Sampling and inversion of data in diffraction particle sizing

In optical diffraction particle sizing a numerical transform is sought so that a particle size distribution can be determined from angular measurements of near forward scattering. We consider the nonuniqueness and instability of this transform for discrete data. Our arguments are based on the approximation of the kernel by a function to which it is asymptotic. The results, which include an angular sampling criterion and a rescaling of the forward transform, are applied to choosing and developing algorithms for inverting experimental measurements of scattering. Measurements of scattering from distributions of polystyrene spheres are successfully inverted.