In order to image test objects by electromagnetic waves, in particular millimetric waves, a test object is illuminated with the electromagnetic waves, the scattered waves are received, and are evaluated for a representation of the test object in the form of an image based on the principle of "synthetic aperture radar" (SAR). In order to allow as large an area as possible to be imaged with high resolution in a short time, the phase centres of the transmitting and receiving antennas are, according to the invention, moved on a circular path parallel to the respective digital focus planes of the imaging system, and are at the same time shifted linearly in a further direction parallel to the respective focus plane. The method can be used for monitoring people for suspicious objects, for example for monitoring airline passengers at an airport.