The problem of scattering of spherical waves by a bounded obstacle is considered. General scattering theorems are proved. These relate the far-field patterns due to scattering of waves from a point source put in any two different locations. The scatterer can have any of the usual properties, penetrable or impenetrable. The optical theorem is recovered as a corollary. Mixed scattering relations are also established, relating the scattered fields due to a point source and a plane wave.

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A spherical electromagnetic wave is scattered by a bounded perfectly conducting obstacle. A generalization of the plane-wave optical theorem is established. For a spherical scatterer, low frequency results are obtained by approximating the known exact solution (separation of variables). In particular, a closed-form approximation of the scattered wavefield at the source of the incident spherical wave is obtained. This leads to the solution of a near-field inverse problem, where both the source and coincident receiver are located at several points in the vicinity of a small sphere. The same inverse problem is also treated from the knowledge of the leading order term in the low-frequency asymptotic expansion of the scattering cross-section.