Scattering and Absorption Coefficients

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. 

The following combinations of measurements have already been successfully applied or could be applied with the appropriate equipment 

Measurement oftransmittance Td and reflectance Ro of one sample with known layer thickness d. Diffuse irradiation and detection. Evaluation with Eqs. (8.16) and (8.17). 

Measurement of collimated transmission Tc according to Eq. (8.1), in addition to points (1) and/or (2). Determination of the anisotropy factor. 

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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. 

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). 

One must first link the source tb concentrations of each chemical species in the aerosol. Second, the contribution of each chemical species to the particle scattering and absorption coefficients must be determined. 

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). 

Several authors have addressed the determination of the optical properties of aqueous titanium dioxide suspensions in the context of photoreactor modeling (Brandi et al., 1999 Cabrera et al., 1996 Cured et al., 2002 Salaices et al., 2001, 2002 Satuf et al., 2005 Yokota et al., 1999). Among the determined properties are extinction, scattering, and absorption coefficients, as well as the asymmetry parameter of the scattering phase function. In general the procedures involve fitting of a radiative transfer model to the experimental results for reflectance and transmittance of radiation. 

The data presented in Fig. 7.30 obviously have similar characteristics, regardless of the material. The Hale and Bohn data are plotted based on the pore diameter calculated as the inverse of the ppi values reported however, measured pore sizes are generally smaller than nominal sizes computed in this way [255], It may be possible to collapse all of the data for extinction coefficient onto a single curve if the Hale and Bohn data are adjusted to actual pore size rather than a pore size calculated from nominal ppi values. This was not attempted, because actual pore size data were not reported in Ref. 252. Even if the data can be collapsed in this way, it will be necessary to have additional data for the scattering albedo of the material so that the individual scattering and absorption coefficients can be recovered from the extinction coefficient data. 

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

It is of interest to examine the dependence of the mass scattering and absorption coefficients on particle diameter in the two extremes of a D A.) and... 

FIGURE 24.10 Total extinction, scattering, and absorption coefficients for internal versus external mixtures of soot and (NH4)2S04. 

Let us consider the difference in behavior of the scattering and absorption coefficients for the internally and externally mixed aerosols. Consider first the scattering coefficient and the overall composition of 20% soot/80% (NH4)2S04. For 0.05 fim diameter parti-... 

A change in depth clearly changes the shape of the fluorescence signal, while a change in concentration changes only the intensity. For known scattering and absorption coefficients in the tissue the fluorescence lifetime and the depth of a fluorescent inclusion can be determined. 

Detailed data on values of particulate size and resulting scattering and absorption coefficient for various weather and climatic conditions can be obtained from the literature, particularly that of the Air force Geophysics Laboratory, which is also summarized in the RCA Electro-Optics Handbook and in Kopeika and Bordogna (1970). 

T. Burger, J. Kuhn, R. Caps, and J. F. Fricke, Quantitative Determination of the Scattering and Absorption Coefficients from Diffuse Reflectance and Transmittance Measurements Application to Pharmaceutical Powders, Appl. 

T. Burger, H. J. Ploss, Ebel, and J. Fricke, Diffuse Reflectance and Transmittance Spectroscopy for the Quantitative Determination of Scattering and Absorption Coefficients in Quantitative Powder Analysis, Appl. Spectrosc., 51(9), 1323 (1997). 

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and B. C. Wilson, Spatially Resolved Absolute Diffuse Reflectance Measurements for Noninvasive Determination of the Optical Scattering and Absorption Coefficients of Biological Tissue, Appl. Opt., 35(13), 2304 (1996). 

To obtain meff with the use of the three-flux approximation of ERT, the scattering and absorption coefficients of the investigated powder are obtained from diffuse reflectance and transmittance measurements on optically thin samples (for a detailed discussion see [41,74]). Then, at each wavelength, the diffuse reflectance is calculated as a function of the scattering and absorption coefficients for a... 

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