  The main result of this paper is a semi-analytic approximation for the chord
distribution functions of three-dimensional models of microstructure derived
from Gaussian random fields. In the simplest case the chord functions are
equivalent to a standard first-passage time problem, i.e., the probability
density governing the time taken by a Gaussian random process to first exceed a
threshold. We obtain an approximation based on the assumption that successive
chords are independent. The result is a generalization of the independent
interval approximation recently used to determine the exponent of persistence
time decay in coarsening. The approximation is easily extended to more general
models based on the intersection and union sets of models generated from the
iso-surfaces of random fields. The chord distribution functions play an
important role in the characterization of random composite and porous
materials. Our results are compared with experimental data obtained from a
three-dimensional image of a porous Fontainebleau sandstone and a
two-dimensional image of a tungsten-silver composite alloy.
