General solution to the inverse near-forward-scattering particle-sizing problem in multiple-scattering environments: theory.

A general solution to the problem of measuring the size distribution of large particles in optically thick media by using small-angle light scattering is presented. The approach is general in the sense that no assumption of the form of the particle-size distribution function is required, although the particles must be distributed uniformly throughout the medium. The method is based on a successive order, discrete ordinates approach for modeling multiple-scattering phenomena and requires that the particle field be interrogated by using an array of near-forward input light angles. The scattering redistribution matrix is thereby determined, which permits a numerical inversion of the problem to obtain the single-scattering signature. Finally, conventional inverse scattering methods are used to reconstruct the particle-size distribution from the near-forward (single-scattering) light-scattering pattern.