Kubelka-Munk theory

The Kubelka-Munk theory treats the diffuse reflectance of infinitely thick opaque layers [4], a situation achieved in practice for UV/VIS spectroscopy through the use of powder path lengths of at least several millimeters. In this instance, the Kubelka-Munk equation has the form... 

Kubelka-Munk theory, 19 381 24 111 Kubierschky three-column sequence, 3 828-832... 

A quantitative description does become possible, however, if the system under examination satisfies special conditions. These include diffuse, monochromatic illumination, homogeneous pigmentation, isotropic scattering in the coating, no difference in refractive index between vehicle and air, and a coating so thick that the substrate has no effect on the exiting radiation. This is the special case treated by the Kubelka-Munk theory. 

Spectra of solid samples are usually recorded in the units of reflectance (R) or percent reflectance (%/ ), which is analogous to percent transmittance in that reflectance equals the ratio of the reflected radiation to the incident radiation. With diffuse reflectance, the reflected signal is attenuated by two phenomena absorption (coefficient k) and scattering (coefficient s). Lollowing the Kubelka-Munk theory, these two coefficients are related to the reflectance of an infinitely thick sample, by... 

Opaque minerals like iron oxides are frequently examined in the reflectance mode - and usually give diffuse reflectance spectra. Reflectance spectra provide information about the scattering and absorption coefficients of the samples and hence their optical properties. The parameters of reflectance spectra may be described in four different ways (1) by the tristimulus values of the CIE system (see 7.3.3) (2) by the Kubelka-Munk theory and (3) by using the derivative of the reflectance or remission function (Kosmas et al., 1984 Malengreau et ak, 1994 1996 Scheinost et al. 1998) and, (4) more precisely, by band fitting (Scheinost et al. 1999). 

Barrios, J. Heman, L. Morales, J. Tirado, J.L (1986) Effect of grinding in synthetic akaga-neite. J. Colloid Interface Sci. 113 212-217 Barron,V. Montealegre, L. (1986) Iron oxides and color of Triassic sediments Application of the Kubelka-Munk theory. Am. J. Sci. 286 792-802... 

The Kubelka-Munk theory relates q(A) to scattering, absorption, and film thickness (scattering coefficient S, absorption coefficient K, film thickness h). 

The most important and widely used quantity derived from the Kubelka-Munk theory is the reflectance of an opaque (infinitely thick) film that is described by a very simple equation ... 

The method can be rationalized by means of the Kubelka-Munk theory. For standards, see Table 1 ( Tinting strength, relative Photometric ). 

A Reexamination of Paper Yellowing and the Kubelka—Munk Theory... 

Transparent materials interact with light only by absorption. This interaction is formulated quantitatively in the Bouguer-Lambert and Beer s Laws (c.f. i). In paper, however, surface reflection is the dominating type of interaction. This results in very desirable properties like high brightness and opacity, but complicates the interpretation of optical tests with regard to absorption data. The Kubelka-Munk theory attempts to separate the two types of... 

The Kubelka-Munk theory of diffuse reflectance is a good description of the optical properties of paper. The two parameters of the theory, absorption and scattering coefficient, are purely phenomenological, but are closely related to basic properties of paper. The absorption coefficient is approximately a linear function of the chrcmgphore concentration in the paper. The scattering coefficient is related to the nonbonded fiber surface area in the paper, or the area "not in optical contact," and the Fresnel reflectivity of that surface. 

Though the Kubelka-Munk theory has proven to be adequate in many applications, it has significant deficiencies that prevent it from being a total solution for color matching. Kubelka-Munk theory continues to be popular because it provides simple analytical equations and reasonable predictions [2]. 

The Kubelka-Munk theory assumes a linear relation between the colorant characteristic K/S and the colorant concentration. In general, it is found that the K/S ratio of a component colorant is a nonlinear function of the concentration [3]. This means that it will not be possible to adequately describe the colorant behavior by using a linear relation. Figure 4.2a shows the linear relation that results... 

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