In the early 1970s, I came across some articles and a book,Quantitative Stereology, written by the late Ervin E. Underwood. This was the beginning of a lifelong interest in quantifying microstructures and a long-time friendship with a fascinating gentleman.  

Stereology is used to quantify matrix microstructures, as opposed to standard metrology techniques for measuring case depth, plating thickness or particle size. Microstructural measurements are made on a two-dimensional “plane of polish” through a three-dimensional opaque metal. Stereology converts these 2-D measurements into 3-D estimates of microstructural parameters. Most procedures are very simple to use, but there are special considerations for their validity.

This subject has been hampered by confusion due to the use of different mathematical symbols for the same parameters. To minimize this problem, the International Society for Stereology has promoted a standard nomenclature that is constantly evolving as new approaches are developed. The most basic symbols are:

P - Point
L - Line
A - Area
S - Surface
V - Volume
N - Number  

These symbols can be combined in a number of ways to generate different symbols. For example, Pp
represents the point fraction (i.e. the fraction of grid points lying in a phase of interest. While A and S seem to be the same, A is for a flat surface and S is for a curved surface. Thus, S represents the grain-boundary surface area per unit volume. NAis the number of particles per unit, while NVis the number per unit volume.