During recent years, people involved in developing new metals and materials for use in some of the rather extreme conditions of stress, temperature, and environment have relied heavily on the microstructural condition of their materials. In fact, many of the newer materials, such as dispersion-strengthened alloys, have been designed almost entirely by first determining the microstruc ture desired and then finding the right combination of composition, heat treatment, and mechanical working that will result in the de sired microstructure. Furthermore, the extremely high reliability required of materials used today, for example, in aerospace and nuclear energy systems, requires close control on the microstruc tural conditions of materials. This is clearly evident from even a cursory examination of recently written specifications for mate rials where rather precise microstructural parameters are stipu lated. Whereas specifications written several years ago may have included microstructural requirements for details such as ASTM grain size or graphite type, today's specifications are beginning to include such things as volume fraction of phases, mean free path of particles, and grain intercept distances. Rather arbitrary terms such as "medium pearlite" have been replaced by requirements such as "interlamella spacing not to exceed 0. 1 micron. " Finally, materials users have become increasingly aware that when a material does fail, the reason for its failure may be found by examining and "reading" its microstructure. The responsibility for a particular microstructure and a resulting failure is a matter of growing importance in current product liability consider ations.

An improved procedure based on the intercept method of measuring the grain size of single-phase microstructures has been developed that provides a quantitative description of the grain size yet is fast. The procedure combines the statistical advantage of using large numbers with the advantage of interpreting the data as a normal distribution, as verified by the chi square test. Application of the procedure to ferritic microstructures representative of best and worst case conditions indicates that accuracies on the order of 3 percent at a 95 percent confidence level can be achieved. In addition, the procedure is sensitive enough to distinguish a randomly mixed duplex grain structure. The measurements associated with a two-phase microstructure can be more precisely quantified through determination of volume fractions using a Pp measurement based on the use of an appropriate grid network, the coefficient of variation statistic, and the Poisson distribution. The analysis is demonstrated for an a priori system for which the percent accuracy and confidence level can be specified for the volume fraction measurement simply from calculation of the average value for Pp.

Unbiased Stereology, Second Edition is a practical guide to making unbiased 3-D measurements via the microscope. Only those stereological techniques which have been tried and tested by real application are included. Although this technology is essentially mathematical and statistical, the authors do not immerse the reader in complex analysis, but rather provide simple heuristic explanations and references to the original proof, and illustrate the theory by analogies drawn from everyday experience. To give practical experience in application of the techniques, exercises are provided at the end of each chapter, complete with detailed worked answers.

Stereology is a valuable tool for neuroscientists, allowing them to obtain 3-Dimensional information from 2-Dimensional measurements made on appropriately sampled sections (usually obtained from histological sections or MRI/CT/PET scans). This 3-D information is invaluable in correlatingstructural/functional relationships in the pursuit of far greater understanding of the function of the central nervous system. However, in carrying out such measurements, often based on limited data sets, there is a risk of experimenter bias. An important feature of modern design based stereology isto be aware of potential sources of bias and eliminate them during the data collection. With many of the major neuroscience journals now insisting that quantitative data be presented, there is a greater need than ever for neuroscientists to understand the theory and practice behind quantitativemethods, such as those offered by stereology. Quantitative Methods in Neuroscience is a cookbook of stereological methods written especially for neuroscientists. It provides clear and accessible advice about when and when not to use stereology. Throughout the book, the emphasis is on practical guidance, rather than discussions and formulae.Written by leading scientists in the field of stereology, with a Foreword by D.C. Sterio, the book will be a valuable introduction to these methods for neuroscientists, and all those involved in development of new drug programmes.

vi on geometric probability is included, students can be expected to create a few simple programs like those shown, but for other geometries. I am indebted to Tom Hare for critical reviews of the material and an endless enthusiasm to debate and derive stereological relationships; to John Matzka at Plenum Press for patiently instructing me in the intricacies of typesetting; to Chris Russ for helping to program many of these measurement techniques; and especially to Helen Adams, both for her patience with my creative fever to write yet another book, and for pointing out that the title, which I had intended to contrast to "theoretical stereology," can also be understood as the antonym of "impractical stereology." John C. Russ Raleigh,NC July, 1986 Chapter 1: Statistics 1 Accuracy and precision 1 The mean and standard deviation 5 Distributions 7 Comparison 13 Correlation 18 Nonlinear fitting 19 Chapter 2: Image Types 23 Planar sections 23 Projected images 25 Finite sections 28 Space-filling structures and dispersed phases 29 Types of images and contrast mechanisms 31 Sampling 32 Chapter 3: Manual Methods 35 Volume fraction 35 Surface density 38 Contiguity 41 Mean intercept length 42 Line density 43 Grain size determination 55 Curvature 48 Reticles to aid counting 49 Magnification and units 51 Chapter4: Size Distributions 53 Intercept length in spheres 53 Nonspherical shapes 57 Corrections for finite section thickness 59 Lamellae 61 Measurement of profile size 62 Nonspherical particles 69 vii Contents viii Chapter 5: Computer Metlwds 73

Nine international specialists contribute information about the use of image analysis procedures to evaluate microstructural features. Coverage includes an historical overview of how quantitative image analysis developed; the evolution of current television computer-based analysis systems; the scien