Errors in area measurement in thick sections, with special reference to trabecular bone

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Abstract
A formula is derived for the errors caused by section thickness in the measurement of the mean cross-sectional areas of opaque material embedded in a transparent medium. There are some simplifying assumptions which can only be justified by limiting the maximum thickness of the section, but no restriction whatever is placed upon the shape of the opaque material. For isotropic materials a very simple formula is found, relating the relative error in cross-sectional area to measurements of area and boundary profile length on the section surface. The effect of anisotropy in the material may be very large. To illustrate this, numerical calculations are made for two particular classes of simple anisotropic material, those which might be made from isotropic materials by linear distortions.