Measuring through the microscope: development and evolution of stereological methods

Obtaining, by means of microscopy, meaningful measurements pertaining to spatial structures requires methods which allow three-dimensional quantitative information to be derived from the reduced information available on the two-dimensional flat sections of the structure. The most powerful methods to that effect are those of stereology which are based on mathematical principles. This paper reviews the early invention of these methods, which sought to solve practical problems, and their further evolution as more rigorous mathematical foundations were developed. It is demonstrated that stereological methods are essentially sampling methods and that newer trends provide new and sound solutions to old and elusive problems, such as anisotropy or particle number and size.