Effect of Observed Number of Inclusions on the Diameter Distribution at Two-Dimensional Inspection

The effects of observed number of inclusions on the diameter distribution at two-dimensional inspection were evaluated in this work. Microscopic observations were reproduced by numerical calculations. Numerically calculated diameters of circles at cross-sectional planes were aggregated as size and density histograms and those were compared with theoretically calculated histograms. Deviations between the calculated and true density in each class were evaluated quantitatively with the error evaluation index. The reliability of two-dimensional particle size and density histogram was affected by the observed number of particles rather than the observed number of fields and independent of the input three-dimensional particle distribution. Misunderstandings in reading the histograms could be prevented by setting small number of classes when the observed number of particles is small. It is better to decide the goal of reliability level before inspection to optimize the observation time and cost.