“Towards practical physical-optics rendering” by Steinberg, Sen and Yan

  • ©Shlomi Steinberg, Pradeep Sen, and Ling-Qi Yan




    Towards practical physical-optics rendering



    Physical light transport (PLT) algorithms can represent the wave nature of light globally in a scene, and are consistent with Maxwell’s theory of electromagnetism. As such, they are able to reproduce the wave-interference and diffraction effects of real physical optics. However, the recent works that have proposed PLT are too expensive to apply to real-world scenes with complex geometry and materials. To address this problem, we propose a novel framework for physical light transport based on several key ideas that actually makes PLT practical for complex scenes. First, we restrict the spatial coherence shape of light to an anisotropic Gaussian and justify this restriction with general arguments based on entropy. This restriction serves to simplify the rest of the derivations, without practical loss of generality. To describe partially-coherent light, we present new rendering primitives that generalize the radiometric radiance and irradiance, and are based on the well-known Stokes parameters. We are able to represent light of arbitrary spectral content and states of polarization, and with any coherence volume and anisotropy. We also present the wave BSDF to accurately render diffractions and wave-interference effects. Furthermore, we present an approach to importance sample this wave BSDF to facilitate bi-directional path tracing, which has been previously impossible. We show good agreement with state-of-the-art methods, but unlike them we are able to render complex scenes where all the materials are new, coherence-aware physical optics materials, and with performance approaching that of “classical” rendering methods.


    1. Girish S. Agarwal, Greg Gbur, and Emil Wolf. 2004. Coherence properties of sunlight. Optics Letters 29, 5 (Mar 2004), 459. Google ScholarCross Ref
    2. Thomas Auzinger, Wolfgang Heidrich, and Bernd Bickel. 2018. Computational design of nanostructural color for additive manufacturing. ACM Transactions on Graphics 37, 4 (Aug 2018), 1–16. Google ScholarDigital Library
    3. Seung-Hwan Baek, Tizian Zeltner, Hyun Jin Ku, Inseung Hwang, Xin Tong, Wenzel Jakob, and Min H. Kim. 2020. Image-based acquisition and modeling of polarimetric reflectance. ACM Transactions on Graphics 39, 4 (Jul 2020). Google ScholarDigital Library
    4. Laurent Belcour and Pascal Barla. 2017. A Practical Extension to Microfacet Theory for the Modeling of Varying Iridescence. ACM Trans. Graph. 36, 4, Article 65 (July 2017), 14 pages. Google ScholarDigital Library
    5. Ahmad Bilal, Syed Muhammad Hamza, Ziauddin Taj, and Shuaib Salamat. 2019. Comparison of SBR and MLFMM techniques for the computation of RCS of a fighter aircraft. IET Radar, Sonar & Navigation 13, 10 (2019), 1805–1810.Google ScholarCross Ref
    6. Max Born and Emil Wolf. 1999. Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Cambridge University Press, Cambridge New York.Google Scholar
    7. Juan D. Castro, Sahitya Singh, Akshaj Arora, Sara Louie, and Damir Senic. 2019. Enabling Safe Autonomous Vehicles by Advanced mm-Wave Radar Simulations. In 2019 IEEE MTT-S International Microwave Symposium (IMS). IEEE. Google ScholarCross Ref
    8. Pengning Chao, Benjamin Strekha, Rodrick Kuate Defo, Sean Molesky, and Alejandro W. Rodriguez. 2021. Physical limits on electromagnetic response. arXiv:2109.05667 [physics.optics]Google Scholar
    9. Mikhail Charnotskii. 2019. Coherence of radiation from incoherent sources: I Sources on a sphere and far-field conditions. Journal of the Optical Society of America A 36, 8 (Jul 2019), 1433. Google ScholarCross Ref
    10. Yen-Sheng Chen, Fei-Peng Lai, and Jing-Wei You. 2019. Analysis of antenna radiation characteristics using a hybrid ray tracing algorithm for indoor WiFi energy-harvesting rectennas. IEEE Access 7 (2019), 38833–38846.Google ScholarCross Ref
    11. Tom Cuypers, Tom Haber, Philippe Bekaert, Se Baek Oh, and Ramesh Raskar. 2012. Reflectance model for diffraction. ACM Transactions on Graphics 31, 5 (Aug 2012), 1–11. Google ScholarDigital Library
    12. H. Davies. 1954. The reflection of electromagnetic waves from a rough surface. Proceedings of the IEE – Part IV: Institution Monographs 101, 7 (Aug 1954), 209–214. Google ScholarCross Ref
    13. Aristide Dogariu and Emil Wolf. 1998. Spectral changes produced by static scattering on a system of particles. Optics Letters 23, 17 (Sep 1998), 1340. Google ScholarCross Ref
    14. Donald D. Duncan, Daniel V. Hahn, and Michael E. Thomas. 2003. Physics-based polarimetric BRDF models. Optical Diagnostic Methods for Inorganic Materials III (Nov 2003). Google ScholarCross Ref
    15. C. Fabre and N. Treps. 2020. Modes and states in quantum optics. Google ScholarCross Ref
    16. V. Falster, A. Jarabo, and J. R. Frisvad. 2020. Computing the Bidirectional Scattering of a Microstructure Using Scalar Diffraction Theory and Path Tracing. Computer Graphics Forum 39, 7 (Oct 2020), 231–242. Google ScholarCross Ref
    17. Tiantian Feng and Lixin Guo. 2021. Multiview ISAR Imaging for Complex Targets Based on Improved SBR Scattering Model. (2021).Google Scholar
    18. Ari T. Friberg. 1979. On the existence of a radiance function for finite planar sources of arbitrary states of coherence. Journal of the Optical Society of America 69, 1 (Jan 1979), 192. Google ScholarCross Ref
    19. Jorge I. Garcia-Sucerquia and Francisco F. Medina E. 2003. M2 factor invariance through the geometric etendue for Gaussian Schell model sources., 343–346 pages. Google ScholarCross Ref
    20. Joseph Goodman. 2015. Statistical optics. John Wiley & Sons Inc, Hoboken, New Jersey.Google Scholar
    21. Ibón Guillén, Julio Marco, Diego Gutierrez, Wenzel Jakob, and Adrian Jarabo. 2020. A General Framework for Pearlescent Materials. ACM Transactions on Graphics 39, 6 (2020). Google ScholarDigital Library
    22. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda. 2000. Alternative formulation for invariant optical fields: Mathieu beams. Optics Letters 25, 20 (Oct 2000), 1493. Google ScholarCross Ref
    23. James E. Harvey. 2012. Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles. Optical Engineering 51, 1 (Feb 2012). Google ScholarCross Ref
    24. Nicolas Holzschuch and Romain Pacanowski. 2017. A Two-scale Microfacet Reflectance Model Combining Reflection and Diffraction. ACM Trans. Graph. 36, 4, Article 66 (July 2017), 12 pages. Google ScholarDigital Library
    25. Weizhen Huang, Julian Iseringhausen, Tom Kneiphof, Ziyin Qu, Chenfanfu Jiang, and Matthias B. Hullin. 2020. Chemomechanical simulation of soap film flow on spherical bubbles. ACM Transactions on Graphics 39, 4 (Jul 2020). Google ScholarDigital Library
    26. Wenzel Jakob. 2010. Mitsuba renderer. http://www.mitsuba-renderer.orgGoogle Scholar
    27. Adrian Jarabo and Victor Arellano. 2017. Bidirectional Rendering of Vector Light Transport. Computer Graphics Forum 37, 6 (Dec 2017), 96–105. Google ScholarCross Ref
    28. Tom Kneiphof, Tim Golla, and Reinhard Klein. 2019. Real-time Image-based Lighting of Microfacet BRDFs with Varying Iridescence. Computer Graphics Forum 38, 4 (2019), 77–85. Google ScholarCross Ref
    29. Olga Korotkova. 2017. Random Light Beams. CRC Press, Boca Raton.Google Scholar
    30. Olga Korotkova and Emil Wolf. 2005. Generalized Stokes parameters of random electromagnetic beams. Optics Letters 30, 2 (Jan 2005), 198. Google ScholarCross Ref
    31. Gong Lei, Zhensen Wu, and Honglu Hou. 2012. Polarized bidirectional reflectance distribution function for optical substrate and different films. 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment (Oct 2012). Google ScholarCross Ref
    32. Anat Levin, Daniel Glasner, Ying Xiong, Frédo Durand, William Freeman, Wojciech Matusik, and Todd Zickler. 2013. Fabricating BRDFs at high spatial resolution using wave optics. ACM Transactions on Graphics 32, 4 (Jul 2013), 1–14. Google ScholarDigital Library
    33. Ju. V. Linnik. 1959. An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions. Theory of Probability & Its Applications 4, 3 (Jan 1959), 288–299. Google ScholarCross Ref
    34. Leonard Mandel and Emil Wolf. 1995. Optical coherence and quantum optics. Cambridge University Press, Cambridge.Google Scholar
    35. Vidhi Mann and Vipul Rastogi. 2020. FDTD simulation studies on improvement of light absorption in organic solar cells by dielectric nanoparticles. Optical and Quantum Electronics 52, 5 (April 2020). Google ScholarCross Ref
    36. Francisco F. Medina and Giulio Pozzi. 1990. Spatial coherence of anisotropic and astigmatic sources in interference electron microscopy and holography., 1027 pages. Google ScholarCross Ref
    37. David A. B. Miller. 2012. All linear optical devices are mode converters., 23985 pages. Google ScholarCross Ref
    38. Michal Mojzík, Tomáš Skřivan, Alexander Wilkie, and Jaroslav Křivánek. 2016. Bi-Directional Polarised Light Transport. In Eurographics Symposium on Rendering – Experimental Ideas & Implementations, Elmar Eisemann and Eugene Fiume (Eds.). Google ScholarCross Ref
    39. Hans P. Moravec. 1981. 3D graphics and the wave theory. Proceedings of the 8th annual conference on Computer graphics and interactive techniques – SIGGRAPH ’81 (1981). Google ScholarDigital Library
    40. A. Musbach, G. W. Meyer, F. Reitich, and S. H. Oh. 2013. Full Wave Modelling of Light Propagation and Reflection. Computer Graphics Forum 32, 6 (Feb 2013), 24–37. Google ScholarDigital Library
    41. Roger Newton. 1982. Scattering theory of waves and particles. Springer-Verlag, New York.Google Scholar
    42. Se Baek Oh, Sriram Kashyap, Rohit Garg, Sharat Chandran, and Ramesh Raskar. 2010. Rendering Wave Effects with Augmented Light Field. Computer Graphics Forum 29, 2 (May 2010), 507–516. Google ScholarCross Ref
    43. José Pérez and Razvigor Ossikovski. 2016. Polarized light and the Mueller matrix approach. CRC Press, Taylor & Francis Group, Boca Raton, FL. Google ScholarCross Ref
    44. Richard G Priest and Thomas A Gerner. 2000. Polarimetric BRDF in the microfacet model: Theory and measurements. Technical Report. NAVAL RESEARCH LAB WASHINGTON DC.Google Scholar
    45. J. J. Sakurai and Jim Napolitano. 2021. Modern quantum mechanics. Cambridge University Press, Cambridge New York.Google Scholar
    46. Frank Siewert, Heiner Lammert, and Thomas Zeschke. 2008. The Nanometer Optical Component Measuring Machine. Springer Berlin Heidelberg, 193–200. Google ScholarCross Ref
    47. Jos Stam. 1999. Diffraction shaders. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques – SIGGRAPH ’99. ACM Press. Google ScholarDigital Library
    48. Shlomi Steinberg. 2019. Analytic Spectral Integration of Birefringence-Induced Iridescence. Computer Graphics Forum 38, 4 (Jul 2019), 97–110. Google ScholarCross Ref
    49. Shlomi Steinberg. 2020. Accurate Rendering of Liquid-Crystals and Inhomogeneous Optically Anisotropic Media. ACM Transactions on Graphics 39, 3 (Jun 2020), 1–23. Google ScholarDigital Library
    50. Shlomi Steinberg and Ling-Qi Yan. 2021a. A Generic Framework for Physical Light Transport. ACM Transactions on Graphics 40, 4 (Aug 2021), 1–20. Google ScholarDigital Library
    51. Shlomi Steinberg and Ling-Qi Yan. 2021b. Physical Light-Matter Interaction in Hermite-Gauss Space. ACM Trans. Graph. 40, 6, Article 283 (dec 2021), 17 pages. Google ScholarDigital Library
    52. Shlomi Steinberg and Ling-Qi Yan. 2022. Rendering of Subjective Speckle Formed by Rough Statistical Surfaces. ACM Trans. Graph. 41, 1, Article 2 (feb 2022), 23 pages. Google ScholarDigital Library
    53. John Stover. 2012. Optical scattering: measurement and analysis. SPIE Press.Google Scholar
    54. Antoine Toisoul, Daljit Singh Dhillon, and Abhijeet Ghosh. 2018. Acquiring Spatially Varying Appearance of Printed Holographic Surfaces. ACM Trans. Graph. 37, 6, Article 272 (Dec. 2018), 16 pages. Google ScholarDigital Library
    55. Antoine Toisoul and Abhijeet Ghosh. 2017. Practical Acquisition and Rendering of Diffraction Effects in Surface Reflectance. ACM Transactions on Graphics 36, 5 (Jul 2017), 1–16. Google ScholarDigital Library
    56. Z. Velinov, S. Werner, and M. B. Hullin. 2018. Real-Time Rendering of Wave-Optical Effects on Scratched Surfaces. Computer Graphics Forum 37, 2 (2018), 123–134. Google ScholarCross Ref
    57. Bruce Walter, Stephen R. Marschner, Hongsong Li, and Kenneth E. Torrance. 2007. Microfacet Models for Refraction through Rough Surfaces. In Proceedings of the 18th Eurographics Conference on Rendering Techniques (Grenoble, France) (EGSR’07). Eurographics Association, Goslar, DEU, 195–206.Google Scholar
    58. A Walther. 1968. Radiometry and coherence. JOSA 58, 9 (1968), 1256–1259. Google ScholarCross Ref
    59. Tao Wang and Daomu Zhao. 2010. Polarization-induced coherence changes of an electromagnetic light wave on scattering. Optics Letters 35, 18 (Sep 2010), 3108. Google ScholarCross Ref
    60. Craig Warren, Antonios Giannopoulos, and Iraklis Giannakis. 2016. gprMax: Open source software to simulate electromagnetic wave propagation for Ground Penetrating Radar. 209 (Dec 2016).Google Scholar
    61. Andrea Weidlich and Alexander Wilkie. 2008. Realistic rendering of birefringency in uniaxial crystals. ACM Transactions on Graphics 27, 1 (Mar 2008), 1–12. Google ScholarDigital Library
    62. Sebastian Werner, Zdravko Velinov, Wenzel Jakob, and Matthias Hullin. 2017. Scratch Iridescence: Wave-Optical Rendering of Diffractive Surface Structure. Transactions on Graphics (Proceedings of SIGGRAPH Asia) 36, 6 (Nov. 2017). Google ScholarDigital Library
    63. Alexander Wilkie, Robert F. Tobler, and Werner Purgathofer. 2001. Combined Rendering of Polarization and Fluorescence Effects. Rendering Techniques 2001 (2001), 197–204. Google ScholarCross Ref
    64. Serge Winitzki. 2003. Uniform Approximations for Transcendental Functions. Springer Science and Business Media LLC. Google ScholarCross Ref
    65. Emil Wolf. 2007. Introduction to the theory of coherence and polarization of light. Cambridge University Press, Cambridge.Google Scholar
    66. Ling-Qi Yan, Miloš Hašan, Bruce Walter, Steve Marschner, and Ravi Ramamoorthi. 2018. Rendering Specular Microgeometry with Wave Optics. ACM Trans. Graph. 37, 4, Article 75 (July 2018), 10 pages. Google ScholarDigital Library
    67. Sunkyu Yu, Cheng-Wei Qiu, Yidong Chong, Salvatore Torquato, and Namkyoo Park. 2020. Engineered disorder in photonics., 226–243 pages. Google ScholarCross Ref
    68. Andrew Zangwill. 2013. Modern electrodynamics. Cambridge University Press, Cambridge.Google Scholar
    69. Hanwen Zhang, Chia Wei Hsu, and Owen D. Miller. 2019. Scattering concentration bounds: brightness theorems for waves., 1321 pages. Google ScholarCross Ref

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