Fourier representation of the energy distribution of an electromagnetic field scattered by spherical particles.

A solution to the scattering problem for spherical particles is presented in terms of a Fourier series expansion for the electromagnetic field as well as for the corresponding energy distribution. The basic assumptions are the same as for the Mie solution. The Fourier coefficients of the energy distribution show a systematic behavior as functions of the size parameter alpha = 2piR/lambda (R = radius of particle, lambda = wavelength of scattered light), and they depend significantly on the complex index of refraction N = n - in k of the particles (n = real index of refraction, k = absorption index). These coefficients are approximately proportional to the volume of the sphere superimposed with an oscillation of Bessel function type with argument (n - 1) alpha. They can be measured directly without any intricate Fourier analysis; and since they depend in a distinct way on the quantities n and k, they can be used to determine these optical properties of particles of an unknown material. The scattering influence of a gaseous carr er medium can be eliminated without any experimental arrangement just by using an appropriate Fourier coefficient of the scattered energy distribution.