Abstract

The geometrical attenuation model given by Blinn was widely used in the geometrical optics bidirectional reflectance distribution function (BRDF) models. Blinn’s geometrical attenuation model based on symmetrical V-groove assumption and ray scalar theory causes obvious inaccuracies in BRDF curves and negatives the effects of polarization. Aiming at these questions, a modified polarized geometrical attenuation model based on random surface microfacet theory is presented by combining of masking and shadowing effects and polarized effect. The p-polarized, s-polarized and unpolarized geometrical attenuation functions are given in their separate expressions and are validated with experimental data of two samples. It shows that the modified polarized geometrical attenuation function reaches better physical rationality, improves the precision of BRDF model, and widens the applications for different polarization.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2009 (1)

2008 (1)

2007 (3)

2006 (1)

D. Wellems, S. Ortega, D. Bowers, J. Boger, and M. Fetrow, “Long wave infrared polarimetric model: theory, measurements and parameters,” J. Opt. A: Pure Appl. Opt. 8(10), 914–925 (2006).
[Crossref]

2004 (1)

O. G. Cula and K. J. Dana, “3D texture recognition using bidirectional feature histograms,” Int. J. Comput. Vis. 59, 33–60 (2004).
[Crossref]

2002 (1)

R. G. Priest and S. R. Meier, “Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces,” Opt. Eng. 41(5), 988–993 (2002).
[Crossref]

1984 (1)

1967 (1)

1965 (1)

F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4(7), 368–377 (1965).
[Crossref]

Arko, S. A.

D. Wellems, M. Serna, S. H. Sposato, M. P. Fetrow, K. P. Bishop, S. A. Arko, and T. R. Caudill, “Spectral polarimetric BRDF model and comparison to measurements from isotropic roughened glass,” in Workshop on Multi/Hyperspectral Sensors, Measurements, Modeling and Simulation (U.S. Army Aviation and Missile Command, Huntsville, AL, 2000).

Barta, A.

Bassukas, I.

Beard, J.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional Reflectance Model Validation and Utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Bernath, B.

Bishop, K. P.

D. Wellems, M. Serna, S. H. Sposato, M. P. Fetrow, K. P. Bishop, S. A. Arko, and T. R. Caudill, “Spectral polarimetric BRDF model and comparison to measurements from isotropic roughened glass,” in Workshop on Multi/Hyperspectral Sensors, Measurements, Modeling and Simulation (U.S. Army Aviation and Missile Command, Huntsville, AL, 2000).

Bishop., Kenneth P

Matthew P Fetrow., David Wellems., Stephanie H Sposato., Kenneth P Bishop., Thomas R Caudill., Michael L Davis., and Elizabeth R Simrell., “Results of a new polarization simulation,” in Proc. SPIE, vol. 4481, pp. 149–162 (The International Society for Optical Engineering (SPIE), 2001).
[Crossref]

Blinn., James

James Blinn., “Models of light reflection for computer synthesized pictures,” in ACM SIGGRAPH 1977 Proceedings, vol.11 pp. 192–198, International Conference on Computer Graphics and Interactive Techniques (Computer Graphics1977).

Boger, J.

D. Wellems, S. Ortega, D. Bowers, J. Boger, and M. Fetrow, “Long wave infrared polarimetric model: theory, measurements and parameters,” J. Opt. A: Pure Appl. Opt. 8(10), 914–925 (2006).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, NY, 1999).
[Crossref]

Bowers, D.

D. Wellems, S. Ortega, D. Bowers, J. Boger, and M. Fetrow, “Long wave infrared polarimetric model: theory, measurements and parameters,” J. Opt. A: Pure Appl. Opt. 8(10), 914–925 (2006).
[Crossref]

Caudill, T. R.

D. Wellems, M. Serna, S. H. Sposato, M. P. Fetrow, K. P. Bishop, S. A. Arko, and T. R. Caudill, “Spectral polarimetric BRDF model and comparison to measurements from isotropic roughened glass,” in Workshop on Multi/Hyperspectral Sensors, Measurements, Modeling and Simulation (U.S. Army Aviation and Missile Command, Huntsville, AL, 2000).

Caudill., Thomas R

Matthew P Fetrow., David Wellems., Stephanie H Sposato., Kenneth P Bishop., Thomas R Caudill., Michael L Davis., and Elizabeth R Simrell., “Results of a new polarization simulation,” in Proc. SPIE, vol. 4481, pp. 149–162 (The International Society for Optical Engineering (SPIE), 2001).
[Crossref]

Cook, R. L.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” in SIGGRAPH 1981 Proceedings, vol. 15, pp. 307–316, Special Interest Group on Graphics and Interactive Techniques (Computer Graphics, 1981).
[Crossref]

Cula, O. G.

O. G. Cula and K. J. Dana, “3D texture recognition using bidirectional feature histograms,” Int. J. Comput. Vis. 59, 33–60 (2004).
[Crossref]

Dana, K. J.

O. G. Cula and K. J. Dana, “3D texture recognition using bidirectional feature histograms,” Int. J. Comput. Vis. 59, 33–60 (2004).
[Crossref]

Davis., Michael L

Matthew P Fetrow., David Wellems., Stephanie H Sposato., Kenneth P Bishop., Thomas R Caudill., Michael L Davis., and Elizabeth R Simrell., “Results of a new polarization simulation,” in Proc. SPIE, vol. 4481, pp. 149–162 (The International Society for Optical Engineering (SPIE), 2001).
[Crossref]

Dimou, A.

Fetrow, M.

D. Wellems, S. Ortega, D. Bowers, J. Boger, and M. Fetrow, “Long wave infrared polarimetric model: theory, measurements and parameters,” J. Opt. A: Pure Appl. Opt. 8(10), 914–925 (2006).
[Crossref]

Fetrow, M. P.

D. Wellems, M. Serna, S. H. Sposato, M. P. Fetrow, K. P. Bishop, S. A. Arko, and T. R. Caudill, “Spectral polarimetric BRDF model and comparison to measurements from isotropic roughened glass,” in Workshop on Multi/Hyperspectral Sensors, Measurements, Modeling and Simulation (U.S. Army Aviation and Missile Command, Huntsville, AL, 2000).

Fetrow., Matthew P

Matthew P Fetrow., David Wellems., Stephanie H Sposato., Kenneth P Bishop., Thomas R Caudill., Michael L Davis., and Elizabeth R Simrell., “Results of a new polarization simulation,” in Proc. SPIE, vol. 4481, pp. 149–162 (The International Society for Optical Engineering (SPIE), 2001).
[Crossref]

Germer, T. A.

R. G. Priest and T. A. Germer, “Polarimetric BRDF in the microfacet model: theory and measurements,” in Proceedings of the 2000 Meeting of the Military Sensing Symposia Specialty Group on Passive Sensors, pp. 169–181 (Infrared Information Analysis Center, 2000).

Greenberg., Donald P

Xiao D He., Kenneth E Torrance., Francois X Sillion., and Donald P Greenberg., “A comprehensive physical model for light reflection,” in ACM SIGGRAPH 1991 Proceedings, vol. 25, pp. 175–186, Conference on computer graphics and interactive techniques (Computer Graphics1991).

Havrilla, M. J.

He., Xiao D

Xiao D He., Kenneth E Torrance., Francois X Sillion., and Donald P Greenberg., “A comprehensive physical model for light reflection,” in ACM SIGGRAPH 1991 Proceedings, vol. 25, pp. 175–186, Conference on computer graphics and interactive techniques (Computer Graphics1991).

Hegedus, R.

Horvath, G.

Hyde, M. W.

Kimes, D. S.

Ladd, D.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional Reflectance Model Validation and Utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Ladd, S.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional Reflectance Model Validation and Utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Maxwell, J. R.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional Reflectance Model Validation and Utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Meier, S. R.

R. G. Priest and S. R. Meier, “Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces,” Opt. Eng. 41(5), 988–993 (2002).
[Crossref]

Meyer-Rochow, V. B.

Nicodemus, F. E.

F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4(7), 368–377 (1965).
[Crossref]

Ortega, S.

D. Wellems, S. Ortega, D. Bowers, J. Boger, and M. Fetrow, “Long wave infrared polarimetric model: theory, measurements and parameters,” J. Opt. A: Pure Appl. Opt. 8(10), 914–925 (2006).
[Crossref]

Priest, R. G.

R. G. Priest and S. R. Meier, “Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces,” Opt. Eng. 41(5), 988–993 (2002).
[Crossref]

R. G. Priest and T. A. Germer, “Polarimetric BRDF in the microfacet model: theory and measurements,” in Proceedings of the 2000 Meeting of the Military Sensing Symposia Specialty Group on Passive Sensors, pp. 169–181 (Infrared Information Analysis Center, 2000).

Schmidt, J. D.

Serna, M.

D. Wellems, M. Serna, S. H. Sposato, M. P. Fetrow, K. P. Bishop, S. A. Arko, and T. R. Caudill, “Spectral polarimetric BRDF model and comparison to measurements from isotropic roughened glass,” in Workshop on Multi/Hyperspectral Sensors, Measurements, Modeling and Simulation (U.S. Army Aviation and Missile Command, Huntsville, AL, 2000).

Sillion., Francois X

Xiao D He., Kenneth E Torrance., Francois X Sillion., and Donald P Greenberg., “A comprehensive physical model for light reflection,” in ACM SIGGRAPH 1991 Proceedings, vol. 25, pp. 175–186, Conference on computer graphics and interactive techniques (Computer Graphics1991).

Simrell., Elizabeth R

Matthew P Fetrow., David Wellems., Stephanie H Sposato., Kenneth P Bishop., Thomas R Caudill., Michael L Davis., and Elizabeth R Simrell., “Results of a new polarization simulation,” in Proc. SPIE, vol. 4481, pp. 149–162 (The International Society for Optical Engineering (SPIE), 2001).
[Crossref]

Sparrow, E. M.

Sposato, S. H.

D. Wellems, M. Serna, S. H. Sposato, M. P. Fetrow, K. P. Bishop, S. A. Arko, and T. R. Caudill, “Spectral polarimetric BRDF model and comparison to measurements from isotropic roughened glass,” in Workshop on Multi/Hyperspectral Sensors, Measurements, Modeling and Simulation (U.S. Army Aviation and Missile Command, Huntsville, AL, 2000).

Sposato., Stephanie H

Matthew P Fetrow., David Wellems., Stephanie H Sposato., Kenneth P Bishop., Thomas R Caudill., Michael L Davis., and Elizabeth R Simrell., “Results of a new polarization simulation,” in Proc. SPIE, vol. 4481, pp. 149–162 (The International Society for Optical Engineering (SPIE), 2001).
[Crossref]

Torrance, K. E.

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57(9), 1105–1114 (1967).
[Crossref]

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” in SIGGRAPH 1981 Proceedings, vol. 15, pp. 307–316, Special Interest Group on Graphics and Interactive Techniques (Computer Graphics, 1981).
[Crossref]

Torrance., Kenneth E

Xiao D He., Kenneth E Torrance., Francois X Sillion., and Donald P Greenberg., “A comprehensive physical model for light reflection,” in ACM SIGGRAPH 1991 Proceedings, vol. 25, pp. 175–186, Conference on computer graphics and interactive techniques (Computer Graphics1991).

Weiner, S.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional Reflectance Model Validation and Utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Wellems, D.

D. Wellems, S. Ortega, D. Bowers, J. Boger, and M. Fetrow, “Long wave infrared polarimetric model: theory, measurements and parameters,” J. Opt. A: Pure Appl. Opt. 8(10), 914–925 (2006).
[Crossref]

D. Wellems, M. Serna, S. H. Sposato, M. P. Fetrow, K. P. Bishop, S. A. Arko, and T. R. Caudill, “Spectral polarimetric BRDF model and comparison to measurements from isotropic roughened glass,” in Workshop on Multi/Hyperspectral Sensors, Measurements, Modeling and Simulation (U.S. Army Aviation and Missile Command, Huntsville, AL, 2000).

Wellems., David

Matthew P Fetrow., David Wellems., Stephanie H Sposato., Kenneth P Bishop., Thomas R Caudill., Michael L Davis., and Elizabeth R Simrell., “Results of a new polarization simulation,” in Proc. SPIE, vol. 4481, pp. 149–162 (The International Society for Optical Engineering (SPIE), 2001).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, NY, 1999).
[Crossref]

Xia, J.

Yao, G.

Yinlong, Sun

Sun Yinlong, “Statistical ray method for deriving reflection models of rough surfaces,” J. Opt. Soc. Am. A. 24(3), 724–744 (2007).
[Crossref]

Zonios, G.

Appl. Opt. (4)

Int. J. Comput. Vis. (1)

O. G. Cula and K. J. Dana, “3D texture recognition using bidirectional feature histograms,” Int. J. Comput. Vis. 59, 33–60 (2004).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

D. Wellems, S. Ortega, D. Bowers, J. Boger, and M. Fetrow, “Long wave infrared polarimetric model: theory, measurements and parameters,” J. Opt. A: Pure Appl. Opt. 8(10), 914–925 (2006).
[Crossref]

J. Opt. Soc. Am. (1)

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

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

Sun Yinlong, “Statistical ray method for deriving reflection models of rough surfaces,” J. Opt. Soc. Am. A. 24(3), 724–744 (2007).
[Crossref]

Opt. Eng. (1)

R. G. Priest and S. R. Meier, “Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces,” Opt. Eng. 41(5), 988–993 (2002).
[Crossref]

Opt. Express (1)

Other (8)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, New York, NY, 1999).
[Crossref]

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional Reflectance Model Validation and Utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Matthew P Fetrow., David Wellems., Stephanie H Sposato., Kenneth P Bishop., Thomas R Caudill., Michael L Davis., and Elizabeth R Simrell., “Results of a new polarization simulation,” in Proc. SPIE, vol. 4481, pp. 149–162 (The International Society for Optical Engineering (SPIE), 2001).
[Crossref]

R. G. Priest and T. A. Germer, “Polarimetric BRDF in the microfacet model: theory and measurements,” in Proceedings of the 2000 Meeting of the Military Sensing Symposia Specialty Group on Passive Sensors, pp. 169–181 (Infrared Information Analysis Center, 2000).

D. Wellems, M. Serna, S. H. Sposato, M. P. Fetrow, K. P. Bishop, S. A. Arko, and T. R. Caudill, “Spectral polarimetric BRDF model and comparison to measurements from isotropic roughened glass,” in Workshop on Multi/Hyperspectral Sensors, Measurements, Modeling and Simulation (U.S. Army Aviation and Missile Command, Huntsville, AL, 2000).

James Blinn., “Models of light reflection for computer synthesized pictures,” in ACM SIGGRAPH 1977 Proceedings, vol.11 pp. 192–198, International Conference on Computer Graphics and Interactive Techniques (Computer Graphics1977).

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” in SIGGRAPH 1981 Proceedings, vol. 15, pp. 307–316, Special Interest Group on Graphics and Interactive Techniques (Computer Graphics, 1981).
[Crossref]

Xiao D He., Kenneth E Torrance., Francois X Sillion., and Donald P Greenberg., “A comprehensive physical model for light reflection,” in ACM SIGGRAPH 1991 Proceedings, vol. 25, pp. 175–186, Conference on computer graphics and interactive techniques (Computer Graphics1991).

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Figures (13)

Fig. 1
Fig. 1 Geometry of BRDF. Illuminated surface is in the XY plane, surface normal is in Z direction. θi and θr are the zenith angles of incident and reflect light respectively, ϕi and ϕr are their azimuth angles, and ϕ = |ϕiϕr|. α is the polar angle from the mean surface normal Z to the microfacet normal n, θ is the incident angle as measured from the microfacet.
Fig. 2
Fig. 2 Geometrical attenuation effect of Blinn’s symmetrical V-shaped groove assumption.
Fig. 3
Fig. 3 (a) Blinn’s G function curves. (b)T-S fs curves with Blinn’s G when σ=0.25.
Fig. 4
Fig. 4 Three submodels of the masking factor assumption.
Fig. 5
Fig. 5 Three submodels of the shadowing factor assumption.
Fig. 6
Fig. 6 Blinn’s G and modified G curves with different roughness when θi=0°.
Fig. 7
Fig. 7 Fresnel’s reflection.
Fig. 8
Fig. 8 (a) Fresnel reflectance for n=1.8. (b) Fresnel reflectance for n*=1.5+3i.
Fig. 9
Fig. 9 Rs, Rp and Runpol factors when θi=30° for (a) n=1.8 and (b) n*=1.5+3i.
Fig. 10
Fig. 10 Normalized Gs, Gp, Gunpol and Blinn’s G curves when σ=0.5 and n=1.8.
Fig. 11
Fig. 11 Normalized Gs, Gp, Gunpol and Blinn’s G curves when σ=0.5 and n*=1.5+3i.
Fig. 12
Fig. 12 Simulated and measured BRDF of ZnO sample 1.
Fig. 13
Fig. 13 Simulated and measured BRDF of ZnO sample 2.

Equations (31)

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BRDF ( θ i , θ r , ϕ i , ϕ r ) = f ( θ i , θ r , ϕ i , ϕ r ) = d L r ( θ r , ϕ r ) d E i ( θ i , ϕ i ) ( s r 1 )
p ( α ) = C 2 π σ 2 cos 3 α exp ( tan 2 α 2 σ 2 )
f s ( θ i , θ r , ϕ ) = 1 2 π 1 4 σ 2 1 cos 4 α 1 cos θ r cos θ i exp ( tan 2 α 2 σ 2 ) G ( θ i , θ r , ϕ )
cos α = ( cos θ i + cos θ r ) / ( 2 cos θ )
cos 2 θ = cos θ i cos θ r + sin θ i sin θ r cos ϕ
G ( θ i , θ r , ϕ ) = min ( 1 ; 2 cos α cos θ r cos θ ; 2 cos α cos θ i cos θ )
P 1 ( θ r , σ ) = 0 π 2 θ r p ( γ ) d γ
g M 1 ( θ r , σ ) = 0 π 2 θ r 1 p ( γ ) d γ
g M 2 ( θ r , σ ) = π 2 θ r + α π 2 0 p ( γ ) d γ = 0
a a + b = sin α tan θ r + cos α + cos γ sin γ tan θ r sin α tan θ r + cos α
g M 3 ( θ r , σ ) = π 2 θ r π 2 2 θ r + α P ( γ ) a a + b d γ = π 2 θ r π 2 2 θ r + α P ( γ ) sin α tan θ r + cos α + cos γ sin γ tan θ r sin α tan θ r + cos α d γ
g M ( θ r , σ ) = g M 1 + g M 2 + g M 3 = π 2 π 2 θ r p ( γ ) d γ + π 2 θ r π 2 2 θ r + α P ( γ ) sin α tan θ r + cos α + cos γ sin γ tan θ r sin α tan θ r + cos α d γ
g S 1 ( θ i , σ ) = 0 π 2 θ i 1 p ( γ ) d γ
g S 2 ( θ i , σ ) = π 2 θ i + α π 2 0 p ( γ ) d γ = 0
a a + b = cos α cot θ i + cos γ cot θ i + sin α sin γ cos α cot θ i + sin α
g S 3 ( θ i , σ ) = π 2 θ i π 2 θ i + α P ( γ ) a a + b d γ = π 2 θ i π 2 θ i + α P ( γ ) cos α cot θ i + cos γ cot θ i + sin α sin γ cos α cot θ i + sin α d γ
g S ( θ i , σ ) = g S 1 + g S 2 + g S 3 = π 2 π 2 θ i p ( γ ) d γ + π 2 θ i π 2 θ i + α P ( γ ) cos α cot θ i + cos γ cot θ i + sin α sin γ cos α cot θ i + sin α d γ
g ( θ i , θ r , σ ) = min [ g M ( θ r , σ ) , g S ( θ i , σ ) ]
n = n 2 n 1
r s s = E s r E s i = ( n 2 sin 2 θ ) 1 2 cos θ ( n 2 sin 2 θ ) 1 2 + cos θ
r p p = E p r E p i = n 2 cos θ ( n 2 sin 2 θ ) 1 2 n 2 cos θ + ( n 2 sin 2 θ ) 1 2
R s = | r s s 2 |
R p = | r p p 2 |
R unpol = 1 2 ( R s + R s )
θ = 1 2 | θ i + θ r |
R s ( θ i , θ r , n ) = [ ( n 2 sin 2 | θ i + θ r | 2 ) 1 2 cos | θ i + θ r | 2 ( n 2 sin 2 | θ i + θ r | 2 ) 1 2 + cos | θ i + θ r | 2 ] 2
R p ( θ i , θ r , n ) = [ n 2 cos | θ i + θ r | 2 ( n 2 sin 2 | θ i + θ r | 2 ) 1 2 n 2 cos | θ i + θ r | 2 + ( n 2 sin 2 | θ i + θ r | 2 ) 1 2 ] 2
R unpol ( θ i , θ r , n ) = R s ( θ i , θ r , n ) + R p ( θ i , θ r , n ) 2
G s ( θ i , θ r , σ , n ) = g ( θ i , θ r , σ ) R s ( θ i , θ r , n )
G p ( θ i , θ r , σ , n ) = g ( θ i , θ r , σ ) R p ( θ i , θ r , n )
G unpol ( θ i , θ r , σ , n ) = g ( θ i , θ r , σ ) R unpol ( θ i , θ r , n )

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