  We consider an observer in a (2+1)-spacetime without matter and cosmological
constant who measures spacetime geometry by emitting lightrays which return to
him at a later time. We investigate several quantities associated with such
lightrays: the return time, the directions into which light needs to be emitted
to return and the frequency shift between the lightray at its emission and its
return. We derive explicit expressions for these quantities as functions on the
reduced phase space and show how they allow the observer to reconstruct the
full geometry of the spacetime in finite eigentime. We comment on conceptual
issues. In particular, we clarify the relation between these quantities and
Dirac observables and show that Wilson loops arise naturally in these
quantities.
