An illumination source of predominantly non-directional and incoherent millimeter-wave radiation for illuminating an area for passive millimeter-wave imaging comprises a container with at least a partly reflective internal surface and a plurality of exit apertures and a primary source of millimeter-wave radiation for emitting millimeter-wave radiation into the container. The primary source and the container are arranged so that a proportion of the millimeter-wave radiation emitted by the source undergoes reflection within the container before being emitted through the apertures, such that the different paths lengths are at least equal to the coherence length of the radiation. This is facilitated if the bandwidth of the radiation is preferably at least 1 GHz. The container may be a box in which a waveguide is used to couple radiation from the primary source into the box. Alternatively, the container may be formed from a mesh and the plurality of holes is provided by the holes in the mesh.