Do t-matrix superposition without translation to a cluster origin

Currently, the Mackowski multisphere superposition code computes holograms extremely slowly for particles that are spaced apart (e.g., several spheres on a ~5 micron droplet). This is partly because the scattered field is expanded in vector spherical harmonics (VSH) about the cluster center of mass. Thus, while an expansion about individual spheres might only require ~10 orders, using the VSH translation theorem forces the final expansion to require ~50 orders. Since we have to sum over every order l (and for every order, over all the magnetic quantum numbers, -l to l) for every single point at which we calculate an electric field, this can take a very long time.

The cluster-centered approach makes sense for dense clusters with many particles, where one would pay a penalty in multiple loops over the field points in a sphere-centered approach and the VSH translation does not require too many additional orders. But for certain problems, it may be advantageous to use the multisphere superposition code (F90 version?) to calculate the sphere-centered expansion coefficients for each sphere, but then to use the sphere-centered coefficients to calculate VSH expansions about each sphere. This would essentially amount to a higher-order correction to our current Mie superposition formalism, in which we manually keep track of the phase differences in the field scattered by different particles.

It isn't clear a priori when the sphere-centered approach is faster than the cluster-centered approach. Possibly the code could automatically detect egregious cases (e.g., particles spaced very far apart), or cases in which the number of orders in the cluster-centered expansion greatly exceeds the maximum order for any given sphere.