Abstract

Microfacet-based BRDF models are a common tool to describe light scattering from glossy surfaces. Apart from their wide-ranging applications in optics, such models also play a significant role in computer graphics for photorealistic rendering purposes. In this paper, we mainly investigate the computer graphics aspect of this technology, and present a polarisation-aware brute force simulation of light interaction with both single and multiple layered micro-facet surfaces. Such surface models are commonly used in computer graphics, but the resulting BRDF is ultimately often only approximated. Recently, there has been work to try to make these approximations more accurate, and to better understand the behaviour of existing analytical models. However, these brute force verification attempts still emitted the polarisation state of light and, as we found out, this renders them prone to mis-estimating the shape of the resulting BRDF lobe for some particular material types, such as smooth layered dielectric surfaces. For these materials, non-polarising computations can mis-estimate some areas of the resulting BRDF shape by up to 23%. But we also identified some other material types, such as dielectric layers over rough conductors, for which the difference turned out to be almost negligible. The main contribution of our work is to clearly demonstrate that the effect of polarisation is important for accurate simulation of certain material types, and that there are also other common materials for which it can apparently be ignored. As this required a BRDF simulator that we could rely on, a secondary contribution is that we went to considerable lengths to validate our software. We compare it against a state-of-art model from graphics, a library from optics, and also against ellipsometric measurements of real surface samples.

© 2017 Optical Society of America

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References

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2017 (1)

N. Holzschuch and R. Pacanowski, “A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction,” ACM Transactions on Graphics 36, 12 (2017).
[Crossref]

2016 (3)

M. M. Bagher, J. Snyder, and D. Nowrouzezahrai, “A non-parametric factor microfacet model for isotropic brdfs,” ACM Transaction on Graphics 35, 1–16 (2016).
[Crossref]

B. Raymond, G. Guennebaud, and P. Barla, “Multi-Scale Rendering of Scratched Materials using a Structured SV-BRDF Model,” ACM Transactions on Graphics 35, 54 (2016).
[Crossref]

E. Heitz, J. Hanika, E. D’Eon, and C. Dachsbacher, “Multiple-scattering microfacet BSDFs with the smith model,” ACM Transaction on Graphics 35, 1–14 (2016).
[Crossref]

2015 (3)

H. Liu, J. Zhu, and K. Wang, “Modified polarized geometrical attenuation model for bidirectional reflection distribution function based on random surface microfacet theory,” Opt. Express 23, 22788–22799 (2015).
[Crossref] [PubMed]

F. Wu and C. Zheng, “Microfacet-based interference simulation for multilayer films,” Graphical Models 78, 26–35 (2015).
[Crossref]

T. Ma, X. Hu, L. Zhang, J. Lian, X. He, Y. Wang, and Z. Xian, “An evaluation of skylight polarization patterns for navigation,” Sensors 15, 5895–5913 (2015).
[Crossref] [PubMed]

2014 (5)

C. Liu and J. Gu, “Discriminative illumination: Per-pixel classification of raw materials based on optimal projections of spectral brdf,” IEEE Transactions on Pattern Analysis and Machine Intelligence 36, 86–98 (2014).
[Crossref]

C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Discrete ordinate method for polarized light transport solution and subsurface BRDF computation,” Computers and Graphics 45, 17–27 (2014).
[Crossref]

E. Heitz, “Understanding the masking-shadowing function in microfacet-based BRDFs,” Journal of Computer Graphics Techniques 3, 48–107 (2014).

E. Heitz and E. D’Eon, “Importance sampling microfacet-based BSDFs using the distribution of visible normals,” Computer Graphics Forum 33, 103–112 (2014).
[Crossref]

W. Jakob, E. D’Eon, O. Jakob, and S. Marschner, “A comprehensive framework for rendering layered materials,” ACM Transaction on Graphics 33, 1–14 (2014).

2012 (1)

K. Berger, A. Wilkie, A. Weidlich, and M. Magnor, “Modeling and verifying the polarizing reflectance of real-world metallic surfaces,” Computer Graphics and Applications 32, 24–33 (2012).
[Crossref] [PubMed]

2011 (1)

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Transactions on Graphics 30, 129 (2011).
[Crossref]

2010 (1)

A. Ghosh, T. Chen, P. Peers, C. A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Transaction on Graphics 29, 1–12 (2010).
[Crossref]

2009 (1)

2008 (1)

C. Donner, T. Weyrich, E. d’Eon, R. Ramamoorthi, and S. Rusinkiewicz, “A layered, heterogeneous reflectance model for acquiring and rendering human skin,” ACM Transaction on Graphics 27, 1–12 (2008).
[Crossref]

2007 (1)

2003 (1)

X. Granier and W. Heidrich, “A simple layered RGB BRDF model,” Graphical Models 65, 171–184 (2003).
[Crossref]

2001 (1)

H. Hirayama, K. Kaneda, H. Yamashita, Y. Yamaji, and Y. Monden, “Visualization of optical phenomena caused by multilayer films based on wave optics,” The Visual Computer 17, 106–120 (2001).
[Crossref]

2000 (1)

M. Ashikhmin and P. Shirley, “An anisotropic phong brdf model,” J. Graph. Tools 5, 25–32 (2000).
[Crossref]

1996 (1)

1990 (1)

L. B. Wolff and D. J. Kurlander, “Ray tracing with polarization parameters,” IEEE Comput. Graph. Appl. 10, 44–55 (1990).
[Crossref]

1982 (1)

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Transaction on Graphics 1, 7–24 (1982).
[Crossref]

1967 (2)

B. Smith, “Geometrical shadowing of a random rough surface,” IEEE Transactions on Antennas and Propagation 15, 668–671 (1967).
[Crossref]

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

Arqués, D.

I. Icart and D. Arqués, “A physically-based brdf model for multilayer systems with uncorrelated rough boundaries,” in “Proceedings of the Eurographics Workshop on Rendering Techniques 2000,” (Springer-Verlag, London, UK, UK, 2000), pp. 353–364.

Arvo, J. R.

S. H. Westin, J. R. Arvo, and K. E. Torrance, “Predicting reflectance functions from complex surfaces,” in “Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1992), SIGGRAPH ’92, pp. 255–264.

Ashikhmin, M.

M. Ashikhmin and P. Shirley, “An anisotropic phong brdf model,” J. Graph. Tools 5, 25–32 (2000).
[Crossref]

Bagher, M. M.

M. M. Bagher, J. Snyder, and D. Nowrouzezahrai, “A non-parametric factor microfacet model for isotropic brdfs,” ACM Transaction on Graphics 35, 1–16 (2016).
[Crossref]

Bala, K.

P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination, 2nd ed. (A K Peters, 2006)
[Crossref]

Barla, P.

B. Raymond, G. Guennebaud, and P. Barla, “Multi-Scale Rendering of Scratched Materials using a Structured SV-BRDF Model,” ACM Transactions on Graphics 35, 54 (2016).
[Crossref]

Bekaert, P.

P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination, 2nd ed. (A K Peters, 2006)
[Crossref]

Berger, K.

K. Berger, A. Wilkie, A. Weidlich, and M. Magnor, “Modeling and verifying the polarizing reflectance of real-world metallic surfaces,” Computer Graphics and Applications 32, 24–33 (2012).
[Crossref] [PubMed]

Bouatouch, K.

C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Discrete ordinate method for polarized light transport solution and subsurface BRDF computation,” Computers and Graphics 45, 17–27 (2014).
[Crossref]

C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Computation of polarized subsurface BRDF for rendering,” in “Proceedings of Graphics Interface 2014,” (Canadian Information Processing Society, Toronto, Ont., Canada, Canada, 2014), GI ’14, pp. 201–208.

Bringier, B.

M. RibardiËre, B. Bringier, D. Meneveaux, and L. Simonot, “STD: Student’s t-distribution of slopes for microfacet based BSDFs,” Computer Graphics Forum (2017).
[Crossref]

Busch, J.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Transactions on Graphics 30, 129 (2011).
[Crossref]

Cabral, B.

B. Cabral, N. Max, and R. Springmeyer, “Bidirectional reflection functions from surface bump maps,” in “Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1987), SIGGRAPH ’87, pp. 273–281.

Chen, T.

A. Ghosh, T. Chen, P. Peers, C. A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Transaction on Graphics 29, 1–12 (2010).
[Crossref]

Collin, C.

C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Discrete ordinate method for polarized light transport solution and subsurface BRDF computation,” Computers and Graphics 45, 17–27 (2014).
[Crossref]

C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Computation of polarized subsurface BRDF for rendering,” in “Proceedings of Graphics Interface 2014,” (Canadian Information Processing Society, Toronto, Ont., Canada, Canada, 2014), GI ’14, pp. 201–208.

Cook, R. L.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Transaction on Graphics 1, 7–24 (1982).
[Crossref]

Creusere, C. D.

D’Eon, E.

E. Heitz, J. Hanika, E. D’Eon, and C. Dachsbacher, “Multiple-scattering microfacet BSDFs with the smith model,” ACM Transaction on Graphics 35, 1–14 (2016).
[Crossref]

W. Jakob, E. D’Eon, O. Jakob, and S. Marschner, “A comprehensive framework for rendering layered materials,” ACM Transaction on Graphics 33, 1–14 (2014).

E. Heitz and E. D’Eon, “Importance sampling microfacet-based BSDFs using the distribution of visible normals,” Computer Graphics Forum 33, 103–112 (2014).
[Crossref]

C. Donner, T. Weyrich, E. d’Eon, R. Ramamoorthi, and S. Rusinkiewicz, “A layered, heterogeneous reflectance model for acquiring and rendering human skin,” ACM Transaction on Graphics 27, 1–12 (2008).
[Crossref]

Dachsbacher, C.

E. Heitz, J. Hanika, E. D’Eon, and C. Dachsbacher, “Multiple-scattering microfacet BSDFs with the smith model,” ACM Transaction on Graphics 35, 1–14 (2016).
[Crossref]

Debevec, P.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Transactions on Graphics 30, 129 (2011).
[Crossref]

A. Ghosh, T. Chen, P. Peers, C. A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Transaction on Graphics 29, 1–12 (2010).
[Crossref]

Donner, C.

C. Donner, T. Weyrich, E. d’Eon, R. Ramamoorthi, and S. Rusinkiewicz, “A layered, heterogeneous reflectance model for acquiring and rendering human skin,” ACM Transaction on Graphics 27, 1–12 (2008).
[Crossref]

Dorsey, J.

J. Dorsey and P. Hanrahan, “Modeling and rendering of metallic patinas,” in “ACM SIGGRAPH 2005 Courses,” (ACM, New York, NY, USA, 2005), SIGGRAPH ’05.

Dutré, P.

P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination, 2nd ed. (A K Peters, 2006)
[Crossref]

Ellis, K. K.

Firby, P.

P. Firby and D. Stone, “Interference in computer graphics,” Computer Graphics Forum (1985).

Foo, S.-C.

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in “Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, NY, USA, 1997), SIGGRAPH ’97, pp. 117–126.

Fyffe, G.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Transactions on Graphics 30, 129 (2011).
[Crossref]

Germer, T.

T. Germer, “SCATMECH: Polarized light scattering C++ class library,” National Institute of Standards and Technology, Gaithersburg, ML (2015).

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,” (2000), pp. 169–181.

Ghosh, A.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Transactions on Graphics 30, 129 (2011).
[Crossref]

A. Ghosh, T. Chen, P. Peers, C. A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Transaction on Graphics 29, 1–12 (2010).
[Crossref]

J. Kim, S. Izadi, and A. Ghosh, “Single-shot layered reflectance separation using a polarized light field camera,” (The Eurographics Association, 2016).

Goldstein, D.

D. Goldstein, Polarized Light, Revised And Expanded (CRC Press, 2003), 2 edition ed.
[Crossref]

Gondek, J. S.

J. S. Gondek, G. W. Meyer, and J. G. Newman, “Wavelength dependent reflectance functions,” in “Proceedings of the 21st annual conference on Computer graphics and interactive techniques,” (ACM, 1994), pp. 213–220.

Granier, X.

X. Granier and W. Heidrich, “A simple layered RGB BRDF model,” Graphical Models 65, 171–184 (2003).
[Crossref]

Greenberg, D. P.

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in “Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, NY, USA, 1997), SIGGRAPH ’97, pp. 117–126.

X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg, “A comprehensive physical model for light reflection,” in “Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1991), SIGGRAPH ’91, pp. 175–186.

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C. Liu and J. Gu, “Discriminative illumination: Per-pixel classification of raw materials based on optimal projections of spectral brdf,” IEEE Transactions on Pattern Analysis and Machine Intelligence 36, 86–98 (2014).
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B. Raymond, G. Guennebaud, and P. Barla, “Multi-Scale Rendering of Scratched Materials using a Structured SV-BRDF Model,” ACM Transactions on Graphics 35, 54 (2016).
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J. Dorsey and P. Hanrahan, “Modeling and rendering of metallic patinas,” in “ACM SIGGRAPH 2005 Courses,” (ACM, New York, NY, USA, 2005), SIGGRAPH ’05.

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Havrilla, M. J.

He, X.

T. Ma, X. Hu, L. Zhang, J. Lian, X. He, Y. Wang, and Z. Xian, “An evaluation of skylight polarization patterns for navigation,” Sensors 15, 5895–5913 (2015).
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He, X. D.

X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg, “A comprehensive physical model for light reflection,” in “Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1991), SIGGRAPH ’91, pp. 175–186.

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X. Granier and W. Heidrich, “A simple layered RGB BRDF model,” Graphical Models 65, 171–184 (2003).
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E. Heitz, J. Hanika, E. D’Eon, and C. Dachsbacher, “Multiple-scattering microfacet BSDFs with the smith model,” ACM Transaction on Graphics 35, 1–14 (2016).
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E. Heitz, “Understanding the masking-shadowing function in microfacet-based BRDFs,” Journal of Computer Graphics Techniques 3, 48–107 (2014).

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E. Heitz, “Generating procedural beckmann surfaces,” Tech. rep., Unity Technologies (2015).

Hirayama, H.

H. Hirayama, K. Kaneda, H. Yamashita, Y. Yamaji, and Y. Monden, “Visualization of optical phenomena caused by multilayer films based on wave optics,” The Visual Computer 17, 106–120 (2001).
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Holzschuch, N.

N. Holzschuch and R. Pacanowski, “A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction,” ACM Transactions on Graphics 36, 12 (2017).
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N. Holzschuch and R. Pacanowski, “Identifying diffraction effects in measured reflectances,” in “Proceedings of the Third Workshop on Material Appearance Modeling: Issues and Acquisition,” (Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 2015), MAM ’15, pp. 31–34.

Hu, X.

T. Ma, X. Hu, L. Zhang, J. Lian, X. He, Y. Wang, and Z. Xian, “An evaluation of skylight polarization patterns for navigation,” Sensors 15, 5895–5913 (2015).
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Hyde, M. W.

Icart, I.

I. Icart and D. Arqués, “A physically-based brdf model for multilayer systems with uncorrelated rough boundaries,” in “Proceedings of the Eurographics Workshop on Rendering Techniques 2000,” (Springer-Verlag, London, UK, UK, 2000), pp. 353–364.

Izadi, S.

J. Kim, S. Izadi, and A. Ghosh, “Single-shot layered reflectance separation using a polarized light field camera,” (The Eurographics Association, 2016).

Jakob, O.

W. Jakob, E. D’Eon, O. Jakob, and S. Marschner, “A comprehensive framework for rendering layered materials,” ACM Transaction on Graphics 33, 1–14 (2014).

Jakob, W.

W. Jakob, E. D’Eon, O. Jakob, and S. Marschner, “A comprehensive framework for rendering layered materials,” ACM Transaction on Graphics 33, 1–14 (2014).

Kaneda, K.

H. Hirayama, K. Kaneda, H. Yamashita, Y. Yamaji, and Y. Monden, “Visualization of optical phenomena caused by multilayer films based on wave optics,” The Visual Computer 17, 106–120 (2001).
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Kim, J.

J. Kim, S. Izadi, and A. Ghosh, “Single-shot layered reflectance separation using a polarized light field camera,” (The Eurographics Association, 2016).

Krivanek, J.

M. Mojzik, T. Skrivan, A. Wilkie, and J. Krivanek, “Bi-directional polarised light transport,” “Eurographics Symposium on Rendering,” (The Eurographics Association, 2016).

Krueger, W.

P. Hanrahan and W. Krueger, “Reflection from layered surfaces due to subsurface scattering,” in “Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1993), SIGGRAPH ’93, pp. 165–174.

Kurlander, D. J.

L. B. Wolff and D. J. Kurlander, “Ray tracing with polarization parameters,” IEEE Comput. Graph. Appl. 10, 44–55 (1990).
[Crossref]

Lafortune, E. P. F.

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in “Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, NY, USA, 1997), SIGGRAPH ’97, pp. 117–126.

Larboulette, C.

A. Wilkie, A. Weidlich, C. Larboulette, and W. Purgathofer, “A reflectance model for diffuse fluorescent surfaces,” in “Proceedings of the 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia,” (ACM, New York, NY, USA, 2006), GRAPHITE ’06, pp. 321–331.

Li, H.

B. Walter, S. R. Marschner, H. Li, and K. E. Torrance, “Microfacet models for refraction through rough surfaces,” in “Proceedings of the 18th Eurographics Conference on Rendering Techniques,” (Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 2007), EGSR’07, pp. 195–206.

Lian, J.

T. Ma, X. Hu, L. Zhang, J. Lian, X. He, Y. Wang, and Z. Xian, “An evaluation of skylight polarization patterns for navigation,” Sensors 15, 5895–5913 (2015).
[Crossref] [PubMed]

LiKamWa, P.

C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Discrete ordinate method for polarized light transport solution and subsurface BRDF computation,” Computers and Graphics 45, 17–27 (2014).
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C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Computation of polarized subsurface BRDF for rendering,” in “Proceedings of Graphics Interface 2014,” (Canadian Information Processing Society, Toronto, Ont., Canada, Canada, 2014), GI ’14, pp. 201–208.

Liu, C.

C. Liu and J. Gu, “Discriminative illumination: Per-pixel classification of raw materials based on optimal projections of spectral brdf,” IEEE Transactions on Pattern Analysis and Machine Intelligence 36, 86–98 (2014).
[Crossref]

Liu, H.

Ma, T.

T. Ma, X. Hu, L. Zhang, J. Lian, X. He, Y. Wang, and Z. Xian, “An evaluation of skylight polarization patterns for navigation,” Sensors 15, 5895–5913 (2015).
[Crossref] [PubMed]

Magnor, M.

K. Berger, A. Wilkie, A. Weidlich, and M. Magnor, “Modeling and verifying the polarizing reflectance of real-world metallic surfaces,” Computer Graphics and Applications 32, 24–33 (2012).
[Crossref] [PubMed]

Marschner, S.

W. Jakob, E. D’Eon, O. Jakob, and S. Marschner, “A comprehensive framework for rendering layered materials,” ACM Transaction on Graphics 33, 1–14 (2014).

Marschner, S. R.

B. Walter, S. R. Marschner, H. Li, and K. E. Torrance, “Microfacet models for refraction through rough surfaces,” in “Proceedings of the 18th Eurographics Conference on Rendering Techniques,” (Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 2007), EGSR’07, pp. 195–206.

Max, N.

B. Cabral, N. Max, and R. Springmeyer, “Bidirectional reflection functions from surface bump maps,” in “Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1987), SIGGRAPH ’87, pp. 273–281.

Meneveaux, D.

M. RibardiËre, B. Bringier, D. Meneveaux, and L. Simonot, “STD: Student’s t-distribution of slopes for microfacet based BSDFs,” Computer Graphics Forum (2017).
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Meyer, G. W.

B. E. Smits and G. W. Meyer, Newton’s Colors: Simulating Interference Phenomena in Realistic Image Synthesis (SpringerBerlin Heidelberg, Berlin, Heidelberg, 1992), pp. 185–194.

J. S. Gondek, G. W. Meyer, and J. G. Newman, “Wavelength dependent reflectance functions,” in “Proceedings of the 21st annual conference on Computer graphics and interactive techniques,” (ACM, 1994), pp. 213–220.

Mojzik, M.

M. Mojzik, T. Skrivan, A. Wilkie, and J. Krivanek, “Bi-directional polarised light transport,” “Eurographics Symposium on Rendering,” (The Eurographics Association, 2016).

Monden, Y.

H. Hirayama, K. Kaneda, H. Yamashita, Y. Yamaji, and Y. Monden, “Visualization of optical phenomena caused by multilayer films based on wave optics,” The Visual Computer 17, 106–120 (2001).
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Newman, J. G.

J. S. Gondek, G. W. Meyer, and J. G. Newman, “Wavelength dependent reflectance functions,” in “Proceedings of the 21st annual conference on Computer graphics and interactive techniques,” (ACM, 1994), pp. 213–220.

Nowrouzezahrai, D.

M. M. Bagher, J. Snyder, and D. Nowrouzezahrai, “A non-parametric factor microfacet model for isotropic brdfs,” ACM Transaction on Graphics 35, 1–16 (2016).
[Crossref]

Pacanowski, R.

N. Holzschuch and R. Pacanowski, “A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction,” ACM Transactions on Graphics 36, 12 (2017).
[Crossref]

N. Holzschuch and R. Pacanowski, “Identifying diffraction effects in measured reflectances,” in “Proceedings of the Third Workshop on Material Appearance Modeling: Issues and Acquisition,” (Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 2015), MAM ’15, pp. 31–34.

Pattanaik, S.

C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Discrete ordinate method for polarized light transport solution and subsurface BRDF computation,” Computers and Graphics 45, 17–27 (2014).
[Crossref]

C. Collin, S. Pattanaik, P. LiKamWa, and K. Bouatouch, “Computation of polarized subsurface BRDF for rendering,” in “Proceedings of Graphics Interface 2014,” (Canadian Information Processing Society, Toronto, Ont., Canada, Canada, 2014), GI ’14, pp. 201–208.

Peers, P.

A. Ghosh, T. Chen, P. Peers, C. A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Transaction on Graphics 29, 1–12 (2010).
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Priest, R. G.

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,” (2000), pp. 169–181.

Purgathofer, W.

A. Wilkie, R. F. Tobler, and W. Purgathofer, “Combined rendering of polarization and fluorescence effects,” in “Eurographics Workshop on Rendering,” S. J. Gortle and K. Myszkowski, eds. (The Eurographics Association, 2001).

A. Wilkie, C. Ulbricht, R. F. Tobler, G. Zotti, and W. Purgathofer, “An analytical model for skylight polarisation,” in “Eurographics Workshop on Rendering,” (The Eurographics Association, 2004).

A. Wilkie, A. Weidlich, C. Larboulette, and W. Purgathofer, “A reflectance model for diffuse fluorescent surfaces,” in “Proceedings of the 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia,” (ACM, New York, NY, USA, 2006), GRAPHITE ’06, pp. 321–331.

Ramamoorthi, R.

C. Donner, T. Weyrich, E. d’Eon, R. Ramamoorthi, and S. Rusinkiewicz, “A layered, heterogeneous reflectance model for acquiring and rendering human skin,” ACM Transaction on Graphics 27, 1–12 (2008).
[Crossref]

Raymond, B.

B. Raymond, G. Guennebaud, and P. Barla, “Multi-Scale Rendering of Scratched Materials using a Structured SV-BRDF Model,” ACM Transactions on Graphics 35, 54 (2016).
[Crossref]

RibardiËre, M.

M. RibardiËre, B. Bringier, D. Meneveaux, and L. Simonot, “STD: Student’s t-distribution of slopes for microfacet based BSDFs,” Computer Graphics Forum (2017).
[Crossref]

Rusinkiewicz, S.

C. Donner, T. Weyrich, E. d’Eon, R. Ramamoorthi, and S. Rusinkiewicz, “A layered, heterogeneous reflectance model for acquiring and rendering human skin,” ACM Transaction on Graphics 27, 1–12 (2008).
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M. Ashikhmin and P. Shirley, “An anisotropic phong brdf model,” J. Graph. Tools 5, 25–32 (2000).
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X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg, “A comprehensive physical model for light reflection,” in “Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1991), SIGGRAPH ’91, pp. 175–186.

Simonot, L.

M. RibardiËre, B. Bringier, D. Meneveaux, and L. Simonot, “STD: Student’s t-distribution of slopes for microfacet based BSDFs,” Computer Graphics Forum (2017).
[Crossref]

Skrivan, T.

M. Mojzik, T. Skrivan, A. Wilkie, and J. Krivanek, “Bi-directional polarised light transport,” “Eurographics Symposium on Rendering,” (The Eurographics Association, 2016).

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B. Smith, “Geometrical shadowing of a random rough surface,” IEEE Transactions on Antennas and Propagation 15, 668–671 (1967).
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B. E. Smits and G. W. Meyer, Newton’s Colors: Simulating Interference Phenomena in Realistic Image Synthesis (SpringerBerlin Heidelberg, Berlin, Heidelberg, 1992), pp. 185–194.

Snyder, J.

M. M. Bagher, J. Snyder, and D. Nowrouzezahrai, “A non-parametric factor microfacet model for isotropic brdfs,” ACM Transaction on Graphics 35, 1–16 (2016).
[Crossref]

Sparrow, E. M.

Springmeyer, R.

B. Cabral, N. Max, and R. Springmeyer, “Bidirectional reflection functions from surface bump maps,” in “Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1987), SIGGRAPH ’87, pp. 273–281.

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D. C. Tannenbaum, P. Tannenbaum, and M. J. Wozny, “Polarization and birefringency considerations in rendering,” in “Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1994), SIGGRAPH ’94, pp. 221–222.

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D. C. Tannenbaum, P. Tannenbaum, and M. J. Wozny, “Polarization and birefringency considerations in rendering,” in “Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1994), SIGGRAPH ’94, pp. 221–222.

Thilak, V.

Tobler, R. F.

A. Wilkie, C. Ulbricht, R. F. Tobler, G. Zotti, and W. Purgathofer, “An analytical model for skylight polarisation,” in “Eurographics Workshop on Rendering,” (The Eurographics Association, 2004).

A. Wilkie, R. F. Tobler, and W. Purgathofer, “Combined rendering of polarization and fluorescence effects,” in “Eurographics Workshop on Rendering,” S. J. Gortle and K. Myszkowski, eds. (The Eurographics Association, 2001).

Torrance, K. E.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” ACM Transaction on Graphics 1, 7–24 (1982).
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B. Walter, S. R. Marschner, H. Li, and K. E. Torrance, “Microfacet models for refraction through rough surfaces,” in “Proceedings of the 18th Eurographics Conference on Rendering Techniques,” (Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 2007), EGSR’07, pp. 195–206.

S. H. Westin, J. R. Arvo, and K. E. Torrance, “Predicting reflectance functions from complex surfaces,” in “Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1992), SIGGRAPH ’92, pp. 255–264.

X. D. He, K. E. Torrance, F. X. Sillion, and D. P. Greenberg, “A comprehensive physical model for light reflection,” in “Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1991), SIGGRAPH ’91, pp. 175–186.

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in “Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, NY, USA, 1997), SIGGRAPH ’97, pp. 117–126.

Tunwattanapong, B.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Transactions on Graphics 30, 129 (2011).
[Crossref]

Ulbricht, C.

A. Wilkie, C. Ulbricht, R. F. Tobler, G. Zotti, and W. Purgathofer, “An analytical model for skylight polarisation,” in “Eurographics Workshop on Rendering,” (The Eurographics Association, 2004).

Voelz, D. G.

Walter, B.

B. Walter, S. R. Marschner, H. Li, and K. E. Torrance, “Microfacet models for refraction through rough surfaces,” in “Proceedings of the 18th Eurographics Conference on Rendering Techniques,” (Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 2007), EGSR’07, pp. 195–206.

Wang, K.

Wang, Y.

T. Ma, X. Hu, L. Zhang, J. Lian, X. He, Y. Wang, and Z. Xian, “An evaluation of skylight polarization patterns for navigation,” Sensors 15, 5895–5913 (2015).
[Crossref] [PubMed]

Ward, G. J.

G. J. Ward, “Measuring and modeling anisotropic reflection,” in “Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1992), SIGGRAPH ’92, pp. 265–272.

Weidlich, A.

K. Berger, A. Wilkie, A. Weidlich, and M. Magnor, “Modeling and verifying the polarizing reflectance of real-world metallic surfaces,” Computer Graphics and Applications 32, 24–33 (2012).
[Crossref] [PubMed]

A. Wilkie and A. Weidlich, “Polarised light in computer graphics,” in “SIGGRAPH Asia 2012 Courses,” (ACM, New York, NY, USA, 2012), SA ’12, pp. 8:1–8:87.

A. Wilkie and A. Weidlich, “A standardised polarisation visualisation for images,” in “Proceedings of the 26th Spring Conference on Computer Graphics,” (ACM, New York, NY, USA, 2010), SCCG ’10, pp. 43–50.

A. Wilkie and A. Weidlich, “How to write a polarisation ray tracer,” in “SIGGRAPH Asia 2011 Courses,” (ACM, New York, NY, USA, 2011), SA ’11, pp. 8:1–8:36.

A. Wilkie, A. Weidlich, C. Larboulette, and W. Purgathofer, “A reflectance model for diffuse fluorescent surfaces,” in “Proceedings of the 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia,” (ACM, New York, NY, USA, 2006), GRAPHITE ’06, pp. 321–331.

A. Weidlich and A. Wilkie, “Arbitrarily layered micro-facet surfaces,” in “Proceedings of the 5th International Conference on Computer Graphics and Interactive Techniques in Australia and Southeast Asia,” (ACM, New York, NY, USA, 2007), GRAPHITE ’07, pp. 171–178.

Westin, S. H.

S. H. Westin, J. R. Arvo, and K. E. Torrance, “Predicting reflectance functions from complex surfaces,” in “Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1992), SIGGRAPH ’92, pp. 255–264.

Weyrich, T.

C. Donner, T. Weyrich, E. d’Eon, R. Ramamoorthi, and S. Rusinkiewicz, “A layered, heterogeneous reflectance model for acquiring and rendering human skin,” ACM Transaction on Graphics 27, 1–12 (2008).
[Crossref]

Wilkie, A.

K. Berger, A. Wilkie, A. Weidlich, and M. Magnor, “Modeling and verifying the polarizing reflectance of real-world metallic surfaces,” Computer Graphics and Applications 32, 24–33 (2012).
[Crossref] [PubMed]

A. Wilkie and A. Weidlich, “Polarised light in computer graphics,” in “SIGGRAPH Asia 2012 Courses,” (ACM, New York, NY, USA, 2012), SA ’12, pp. 8:1–8:87.

A. Wilkie and A. Weidlich, “How to write a polarisation ray tracer,” in “SIGGRAPH Asia 2011 Courses,” (ACM, New York, NY, USA, 2011), SA ’11, pp. 8:1–8:36.

A. Wilkie, C. Ulbricht, R. F. Tobler, G. Zotti, and W. Purgathofer, “An analytical model for skylight polarisation,” in “Eurographics Workshop on Rendering,” (The Eurographics Association, 2004).

A. Wilkie and A. Weidlich, “A standardised polarisation visualisation for images,” in “Proceedings of the 26th Spring Conference on Computer Graphics,” (ACM, New York, NY, USA, 2010), SCCG ’10, pp. 43–50.

A. Wilkie, R. F. Tobler, and W. Purgathofer, “Combined rendering of polarization and fluorescence effects,” in “Eurographics Workshop on Rendering,” S. J. Gortle and K. Myszkowski, eds. (The Eurographics Association, 2001).

M. Mojzik, T. Skrivan, A. Wilkie, and J. Krivanek, “Bi-directional polarised light transport,” “Eurographics Symposium on Rendering,” (The Eurographics Association, 2016).

A. Wilkie, A. Weidlich, C. Larboulette, and W. Purgathofer, “A reflectance model for diffuse fluorescent surfaces,” in “Proceedings of the 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia,” (ACM, New York, NY, USA, 2006), GRAPHITE ’06, pp. 321–331.

A. Weidlich and A. Wilkie, “Arbitrarily layered micro-facet surfaces,” in “Proceedings of the 5th International Conference on Computer Graphics and Interactive Techniques in Australia and Southeast Asia,” (ACM, New York, NY, USA, 2007), GRAPHITE ’07, pp. 171–178.

Wilson, C. A.

A. Ghosh, T. Chen, P. Peers, C. A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Transaction on Graphics 29, 1–12 (2010).
[Crossref]

Wolff, L. B.

L. B. Wolff and D. J. Kurlander, “Ray tracing with polarization parameters,” IEEE Comput. Graph. Appl. 10, 44–55 (1990).
[Crossref]

Wozny, M. J.

D. C. Tannenbaum, P. Tannenbaum, and M. J. Wozny, “Polarization and birefringency considerations in rendering,” in “Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1994), SIGGRAPH ’94, pp. 221–222.

Wu, F.

F. Wu and C. Zheng, “Microfacet-based interference simulation for multilayer films,” Graphical Models 78, 26–35 (2015).
[Crossref]

Xian, Z.

T. Ma, X. Hu, L. Zhang, J. Lian, X. He, Y. Wang, and Z. Xian, “An evaluation of skylight polarization patterns for navigation,” Sensors 15, 5895–5913 (2015).
[Crossref] [PubMed]

Yamaji, Y.

H. Hirayama, K. Kaneda, H. Yamashita, Y. Yamaji, and Y. Monden, “Visualization of optical phenomena caused by multilayer films based on wave optics,” The Visual Computer 17, 106–120 (2001).
[Crossref]

Yamashita, H.

H. Hirayama, K. Kaneda, H. Yamashita, Y. Yamaji, and Y. Monden, “Visualization of optical phenomena caused by multilayer films based on wave optics,” The Visual Computer 17, 106–120 (2001).
[Crossref]

Yu, X.

A. Ghosh, G. Fyffe, B. Tunwattanapong, J. Busch, X. Yu, and P. Debevec, “Multiview face capture using polarized spherical gradient illumination,” ACM Transactions on Graphics 30, 129 (2011).
[Crossref]

Zhang, L.

T. Ma, X. Hu, L. Zhang, J. Lian, X. He, Y. Wang, and Z. Xian, “An evaluation of skylight polarization patterns for navigation,” Sensors 15, 5895–5913 (2015).
[Crossref] [PubMed]

Zheng, C.

F. Wu and C. Zheng, “Microfacet-based interference simulation for multilayer films,” Graphical Models 78, 26–35 (2015).
[Crossref]

Zhu, J.

Zotti, G.

A. Wilkie, C. Ulbricht, R. F. Tobler, G. Zotti, and W. Purgathofer, “An analytical model for skylight polarisation,” in “Eurographics Workshop on Rendering,” (The Eurographics Association, 2004).

ACM Transaction on Graphics (6)

M. M. Bagher, J. Snyder, and D. Nowrouzezahrai, “A non-parametric factor microfacet model for isotropic brdfs,” ACM Transaction on Graphics 35, 1–16 (2016).
[Crossref]

C. Donner, T. Weyrich, E. d’Eon, R. Ramamoorthi, and S. Rusinkiewicz, “A layered, heterogeneous reflectance model for acquiring and rendering human skin,” ACM Transaction on Graphics 27, 1–12 (2008).
[Crossref]

A. Ghosh, T. Chen, P. Peers, C. A. Wilson, and P. Debevec, “Circularly polarized spherical illumination reflectometry,” ACM Transaction on Graphics 29, 1–12 (2010).
[Crossref]

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Supplementary Material (4)

NameDescription
» Code 1       Pseudo code of simulating reflection on micro-facet layered surfaces
» Dataset 1       Simulation results for reflection on micro-facet layered surfaces
» Visualization 1       Visual difference of simulation 1
» Visualization 2       Visual difference of simulation 2

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Figures (12)

Fig. 1
Fig. 1 Two single layered Beckmann meshes of height field size 400×400, with roughness parameters 0.1(a) and 0.4(b).
Fig. 2
Fig. 2 Two example paths for photon tracing on a layered surface model. Note that apart from wave optics effects, we cover all possible interactions of photons with such a surface model - for reasons of clarity, not all possibilities, such as re-propagation of photons back to a lower layer due to multi-scattering within an intermediate layer, are shown here. Interactions with single layer surfaces are a trivial subset of this diagram.
Fig. 3
Fig. 3 Flowchart of our simulation algorithm. The numbers correspond to the algorithm step numbers used in Section 3.3.
Fig. 4
Fig. 4 Stoke parameters patterns generated by our simulation (top) and by SCATMECH (middle), and their differences plots(bottom). Corresponding Stokes parameter plots have the same colour bars. The differences in Stokes component S3 are due to SCATMECH not considering multi-bounce events.
Fig. 5
Fig. 5 Six samples prepared for our experiments, permanently mounted on a stable flat backing surface. A standard gold coating for scanning electron microscopy has been applied. The right sample in the middle row is 1200 grain sandpaper, which was the one we selected for detailed measurements.
Fig. 6
Fig. 6 The micro-structure of 1200 grain sandpaper (a) imaged by SEM, and (b) our procedural model. The right image in subfigures (a) and (b) is an enlargement of the image on the left. In subfigure (b), the procedurally modelled surface is generated via a large amount of simulated crystals that are placed on a backing surface.
Fig. 7
Fig. 7 AOP (angle of polarisation) and DOLP (degree of linear polarisation) values from gold-coated 1200 grain sandpaper measurement and simulation at different reflection angles in the incident plane, for an incident angle of 30° (see Section 4.4 for the definition of AOP and DOLP). pl_angle and co_angle show the angle of light source filter and compensator, respectively: the six plots correspond to the canonical inputs mentioned in the text (linear polarisation at 0°, 45°, 90° and 135°, and left and right circular light).
Fig. 8
Fig. 8 AOP and DOLP values for measurement vs. simulation, incident angle 45°. Same experiment as shown in Fig. 7
Fig. 9
Fig. 9 AOP and DOLP values for measurement vs. simulation, incident angle 60°. Same set-up as in Fig. 7.
Fig. 10
Fig. 10 The difference magnitudes(ADM) of the BRDF lobe (from top-down viewing point at the surface) of simulation 1 (top layer: η1 = 1.5, α1 = 0.1, bottom layer: η2 = 2.4, α2 = 0.1). 15% ∼ 23% of difference can be observed for this double layered dielectric surface. High differences mainly lie at the grazing angle of forward scattering area. Specifically, subfigure (d) corresponds to the difference between Fig. 11(a) and Fig. 11(b).
Fig. 11
Fig. 11 Polarising (left) and non-polarising (right) rendering results of surface in simulation 1 (top layer: η1 = 1.5, α1 = 0.1, bottom layer: η2 = 2.4, α2 = 0.1) with incident angle θ = 65°, which can be considered as top-down view of the surface illuminated by directional point light source. The right image is larger than the left one, which show mis-estimations of non-polarising simulations. A more direct visual comparison can be seen in Visualization 1. Rendering results of rest simulations are in Dataset 1 [60].
Fig. 12
Fig. 12 Difference magnitudes of simulation 7 (top layer: η1 = 1.5, α1 = 0.1, bottom layer: gold, α2 = 0.1) with θ = 60° and θ = 80°. 5% and 7% of AMD values, 8% and 14% of MDM values can be observed at incident angles of θ = 60° and θ = 80°.

Tables (4)

Tables Icon

Table 1 Comparisons of our simulation results against previously published simulation data [6] for a single layer dielectric surface (η = 1.5). Here, R, T, TI and R′, T′, TI′ correspond to reflected, transmitted and total scattered intensities from the data of Heitz, and our simulations. The subscripts m and s denote multi-scattered and single-scattered intensities. The worst and best matches are highlighted in italic and boldface, respectively.

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Table 2 Validation comparisons for a single layer conductive surface. The same variable names and labels as in Table 1 are used.

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Table 3 Simulations summary on difference magnitudes of double layered dielectric surfaces with Brewster incident angles in Section 5.2.

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Table 4 Summary of ADM and MDM differences for all the simulations discussed in Section 5.3.

Equations (7)

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F s = ( E r s E s ) 2 = ( n 0 c o s θ i a ) 2 + b 2 ( n 0 c o s θ i + a ) 2 + b 2
F p = ( E r p E p ) 2 = ( a n 0 s i n θ i t a n θ i ) 2 + b 2 ( a + n 0 s i n θ i t a n θ i ) 2 + b 2
t a n θ s = 2 b n 0 c o s θ i n 0 2 c o s 2 θ i a 2 b 2
t a n θ p = 2 n 0 c o s θ i [ ( n 1 2 k 2 ) b 2 n 1 k a ] ( n 1 2 + k 2 ) c o s 2 θ i n 0 2 ( a 2 + b 2 )
2 a 2 = ( n 1 2 k 2 n 0 s i n 2 θ i ) + 4 n 1 2 k 2 + n 1 2 k 2 n 0 s i n 2 θ i
2 b 2 = ( n 1 2 k 2 n 0 s i n 2 θ i ) + 4 n 1 2 k 2 n 1 2 + k 2 + n 0 s i n 2 θ i
M r = 1 2 ( A B 0 0 B A 0 0 0 0 C S 0 0 S C )

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