Constrained eigenfunction method for the inversion of remote sensing data: application to particle size determination from light scattering measurements

Abstract

The Fredholm equation representing light scattering by an ensemble of uniform dielectric spheres is inverted to obtain the particle size distribution responsible for the scattering features. The method of deconvolution involves a constrained expansion of the solution in Schmidt-Hilbert eigenfunctions of the scattering kernels. That solution is obtained which minimizes the sum of the squared residual errors subject to a trial function constraint. The method is, thus, dualistic to the well-known Phillips-Twomey method of constrained linear inversion for the solution by matrix techniques of a Fredholm equation of the first kind in the presence of error. The method is implemented in doubly iterative fashion, and test deconvolutions containing various levels of error are presented.