Abstract

We apply functional analysis to the scattered electromagnetic field of a particle with spherical symmetry to obtain a pair of integral transforms for converting the Mie-scattering amplitudes $S_{\perp }(\theta )$ and $S_{\Vert }(\theta )$ into the Mie coefficients $a_n$ and $b_n.$ In the case of a homogeneous sphere, a simple mathematical construction is derived that uniquely inverts the Mie coefficients to find the refractive index and the radius of the particle. A more general method for construction of the refractive-index profile of an arbitrary sphere is discussed that follows from the treatment of Newton and Sabatier.

© 2000 Optical Society of America

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