  We present an explicitly gauge-invariant observable of {\em any} general
gravitational perturbation, $h_{\mu\nu}$ (\textit{not} necessarily due to
gravitational waves (GWs)), in a laser interferometry-based GW detector,
identifying the signature as the proper time elapsed of the beamsplitter
observer, between two events: when a photon passes through the beamsplitter,
and when the same photon returns to the beamsplitter after traveling through
the interferometer arm and reflecting off the far mirror. Our formalism applies
to simple Michelson interferometers and can be generalized to more advanced
setups. We demonstrate that the proper time observable for a plane GW is
equivalent to the detector strain commonly used by the GW community, though now
the common framework can be easily generalized for other types of signals, such
as dark matter clumps or spacetime fluctuations from quantum gravity. We
provide a simple recipe for computing the proper time observable for a general
metric perturbation in linearized gravity and explicitly show that it is
invariant under diffeomorphisms of the perturbation, as any physical observable
should be.
