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Improve integration of Mueller matrix over phi (azimuthal angle) #154

Open GoogleCodeExporter opened 9 years ago

GoogleCodeExporter commented 9 years ago 
There are several ideas to be considered:
1) Currently Romberg integration is internally replaced by simple trapezoid 
rule due to periodicity. This can be made explicit to add flexibility. Probably 
error estimates can also be improved by direct analysis of (simpler) numerical 
scheme.
2) If Mueller matrix element is written as a double sum over dipoles, each 
summand can be integrated. So the final integrated result is also a double sum, 
which can probably be evaluated by some FFT-trick. However, special 
consideration will probably be required for other multipliers (like cos2phi, 
etc.).
3) Integration over phi seems to be related to issue 138. In particular, 
integration over phi should leave only m=0 spherical harmonics. So if a partial 
expansion (Fourier over phi) can be efficiently performed - it will give all 
the required results.

Original issue reported on code.google.com by yurkin on 18 Sep 2012 at 3:41

GoogleCodeExporter commented 9 years ago

Original comment by yurkin on 4 Jul 2013 at 9:46