Abstract

A full Mie scattering subroutine is employed to calculate what we call the linear polarization phase function (LPPF; percent polarization and e-vector orientation of radiation as a function of scattering angle) that results from refraction of the direct solar beam from air into water followed by single scattering by spherical hydrosols. The separate effects of refraction at the air–water interface, hydrosol size, the real and imaginary parts of the hydrosol refractive index, and absorption by the surrounding medium (water) on the LPPF are investigated. All of the above factors are found to alter the LPPF, changing the value of the maximum percent polarization (Pmax), the location of Pmax, the number of fluctuations in the LPPF, or the location of the neutral points (points of 0 percent polarization), though absorption by the surrounding medium is found to have only a minimal effect. The character and extent of the influence on the LPPF is found to depend on the scattering regime (Rayleigh, Mie, or geometric optics). We conclude that in calculating underwater polarization, it is important to take into consideration Mie scattering even in relatively clear waters. We also find a coupling between the partial polarization and the e-vector orientation, which suggests that for some polarization-based visual tasks, only one of these would suffice. Other implications for aquatic animal polarization vision are discussed.

© 2012 Optical Society of America

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

2011

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Phil. Trans. R. Soc. B 366, 671–679 (2011).
[CrossRef]

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

S. Johnsen, N. J. Marshall, and E. A. Widder, “Polarization sensitivity as a contrast enhancer in pelagic predators: lessons from in situ polarization imaging of transparent zooplankton,” Phil. Trans. R. Soc. B 366, 655–670 (2011).
[CrossRef]

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

Y. You, A. Tonizzo, A. A. Gilerson, M. E. Cummings, P. Brady, J. M. 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]

2010

2009

2008

A. Lerner, N. Meltser, N. Sapir, C. Erlick, N. Shashar, and M. Broza, “Reflected polarization guides chironomid females to oviposition sites,” J. Exp. Biol. 211, 3536–3543 (2008).
[CrossRef]

2007

J. Marshall, T. W. Cronin, and S. Kleinlogel, “Stomatopod eye structure and function: a review,” Arthropod Struct. Devel. 36, 420–448 (2007).
[CrossRef]

M. J. Henze and T. Labhart, “Haze, clouds and limited sky visibility: polarotactic orientation of crickets under difficult stimulus conditions,” J. Exp. Biol. 210, 3266–3276 (2007).
[CrossRef]

R. Hegedu¨s, S. Akesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[CrossRef]

2006

G. Kriska, P. Malik, Z. Csabai, and G. Horváth, “Why do highly polarizing black burnt-up stubble-fields not attract aquatic insects? An exception proving the rule,” Vis. Res. 46, 4382–4386 (2006).
[CrossRef]

S. Sabbah and N. Shashar, “Polarization contrast of zooplankton: a model for polarization-based sighting distance,” Vis. Res. 46, 444–456 (2006).
[CrossRef]

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100, 137–142 (2006).
[CrossRef]

S. Sabbah, A. Barta, J. Gal, G. Horvath, and N. Shashar, “Experimental and theoretical study of skylight polarization transmitted through Snell’s window of a flat water surface,” J. Opt. Soc. Am. A 23, 1978–1988 (2006).
[CrossRef]

2005

P. C. Y. Chang, J. G. Walker, and K. I. Hopcraft, “Ray tracing in absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 96, 327–341 (2005).
[CrossRef]

2004

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

2003

A. Sinyuk, O. Torres, and O. Dubovik, “Combined use of satellite and surface observations to infer the imaginary part of refractive index of Saharan dust,” Geophys. Res. Lett. 30, 53-1–53-4 (2003).
[CrossRef]

2002

T. Labhart and E. P. Meyer, “Neural mechanisms in insect navigation: polarization compass and odometer,” Curr. Opin. Neurobiol. 12, 707–714 (2002).
[CrossRef]

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

2001

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001).
[CrossRef]

M. Chami, R. Santer, and E. Dilligeard, “Radiative transfer model for the computation of radiance and polarization in an ocean-atmosphere system: polarization properties of suspended matter for remote sensing,” Appl. Opt. 40, 2398–2416 (2001).
[CrossRef]

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

T. W. Cronin and N. Shashar, “The linearly polarized light field in clear, tropical marine waters: spatial and temporal variation of light intensity, degree of polarization and e-vector angle,” J. Exp. Biol. 204, 2461–2467 (2001).

1999

G. Horvath and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” J. Comp. Physiol. A 184, 1–7 (1999).
[CrossRef]

R. Schwind, “Daphnia pulex swims towards the most strongly polarized light: a response that leads to ‘shore flight’,” J. Exp. Biol. 202, 3631–3635 (1999).

1998

N. Shashar, R. T. Hanlon, and A. D. Petz, “Polarization vision helps detect transparent prey,” Nature 393, 222–223 (1998).
[CrossRef]

1996

N. Shashar and T. W. Cronin, “Polarization contrast vision in octopus,” J. Exp. Biol. 199, 999–1004 (1996).

1995

G. Horváth and D. Varjú, “Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell’s window of the flat water surface,” Vis. Res. 35, 1651–1666 (1995).
[CrossRef]

1983

J. W. Hovenier and C. V. M. Van der Mee, “Fundamental reletionships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

1980

1973

1970

V. A. Timofeyeva, “The degree of polarization of light in turbid media,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. (Engl. Transl.) 6, 513–522 (1970).

1962

V. A. Timofeyeva, “Spatial distribution of the degree of polarization of natural light in the sea,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. (Engl. Transl.) 12, 1160–1164 (1962).

1958

A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).

Adams, C. N.

Ahmed, S. A.

Akesson, S.

R. Hegedu¨s, S. Akesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[CrossRef]

Arnone, R. A.

Barnard, A. H.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

Barta, A.

Bogucki, D.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Bohren, C. F.

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

Boss, E.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

Brady, P.

Bricaud, A.

Broza, M.

A. Lerner, N. Meltser, N. Sapir, C. Erlick, N. Shashar, and M. Broza, “Reflected polarization guides chironomid females to oviposition sites,” J. Exp. Biol. 211, 3536–3543 (2008).
[CrossRef]

Cabannes, J.

J. Cabannes, La diffusion moléculaire de la lumière (Presses Universitaires de France, 1929).

Cartron, L.

L. Cartron, N. Yossef, A. Lerner, S. D. McCusker, A.-S. Darmaillacq, L. Dickel, and N. Shashar, “Polarization vision can improve object detection in turbid waters by cuttlefish,” J. Exp. Mar. Biol. Ecol. (to be published).

Chami, M.

Chandrasekhar, S.

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

Chang, G. C.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

Chang, P. C. Y.

P. C. Y. Chang, J. G. Walker, and K. I. Hopcraft, “Ray tracing in absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 96, 327–341 (2005).
[CrossRef]

Chiao, C.-C.

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

Cronin, T. W.

J. Marshall, T. W. Cronin, and S. Kleinlogel, “Stomatopod eye structure and function: a review,” Arthropod Struct. Devel. 36, 420–448 (2007).
[CrossRef]

T. W. Cronin and N. Shashar, “The linearly polarized light field in clear, tropical marine waters: spatial and temporal variation of light intensity, degree of polarization and e-vector angle,” J. Exp. Biol. 204, 2461–2467 (2001).

N. Shashar and T. W. Cronin, “Polarization contrast vision in octopus,” J. Exp. Biol. 199, 999–1004 (1996).

Csabai, Z.

G. Kriska, P. Malik, Z. Csabai, and G. Horváth, “Why do highly polarizing black burnt-up stubble-fields not attract aquatic insects? An exception proving the rule,” Vis. Res. 46, 4382–4386 (2006).
[CrossRef]

Cummings, M. E.

Darmaillacq, A.-S.

L. Cartron, N. Yossef, A. Lerner, S. D. McCusker, A.-S. Darmaillacq, L. Dickel, and N. Shashar, “Polarization vision can improve object detection in turbid waters by cuttlefish,” J. Exp. Mar. Biol. Ecol. (to be published).

Dickel, L.

L. Cartron, N. Yossef, A. Lerner, S. D. McCusker, A.-S. Darmaillacq, L. Dickel, and N. Shashar, “Polarization vision can improve object detection in turbid waters by cuttlefish,” J. Exp. Mar. Biol. Ecol. (to be published).

Dickey, T. D.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

Dierssen, H. M.

Dilligeard, E.

Dubovik, O.

A. Sinyuk, O. Torres, and O. Dubovik, “Combined use of satellite and surface observations to infer the imaginary part of refractive index of Saharan dust,” Geophys. Res. Lett. 30, 53-1–53-4 (2003).
[CrossRef]

Erlick, C.

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Phil. Trans. R. Soc. B 366, 671–679 (2011).
[CrossRef]

A. Lerner, N. Meltser, N. Sapir, C. Erlick, N. Shashar, and M. Broza, “Reflected polarization guides chironomid females to oviposition sites,” J. Exp. Biol. 211, 3536–3543 (2008).
[CrossRef]

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” in Recent Research Developments in Experimental & Theoretical Biology, S. G. Pandalai, ed. (Transworld Research Network, 2005), pp. 123–176.

Fournier, G. R.

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007).

Fu, Q.

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100, 137–142 (2006).
[CrossRef]

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001).
[CrossRef]

Gal, J.

Gardner, W. D.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

Gilerson, A.

Gilerson, A. A.

Gray, D. J.

Gross, B. M.

Hale, G. M.

Hanlon, R. T.

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

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

N. Shashar, R. T. Hanlon, and A. D. Petz, “Polarization vision helps detect transparent prey,” Nature 393, 222–223 (1998).
[CrossRef]

Hawryshyn, C. W.

C. W. Hawryshyn, “Mechanisms of ultraviolet polarization vision in fishes,” in Sensory Processing in Aquatic Environments, S. P. Collin and N. J. Marshall, eds. (Springer, 2003), pp. 252–265.

He, M.-X.

Hegedu¨s, R.

R. Hegedu¨s, S. Akesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[CrossRef]

Henze, M. J.

M. J. Henze and T. Labhart, “Haze, clouds and limited sky visibility: polarotactic orientation of crickets under difficult stimulus conditions,” J. Exp. Biol. 210, 3266–3276 (2007).
[CrossRef]

Hopcraft, K. I.

P. C. Y. Chang, J. G. Walker, and K. I. Hopcraft, “Ray tracing in absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 96, 327–341 (2005).
[CrossRef]

Horvath, G.

Horváth, G.

R. Hegedu¨s, S. Akesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[CrossRef]

G. Kriska, P. Malik, Z. Csabai, and G. Horváth, “Why do highly polarizing black burnt-up stubble-fields not attract aquatic insects? An exception proving the rule,” Vis. Res. 46, 4382–4386 (2006).
[CrossRef]

G. Horváth and D. Varjú, “Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell’s window of the flat water surface,” Vis. Res. 35, 1651–1666 (1995).
[CrossRef]

G. Horváth and D. Varjú, Polarized Light in Animal Vision: Polarization Patterns in Nature (Springer Verlag, 2004).

Hovenier, J. W.

J. W. Hovenier and C. V. M. Van der Mee, “Fundamental reletionships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Hu, L.

Huffman, D. R.

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

Ivanoff, A.

A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier Scientific, 1976), p. 231.

Johnsen, S.

S. Johnsen, N. J. Marshall, and E. A. Widder, “Polarization sensitivity as a contrast enhancer in pelagic predators: lessons from in situ polarization imaging of transparent zooplankton,” Phil. Trans. R. Soc. B 366, 655–670 (2011).
[CrossRef]

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

Jonasz, M.

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007).

Kattawar, G. W.

Kleinlogel, S.

J. Marshall, T. W. Cronin, and S. Kleinlogel, “Stomatopod eye structure and function: a review,” Arthropod Struct. Devel. 36, 420–448 (2007).
[CrossRef]

Kriska, G.

G. Kriska, P. Malik, Z. Csabai, and G. Horváth, “Why do highly polarizing black burnt-up stubble-fields not attract aquatic insects? An exception proving the rule,” Vis. Res. 46, 4382–4386 (2006).
[CrossRef]

Labhart, T.

M. J. Henze and T. Labhart, “Haze, clouds and limited sky visibility: polarotactic orientation of crickets under difficult stimulus conditions,” J. Exp. Biol. 210, 3266–3276 (2007).
[CrossRef]

T. Labhart and E. P. Meyer, “Neural mechanisms in insect navigation: polarization compass and odometer,” Curr. Opin. Neurobiol. 12, 707–714 (2002).
[CrossRef]

Lerner, A.

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Phil. Trans. R. Soc. B 366, 671–679 (2011).
[CrossRef]

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

A. Lerner, N. Meltser, N. Sapir, C. Erlick, N. Shashar, and M. Broza, “Reflected polarization guides chironomid females to oviposition sites,” J. Exp. Biol. 211, 3536–3543 (2008).
[CrossRef]

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” in Recent Research Developments in Experimental & Theoretical Biology, S. G. Pandalai, ed. (Transworld Research Network, 2005), pp. 123–176.

L. Cartron, N. Yossef, A. Lerner, S. D. McCusker, A.-S. Darmaillacq, L. Dickel, and N. Shashar, “Polarization vision can improve object detection in turbid waters by cuttlefish,” J. Exp. Mar. Biol. Ecol. (to be published).

Lotsberg, J. K.

Malik, P.

G. Kriska, P. Malik, Z. Csabai, and G. Horváth, “Why do highly polarizing black burnt-up stubble-fields not attract aquatic insects? An exception proving the rule,” Vis. Res. 46, 4382–4386 (2006).
[CrossRef]

Marshall, J.

J. Marshall, T. W. Cronin, and S. Kleinlogel, “Stomatopod eye structure and function: a review,” Arthropod Struct. Devel. 36, 420–448 (2007).
[CrossRef]

Marshall, N. J.

S. Johnsen, N. J. Marshall, and E. A. Widder, “Polarization sensitivity as a contrast enhancer in pelagic predators: lessons from in situ polarization imaging of transparent zooplankton,” Phil. Trans. R. Soc. B 366, 655–670 (2011).
[CrossRef]

Mathger, L. M.

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

McCusker, S. D.

L. Cartron, N. Yossef, A. Lerner, S. D. McCusker, A.-S. Darmaillacq, L. Dickel, and N. Shashar, “Polarization vision can improve object detection in turbid waters by cuttlefish,” J. Exp. Mar. Biol. Ecol. (to be published).

Meltser, N.

A. Lerner, N. Meltser, N. Sapir, C. Erlick, N. Shashar, and M. Broza, “Reflected polarization guides chironomid females to oviposition sites,” J. Exp. Biol. 211, 3536–3543 (2008).
[CrossRef]

Meyer, E. P.

T. Labhart and E. P. Meyer, “Neural mechanisms in insect navigation: polarization compass and odometer,” Curr. Opin. Neurobiol. 12, 707–714 (2002).
[CrossRef]

Milbury, C. A.

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

Mobley, C. D.

C. D. Mobley, Light and Water (Academic, 1994).

Morel, A.

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

A. Morel, “Diffusion de la lumière par les eaux de mer. Résultats expérimentaux et approche théorique,” in Optics of the Sea, AGARD: Lecture Series (NATO, 1973), pp. 3.1.1–3.1.76.

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

Moshary, F.

Pegau, W. S.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

Petz, A. D.

N. Shashar, R. T. Hanlon, and A. D. Petz, “Polarization vision helps detect transparent prey,” Nature 393, 222–223 (1998).
[CrossRef]

Petzold, T. J.

T. J. Petzold, “Volume scattering functions for selected natural waters,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson & Ross, 1977), pp. 150–174.

Querry, M. R.

Sabbah, S.

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

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Phil. Trans. R. Soc. B 366, 671–679 (2011).
[CrossRef]

S. Sabbah and N. Shashar, “Polarization contrast of zooplankton: a model for polarization-based sighting distance,” Vis. Res. 46, 444–456 (2006).
[CrossRef]

S. Sabbah, A. Barta, J. Gal, G. Horvath, and N. Shashar, “Experimental and theoretical study of skylight polarization transmitted through Snell’s window of a flat water surface,” J. Opt. Soc. Am. A 23, 1978–1988 (2006).
[CrossRef]

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” in Recent Research Developments in Experimental & Theoretical Biology, S. G. Pandalai, ed. (Transworld Research Network, 2005), pp. 123–176.

Santer, R.

Sapir, N.

A. Lerner, N. Meltser, N. Sapir, C. Erlick, N. Shashar, and M. Broza, “Reflected polarization guides chironomid females to oviposition sites,” J. Exp. Biol. 211, 3536–3543 (2008).
[CrossRef]

Schwind, R.

R. Schwind, “Daphnia pulex swims towards the most strongly polarized light: a response that leads to ‘shore flight’,” J. Exp. Biol. 202, 3631–3635 (1999).

Shashar, N.

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

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Phil. Trans. R. Soc. B 366, 671–679 (2011).
[CrossRef]

A. Lerner, N. Meltser, N. Sapir, C. Erlick, N. Shashar, and M. Broza, “Reflected polarization guides chironomid females to oviposition sites,” J. Exp. Biol. 211, 3536–3543 (2008).
[CrossRef]

S. Sabbah, A. Barta, J. Gal, G. Horvath, and N. Shashar, “Experimental and theoretical study of skylight polarization transmitted through Snell’s window of a flat water surface,” J. Opt. Soc. Am. A 23, 1978–1988 (2006).
[CrossRef]

S. Sabbah and N. Shashar, “Polarization contrast of zooplankton: a model for polarization-based sighting distance,” Vis. Res. 46, 444–456 (2006).
[CrossRef]

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

T. W. Cronin and N. Shashar, “The linearly polarized light field in clear, tropical marine waters: spatial and temporal variation of light intensity, degree of polarization and e-vector angle,” J. Exp. Biol. 204, 2461–2467 (2001).

N. Shashar, R. T. Hanlon, and A. D. Petz, “Polarization vision helps detect transparent prey,” Nature 393, 222–223 (1998).
[CrossRef]

N. Shashar and T. W. Cronin, “Polarization contrast vision in octopus,” J. Exp. Biol. 199, 999–1004 (1996).

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” in Recent Research Developments in Experimental & Theoretical Biology, S. G. Pandalai, ed. (Transworld Research Network, 2005), pp. 123–176.

L. Cartron, N. Yossef, A. Lerner, S. D. McCusker, A.-S. Darmaillacq, L. Dickel, and N. Shashar, “Polarization vision can improve object detection in turbid waters by cuttlefish,” J. Exp. Mar. Biol. Ecol. (to be published).

Sigalov, A.

A. Sigalov, The Fredy and Nadine Herrmann Institute of Earth Sciences, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel (personal communication, 2008).

Sinyuk, A.

A. Sinyuk, O. Torres, and O. Dubovik, “Combined use of satellite and surface observations to infer the imaginary part of refractive index of Saharan dust,” Geophys. Res. Lett. 30, 53-1–53-4 (2003).
[CrossRef]

Souaidia, N.

Stamnes, J. J.

Stramski, D.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

D. Stramski, A. Bricaud, and A. Morel, “Modeling the inherent optical properties of the ocean based on the detailed composition of the planktonic community,” Appl. Opt. 40, 2929–2945 (2001).
[CrossRef]

Sullivan, J. M.

Sun, W.

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100, 137–142 (2006).
[CrossRef]

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001).
[CrossRef]

Timofeyeva, V. A.

V. A. Timofeyeva, “The degree of polarization of light in turbid media,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. (Engl. Transl.) 6, 513–522 (1970).

V. A. Timofeyeva, “Spatial distribution of the degree of polarization of natural light in the sea,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. (Engl. Transl.) 12, 1160–1164 (1962).

Tonizzo, A.

Torres, O.

A. Sinyuk, O. Torres, and O. Dubovik, “Combined use of satellite and surface observations to infer the imaginary part of refractive index of Saharan dust,” Geophys. Res. Lett. 30, 53-1–53-4 (2003).
[CrossRef]

Twardowski, M. S.

Van der Mee, C. V. M.

J. W. Hovenier and C. V. M. Van der Mee, “Fundamental reletionships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Varjú, D.

G. Horváth and D. Varjú, “Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell’s window of the flat water surface,” Vis. Res. 35, 1651–1666 (1995).
[CrossRef]

G. Horváth and D. Varjú, Polarized Light in Animal Vision: Polarization Patterns in Nature (Springer Verlag, 2004).

Voss, K. J.

K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18, 19672–19680 (2010).
[CrossRef]

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Walker, J. G.

P. C. Y. Chang, J. G. Walker, and K. I. Hopcraft, “Ray tracing in absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 96, 327–341 (2005).
[CrossRef]

Waterman, T. H.

A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).

T. H. Waterman, “Polarization sensitivity,” in Comparative Physiology and Evolution of Vision in Invertebrates B: Invertebrates Visual Centers and Behavior I, H. Autrum, ed. (Springer-Verlag, 1981), pp. 281–469.

Wehner, R.

R. Hegedu¨s, S. Akesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[CrossRef]

G. Horvath and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” J. Comp. Physiol. A 184, 1–7 (1999).
[CrossRef]

Widder, E. A.

S. Johnsen, N. J. Marshall, and E. A. Widder, “Polarization sensitivity as a contrast enhancer in pelagic predators: lessons from in situ polarization imaging of transparent zooplankton,” Phil. Trans. R. Soc. B 366, 655–670 (2011).
[CrossRef]

Yossef, N.

L. Cartron, N. Yossef, A. Lerner, S. D. McCusker, A.-S. Darmaillacq, L. Dickel, and N. Shashar, “Polarization vision can improve object detection in turbid waters by cuttlefish,” J. Exp. Mar. Biol. Ecol. (to be published).

You, Y.

Young, A. T.

Zaneveld, J. R. V.

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

Zhang, X.

Zhou, J.

Appl. Opt.

Arthropod Struct. Devel.

J. Marshall, T. W. Cronin, and S. Kleinlogel, “Stomatopod eye structure and function: a review,” Arthropod Struct. Devel. 36, 420–448 (2007).
[CrossRef]

Astron. Astrophys.

J. W. Hovenier and C. V. M. Van der Mee, “Fundamental reletionships relevant to the transfer of polarized light in a scattering atmosphere,” Astron. Astrophys. 128, 1–16 (1983).

Curr. Opin. Neurobiol.

T. Labhart and E. P. Meyer, “Neural mechanisms in insect navigation: polarization compass and odometer,” Curr. Opin. Neurobiol. 12, 707–714 (2002).
[CrossRef]

Geophys. Res. Lett.

A. Sinyuk, O. Torres, and O. Dubovik, “Combined use of satellite and surface observations to infer the imaginary part of refractive index of Saharan dust,” Geophys. Res. Lett. 30, 53-1–53-4 (2003).
[CrossRef]

Izv. Acad. Sci., USSR

V. A. Timofeyeva, “The degree of polarization of light in turbid media,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. (Engl. Transl.) 6, 513–522 (1970).

V. A. Timofeyeva, “Spatial distribution of the degree of polarization of natural light in the sea,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. (Engl. Transl.) 12, 1160–1164 (1962).

J. Comp. Physiol. A

G. Horvath and R. Wehner, “Skylight polarization as perceived by desert ants and measured by video polarimetry,” J. Comp. Physiol. A 184, 1–7 (1999).
[CrossRef]

J. Exp. Biol.

T. W. Cronin and N. Shashar, “The linearly polarized light field in clear, tropical marine waters: spatial and temporal variation of light intensity, degree of polarization and e-vector angle,” J. Exp. Biol. 204, 2461–2467 (2001).

A. Lerner, N. Meltser, N. Sapir, C. Erlick, N. Shashar, and M. Broza, “Reflected polarization guides chironomid females to oviposition sites,” J. Exp. Biol. 211, 3536–3543 (2008).
[CrossRef]

M. J. Henze and T. Labhart, “Haze, clouds and limited sky visibility: polarotactic orientation of crickets under difficult stimulus conditions,” J. Exp. Biol. 210, 3266–3276 (2007).
[CrossRef]

N. Shashar and T. W. Cronin, “Polarization contrast vision in octopus,” J. Exp. Biol. 199, 999–1004 (1996).

R. Schwind, “Daphnia pulex swims towards the most strongly polarized light: a response that leads to ‘shore flight’,” J. Exp. Biol. 202, 3631–3635 (1999).

J. Geophys. Res. Oceans

E. Boss, W. S. Pegau, W. D. Gardner, J. R. V. Zaneveld, A. H. Barnard, M. S. Twardowski, G. C. Chang, and T. D. Dickey, “Spectral particulate attenuation and particle size distribution in the bottom boundary layer of a continental shelf,” J. Geophys. Res. Oceans 106, 9509–9516 (2001).
[CrossRef]

J. Mar. Res.

A. Ivanoff and T. H. Waterman, “Factors, mainly depth and wavelength, affecting the degree of underwater light polarization,” J. Mar. Res. 16, 283–307 (1958).

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100, 137–142 (2006).
[CrossRef]

P. C. Y. Chang, J. G. Walker, and K. I. Hopcraft, “Ray tracing in absorbing media,” J. Quant. Spectrosc. Radiat. Transfer 96, 327–341 (2005).
[CrossRef]

Mar. Freshw. Behav. Physiol.

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

Nature

N. Shashar, R. T. Hanlon, and A. D. Petz, “Polarization vision helps detect transparent prey,” Nature 393, 222–223 (1998).
[CrossRef]

Opt. Express

Phil. Trans. R. Soc. B

S. Johnsen, N. J. Marshall, and E. A. Widder, “Polarization sensitivity as a contrast enhancer in pelagic predators: lessons from in situ polarization imaging of transparent zooplankton,” Phil. Trans. R. Soc. B 366, 655–670 (2011).
[CrossRef]

A. Lerner, S. Sabbah, C. Erlick, and N. Shashar, “Navigation by light polarization in clear and turbid waters,” Phil. Trans. R. Soc. B 366, 671–679 (2011).
[CrossRef]

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

Proc. R. Soc. A

R. Hegedu¨s, S. Akesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007).
[CrossRef]

Prog. Oceanogr.

D. Stramski, E. Boss, D. Bogucki, and K. J. Voss, “The role of seawater constituents in light backscattering in the ocean,” Prog. Oceanogr. 61, 27–56 (2004).
[CrossRef]

Vis. Res.

G. Horváth and D. Varjú, “Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell’s window of the flat water surface,” Vis. Res. 35, 1651–1666 (1995).
[CrossRef]

G. Kriska, P. Malik, Z. Csabai, and G. Horváth, “Why do highly polarizing black burnt-up stubble-fields not attract aquatic insects? An exception proving the rule,” Vis. Res. 46, 4382–4386 (2006).
[CrossRef]

S. Sabbah and N. Shashar, “Polarization contrast of zooplankton: a model for polarization-based sighting distance,” Vis. Res. 46, 444–456 (2006).
[CrossRef]

Other

M. Jonasz and G. R. Fournier, Light Scattering by Particles in Water: Theoretical and Experimental Foundations (Academic, 2007).

A. Morel, “Diffusion de la lumière par les eaux de mer. Résultats expérimentaux et approche théorique,” in Optics of the Sea, AGARD: Lecture Series (NATO, 1973), pp. 3.1.1–3.1.76.

J. Cabannes, La diffusion moléculaire de la lumière (Presses Universitaires de France, 1929).

A. Sigalov, The Fredy and Nadine Herrmann Institute of Earth Sciences, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel (personal communication, 2008).

T. J. Petzold, “Volume scattering functions for selected natural waters,” in Light in the Sea, J. E. Tyler, ed. (Dowden, Hutchinson & Ross, 1977), pp. 150–174.

P. Laven, “MiePlot v4.2,” http://www.philiplaven.com/mieplot.htm .

N. G. Jerlov, Marine Optics (Elsevier Scientific, 1976), p. 231.

C. D. Mobley, Light and Water (Academic, 1994).

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

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

G. W. Kattawar, “Polarization of light in the ocean,” in Ocean Optics, R. W. Spinrad, K. L. Carder, and M. J. Perry, eds. (Oxford University, 1994), pp. 202–225.

G. Horváth and D. Varjú, Polarized Light in Animal Vision: Polarization Patterns in Nature (Springer Verlag, 2004).

S. Sabbah, A. Lerner, C. Erlick, and N. Shashar, “Under water polarization vision—a physical examination,” in Recent Research Developments in Experimental & Theoretical Biology, S. G. Pandalai, ed. (Transworld Research Network, 2005), pp. 123–176.

T. H. Waterman, “Polarization sensitivity,” in Comparative Physiology and Evolution of Vision in Invertebrates B: Invertebrates Visual Centers and Behavior I, H. Autrum, ed. (Springer-Verlag, 1981), pp. 281–469.

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

C. W. Hawryshyn, “Mechanisms of ultraviolet polarization vision in fishes,” in Sensory Processing in Aquatic Environments, S. P. Collin and N. J. Marshall, eds. (Springer, 2003), pp. 252–265.

L. Cartron, N. Yossef, A. Lerner, S. D. McCusker, A.-S. Darmaillacq, L. Dickel, and N. Shashar, “Polarization vision can improve object detection in turbid waters by cuttlefish,” J. Exp. Mar. Biol. Ecol. (to be published).

Cited By

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Figures (12)

Fig. 1.
Fig. 1.

LPPF of the partial polarization (P, upper panels) and the e-vector orientation (α, lower panels) versus scattering angle, Θsca, for refraction from air to water followed by single scattering by monodisperse Rayleigh spherical scatterers (scatterer radius r=104μm) for different angles of refraction in the water, as represented by different SZA. Incoming light wavelength λ=450nm; medium refractive index=1.337 (water at 450 nm). α=0° represents horizontal alignment. Note the change in the location of the neutral points (P=0) and the change in the value of P in the F/B directions (0°/180° scattering angle).

Fig. 2.
Fig. 2.

LPPF for refraction from air to water followed by single scattering by spherical scatterers in the (a) Rayleigh (r=104μm), (b) Mie (r=1μm), and (c) geometric (r=100μm) regimes. Particle refractive index m=1.53+i0.005 (sand/mineral); solar zenith and azimuthal angles=90° and 270°, respectively. Note the multiple minima and maxima (fluctuations) due to interference in (b), the shift of the polarization maximum (Pmax) toward 80° scattering angle and the shift of the neutral points in (b), and the change in the e-vector phase function between the three regimes (lower panels).

Fig. 3.
Fig. 3.

LPPF for refraction from air to water followed by single scattering by spherical scatterers as in Fig. 2 using monodisperse spherical Mie scatterers (r=1μm) with different scatterer real refractive indices, mre= (a) 1.43, (b) 1.53, and (c) 1.63. Scatterer imaginary refractive index mim=0.005. Note the variation in the number of fluctuations in the partial polarization phase function (upper panels) and the change in the e-vector phase function (lower panels) with increasing real refractive index.

Fig. 4.
Fig. 4.

LPPF for refraction from air to water followed by single scattering by spherical scatterers as in Fig. 3 but for monodisperse spherical Mie scatterers (r=1μm) with different scatterer imaginary refractive indices, mim=(a) 0.0, (b) 0.01, (c) 0.1, and (d) 1.0. Refer to Fig. 2(b) for mim=0.005. Scatterer real refractive index mre=1.53. Note the change in the LPPF with increasing imaginary refractive index, particularly the shift in Pmax toward 60° scattering angle in the case of the highest absorption value, (d).

Fig. 5.
Fig. 5.

LPPF for refraction from air to water followed by single scattering by spherical scatterers as in Fig. 3 but for monodisperse spherical geometric scatterers (r=100μm) with different scatterer real refractive indices, mre= (a) 1.43, (b) 1.53, and (c) 1.63. Scatterer imaginary refractive index mim=0.005. Note the shift in Pmax toward lower scattering angle with increasing real refractive index, and the change in the e-vector phase function in the range of 30°–60° scattering angle.

Fig. 6.
Fig. 6.

LPPF for refraction from air to water followed by single scattering by spherical scatterers but for monodisperse spherical geometric scatterers (r=100μm) with different scatterer imaginary refractive indices, mim= (a) 0.1, (b) 0.5, and (c) 1.0. See Fig. 2(c) for mim=0.005. Scatterer real refractive index mre=1.53. Note the shift in Pmax toward lower scattering angles and the decrease in Pmax with increasing scatterer imaginary refractive index. Note also the small changes in the e-vector phase function in the range of 30°–60° scattering angle.

Fig. 7.
Fig. 7.

LPPF for refraction from air to water followed by single scattering by different Junge size distributions of spherical particles, where N(D)=N0(D/D0)z, according to values measured in the ocean [30]. N is the particle concentration (particles m3), and D is the scatterer diameter (μm). Junge power z= (a) 2.5, (b) 3, (c) 4, and (d) 5. Note (a) the shift in Pmax to scattering angles lower than 90° when geometric scatterers dominate, (b, c) the shift in Pmax back to 100° scattering angle when Mie scatterers dominate, and (d) the shift in Pmax back again toward 90° when Rayleigh scatterers dominate. In (b, c), note also the decrease in the value of Pmax when Mie scatterers dominate.

Fig. 8.
Fig. 8.

LPPF for refraction from air to water followed by single scattering by a Junge size distribution of spherical particles (Junge power z=4) with different scatterer real refractive indices, mre= (a) 1.43, (b) 1.53, and (c) 1.63. Note the decrease in Pmax and the shift of the peak toward higher scattering angles with increasing scatterer real refractive index.

Fig. 9.
Fig. 9.

LPPF for refraction from air to water followed by single scattering by a Junge size distributions of spherical particles (Junge power z=4) with different scatterer imaginary refractive indices, mim= (a) 0.0, (b) 0.1, and (c) 1.0. Refer to Fig. 7(c) for mim=0.005. Scatterer real refractive index mre=1.53. Note the change in the e-vector orientation phase function and the (a, c) decrease and (b) increase in the value of Pmax with changing imaginary index.

Fig. 10.
Fig. 10.

LPPF for refraction from air to water followed by single scattering by monodisperse spherical Mie sand and mineral scatterers (r=1μm) in absorbing sea water. The medium imaginary refractive index, medim= (a) 0.0001, (b) 0.001, and (c, d) 0.01. All other parameters are as in Fig. 2(b), except in (d), where the imaginary part of the scatterer refractive index is set to 0.000. Note (c) the small increase in the fluctuations of the partial polarization (P) for a strong medium absorption of 0.01 at scattering angles around 120° and (d) the more than 10% increase at scattering angles greater than 160° with the nonabsorbing scatterer. No effect of the absorption of the medium on the e-vector LPPF (lower panels) is detected.

Fig. 11.
Fig. 11.

LPPF for refraction from air to water followed by single scattering by spherical scatterers as in Fig. 10 but for monodisperse geometric spherical sand and mineral scatterers (r=100μm). Note (c) that the LPPF changes only for mim=0.01.

Fig. 12.
Fig. 12.

LPPF for refraction from air to water followed by single scattering by spherical scatterers as in Fig. 10 but for a Junge size distribution of spherical sand and mineral scatterers (Junge power z=4). Note that there is only a small change in the LPPF with increasing medium absorption.

Tables (1)

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Table 1. Effects of Different Processes and Mechanisms on Underwater Polarizationa

Equations (9)

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P=Q2+U2+V2I,
α=12arctan|UQ|.
S11(k,Θsca)=12(|S22|+|S12|),
S12(k,Θsca)=12(|S22||S12|),
S33(k,Θsca)=Re(S2)·conj(S1),
S34(k,Θsca)=Im(S2)·conj(S1).
Sij(Θsca)=kSij(k,Θsca)·QC(k)kQC(k),
QC(k)=Qsca(k)·C(k),
Msca(Θsca)=[S11S1200S12S110000S33S3400S34S33].

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