Scattering coefficient: absorption

The expression exp(-cxx) describes the reduction of the wave amplitude in absorbing materials. The damping coefficient a can be split into an absorption coefficient Oa and the scattering coefficient Oj. 

When both absorption and scattering are present, the Beer-Lambert law must be replaced by the Kubelka-Munk equation employing the absorption and scattering coefficients iC and S, respectively. This gives the redectivity... 

The extinction coefficient is dependent on the presence of gases and molecules that scatter and absorb light in the atmosphere. The extinction coefficient may be considered as the sum of the air and pollutant scattering and absorption interactions, as shown in Eq. (10-4) ... 

The values of r and a in Table 4-2 show that photoelectric absorption generally makes the greater contribution to the mass absorption coefficient. Absorption leading to scattering, which will be discussed in the next section, gains in relative importance as atomic number Z and wavelength X decrease. 

Wavelength of Primary Beam, A Exciting Potential, V Scattering Coefficient, a Photoelectric Absorption Coefficient, T cr/r... 

Complex processes are involved in transmittance and reflectance of scattered radiation, which are theoretically described by Schuster [4]. In an ideal scattering medium all fluxes of light can be summed up as components of two vectors. Vector I stands for the light flux in the direction of the incident light, and the vector J describes the light intensity in the antiparallel direction. With k, the absorption coefficient, and 5", the scattering coefficient, the two Schuster equations are as follows ... 

K is the absorption coefficient, a function of the frequency v S is the scattering coefficient... 

If the scattering coefficient does not depend on the infrared frequency, the Kubelka-Munk function transforms the measured spectrum RJ V) into the absorption spectrum K v). In situ cells for DRIFT studies of catalysts have been described [10] and are commercially available. 

Since then, number of researcher have studied and experimented with TRS including Chance and Oda [61] [63] [76] [80] [81] [73] [82] [113] [114], TRS instruments rely on a picosecond pulsed laser with a detector that is designed to detect the time evolution of the light intensity [44], With the time profile of light intensity through the medium, it is possible to measure both absorption and reduced scattering coefficients [32], A ma-... 

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. L. Jacques, and Y. Hefetz. Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time-resolved diffuse reflectance measurements. Applied Optics, 31 3509-3517, 1992. 

Y. Yamashita, M. Oda, H. Naruse, and M. Tamura. In vivo measurement of reduced scattering and absorption coefficients of living tissue using time-resolved spectroscopy. OSA TOPS, 2 387-390, 1996. 

This analytical approach is difficult to apply to individual pigments because physical data relating to refractive index, dispersion curves and the absorption curves in the solid state are not available. A colligative approach, based on the Kubelka-Munk analysis which characterises pigments by only two constants, an absorption and a scattering coefficient, has been applied with considerable success to the computation of the proportions of pigments in mixtures needed to match a given colour. Much of the book Colour physics for industry is devoted to this topic [37]. 

The tinctorial strength in white reductions is thus quantitatively defined by the Kubelka-Munk relation between the spectral absorption coefficient K and the spectral scattering coefficient S in which [ refers to the reflection of a completely opaque layer. The ratio K/S is proportional to the tinctorial strength. 

Figure 8.13. Fluorescence intensity under normal incidence (fi = 1) of transparent and scattering samples as a function of the absorption and scattering coefficient. Note the increase of fluorescence when going from transparent to weakly scattering samples.

Besides the fluorescence coefficient, the optical absorption and scattering coefficients of the sample are the most important parameters in quantative fluorescence spectroscopy of turbid media. In principle two or, if the anisotropy parameter has to be determined, three independent measurements are sufficient to separate the coefficients that appear in all equations as sums or proportions. However, for better accuracy, one of the geometrical parameters (sample thickness, angle of incidence, distance from the irradiated spot) as well as the wavelength of irradiation should be varied over a wide range, and then the data should be fitted with the help of the corresponding model equation. 

In commercial filter paper for chemical purposes, the scattering coefficient parallel to the layer, o = 220 cm 1, is significantly different from the scattering coefficient perpendicular to thelayer, absorption coefficients of dyed cellulose have been determined in the range of 1 < k < 200 cm 1. The values are proportional to the analytical concentration of the dye. 

Fi gure 8.20. Fluorescence reabsorption in a semi-infinite scattering layer. Ordinate fraction of emitted to true fluorescence intensity. Abscissa diffuse reflectance at the fluorescence wavelength. Parameter diffuse reflectance at the absorption wavelength, The scattering coefficient is assumed to be independent of A (S° = S ). 

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... 

Hence, if the scattering coefficient remains constant during a measurement, the absorption may be deduced from the reflectance. 

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