Distribution‐free estimation of sphere size distributions from slabs showing overprojection and truncation, with a review of previous methods

Abstract

SUMMARY: A distribution‐free method is presented for unfolding the size distribution of an aggregate of disjoint opaque spherical particles in a translucent medium, from the circular profiles observed in the orthogonal projection of sections of a certain thickness through the medium. This situation pertains especially to light and transmission electron microscopy. The model accounts for overprojection (or ‘Holmes effect’) due to section thickness, and for two forms of truncation (or ‘missing profiles’ mechanisms), simultaneously. The profile data may be grouped into an arbitrary class system, chosen by the user, and the procedure can be programmed in a medium‐size desk calculator. In order to incorporate the above features, however, we had to choose a finite‐difference unfolding algorithm, the advantages and disadvantages of which are discussed early in the paper in the context of the main alternative unfolding procedures hitherto available. The performance of the method is tested against three sets of real data previously analysed by a maximum likelihood method (Keiding et al., 1972).