“Reflectance Model for Diffraction” by Cuypers, Oh, Haber, Bekaert and Raskar

  • ©Tom Cuypers, Se Baek Oh, Tom Haber, Philippe Bekaert, and Ramesh Raskar




    Reflectance Model for Diffraction



    We present a novel method of simulating wave effects in graphics using ray-based renderers with a new function: the Wave BSDF (Bidirectional Scattering Distribution Function). Reflections from neighboring surface patches represented by local BSDFs are mutually independent. However, in many surfaces with wavelength-scale microstructures, interference and diffraction requires a joint analysis of reflected wavefronts from neighboring patches. We demonstrate a simple method to compute the BSDF for the entire microstructure, which can be used independently for each patch. This allows us to use traditional ray-based rendering pipelines to synthesize wave effects. We exploit the Wigner Distribution Function (WDF) to create transmissive, reflective, and emissive BSDFs for various diffraction phenomena in a physically accurate way. In contrast to previous methods for computing interference, we circumvent the need to explicitly keep track of the phase of the wave by using BSDFs that include positive as well as negative coefficients. We describe and compare the theory in relation to well-understood concepts in rendering and demonstrate a straightforward implementation. In conjunction with standard raytracers, such as PBRT, we demonstrate wave effects for a range of scenarios such as multibounce diffraction materials, holograms, and reflection of high-frequency surfaces.


    Abramowitz, M. and Stegun, I. A. 1965. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publication, New York. Google ScholarDigital Library
    Alonso, M. A. 2004. Wigner functions for nonparaxial, arbitrarily polarized electromagnetic wave fields in free space. J. Opt. Soc. Amer. A 21, 11, 2233–2243.Google ScholarCross Ref
    Bastiaans, M. 1997. Application of the wigner distribution function in optics. In The Wigner Distribution – Theory and Applications in Signal Processing, Elsevier Science.Google Scholar
    Bastiaans, M. J. 1977. Frequency-Domain treatment of partial coherence. Optica Acta 24, 3, 261–274.Google ScholarCross Ref
    Bastiaans, M. J. 2009. Wigner distribution in optics. In Phase-Space Optics: Fundamenals and Applications, M. Testorf, B. Hennelly, and J. Ojeda-Castañeda, Eds, McGraw-Hill, New York, 1–44.Google Scholar
    Bastiaans, M. J. and van de Mortel, P. G. J. 1996. Wigner distribution function of a circular aperture. J. Opt. Soc. Am. A 13, 8, 1698–1703.Google ScholarCross Ref
    Benton, S. A. 1969. Hologram reconstruction with extended incoherent sources. J. Opt. Soc. Amer. 59, 1545–1546.Google Scholar
    Chandak, A., Lauterbach, C., Taylor, M., Ren, Z., and Manocha, D. 2008. Ad-frustum: Adaptive frustum tracing for interactive sound propagation. IEEE Trans. Vis. Comput. Graph. 14, 6, 1707–1722. Google ScholarDigital Library
    Dachsbacher, C., Stamminger, M., Drettakis, G., and Durand, F. 2007. Implicit visibility and antiradiance for interactive global illumination. ACM SIGGRAPH 26, 3. Google ScholarDigital Library
    Freniere, E. R., Gregory, G. G., and Hassler, R. A. 1999. Edge diffraction in monte carlo ray tracing. Proc. SPIE 3780, 151–157.Google Scholar
    Goodman, J. W. 1984. Statistical properties of laser speckle patterns. In Laser Spekcle and Related Phenomena, 2nd Ed., J. C. Dainty, Ed., Springer, Chapter 2.Google Scholar
    Goodman, J. W. 2005. Introduction to Fourier Optics, 3rd ed. Roberts & Co., Englewood, Co.Google Scholar
    Hoover, B. G. and Gamiz, V. L. 2006. Coherence solution for bidirectional reflectance distribution of surfaces with wavelength-scale statistics. J. Opt. Soc. Amer. A 23, 314–328.Google ScholarCross Ref
    Hothersall, D., Chandler-Wilde, S., and Hajmirzae, M. 1991. Efficiency of single noise barriers. J. Sound Vibr. 146, 2.Google ScholarCross Ref
    Jensen, H. W. 1996. Global illumination using photon maps. In Proceedings of the Eurographics Workshop on Rendering Techniques. Springer, 21–30. Google ScholarDigital Library
    Jensen, H. W. and Christensen, P. H. 1998. Efficient simulation of light transport in scences with participating media using photon maps. In Proceedings of the ACM SIGGRAPH Conference. ACM, 311–320. Google ScholarDigital Library
    Kajiya, J. T. 1986. The rendering equations. In Comput. Graph. 20, 143–150. Google ScholarDigital Library
    Kouyoumjian, R. and Pathak, P. 1974. A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface. Proc. IEEE~11.Google Scholar
    Lindsay, C. and Agu, E. 2006. Physically-Based real-time diffraction using spherical harmonics. In Advances in Visual Computing, Springer, 505–517. Google ScholarDigital Library
    Moravec, H. P. 1981. 3d graphics and the wave theory. In Proceedings of SIGGRAPH . Vol. 15, ACM, 289–296. Google ScholarDigital Library
    Oh, S. B., Kashyap, S., Garg, R., Chandran, S., and Raskar, R. 2010. Rendering wave effects with augmented light fields. In Proceedings of the EuroGraphics Conference.Google Scholar
    Pharr, M. and Humphreys, G. 2004. Physically Based Rendering: From Theory to Implementation. Morgan Kaufmann Publishers Inc., San Francisco, CA. Google ScholarDigital Library
    Plesniak, W. and Halle, M. 2005. Computed holograms and holographic video display of 3d data. In ACM SIGGRAPH Course, ACM, 69. Google ScholarDigital Library
    Rick, T. and Mathar, R. 2007. Fast edge-diffraction-based radio wave propagation model for graphics hardware. In Proceedings of the International ITG-Conference on Antennas. 15–19.Google Scholar
    Siltanen, S., Lokki, T., Kiminki, S., and Savioja, L. 2007. The room acoustic rendering equation. J. Acoust. Soc. Amer. 122, 3, 1624–1635.Google ScholarCross Ref
    Stam, J. 1999. Diffraction shaders. In Proceedings of the SIGGRAPH Conference 2001. Google ScholarDigital Library
    Sun, Y. 2006. Rendering biological iridescences with RGB-based renderers. ACM Trans. Graph. 25, 1, 100–129. Google ScholarDigital Library
    Sun, Y., Fracchia, F. D., Drew, M. S., and Calvert, T. W. 2000. Rendering iridescent colors of optical disks. In Proceedings of the Eurographics Workshop on Rendering (EGWR). 341–352. Google ScholarDigital Library
    Tannenbaum, D. C., Tannenbaum, P., and Wozny, M. J. 1994. Polarization and birefringency considerations in rendering. In Proceedings of the ACM SIGGRAPH Conference. 221–222. Google ScholarDigital Library
    Torres, R. R., Svensson, U. P., and Kleiner, M. 2001. Computation of edge diffraction for more accurate room acoustics auralization. Acoust. Soc. Amer. J. 109, 2.Google ScholarCross Ref
    Tsingos, N. 2000. A geometrical approach to modeling reflectance functions of diffracting surfaces. Tech. rep.Google Scholar
    Tsingos, N., Dachsbacher, C., Lefebvre, S., and Dellepiane, M. 2007. Instant sound scattering. In Proceedings of the Eurographics Symposium on Rendering(EGSR). Google ScholarDigital Library
    Tsingos, N., Funkhouser, T., Ngan, A., and Carlbom, I. 2001. Modeling acoustics in virtual environments using the uniform theory of diffraction. In Proceedings of the ACM SIGGRAPH Conference. ACM. Google ScholarDigital Library
    Walther, A. 1973. Radiometry and coherence. J. Opti. Soc. Amer. 63, 12, 1622–1623.Google ScholarCross Ref
    Ward, G. J. 1992. Measuring and modeling anisotropic reflection. Proc. the SIGGRAPH Conference 26, 2, 265–272. Google ScholarDigital Library
    Whitted, T. 1980. An improved illumination model for shaded display. Comm. ACM 23, 6, 343–349. Google ScholarDigital Library
    Wolf, E. 1978. Coherence and Radiometry. J. Opti. Soc. Amer. 68, 1, 6–17.Google ScholarCross Ref
    Zhang, Z. and Levoy, M. 2009. Wigner distributions and how they relate to the light field. In Proceedings of the IEEE Internatinoal Conference on Computational Photography.Google Scholar
    Ziegler, R., Bucheli, S., Ahrenberg, L., Magnor, M., and Gross, M. 2007. A bidirectional light field – hologram transform. Comput. Graph. Forum 26, 3, 435–446.Google ScholarCross Ref
    Ziegler, R., Croci, S., and Gross, M. H. 2008. Lighting and occlusion in a wave-based framework. Comput. Graph. Forum 27, 2, 211–220.Google ScholarCross Ref

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