Analytic light-scattering solution of two merging spheres using Sh-matrices

We use the Sh-matrix formalism that contains the shape-dependent parameters of the T-matrix to derive an analytic solution for the light scattering from two merging spheres at different degrees of merging. The integral expressions for the Sh-matrix elements are simpler than those of the T-matrix elements and, for two merging spheres, these integrals can be solved analytically. Our calculations show that when the spheres merge, the primary fringes that are circular for non-merging spheres become distorted. Secondary fringes due to the interference of the waves emanating from the two spheres begin to appear when the spheres are merged approximately 50%.