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The Scattering Matrix
The Stokes vector of a scattered wave in the far-field,
,
can be expressed in terms of the
incident Stokes vector, ,
by means of a linear transformation,
|
(3.22) |
where
is a 44 matrix having, in general, 16 real
independent elements, and
is the scattering cross-section.
At optical wavelengths, it is not possible
for an instrument to introduce non-linear effects and so there is no
loss of generality by using a linear transformation (Hansen and Travis, 1974).
When the scatterers are isotropic, homogeneous spheres, the scattering matrix
reduces to four independent elements,
|
(3.23) |
Two important types of scattering for which equation (2.23)
is applicable are Rayleigh and Mie.
In order to conserve energy upon a scattering event,
one component of the phase matrix must be normalized.
This constraint is expressed as,
|
(3.24) |
where the P11 element, also known as the phase function,
relates scattered radiance to incident radiance.
Next: Types of Scattering
Up: Basic Processes in Earth's
Previous: Scattering
Chris McLinden
1999-07-22