Unfolding Particle Size Distributions

This paper treats the unfolding problem of estimating the density distribution of particles dispersed in a three-dimensional specimen. A general framework is set in terms of a probabilistic model for the distribution of a discrete number of particle sizes with prescribed shapes which are sampled and observed by processes capable of being modeled. The general formulation allows density estimates and standard deviation estimates for each particle size in the distribution to be made with data from observational processes that may distort or truncate the sampled information. The method is related to the earlier works on unfolding or estimating the density distribution of spherical particles sectioned by planar probes. The method is also used to develop a more accurate estimate for the density distribution of spherical voids where the observational process is the indirect microscopy of a replicated surface.