  Single and multi-photon ionization of aligned molecular ensembles is
examined, with a particular focus on the link between the molecular axis
distribution and observable in various angle-integrated and angle-resolved
measurements. To maintain generality the problem is treated geometrically, with
the aligned ensemble cast in terms of axis distribution moments, and the
response of observables in terms of couplings to these moments. Within this
formalism the angular momentum coupling is treated analytically, allowing for
general characteristics - independent of the details of the ionization dynamics
of a specific molecule - to be determined. Limiting cases are explored in order
to provide a phenomenology which should be readily applicable to a range of
experimental measurements, and illustrate how observables can be sensitive to
fine details of the alignment, i.e. higher-order moments of the axis
distribution, which are often neglected in experimental studies. We hope that
this detailed and comprehensive treatment will bridge the gap between existing
theoretical and experimental works, and provide both quantitative physical
insights and a useful general phenomenology for researchers working with
aligned molecular ensembles.
