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April 1, 1954Journal of the Optical Society of America

New Contributions to the Optics of Intensely Light-Scattering Materials Part II: Nonhomogeneous Layers*

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PKPaul KubelkaMinistry of Agriculture, Livestock, and Food Supply

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Overview

Theoretical analysis demonstrates direction-dependent reflectance in nonhomogeneous scattering layers, highlighting improved optical modeling for multilayer materials.

Key Points

  • Extend the Kubelka-Munk optical theory to nonhomogeneous light-scattering layers where scattering and absorption coefficients vary as a function of depth.
  • Formulated differential equations with distance-dependent scattering coefficient S(x) and absorption coefficient K(x) across layer depth.
  • Introduced an integral substitution variable p = ∫S(x)dx for media with constant K/S ratios to map nonhomogeneous systems to homogeneous solutions.
  • Derived analytical formulas for composite transmittance, reflectance, and contrast ratio across multiple stacked sheets on black, gray, and white backing surfaces.
  • Demonstrated theoretically and experimentally that reflectance and absorption depend on the direction of illumination in nonhomogeneous specimens.
  • Showed that transmittance through nonhomogeneous specimens remains invariant regardless of illumination direction.
  • Established composite equations calculating stacked transmittance (T1,2) and reflectance (R1,2) using single-sheet parameters and inverse-illumination reflectance.

Cite This Study

Paul Kubelka (1954) studied this question.

synapsesocial.com/papers/69d6bf2cfca0359822aa82fchttps://doi.org/10.1364/josa.44.000330
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