  We show that the projection of an axisymmetric three-dimensional orientation
distribution to two dimensions can be cast into an Abel transform. Based on
this correspondence, we derive an exact integral inverse, which allows for the
quantification of three-dimensional uniaxial alignment of rodlike units from
two-dimensional sliced images, thus providing an alternative to X-ray or
tomographic analysis. A matrix representation of the projection and its inverse
is derived, providing a direct relationship between two- and three-dimensional
order parameters for both polar and non-polar systems.
