Radiation scattering coefficients

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 ... 

We note that since Q involves the scattering coefficients, the radiation pressure force has resonance or near-resonance behavior. This first was observed and analyzed by Ashkin and Dziedzic (1977) in their study of microparticle levitation by radiation pressure. They made additional measurements (Ashkin and Dziedzic, 1981) of the laser power required to levitate a microdroplet, and Fig. 19 presents their data for a silicone droplet. The morphological resonance spectrum for the 180° backscattered light shows well-defined peaks at wavelengths corresponding to frequencies close to natural frequencies of the sphere. The laser power shows the same resonance structures in reverse, that is, when the scattered intensity is high the laser power required to levitate the droplet is low. 

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... 

When the photocatalytic degradation of a dye or of any other nontransparent contaminant is considered, the effect of the dye on the optical properties of the aqueous medium has to be accoimted for. The dye absorbs radiation but does not scatter it therefore, the scattering coefficient for the medium is equal to the scattering coefficient of the catalyst particles... 

If the electric vector of the exciting radiation is oriented in b direction, parallel to the plane of the direction of irradiation and observation, then the scattering coefficient is given by ... 

Very useful information may be derived from the intensities in spectra which are obtained with the electric vector of the exciting radiation oriented parallely and perpendicularly to the plane of observation (Eqs. 2.4-7 and 2.4-8). The ratio of the two scattering coefficients is known as the depolarization ratio p ... 

Fig. 3.5-4 b shows the intensity of the Raman radiation of a forward-scattering arrangement. At an optimum thickness , the Raman radiation has a maximum, which increases as the elastic scattering coefficient decreases. The exciting radiation which emerges from the sample (Fig. 3.5-4 d) has a lower intensity if the elastic scattering coefficient r is higher. 

Fig. 3.5-13 demonstrates the influence of sample and instrumental parameters on the intensities of the observed Raman lines, excited with the Nd YAG laser at 1064 nm. The lower abscissa shows the absolute wavenumber scale, the upper abscissa represents the Raman shift. The relative intensity of Raman radiation is calculated by Eq. 3.5-9, taking into account the absorption coefficient a cm ) of water (Fig. 3.5-3) and a constant Raman scattering coefficient (assumed to be equal to 1 cm ). The elastic scattering coefficients as parameters, r = 0, 10, 100, 500 cm , describe the properties of a liquid, a coarse, a medium, and a fine powder, respectively. The traces show the relative output voltage of a Germanium detector. 

Theory of Kubelka and Munk. This theory was developed by, and named after, the Czechoslovakian physical chemists P. Kubelka and F. Munk in 1931 and is applied to the evaluation of reflectance measurements. This theory for the propagation of radiation in opaque media, using an absorption coefficient and a scatter coefficient. For an opaque layer it can be shown that the reflectance depends only on the ratio of these coefficients. The ratio of the coefficients is approximately proportional to the dye concentration of dyed materials. 

The estimate of the performances of the detector requires detailed Monte-carlo simulations that have to take into account the detector layout and the physical characteristics of the Cerenkov radiator which surrounds the detector tight refraction index, tight absorption and scattering coefficients, in seawater (or ice). These quantities must be accurately measured in situ [38],... 

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