3D particle size distributions from 2D observations: stereology for natural applications

We have developed a general formulation for stereological analysis of particle distributions which is applicable to any particle size or size distribution (not limited to log-normal, unimodal, etc.). We have applied numerical techniques to define intersection probability distributions for any shapes (previously only known for spheres), and quantified the errors involved in using spherical coefficients for various non-spherical particles. This stereological technique is based on knowing the probability distribution of random cross-sections through various particles so that `small circleʹ cross-sections can be subtracted from an observed population to provide the 3D size distribution of particles. The results indicate that the most important parameter controlling calculated size distribution is particle aspect ratio. For a distribution of particles with a specific aspect ratio or range of aspect ratios, variations of particle form (spherical vs. cubic; rectangular vs. elliptical) do not alter the results, so the technique can be applied to a range of particle shapes. Applications can be made in a petrology, volcanology, and other fields, only a few of which can also be treated using expensive X-ray techniques.