin, R. Calwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[CrossRef]

N. Shashar, P. Rutledge, and T. Cronin, “Polarization vision in cuttlefish—a concealed communciation channel?” J. Exp. Biol. 199, 2077–2084 (1996).

Cummings, M.

Demyanenko, O. P.

P. A. K. I. I. Kondilenko, V. A. Klimenko, and O. P. Demyanenko, “Transverse cross section of the Raman scattering of the ν1 vibration of the water molecule in the liquid and gaseous states,” Opt. Spectrosc. 43, 384–386 (1977).

Derr, V. E.

Dickey, T. D.

T. D. Dickey, G. W. Kattawar, and K. J. Voss, “Shedding new light on light in the ocean,” Phys. Today 64(4), 44–49 (2011).
[CrossRef]

Dierssen, H. M.

Ding, K.

Faris, G. W.

Flamarique, I.

I. Flamarique and F. Hárosi, “Visual pigments and dichroism of anchovy cones: a model system for polarization detection,” Vis. Neurosci. 19, 467–473 (2002).
[CrossRef]

Fraser, R. S.

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

Furtek, R.

Garcia, R. D. M.

R. D. M. Garcia, “Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium,” J. Quant. Spectrosc. Radiat. Transfer 113, 306–317 (2012).
[CrossRef]

Gilerson, A. A.

Gleason, A. C. R.

Goldizen, A.

T. Chiou, S. Kleinlogel, T. Cronin, R. Calwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
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Gordon, H. R.

Gray, D. J.

Hagan, R.

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity on silvery fish,” Vis. Res. 40, 71–75 (2000).
[CrossRef]

Hanlon, R.

N. Shashar, C. Milbury, and R. Hanlon, “Polarization vision in cephalopods: neuroanatomical and behavioral features that illustrate aspects of form and function,” Mar. Freshwater Behav. Physiol. 35, 57–68 (2002).
[CrossRef]

Hanlon, R. T.

N. Shashar, S. Johnsen, A. Lerner, S. Sabbah, C. C. Chiao, L. M. Mäthger, and R. T. Hanlon, “Underwater linear polarization: physical limitations to biological functions,” Phil. Trans. R. Soc. B 366, 649–654 (2011).
[CrossRef]

L. M. Mäthger and R. T. Hanlon, “Anatomical basis for camouflaged polarized light communication in squid,” Biol. Lett 2, 494–496 (2006).
[CrossRef]

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity on silvery fish,” Vis. Res. 40, 71–75 (2000).
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I. Flamarique and F. Hárosi, “Visual pigments and dichroism of anchovy cones: a model system for polarization detection,” Vis. Neurosci. 19, 467–473 (2002).
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Hoge, F. E.

Horvath, G.

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[CrossRef]

Hunt, A. J.

D. B. Shapiro, A. J. Hunt, and M. S. Quinby-Hunt, “Circular polarization effects in the light scattering from single and suspensions of dinoflagellates,” in Underwater Imaging, Photography and Visibility (SPIE, 1991).

Ivanoff, A.

A. Ivanoff, N. Jerlov, and T. H. Waterman, “A comparative study of irradiance, beam transmittance and scattering in the sea near Bermuda,” Limnol. Oceanogr. 6, 129–148 (1961).
[CrossRef]

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 283–307 (1958).

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A. Ivanoff, N. Jerlov, and T. H. Waterman, “A comparative study of irradiance, beam transmittance and scattering in the sea near Bermuda,” Limnol. Oceanogr. 6, 129–148 (1961).
[CrossRef]

Johnsen, S.

N. Shashar, S. Johnsen, A. Lerner, S. Sabbah, C. C. Chiao, L. M. Mäthger, and R. T. Hanlon, “Underwater linear polarization: physical limitations to biological functions,” Phil. Trans. R. Soc. B 366, 649–654 (2011).
[CrossRef]

Kattawar, G. W.

P.-W. Zhai, G. W. Kattawar, and Y. Hu, “Comment on the transmission matrix for a dielectric interface,” J. Quant. Spectrosc. Radiat. Transfer 113, 1981–1984 (2012).
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T. D. Dickey, G. W. Kattawar, and K. J. Voss, “Shedding new light on light in the ocean,” Phys. Today 64(4), 44–49 (2011).
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K. J. Voss, A. C. R. Gleason, H. R. Gordon, G. W. Kattawar, and Y. You, “Observation of non-principal plane neutral points in the in-water upwelling polarized light field,” Opt. Express 19, 5942–5952 (2011).
[CrossRef]

Y. You, A. Tonizzo, A. A. Gilerson, M. Cummings, P. Brady, J. Sullivan, M. S. Twardowski, H. M. Dierssen, S. A. Ahmed, and G. W. Kattawar, “Measurements and simulations of polarization states of underwater light in clear oceanic waters,” Appl. Opt. 50, 4873–4893 (2011).
[CrossRef]

Y. You, P. W. Zhai, G. W. Kattawar, and P. Yang, “Polarized radiance fields under a dynamic ocean surface: a three-dimensional radiative transfer solution,” Appl. Opt. 48, 3019–3029 (2009).
[CrossRef]

P. W. Zhai, G. W. Kattawar, and P. Yang, “Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. II. The hybrid matrix operator–Monte Carlo method,” Appl. Opt. 47, 1063–1071 (2008).
[CrossRef]

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, 1037–1047 (2008).
[CrossRef]

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

G. W. Kattawar and X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31, 6491–6500 (1992).
[CrossRef]

G. W. Kattawar and 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 and G. N. Plass, “Asymptotic radiance and polarization in optically thick media: ocean and clouds,” Appl. Opt. 15, 3166–3178 (1976).
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Y. Kawata and A. Yamazaki, “Multiple scattering analysis of airborne POLDER image data over the sea,” IEEE Trans. Geosci. Remote Sens. 36, 51–60 (1998).
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J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer, “Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean,” Limnol. Oceanogr. 43, 564–576 (1998).
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T. Chiou, S. Kleinlogel, T. Cronin, R. Calwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
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N. Shashar, S. Johnsen, A. Lerner, S. Sabbah, C. C. Chiao, L. M. Mäthger, and R. T. Hanlon, “Underwater linear polarization: physical limitations to biological functions,” Phil. Trans. R. Soc. B 366, 649–654 (2011).
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T. Chiou, S. Kleinlogel, T. Cronin, R. Calwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
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Marshall, B. R.

Marshall, J.

T. Chiou, S. Kleinlogel, T. Cronin, R. Calwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[CrossRef]

Mäthger, L. M.

N. Shashar, S. Johnsen, A. Lerner, S. Sabbah, C. C. Chiao, L. M. Mäthger, and R. T. Hanlon, “Underwater linear polarization: physical limitations to biological functions,” Phil. Trans. R. Soc. B 366, 649–654 (2011).
[CrossRef]

L. M. Mäthger and R. T. Hanlon, “Anatomical basis for camouflaged polarized light communication in squid,” Biol. Lett 2, 494–496 (2006).
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D. Collins, J. A. Bell, R. Zanoni, I. S. McDermid, B. Breckinridge, and C. A. Sepulveda, “Recent progress in the measurement of temperature and salinity by optical scattering,” Proc. SPIE 489, 247–269 (1984).
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N. Shashar, C. Milbury, and R. Hanlon, “Polarization vision in cephalopods: neuroanatomical and behavioral features that illustrate aspects of form and function,” Mar. Freshwater Behav. Physiol. 35, 57–68 (2002).
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N. Shashar, P. Rutledge, and T. Cronin, “Polarization vision in cuttlefish—a concealed communciation channel?” J. Exp. Biol. 199, 2077–2084 (1996).

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N. Shashar, S. Johnsen, A. Lerner, S. Sabbah, C. C. Chiao, L. M. Mäthger, and R. T. Hanlon, “Underwater linear polarization: physical limitations to biological functions,” Phil. Trans. R. Soc. B 366, 649–654 (2011).
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Sepulveda, C. A.

D. Collins, J. A. Bell, R. Zanoni, I. S. McDermid, B. Breckinridge, and C. A. Sepulveda, “Recent progress in the measurement of temperature and salinity by optical scattering,” Proc. SPIE 489, 247–269 (1984).
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D. B. Shapiro, A. J. Hunt, and M. S. Quinby-Hunt, “Circular polarization effects in the light scattering from single and suspensions of dinoflagellates,” in Underwater Imaging, Photography and Visibility (SPIE, 1991).

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N. Shashar, S. Johnsen, A. Lerner, S. Sabbah, C. C. Chiao, L. M. Mäthger, and R. T. Hanlon, “Underwater linear polarization: physical limitations to biological functions,” Phil. Trans. R. Soc. B 366, 649–654 (2011).
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N. Shashar, C. Milbury, and R. Hanlon, “Polarization vision in cephalopods: neuroanatomical and behavioral features that illustrate aspects of form and function,” Mar. Freshwater Behav. Physiol. 35, 57–68 (2002).
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N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity on silvery fish,” Vis. Res. 40, 71–75 (2000).
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N. Shashar, P. Rutledge, and T. Cronin, “Polarization vision in cuttlefish—a concealed communciation channel?” J. Exp. Biol. 199, 2077–2084 (1996).

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

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T. Chiou, S. Kleinlogel, T. Cronin, R. Calwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
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Smith, R. C.

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

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Stramski, D.

J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer, “Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean,” Limnol. Oceanogr. 43, 564–576 (1998).
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S. Sugihara, M. Kishino, and N. Okami, “Contribution of Raman scattering to upward irradiance in the sea,” J. Oceanogr. Soc. Jpn. 40, 397–404 (1984).
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Sullivan, J.

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D. A. Leonard and H. E. Sweeney, “Remote sensing of ocean physical properties: a comparison of Raman and Brillouin techniques,” Proc. SPIE 925, 407–414 (1988).
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T. H. Waterman and W. E. Westell, “Quantitative effects of the sun’s position on submarine light polarization,” J. Mar. Res. 15, 149–169 (1956).

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E. P. Zege and L. Chaikovskaya, “New approach to the polarized radiative transfer problem,” J. Quant. Spectrosc. Radiat. Transfer 55, 19–31 (1996).
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G. W. Kattawar and X. Xu, “Filling in of Fraunhofer lines in the ocean by Raman scattering,” Appl. Opt. 31, 6491–6500 (1992).
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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, 1037–1047 (2008).
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P. W. Zhai, G. W. Kattawar, and P. Yang, “Impulse response solution to the three-dimensional vector radiative transfer equation in atmosphere-ocean systems. II. The hybrid matrix operator–Monte Carlo method,” Appl. Opt. 47, 1063–1071 (2008).
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Y. You, P. W. Zhai, G. W. Kattawar, and P. Yang, “Polarized radiance fields under a dynamic ocean surface: a three-dimensional radiative transfer solution,” Appl. Opt. 48, 3019–3029 (2009).
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J. T. Adams and D. J. Gray, “Neutral points in an atmosphere-ocean system. 2: downwelling light field,” Appl. Opt. 50, 335–346 (2011).
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Y. You, A. Tonizzo, A. A. Gilerson, M. Cummings, P. Brady, J. Sullivan, M. S. Twardowski, H. M. Dierssen, S. A. Ahmed, and G. W. Kattawar, “Measurements and simulations of polarization states of underwater light in clear oceanic waters,” Appl. Opt. 50, 4873–4893 (2011).
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J. T. Adams, D. J. Gray, and S. Rayner, “Observation of non-principal plane neutral points in the upwelling polarized light field above a water surface,” Appl. Opt. 51, 5387–5391 (2012).
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Compt. Rend.

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

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Curr. Biol.

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J. Oceanogr. Soc. Jpn.

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J. Opt. Soc. Am. A

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Limnol. Oceanogr.

G. W. Kattawar and 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]

A. Ivanoff, N. Jerlov, and T. H. Waterman, “A comparative study of irradiance, beam transmittance and scattering in the sea near Bermuda,” Limnol. Oceanogr. 6, 129–148 (1961).
[CrossRef]

J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer, “Effect of Raman scattering on the average cosine and diffuse attenuation coefficient of irradiance in the ocean,” Limnol. Oceanogr. 43, 564–576 (1998).
[CrossRef]

Mar. Freshwater Behav. Physiol.

N. Shashar, C. Milbury, and R. Hanlon, “Polarization vision in cephalopods: neuroanatomical and behavioral features that illustrate aspects of form and function,” Mar. Freshwater Behav. Physiol. 35, 57–68 (2002).
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Opt. Express

Opt. Spectrosc.

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

P. A. K. I. I. Kondilenko, V. A. Klimenko, and O. P. Demyanenko, “Transverse cross section of the Raman scattering of the ν1 vibration of the water molecule in the liquid and gaseous states,” Opt. Spectrosc. 43, 384–386 (1977).

Phil. Trans. R. Soc. B

N. Shashar, S. Johnsen, A. Lerner, S. Sabbah, C. C. Chiao, L. M. Mäthger, and R. T. Hanlon, “Underwater linear polarization: physical limitations to biological functions,” Phil. Trans. R. Soc. B 366, 649–654 (2011).
[CrossRef]

Philos. Mag. J. Sci.

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

Phys. Today

T. D. Dickey, G. W. Kattawar, and K. J. Voss, “Shedding new light on light in the ocean,” Phys. Today 64(4), 44–49 (2011).
[CrossRef]

Proc. SPIE

D. A. Leonard and H. E. Sweeney, “Remote sensing of ocean physical properties: a comparison of Raman and Brillouin techniques,” Proc. SPIE 925, 407–414 (1988).
[CrossRef]

D. Collins, J. A. Bell, R. Zanoni, I. S. McDermid, B. Breckinridge, and C. A. Sepulveda, “Recent progress in the measurement of temperature and salinity by optical scattering,” Proc. SPIE 489, 247–269 (1984).
[CrossRef]

Sci. News

S. Milius, “Mantis shrimp flub color vision test,” Sci. News 182(6), 11 (2012).

Sci. Proc. R. Dublin Soc.

H. H. Poole, “The angular distribution of submarine daylight in deep water,” Sci. Proc. R. Dublin Soc. 24, 29–42 (1945).

Science

T. H. Waterman, “Polarization patterns in submarine illumination,” Science 120, 927–932 (1954).
[CrossRef]

Vis. Neurosci.

I. Flamarique and F. Hárosi, “Visual pigments and dichroism of anchovy cones: a model system for polarization detection,” Vis. Neurosci. 19, 467–473 (2002).
[CrossRef]

Vis. Res.

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity on silvery fish,” Vis. Res. 40, 71–75 (2000).
[CrossRef]

G. D. Bernard and R. Wehner, “Functional similarities between polarization vision and color vision,” Vis. Res. 17, 1019–1028 (1977).
[CrossRef]

Other

D. B. Shapiro, A. J. Hunt, and M. S. Quinby-Hunt, “Circular polarization effects in the light scattering from single and suspensions of dinoflagellates,” in Underwater Imaging, Photography and Visibility (SPIE, 1991).

R. Walraven, “Polarization imagery,” in Optical Polarimetry: Instrumentation and Applications, R. M. A. Azzam and D. L. Coffeen, eds. (SPIE, 1977), pp. 164–167.

K von Frisch, “Die Richtungsorienttierung der Bienen,” in Verhandlungen der Deutschen Zoologischen Gesellschaft Freiburg (1952), pp. 58–72.

V. A. Timofeeva, “Optics of turbid waters (results of laboratory studies),” in Optical Aspects of Oceanography, N. Jerlov and E. Nielsen, eds. (Academic, 1974), pp. 177–219.

J. A. Barral, Oeuvres de Francois Arago I–V (Gide/Weigel, 1858).

A. Morel, “Optical properties of pure water and pure seawater,” in Optical Aspects of Oceanography, N. G. Jerlov and E. S. Nielsen, eds. (Academic, 1974), pp. 1–24.

C. H. Chang and L. A. Young, “Seawater temperature measurements from Raman spectra,” Res. Note 920, N62269-72-C-0204, ARPA Order No. 1911 (1972).

C. Mobley, Light and Water-Radiative Transfer in Natural Waters (Academic, 1994).

X. Xu, “Significance of Raman scattering in the ocean,” dissertation (Texas A&M University, 1994).

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Figures (5)

Fig. 1.
Fig. 1.

Transmittance T11 and the other normalized transmission Mueller matrix elements T12/T11, T33/T11, and T34/T11. It should also be noted that T21=T12.

Fig. 2.
Fig. 2.

Reflectance R11 and the other normalized transmission Mueller matrix elements R12/R11, R33/R11, and R34/R11. The vertical dashed line denotes the critical angle.

Fig. 3.
Fig. 3.

Degree of polarization (P=|Q/I|) as a function of viewing angle for scattering in the water according to the Rayleigh phase matrix for several single scattering albedos.

Fig. 4.
Fig. 4.

Water Raman band computed from the data given in Walrafen [60] with incident light of wavelength 488 nm.

Fig. 5.
Fig. 5.

Reduced Mueller matrix for Raman scattering (dashed curve, ρ=0.17) and fluctuation scattering (solid curve, ρ=0.047).

Tables (1)

Tables Icon

Table 1. Correspondence Between Color Vision in Humans (Left Column) and Polarization Vision in Invertebrates (Right Column)

Equations (13)

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TAW=κ[α+ηαη00αηα+η0000γRe0000γRe],
α=12[2sinθtcosθisin(θi+θt)cos(θiθt)]2,η=12[2sinθtcosθisin(θi+θt)]2,
γRe=4sin2θtcos2θisin2(θi+θt)cos(θiθt),κ=ncosθtcosθi,
RWA=[α+ηαη00αηα+η0000γReγIm00γImγRe],
α=12[tan(θiθt)tan(θi+θt)]2,η=12[sin(θiθt)sin(θi+θt)]2,
γRe=tan(θiθt)sin(θiθt)tan(θi+θt)sin(θi+θt),γIm=0,
α=12|n¯2cosθiisin2θin¯2n¯2cosθi+isin2θin¯2|2,η=12|cosθiisin2θin¯2cosθi+isin2θin¯2|2,
γ=[n¯2cosθi+isin2θin¯2n¯2cosθiisin2θin¯2][cosθiisin2θin¯2cosθi+isin2θin¯2].
R33min/R11=6n¯2n¯41(1+n¯2)2,R34min/R11=4n¯(1n¯2)(1+n¯2)2,
θmin=cos11n¯21+n¯2.
βR(θ)=316π1+3ρ1+2ρ(1+1ρ1+3ρcos2θ),
ρ=II||.
Mred=(1(1ρ)(μ21)(1+μ2)+(3μ2)ρ00(1ρ)(μ21)(1+μ2)+(3μ2)ρ(1ρ)(μ2+1)(1+μ2)+(3μ2)ρ0000(22ρ)μ(1+μ2)+(3μ2)ρ0000(26ρ)μ(1+μ2)+(3μ2)ρ),

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