Recent VLBI development provides opportunities for aperture synthesis, or super synthesis, with terrestrial interferometer antennas, and also in the near future with orbiting antennas. In this connection it is useful to consider the potential mapping capability of a single interferometer. Usually one would assume the use of image restoration procedures to be indispensable for observations with a single interferometer, because the uv-plane is covered only on an elliptical track, and is very much unfilled. High and distant sidelobes of the synthesized beam, caused by gaps in the coverage of the uv-plane, are usually considered to be influenced only to a small degree by any weighting function by which the visibility function is multiplied in the Fourier image formation algorithm. It has been shown that the mean-squared value of the point-source response function is invariant with respect to the weighting function (Doubinsky 1983). However, this does not prohibit the modulation of the point-source response by the visibility weighting function. This study shows that one can suppress the sidelobes in two symmetrical sectors of the point-source response with the help of such modulation. Thus for a line-shaped source model (that is, linear within the angular resolution of the synthesized beam) one could map without excessive distortion by Fourier transformation alone (Doubinsky 1979). The exclusion of restoration procedures, which are largely empirical, increases the reliability of the image when the source structure is extended and the signal-to-noise ratio is low. It also saves much computer time.