Stereology is the study of the three-dimensional structure of materials from two-dimensional sections or projections. By suitable statistical measurements on the test plane or projection plane, and by utilizing the basic equations of stereology, the true three-dimensional quantities can be calculated. Such attributes of the structure as points P, lines L, surfaces S, volumes V, numbers N, as well as spacings, sizes, curvatures, etc. can be obtained without a priori assumptions.In this review, the basic relationships of quantitative stereology are summarized, both for opaque and transparent materials. Thus the image to be analyzed may derive from a photograph of a metallic polished surface or from an electron transmission micrograph obtained from a biological slice or replica. The complete quantitative characterization of the microstructure involves data obtained from both reflected images and transmitted (or projected) images. We will discuss the relationships applicable to each type of image, then show their interrelationships.
Quantitative Characterization of Stress Concentration in the Presence of Closely Spaced Hard Inclusions in Two-Dimensional Linear Elasticity