Inverse Mie problem

We apply functional analysis to the scattered electromagnetic field of a pa rticle with spherical symmetry to obtain a pair of integral transforms for converting the Mie-scattering amplitudes S-perpendicular to(theta) and S-l( theta) into the Mie coefficients a(n) and b(n). In the case of a homogeneou s sphere, a simple mathematical construction is derived that uniquely inver ts the Mie coefficients to find the refractive index and the radius of the particle. A more general method for construction of the refractive-index pr ofile of an arbitrary sphere is discussed that follows from the treatment o f Newton and Sabatier. (C) 2000 Optical Society of America [S0740-3232(91)0 0801-3] OCIS codes: 290.3200, 290.4020.