Paul Kubelka

Bio: Paul Kubelka is an academic researcher from Ministry of Agriculture. The author has contributed to research in topics: Light scattering & Transmittance. The author has an hindex of 2, co-authored 2 publications receiving 2850 citations.

New contributions to the optics of intensely light-scattering materials.

Abstract: The system of differential equations of Kubelka-Munk, -di=-(S+K)idx+Sjdx, dj=-(S+K)jdx+Sidx(i, j⋯ intensities of the light traveling inside a plane-parallel light-scattering specimen towards its unilluminated and its illuminated surface; x⋯ distance from the unilluminated surface S, K⋯ constants), has been derived from a simplified model of traveling of light in the material. Now, without simplifying assumptions the following exact system is derived: -di=-12(S+K)uidx+12Svjdx,dj=-12(S+K)vjdx+12Suidx,u≡∫0π/2(∂i/i∂φ)(dφ/cosφ), v≡∫0π/2(∂j/j∂φ)(dφ/cosφ), φ≡angle from normal of the light). Both systems become identical when u=v=2, that is, for instance, when the material is perfectly dull and when the light, is perfectly diffused or if it is parallel and hits the specimen under an angle of 60° from normal. Consequently, the different formulas Kubelka-Munk got by integration of their differential equations are exact when these conditions are fulfilled. The Gurevic and Judd formulas, although derived in another way by their authors, may be got from the Kubelka-Munk differential equations too. Consequently, they are exact under the same conditions. The integrated equations may be adapted for practical use by introducing hyperbolic functions and the secondary constants a=12(1/R∞+R∞) and b=12(1/R∞-R∞), (R∞≡reflectivity). Reflectance R, for instance, is then represented by the formula R=1-Rg(a-b ctghbSX)a+b ctghbSX-Rg(Rg≡reflectance of the backing, X=thickness of the specimen) and transmittance T by the formula T=ba sinhbSX+b coshbSX.In many practical cases the exact formulas may be replaced by appropriated approximations.

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

Abstract: The derived laws apply to layers whose scattering coefficient S and absorption coefficient K vary vertically to the surface of the layer. In the general case the differential equations of the preceding paper [ P. Kubelka , J. Opt. Soc. Am.38, 448 ( 1948)] must be used; the coefficients, however, hitherto constant, now are functions of the distance x from the surface. In the practically important case in which K/S is constant, one may introduce the variable p, such that p≡∫0x(x)dx. One reduces thereby the nonhomogeneous to the previously treated homogeneous case.Transmittance T1,2 and reflectance R1,2 of two nonhomogeneous sheets can be calculated by the following equations: T1,2=T1T21-R1R2, R1,2=R1+T12R21-R1R2,where T1, T2, R1, R2 are the transmittances and reflectances of the single sheets, and R1 represents the reflectance of the first sheet when illuminated in the inverse direction. Analogous formulas for more sheets and formulas relating transmittance, reflectance for specimens upon black, gray or white backing surfaces, and contrast ratio, are derived.It is shown by theory and experiment that reflectance and absorption of a nonhomogeneous specimen depend on the direction of illumination, whereas transmittance does not.

A review of the optical properties of biological tissues

Abstract: The known optical properties (absorption, scattering, total attenuation, effective attenuation, and/or anisotropy coefficients) of various biological tissues at a variety of wavelengths are reviewed. The theoretical foundations for most experimental approaches are outlined. Relations between Kubelka-Munk parameters and transport coefficients are listed. The optical properties of aorta, liver, and muscle at 633 nm are discussed in detail. An extensive bibliography is provided. >

Theory of Reflectance and Emittance Spectroscopy

Abstract: Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Bidirectional reflectance spectroscopy: 1. Theory

Abstract: An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.

Geometrical considerations and nomenclature for reflectance

Abstract: Report presenting a unified approach to the specification of reflectance, in terms of both incident- and reflected- beam geometry. Nomenclature to facilitate this approach is proposed. Nomenclature for categorizing and specifying reflectance quantities for a variety of different beam configurations (both incident and reflected beams) is described, and all are defined and interrelated in terms of the bidirectional reflectance-distribution function. The conditions under which the formalism can be applied, including situations involving considerable sub-surface scattering, are carefully established. The entire treatment is limited to the domain of classical geometrical-optics radiometry and does not take into account interference and diffraction phenomena, such as are frequently encountered with highly coherent radiant flux.