  Decomposing the field scattered by an object into vector spherical harmonics
(VSH) is the prime task when discussing its optical properties on more
analytical grounds. Thus far, it was frequently required in the decomposition
that the scattered field is available on a spherical surface enclosing the
scatterer; being with that adapted to the spatial dependency of the VSHs but
being rather incompatible with many numerical solvers. To mitigate this
problem, we propose an orthogonal expression for the decomposition that holds
for any surface that encloses the scatterer, independently of its shape. We
also show that the orthogonal relations remain unchanged when the radiative VSH
used for the expansion of the scattered field are substituted by the VSH used
for the expansion of the illumination as test functions. This is a key factor
for the numerical stability of our decomposition. As example, we use a
finite-element based solver to compute the multipole response of a nanorod
illuminated by a plane wave and study its convergence properties.
