On the problem of processing data from a cross-sectional image of grained structure

The anisotropy of a grained structure is a consequence of non-uniform distribution of spatial orientation of grains. Conventional stereological methods allow determine spatial distribution of grain orientation from lines distribution observed on structure cross sections. The distribution of grain's surface orientation in space is determined by measuring the total length of cross sections on a cutting plane. In this paper, we indicate partial but significant problem of stereology. A rectangular model of grained structure is considered. Then the kernel function, which connects the probability density function (distribution) of lengths of rectangles intersections visible on observation planes with size of rectangles sides, is calculated.