“Computing the scattering properties of participating media using Lorenz-Mie theory” by Frisvad, Christensen and Jensen

This paper introduces a theoretical model for computing the scattering properties of participating media and translucent materials. The model takes as input a description of the components of a medium and computes all the parameters necessary to render it. These parameters are the extinction and scattering coefficients, the phase function, and the index of refraction, Our theory is based on a robust generalization of the Lorenz-Mie theory. Previous models using Lorenz-Mie theory have been limited to non-absorbing media with spherical particles such as paints and clouds. Our generalized theory is capable of handling both absorbing host media and non-spherical particles, which significantly extends the classes of media and materials that can be modeled. We use the theory to computer optical properties for different types of ice and ocean water, and we derive a novel appearance model for milk parameterized by the fat and protein contents. Our results show that we are able to match measured scattering properties in cases where the classical Lorez-Mie theory breaks down, and we can compute properties for media that cannot be measured using existing techniques in computer graphics.

1. Attaie, R., and Richtert, R. L. 2000. Size distribution of fat globules in goat milk. Journal of Dairy Science 83, 940–944.Google ScholarCross Ref
2. Babin, M., Morel, A., Fell, V. F.-S. F., and Stramski, D. 2003. Light scattering properties of marine particles in coastal and open ocean waters as related to the particle mass concentration. Limnology and Oceanography 48, 2, 843–859.Google ScholarCross Ref
3. Babin, M., Stramski, D., Ferrari, G. M., Claustre, H., Bricaud, A., Obolensky, G., and Hoepffner, N. 2003. Variations in the light absorption coefficients of phytoplankton, nonalgal particles, and dissolved organic matter in coastal waters around Europe. Journal of Geophysical Research 108, C7, 3211 (July), 4-1-20.Google ScholarCross Ref
4. Bohren, C. F., and Gilra, D. P. 1979. Extinction by a spherical particle in an absorbing medium. Journal of Colloid and Interface Science 72, 2 (November), 215–221.Google ScholarCross Ref
5. Bohren, C. F., and Huffman, D. R. 1983. Absorption and Scattering of Light by Small Particles. John Wiley & Sons, Inc.Google Scholar
6. Born, M., and Wolf, E. 1999. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, seventh (expanded) ed. Cambridge University Press.Google Scholar
7. Bricaud, A., Babin, M., Morel, A., and Claustre, H. 1995. Variability in the chlorophyll-specific absorption coefficients of natural phytoplankton: Analysis and parameterization. Journal of Geophysical Research 100, C7 (July), 13321–13332.Google ScholarCross Ref
8. Cachorro, V. E., and Salcedo, L. L. 1991. New improvements for Mie scattering calculations. Journal of Electromagnetic Waves and Applications 5, 9, 913–926.Google ScholarCross Ref
9. Callet, P. 1996. Pertinent data for modelling pigmented materials in realistic rendering. Computer Graphics Forum 15, 2, 119–127.Google ScholarCross Ref
10. Chandrasekhar, S. 1950. Radiative Transfer. Oxford, Clarendon Press. Unabridged and slightly revised version published by Dover Publications, Inc. in 1960.Google Scholar
11. Crofcheck, C. L., Payne, F. A., and Mengü C, M. P. 2002. Characterization of milk properties with a radiative transfer model. Applied Optics 41, 10 (April), 2028–2037.Google ScholarCross Ref
12. Dave, J. V. 1969. Scattering of electromagnetic radiation by a large, absorbing sphere. IBM Journal of Research and Development 13, 3 (May), 302–313.Google ScholarDigital Library
13. Dieckmann, G., Hemleben, C., and Spindler, M. 1987. Biogenic and mineral inclusions in a green iceberg from the weddell sea, antarctica. Polar Biology 7, 1, 31–33.Google ScholarCross Ref
14. Du, H., Fuh, R.-C. A., Li, J., Corkan, L. A., and Lindsey, J. S. 1998. PhotochemCAD: A computer-aided design and research tool in photochemistry. Photochemistry and Photobiology 68, 2, 141–142.Google Scholar
15. Fox, P. F., and McSweeney, P. L. H. 1998. Dairy Chemistry and Biochemistry. Blackie Academic & Professional, London.Google Scholar
16. Fu, Q., and Sun, W. 2006. Apparent optical properties of spherical particles in absorbing medium. Journal of Quantitative Spectroscopy and Radiative Transfer 100, 1–3, 137–142.Google ScholarCross Ref
17. Gray, D. E., Ed. 1972. American Institute of Physics Handbook, 3rd ed. McGraw-Hill.Google Scholar
18. Grenfell, T. C., and Perovich, D. K. 1981. Radiation absorption coefficients of polycrystalline ice from 400–1400 nm. Journal of Geophysical Research 86, C8 (August), 7447–7450.Google ScholarCross Ref
19. Grenfell, T. C., and Warren, S. G. 1999. Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation. Journal of Geophysical Research 104, D24 (December), 31, 697-31, 709.Google ScholarCross Ref
20. Grenfell, T. C., Neshyba, S. P., and Warren, S. G. 2005. Representation of a non-spherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 3. Hollow columns and plates. Journal of Geophysical Research 110, D17203 (August), 1–15.Google ScholarCross Ref
21. Grenfell, T. C. 1983. A theoretical model of the optical properties of sea ice in the visible and near infrared. Journal of Geophysical Research 88, C14 (November), 9723–9735.Google ScholarCross Ref
22. Hale, G. M., and Querry, M. R. 1973. Optical constants of water in the 200-nm to 200-μm wavelength region. Applied Optics 12, 3 (March), 555–563.Google ScholarCross Ref
23. Hawkins, T., Einarsson, P., and Debevec, P. 2005. Acquisition of time-varying participating media. Proceedings of ACM SIGGRAPH 2005 24, 3, 812–815. Google ScholarDigital Library
24. Henyey, L. G., and Greenstein, J. L. 1940. Diffuse radiation in the galaxy. Annales d’Astrophysique 3, 117–137. Also in The Astrophysical Journal 93, 1941.Google Scholar
25. Jackèl, D., and Walter, B. 1997. Modeling and rendering of the atmosphere using Mie-scattering. Computer Graphics Forum 16, 4, 201–210.Google ScholarCross Ref
26. Jensen, H. W., Marschner, S. R., Levoy, M., and Hanrahan, P. 2001. A practical model for subsurface light transport. In Proceedings of SIGGRAPH 2001, 511–518. Google ScholarDigital Library
27. Kattawar, G. W., and Plass, G. N. 1967. Electromagnetic scattering from absorbing spheres. Applied Optics 6, 8 (August), 1377–1382.Google Scholar
28. Lee, Jr., R. L. 1990. Green icebergs and remote sensing. Journal of Optical Society America A 7, 10 (October), 1862–1874.Google ScholarCross Ref
29. Lide, D. R., Ed. 2006. CRC Handbook of Chemistry and Physics, 87th ed. CRC Press.Google Scholar
30. Light, B., Maykut, G. A., and Grenfell, T. C. 2003. Effects of temperature on the microstructure of first-year arctic sea ice. Journal of Geophysical Research 108, C2, 3051 (February), 33-1-16.Google ScholarCross Ref
31. Light, B., Maykut, G. A., and Grenfell, T. C. 2004. A temperature-dependent, structural-optical model of first-year sea ice. Journal of Geophysical Research 109, C06013 (June), 1–16.Google ScholarCross Ref
32. Lorenz, L. 1890. Lysbevægelser i og uden for en af plane Lysbølger belyst Kugle. Det kongelig danske Videnskabernes Selskabs Skrifter, 2–62. 6. Række, Naturvidenskabelig og Mathematisk Afdeling VI, 1.Google Scholar
33. Mackowski, D. W., Altenkirch, R. A., and Menguc, M. P. 1990. Internal absorption cross sections in a stratified sphere. Applied Optics 29, 10 (April), 1551–1559.Google ScholarCross Ref
34. Michalski, M.-C., Briard, V., and Michel, F. 2001. Optical parameters of milk fat globules for laser light scattering measurements. Lait 81, 787–796.Google ScholarCross Ref
35. Mie, G. 1908. Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Annalen der Physik 25, 3, 377–445. IV. Folge.Google ScholarCross Ref
36. Mundy, W. C., Roux, J. A., and Smith, A. M. 1974. Mie scattering by spheres in an absorbing medium. Journal of the Optical Society of America 64, 12 (December), 1593–1597.Google ScholarCross Ref
37. Narasimhan, S. G., Gupta, M., Donner, C., Ramamoorthi, R., Nayar, S. K., and Jensen, H. W. 2006. Acquiring scattering properties of participating media by dilution. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2006) 25, 3 (July), 1003–1012. Google ScholarDigital Library
38. Neshyba, S. P., Grenfell, T. C., and Warren, S. G. 2003. Representation of a non-spherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 2. Hexagonal columns and plates. Journal of Geophysical Research 108, D15, 4448 (August) 6-1-18.Google ScholarCross Ref
39. Olson, D. W., White, C. H., and Richter, R. L. 2004. Effect of pressure and fat content on particle sizes in microfluidized milk. Journal of Dairy Science 87, 10, 3217–3223.Google ScholarCross Ref
40. Palik, E. D., Ed. 1985. Handbook of Optical Constants of Solids. Academic Press.Google Scholar
41. Pegau, W. S., Gray, D., and Zaneveld, J. R. V. 1997. Absorption and attenuation of visible and near-infrared light in water: Dependence on temperature and salinity. Applied Optics 36, 24 (August), 6035–6046.Google ScholarCross Ref
42. Pope, R. M., and Fry, E. S. 1997. Absorption spectrum (380–700 nm) of pure water. ii. integrating cavity measurements. Applied Optics 36, 33 (November), 8710–8723.Google ScholarCross Ref
43. Randrianalisoa, J., Baillis, D., and Pilon, L. 2006. Modeling radiation characteristics of semitransparent media containing bubbles or particles. Journal of the Optical Society of America A 23, 7 (July), 1645–1656.Google ScholarCross Ref
44. Riley, K., Ebert, D. S., Kraus, M., Tessendorf, J., and Hansen, C. 2004. Efficient rendering of atmospheric phenomena. In Proceedings of Eurographics Symposium on Rendering 2004, H. W. Jensen and A. Keller, Eds., 375–386. Google ScholarCross Ref
45. Rushmeier, H. 1995. Input for participating media. In Realistic Input for Realistic Images, ACM SIGGRAPH ’95 Course Notes. Also appeared in the ACM SIGGRAPH ’98 Course Notes – A Basic Guide to Global Illumination. Google ScholarDigital Library
46. Schmidt, D. G., Walstra, P., and Buchheim, W. 1973. The size distribution of casein micelles in cow’s milk. Netherland’s Milk Dairy Journal 27, 128–142.Google Scholar
47. Stockman, A., and Sharpe, L. T. 2000. The spectral sensitivities of the middle-and long-wavelength-sensitive cones derived from measurements in observers of known genotype. Vision Research 40, 13, 1711–1737.Google ScholarCross Ref
48. Tong, X., Wang, J., Lin, S., Guo, B., and Shum, H. 2005. Modeling and rendering of quasi-homogeneous materials. Proceedings of ACM SIGGRAPH 2005 24, 3, 1054–1061. Google ScholarDigital Library
49. van de Hulst, H. C. 1949. On the attenuation of plane waves by obstacles of arbitrary size and form. Physica 15, 8–9 (September), 740–746.Google ScholarCross Ref
50. van de Hulst, H. C. 1957, 1981. Light Scattering by Small Particles. Dover Publications, Inc., New York. Unabridged and corrected republication of the work originally published in 1957.Google Scholar
51. Videen, G., and Sun, W. 2003. Yet another look at light scattering from particles in absorbing media. Applied Optics 42, 33 (November), 6724–6727.Google ScholarCross Ref
52. Walstra, P., and Jenness, R. 1984. Dairy Chemistry and Physics. John Wiley & Sons, New York.Google Scholar
53. Walstra, P. 1975. Effect of homogenization on the fat globule size distribution in milk. Netherland’s Milk Dairy Journal 29, 279–294.Google Scholar
54. Warren, S. G., Roesler, C. S., Morgan, V. I., Brandt, R. E., Goodwin, I. D., and Allison, I. 1993. Green icebergs formed by freezing of organic-rich seawater to the base of antarctic ice shelves. Journal of Geophysical Research 98, C4 (April), 6921–6928.Google Scholar
55. Warren, S. G., Brandt, R. E., and Grenfell, T. C. 2006. Visible and near-ultraviolet absorption spectrum of ice from transmission of solar radiation into snow. Applied Optics 45, 21 (July), 5320–5334.Google ScholarCross Ref
56. Warren, S. G. 1984. Optical constants of ice from the ultraviolet to the microwave. Applied Optics 23, 8 (April), 1206–1225.Google ScholarCross Ref
57. Wiscombe, W. J. 1980. Improved Mie scattering algorithms. Applied Optics 19, 9 (May), 1505–1509.Google ScholarCross Ref
58. Wu, Z. S., and Wang, Y. P. 1991. Electromagnetic scattering for multilayered sphere: Recursive algorithms. Radio Science 26, 6, 1393–1401.Google ScholarCross Ref
59. Wyman, D. R., Patterson, M. S., and Wilson, B. C. 1989. Similarity relations for the interaction parameters in radiation transport. Applied Optics 28 (December), 5243–5249.Google ScholarCross Ref
60. Yang, P., Gao, B.-C., Wiscombe, W. J., Mischenko, M. I., Platnick, S. E., Huang, H.-L., Baum, B. A., Hu, Y. X., Winker, D. M., Tsay, S.-C., and Park, S. K. 2002. Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium. Applied Optics 41, 15 (May), 2740–2758.Google ScholarCross Ref
61. Yang, W. 2003. Improved recursive algorithm for light scattering by a multilayered sphere. Applied Optics 42, 9 (March), 1710–1720.Google ScholarCross Ref
62. Yin, J., and Pilon, L. 2006. Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium. Journal of the Optical Society of America A 23, 11 (November), 2784–2796.Google ScholarCross Ref