Synthesis of integral transform solutions for the reconstruction of particle-size distributions from forward-scattered light.

Five integral transform solutions to the Fredholm integral equation that describes the forward-scattering properties of the distributions of spherical particles in the Fraunhofer diffraction regime have been studied. We have systematically reformulated the family of solutions, including four derivations by three other research groups and one developed as part of this work, using a standardized notation. This synthesis elucidates the mathematical interrelationships and fosters an understanding of the inversion performance of the five solutions. Finally a series of numerical experiments was carried out to demonstrate the relative performance of the techniques when applied to identical sets of simulated forward-scattering signatures.