  The aims of this letter are two. First, to show the angular gauge-invariance
on the response of interferometers to gravitational waves (GWs). In this
process, after resuming for completeness results on the Transverse-Traceless
(TT) gauge, where, in general, the theoretical computations on GWs are
performed, we analyse the gauge of the local observer, which represents the
gauge of a laboratory environment on Earth. The gauge-invariance between the
two gauges is shown in its full angular and frequency dependences. In previous
works in the literature this gauge-invariance was shown only in the low
frequencies approximation or in the simplest geometry of the interferometer
with respect to the propagating GW (i.e. both of the arms of the interferometer
are perpendicular to the propagating GW). Second, as far as the computation of
the response functions in the gauge of the local observer is concerned, a
common misconception about interferometers is also clarified. Such a
misconception purports that, as the wavelength of laser light and the length of
an interferometer's arm are both stretched by a GW, no effect should be
visible, invoking an analogy with cosmological redshift in an expanding
universe.
