Unfolding Particle Size Distributions

Abstract

General treatment for unfolding particle size distributions in a 3-dimensional specimen is possible if the particles spacial distribution, the sampling method, and the observational method are described by probabilistic models. Particles -within “k” discrete groups are sized -with a single characteristic dimension (e.g., diameters for spheres). The spacial distribution of particle centers is assumed uniform. The sample consists of all particles intersected by a probe. AF_i/τ is the intersection probability for an i^th size particle, with A the characteristic dimension of the probe and τ the specimen volume. The observations of sampled particles are sized into c cells. P_ji is the conditional probability that an i^th size particle is in the j^th cell. The number of observations in the j^th cell is mj. The expected values and the covariances of the m_i’s are linear functions of the specimen population densities ρ̑_i. Population density estimates ρ_i, and their covariances follow from the Gauss-Markov Theorem.