Please try again. Phenomenological Theories of Absorption and Scattering of Tightly Packed Particles, Experimental Testing of the “Kubelka-Munk” Theory, Reflectance Spectra Obtained by Attenuated Total Reflection. . A ≈ In 1969, the English translation of his book entitled Reflectance Spectroscopy (long in preparation and translation) was published. The layers are considered to be semi-infinite. β 2 2 He began by using {log(1/R)} as a metric of absorption. {\displaystyle R(\mu _{0})=1-H(\mu _{0}){\sqrt {1-\omega _{0}}}}, Here ω0 is known as the albedo of single scatter σ/(α+σ), representing the fraction of the radiation lost by scattering in a medium where both absorption (α) and scattering (σ) take place. When the plane parallel layers have surfaces, they have been variously called plates, sheets, or slabs. [4], Furthermore, they argued that it was irrelevant layers whether the light moving from one layer to another was reflected specularly or diffusely. The energy flux in the two directions through the phase boundary caused by this is equal, however, so that 'total reflection takes place. 2 − + The planes are not necessarily physical surfaces which refract and reflect light, but may just describe a mathematical plane, suspended in space. 2 He describes his work as addressing a "mathematical problem of some interest". α and then we obtain the: Additionally, Kortüm derived "the Kubelka-Munk exponential solution" by defining k and s as the absorption and scattering coefficient per centimeter of the material and substituting: K ≡ 2k and S ≡ 2s, while pointing out in a footnote that S is a back-scattering coefficient. = = ∞ ) ) This page was last edited on 11 November 2020, at 10:37. Many of the solutions appear deceptively simple due to the work of (Chandra) Chandrasekhar. Generally, a semi-infinite layer is envisioned as a being bounded by two flat parallel planes, each extending indefinitely, and normal (perpendicular) to the direction of a collimated (or directed) incident beam. In the 1920s and 30s, Albert H. Taylor, Arthur C. Hardy , and others of the General Electric company developed a series of instruments that were capable of easily recording spectral data "in reflection". Unable to add item to List. This rather old and very troublesome procedure, which is length incapable of very accurate results, has recently been modified by Fahren fort by replacing the air-sample phase boundary by the phase boundary between a dielectric of higher refractive index (n ) and the sample (n ). For the case of infinitesimal layers, α His photographs of the scattering process are breathtaking. n , In 1976, Hecht wrote a lengthy paper comprehensively describing the myriad of mathematical treatments that had been proposed to deal with diffuse reflectance. ∞ − v ( = − For particulate samples, a layer is representative if each type of particle in the sample makes up the same fraction of volume and surface area in the layer as in the sample. + Implicit in the Representative Layer Theory is that absorption occurs at the molecular level, but that scatter is from a whole particle.