“Light diffusion in multi-layered translucent materials” by Donner and Jensen

This paper introduces a shading model for light diffusion in multi-layered translucent materials. Previous work on diffusion in translucent materials has assumed smooth semi-infinite homogeneous materials and solved for the scattering of light using a dipole diffusion approximation. This approximation breaks down in the case of thin translucent slabs and multi-layered materials. We present a new efficient technique based on multiple dipoles to account for diffusion in thin slabs. We enhance this multipole theory to account for mismatching indices of refraction at the top and bottom of of translucent slabs, and to model the effects of rough surfaces. To model multiple layers, we extend this single slab theory by convolving the diffusion profiles of the individual slabs. We account for multiple scattering between slabs by using a variant of Kubelka-Munk theory in frequency space. Our results demonstrate diffusion of light in thin slabs and multi-layered materials such as paint, paper, and human skin.

1. Blinn, J. F. 1982. Light reflection functions for simulation of clouds and dusty surfaces. In Computer Graphics (Proceedings of ACM SIGGRAPH 1982), ACM, vol. 16, 21–29. Google ScholarDigital Library
2. Borshukov, G., and Lewis, J. P. 2003. Realistic human face rendering for “The Matrix Reloaded”. In ACM SIGGRAPH 2003 Sketches & Applications, ACM, 1. Google ScholarDigital Library
3. Chen, Y., Tong, X., Wang, J., Lin, S., Guo, B., and Shum, H.-Y. 2004. Shell texture functions. ACM Trans. Graphic. 23, 343–353. Google ScholarDigital Library
4. Contini, D., Martelli, F., and Zaccanti, G. 1997. Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory. Appl. Opt. 36, 19, 4587–4599.Google ScholarCross Ref
5. Dorsey, J., Edelman, A., Jensen, H. W., Legakis, J., and Pedersen, H. K. 1999. Modeling and rendering of weathered stone. In Proceedings of ACM SIGGRAPH 1999, ACM Press/Addison-Wesley Publishing Co., New York, Computer Graphics Proceedings, 225–234. Google ScholarDigital Library
6. Egan, W. G., Hilgeman, T. W., and Reichman, J. 1973. Determination of absorption and scattering coefficients for nonhomogeneous media. 2: Experiment. Appl. Opt. 12, 1816–1823.Google ScholarCross Ref
7. Farrell, T. J., and Patterson, M. S. 1992. A diffusion theory model of spatially resolved, steady-state diffuse reflections for the noninvasive determination of tissue optical properties in vivo. Med. Phys. 19, 4, 879–888.Google ScholarCross Ref
8. Fukshansky, L., Von Remisoksky, A. M., and McClendon, J. 1993. Absorption spectra of leaves corrected for scattering and distributional error: a radiative transfer and absorption statistics treatment. Photochem. Photobiol. 57, 3, 538–555.Google ScholarCross Ref
9. Glassner, A. S. 1995. Principles of Digital Image Synthesis. Morgan Kaufmann. Google ScholarDigital Library
10. Glasstone, S., and Sesonske, A. 1955. Nuclear Reactor Engineering. Van Nostrand Company.Google Scholar
11. Haase, C. S., and Meyer, G. W. 1992. Modeling pigmented materials for realistic image synthesis. ACM Trans. Graphic. 11, 4, 305–335. Google ScholarDigital Library
12. Hanrahan, P., and Krueger, W. 1993. Reflection from layered surfaces due to subsurface scattering. In Proceedings of ACM SIGGRAPH 1999, ACM Press/Addison-Wesley Publishing Co., New York, Computer Graphics Proceedings, 164–174. Google ScholarDigital Library
13. Hemenger, R. P. 1977. Optical properties of turbid media with specularly reflecting boundaries: applications to biological problems. Appl. Opt. 16, 7, 2007–2012.Google ScholarCross Ref
14. Hery, C. 2003. Implementing a skin bssrdf. ACM SIGGRAPH 2003 Course 9, 73–88.Google Scholar
15. Ishimaru, A. 1978. Wave Propagation and Scattering in Random Media. Oxford University Press.Google Scholar
16. Jensen, H. W., and Buhler, J. 2002. A rapid hierarchical rendering technique for translucent materials. ACM Trans. Graphic. 21, 576–581. Google ScholarDigital Library
17. Jensen, H. W., Legakis, J., and Dorsey, J. 1999. Rendering of wet materials. In Rendering Techniques ’99, 273–282. Google ScholarDigital Library
18. Jensen, H. W., Marschner, S. R., Levoy, M., and Hanrahan, P. 2001. A practical model for subsurface light transport. In Proceedings of ACM SIGGRAPH 2001, ACM Press/Addison-Wesley Publishing Co., New York, Computer Graphics Proceedings, 511–518. Google ScholarDigital Library
19. Keijzer, M., Star, W. M., and Storchi, P. R. M. 1988. Optical diffusion in layered media. Appl. Opt. 27, 9, 1820–1824.Google ScholarCross Ref
20. Krishnaswamy, A., and Baronoski, G. V. G. 2004. A biophysically-based spectral model of light interaction with human skin. In Proceedings of EURO-GRAPHICS 2004, vol. 23.Google Scholar
21. Kubelka, P. 1954. New contributions to the optics of intensely light-scattering materials. part ii: Non homogeneous layers. J. Opt. Soc. Am. 44, 4, 330–335.Google ScholarCross Ref
22. Mertens, T., Kautz, J., Bekaert, P., Seidel, H.-P., and Reeth, F. V. 2003. Interactive rendering of translucent deformable objects. In Proceedings of the 14th Eurographics Workshop on Rendering, 130–140. Google ScholarDigital Library
23. Nicodemus, F. E., Richmond, J. C., Hsia, J. J., Ginsberg, I. W., and Limperis, T. 1977. Geometrical Considerations and Nomenclature for Reflectance. National Bureau of Standards.Google Scholar
24. Patterson, M. S., Chance, B., and Wilson, B. C. 1989. Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties. Appl. Opt. 28, 12, 2331–2336.Google ScholarCross Ref
25. Pharr, M., and Hanrahan, P. 2000. Monte carlo evaluation of non-linear scattering equations for subsurface reflection. In Proceedings of ACM SIGGRAPH 2000, ACM Press/Addison-Wesley Publishing Co., New York, Computer Graphics Proceedings, 75–84. Google ScholarDigital Library
26. Stam, J. 2001. An illumination model for a skin layer bounded by rough surfaces. In Proceedings of the 12th Eurographics Workshop on Rendering, 39–52. Google ScholarDigital Library
27. Torrance, K. E., and Sparrow, E. M. 1967. Theory for off-specular reflection from roughened surfaces. J. Opt. Soc. Am. 57, 1105–1114.Google ScholarCross Ref
28. Tuchin, V. 2000. Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis. SPIE Press.Google Scholar
29. Wang, L. V. 1998. Rapid modeling of diffuse reflectance of light in turbid slabs. J. Opt. Soc. Am. A 15, 4, 936–944.Google ScholarCross Ref