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A comprehensive set of stereological formulae for embedded aggregates of not‐necessarily‐convex particles
Author(s) -
Miles R. E.
Publication year - 1985
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1985.tb02606.x
Subject(s) - disjoint sets , planar , regular polygon , section (typography) , aggregate (composite) , isotropy , particle (ecology) , convex set , mathematics , cross section (physics) , geometry , combinatorics , physics , computer science , materials science , convex optimization , optics , nanotechnology , oceanography , computer graphics (images) , geology , operating system , quantum mechanics
SUMMARY Theoretical stereological approaches to particle aggregates characteristically suppose that each particle is convex, so that upon sectioning, each particle gives rise to either 0 or 1 convex planar profile. Actually, the essential requirement in such approaches is that each planar section profile be connected; such particles need not be convex. In this paper, aggregates of quite general non‐convex particles, whose individual planar section profiles may thus comprise a number of disjoint connected regions, are considered. For this, it is necessary to anticipate the ultimate technical development of ultra‐sensitive devices (or other methods) capable of identifying in a planar section those disjoint connected regions stemming from the same particle. With this assumption, it is shown how, using the ‘4‐linc’—a new line section characteristic—to estimate the aggregate volume moment ratio , the standard isotropic section theory fully extends. To complete the picture, the recent development by Jensen & Gundersen of estimators for is extended to the ‘restricted’ case considered here. Allowing the particle volume distribution to belong to a two‐parameter family, these two parameters, N v and the aggregate mean values may all be estimated.