Practical approach to the estimation of the overall mean caliper diameter of a population of spheres and its application to data where small profiles are missed

Abstract

SUMMARYIn the morphometry laboratory a practical, accurate, and computationally simple procedure is needed when the estimation of the number of spherical particles per unit volume (Nv) is pursued. In addition, this procedure should be able to deal with the very real problem of profiles too small to be counted.Two computationally simple methods, the size class analysis method and the mean profile diameter method, were examined in detail. Computer‐generated random profiles from various size‐distributions of spheres were analysed by both methods. The percents error to be expected with various sphere distributions with a relatively large number of missed small profiles were determined for both methods. The accuracy of the size class analysis method was poor when a significant number of small profiles were missed. In this situation the accuracy of this method could be greatly improved by applying a simple modification to the procedure. A size class was identified which was larger than the largest missed profile but smaller than the diameter of the smallest sphere in the population. All contributions of this size class and all smaller size classes were deleted from the computation of Nv.The mean profile diameter method was found to be difficult to apply to distributions containing missed small profiles. Missed small profiles were handled more predictably by the modified size class analysis method.