  We describe the statistics of chaotic wavefunctions near periodic orbits
using a basis of states which optimise the effect of scarring. These states
reflect the underlying structure of stable and unstable manifolds in phase
space and provide a natural means of characterising scarring effects in
individual wavefunctions as well as their collective statistical properties. In
particular, these states may be used to find scarring in regions of the
spectrum normally associated with antiscarring and suggest a characterisation
of templates for scarred wavefunctions which vary over the spectrum. The
results are applied to quantum maps and billiard systems.
