When a transmitting apertureA0and a receiving apertureB0are coupled in the Fraunhofer region, the ratio of received to transmitted power is given by the Friis formula. It is well known that the Fraunhofer gainsGa0andGb0ofA0andB0are constant and are determined independently.In the paper, the product of the gainsGaGbin the Fresnel region is determined as an integral over both apertures, assuming the gainsGaandGbforA0andB0. It is pointed out thatGaGbcannot generally be separated into the individual factors, but a formula similar to that of Friis still holds in the Fresnel region. The author proposes to define the ‘gain-product reduction factor’,γaγb, as the ratioGaGbGa0Gb0. The individual gainGaorGbmay be determined only whenA0andB0are identical and the illuminations of both apertures are the same. Then the ‘gain reduction factor’,γ, is defined as the ratioGa/Ga0.Assuming uniform amplitude and phase of illumination overA0andB0,γaγbandγare determined for circular and rectangular apertures. For circular apertures, the same factors are determined for a set of illuminations which approximate to commonly used tapers, and the effect of defocusing the primary feed in lenses and dishes is also discussed.