Kubelka-Munk formula

Grayness of a fabric swatch is not directly proportional to its content of black pigment (or artificial sod). A basic formula relating reflectance to the pigment content or concentration can be appHed to the evaluation of detergency test swatches (51,99—101). In simple form, an adaptation of the Kubelka-Munk equation, it states that the quantity (1 — i ) /2R (where R is the fraction of light reflected from the sample) is a linear function of the sod content of the sample. 

The Kubelka-Munk type is designed for spectra that are measured in diffuse reflectance. The spectral intensities in Kubelka-Munk units are more linear in concentration than those in absorbance units. The conversion formula is... 

Other scientists in the field [24-28] derived expressions similar to those of Schuster [20] and Kubelka and Munk [21]. Earlier theories developed by Gurevic [29] and Judd [30,31] were shown by Kubelka [22] to be special cases of the K-M theory, while Ingle [32] showed that the formulas derived by Smith [33], Amy [34], and Bruce [35] can be derived from the equations of Kubelka and Munk. 

Because the simplified solufion obfained by Kubelka is a two-constant equation and therefore experimentally testable, and because so many other workers derivations are derivable from Kubelka and Munk s work, their solution is the most widely accepted, tested and used. Other workers have derived solutions to the radiation transfer equation that are more complicated than these two-constant formulas. For example, a third constant has been added to account for different fractions of forward and back scattering [36]. Ryde [37,38] included four constants since a difference in the scattering between incident light and internally diffused light is assumed, while Duntley [39] developed a model with eight constants, as a difference between both the absorption and scattering coefficients due to incident and internally diffused radiation was assumed. However, none of these theories is readily applicable in practice, and therefore the treatment of Kubelka is most often applied. 

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