Applying the first-order perturbation theory, we have derived a theorem which states that, under specific conditions, the sum of the scattering matrices of two nonspherical particles can be replaced by the scattering matrix of a sphere. Consequently, a polydispersion of such nonspherical particles can be replaced by a polydispersion of spheres, without changing scattering characteristics of the polydispersion. This implies the nonuniqueness of the inverse-scattering problem. To verify the validity of the theorem, the differential scattering cross sections of several nonspherical rotationally symmetric particles have been calculated using the extended boundary condition method. The results show that the theorem is satisfied with accuracy expected from the first-order perturbation theory.
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