Bias of a length density estimator based on vertical projections

Attention is paid to the stereological estimator of the length density of lineal features in three-dimensional space. In Gokhale (J. Microsc. (1990) 159, 133-141), the estimator based on measurements performed on a projection of the content of vertical slices with a given thickness Delta was derived. The aim of this paper is to show that using five vertical slices with systematically chosen orientations yields a reliable result, i.e. the bias of the estimator is smaller than 5%. In the case of a choice of the vertical axis such that most lineal features are not perpendicular or nearly perpendicular to the vertical axis, a reliable result can be obtained using only three systematic orientations of vertical slices.