modality test, corpuscle problem, stereology

The aim of the paper is to present a method for modality testing of particle sizes that are contained in an opaque material. Such particles cannot be usually observed directly, so a cross-section is usually taken and only 2D circular profiles are observed. Since the cross-section does not run through the center of the particles, the observed 2D radii are smaller than the real radii of the 3D spheres. The presented paper proposes a probabilistic method for estimating the 3D sphere radii from 2D section radii together with the likelihood-ratio test for bimodality. During the process, a differential evolution algorithm is used for optimalization of the unknown distribution parameters.