Spectral scattering coefficient

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. 

Using the number of the scatterers per unit volume Ns (particles/m3) and assuming independent scattering from each scatterer, the spectral scattering coefficient for uniformly distributed monosize scatterers is defined as... 

When the particle diameter is not uniform, we can describe the distribution NS(R) dR, that is, the number of particles with a radius between R + dR per unit volume (number density). Note that NS(R) dR has a dimension of particles/m3. Then, assuming independent scattering, we can define the average spectral scattering coefficient as... 

Mel nikova, I. N., and V. V. Mikhaylov, Spectral Scattering and Absorption Coefficients in Strati Derived from Aircraft Measurements, J. Atmos. Set, 51, 925-931 (1994). 

Penndorf. R.B., (1957) Tables of the refractive index for standard air and the Rayleigh scattering coefficient for the spectral region between 0.2 and 20 microns and their applications on atmospheric optics. J. Opt. Soc. Amer., 47 (2), 176). 

Sample variability is a critical issue in prospective application. For optical technologies, variations in tissue optical properties such as absorption and scattering coefficients can create distortions in measured spectra. This section provides a brief overview of techniques to correct turbidity-induced spectral and intensity distortions in fluorescence and Raman spectroscopy, respectively. In particular, photon migration... 

This example illustrates that measurements of absolute scattering coefficients and quantitative analyses are somewhat more difficult in NIR FT Raman spectroscopy than in the visible region, where absorption can usually be neglected. In any case, it is necessary to carefully calibrate (D Orazio and Schrader, 1974, 1976) the spectral sen.sitivity of the instrument. 

Most spectroscopic software can convert spectra to K-M units on demand. With a constant scattering coefficient, at least within a limited spectral range, the transformed spectra resemble those obtained by conventional transmission spectroscopy. The relative error for K-M unit-based intensities is minimal for reflectance values between 0.2 and 0.7, which is a similar statement as obtainable for absorbance values... 

The scatter coefficient kr(A) of Rayleigh scattering in dry air is reproduced well by an equation presented by R.E. Bird and C. Riordan [5.38]. This gives the following for the spectral transmissivity with A in /j,m... 

In this formula 8 is the scattering coefficient of the colored substance itself, which is assumed to be independent of the wavelength. The spectral dependence of the magnitude F R ) thus reproduees the true contour of the absorption spectrum of the diluted substance, giving log up to an indefinite constant. The relation (2) has been proved to adequately represent the spectrum of that substance, in cases when it was also available in such a form as to allow an ordinary transmittance measurement (24). 

After conversion of decadic beam attenuation value into log (value x 2.303), the spectral attenuation (280-320 nm) was exponentially regressed against wavelength to estimate w32o computed by subtracting scattering coefficient for pure water bj. 

Here, k> and aK are the spectral absorption and scattering coefficients, respectively. The attenuation of radiation intensity by the medium is proportional to both of these coefficients. The spectral attenuation (or extinction) coefficient is expressed by the sum of the absorption and scattering coefficients, as... 

Hendricks and Howell [253] measured the spectral normal transmittance and normal hemispherical reflectance of three sample thicknesses each of reticulated partially stabilized zirconia and silicon carbide at pore sizes of 10, 20, and 65 ppi. The measurements covered a spectral range of 400-500 nm. They used an inverse discrete ordinates method to find the spectrally dependent absorption and scattering coefficients as well as the constants appropri-... 

For small particles, a simplified approach to modeling the spectral scattering and absorption coefficient is given by Mengiic and Viskanta [71]. 

Table 1. Typical absorption and scattering coefficients of tissues in the red/near-infrared spectral region (600-800 nm) and resulting approximate effective attenuation coefficient and penetration depth. Note that for any tissue type, there is considerable patient-to-patient and, for tumors, lesion-to-lesion variation in these properties...

The penetration depth depends on the absorption and scattering coefficients of the sample. It can be maximized by choosing the optimum wavelength. For a wavelength-specific measurement of the spectral characteristic of the sample the broad spectral range of the light source can be dispersed by a prism (Fig. 7.40) and the interference can be measured by a CCD-detector as a function of the wavelength. 

Kubelka-Munk scattering coefficient [m ] relative spectral damage scission indice temperature [°C]... 

Here k is the molar extinction coefficient and 5 is a scattering coefficient which varies with particle size and packing. While the Christiansen effect seen in transmission spectra of powders appears to be absent, spectral distortion can occur in diffuse reflection spectra if the particle size is not uniformly fine. Strongly scattering, or black samples such as coal can be handled by this technique. 

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