The 3D size distribution of spheres from 2D size distributions


My field of applications is the study and the research of new multifasic polymeric systems rubber (EPR) embedded in a semicrystalline matrix. The quantitative morphological analysis was performed microtomed samples (in cryo modality under theTg conditions), obtaining the thin section useful for TEM analysis evaluation. Afterwards the image obtained was analysed in Image Analysis in order to obtain a quantitative particle-size distribution of the dispersed size (rubber). Assuming that the dispersed particles closely approach spherical shape, I d’ like to use a mathematical approach (or morphological Image Analysis macro) that permit me to convert the two-dimensional distribution of particle sections into the corresponding three-dimensional distribution of particle size. Moreover the approach should consider that the particles are intersected by a random plane can be measured by means TEM. The mathematical corrections, for converting the distribution of visible section diameters, should obtain a more realistic distribution. Image J can be useful in this quantification ?
Many thanks in advantage for all info that you give me regarding that topic.


I knew the possibility to use the Stereology that could gives me tools to calculate parameters of spherical particles based on diameter distribution on 2D sections, so I’d like to read a pratical example.

Yes. you may want to consult E. Weibel’s Stereological Methods as that problem is a classical example resolved via stereology.

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