Abstract

The Multiangle Imaging Spectroradiometer makes use of an onboard calibration system that includes two Spectralon panels that are used to reflect sunlight into the cameras. During preflight testing, these panels were quantified in terms of their bidirectional reflectance distribution function, which was measured as a function of the source-incident and detector view angles and at laser wavelengths of 442.0, 632.8, and 859.9 nm. Principal plane measurements are presented in which polarizations of the source and detector are analyzed. These data are unique and valuable in modeling Spectralon reflectance properties and for experiments in which polarization sensitivities are important.

© 1999 Optical Society of America

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    [CrossRef]
  2. C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the Multi-angle Imaging SpectroRadiometer (MISR),” Metrologia 30, 213–221 (1993).
    [CrossRef]
  3. C. J. Bruegge, N. L. Chrien, D. A. Haner, “A Spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. (to be published).
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    [CrossRef]
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    [CrossRef]
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1998 (2)

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

D. A. Haner, B. T. McGuckin, R. T. Menzies, C. J. Bruegge, V. Duval, “Directional–hemispherical reflectance for Spectralon by integration of its bidirectional reflectance,” Appl. Opt. 37, 3996–3999 (1998).
[CrossRef]

1997 (1)

1996 (1)

1993 (2)

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, A. W. Springstein, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805–814 (1993).
[CrossRef]

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the Multi-angle Imaging SpectroRadiometer (MISR),” Metrologia 30, 213–221 (1993).
[CrossRef]

1989 (1)

1969 (2)

D. C. Cramer, M. E. Blair, “Some polarization characteristics of magnesium oxide and other diffuse reflectors,” Appl. Opt. 8, 1597–1605 (1969).
[CrossRef]

K. E. Torrance, “Theoretical polarization of off-specular reflection peaks,” J. Heat Transfer 91, 287–290 (1969).
[CrossRef]

1968 (1)

1967 (1)

1966 (1)

Ackerman, T. P.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Barnes, R. A.

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

Beckert, J. C.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Biggar, S. F.

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

Birkebak, R. C.

Blair, M. E.

Brothers, A. M.

Bruegge, C. J.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

D. A. Haner, B. T. McGuckin, R. T. Menzies, C. J. Bruegge, V. Duval, “Directional–hemispherical reflectance for Spectralon by integration of its bidirectional reflectance,” Appl. Opt. 37, 3996–3999 (1998).
[CrossRef]

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the Multi-angle Imaging SpectroRadiometer (MISR),” Metrologia 30, 213–221 (1993).
[CrossRef]

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, A. W. Springstein, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805–814 (1993).
[CrossRef]

S. P. Flasse, M. M. Verstraete, B. Pinty, C. J. Bruegge, “Modeling Spectralon’s bidirectional reflectance for in-flight calibration of Earth-orbiting sensors,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, A. Schowengerdt, eds., Proc. SPIE1938, 100–108 (1993).
[CrossRef]

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

C. J. Bruegge, N. L. Chrien, D. A. Haner, “A Spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. (to be published).

Butler, J. J.

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

Chrien, N. L.

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the Multi-angle Imaging SpectroRadiometer (MISR),” Metrologia 30, 213–221 (1993).
[CrossRef]

C. J. Bruegge, N. L. Chrien, D. A. Haner, “A Spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. (to be published).

Conel, J. E.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Cramer, D. C.

Davies, R.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Diner, D. J.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the Multi-angle Imaging SpectroRadiometer (MISR),” Metrologia 30, 213–221 (1993).
[CrossRef]

Duval, V.

Duval, V. G.

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the Multi-angle Imaging SpectroRadiometer (MISR),” Metrologia 30, 213–221 (1993).
[CrossRef]

Early, E. A.

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

Egan, W. G.

Esproles, C.

Flasse, S. P.

S. P. Flasse, M. M. Verstraete, B. Pinty, C. J. Bruegge, “Modeling Spectralon’s bidirectional reflectance for in-flight calibration of Earth-orbiting sensors,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, A. Schowengerdt, eds., Proc. SPIE1938, 100–108 (1993).
[CrossRef]

Gerstl, S. A. W.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Ginsburg, I. W.

F. E. Nicodemus, J. C. Richmmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. GPO, Washington, D.C., 1977).

Gordon, H. R.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Grusauskas, J.

Hallock, H. B.

Haner, D. A.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. GPO, Washington, D.C., 1977).

Johnson, B. C.

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

Kahn, R.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. GPO, Washington, D.C., 1977).

Martonchik, J. V.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

McCoyd, G. C.

McGuckin, B. T.

Menzies, R. T.

Muller, J.-P.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Myneni, R.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. GPO, Washington, D.C., 1977).

Pavlov, M. M.

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

Pinty, B.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

S. P. Flasse, M. M. Verstraete, B. Pinty, C. J. Bruegge, “Modeling Spectralon’s bidirectional reflectance for in-flight calibration of Earth-orbiting sensors,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, A. Schowengerdt, eds., Proc. SPIE1938, 100–108 (1993).
[CrossRef]

Rainen, R. A.

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, A. W. Springstein, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805–814 (1993).
[CrossRef]

Reilly, T. H.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Richmmond, J. C.

F. E. Nicodemus, J. C. Richmmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. GPO, Washington, D.C., 1977).

Sellers, R. J.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

Sparrow, E. M.

Springstein, A. W.

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, A. W. Springstein, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805–814 (1993).
[CrossRef]

Spyak, P. R.

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

Stiegman, A. E.

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, A. W. Springstein, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805–814 (1993).
[CrossRef]

Torrance, K. E.

Verstraete, M. M.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

S. P. Flasse, M. M. Verstraete, B. Pinty, C. J. Bruegge, “Modeling Spectralon’s bidirectional reflectance for in-flight calibration of Earth-orbiting sensors,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, A. Schowengerdt, eds., Proc. SPIE1938, 100–108 (1993).
[CrossRef]

Walker, J. A.

J. A. Walker, “Models and validation measurements of bidirectional reflectance factor for diffuse reflecting materials,” (M.S. thesis, Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998).

Appl. Opt. (6)

IEEE Trans. Geosci. Remote Sens. (1)

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J.-P. Muller, R. Myneni, R. J. Sellers, B. Pinty, M. M. Verstraete, “Multiangle Imaging SpectroRadiometer (MISR) description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[CrossRef]

J. Heat Transfer (1)

K. E. Torrance, “Theoretical polarization of off-specular reflection peaks,” J. Heat Transfer 91, 287–290 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

Metrologia (1)

C. J. Bruegge, V. G. Duval, N. L. Chrien, D. J. Diner, “Calibration plans for the Multi-angle Imaging SpectroRadiometer (MISR),” Metrologia 30, 213–221 (1993).
[CrossRef]

Opt. Eng. (1)

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, A. W. Springstein, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805–814 (1993).
[CrossRef]

Other (5)

C. J. Bruegge, N. L. Chrien, D. A. Haner, “A Spectralon BRF data base for MISR calibration applications,” Remote Sens. Environ. (to be published).

E. A. Early, R. A. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. R. Spyak, M. M. Pavlov, “Bi-directional reflectance round robin in support of the Earth Observing System program,” J. Atmos. Oceanic Technol. (to be published).

S. P. Flasse, M. M. Verstraete, B. Pinty, C. J. Bruegge, “Modeling Spectralon’s bidirectional reflectance for in-flight calibration of Earth-orbiting sensors,” in Recent Advances in Sensors, Radiometric Calibration, and Processing of Remotely Sensed Data, P. S. Chavez, A. Schowengerdt, eds., Proc. SPIE1938, 100–108 (1993).
[CrossRef]

J. A. Walker, “Models and validation measurements of bidirectional reflectance factor for diffuse reflecting materials,” (M.S. thesis, Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998).

F. E. Nicodemus, J. C. Richmmond, J. J. Hsia, I. W. Ginsburg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. GPO, Washington, D.C., 1977).

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Figures (7)

Fig. 1
Fig. 1

Optical setup in which s is the reflecting surface, d is the polarization-sensitive detector, and B is the polarized incident beam. Subscript i is the incident angles and r is the reflecting angles. The z axis is coincident with the surface normal, θ is the elevation angle with respect to the surface normal, and ϕ is the azimuthal angle defined with respect to the incident beam.

Fig. 2
Fig. 2

BDRF as a function of polarization at 442.0 nm for a range of detector angles. Negative values correspond to backward scattering angles. ϕ r = 0°; —, f ss ; —-, f sp ; ×××, f pp ; +++, f ps ; and … , f ideal.

Fig. 3
Fig. 3

Fraction polarization at 442.0 nm as a function of the detector angle. Negative values correspond to backward-scattering angles. ϕ r = 0°; —, P s ; —–, P p ; and +++, P u .

Fig. 4
Fig. 4

BDRF as a function of polarization at 632.8 nm for a range of detector angles. Negative values correspond to backward-scattering angles. —, f ss ; —-, f sp ; ×××, f pp ; +++, f ps ; and … , f ideal.

Fig. 5
Fig. 5

Fraction polarization at 632.8 nm as a function of the detector angle. Negative values correspond to backward-scattering angles. ϕ r = 0°; —, P s ; —–, P p ; and +++, P u .

Fig. 6
Fig. 6

BRDF as a function of polarization at 859.9 nm for a range of detector angles. Negative values correspond to backward-scattering angles. —, f ss ; —-, f sp ; ×××, f pp ; +++, f ps ; and … , f ideal.

Fig. 7
Fig. 7

Fraction polarization at 859.9 nm as a function of the detector angle. Negative values correspond to backward-scattering angles. ϕ r = 0°; —, P s ; —–, P p ; and +++, P u .

Equations (8)

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firθi, ϕi; θr, ϕr; λ=dLrθi, ϕi; θr, ϕr; Ei; λdEiθi, ϕi; λ.
fuuθi, ϕi; θr, ϕr; λ=dLsθi, ϕi; θr, ϕr; Eu; λdEuθi, ϕi; λ+dLpθi, ϕi; θr, ϕr; Eu; λdEuθi, ϕi; λ.
dEuθi, ϕi; λ=2dEsθi, ϕi; λ=2dEpθi, ϕi; λ,
fusθi, ϕi; θr, ϕr; λ=dLsθi, ϕi; θr, ϕr; Es; λ2dEsθi, ϕi; λ+dLpθi, ϕi; θr, ϕr; Ep; λ2dEpθi, ϕi; λ.
fsuθi, ϕi; θr, ϕr; λ=dLsθi, ϕi; θr, ϕr; Es; λdEsθi, ϕi; λ+dLpθi, ϕi; θr, ϕr; Es; λdEsθi, ϕi; λ.
Ps=fss-fspfss+fsp, Pp=fpp-fpsfpp+fps.
Pu=fss+fps-fpp+fspfss+fsp+fpp+fps.
firθi, ϕi; θr, ϕr; λ=Vrθi, ϕi; θr, ϕr; Es; λ/VrefVi,filter/Vref10NDΩd cos θr,

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