The far field phase function and efficiency factors

The radial components (Eor, 7/or) are of order (1/r ) as r - oo, and thus do not contribute that is, the scattered wave becomes transverse at large r. In order to obtain the single-scattering phase function we are interested only in relative fluxes, and can set the flux equal to the square of the real amplitude of the electric vector. The two polarization components of the flux are 

Averaging over all states of polarization and adding yields (since (cos / ) = (sin (/ = i) 

The value for c is determined as follows. Let tt Fq be the incident flux and tt F be the scattered flux at a distance r a from the particle. According to Eq. (3.8.28), the magnitude of the incident flux is 

The fraction of JtFo scattered by a particle of effective scattering cross section Xs is XsttFo. This flux is scattered in all directions, and the fraction crossing a differential area dA normal to the direction of propagation along r is jtFr dm, where dm = sin 9 A9 d / is the element of solid angle subtended at the particle by dA. Hence, by the law of the conservation of energy. 

We define the efficiency factors for extinction, scattering, and absorption by, respectively. 

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