Extinction matrix

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Some applications require a complete extinction matrix K either for fixed 
orientation or orientation-averaged. For fixed orientation K can be easily 
obtained from the amplitude scattering matrix at forward direction - 
Eqs.(2.140)-(2.146) in Mishchenko's book (2002). For complete orientation 
averaging of mirror-symmetric particle K is trivially expressed through <Cext> 
- Eq.(4.32).

The most problematic case is chiral particles and/or partial orientation 
averaging. Then K has non-diagonal elements, e.g. K14 and K41. Computing 
averaged K is, in principle, possible by doing averaging manually (with scripts 
and multiple runs), but doing it in the framework of the existent orientation 
averaging machinery in ADDA would be much more convenient.

Having the extinction matrix will also help to determine Cext for circular (or 
arbitrary) incident polarization (issue 30) - Eq.2.159.

The first implementation of this feature should be based on Eqs.(2.140)-(2.146) 
mentioned above, but they are valid only for the plane incident wave (like the 
far-field expression for Cext). An interesting idea is to generalize the 
definition of K to Gaussian beams. I am not sure if that any sense in the first 
place, but that can only be made through some volume integral definition for K 
(to be derived).

Original issue reported on code.google.com by yurkin on 11 Mar 2014 at 2:06

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I forgot to mention that averaging of K over alpha can always be done 
analytically, both for complete and incomplete ranges, using Eq.(4.29). And it 
is completely rigorous, in contrast to current two-polarization averages used 
for Cext and Cabs (they latter depend on the incident polarization for 
incomplete alpha averaging).

Original comment by yurkin on 11 Mar 2014 at 2:12