Estimation of sheet thickness distributions from linear and plane sections

A biological "membrane" or a "barrier" can often be modelled by a sheet, namely a portion of space comprised between 2 smooth, quasi-parallel faces, such that sheet thickness is in general variable but very small in relation to face extent. Sheet thickness measurements are often of interest to the morphometrist, the physiologist and the pathologist. In the present paper, some stereological techniques are developed for estimating true sheet thickness distributions, and their moments, from the apparent thickness or intercept length measurements obtained, respectively, via random plane or linear sections. An important premise for the models to work is that of isotropic random ("non-preferential") sheet orientation relative to the sectioning probe.