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

A clarification on a common misconception about interferometric detectors of gravitational waves