Abstract

Polarization states of the underwater light field were measured by a hyperspectral and multiangular polarimeter and a video polarimeter under various atmospheric, surface, and water conditions, as well as solar and viewing geometries, in clear oceanic waters near Port Aransas, Texas. Some of the first comprehensive comparisons were made between the measured polarized light, including the degree and angle of linear polarization and linear Stokes parameters (Q and U), and those from Monte Carlo simulations that used concurrently measured water inherent optical properties and particle volume scattering functions as input. For selected wavelengths in the visible spectrum, measured and model-simulated polarization characteristics were found to be consistent in most cases. Measured degree and angle of linear polarization are found to be largely determined by an in-water single-scattering model. Model simulations suggest that the degree of linear polarization (DoLP) at horizontal viewing directions is highly dependent on the viewing azimuth angle for a low solar elevation. This implies that animals can use the DoLP signal for orientation.

© 2011 Optical Society of America

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2011

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] [PubMed]

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] [PubMed]

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] [PubMed]

2010

A. Tonizzo, J. Zhou, A. Gilerson, B. Gross, F. Moshary and S. Ahmed, “The impact of algal fluorescence on the underwater polarized light field,” Proc. SPIE 7678, 76780K (2010).
[CrossRef]

2009

2008

2007

S. Sabbah and N. Shashar, “Light polarization under water near sunrise,” J. Opt. Soc. Am. A 24, 2049–2056 (2007).
[CrossRef]

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

2006

2004

N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exp. Biol. 207, 3619–3628 (2004).
[CrossRef] [PubMed]

2002

2001

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. 40, 400–412 (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).
[PubMed]

1999

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Ocean. Technol. 16, 691–707 (1999).
[CrossRef]

1997

1995

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

S. A. Clough and M. J. Iacono, “Line-by-line calculations of atmospheric fluxes and cooling rates 2. Application to carbon dioxide, ozone, methane, nitrous oxide, and the halocarbons,” J. Geophys. Res. 100, 16519–16535 (1995).
[CrossRef]

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]

1984

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

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

1974

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610(1974).
[CrossRef]

1973

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

1972

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]

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] [PubMed]

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

1941

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

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. Tonizzo, J. Zhou, A. Gilerson, B. Gross, F. Moshary and S. Ahmed, “The impact of algal fluorescence on the underwater polarized light field,” Proc. SPIE 7678, 76780K (2010).
[CrossRef]

Ahmed, S. A.

Arnone, R. A.

Bailey, S. W.

G. C. Feldman and C. R. McClain, Ocean Color Web, MODerate-resolution Imaging Spectroradiometer (MODIS) Aqua Sensor Reprocessing 2009.1, N. Kuring and S. W. Bailey, eds. (NASA Goddard Space Flight Center, 4 Dec. 2010), http://oceancolor.gsfc.nasa.gov/.

Barta, A.

Boynton, G. C.

Broquez, C.

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

Brown, I.

Chaikovskaya, L. I.

Chami, M.

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

Chandrasekhar, S.

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

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] [PubMed]

Clough, S. A.

S. A. Clough and M. J. Iacono, “Line-by-line calculations of atmospheric fluxes and cooling rates 2. Application to carbon dioxide, ozone, methane, nitrous oxide, and the halocarbons,” J. Geophys. Res. 100, 16519–16535 (1995).
[CrossRef]

Cox, C.

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

Cronin, T. W.

N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exp. Biol. 207, 3619–3628 (2004).
[CrossRef] [PubMed]

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).
[PubMed]

Donaghay, P. L.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Ocean. Technol. 16, 691–707 (1999).
[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] [PubMed]

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), Vol.  1, pp. 123–176.

Feldman, G. C.

G. C. Feldman and C. R. McClain, Ocean Color Web, MODerate-resolution Imaging Spectroradiometer (MODIS) Aqua Sensor Reprocessing 2009.1, N. Kuring and S. W. Bailey, eds. (NASA Goddard Space Flight Center, 4 Dec. 2010), http://oceancolor.gsfc.nasa.gov/.

Freeman, S. A.

Fry, E. S.

Gál, J.

Gilerson, A.

A. Tonizzo, J. Zhou, A. Gilerson, B. Gross, F. Moshary and S. Ahmed, “The impact of algal fluorescence on the underwater polarized light field,” Proc. SPIE 7678, 76780K (2010).
[CrossRef]

A. Tonizzo, J. Zhou, A. Gilerson, M. S. Twardowski, D. J. Gray, R. A. Arnone, B. M. Gross, F. Moshary, and S. A. Ahmed, “Polarized light in coastal waters: hyperspectral and multiangular analysis,” Opt. Express 17, 5666–5682 (2009).
[CrossRef] [PubMed]

Gordon, H. R.

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]

Gross, B.

A. Tonizzo, J. Zhou, A. Gilerson, B. Gross, F. Moshary and S. Ahmed, “The impact of algal fluorescence on the underwater polarized light field,” Proc. SPIE 7678, 76780K (2010).
[CrossRef]

Gross, B. M.

Guinn, J. A.

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

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] [PubMed]

Hansen, J. E.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610(1974).
[CrossRef]

He, M.-X.

Henyey, L. G.

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

Hojerslev, N. K.

Horvath, G.

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

Horváth, G.

Hu, L.

Iacono, M. J.

S. A. Clough and M. J. Iacono, “Line-by-line calculations of atmospheric fluxes and cooling rates 2. Application to carbon dioxide, ozone, methane, nitrous oxide, and the halocarbons,” J. Geophys. Res. 100, 16519–16535 (1995).
[CrossRef]

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).

A. Ivanoff, “Polarization measurements in the sea,” in Optical Aspects of Oceanography, N.Jerlov and E.Nielsen, eds. (Academic, 1974), pp. 151–176.

Jerlov, N.

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.

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] [PubMed]

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] [PubMed]

Katsev, I. L.

Kattawar, G. W.

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] [PubMed]

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. 40, 400–412 (2001).
[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, G. N. Plass, and J. A. Guinn, Jr., “Monte Carlo calculations of the polarization of radiation in the Earth’s atmosphere-ocean system,” J. Phys. Oceanogr. 3, 353–372(1973).
[CrossRef]

G. W. Kattawar and G. N. Plass, “Degree and direction of polarization of multiple scattered light. 1. Homogeneous cloud layers,” Appl. Opt. 11, 2851–2865 (1972).
[CrossRef] [PubMed]

G. W. Kattawar, “Polarization of light in the sea,” in Ocean Optics, R.W.Spinrad, K.L.Carder, and M.J.Perry, eds. (Oxford University, 1994), pp. 202–219.

Kuring, N.

G. C. Feldman and C. R. McClain, Ocean Color Web, MODerate-resolution Imaging Spectroradiometer (MODIS) Aqua Sensor Reprocessing 2009.1, N. Kuring and S. W. Bailey, eds. (NASA Goddard Space Flight Center, 4 Dec. 2010), http://oceancolor.gsfc.nasa.gov/.

Lenoble, J.

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

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] [PubMed]

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] [PubMed]

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), Vol.  1, pp. 123–176.

Lewis, M. R.

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).

Lundgren, B.

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] [PubMed]

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] [PubMed]

McClain, C. R.

G. C. Feldman and C. R. McClain, Ocean Color Web, MODerate-resolution Imaging Spectroradiometer (MODIS) Aqua Sensor Reprocessing 2009.1, N. Kuring and S. W. Bailey, eds. (NASA Goddard Space Flight Center, 4 Dec. 2010), http://oceancolor.gsfc.nasa.gov/.

McKee, D.

McLean, S. D.

Mobley, C. D.

C. D. Mobley, “HydroLight Users’ Guide,” http://www.sequoiasci.com/downloads/HE5UsersGuide.pdf.

Moshary, F.

A. Tonizzo, J. Zhou, A. Gilerson, B. Gross, F. Moshary and S. Ahmed, “The impact of algal fluorescence on the underwater polarized light field,” Proc. SPIE 7678, 76780K (2010).
[CrossRef]

A. Tonizzo, J. Zhou, A. Gilerson, M. S. Twardowski, D. J. Gray, R. A. Arnone, B. M. Gross, F. Moshary, and S. A. Ahmed, “Polarized light in coastal waters: hyperspectral and multiangular analysis,” Opt. Express 17, 5666–5682 (2009).
[CrossRef] [PubMed]

Munk, W.

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[CrossRef] [PubMed]

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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] [PubMed]

Yang, P.

Zaneveld, J. R. V.

M. S. Twardowski, J. M. Sullivan, P. L. Donaghay, and J. R. V. Zaneveld, “Microscale quantification of the absorption by dissolved and particulate material in coastal waters with an ac-9,” J. Atmos. Ocean. Technol. 16, 691–707 (1999).
[CrossRef]

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A. Tonizzo, J. Zhou, A. Gilerson, B. Gross, F. Moshary and S. Ahmed, “The impact of algal fluorescence on the underwater polarized light field,” Proc. SPIE 7678, 76780K (2010).
[CrossRef]

A. Tonizzo, J. Zhou, A. Gilerson, M. S. Twardowski, D. J. Gray, R. A. Arnone, B. M. Gross, F. Moshary, and S. A. Ahmed, “Polarized light in coastal waters: hyperspectral and multiangular analysis,” Opt. Express 17, 5666–5682 (2009).
[CrossRef] [PubMed]

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[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).
[PubMed]

N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exp. Biol. 207, 3619–3628 (2004).
[CrossRef] [PubMed]

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[CrossRef]

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

J. Opt. Soc. Am. A

J. Phys. Oceanogr.

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

Limnol. Oceanogr.

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]

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[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

Proc. SPIE

A. Tonizzo, J. Zhou, A. Gilerson, B. Gross, F. Moshary and S. Ahmed, “The impact of algal fluorescence on the underwater polarized light field,” Proc. SPIE 7678, 76780K (2010).
[CrossRef]

Science

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

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J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610(1974).
[CrossRef]

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

Other

A. Ivanoff, “Polarization measurements in the sea,” in Optical Aspects of Oceanography, N.Jerlov and E.Nielsen, eds. (Academic, 1974), pp. 151–176.

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), Vol.  1, pp. 123–176.

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Figures (21)

Fig. 1
Fig. 1

Photos of the two polarization instruments during deployment in the clear oceanic stations: (a) CCNY polarimeter taking near-surface measurements and (b) diver-operated UT video polarimeter. (Photos by Erich Schlegel.) (c) Viewing geometries for both polarimeters (arrows indicate instrument orientations).

Fig. 2
Fig. 2

(a) Locations of the two field stations in the Gulf of Mexico (magenta circles) overlain on satellite-derived mean chlorophyll a distributions for the month of June 2010 from the MODIS Aqua sensor. (b) and (c) Normalized radiance for the two locations at 7 and 1 m depth and extrapolated to the surface ( 0 ). Inset in (b) and (c) is the normalized radiance spectra for the two locations at 1 m , measured and simulated with Hydrolight (elastic and with Raman and chlorophyll fluorescence components).

Fig. 3
Fig. 3

(a) and (b) Particulate and CDOM absorption ( a pg ) and attenuation ( c pg ) spectra measured using the WET Labs ac-9–MASCOT package at stations B1, B4, and A1. Error bars represent 1 standard deviation of the mean value obtained during each measurement. (c) and (d) Vertical profiles of a pg and c pg for selected wavelengths at station A1. (e) and (f) Same as (c) and (d), but for station B1.

Fig. 4
Fig. 4

(a)  β ( θ ) measured at selected stations using the MASCOT. Error bars show vertical variations. (b) Comparison of the MASCOT-measured β ( θ ) , a 0 ° to 180 ° extrapolated β ( θ ) function based on the MASCOT measurement, a scaled H-G phase function, and a scaled Petzold phase function.

Fig. 5
Fig. 5

(a)–(i) DoLP patterns from CCNY measurements and from simulations at ac-9 wavelengths for station B1; the vertical dashed line indicates the angle that corresponds to a 94 ° scattering angle; the vertical dotted line indicates the edge of Snell’s window, with angles within the window to its left. Details of this station can be found in Table 1 and are listed in the figure title for convenience, where SE stands for solar elevation, VA stands for viewing azimuth, and z is the detector depth. (j)–(r) Standard deviations for the DoLP measurements at ac-9 wavelengths for station B1.

Fig. 6
Fig. 6

DoLP spectra from simulations (solid curves) and from CCNY polarimeter measurements (dashed curves) at relevant instrument angles for station B2. Measured data points at 715 nm for station B2 are not shown due to substantial uncertainties in this case.

Fig. 7
Fig. 7

Same as Figs. 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h, 5i, but with a fixed wavelength ( 510 nm ) and various combinations of SE and VA angles. The water IOPs and VSFs were similar for all six stations.

Fig. 8
Fig. 8

Same as Fig. 7, but for stations B7 to B8 (larger depth) and A1 to A4 (slightly more turbid water body and higher sea state condition).

Fig. 9
Fig. 9

(a) Direct comparison of DoLP at 10 m , from UT video polarimeter measurements and from simulations. (b)–(d) Model-simulated and measured DoLP as a function of the viewing azimuth angle for selected instrument angles.

Fig. 10
Fig. 10

Normalized Stokes components Q / I (top panels) and U / I (middle panels) from measurement and simulation at stations B3, B5, and B6. The radiance (I component) patterns are also shown in the bottom panels for reference.

Fig. 11
Fig. 11

Same as Fig. 10, but for stations A2, B7, and B8.

Fig. 12
Fig. 12

Two definitions of the AoLP when looking into the direction of light propagation: (a) varying from 90 ° to 90 ° [20]; (b) varying from 0 ° to 180 ° [16].

Fig. 13
Fig. 13

Similar to Figs. 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h, 5i, but showing the comparison of measured and simulated AoLP at all nine wavelengths for station B2. The AoLP is defined from 90 ° to 90 ° , as shown in Fig. 12a.

Fig. 14
Fig. 14

AoLP outside the principal plane from CCNY polarimeter measurements (dashed curve with symbols) and from simulations (solid curves), with various solar elevation angles, viewing azimuth angles, and instrument depths. The AoLP is defined from 90 ° to 90 ° , as shown in Fig. 12a.

Fig. 15
Fig. 15

Same as Fig. 9, but shows the AoLP [defined from 0 ° to 180 ° , as shown in Fig. 12b].

Fig. 16
Fig. 16

Measured DoLP (symbols) at selected stations as a function of the scattering angle. Black crosses indicate viewing angles out of Snell’s cone; red circles indicate viewing angles in Snell’s cone. Predictions by single-scattering approximations are also shown for comparison. Gray solid curves, without Fresnel refraction; blue dashed curves, with Fresnel refraction. Both are rescaled to match the maximum value in the measurements.

Fig. 17
Fig. 17

Same as Fig. 16, but shows measured AoLP at selected non-principal-plane stations as compared with single-scattering approximations.

Fig. 18
Fig. 18

Effects of multiple scattering on the in-water DoLP pattern as a function of the scattering angle. The order of scattering is denoted by n. Geometries and optical properties for station B1 are used.

Fig. 19
Fig. 19

DoLP as a function of the scattering angle for various solar elevations at 1 m below surface in the clear water case (water IOPs and VSF from station B1). (a) Viewing azimuth = 0 ° , (b) viewing azimuth = 90 ° , and (c) viewing azimuth = 180 ° .

Fig. 20
Fig. 20

Same as Fig. 18, but shows DoLP and AoLP for various detector depths and water turbidities. (a) and (c) Clear water (water IOPs and VSF from station B1), and (b) and (d) turbid water (water IOPs and VSF from station A1). Solid curves, detector at 1 m below surface; dotted curves, 7 m below surface.

Fig. 21
Fig. 21

Simulated DoLP and AoLP along the horizontal viewing direction (an instrument angle of 0 ° ) at various detector depths in the clear and turbid water conditions as a function of the viewing azimuth angle. Solid curves, solar elevation = 20 ° ; dotted curves, solar elevation = 75 ° .

Tables (2)

Tables Icon

Table 1 Relevant Parameters for the Two Stations

Tables Icon

Table 2 Comparisons of the Particulate Scattering Coefficient b p Derived from the Extended VSFs and that Derived from ac-9 Measurements ( c pg a pg for b p )

Equations (10)

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

DoLP = Q 2 + U 2 I .
tan ( 2 χ ) = U Q .
S 12 / S 11 = ( 1 ρ ) ( μ 2 1 ) ( 1 + μ 2 ) + ( 3 μ 2 ) ρ , S 22 / S 11 = ( 1 ρ ) ( μ 2 + 1 ) ( 1 + μ 2 ) + ( 3 μ 2 ) ρ , S 33 / S 11 = 2 ( 1 ρ ) μ ( 1 + μ 2 ) + ( 3 μ 2 ) ρ , S 44 / S 11 = 2 ( 1 3 ρ ) μ ( 1 + μ 2 ) + ( 3 μ 2 ) ρ .
I ( θ , ϕ ) = L ( σ 2 ) · P ( Θ ) · L ( σ 1 ) · I 0 ,
L ( σ ) = [ 1 0 0 0 0 cos ( 2 σ ) sin ( 2 σ ) 0 0 sin ( 2 σ ) cos ( 2 σ ) 0 0 0 0 1 ] .
cos σ 1 = cos θ 2 cos θ 1 cos Θ sin θ 1 sin Θ , cos σ 2 = cos θ 1 cos θ 2 cos Θ sin θ 2 sin Θ ,
I ( θ , ϕ ) = [ S 11 ( Θ ) , S 12 ( Θ ) cos ( 2 σ 2 ) , S 12 ( Θ ) sin ( 2 σ 2 ) , 0 ] T
F = [ 1 2 ( a 2 + b 2 ) 1 2 ( a 2 b 2 ) 0 0 1 2 ( a 2 b 2 ) 1 2 ( a 2 + b 2 ) 0 0 0 0 a b 0 0 0 0 a b ] ,
a = 2 cos θ i n cos θ i + cos θ r , b = 2 cos θ i cos θ i + n cos θ r ,
I ( θ , ϕ ) = L ( σ 2 ) · P ( Θ ) · L ( σ 1 ) · F · I 0 .

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