Extinction, cross section

Extinction Coefficient a measure of the ability of particles or gases to absorb and scatter photons from a beam of light a number that is proportional to the number of photons removed from the sight path per unit length. See absorption. Extinction Cross Section the amount of light scattered and absorbed by a particle divided by its physical cross section. 

In order to calculate particle size distributions in the adsorption regime and also to determine the relative effects of wavelength on the extinction cross section and imaginary refractive index of the particles, a series of turbidity meas irements were made on the polystyrene standards using a variable wavelength UV detector. More detailed discussions are presented elsewhere (23) > shown here is a brief summary of some of the major results and conclusions. 

Calculations of the extinction cross section at a given wave-... 

Figure 9. Experimental extinction cross section Rest for polystyrene as a function of particle diameter at 220 run...

In this Section we want to present one of the fingerprints of noble-metal cluster formation, that is the development of a well-defined absorption band in the visible or near UV spectrum which is called the surface plasma resonance (SPR) absorption. SPR is typical of s-type metals like noble and alkali metals and it is due to a collective excitation of the delocalized conduction electrons confined within the cluster volume [15]. The theory developed by G. Mie in 1908 [22], for spherical non-interacting nanoparticles of radius R embedded in a non-absorbing medium with dielectric constant s i (i.e. with a refractive index n = Sm ) gives the extinction cross-section a(o),R) in the dipolar approximation as ... 

One can now define the extinction cross-section by dividing by the incident irradiance. 

In terms of the scattering coefficients the scattering and extinction cross-sections are given by... 

In the general case, individual particles have differing compositions and refractive indices and to take this into account in detail is not possible from a practical point of view. To allow for a variation of refractive index, a convenient model is that of a mixture of aerosols from the several sources, each with its own extinction cross-section. The particles are assumed not to coagulate so that the aerosol is not mixed on the individual particle basis. Such an aerosol is known as an external mixture. This model would also be applicable, approximately, to an aerosol mixture whose particles are growing in size by gas-to-particle conversion. 

They can be calculated from theory if the extinction cross-section and mass distributions are known. Calculations of this type have recently been made by Ouimette ( ,). ... 

It follows from (3.20) that the extinction cross section Cext may be written as the sum of the absorption cross section Cabs and the scattering cross section Csca ... 

The mass attenuation coefficient am, defined as the extinction cross section per unit particle mass, is related to the volume attenuation coefficient by... 

It also follows from (8.17) and (8.23) that the circular dichroism of a suspension of spheres is proportional to the difference between the extinction cross sections for left-circularly and right-circularly polarized light ... 

Plots of each of these quantities as a function of particle size would look quite different and, therefore, would tell different stories. Except for a scale factor, each of them plotted as a function of wavelength for the same particle size would be identical. In our first example of extinction (Fig. 4.6) we displayed the efficiency Qext, as we shall often do in this chapter. In Chapter 12, however, our preference switches to the extinction cross section per unit particle volume. Unnormalized extinction cross sections (strictly speaking, the differential scattering cross section integrated over the acceptance angle of the detector) are more appropriate in Section 13.5 on particle sizing. 

The origin of the misconception that the absorption spectrum of particles in the Rayleigh limit is not appreciably different from that of the bulk parent material is easy to trace. Again, for convenience, let us take the particles to be in free space. In Chapter 3 we defined the volume attenuation coefficient av as the extinction cross section per unit particle volume if absorption dominates extinction, then av for a sphere is 3Qabs/4a, where a is the radius. If we assume that n k, which is true for most insulating solids at visible wavelengths, then... 

In previous chapters we have always taken particles to be in a nonabsorbing medium. We now briefly remove this restriction. The notion of extinction by particles in an absorbing medium is not devoid of controversy more than one interpretation is possible. But Bohren and Gilra (1979) showed that if the extinction cross section is interpreted as the reduction in area of a detector because of the presence of a particle [see Section 3.4, particularly the development leading up to (3.34)], then the optical theorem for a spherical particle in an absorbing medium is formally similar to that for a nonabsorbing medium ... 

Figure 12.7 Calculated extinction cross section per unit volume of a silicon carbide ellipsoid with geometrical factors 0.1, 0.3, and 0.6. Cext - Cabs for sufficiently small absorbing particles.

Figure 12.12 Maximum infrared extinction cross sections of spheres normalized by the value in the Rayleigh limit.

Chylek, P., 1976. Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section, J. Opt. Soc. Am., 66, 285-287. 

Spinhime, J. D., J. A. Reagan, and B. M. Herman, 1980. Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique, J. Appl. Meteorol., 19, 426-438. 

The extinction cross-section Cgxt for spherical particles can be approximated by using Mie theory ... 

Information on particulate matter production in test fires has been compiled in Tables II-V. In a few instances, extinction cross sections were directly measured and used to derive the properties of the smoke particles. It is clear in all cases that available information is scanty, variable and uncertain. Because we are no experts in combustion research, we have checked our analysis with several combustion specialists and have gotten... 

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