Imaging spheres with general incident wavefronts using a dipole decomposition

Although scattering from spheres with plane wave illumination was solved precisely by Mie in 1909, often it is of interest to image spheres with non-planar illumination. An extension of Mie theory which incorporates non-planar illumination requires knowledge of the coefficients for a spherical harmonic expansion of the incident wavefront about the center of the sphere. These coefficients have been determined for a few special cases, such as Gaussian beams, which have a relatively simple model. Using a vectorized Huygen's principle, a general vector wavefront can be represented as a superposition of dipole sources. We have computed the spherical wave function expansion coefficients of an arbitrarily placed dipole and hence the scattering from a sphere illuminated by a general wavefront can be computed. As a special case, Mie's solution of plane wave scattering was recovered. Potential applications include scattering with partially coherent illumination. Experimental results from the scattering from polystyrene spheres using Köhler illumination show agreement with numerical tests.