Statistical optics and effective medium theories of color

  • Avner Friedman
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 57)


Measurements of color are typically made by determining the spectral intensity of light diffusely reflected from images. In xerography color images are heterogeneous systems composed of light absorbing pigments of different colors and sizes suspended in a semitransparent binder. Classical textbook optics predicts the intensity of light specularly reflected from smooth homogeneous surfaces, but cannot provide the detailed information required for these complex optical systems. On October 30, 1992 Robert J. Meyer from Webster Research Center of Xerox has described how statistical optics and effective medium theories predict the intensity of light diffusely reflected from a rough surface of a body containing many small particles; such systems occur within the color image photocopier. He indicated some shortcomings of the dynamic effective medium theory and presented open problems.


Specular Reflection Effective Medium Theory Statistical Optic Constant Electric Field Image Layer 
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  1. [1]
    A. Friedman, Mathematics in Industrial Problems, Part 2, IMA Volume 24, Springer-Verlag, New York (1989).MATHGoogle Scholar
  2. [2]
    A. Friedman, Mathematics in Industrial Problems, Part 5, IMA Volume 49, Springer-Verlag, New York (1992).Google Scholar
  3. [3]
    M. Born and E. Wolf, Principles of Optics, 6th edition, Pergamon Press, Oxford (1985).Google Scholar
  4. [4]
    D.M. Wood and N.W. Ashroft, Effective medium theory of optical properties of small particle composites, Phil. Mag., 35 (1977), 269–280.CrossRefGoogle Scholar
  5. [5]
    Yu. E. Lozovik and A.V. Klyuchnik, The dielectric function and collective oscillations in inhomogeneous systems, in “The Dielectric Function of Condensed Systems,” L.V. Keldysh, D.A. Kirzhnita. and A.A. Maraderdin eds., pp. 299–387, North-Holland, Amsterdam (1989).Google Scholar
  6. [6]
    D.A.G. Bruggeman, Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen, Annalen der Physik, 24 (1935), 636–679.CrossRefGoogle Scholar
  7. [7]
    P. Sheng, Microstructures and physical properties of composites,in “Homogenization and Effective Moduli of Materials and Media,” IMA Volume 1, eds. J.L. Ericksen, D. Kinderlehrer, R. Kohn and J.-L. Lions, Springer-Verlag, New York (1986), pp. 196–227.Google Scholar
  8. [8]
    R.J. Meyer and C.B. Duke,, submitted to Color Research and Applications.Google Scholar
  9. [9]
    O. Wiener, Theory of refraction constants, Ber. Sächs. Ges. Wiss. (Math. Phys. Kl.), 62 (1910), 256–277Google Scholar
  10. [10]
    D. Stroud and F.P. Pan, Self-consistent approach to electromagnetic wave propagation in composite media: Application to model granular metals, Physical Review, 17 (1978), 1602–1610.MATHCrossRefGoogle Scholar
  11. [11]
    P. Chÿlek and V. Srivastava, Dielectric constant of a composite inhomogeneous medium, Physical Review B, 27 (1983), 5098–5106.CrossRefGoogle Scholar
  12. [12]
    J.M. Ziman, Principles of the Theory of Solids, 2nd ed., Cambridge University Press, Cambridge (1972).Google Scholar
  13. [13]
    C. Kittel, Introduction to Solid State Physics,6th edition, John Wiley, New York (1986).Google Scholar
  14. [14]
    A.J. Sievers and J.B. Page, A generalized Lyddane-Sachs-Teller relation for solids and liquids, Infrared Physics, 32 (1991), 425–433.CrossRefGoogle Scholar
  15. [15]
    J.M. Zavislan, Ph.D. thesis, University of Rochester, Rochester, N.Y. (1987).Google Scholar
  16. [16]
    W.L. McMillan, X-ray scattering from liquid crystals. I. Cholesteryl nonaoate and Myristate, Physical Review A, 6 (1972), 936–946.CrossRefGoogle Scholar
  17. [17]
    A. Friedman, Mathematics in Industrial Problems, Part 3, IMA Volume 31, Springer-Verlag, New York (1990).MATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Avner Friedman
    • 1
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA

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