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A network of large-scale laser interferometers is currently employed forsearches of gravitational waves from various astrophysical sources. Thefrequency dependence of the dynamic response of these detectors introducescorrections to their antenna patterns which in principle can affect the outcomeof the associated data-analysis algorithms. The magnitude of these correctionsand the corresponding systematic errors have recently been estimated forsearches of periodic and stochastic gravitational waves (CQG 25 (2008) 184017).However, the calculation of the detector response in that paper followed thetraditional semi-rigorous approach which does not properly take into accountthe curved nature of spacetime. The question then arises as to whether theresults will be the same if the calculation is done within the rigorousframework of general relativity. In this paper we provide such a derivation ofthe response of the detectors to gravitational waves. We obtain the photonpropagation time from the solution of the equation for null geodesics andcalculate the corresponding phase delay by solving the eikonal equation forcurved spacetime. The calculations are then extended to include phaseamplification from multi-beam interference in Fabry-Perot resonators which playan important role in the formation of the signal in these detectors.

On the round-trip time for a photon propagating in the field of a plane gravitational wave