Abstract

Experiments are presented for recovering the histograms of particle size from the optical transform intensity of spherical particles. We describe a novel inversion formula, and we provide computational details for obtaining particulate sizes from the transform intensity. The intensity is given by an integral over the size distribution multiplied by an Airy function (transform intensity for a single particle). The inversion formula is derived from the intensity using Bessel-delta identities and Abel transforms. By multiplying the intensity by an appropriate kernel and integrating over the diffraction angle, recovery of the particle size distribution is obtained. In the experiments, we use chrome masks with large numbers of tiny circular apertures of disks. These have been generated with three separate distributions: the gamma, the log-normal, and the bimodal exponential.

© 1991 Optical Society of America