The stereology of projected images

Abstract

SUMMARYA generalized, geometrical approach is adopted in reviewing the basic relationships of projected structures. Projections of features from a plane to a projection line, and from a three‐dimensional foil to a projection plane are considered briefly. The relationships that apply to apparent and total projections are next assembled for lines, surfaces and bounded regions. The properties of convex bodies, the geometrical attributes, and the related projected quantities are enumerated. The inter‐relationships of important microstructural parameters are expressed for convex bodies in space, in sections, and in the projection plane.Based on the important concept of total projection, expressions are obtained that correct for truncation and overlap of particles in foils. Approximations to the total projection are developed for lines obscured by surfaces, and for points hidden by surfaces in space. Finally methods for determining size distributions of particles in thin foils are reviewed and recent modifications to the original procedures are discussed.