Optimization for optically soft particles

[myurkin]

There is some relevance of the DDA simulations for particles with refractive index close to 1. More specifically, when the Born approximation captures the large part of the final solution. The simplest idea is to exactly calculate the scattering of the incident plane wave, leading to corrections similar to "-scat igt_so", but dependent on the scattering angle. Quick tests show great potential for cubes. So it make sense to implement additional argument to -scat.

Unfortunately, those corrections can be overwhelmed by shape errors. In particular, the first results for spheres show almost no correction along the above lines. This makes it related to the weighted discretization - #12. Another relevant issue is #59.

And it is also interesting (at least from a theoretical standpoint) to study the limit of m->1. For instance, specifying m=1 in the command line may cause ADDA to produce the first non-zero order of (m-1) for all scattering quantities. In this respect, ADDA can be made a convenient (and accurate) tool for calculating the Born (or Rayleigh-Debye-Gans) result (and corresponding integrals). The first step for that would be to audit the internal numerics of ADDA, whether it is possible to extract the infinitesimal parts in all derivations.

[inzhevatkin]

I will work on it

[myurkin]

Concerning the soft spheres, one can completely isolate the Born approximation from the scattering problem and compute it fully analytically. The DDA will then be used only for the next-order term. This can be extended to any shapes for each analytical Born approximation is feasible. This corresponds to rigorous expansion of the DDA results in orders of susceptibility. I have some draft with corresponding equations - contact me, if interested.