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A consistent approach for an exhaustive solution of the problem ofpropagation of light rays in the field of gravitational waves emitted by alocalized source of gravitational radiation is developed in the firstpost-Minkowskian and quadrupole approximation of General Relativity. Wedemonstrate that the equations of light propagation in the retardedgravitational field of an arbitrary localized source emitting quadrupolargravitational waves can be integrated exactly. The influence of thegravitational field on the light propagation is examined not only in the wavezone but also in cases when light passes through the intermediate and nearzones of the source. Explicit analytic expressions for light deflection andintegrated time delay (Shapiro effect) are obtained accounting for all possibleretardation effects and arbitrary relative locations of the source ofgravitational waves, that of light rays, and the observer. It is shown that theADM and harmonic gauge conditions can both be satisfied simultaneously outsidethe source of gravitational waves. Their use drastically simplifies theintegration of light propagation equations and those for the motion of lightsource and observer in the field of the source of gravitational waves, leadingto the unique interpretation of observable effects. The two limiting cases ofsmall and large values of impact parameter are elaborated in more detail.Explicit expressions for Shapiro effect and deflection angle are obtained interms of the transverse-traceless part of the space-space components of themetric tensor. We also discuss the relevance of the developed formalism forinterpretation of radio interferometric and timing observations, as well as fordata processing algorithms for future gravitational wave detectors.Comment: 43 pages, 4 Postscript figures, uses revtex.sty, accepted to Phys.  Rev. D, minor corrections in formulae regarding algebraic sign

Astrometric and timing effects of gravitational waves from localized sources