The pair correlation function for point and fibre systems and its stereological determination by planar sections

Traditional stereology consists nearly completely in the determination of particle size distributions and mean values such as Vv and Sv. However, for the description of the 'inner' structure of random structures second-order characteristics such as the pair correlation function or reduced second moment function are useful. In the present paper stereological estimation of second-order quantities for centres of random sphere systems and for random fibre systems are considered. In the case of sphere systems stereological formulae are given which connect the pair correlation function of the sphere centres with quantities available from planar, linear and thin sections. For random fibre systems some exact and approximate stereological methods are suggested which enable the determination of second-order quantities from planar and thin intersections.