analytical orientation averaging of cross-sections

[baptiste auguie]

Hi,

Is anyone aware of an existing implementation of analytical
orientation averaging in the coupled-dipole framework?
There seems to be two schools of thought here; those who would work on
the interaction matrix directly [*], and others who would go from DDA
to T-matrix, then use existing analytical formulas [**].

[*] Orientational Averaging of Integrated Cross Sections in the
Discrete Dipole Method. N. G. Khlebtsov, Opt. Spectrosc. 90, 408
(2001)
[**] D. W. Mackowski. Discrete dipole moment method for calculation of
the T matrix for nonspherical particles. J. Opt. Soc. Amer. A 19
(2002)

Best regards,

baptiste

[Maxim Yurkin]

Hi Baptiste,

As far as I know, the papers that you mentioned is basically the state-of-the-art. And I am not aware of any widely-used
implementations. But I think that Dan Macknowski has some proof-of-principle implementation that he might share. So
contacting him seems to be a good idea.

From the other side, my feeling is that an efficient numerical quadrature would be in many cases faster than the
analytical formulae. Moreover, the latter are anyway truncated to some extent and hence not perfectly accurate. In this
respect, the recent paper by Antti Penttila may be of relevance:
A. Penttil� and K. Lumme, �Optimal cubature on the sphere and other orientation averaging schemes,� J. Quant. Spectrosc.
Radiat. Transfer 112, 1741-1746 (2011). doi: 10.1016/j.jqsrt.2011.02.001

But, of course, analytical formulae are still useful in some cases.

Maxim.

[baptiste]

Hi Maxim,

Thanks for your input.
Funny you should mention Dan Mackowski, as I recently contacted him
with a very similar request (orientation-averaging in the T-matrix
framework, for circular polarisation). Unfortunately I've never met
him and he is busy with other projects.

I'm surprised numerical integration would be faster than analytical
formulas; then again, looking at these formulas I could believe it :)
As far as numerical integration goes, it find that Quasi-Monte Carlo
is a nice alternative to weighted numerical quadrature rules.
Following the same reference you suggest, I recently implemented QMC
using Halton sequences in my cda package (sparse collections of
Rayleigh-sized particles [*]), and it performed better than Gauss-
Legendre quadrature in practically all cases.

Best,

baptiste

[*]: http://www.scattport.org/index.php/programs-menu/multiple-particle-scattering-menu/480-coupled-dipole-simulations-cda
http://cran.r-project.org/web/packages/cda/index.html

On Sep 8, 12:29 am, Maxim Yurkin <yur...@gmail.com> wrote:
> Hi Baptiste,
>
> As far as I know, the papers that you mentioned is basically the state-of-the-art. And I am not aware of any widely-used
> implementations. But I think that Dan Macknowski has some proof-of-principle implementation that he might share. So
> contacting him seems to be a good idea.
>
>  From the other side, my feeling is that an efficient numerical quadrature would be in many cases faster than the
> analytical formulae. Moreover, the latter are anyway truncated to some extent and hence not perfectly accurate. In this
> respect, the recent paper by Antti Penttila may be of relevance:

> A. Penttil and K. Lumme, Optimal cubature on the sphere and other orientation averaging schemes, J. Quant. Spectrosc.