R. M. A. Azzam. Photopolarimetric measurement of the mueller matrix by fourier analysis of a single detected signal. Opt. Lett., 2(6):148–150, Jun 1978. URL:, doi:10.1364/OL.2.000148.


R. M. A. Azzam. Phase shifts that accompany total internal reflection at a dielectric–dielectric interface. J. Opt. Soc. Am. A, 21(8):1559–1563, Aug 2004. URL:, doi:10.1364/JOSAA.21.001559.


Seung-Hwan Baek, Daniel S. Jeon, Xin Tong, and Min H. Kim. Simultaneous acquisition of polarimetric svbrdf and normals. ACM Transactions on Graphics (Proc. SIGGRAPH Asia 2018), 37(6):268:1–15, 2018. URL:, doi:10.1145/3272127.3275018.


Seung-Hwan Baek, Tizian Zeltner, Hyun Jin Ku, Inseung Hwang, Xin Tong, Wenzel Jakob, and Min H. Kim. Image-based acquisition and modeling of polarimetric reflectance. Transactions on Graphics (Proceedings of SIGGRAPH), July 2020. doi:10.1145/3386569.3392387.


Sai Praveen Bangaru, Tzu-Mao Li, and Frédo Durand. Unbiased warped-area sampling for differentiable rendering. ACM Trans. Graph., nov 2020. URL:, doi:10.1145/3414685.3417833.


Michael Bass, Casimer DeCusatis, Jay Enoch, Vasudevan Lakshminarayanan, Guifang Li, Carolyn Macdonald, Virendra Mahajan, and Eric Van Stryland. Handbook of Optics, Third Edition Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments(Set). McGraw-Hill, Inc., USA, 3 edition, 2009. ISBN 0071498893.


Brent Burley. Physically Based Shading at Disney. SIGGRAPH 2012 Course Notes, 2012. URL:


Brent Burley. Extending the Disney BRDF to a BSDF with Integrated Subsurface Scattering. SIGGRAPH 2015 Course Notes, 2015. URL:


David Clarke. Stellar Polarimetry, Appendix A: The Fresnel Laws. John Wiley & Sons, Ltd, 2009. ISBN 9783527628322. doi:


E. Collett. Field Guide to Polarization. Field Guide Series. Society of Photo Optical, 2005. ISBN 9780819458681.


Edward Collett. Mueller-stokes matrix formulation of fresnel's equations. American Journal of Physics, 39(5):517–528, 1971. doi:10.1119/1.1986205.


Edward Collett. Polarized light : fundamentals and application. Marcel Dekker New York, 1993. ISBN 0824787293.


Tom Duff, James Burgess, Per Christensen, Christophe Hery, Andrew Kensler, Max Liani, and Ryusuke Villemin. Building an orthonormal basis, revisited. Journal of Computer Graphics Techniques (JCGT), 6(1):1–8, March 2017. URL:


Augustin Jean Fresnel. Mémoire sur la loi des modifications que la réflexion imprime à la lumière polarisée. Académie des Sciences, 1823.


G. Friedmann and H. S. Sandhu. Phase change on reflection from isotropic dielectrics. American Journal of Physics, 33(2):135–138, 1965. doi:10.1119/1.1971270.


R. H. Muller Hauge and C. G. Smith. Conventions and formulas for using the mueller-stokes calculus in ellipsometry. Surface Science, 1980.


Eugene Hecht. Optics. Addison-Wesley, 4th edition, 1998.


Eric Heitz and Eugene D'Eon. Importance sampling microfacet-based bsdfs using the distribution of visible normals. Computer Graphics Forum, June 2014.


Eric Heitz, Jonathan Dupuy, Cyril Crassin, and Carsten Dachsbacher. The sggx microflake distribution. ACM Trans. Graph. (Proc. SIGGRAPH), July 2015. URL:, doi:10.1145/2766988.


L.G. Henyey and J.L. Greenstein. Diffuse radiation in the galaxy. The Astrophysical Journal, 93:70–83, 1941.


Wenzel Jakob and Johannes Hanika. A low-dimensional function space for efficient spectral upsampling. Computer Graphics Forum (Proceedings of Eurographics), March 2019. URL:


Wenzel Jakob, Jonathan T. Moon, Adam Arbree, Kavita Bala, and Steve Marschner. A radiative transfer framework for rendering materials with anisotropic structure. ACM Trans. Graph. (Proc. SIGGRAPH), 29(10):53:1–53:13, July 2010. doi:10.1145/1778765.1778790.


Adrian Jarabo and Victor Arellano. Bidirectional rendering of vector light transport. Computer Graphics Forum, 2018.


Wojciech Jarosz, Afnan Enayet, Andrew Kensler, Charlie Kilpatrick, and Per Christensen. Orthogonal array sampling for Monte Carlo rendering. Computer Graphics Forum (Proceedings of EGSR), 38(4):135–147, July 2019. doi:10/gf6rx5.


Achuta Kadambi, Vage Taamazyan, Boxin Shi, and Ramesh Raskar. Depth sensing using geometrically constrained polarization normals. International Journal of Computer Vision, 125(1):34–51, Dec 2017. URL:, doi:10.1007/s11263-017-1025-7.


missing booktitle in Kensler2013CorrelatedMS


Diederik P Kingma and Jimmy Ba. Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.


Thomas Kollig and Alexander Keller. Efficient Multidimensional Sampling. Computer Graphics Forum, 21(3):557–563, 2002. doi:10.1111/1467-8659.00706.


Guillaume Loubet, Nicolas Holzschuch, and Wenzel Jakob. Reparameterizing discontinuous integrands for differentiable rendering. Transactions on Graphics (Proceedings of SIGGRAPH Asia), December 2019. doi:10.1145/3355089.3356510.


Bailey Miller, Iliyan Georgiev, and Wojciech Jarosz. A null-scattering path integral formulation of light transport. ACM Trans. Graph. (Proc. SIGGRAPH), July 2019. URL:, doi:10.1145/3306346.3323025.


Don P. Mitchell and Arun N. Netravali. Reconstruction filters in computer-graphics. SIGGRAPH Comput. Graph., 22(4):221–228, June 1988.


Michal Mojzik, Tomas Skrivan, Alexander Wilkie, and Jaroslav Krivanek. Bi-Directional Polarised Light Transport. In Eurographics Symposium on Rendering. 2016.


Merlin Nimier-David, Delio Vicini, Tizian Zeltner, and Wenzel Jakob. Mitsuba 2: a retargetable forward and inverse renderer. Transactions on Graphics (Proceedings of SIGGRAPH Asia), December 2019. URL:


Minsu Oh and Thomas Vandervelde. Bridging the gaps between different sign conventions of fresnel reflection coefficients towards a universal form. In 2020 IEEE 63rd International Midwest Symposium on Circuits and Systems (MWSCAS), volume, 707–713. 2020. doi:10.1109/MWSCAS48704.2020.9184440.


E.D. Palik and G. Ghosh. Handbook of optical constants of solids. Academic press, 1998.


Edward D Palik and Edward J Prucha. Handbook of optical constants of solids. Academic Press, Boston, MA, 1997. URL:


Matt Pharr, Wenzel Jakob, and Greg Humphreys. Physically Based Rendering: From Theory to Implementation (3rd ed.). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 3rd edition, October 2016. ISBN 9780128006450.


Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. On the importance of initialization and momentum in deep learning. In International conference on machine learning, 1139–1147. 2013.


T. S. Trowbridge and K. P. Reitz. Average irregularity representation of a rough surface for ray reflection. J. Opt. Soc. Am., 65(5):531–536, May 1975.


Eric Veach. Robust Monte Carlo Methods for Light Transport Simulation. Stanford University, Stanford, CA, USA, 1998. ISBN 0591907801.


Delio Vicini, Sébastien Speierer, and Wenzel Jakob. Path replay backpropagation: differentiating light paths using constant memory and linear time. ACM Trans. Graph., jul 2021. URL:, doi:10.1145/3450626.3459804.


Bruce Walter, Stephen R. Marschner, Hongsong Li, and Kenneth E. Torrance. Microfacet Models for Refraction through Rough Surfaces. Rendering Techniques (Proceedings EG Symposium on Rendering), 2007.


Alexander Wilkie and Andrea Weidlich. A standardised polarisation visualisation for images. In Proceedings of the 26th Spring Conference on Computer Graphics, SCCG '10, 43–50. New York, NY, USA, 2010. Association for Computing Machinery. URL:, doi:10.1145/1925059.1925070.


Alexander Wilkie and Andrea Weidlich. Polarised light in computer graphics. In SIGGRAPH Asia 2012 Courses, SA '12. New York, NY, USA, 2012. Association for Computing Machinery. URL:, doi:10.1145/2407783.2407791.


L.B. Wolff and D.J. Kurlander. Ray tracing with polarization parameters. IEEE Computer Graphics and Applications, 10(6):44–55, 1990. doi:10.1109/38.62695.


Tizian Zeltner, Sébastien Speierer, Iliyan Georgiev, and Wenzel Jakob. Monte carlo estimators for differential light transport. Transactions on Graphics (Proceedings of SIGGRAPH), August 2021. doi:10.1145/3450626.3459807.


Rolf H. Muller. Definitions and conventions in ellipsometry. Surface Science, 16:14–33, August 1969. doi:10.1016/0039-6028(69)90003-X.


Ertan Salik. Quantitative investigation of Fresnel reflection coefficients by polarimetry. American Journal of Physics, 80(3):216–224, March 2012. doi:10.1119/1.3672851.