Scattering coefficient: attenuation

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... 

In granular solids or in analysis of liquids or slurries in which a considerable amount of particulate material exists, the scattering effect attenuates the optical signal in addition to the absorption. Scattering back from the body of the sample toward the surface produces the intensity to be measured as diffuse reflectance. Scattering also controls the depth of penetration of the sample as well as does its absorptivity (10). The complexity of these two factors acting at once is difficult to predict a priori. This is another reason why the empirical method and the empirical equation coefficients produced by a training set are essential. 

In contrast to AOP s, inherent optical properties (lOP s) depend solely on the water and its optically active constituents. The lOP s include the beam absorption coefficient a , beam scattering coefficient fi , and beam attenuation coefficient c , which are related as follows ... 

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. 

Scattering of ultrasonic waves dominates over other types of losses in the intermediate wavelength regime (X rp), which represents the case of a system with rather coarse particles (>10 pm) subjected to rather high frequencies (>10 MHz). In the IWR the interaction of ultrasound with the disperse system results in the generation of many types of different waves, and thus many more scattering coefficients are required for the evaluation of the attenuation due to scattering. 

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... 

The factor ju g is the transport scattering coefficient of the tissue (which combines the actual scattering probability and the forward nature of light scattering in soft tissues). Some numerical values, presented in Table 1, will clarify this relationship. Note that the attenuation increases, i.e. the penetration depth decreases, equally with increase in absorption or scatter both are equally important in determining the resulting effective treatment depth. 

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 reduction in intensity of a beam can occur by two mechanisms. One involves the deflection or scattering of the particles from the direct line of path between the source and the detector and is described by the scattering coefficient ii. The second mode of reduction is the complete transfer of the projectile energy to the absorbing material (the particles are "captured" ) and is designated by the energy) absorption co cient The (total) attenuation coefficient in (6.7) is the sum of both these modes. 

Absorption and scattering occur simultaneously because all molecules (and particles) both absorb and scatter. The attenuation of radiant energy in a medium is expressed by the extinction coefficient, which is the sum of absorption and scattering,... 

It should be emphasized that the absorption coefficient is a much more restricted concept than the attenuation coefficient. Attenuation also includes the purely elastic process in which the photon is merely deflected and does not give up any of its initial energy to the absorber. In a photoelectric interaction, the entire energy of the incident photon is absorbed by an atom of the medium, while in the Compton effect, some energy is absorbed and appears in the medium as the kinetic energy of a Compton recoil electron the balance of the incident energy is not absorbed and is present as a Compton scattered photon. 

The actual signal arising from any aerosol concentration, used in the evaluation, is associated with the two aforementioned scattering parameters, i.e. the volume back-scattering coefficient fi and the extinction coefficient a. The latter appears in the exponential factor exp[ 2 f oc R, A) dR] and accounts for the total atmospheric attenuation of the laser beam... 

Next, we will briefly discuss methods for separating the linear absorption coefficient ocq and the scattering coefficient So(= Sim + 5op) from the overall attenuation coefficient p (Eq. 11). In principle, this is done by measuring the total amount of transmitted light including scattered components (the overall... 

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