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.

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.

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

[Crossref]

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]

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

[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]

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

[Crossref]

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]

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.

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]

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]

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.

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]

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.

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

[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]

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]

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]

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]

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]

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

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

[Crossref]

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

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.

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]

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

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.

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).

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

[Crossref]

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.

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

[Crossref]

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.

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]

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]

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

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.

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]

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.

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

[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]

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]

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

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]

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.

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]

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.

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

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).

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).

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]

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

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

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.

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

[Crossref]

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.

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.

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.

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]

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.

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]

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]

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]

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).

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.

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.

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]

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.

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

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]

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.

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]

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.

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.

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]

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.

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.

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]

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]

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]

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]

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

[Crossref]

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.

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]

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

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

[Crossref]

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.

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. 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.

J. Stam, “Diffraction shaders,” in “Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1999), SIGGRAPH ’99, pp. 101–110.

J. Stam, “An illumination model for a skin layer bounded by rough surfaces,” in “Proceedings of the 12th Eurographics Workshop on Rendering Techniques,” (Springer-Verlag, 2001), pp. 39–52.

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

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.

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.

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).

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

[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]

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.

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. 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).

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.

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]

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.

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.

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.

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]

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.

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]

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

[Crossref]

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.

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]

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]

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]

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]

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]

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

[Crossref]

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).

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

[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).

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]

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]

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]

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]

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

[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]

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]

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. 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]

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

[Crossref]

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

[Crossref]

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

[Crossref]

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

[Crossref]

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]

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

[Crossref]

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

M. W. Hyde, J. D. Schmidt, and M. J. Havrilla, “A geometrical optics polarimetric bidirectional reflectance distribution function for dielectric and metallic surfaces,” Opt. Express 17, 22138–22153 (2009).

[Crossref]

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]

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]

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]

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.

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.

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 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 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.

C. Wang, “Simulation results of reflection on micro-facet layered surfaces,” figshare (2017) [retrieved 6 Sep. 2017], https://doi.org/10.6084/m9.figshare.5086960 .

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

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

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

C. Wang, “Pseudo code of simulating reflection on micro-facet layered surfaces,” figshare (2017) [retrieved 10 June 2017], https://doi.org/10.6084/m9.figshare.5086930 .

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

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.

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.

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.

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.

J. Stam, “Diffraction shaders,” in “Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques,” (ACM, New York, NY, USA, 1999), SIGGRAPH ’99, pp. 101–110.

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.

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.

J. Stam, “An illumination model for a skin layer bounded by rough surfaces,” in “Proceedings of the 12th Eurographics Workshop on Rendering Techniques,” (Springer-Verlag, 2001), pp. 39–52.

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.

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

[Crossref]

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

[Crossref]

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.

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

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.

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.

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.

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

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.

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]

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.