Principles of an image-based algorithm for the quantification of dependencies between particle selections in sampling studies

摘要

A generalization of Gy's model for the fundamental sampling error introduced the new 'parameter for the dependent selection of particles', denoted as C_ij. This allows for modeling deviations from the ideal situation where the selection of a pair of particles is composed of two independent selections. The generalized model potentially leads to more accurate variance estimates in the case of clustering of particles, differences in densities or sizes of the particles or repulsive inter-particle forces. A straightforward and practically applicable method is needed for the determination of this parameter for miscellaneous mixtures in industrial settings.