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Estimation of the size and orientation distribution of filamentary features from measurements on a two‐dimensional section
Author(s) -
Hilliard J. E.,
Anacker D. C.
Publication year - 1974
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.1365-2818.1974.tb03964.x
Subject(s) - radius , orientation (vector space) , cross section (physics) , curvature , radius of curvature , geometry , section (typography) , distribution (mathematics) , physics , optics , joint (building) , materials science , mathematics , mathematical analysis , mean curvature , architectural engineering , computer security , quantum mechanics , mean curvature flow , computer science , advertising , engineering , business
SUMMARY A procedure is described for determining the joint distribution L v ( r , ø, θ) of the radii ( r ) and orientation (ø, θ) of a filamentary structure from measurements on a single section. For tubular filaments it is also possible to determine the wall‐thickness distribution. The following assumptions are made: (1) that the filaments have a circular cross‐section; (2) that the length and radius of curvature of the filaments are large compared with their radii. The analysis is also applicable to transmitted images if the thickness of the slice is small compared with the average radius of the filaments.