INVERSION OF LIGHT-SCATTERING MEASUREMENTS FOR PARTICLE-SIZE AND OPTICAL-CONSTANTS - THEORETICAL-STUDY

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. W e obtain the solution by expanding the distribution function as a line ar combination of a set of orthonormal basis functions. The set of ort honormal basis functions is composed of Schmidt-Hilbert eigenfunctions and a set of supplemental basis functions, which have been orthogonal ized with respect to the Schmidt-Hilbert eigenfunctions by using the G ram-Schmidt orthogonalization procedure. We use the orthogonality prop erties of the basis functions and of the eigenvectors of the kernel co variance matrix to obtain the solution that minimizes the residual err ors subject to a trial function constraint. The inversion process is d escribed, and results from the inversion of several simulated data set s are presented.